Subgroups — C₆₇×#61055 #30740306

Order 17152.

2764 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
8	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3271	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3270	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3060	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#465×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#577×C₆₇	—	2	8	no	—
29	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₆₇	—	2	8	no	—
36	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
48	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#550×C₆₇	C₂²	1	2	yes	complemented
54	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
55	#548×C₆₇	C₂²	1	2	yes	—
56	#548×C₆₇	C₂²	1	2	yes	complemented
57	#547×C₆₇	—	2	2	no	—
58	#547×C₆₇	C₂²	1	2	yes	complemented
59	#546×C₆₇	—	2	2	no	—
60	#546×C₆₇	—	2	2	no	—
61	#546×C₆₇	C₂²	1	2	yes	complemented
62	#546×C₆₇	C₂²	1	2	yes	complemented
63	D₄²×C₆₇	—	2	2	no	—
64	D₄²×C₆₇	C₂²	1	2	yes	—
65	#537×C₆₇	—	2	1	no	—
66	#537×C₆₇	—	2	1	no	—
67	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#536×C₆₇	—	2	1	no	—
70	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#535×C₆₇	—	2	1	no	—
72	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#525×C₆₇	—	2	1	no	—
74	#525×C₆₇	—	2	1	no	—
75	#525×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
77	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×#121×C₆₇	—	2	1	no	—
79	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
80	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#497×C₆₇	C₂²	1	2	yes	complemented
83	#496×C₆₇	C₂²	1	2	yes	complemented
84	#495×C₆₇	C₂²	1	2	yes	complemented
85	#492×C₆₇	C₂²	1	2	yes	complemented
86	#470×C₆₇	C₂²	1	2	yes	complemented
87	#469×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#465×C₆₇	C₂²	1	2	yes	complemented
91	#465×C₆₇	C₂²	1	2	yes	complemented
92	#465×C₆₇	C₂²	1	2	yes	complemented
93	#465×C₆₇	C₂²	1	2	yes	complemented
94	#464×C₆₇	C₂²	1	2	yes	complemented
95	#464×C₆₇	C₂²	1	2	yes	complemented
96	#463×C₆₇	C₂²	1	2	yes	complemented
97	#463×C₆₇	C₂²	1	2	yes	complemented
98	#462×C₆₇	C₂²	1	2	yes	complemented
99	#461×C₆₇	C₂²	1	2	yes	complemented
100	#460×C₆₇	C₂²	1	2	yes	complemented
101	#459×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	2	yes	complemented
103	#452×C₆₇	C₂²	1	2	yes	complemented
104	#452×C₆₇	C₂²	1	2	yes	complemented
105	#452×C₆₇	C₂²	1	2	yes	complemented
106	#451×C₆₇	C₂²	1	2	yes	complemented
107	#451×C₆₇	C₂²	1	2	yes	complemented
108	#450×C₆₇	C₂²	1	2	yes	complemented
109	#450×C₆₇	C₂²	1	2	yes	complemented
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	2	yes	complemented
116	#447×C₆₇	C₂²	1	2	yes	complemented
117	#447×C₆₇	C₂²	1	2	yes	complemented
118	#442×C₆₇	C₂²	1	2	yes	complemented
119	#441×C₆₇	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
122	#435×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
126	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	2₋¹⁺⁴×C₆₇	—	2	4	no	—
138	2₋¹⁺⁴×C₆₇	—	4	2	no	—
139	H(5,𝔽₂)×C₆₇	—	2	4	no	—
140	H(5,𝔽₂)×C₆₇	—	4	2	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	—	2	2	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	1	no	—
147	C₂×#41×C₆₇	—	2	1	no	—
148	C₂×#41×C₆₇	—	2	4	no	—
149	C₂×#41×C₆₇	—	2	4	no	—
150	C₂×#41×C₆₇	—	4	2	no	—
151	C₂×#41×C₆₇	—	4	2	no	—
152	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×#41×C₆₇	C₂³	1	2	yes	—
157	C₂×#41×C₆₇	C₂³	1	2	yes	—
158	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×Q₈×C₆₇	—	2	1	no	—
164	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₂²×D₄×C₆₇	—	2	1	no	—
169	C₂²×D₄×C₆₇	—	2	1	no	—
170	C₂²×D₄×C₆₇	—	2	1	no	—
171	C₂²×D₄×C₆₇	—	2	1	no	—
172	C₂²×D₄×C₆₇	—	2	2	no	—
173	C₂²×D₄×C₆₇	—	2	2	no	—
174	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
177	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂³×C₄×C₆₇	—	2	1	no	—
179	C₂³×C₄×C₆₇	—	2	1	no	—
180	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
181	#137×C₆₇	—	2	4	no	—
182	#137×C₆₇	—	2	8	no	—
183	#137×C₆₇	—	4	2	no	—
184	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
185	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
186	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
187	#135×C₆₇	—	2	4	no	—
188	#135×C₆₇	—	2	4	no	—
189	#135×C₆₇	—	2	4	no	—
190	#135×C₆₇	—	2	4	no	—
191	#135×C₆₇	—	2	4	no	—
192	#135×C₆₇	—	2	8	no	—
193	#135×C₆₇	—	2	4	no	—
194	#135×C₆₇	—	2	4	no	—
195	#135×C₆₇	D₄	1	8	yes	complemented
196	C₂×Q₁₆×C₆₇	—	2	4	no	—
197	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
199	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
202	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×SD₁₆×C₆₇	—	2	4	no	—
204	C₂×SD₁₆×C₆₇	—	2	4	no	—
205	C₂×SD₁₆×C₆₇	—	2	8	no	—
206	C₂×SD₁₆×C₆₇	—	2	4	no	—
207	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
209	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
212	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
215	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
217	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
218	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
219	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×D₈×C₆₇	—	2	4	no	—
222	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×D₈×C₆₇	C₂³	1	2	yes	—
224	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×D₈×C₆₇	C₂³	1	2	yes	—
227	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
228	#131×C₆₇	—	2	4	no	—
229	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
230	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
232	C₂²×C₈×C₆₇	—	2	4	no	—
233	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
235	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
236	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
238	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
239	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈×C₆₇	—	2	2	no	—
241	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
242	#127×C₆₇	—	2	2	no	—
243	#127×C₆₇	C₂³	1	2	yes	—
244	#124×C₆₇	—	2	2	no	—
245	#124×C₆₇	—	2	2	no	—
246	#124×C₆₇	C₂³	1	2	yes	—
247	#124×C₆₇	C₂³	1	2	yes	—
248	#123×C₆₇	—	2	2	no	—
249	#123×C₆₇	—	2	2	no	—
250	#123×C₆₇	—	2	2	no	—
251	#123×C₆₇	—	2	2	no	—
252	#123×C₆₇	—	2	2	no	—
253	#123×C₆₇	D₄	1	2	yes	—
254	C₂²⋊Q₈×C₆₇	—	2	1	no	—
255	C₂²⋊Q₈×C₆₇	—	2	1	no	—
256	C₂²⋊Q₈×C₆₇	—	2	1	no	—
257	C₂²⋊Q₈×C₆₇	—	2	1	no	—
258	C₂²⋊Q₈×C₆₇	—	2	1	no	—
