Subgroups — C₆₇×#61075 #30740326

Order 17152.

2740 conjugacy classes of subgroups.

The subgroup lattice has 1412 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×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3285	C₂	1	2	yes	maximal, complemented
6	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3275	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×#3266	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#448×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2933	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
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂³×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#577×C₆₇	—	2	8	no	—
29	C₂×#137×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
35	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#550×C₆₇	C₂²	1	2	yes	—
50	D₄×Q₈×C₆₇	—	2	1	no	—
51	D₄×Q₈×C₆₇	—	2	1	no	—
52	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
53	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
54	#548×C₆₇	—	2	1	no	—
55	#548×C₆₇	—	2	1	no	—
56	#548×C₆₇	C₂²	1	2	yes	—
57	#548×C₆₇	C₂²	1	2	yes	complemented
58	#548×C₆₇	C₂²	1	2	yes	complemented
59	#546×C₆₇	—	2	2	no	—
60	#546×C₆₇	C₂²	1	2	yes	—
61	D₄²×C₆₇	—	2	2	no	—
62	D₄²×C₆₇	C₂²	1	2	yes	—
63	#537×C₆₇	—	2	1	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic
65	#536×C₆₇	—	2	2	no	—
66	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#535×C₆₇	—	2	1	no	—
69	#535×C₆₇	C₂²	1	1	yes	characteristic
70	#525×C₆₇	—	2	1	no	—
71	#525×C₆₇	—	2	2	no	—
72	#525×C₆₇	C₂²	1	1	yes	characteristic
73	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×#121×C₆₇	—	2	1	no	—
75	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
76	#520×C₆₇	C₂²	1	1	yes	characteristic
77	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#497×C₆₇	C₂²	1	2	yes	complemented
79	#496×C₆₇	C₂²	1	2	yes	complemented
80	#495×C₆₇	C₂²	1	2	yes	complemented
81	#492×C₆₇	C₂²	1	2	yes	complemented
82	#470×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#467×C₆₇	C₂²	1	2	yes	complemented
87	#466×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#464×C₆₇	C₂²	1	2	yes	complemented
92	#464×C₆₇	C₂²	1	2	yes	complemented
93	#463×C₆₇	C₂²	1	2	yes	complemented
94	#462×C₆₇	C₂²	1	2	yes	complemented
95	#461×C₆₇	C₂²	1	2	yes	complemented
96	#460×C₆₇	C₂²	1	2	yes	complemented
97	#460×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	2	yes	complemented
100	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#452×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#451×C₆₇	C₂²	1	2	yes	complemented
104	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#450×C₆₇	C₂²	1	2	yes	complemented
106	#450×C₆₇	C₂²	1	2	yes	complemented
107	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#448×C₆₇	C₂²	1	2	yes	complemented
112	#448×C₆₇	C₂²	1	2	yes	complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	2	yes	complemented
116	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#441×C₆₇	C₂²	1	2	yes	complemented
119	#440×C₆₇	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#416×C₆₇	C₂²	1	1	yes	characteristic