259	C₂²⋊Q₈×C₆₇	—	2	2	no	—
260	C₂²⋊Q₈×C₆₇	—	2	1	no	—
261	C₂²⋊Q₈×C₆₇	—	2	2	no	—
262	C₂²⋊Q₈×C₆₇	—	2	2	no	—
263	C₂²⋊Q₈×C₆₇	—	2	2	no	—
264	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
265	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
267	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
268	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
269	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
270	#121×C₆₇	—	2	1	no	—
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	1	no	—
273	#121×C₆₇	—	2	2	no	—
274	#121×C₆₇	—	2	2	no	—
275	#121×C₆₇	—	2	2	no	—
276	#121×C₆₇	—	2	2	no	—
277	#121×C₆₇	—	2	1	no	—
278	#121×C₆₇	—	2	1	no	—
279	#121×C₆₇	—	2	1	no	—
280	#121×C₆₇	—	2	1	no	—
281	#121×C₆₇	—	2	2	no	—
282	#121×C₆₇	—	2	2	no	—
283	#121×C₆₇	—	2	2	no	—
284	#121×C₆₇	—	2	2	no	—
285	#121×C₆₇	—	2	2	no	—
286	#121×C₆₇	D₄	1	1	yes	characteristic
287	#121×C₆₇	D₄	1	1	yes	characteristic
288	#121×C₆₇	C₂³	1	2	yes	—
289	#121×C₆₇	C₂³	1	2	yes	—
290	#121×C₆₇	C₂³	1	2	yes	—
291	#121×C₆₇	C₂³	1	2	yes	—
292	#120×C₆₇	—	2	2	no	—
293	#120×C₆₇	—	2	2	no	—
294	#120×C₆₇	—	2	2	no	—
295	#120×C₆₇	—	2	2	no	—
296	#120×C₆₇	—	2	2	no	—
297	#120×C₆₇	D₄	1	2	yes	—
298	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
299	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
300	C₄×D₄×C₆₇	—	2	2	no	—
301	C₄×D₄×C₆₇	—	2	2	no	—
302	C₄×D₄×C₆₇	—	2	2	no	—
303	C₄×D₄×C₆₇	—	2	2	no	—
304	C₄×D₄×C₆₇	—	2	2	no	—
305	C₄×D₄×C₆₇	—	2	2	no	—
306	C₄×D₄×C₆₇	C₂³	1	2	yes	—
307	C₄×D₄×C₆₇	C₂³	1	2	yes	—
308	C₄×D₄×C₆₇	C₂³	1	2	yes	—
309	C₄×D₄×C₆₇	C₂³	1	2	yes	—
310	#117×C₆₇	—	2	1	no	—
311	#117×C₆₇	—	2	1	no	—
312	#117×C₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
320	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
321	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
323	#106×C₆₇	C₂³	1	2	yes	—
324	#106×C₆₇	C₂³	1	2	yes	—
325	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
326	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
327	#103×C₆₇	C₂³	1	2	yes	—
328	#103×C₆₇	C₂³	1	2	yes	—
329	#103×C₆₇	C₂³	1	2	yes	—
330	#103×C₆₇	C₂³	1	2	yes	—
331	#103×C₆₇	C₂³	1	2	yes	—
332	#103×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	#102×C₆₇	C₂³	1	2	yes	—
335	#102×C₆₇	C₂³	1	2	yes	—
336	#102×C₆₇	C₂³	1	2	yes	—
337	#102×C₆₇	C₂³	1	2	yes	—
338	#102×C₆₇	C₂³	1	2	yes	—
339	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
340	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
341	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
342	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
343	#97×C₆₇	C₂³	1	2	yes	—
344	C₄×C₈×C₆₇	C₂³	1	2	yes	—
345	C₂⁴×C₆₇	—	2	1	no	—
346	C₂⁴×C₆₇	—	2	1	no	—
347	C₂⁴×C₆₇	—	2	2	no	—
348	C₂⁴×C₆₇	—	2	1	no	—
349	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
350	#41×C₆₇	—	2	2	no	—
351	#41×C₆₇	—	2	2	no	—
352	#41×C₆₇	—	2	2	no	—
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	2	4	no	—
357	#41×C₆₇	—	2	2	no	—
358	#41×C₆₇	—	2	2	no	—
359	#41×C₆₇	—	2	4	no	—
360	#41×C₆₇	—	2	2	no	—
361	#41×C₆₇	—	2	2	no	—
362	#41×C₆₇	—	2	2	no	—
363	#41×C₆₇	—	2	2	no	—
364	#41×C₆₇	—	4	4	no	—
365	#41×C₆₇	—	4	4	no	—
366	#41×C₆₇	—	4	1	no	—
367	#41×C₆₇	—	4	1	no	—
368	#41×C₆₇	—	4	1	no	—
369	#41×C₆₇	—	4	1	no	—
370	#41×C₆₇	—	4	2	no	—
371	#41×C₆₇	—	4	2	no	—
372	#41×C₆₇	—	4	4	no	—
373	#41×C₆₇	—	4	4	no	—
374	#41×C₆₇	—	4	4	no	—
375	#41×C₆₇	—	4	4	no	—
376	#41×C₆₇	—	4	8	no	—
377	#41×C₆₇	C₂×D₄	1	4	yes	—
378	#41×C₆₇	C₂×D₄	1	4	yes	complemented
379	C₂×Q₈×C₆₇	—	2	1	no	—
380	C₂×Q₈×C₆₇	—	2	1	no	—
381	C₂×Q₈×C₆₇	—	2	2	no	—
382	C₂×Q₈×C₆₇	—	2	1	no	—
383	C₂×Q₈×C₆₇	—	2	2	no	—
384	C₂×Q₈×C₆₇	—	2	2	no	—
385	C₂×Q₈×C₆₇	—	2	4	no	—
386	C₂×Q₈×C₆₇	—	2	2	no	—
387	C₂×Q₈×C₆₇	—	2	2	no	—
388	C₂×Q₈×C₆₇	—	4	1	no	—
389	C₂×Q₈×C₆₇	—	4	1	no	—
390	C₂×Q₈×C₆₇	—	4	2	no	—
391	C₂×Q₈×C₆₇	—	4	4	no	—
392	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
393	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
395	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	2	1	no	—
400	C₂×D₄×C₆₇	—	2	2	no	—
401	C₂×D₄×C₆₇	—	2	2	no	—
402	C₂×D₄×C₆₇	—	2	4	no	—
403	C₂×D₄×C₆₇	—	2	2	no	—
404	C₂×D₄×C₆₇	—	2	1	no	—
405	C₂×D₄×C₆₇	—	2	1	no	—
406	C₂×D₄×C₆₇	—	2	2	no	—
407	C₂×D₄×C₆₇	—	2	1	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	no	—
410	C₂×D₄×C₆₇	—	2	2	no	—
411	C₂×D₄×C₆₇	—	2	1	no	—
412	C₂×D₄×C₆₇	—	2	2	no	—
413	C₂×D₄×C₆₇	—	2	2	no	—
414	C₂×D₄×C₆₇	—	2	2	no	—
415	C₂×D₄×C₆₇	—	2	2	no	—
416	C₂×D₄×C₆₇	—	2	1	no	—
417	C₂×D₄×C₆₇	—	2	2	no	—
418	C₂×D₄×C₆₇	—	2	1	no	—
419	C₂×D₄×C₆₇	—	2	1	no	—
420	C₂×D₄×C₆₇	—	2	2	no	—
421	C₂×D₄×C₆₇	—	2	2	no	—
422	C₂×D₄×C₆₇	—	2	2	no	—
423	C₂×D₄×C₆₇	—	4	1	no	—
424	C₂×D₄×C₆₇	—	4	1	no	—
425	C₂×D₄×C₆₇	—	4	2	no	—
426	C₂×D₄×C₆₇	—	4	4	no	—
427	C₂×D₄×C₆₇	—	4	8	no	—
428	C₂×D₄×C₆₇	—	4	4	no	—
429	C₂×D₄×C₆₇	—	4	4	no	—
430	C₂×D₄×C₆₇	—	8	4	no	—
431	C₂×D₄×C₆₇	—	8	2	no	—
432	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
435	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
436	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
438	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₆₇	—	2	1	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	—	2	2	no	—
444	C₂²×C₄×C₆₇	—	2	2	no	—
445	C₂²×C₄×C₆₇	—	2	1	no	—
446	C₂²×C₄×C₆₇	—	2	1	no	—
447	C₂²×C₄×C₆₇	—	2	2	no	—
448	C₂²×C₄×C₆₇	—	2	1	no	—
449	C₂²×C₄×C₆₇	—	2	1	no	—
450	C₂²×C₄×C₆₇	—	2	1	no	—
451	C₂²×C₄×C₆₇	—	2	1	no	—
452	C₂²×C₄×C₆₇	—	2	2	no	—
453	C₂²×C₄×C₆₇	—	2	1	no	—
454	C₂²×C₄×C₆₇	—	2	1	no	—
455	C₂²×C₄×C₆₇	—	2	2	no	—
456	C₂²×C₄×C₆₇	—	2	1	no	—
457	C₂²×C₄×C₆₇	—	2	1	no	—
458	C₂²×C₄×C₆₇	—	2	1	no	—
459	C₂²×C₄×C₆₇	—	2	2	no	—
460	C₂²×C₄×C₆₇	—	2	2	no	—
461	C₂²×C₄×C₆₇	—	4	4	no	—
462	C₂²×C₄×C₆₇	—	4	4	no	—
463	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
464	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
465	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
466	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
469	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
470	Q₁₆×C₆₇	—	2	2	no	—
471	Q₁₆×C₆₇	—	2	2	no	—
472	Q₁₆×C₆₇	—	2	4	no	—
473	Q₁₆×C₆₇	—	2	2	no	—
474	Q₁₆×C₆₇	—	4	2	no	—
475	Q₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
476	SD₁₆×C₆₇	—	2	2	no	—
477	SD₁₆×C₆₇	—	2	2	no	—
478	SD₁₆×C₆₇	—	2	4	no	—
479	SD₁₆×C₆₇	—	2	2	no	—
480	SD₁₆×C₆₇	—	2	2	no	—
481	SD₁₆×C₆₇	—	2	4	no	—
482	SD₁₆×C₆₇	—	2	4	no	—
483	SD₁₆×C₆₇	—	2	2	no	—
484	SD₁₆×C₆₇	—	2	2	no	—
485	SD₁₆×C₆₇	—	2	4	no	—
486	SD₁₆×C₆₇	—	4	2	no	—
487	SD₁₆×C₆₇	—	4	2	no	—
488	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
489	SD₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
490	D₈×C₆₇	—	2	2	no	—
491	D₈×C₆₇	—	2	2	no	—
492	D₈×C₆₇	—	2	4	no	—
493	D₈×C₆₇	—	2	2	no	—
494	D₈×C₆₇	—	4	2	no	—
495	D₈×C₆₇	C₂×D₄	1	4	yes	complemented
496	M₁₆×C₆₇	—	2	2	no	—
497	M₁₆×C₆₇	—	2	2	no	—
498	M₁₆×C₆₇	—	2	4	no	—
499	C₂×C₈×C₆₇	—	2	2	no	—
500	C₂×C₈×C₆₇	—	2	2	no	—
501	C₂×C₈×C₆₇	—	2	2	no	—
502	C₂×C₈×C₆₇	—	2	2	no	—
503	C₂×C₈×C₆₇	—	2	2	no	—
504	C₂×C₈×C₆₇	—	2	4	no	—
505	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
506	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
509	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
510	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
511	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₄⋊C₄×C₆₇	—	2	2	no	—
513	C₄⋊C₄×C₆₇	—	2	1	no	—
514	C₄⋊C₄×C₆₇	—	2	1	no	—
515	C₄⋊C₄×C₆₇	—	2	2	no	—
516	C₄⋊C₄×C₆₇	—	2	2	no	—
517	C₄⋊C₄×C₆₇	—	2	2	no	—
518	C₄⋊C₄×C₆₇	—	2	2	no	—
519	C₄⋊C₄×C₆₇	—	2	2	no	—
520	C₄⋊C₄×C₆₇	—	2	2	no	—
521	C₄⋊C₄×C₆₇	—	2	2	no	—
522	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
523	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
524	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
525	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
526	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
527	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
528	C₂²⋊C₄×C₆₇	—	2	2	no	—
529	C₂²⋊C₄×C₆₇	—	2	2	no	—
530	C₂²⋊C₄×C₆₇	—	2	2	no	—
531	C₂²⋊C₄×C₆₇	—	2	2	no	—
532	C₂²⋊C₄×C₆₇	—	2	2	no	—
533	C₂²⋊C₄×C₆₇	—	2	2	no	—
534	C₂²⋊C₄×C₆₇	—	2	2	no	—
535	C₂²⋊C₄×C₆₇	—	2	2	no	—
536	C₂²⋊C₄×C₆₇	—	2	2	no	—
537	C₂²⋊C₄×C₆₇	—	2	2	no	—
538	C₂²⋊C₄×C₆₇	—	2	2	no	—
539	C₂²⋊C₄×C₆₇	—	2	2	no	—
540	C₂²⋊C₄×C₆₇	—	2	2	no	—
541	C₂²⋊C₄×C₆₇	—	2	2	no	—
542	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
543	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
544	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
545	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
546	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
547	C₄²×C₆₇	—	2	2	no	—
548	C₄²×C₆₇	—	2	2	no	—
549	C₄²×C₆₇	C₂⁴	1	2	yes	—
550	C₂³×C₆₇	—	2	2	no	—
551	C₂³×C₆₇	—	2	2	no	—
552	C₂³×C₆₇	—	2	1	no	—
553	C₂³×C₆₇	—	2	1	no	—
554	C₂³×C₆₇	—	2	1	no	—
555	C₂³×C₆₇	—	2	2	no	—
556	C₂³×C₆₇	—	2	1	no	—
557	C₂³×C₆₇	—	4	1	no	—
558	C₂³×C₆₇	—	4	2	no	—
559	C₂³×C₆₇	—	4	2	no	—
560	C₂³×C₆₇	—	4	4	no	—
561	C₂³×C₆₇	—	4	2	no	—
562	C₂³×C₆₇	—	4	2	no	—
563	C₂³×C₆₇	—	4	2	no	—
564	C₂³×C₆₇	—	8	1	no	—
565	C₂³×C₆₇	—	8	1	no	—
566	C₂³×C₆₇	—	8	1	no	—
567	C₂³×C₆₇	—	8	2	no	—
568	C₂³×C₆₇	—	8	1	no	—
569	C₂³×C₆₇	—	8	2	no	—
570	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
571	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
572	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
573	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
574	Q₈×C₆₇	—	2	2	no	—
575	Q₈×C₆₇	—	2	1	no	—
576	Q₈×C₆₇	—	2	1	no	—
577	Q₈×C₆₇	—	2	2	no	—
578	Q₈×C₆₇	—	2	1	no	—
579	Q₈×C₆₇	—	2	1	no	—
580	Q₈×C₆₇	—	2	1	no	—
581	Q₈×C₆₇	—	2	2	no	—
582	Q₈×C₆₇	—	2	1	no	—
583	Q₈×C₆₇	—	4	4	no	—
584	Q₈×C₆₇	—	4	2	no	—
585	Q₈×C₆₇	—	4	2	no	—
586	Q₈×C₆₇	—	4	2	no	—
587	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
588	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
589	D₄×C₆₇	—	2	4	no	—
590	D₄×C₆₇	—	2	4	no	—
591	D₄×C₆₇	—	2	4	no	—
592	D₄×C₆₇	—	2	4	no	—
593	D₄×C₆₇	—	2	2	no	—
594	D₄×C₆₇	—	2	1	no	—
595	D₄×C₆₇	—	2	1	no	—
596	D₄×C₆₇	—	2	2	no	—
597	D₄×C₆₇	—	2	1	no	—
598	D₄×C₆₇	—	2	1	no	—
599	D₄×C₆₇	—	2	1	no	—
600	D₄×C₆₇	—	2	2	no	—
601	D₄×C₆₇	—	2	1	no	—
602	D₄×C₆₇	—	4	2	no	—
603	D₄×C₆₇	—	4	4	no	—
604	D₄×C₆₇	—	4	2	no	—
605	D₄×C₆₇	—	4	2	no	—
606	D₄×C₆₇	—	4	4	no	—
607	D₄×C₆₇	—	4	2	no	—
608	D₄×C₆₇	—	4	2	no	—
609	D₄×C₆₇	—	4	2	no	—
610	D₄×C₆₇	—	4	2	no	—
611	D₄×C₆₇	—	4	4	no	—
612	D₄×C₆₇	—	4	2	no	—
613	D₄×C₆₇	—	4	2	no	—
614	D₄×C₆₇	—	4	4	no	—
615	D₄×C₆₇	—	4	2	no	—
616	D₄×C₆₇	—	8	2	no	—
617	D₄×C₆₇	—	8	2	no	—
618	D₄×C₆₇	—	8	2	no	—
619	D₄×C₆₇	—	8	2	no	—
620	D₄×C₆₇	—	8	2	no	—
621	D₄×C₆₇	C₂²×D₄	1	2	yes	—
622	D₄×C₆₇	C₂²×D₄	1	2	yes	—
623	C₂×C₄×C₆₇	—	2	2	no	—
624	C₂×C₄×C₆₇	—	2	1	no	—
625	C₂×C₄×C₆₇	—	2	1	no	—
626	C₂×C₄×C₆₇	—	2	2	no	—
627	C₂×C₄×C₆₇	—	2	2	no	—
628	C₂×C₄×C₆₇	—	2	4	no	—
629	C₂×C₄×C₆₇	—	2	4	no	—
630	C₂×C₄×C₆₇	—	2	1	no	—
631	C₂×C₄×C₆₇	—	2	1	no	—
632	C₂×C₄×C₆₇	—	2	2	no	—
633	C₂×C₄×C₆₇	—	2	1	no	—
634	C₂×C₄×C₆₇	—	2	1	no	—
635	C₂×C₄×C₆₇	—	2	2	no	—
636	C₂×C₄×C₆₇	—	2	2	no	—
637	C₂×C₄×C₆₇	—	2	2	no	—
638	C₂×C₄×C₆₇	—	2	1	no	—
639	C₂×C₄×C₆₇	—	2	2	no	—
640	C₂×C₄×C₆₇	—	2	1	no	—
641	C₂×C₄×C₆₇	—	4	2	no	—
642	C₂×C₄×C₆₇	—	4	2	no	—
643	C₂×C₄×C₆₇	—	4	4	no	—
644	C₂×C₄×C₆₇	—	4	2	no	—
645	C₂×C₄×C₆₇	—	4	2	no	—
646	C₂×C₄×C₆₇	—	4	2	no	—
647	C₂×C₄×C₆₇	—	4	2	no	—
648	C₂×C₄×C₆₇	—	4	4	no	—
649	C₂×C₄×C₆₇	—	4	4	no	—
650	C₂×C₄×C₆₇	—	4	2	no	—
651	C₂×C₄×C₆₇	—	4	2	no	—
652	C₂×C₄×C₆₇	—	4	2	no	—
653	C₂×C₄×C₆₇	—	8	2	no	—
654	C₂×C₄×C₆₇	—	8	2	no	—
655	C₂×C₄×C₆₇	—	8	1	no	—
656	C₂×C₄×C₆₇	—	8	1	no	—
657	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
660	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
661	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
662	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
663	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
664	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
665	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
666	C₈×C₆₇	—	2	1	no	—
667	C₈×C₆₇	—	2	1	no	—
668	C₈×C₆₇	—	2	2	no	—
669	C₈×C₆₇	—	2	2	no	—
670	C₈×C₆₇	C₂²×D₄	1	2	yes	—
671	C₈×C₆₇	C₂²×D₄	1	2	yes	—
672	C₂²×C₆₇	—	2	1	no	—
673	C₂²×C₆₇	—	2	1	no	—
674	C₂²×C₆₇	—	2	1	no	—
675	C₂²×C₆₇	—	2	1	no	—
676	C₂²×C₆₇	—	2	1	no	—
677	C₂²×C₆₇	—	2	2	no	—
678	C₂²×C₆₇	—	2	1	no	—
679	C₂²×C₆₇	—	2	2	no	—
680	C₂²×C₆₇	—	2	2	no	—
681	C₂²×C₆₇	—	2	2	no	—
682	C₂²×C₆₇	—	2	2	no	—
683	C₂²×C₆₇	—	2	1	no	—
684	C₂²×C₆₇	—	4	4	no	—
685	C₂²×C₆₇	—	4	1	no	—
686	C₂²×C₆₇	—	4	1	no	—
687	C₂²×C₆₇	—	4	1	no	—
688	C₂²×C₆₇	—	4	1	no	—
689	C₂²×C₆₇	—	4	1	no	—
690	C₂²×C₆₇	—	4	1	no	—
691	C₂²×C₆₇	—	4	2	no	—
692	C₂²×C₆₇	—	4	1	no	—
693	C₂²×C₆₇	—	4	1	no	—
694	C₂²×C₆₇	—	4	2	no	—
695	C₂²×C₆₇	—	4	2	no	—
696	C₂²×C₆₇	—	4	1	no	—
697	C₂²×C₆₇	—	4	1	no	—
698	C₂²×C₆₇	—	8	4	no	—
699	C₂²×C₆₇	—	8	4	no	—
700	C₂²×C₆₇	—	16	2	no	—
701	C₂²×C₆₇	—	16	4	no	—
702	C₂²×C₆₇	D₄²	1	2	yes	—
703	C₂²×C₆₇	#577	1	2	yes	complemented
704	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
705	C₄×C₆₇	—	2	2	no	—
706	C₄×C₆₇	—	2	1	no	—
707	C₄×C₆₇	—	2	1	no	—
708	C₄×C₆₇	—	2	2	no	—
709	C₄×C₆₇	—	2	2	no	—
710	C₄×C₆₇	—	2	2	no	—