131	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊C₈×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	2	no	—
143	C₂×#41×C₆₇	—	2	1	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	4	no	—
147	C₂×#41×C₆₇	—	4	2	no	—
148	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×#41×C₆₇	C₂³	1	2	yes	—
152	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×#41×C₆₇	C₂³	1	2	yes	—
154	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
156	C₂²×Q₈×C₆₇	—	2	1	no	—
157	C₂²×Q₈×C₆₇	—	2	1	no	—
158	C₂²×Q₈×C₆₇	—	2	1	no	—
159	C₂²×Q₈×C₆₇	—	2	1	no	—
160	C₂²×Q₈×C₆₇	—	2	4	no	—
161	C₂²×Q₈×C₆₇	—	4	2	no	—
162	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
164	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
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	2	no	—
172	C₂²×D₄×C₆₇	—	2	2	no	—
173	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
175	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₆₇	—	2	1	no	—
177	C₂³×C₄×C₆₇	—	2	1	no	—
178	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
179	#137×C₆₇	—	2	4	no	—
180	#137×C₆₇	—	2	4	no	—
181	#137×C₆₇	—	2	8	no	—
182	#137×C₆₇	—	2	8	no	—
183	#137×C₆₇	—	2	8	no	—
184	#137×C₆₇	—	2	4	no	—
185	#137×C₆₇	D₄	1	8	yes	complemented
186	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
187	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
188	#135×C₆₇	—	2	4	no	—
189	#135×C₆₇	—	2	8	no	—
190	#135×C₆₇	—	4	2	no	—
191	C₂×Q₁₆×C₆₇	—	2	8	no	—
192	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
194	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
195	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
196	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
198	C₂×SD₁₆×C₆₇	—	2	4	no	—
199	C₂×SD₁₆×C₆₇	—	2	8	no	—
200	C₂×SD₁₆×C₆₇	—	2	8	no	—
201	C₂×SD₁₆×C₆₇	—	4	2	no	—
202	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
203	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
205	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
209	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
210	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
212	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
213	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
215	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₆₇	C₂³	1	2	yes	—
217	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
218	#131×C₆₇	—	2	4	no	—
219	C₂×M₁₆×C₆₇	—	2	4	no	—
220	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
221	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
222	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
226	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈×C₆₇	—	2	1	no	—
229	C₄⋊Q₈×C₆₇	—	2	2	no	—
230	C₄⋊Q₈×C₆₇	—	2	2	no	—
231	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
232	#127×C₆₇	—	2	2	no	—
233	#127×C₆₇	C₂³	1	2	yes	—
234	#124×C₆₇	—	2	1	no	—
235	#124×C₆₇	—	2	2	no	—
236	#124×C₆₇	—	2	2	no	—
237	#124×C₆₇	—	2	2	no	—
238	#124×C₆₇	C₂³	1	2	yes	—
239	#124×C₆₇	C₂³	1	2	yes	—
240	#123×C₆₇	—	2	2	no	—
241	#123×C₆₇	—	2	1	no	—
242	#123×C₆₇	—	2	2	no	—
243	#123×C₆₇	—	2	2	no	—
244	#123×C₆₇	D₄	1	2	yes	—
245	C₂²⋊Q₈×C₆₇	—	2	1	no	—
246	C₂²⋊Q₈×C₆₇	—	2	2	no	—
247	C₂²⋊Q₈×C₆₇	—	2	2	no	—
248	C₂²⋊Q₈×C₆₇	—	2	1	no	—
249	C₂²⋊Q₈×C₆₇	—	2	1	no	—
250	C₂²⋊Q₈×C₆₇	—	2	2	no	—
251	C₂²⋊Q₈×C₆₇	—	2	2	no	—
252	C₂²⋊Q₈×C₆₇	—	2	2	no	—
253	C₂²⋊Q₈×C₆₇	—	2	2	no	—
254	C₂²⋊Q₈×C₆₇	—	2	2	no	—
255	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
256	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
257	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
260	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
261	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
262	#121×C₆₇	—	2	1	no	—
263	#121×C₆₇	—	2	2	no	—
264	#121×C₆₇	—	2	2	no	—
265	#121×C₆₇	—	2	2	no	—
266	#121×C₆₇	—	2	2	no	—
267	#121×C₆₇	—	2	1	no	—
268	#121×C₆₇	—	2	1	no	—
269	#121×C₆₇	—	2	1	no	—
270	#121×C₆₇	—	2	1	no	—
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	2	no	—
273	#121×C₆₇	—	2	2	no	—
274	#121×C₆₇	—	2	2	no	—
275	#121×C₆₇	D₄	1	1	yes	characteristic
276	#121×C₆₇	D₄	1	1	yes	characteristic
277	#121×C₆₇	C₂³	1	2	yes	—
278	#121×C₆₇	C₂³	1	2	yes	—
279	#121×C₆₇	C₂³	1	2	yes	—
280	#121×C₆₇	C₂³	1	1	yes	characteristic
281	#121×C₆₇	C₂³	1	1	yes	characteristic
282	#120×C₆₇	—	2	1	no	—
283	#120×C₆₇	—	2	2	no	—
284	#120×C₆₇	—	2	2	no	—
285	#120×C₆₇	—	2	2	no	—
286	#120×C₆₇	—	2	2	no	—
287	#120×C₆₇	D₄	1	2	yes	—
288	C₄×Q₈×C₆₇	—	2	1	no	—
289	C₄×Q₈×C₆₇	—	2	1	no	—
290	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
291	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
292	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
293	C₄×D₄×C₆₇	—	2	2	no	—
294	C₄×D₄×C₆₇	—	2	2	no	—
295	C₄×D₄×C₆₇	—	2	1	no	—
296	C₄×D₄×C₆₇	—	2	1	no	—
297	C₄×D₄×C₆₇	—	2	2	no	—
298	C₄×D₄×C₆₇	—	2	2	no	—
299	C₄×D₄×C₆₇	—	2	2	no	—
300	C₄×D₄×C₆₇	—	2	2	no	—
301	C₄×D₄×C₆₇	—	2	2	no	—
302	C₄×D₄×C₆₇	C₂³	1	2	yes	—
303	C₄×D₄×C₆₇	C₂³	1	2	yes	—
304	C₄×D₄×C₆₇	C₂³	1	2	yes	—
305	#117×C₆₇	—	2	1	no	—
306	#117×C₆₇	—	2	2	no	—
307	#117×C₆₇	C₂³	1	1	yes	characteristic
308	#117×C₆₇	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
313	#107×C₆₇	C₂³	1	2	yes	—
314	#106×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	2	yes	—
322	#103×C₆₇	C₂³	1	1	yes	characteristic
323	#103×C₆₇	C₂³	1	1	yes	characteristic
324	#103×C₆₇	C₂³	1	1	yes	characteristic
325	#103×C₆₇	C₂³	1	1	yes	characteristic
326	#102×C₆₇	C₂³	1	1	yes	characteristic
327	#102×C₆₇	C₂³	1	1	yes	characteristic
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	1	yes	characteristic
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₂⁴×C₆₇	—	2	1	no	—
342	C₂⁴×C₆₇	—	2	2	no	—
343	C₂⁴×C₆₇	—	2	1	no	—
344	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
345	#41×C₆₇	—	2	2	no	—
346	#41×C₆₇	—	2	2	no	—
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	4	no	—
349	#41×C₆₇	—	2	4	no	—
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	—	4	4	no	—
357	#41×C₆₇	—	4	1	no	—
358	#41×C₆₇	—	4	1	no	—
359	#41×C₆₇	—	4	2	no	—
360	#41×C₆₇	—	4	2	no	—
361	#41×C₆₇	—	4	4	no	—
362	#41×C₆₇	—	4	8	no	—
363	#41×C₆₇	—	4	4	no	—
364	#41×C₆₇	—	4	4	no	—
365	#41×C₆₇	C₂×D₄	1	4	yes	—
366	C₂×Q₈×C₆₇	—	2	1	no	—
367	C₂×Q₈×C₆₇	—	2	1	no	—
368	C₂×Q₈×C₆₇	—	2	2	no	—
369	C₂×Q₈×C₆₇	—	2	2	no	—