711	C₄×C₆₇	—	2	2	no	—
712	C₄×C₆₇	—	4	2	no	—
713	C₄×C₆₇	—	4	1	no	—
714	C₄×C₆₇	—	4	1	no	—
715	C₄×C₆₇	—	4	2	no	—
716	C₄×C₆₇	—	4	2	no	—
717	C₄×C₆₇	D₄²	1	2	yes	—
718	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
719	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
720	#61055	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
721	C₂×C₆₇	—	2	2	no	—
722	C₂×C₆₇	—	2	2	no	—
723	C₂×C₆₇	—	4	1	no	—
724	C₂×C₆₇	—	4	2	no	—
725	C₂×C₆₇	—	4	2	no	—
726	C₂×C₆₇	—	4	2	no	—
727	C₂×C₆₇	—	8	1	no	—
728	C₂×C₆₇	—	8	1	no	—
729	C₂×C₆₇	—	8	2	no	—
730	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
731	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
732	C₂×C₆₇	#3584	1	1	yes	characteristic
733	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
734	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
735	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
736	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
737	#3284	C₂×C₆₇	1	2	yes	complemented
738	#3282	C₂×C₆₇	1	2	yes	complemented
739	#3282	C₂×C₆₇	1	2	yes	complemented
740	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
741	#3271	C₂×C₆₇	1	2	yes	complemented
742	#3270	C₂×C₆₇	1	2	yes	complemented
743	#3267	C₂×C₆₇	1	2	yes	complemented
744	#3264	C₂×C₆₇	1	2	yes	complemented
745	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
746	#3060	C₂×C₆₇	1	1	yes	characteristic, complemented
747	C₂×#465	C₂×C₆₇	1	1	yes	characteristic, complemented
748	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
749	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
750	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
751	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
752	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
753	#3006	C₂×C₆₇	1	1	yes	characteristic, complemented
754	#2952	C₂×C₆₇	1	1	yes	characteristic, complemented
755	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
756	C₆₇	#61055	1	1	yes	characteristic, direct product factor, Sylow
757	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
759	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
760	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	#577	—	2	8	no	—
762	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
764	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
767	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	C₂×#135	—	2	8	no	—
769	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
770	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
771	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
772	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
774	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
776	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
777	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
780	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
782	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
785	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	#550	C₂²×C₆₇	1	2	yes	complemented
787	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
788	#548	C₂²×C₆₇	1	2	yes	—
789	#548	C₂²×C₆₇	1	2	yes	complemented
790	#547	—	2	2	no	—
791	#547	C₂²×C₆₇	1	2	yes	complemented
792	#546	—	2	2	no	—
793	#546	—	2	2	no	—
794	#546	C₂²×C₆₇	1	2	yes	complemented
795	#546	C₂²×C₆₇	1	2	yes	complemented
796	D₄²	—	2	2	no	—
797	D₄²	C₂²×C₆₇	1	2	yes	—
798	#537	—	2	1	no	—
799	#537	—	2	1	no	—
800	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
801	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
802	#536	—	2	1	no	—
803	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
804	#535	—	2	1	no	—
805	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#525	—	2	1	no	—
807	#525	—	2	1	no	—
808	#525	C₂²×C₆₇	1	1	yes	characteristic
809	C₂×C₂²⋊Q₈	—	2	1	no	—
810	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	C₂×#121	—	2	1	no	—
812	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
813	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
814	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	#497	C₂²×C₆₇	1	2	yes	complemented
816	#496	C₂²×C₆₇	1	2	yes	complemented
817	#495	C₂²×C₆₇	1	2	yes	complemented
818	#492	C₂²×C₆₇	1	2	yes	complemented
819	#470	C₂²×C₆₇	1	2	yes	complemented
820	#469	C₂²×C₆₇	1	2	yes	complemented
821	#465	C₂²×C₆₇	1	2	yes	complemented
822	#465	C₂²×C₆₇	1	2	yes	complemented
823	#465	C₂²×C₆₇	1	2	yes	complemented
824	#465	C₂²×C₆₇	1	2	yes	complemented
825	#465	C₂²×C₆₇	1	2	yes	complemented
826	#465	C₂²×C₆₇	1	2	yes	complemented
827	#464	C₂²×C₆₇	1	2	yes	complemented
828	#464	C₂²×C₆₇	1	2	yes	complemented
829	#463	C₂²×C₆₇	1	2	yes	complemented
830	#463	C₂²×C₆₇	1	2	yes	complemented
831	#462	C₂²×C₆₇	1	2	yes	complemented
832	#461	C₂²×C₆₇	1	2	yes	complemented
833	#460	C₂²×C₆₇	1	2	yes	complemented
834	#459	C₂²×C₆₇	1	2	yes	complemented
835	#452	C₂²×C₆₇	1	2	yes	complemented
836	#452	C₂²×C₆₇	1	2	yes	complemented
837	#452	C₂²×C₆₇	1	2	yes	complemented
838	#452	C₂²×C₆₇	1	2	yes	complemented
839	#451	C₂²×C₆₇	1	2	yes	complemented
840	#451	C₂²×C₆₇	1	2	yes	complemented
841	#450	C₂²×C₆₇	1	2	yes	complemented
842	#450	C₂²×C₆₇	1	2	yes	complemented
843	#449	C₂²×C₆₇	1	2	yes	complemented
844	#449	C₂²×C₆₇	1	2	yes	complemented
845	#449	C₂²×C₆₇	1	2	yes	complemented
846	#449	C₂²×C₆₇	1	2	yes	complemented
847	#448	C₂²×C₆₇	1	2	yes	complemented
848	#448	C₂²×C₆₇	1	2	yes	complemented
849	#447	C₂²×C₆₇	1	2	yes	complemented
850	#447	C₂²×C₆₇	1	2	yes	complemented
851	#442	C₂²×C₆₇	1	2	yes	complemented
852	#441	C₂²×C₆₇	1	2	yes	complemented
853	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
854	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
855	#435	C₂²×C₆₇	1	2	yes	complemented
856	#435	C₂²×C₆₇	1	2	yes	complemented
857	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
858	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
859	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic, complemented
860	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
861	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
862	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
863	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
864	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
865	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
866	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
867	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