370	C₂×Q₈×C₆₇	—	2	1	no	—
371	C₂×Q₈×C₆₇	—	2	2	no	—
372	C₂×Q₈×C₆₇	—	2	2	no	—
373	C₂×Q₈×C₆₇	—	2	4	no	—
374	C₂×Q₈×C₆₇	—	2	4	no	—
375	C₂×Q₈×C₆₇	—	2	2	no	—
376	C₂×Q₈×C₆₇	—	2	4	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	2	2	no	—
379	C₂×Q₈×C₆₇	—	4	4	no	—
380	C₂×Q₈×C₆₇	—	4	2	no	—
381	C₂×Q₈×C₆₇	—	4	2	no	—
382	C₂×Q₈×C₆₇	—	4	1	no	—
383	C₂×Q₈×C₆₇	—	4	2	no	—
384	C₂×Q₈×C₆₇	—	4	4	no	—
385	C₂×Q₈×C₆₇	—	4	4	no	—
386	C₂×Q₈×C₆₇	—	4	4	no	—
387	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
388	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
389	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
391	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
393	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×D₄×C₆₇	—	2	1	no	—
395	C₂×D₄×C₆₇	—	2	2	no	—
396	C₂×D₄×C₆₇	—	2	4	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	2	2	no	—
400	C₂×D₄×C₆₇	—	2	1	no	—
401	C₂×D₄×C₆₇	—	2	1	no	—
402	C₂×D₄×C₆₇	—	2	1	no	—
403	C₂×D₄×C₆₇	—	2	2	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	1	no	—
406	C₂×D₄×C₆₇	—	2	2	no	—
407	C₂×D₄×C₆₇	—	2	2	no	—
408	C₂×D₄×C₆₇	—	2	2	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	—	4	1	no	—
416	C₂×D₄×C₆₇	—	4	2	no	—
417	C₂×D₄×C₆₇	—	4	4	no	—
418	C₂×D₄×C₆₇	—	4	8	no	—
419	C₂×D₄×C₆₇	—	4	4	no	—
420	C₂×D₄×C₆₇	—	8	4	no	—
421	C₂×D₄×C₆₇	—	8	2	no	—
422	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
424	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
425	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
426	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
428	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₆₇	—	2	1	no	—
431	C₂²×C₄×C₆₇	—	2	1	no	—
432	C₂²×C₄×C₆₇	—	2	2	no	—
433	C₂²×C₄×C₆₇	—	2	2	no	—
434	C₂²×C₄×C₆₇	—	2	1	no	—
435	C₂²×C₄×C₆₇	—	2	2	no	—
436	C₂²×C₄×C₆₇	—	2	2	no	—
437	C₂²×C₄×C₆₇	—	2	2	no	—
438	C₂²×C₄×C₆₇	—	2	1	no	—
439	C₂²×C₄×C₆₇	—	2	1	no	—
440	C₂²×C₄×C₆₇	—	2	1	no	—
441	C₂²×C₄×C₆₇	—	2	1	no	—
442	C₂²×C₄×C₆₇	—	2	2	no	—
443	C₂²×C₄×C₆₇	—	2	2	no	—
444	C₂²×C₄×C₆₇	—	2	1	no	—
445	C₂²×C₄×C₆₇	—	2	1	no	—
446	C₂²×C₄×C₆₇	—	2	2	no	—
447	C₂²×C₄×C₆₇	—	4	4	no	—
448	C₂²×C₄×C₆₇	—	4	4	no	—
449	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
455	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	Q₁₆×C₆₇	—	2	4	no	—
457	Q₁₆×C₆₇	—	2	4	no	—
458	Q₁₆×C₆₇	—	2	2	no	—
459	Q₁₆×C₆₇	—	2	4	no	—
460	Q₁₆×C₆₇	—	4	1	no	—
461	Q₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
462	SD₁₆×C₆₇	—	2	4	no	—
463	SD₁₆×C₆₇	—	2	4	no	—
464	SD₁₆×C₆₇	—	2	4	no	—
465	SD₁₆×C₆₇	—	2	2	no	—
466	SD₁₆×C₆₇	—	2	2	no	—
467	SD₁₆×C₆₇	—	2	4	no	—
468	SD₁₆×C₆₇	—	2	4	no	—
469	SD₁₆×C₆₇	—	2	4	no	—
470	SD₁₆×C₆₇	—	4	2	no	—
471	SD₁₆×C₆₇	—	4	2	no	—
472	SD₁₆×C₆₇	—	4	1	no	—
473	SD₁₆×C₆₇	—	4	1	no	—
474	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
475	D₈×C₆₇	—	2	2	no	—
476	D₈×C₆₇	—	2	4	no	—
477	D₈×C₆₇	—	4	1	no	—
478	M₁₆×C₆₇	—	2	2	no	—
479	M₁₆×C₆₇	—	2	4	no	—
480	M₁₆×C₆₇	—	2	4	no	—
481	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
482	C₂×C₈×C₆₇	—	2	2	no	—
483	C₂×C₈×C₆₇	—	2	2	no	—
484	C₂×C₈×C₆₇	—	2	4	no	—
485	C₂×C₈×C₆₇	—	2	4	no	—
486	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
487	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
488	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
490	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
492	C₄⋊C₄×C₆₇	—	2	1	no	—
493	C₄⋊C₄×C₆₇	—	2	2	no	—
494	C₄⋊C₄×C₆₇	—	2	2	no	—
495	C₄⋊C₄×C₆₇	—	2	2	no	—
496	C₄⋊C₄×C₆₇	—	2	2	no	—
497	C₄⋊C₄×C₆₇	—	2	2	no	—
498	C₄⋊C₄×C₆₇	—	2	2	no	—
499	C₄⋊C₄×C₆₇	—	2	2	no	—
500	C₄⋊C₄×C₆₇	—	2	2	no	—
501	C₄⋊C₄×C₆₇	—	2	1	no	—
502	C₄⋊C₄×C₆₇	—	2	1	no	—
503	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
504	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
505	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
506	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
507	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
510	C₂²⋊C₄×C₆₇	—	2	2	no	—
511	C₂²⋊C₄×C₆₇	—	2	1	no	—
512	C₂²⋊C₄×C₆₇	—	2	1	no	—
513	C₂²⋊C₄×C₆₇	—	2	1	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	2	2	no	—
516	C₂²⋊C₄×C₆₇	—	2	2	no	—
517	C₂²⋊C₄×C₆₇	—	2	2	no	—
518	C₂²⋊C₄×C₆₇	—	2	2	no	—
519	C₂²⋊C₄×C₆₇	—	2	2	no	—
520	C₂²⋊C₄×C₆₇	—	2	2	no	—
521	C₂²⋊C₄×C₆₇	—	2	2	no	—
522	C₂²⋊C₄×C₆₇	—	2	2	no	—
523	C₂²⋊C₄×C₆₇	—	2	2	no	—
524	C₂²⋊C₄×C₆₇	—	2	1	no	—
525	C₂²⋊C₄×C₆₇	—	2	1	no	—
526	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
527	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
528	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
529	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
530	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
531	C₄²×C₆₇	—	2	2	no	—
532	C₄²×C₆₇	—	2	2	no	—
533	C₄²×C₆₇	—	2	2	no	—
534	C₄²×C₆₇	—	2	1	no	—
535	C₄²×C₆₇	C₂⁴	1	2	yes	—
536	C₂³×C₆₇	—	2	2	no	—
537	C₂³×C₆₇	—	2	2	no	—
538	C₂³×C₆₇	—	2	1	no	—
539	C₂³×C₆₇	—	2	1	no	—
540	C₂³×C₆₇	—	2	2	no	—
541	C₂³×C₆₇	—	2	1	no	—
542	C₂³×C₆₇	—	4	1	no	—
543	C₂³×C₆₇	—	4	2	no	—
544	C₂³×C₆₇	—	4	4	no	—
545	C₂³×C₆₇	—	4	2	no	—
546	C₂³×C₆₇	—	4	2	no	—
547	C₂³×C₆₇	—	8	1	no	—
548	C₂³×C₆₇	—	8	1	no	—
549	C₂³×C₆₇	—	8	2	no	—
550	C₂³×C₆₇	—	8	1	no	—
551	C₂³×C₆₇	—	8	2	no	—
552	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
553	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
555	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	Q₈×C₆₇	—	2	4	no	—
557	Q₈×C₆₇	—	2	2	no	—
558	Q₈×C₆₇	—	2	2	no	—
559	Q₈×C₆₇	—	2	1	no	—
560	Q₈×C₆₇	—	2	1	no	—
561	Q₈×C₆₇	—	2	2	no	—
562	Q₈×C₆₇	—	2	1	no	—
563	Q₈×C₆₇	—	2	2	no	—
564	Q₈×C₆₇	—	2	1	no	—
565	Q₈×C₆₇	—	2	1	no	—
566	Q₈×C₆₇	—	4	4	no	—
567	Q₈×C₆₇	—	4	4	no	—
568	Q₈×C₆₇	—	4	4	no	—
569	Q₈×C₆₇	—	4	2	no	—
570	Q₈×C₆₇	—	4	2	no	—
571	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
572	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
573	D₄×C₆₇	—	2	4	no	—
574	D₄×C₆₇	—	2	4	no	—
575	D₄×C₆₇	—	2	4	no	—
576	D₄×C₆₇	—	2	2	no	—
577	D₄×C₆₇	—	2	1	no	—
578	D₄×C₆₇	—	2	2	no	—
579	D₄×C₆₇	—	2	1	no	—
580	D₄×C₆₇	—	2	1	no	—
581	D₄×C₆₇	—	2	1	no	—
582	D₄×C₆₇	—	2	1	no	—
583	D₄×C₆₇	—	2	2	no	—
584	D₄×C₆₇	—	4	2	no	—
585	D₄×C₆₇	—	4	4	no	—
586	D₄×C₆₇	—	4	2	no	—
587	D₄×C₆₇	—	4	4	no	—
588	D₄×C₆₇	—	4	2	no	—
589	D₄×C₆₇	—	4	4	no	—
590	D₄×C₆₇	—	4	2	no	—
591	D₄×C₆₇	—	4	2	no	—
592	D₄×C₆₇	—	4	2	no	—
593	D₄×C₆₇	—	4	2	no	—