868	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
869	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
870	2₋¹⁺⁴	—	2	4	no	—
871	2₋¹⁺⁴	—	4	2	no	—
872	H(5,𝔽₂)	—	2	4	no	—
873	H(5,𝔽₂)	—	4	2	no	—
874	C₂×#41	—	2	1	no	—
875	C₂×#41	—	2	1	no	—
876	C₂×#41	—	2	2	no	—
877	C₂×#41	—	2	1	no	—
878	C₂×#41	—	2	1	no	—
879	C₂×#41	—	2	1	no	—
880	C₂×#41	—	2	1	no	—
881	C₂×#41	—	2	4	no	—
882	C₂×#41	—	2	4	no	—
883	C₂×#41	—	4	2	no	—
884	C₂×#41	—	4	2	no	—
885	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
886	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×#41	C₂³×C₆₇	1	2	yes	—
889	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×#41	C₂³×C₆₇	1	2	yes	—
891	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
894	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
896	C₂²×Q₈	—	2	1	no	—
897	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
899	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
900	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
901	C₂²×D₄	—	2	1	no	—
902	C₂²×D₄	—	2	1	no	—
903	C₂²×D₄	—	2	1	no	—
904	C₂²×D₄	—	2	1	no	—
905	C₂²×D₄	—	2	2	no	—
906	C₂²×D₄	—	2	2	no	—
907	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
908	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
909	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
910	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂³×C₄	—	2	1	no	—
912	C₂³×C₄	—	2	1	no	—
913	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
914	#137	—	2	4	no	—
915	#137	—	2	8	no	—
916	#137	—	4	2	no	—
917	AGL(1,ℤ/8)	—	2	4	no	—
918	AGL(1,ℤ/8)	—	2	8	no	—
919	AGL(1,ℤ/8)	—	4	2	no	—
920	#135	—	2	4	no	—
921	#135	—	2	4	no	—
922	#135	—	2	4	no	—
923	#135	—	2	4	no	—
924	#135	—	2	4	no	—
925	#135	—	2	8	no	—
926	#135	—	2	4	no	—
927	#135	—	2	4	no	—
928	#135	D₄×C₆₇	1	8	yes	complemented
929	C₂×Q₁₆	—	2	4	no	—
930	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
933	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
934	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
935	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
936	C₂×SD₁₆	—	2	4	no	—
937	C₂×SD₁₆	—	2	4	no	—
938	C₂×SD₁₆	—	2	8	no	—
939	C₂×SD₁₆	—	2	4	no	—
940	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
941	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
942	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
943	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
945	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
947	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
948	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
949	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
950	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
951	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
952	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
953	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
954	C₂×D₈	—	2	4	no	—
955	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
956	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
957	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
958	C₂×D₈	C₂³×C₆₇	1	2	yes	—
959	C₂×D₈	C₂³×C₆₇	1	2	yes	—
960	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
961	#131	—	2	4	no	—
962	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
963	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
964	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
965	C₂²×C₈	—	2	4	no	—
966	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
967	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
968	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
969	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
970	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
971	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
972	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
973	C₄⋊Q₈	—	2	2	no	—
974	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
975	#127	—	2	2	no	—
976	#127	C₂³×C₆₇	1	2	yes	—
977	#124	—	2	2	no	—
978	#124	—	2	2	no	—
979	#124	C₂³×C₆₇	1	2	yes	—
980	#124	C₂³×C₆₇	1	2	yes	—
981	#123	—	2	2	no	—
982	#123	—	2	2	no	—
983	#123	—	2	2	no	—
984	#123	—	2	2	no	—
985	#123	—	2	2	no	—
986	#123	D₄×C₆₇	1	2	yes	—
987	C₂²⋊Q₈	—	2	1	no	—
988	C₂²⋊Q₈	—	2	1	no	—
989	C₂²⋊Q₈	—	2	1	no	—
990	C₂²⋊Q₈	—	2	1	no	—
991	C₂²⋊Q₈	—	2	1	no	—
992	C₂²⋊Q₈	—	2	2	no	—
993	C₂²⋊Q₈	—	2	1	no	—
994	C₂²⋊Q₈	—	2	2	no	—
995	C₂²⋊Q₈	—	2	2	no	—
996	C₂²⋊Q₈	—	2	2	no	—
997	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
998	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
999	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1000	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1001	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1002	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
1003	#121	—	2	1	no	—
1004	#121	—	2	2	no	—
1005	#121	—	2	1	no	—
1006	#121	—	2	2	no	—
1007	#121	—	2	2	no	—
1008	#121	—	2	2	no	—
1009	#121	—	2	2	no	—
1010	#121	—	2	1	no	—
1011	#121	—	2	1	no	—
1012	#121	—	2	1	no	—
1013	#121	—	2	1	no	—
1014	#121	—	2	2	no	—
1015	#121	—	2	2	no	—
1016	#121	—	2	2	no	—
1017	#121	—	2	2	no	—
1018	#121	—	2	2	no	—
1019	#121	D₄×C₆₇	1	1	yes	characteristic
1020	#121	D₄×C₆₇	1	1	yes	characteristic
1021	#121	C₂³×C₆₇	1	2	yes	—
1022	#121	C₂³×C₆₇	1	2	yes	—
1023	#121	C₂³×C₆₇	1	2	yes	—
1024	#121	C₂³×C₆₇	1	2	yes	—
1025	#120	—	2	2	no	—
1026	#120	—	2	2	no	—
1027	#120	—	2	2	no	—
1028	#120	—	2	2	no	—
1029	#120	—	2	2	no	—
1030	#120	D₄×C₆₇	1	2	yes	—
1031	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1032	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1033	C₄×D₄	—	2	2	no	—
1034	C₄×D₄	—	2	2	no	—
1035	C₄×D₄	—	2	2	no	—
1036	C₄×D₄	—	2	2	no	—
1037	C₄×D₄	—	2	2	no	—
1038	C₄×D₄	—	2	2	no	—
1039	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1040	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1041	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1042	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1043	#117	—	2	1	no	—
1044	#117	—	2	1	no	—
1045	#117	C₂³×C₆₇	1	1	yes	characteristic
1046	C₂×C₄⋊C₄	—	2	1	no	—
1047	C₂×C₄⋊C₄	—	2	1	no	—
1048	C₂×C₄⋊C₄	—	2	1	no	—
1049	C₂×C₄⋊C₄	—	2	2	no	—
1050	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	—	2	1	no	—
1053	C₂×C₂²⋊C₄	—	2	1	no	—
1054	C₂×C₂²⋊C₄	—	2	2	no	—
1055	C₂×C₂²⋊C₄	—	2	2	no	—
1056	#106	C₂³×C₆₇	1	2	yes	—
1057	#106	C₂³×C₆₇	1	2	yes	—
1058	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1059	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1060	#103	C₂³×C₆₇	1	2	yes	—
1061	#103	C₂³×C₆₇	1	2	yes	—
1062	#103	C₂³×C₆₇	1	2	yes	—
1063	#103	C₂³×C₆₇	1	2	yes	—
1064	#103	C₂³×C₆₇	1	2	yes	—
1065	#103	C₂³×C₆₇	1	2	yes	—
1066	#102	C₂³×C₆₇	1	2	yes	—
1067	#102	C₂³×C₆₇	1	2	yes	—
1068	#102	C₂³×C₆₇	1	2	yes	—
1069	#102	C₂³×C₆₇	1	2	yes	—
1070	#102	C₂³×C₆₇	1	2	yes	—
1071	#102	C₂³×C₆₇	1	2	yes	—
1072	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1073	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1074	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1075	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1076	#97	C₂³×C₆₇	1	2	yes	—
1077	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1078	C₂⁴	—	2	1	no	—
1079	C₂⁴	—	2	1	no	—
1080	C₂⁴	—	2	2	no	—
1081	C₂⁴	—	2	1	no	—
1082	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	#41	—	2	2	no	—
1084	#41	—	2	2	no	—
1085	#41	—	2	2	no	—
1086	#41	—	2	2	no	—
1087	#41	—	2	2	no	—
1088	#41	—	2	2	no	—
1089	#41	—	2	4	no	—
1090	#41	—	2	2	no	—
1091	#41	—	2	2	no	—
1092	#41	—	2	4	no	—
1093	#41	—	2	2	no	—
1094	#41	—	2	2	no	—
1095	#41	—	2	2	no	—
1096	#41	—	2	2	no	—
1097	#41	—	4	4	no	—
1098	#41	—	4	4	no	—
1099	#41	—	4	1	no	—
1100	#41	—	4	1	no	—
1101	#41	—	4	1	no	—
1102	#41	—	4	1	no	—
1103	#41	—	4	2	no	—
1104	#41	—	4	2	no	—
1105	#41	—	4	4	no	—
1106	#41	—	4	4	no	—
1107	#41	—	4	4	no	—
1108	#41	—	4	4	no	—
1109	#41	—	4	8	no	—
1110	#41	C₂×D₄×C₆₇	1	4	yes	—
1111	#41	C₂×D₄×C₆₇	1	4	yes	complemented
1112	C₂×Q₈	—	2	1	no	—
1113	C₂×Q₈	—	2	1	no	—
1114	C₂×Q₈	—	2	2	no	—
1115	C₂×Q₈	—	2	1	no	—
1116	C₂×Q₈	—	2	2	no	—
1117	C₂×Q₈	—	2	2	no	—
1118	C₂×Q₈	—	2	4	no	—
1119	C₂×Q₈	—	2	2	no	—
1120	C₂×Q₈	—	2	2	no	—
1121	C₂×Q₈	—	4	1	no	—
1122	C₂×Q₈	—	4	1	no	—
1123	C₂×Q₈	—	4	2	no	—
1124	C₂×Q₈	—	4	4	no	—
1125	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1126	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1128	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1129	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1130	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1131	C₂×D₄	—	2	1	no	—
1132	C₂×D₄	—	2	1	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	2	4	no	—
1136	C₂×D₄	—	2	2	no	—
1137	C₂×D₄	—	2	1	no	—
1138	C₂×D₄	—	2	1	no	—
1139	C₂×D₄	—	2	2	no	—
1140	C₂×D₄	—	2	1	no	—
1141	C₂×D₄	—	2	1	no	—
1142	C₂×D₄	—	2	1	no	—
1143	C₂×D₄	—	2	2	no	—
1144	C₂×D₄	—	2	1	no	—
1145	C₂×D₄	—	2	2	no	—
1146	C₂×D₄	—	2	2	no	—
1147	C₂×D₄	—	2	2	no	—
1148	C₂×D₄	—	2	2	no	—
1149	C₂×D₄	—	2	1	no	—
1150	C₂×D₄	—	2	2	no	—
1151	C₂×D₄	—	2	1	no	—
1152	C₂×D₄	—	2	1	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	2	2	no	—
1155	C₂×D₄	—	2	2	no	—
1156	C₂×D₄	—	4	1	no	—
1157	C₂×D₄	—	4	1	no	—
1158	C₂×D₄	—	4	2	no	—
1159	C₂×D₄	—	4	4	no	—
1160	C₂×D₄	—	4	8	no	—
1161	C₂×D₄	—	4	4	no	—
1162	C₂×D₄	—	4	4	no	—
1163	C₂×D₄	—	8	4	no	—
1164	C₂×D₄	—	8	2	no	—
1165	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1166	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1167	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1168	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1169	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1170	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1171	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1172	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1173	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1174	C₂²×C₄	—	2	1	no	—
1175	C₂²×C₄	—	2	1	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	2	1	no	—
1179	C₂²×C₄	—	2	1	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	1	no	—
1182	C₂²×C₄	—	2	1	no	—
1183	C₂²×C₄	—	2	1	no	—
1184	C₂²×C₄	—	2	1	no	—
1185	C₂²×C₄	—	2	2	no	—
1186	C₂²×C₄	—	2	1	no	—
1187	C₂²×C₄	—	2	1	no	—
1188	C₂²×C₄	—	2	2	no	—
1189	C₂²×C₄	—	2	1	no	—
1190	C₂²×C₄	—	2	1	no	—
1191	C₂²×C₄	—	2	1	no	—
1192	C₂²×C₄	—	2	2	no	—
1193	C₂²×C₄	—	2	2	no	—
1194	C₂²×C₄	—	4	4	no	—
1195	C₂²×C₄	—	4	4	no	—
1196	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1197	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1198	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1202	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1203	Q₁₆	—	2	2	no	—
1204	Q₁₆	—	2	2	no	—
1205	Q₁₆	—	2	4	no	—
1206	Q₁₆	—	2	2	no	—
1207	Q₁₆	—	4	2	no	—
1208	Q₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1209	SD₁₆	—	2	2	no	—
1210	SD₁₆	—	2	2	no	—
1211	SD₁₆	—	2	4	no	—
1212	SD₁₆	—	2	2	no	—
1213	SD₁₆	—	2	2	no	—
1214	SD₁₆	—	2	4	no	—
1215	SD₁₆	—	2	4	no	—
1216	SD₁₆	—	2	2	no	—
1217	SD₁₆	—	2	2	no	—
1218	SD₁₆	—	2	4	no	—
1219	SD₁₆	—	4	2	no	—
1220	SD₁₆	—	4	2	no	—
1221	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1222	SD₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1223	D₈	—	2	2	no	—
1224	D₈	—	2	2	no	—
1225	D₈	—	2	4	no	—
1226	D₈	—	2	2	no	—
1227	D₈	—	4	2	no	—
1228	D₈	C₂×D₄×C₆₇	1	4	yes	complemented
1229	M₁₆	—	2	2	no	—
1230	M₁₆	—	2	2	no	—
1231	M₁₆	—	2	4	no	—
1232	C₂×C₈	—	2	2	no	—
1233	C₂×C₈	—	2	2	no	—
1234	C₂×C₈	—	2	2	no	—
1235	C₂×C₈	—	2	2	no	—
1236	C₂×C₈	—	2	2	no	—
1237	C₂×C₈	—	2	4	no	—
1238	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
1239	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1240	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1241	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1242	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1243	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1244	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1245	C₄⋊C₄	—	2	2	no	—
1246	C₄⋊C₄	—	2	1	no	—
1247	C₄⋊C₄	—	2	1	no	—
1248	C₄⋊C₄	—	2	2	no	—
1249	C₄⋊C₄	—	2	2	no	—
1250	C₄⋊C₄	—	2	2	no	—
1251	C₄⋊C₄	—	2	2	no	—
1252	C₄⋊C₄	—	2	2	no	—
1253	C₄⋊C₄	—	2	2	no	—
1254	C₄⋊C₄	—	2	2	no	—
1255	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1256	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1257	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1258	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1259	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1260	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	2	no	—
1267	C₂²⋊C₄	—	2	2	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	—	2	2	no	—
1271	C₂²⋊C₄	—	2	2	no	—
1272	C₂²⋊C₄	—	2	2	no	—
1273	C₂²⋊C₄	—	2	2	no	—
1274	C₂²⋊C₄	—	2	2	no	—
1275	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1276	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1277	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1278	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1279	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1280	C₄²	—	2	2	no	—