594	D₄×C₆₇	—	4	2	no	—
595	D₄×C₆₇	—	4	4	no	—
596	D₄×C₆₇	—	4	2	no	—
597	D₄×C₆₇	—	8	2	no	—
598	D₄×C₆₇	—	8	2	no	—
599	D₄×C₆₇	—	8	2	no	—
600	D₄×C₆₇	—	8	2	no	—
601	D₄×C₆₇	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₆₇	—	2	2	no	—
603	C₂×C₄×C₆₇	—	2	4	no	—
604	C₂×C₄×C₆₇	—	2	1	no	—
605	C₂×C₄×C₆₇	—	2	2	no	—
606	C₂×C₄×C₆₇	—	2	2	no	—
607	C₂×C₄×C₆₇	—	2	2	no	—
608	C₂×C₄×C₆₇	—	2	4	no	—
609	C₂×C₄×C₆₇	—	2	1	no	—
610	C₂×C₄×C₆₇	—	2	2	no	—
611	C₂×C₄×C₆₇	—	2	1	no	—
612	C₂×C₄×C₆₇	—	2	1	no	—
613	C₂×C₄×C₆₇	—	2	1	no	—
614	C₂×C₄×C₆₇	—	2	2	no	—
615	C₂×C₄×C₆₇	—	2	1	no	—
616	C₂×C₄×C₆₇	—	2	1	no	—
617	C₂×C₄×C₆₇	—	2	2	no	—
618	C₂×C₄×C₆₇	—	2	1	no	—
619	C₂×C₄×C₆₇	—	2	2	no	—
620	C₂×C₄×C₆₇	—	2	1	no	—
621	C₂×C₄×C₆₇	—	4	2	no	—
622	C₂×C₄×C₆₇	—	4	4	no	—
623	C₂×C₄×C₆₇	—	4	4	no	—
624	C₂×C₄×C₆₇	—	4	2	no	—
625	C₂×C₄×C₆₇	—	4	4	no	—
626	C₂×C₄×C₆₇	—	4	4	no	—
627	C₂×C₄×C₆₇	—	4	2	no	—
628	C₂×C₄×C₆₇	—	4	4	no	—
629	C₂×C₄×C₆₇	—	4	2	no	—
630	C₂×C₄×C₆₇	—	4	2	no	—
631	C₂×C₄×C₆₇	—	4	2	no	—
632	C₂×C₄×C₆₇	—	8	2	no	—
633	C₂×C₄×C₆₇	—	8	1	no	—
634	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
635	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
636	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
637	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
639	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
640	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
641	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
642	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
643	C₈×C₆₇	—	2	1	no	—
644	C₈×C₆₇	—	2	1	no	—
645	C₈×C₆₇	—	2	2	no	—
646	C₈×C₆₇	—	2	1	no	—
647	C₈×C₆₇	—	2	1	no	—
648	C₈×C₆₇	C₂²×D₄	1	4	yes	—
649	C₂²×C₆₇	—	2	1	no	—
650	C₂²×C₆₇	—	2	1	no	—
651	C₂²×C₆₇	—	2	1	no	—
652	C₂²×C₆₇	—	2	1	no	—
653	C₂²×C₆₇	—	2	1	no	—
654	C₂²×C₆₇	—	2	2	no	—
655	C₂²×C₆₇	—	2	1	no	—
656	C₂²×C₆₇	—	2	2	no	—
657	C₂²×C₆₇	—	2	2	no	—
658	C₂²×C₆₇	—	2	2	no	—
659	C₂²×C₆₇	—	2	1	no	—
660	C₂²×C₆₇	—	4	4	no	—
661	C₂²×C₆₇	—	4	1	no	—
662	C₂²×C₆₇	—	4	1	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	4	2	no	—
666	C₂²×C₆₇	—	4	1	no	—
667	C₂²×C₆₇	—	4	1	no	—
668	C₂²×C₆₇	—	4	2	no	—
669	C₂²×C₆₇	—	4	2	no	—
670	C₂²×C₆₇	—	4	1	no	—
671	C₂²×C₆₇	—	4	1	no	—
672	C₂²×C₆₇	—	8	4	no	—
673	C₂²×C₆₇	—	16	2	no	—
674	C₂²×C₆₇	—	16	4	no	—
675	C₂²×C₆₇	D₄²	1	2	yes	—
676	C₂²×C₆₇	#577	1	2	yes	complemented
677	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	2	1	no	—
680	C₄×C₆₇	—	2	1	no	—
681	C₄×C₆₇	—	2	2	no	—
682	C₄×C₆₇	—	2	4	no	—
683	C₄×C₆₇	—	2	2	no	—
684	C₄×C₆₇	—	2	2	no	—
685	C₄×C₆₇	—	4	1	no	—
686	C₄×C₆₇	—	4	1	no	—
687	C₄×C₆₇	—	4	1	no	—
688	C₄×C₆₇	—	4	2	no	—
689	C₄×C₆₇	—	4	2	no	—
690	C₄×C₆₇	—	4	1	no	—
691	C₄×C₆₇	D₄²	1	2	yes	—
692	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
693	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	#61075	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
695	C₂×C₆₇	—	2	2	no	—
696	C₂×C₆₇	—	2	2	no	—
697	C₂×C₆₇	—	4	1	no	—
698	C₂×C₆₇	—	4	2	no	—
699	C₂×C₆₇	—	4	2	no	—
700	C₂×C₆₇	—	8	1	no	—
701	C₂×C₆₇	—	8	1	no	—
702	C₂×C₆₇	—	8	2	no	—
703	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