1281	C₄²	—	2	2	no	—
1282	C₄²	C₂⁴×C₆₇	1	2	yes	—
1283	C₂³	—	2	2	no	—
1284	C₂³	—	2	2	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	2	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	4	1	no	—
1291	C₂³	—	4	2	no	—
1292	C₂³	—	4	2	no	—
1293	C₂³	—	4	4	no	—
1294	C₂³	—	4	2	no	—
1295	C₂³	—	4	2	no	—
1296	C₂³	—	4	2	no	—
1297	C₂³	—	8	1	no	—
1298	C₂³	—	8	1	no	—
1299	C₂³	—	8	1	no	—
1300	C₂³	—	8	2	no	—
1301	C₂³	—	8	1	no	—
1302	C₂³	—	8	2	no	—
1303	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1304	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1305	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1306	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1307	Q₈	—	2	2	no	—
1308	Q₈	—	2	1	no	—
1309	Q₈	—	2	1	no	—
1310	Q₈	—	2	2	no	—
1311	Q₈	—	2	1	no	—
1312	Q₈	—	2	1	no	—
1313	Q₈	—	2	1	no	—
1314	Q₈	—	2	2	no	—
1315	Q₈	—	2	1	no	—
1316	Q₈	—	4	4	no	—
1317	Q₈	—	4	2	no	—
1318	Q₈	—	4	2	no	—
1319	Q₈	—	4	2	no	—
1320	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1321	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1322	D₄	—	2	4	no	—
1323	D₄	—	2	4	no	—
1324	D₄	—	2	4	no	—
1325	D₄	—	2	4	no	—
1326	D₄	—	2	2	no	—
1327	D₄	—	2	1	no	—
1328	D₄	—	2	1	no	—
1329	D₄	—	2	2	no	—
1330	D₄	—	2	1	no	—
1331	D₄	—	2	1	no	—
1332	D₄	—	2	1	no	—
1333	D₄	—	2	2	no	—
1334	D₄	—	2	1	no	—
1335	D₄	—	4	2	no	—
1336	D₄	—	4	4	no	—
1337	D₄	—	4	2	no	—
1338	D₄	—	4	2	no	—
1339	D₄	—	4	4	no	—
1340	D₄	—	4	2	no	—
1341	D₄	—	4	2	no	—
1342	D₄	—	4	2	no	—
1343	D₄	—	4	2	no	—
1344	D₄	—	4	4	no	—
1345	D₄	—	4	2	no	—
1346	D₄	—	4	2	no	—
1347	D₄	—	4	4	no	—
1348	D₄	—	4	2	no	—
1349	D₄	—	8	2	no	—
1350	D₄	—	8	2	no	—
1351	D₄	—	8	2	no	—
1352	D₄	—	8	2	no	—
1353	D₄	—	8	2	no	—
1354	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1355	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1356	C₂×C₄	—	2	2	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	2	no	—
1360	C₂×C₄	—	2	2	no	—
1361	C₂×C₄	—	2	4	no	—
1362	C₂×C₄	—	2	4	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	2	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	2	no	—
1369	C₂×C₄	—	2	2	no	—
1370	C₂×C₄	—	2	2	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	2	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	4	2	no	—
1375	C₂×C₄	—	4	2	no	—
1376	C₂×C₄	—	4	4	no	—
1377	C₂×C₄	—	4	2	no	—
1378	C₂×C₄	—	4	2	no	—
1379	C₂×C₄	—	4	2	no	—
1380	C₂×C₄	—	4	2	no	—
1381	C₂×C₄	—	4	4	no	—
1382	C₂×C₄	—	4	4	no	—
1383	C₂×C₄	—	4	2	no	—
1384	C₂×C₄	—	4	2	no	—
1385	C₂×C₄	—	4	2	no	—
1386	C₂×C₄	—	8	2	no	—
1387	C₂×C₄	—	8	2	no	—
1388	C₂×C₄	—	8	1	no	—
1389	C₂×C₄	—	8	1	no	—
1390	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1391	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1392	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1393	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1394	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1395	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1396	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1397	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1398	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1399	C₈	—	2	1	no	—
1400	C₈	—	2	1	no	—
1401	C₈	—	2	2	no	—
1402	C₈	—	2	2	no	—
1403	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1404	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1405	C₂²	—	2	1	no	—
1406	C₂²	—	2	1	no	—
1407	C₂²	—	2	1	no	—
1408	C₂²	—	2	1	no	—
1409	C₂²	—	2	2	no	—
1410	C₂²	—	2	1	no	—
1411	C₂²	—	2	1	no	—
1412	C₂²	—	2	2	no	—
1413	C₂²	—	2	1	no	—
1414	C₂²	—	2	2	no	—
1415	C₂²	—	2	2	no	—
1416	C₂²	—	2	2	no	—
1417	C₂²	—	4	4	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	1	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	4	2	no	—
1423	C₂²	—	4	1	no	—
1424	C₂²	—	4	1	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	2	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	2	no	—
1431	C₂²	—	8	4	no	—
1432	C₂²	—	8	4	no	—
1433	C₂²	—	16	2	no	—
1434	C₂²	—	16	4	no	—
1435	C₂²	D₄²×C₆₇	1	2	yes	—
1436	C₂²	#577×C₆₇	1	2	yes	complemented
1437	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1438	C₄	—	2	2	no	—
1439	C₄	—	2	2	no	—
1440	C₄	—	2	1	no	—
1441	C₄	—	2	1	no	—
1442	C₄	—	2	2	no	—
1443	C₄	—	2	2	no	—
1444	C₄	—	2	2	no	—
1445	C₄	—	4	2	no	—
1446	C₄	—	4	2	no	—
1447	C₄	—	4	1	no	—
1448	C₄	—	4	1	no	—
1449	C₄	—	4	2	no	—
1450	C₄	D₄²×C₆₇	1	2	yes	—
1451	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1452	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1453	C₂	—	2	2	no	—
1454	C₂	—	2	2	no	—
1455	C₂	—	4	1	no	—
1456	C₂	—	4	2	no	—
1457	C₂	—	4	2	no	—
1458	C₂	—	4	2	no	—
1459	C₂	—	8	1	no	—
1460	C₂	—	8	1	no	—
1461	C₂	—	8	2	no	—
1462	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1463	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1464	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₂²×#135×C₆₇	C₂	semidirect
3. C₆₇×#3489	C₂	semidirect
4. C₆₇×#3488	C₂	semidirect
5. C₆₇×#3284	C₂	semidirect
6. C₆₇×#3282	C₂	semidirect
7. C₆₇×#3282	C₂	semidirect
8. D₄×SD₁₆×C₆₇	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3270	C₂	semidirect
11. C₆₇×#3267	C₂	semidirect
12. C₆₇×#3264	C₂	semidirect
13. C₆₇×#3154	C₂	semidirect
14. C₆₇×#3060	C₂	semidirect
15. C₂×#465×C₆₇	C₂	semidirect
16. C₆₇×#3046	C₂	semidirect
17. C₆₇×#3045	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3012	C₂	semidirect
20. C₆₇×#3007	C₂	semidirect
21. C₆₇×#3006	C₂	semidirect
22. C₆₇×#2952	C₂	semidirect
23. C₆₇×#2929	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
25. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
27. C₂²×#41×C₆₇	C₂²	semidirect
29. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
38. C₂×#135×C₆₇	C₂²	semidirect
39. C₂×#135×C₆₇	C₂²	semidirect
40. C₂×#135×C₆₇	C₂²	semidirect
41. C₂×#135×C₆₇	C₂²	semidirect
42. C₂×#135×C₆₇	C₂²	semidirect
43. C₂×#135×C₆₇	C₂²	semidirect
44. C₂×#135×C₆₇	C₂²	semidirect
45. C₂²×Q₁₆×C₆₇	C₂²	semidirect
46. C₂²×SD₁₆×C₆₇	C₂²	semidirect
47. C₂²×SD₁₆×C₆₇	C₂²	semidirect
48. C₂²×SD₁₆×C₆₇	C₂²	semidirect
49. C₂²×SD₁₆×C₆₇	C₂²	semidirect
50. C₂²×D₈×C₆₇	C₂²	semidirect
51. C₂×#131×C₆₇	C₂²	semidirect
52. C₂³×C₈×C₆₇	C₂²	semidirect
53. #550×C₆₇	C₂²	semidirect
54. D₄×Q₈×C₆₇	C₂²	semidirect
56. #548×C₆₇	C₂²	semidirect
58. #547×C₆₇	C₂²	semidirect
61. #546×C₆₇	C₂²	semidirect
62. #546×C₆₇	C₂²	semidirect
67. #537×C₆₇	C₂²	semidirect
68. #537×C₆₇	C₂²	semidirect
70. #536×C₆₇	C₂²	semidirect
72. #535×C₆₇	C₂²	semidirect
77. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
80. #520×C₆₇	C₂²	semidirect
81. #520×C₆₇	C₂²	semidirect
82. #497×C₆₇	C₂²	semidirect
83. #496×C₆₇	C₂²	semidirect
84. #495×C₆₇	C₂²	semidirect
85. #492×C₆₇	C₂²	semidirect
86. #470×C₆₇	C₂²	semidirect
87. #469×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #465×C₆₇	C₂²	semidirect
91. #465×C₆₇	C₂²	semidirect
92. #465×C₆₇	C₂²	semidirect
93. #465×C₆₇	C₂²	semidirect
94. #464×C₆₇	C₂²	semidirect
95. #464×C₆₇	C₂²	semidirect
96. #463×C₆₇	C₂²	semidirect
97. #463×C₆₇	C₂²	semidirect
98. #462×C₆₇	C₂²	semidirect
99. #461×C₆₇	C₂²	semidirect
100. #460×C₆₇	C₂²	semidirect
101. #459×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #452×C₆₇	C₂²	semidirect
104. #452×C₆₇	C₂²	semidirect
105. #452×C₆₇	C₂²	semidirect
106. #451×C₆₇	C₂²	semidirect
107. #451×C₆₇	C₂²	semidirect
108. #450×C₆₇	C₂²	semidirect
109. #450×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #449×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
116. #447×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #442×C₆₇	C₂²	semidirect
119. #441×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #435×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. C₈×D₄×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. C₂×#106×C₆₇	C₂²	semidirect
127. #424×C₆₇	C₂²	semidirect
128. #417×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #417×C₆₇	C₂²	semidirect
131. #417×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. C₂×#102×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
135. #407×C₆₇	C₂²	semidirect
136. #405×C₆₇	C₂²	semidirect
195. #135×C₆₇	D₄	semidirect
378. #41×C₆₇	C₂×D₄	semidirect
475. Q₁₆×C₆₇	C₂×D₄	semidirect
488. SD₁₆×C₆₇	C₂×D₄	semidirect
489. SD₁₆×C₆₇	C₂×D₄	semidirect
495. D₈×C₆₇	C₂×D₄	semidirect
505. C₂×C₈×C₆₇	C₂×D₄	semidirect
703. C₂²×C₆₇	#577	semidirect
720. #61055	C₆₇	direct (N × H)
733. C₂×#577	C₂×C₆₇	semidirect
734. C₂²×#135	C₂×C₆₇	semidirect
735. #3489	C₂×C₆₇	semidirect
736. #3488	C₂×C₆₇	semidirect
737. #3284	C₂×C₆₇	semidirect
738. #3282	C₂×C₆₇	semidirect
739. #3282	C₂×C₆₇	semidirect
740. D₄×SD₁₆	C₂×C₆₇	semidirect
741. #3271	C₂×C₆₇	semidirect
742. #3270	C₂×C₆₇	semidirect
743. #3267	C₂×C₆₇	semidirect
744. #3264	C₂×C₆₇	semidirect
745. #3154	C₂×C₆₇	semidirect
746. #3060	C₂×C₆₇	semidirect
747. C₂×#465	C₂×C₆₇	semidirect
748. #3046	C₂×C₆₇	semidirect
749. #3045	C₂×C₆₇	semidirect
750. #3013	C₂×C₆₇	semidirect
751. #3012	C₂×C₆₇	semidirect
752. #3007	C₂×C₆₇	semidirect
753. #3006	C₂×C₆₇	semidirect
754. #2952	C₂×C₆₇	semidirect
755. #2929	C₂×C₆₇	semidirect
756. C₆₇	#61055	direct (N × H)
757. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
758. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
760. C₂²×#41	C₂²×C₆₇	semidirect
762. C₂×#137	C₂²×C₆₇	semidirect
763. C₂×#137	C₂²×C₆₇	semidirect
764. C₂×#137	C₂²×C₆₇	semidirect
765. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
766. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
767. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
771. C₂×#135	C₂²×C₆₇	semidirect
772. C₂×#135	C₂²×C₆₇	semidirect
773. C₂×#135	C₂²×C₆₇	semidirect
774. C₂×#135	C₂²×C₆₇	semidirect
775. C₂×#135	C₂²×C₆₇	semidirect
776. C₂×#135	C₂²×C₆₇	semidirect
777. C₂×#135	C₂²×C₆₇	semidirect
778. C₂²×Q₁₆	C₂²×C₆₇	semidirect
779. C₂²×SD₁₆	C₂²×C₆₇	semidirect
780. C₂²×SD₁₆	C₂²×C₆₇	semidirect
781. C₂²×SD₁₆	C₂²×C₆₇	semidirect
782. C₂²×SD₁₆	C₂²×C₆₇	semidirect
783. C₂²×D₈	C₂²×C₆₇	semidirect
784. C₂×#131	C₂²×C₆₇	semidirect
785. C₂³×C₈	C₂²×C₆₇	semidirect
786. #550	C₂²×C₆₇	semidirect
787. D₄×Q₈	C₂²×C₆₇	semidirect
789. #548	C₂²×C₆₇	semidirect
791. #547	C₂²×C₆₇	semidirect
794. #546	C₂²×C₆₇	semidirect
795. #546	C₂²×C₆₇	semidirect
800. #537	C₂²×C₆₇	semidirect
801. #537	C₂²×C₆₇	semidirect
803. #536	C₂²×C₆₇	semidirect
805. #535	C₂²×C₆₇	semidirect
810. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
813. #520	C₂²×C₆₇	semidirect
814. #520	C₂²×C₆₇	semidirect
815. #497	C₂²×C₆₇	semidirect
816. #496	C₂²×C₆₇	semidirect
817. #495	C₂²×C₆₇	semidirect
818. #492	C₂²×C₆₇	semidirect
819. #470	C₂²×C₆₇	semidirect
820. #469	C₂²×C₆₇	semidirect
821. #465	C₂²×C₆₇	semidirect
822. #465	C₂²×C₆₇	semidirect
823. #465	C₂²×C₆₇	semidirect
824. #465	C₂²×C₆₇	semidirect
825. #465	C₂²×C₆₇	semidirect
826. #465	C₂²×C₆₇	semidirect
827. #464	C₂²×C₆₇	semidirect
828. #464	C₂²×C₆₇	semidirect
829. #463	C₂²×C₆₇	semidirect
830. #463	C₂²×C₆₇	semidirect
831. #462	C₂²×C₆₇	semidirect
832. #461	C₂²×C₆₇	semidirect
833. #460	C₂²×C₆₇	semidirect
834. #459	C₂²×C₆₇	semidirect
835. #452	C₂²×C₆₇	semidirect
836. #452	C₂²×C₆₇	semidirect
837. #452	C₂²×C₆₇	semidirect
838. #452	C₂²×C₆₇	semidirect
839. #451	C₂²×C₆₇	semidirect
840. #451	C₂²×C₆₇	semidirect
841. #450	C₂²×C₆₇	semidirect
842. #450	C₂²×C₆₇	semidirect
843. #449	C₂²×C₆₇	semidirect
844. #449	C₂²×C₆₇	semidirect
845. #449	C₂²×C₆₇	semidirect
846. #449	C₂²×C₆₇	semidirect
847. #448	C₂²×C₆₇	semidirect
848. #448	C₂²×C₆₇	semidirect
849. #447	C₂²×C₆₇	semidirect
850. #447	C₂²×C₆₇	semidirect
851. #442	C₂²×C₆₇	semidirect
852. #441	C₂²×C₆₇	semidirect
853. C₄×SD₁₆	C₂²×C₆₇	semidirect
854. C₄×SD₁₆	C₂²×C₆₇	semidirect
855. #435	C₂²×C₆₇	semidirect
856. #435	C₂²×C₆₇	semidirect
857. C₈×D₄	C₂²×C₆₇	semidirect
858. C₈×D₄	C₂²×C₆₇	semidirect
859. C₂×#106	C₂²×C₆₇	semidirect
860. #424	C₂²×C₆₇	semidirect
861. #417	C₂²×C₆₇	semidirect
862. #417	C₂²×C₆₇	semidirect
863. #417	C₂²×C₆₇	semidirect
864. #417	C₂²×C₆₇	semidirect
865. C₂×#103	C₂²×C₆₇	semidirect
866. C₂×#102	C₂²×C₆₇	semidirect
867. #408	C₂²×C₆₇	semidirect
868. #407	C₂²×C₆₇	semidirect
869. #405	C₂²×C₆₇	semidirect
928. #135	D₄×C₆₇	semidirect
1111. #41	C₂×D₄×C₆₇	semidirect
1208. Q₁₆	C₂×D₄×C₆₇	semidirect
1221. SD₁₆	C₂×D₄×C₆₇	semidirect
1222. SD₁₆	C₂×D₄×C₆₇	semidirect
1228. D₈	C₂×D₄×C₆₇	semidirect
1238. C₂×C₈	C₂×D₄×C₆₇	semidirect
1436. C₂²	#577×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#577×C₆₇	2
C₂²×#135×C₆₇	2
C₆₇×#3489	2
C₆₇×#3488	2
C₆₇×#3284	2
C₆₇×#3282	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3267	2
C₆₇×#3264	2
C₆₇×#3154	2
C₆₇×#3060	2
C₂×#465×C₆₇	2
C₆₇×#3046	2
C₆₇×#3045	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3007	2
C₆₇×#3006	2
C₆₇×#2952	2
C₆₇×#2929	2
#61055	67

Subgroups — C67×#61055 #30740306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61055 #30740306