704	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
705	C₂×C₆₇	#3586	1	1	yes	characteristic
706	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
707	C₂²×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
708	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
709	#3486	C₂×C₆₇	1	1	yes	characteristic, complemented
710	#3285	C₂×C₆₇	1	2	yes	complemented
711	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
712	#3278	C₂×C₆₇	1	2	yes	complemented
713	#3275	C₂×C₆₇	1	2	yes	complemented
714	#3271	C₂×C₆₇	1	2	yes	complemented
715	#3270	C₂×C₆₇	1	2	yes	complemented
716	#3266	C₂×C₆₇	1	2	yes	complemented
717	#3265	C₂×C₆₇	1	2	yes	complemented
718	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
721	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
722	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
723	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
724	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
725	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#448	C₂×C₆₇	1	1	yes	characteristic, complemented
727	#2947	C₂×C₆₇	1	1	yes	characteristic, complemented
728	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
729	C₆₇	#61075	1	1	yes	characteristic, direct product factor, Sylow
730	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
732	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
733	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
734	#577	—	2	8	no	—
735	C₂×#137	—	2	8	no	—
736	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
737	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
738	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
740	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
742	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
743	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
745	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
746	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
747	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂²×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
749	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
751	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
752	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	#550	C₂²×C₆₇	1	2	yes	—
756	D₄×Q₈	—	2	1	no	—
757	D₄×Q₈	—	2	1	no	—
758	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
759	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
760	#548	—	2	1	no	—
761	#548	—	2	1	no	—
762	#548	C₂²×C₆₇	1	2	yes	—
763	#548	C₂²×C₆₇	1	2	yes	complemented
764	#548	C₂²×C₆₇	1	2	yes	complemented
765	#546	—	2	2	no	—
766	#546	C₂²×C₆₇	1	2	yes	—
767	D₄²	—	2	2	no	—
768	D₄²	C₂²×C₆₇	1	2	yes	—
769	#537	—	2	1	no	—
770	#537	C₂²×C₆₇	1	1	yes	characteristic
771	#536	—	2	2	no	—
772	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
774	#535	—	2	1	no	—
775	#535	C₂²×C₆₇	1	1	yes	characteristic
776	#525	—	2	1	no	—
777	#525	—	2	2	no	—
778	#525	C₂²×C₆₇	1	1	yes	characteristic
779	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
780	C₂×#121	—	2	1	no	—
781	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
782	#520	C₂²×C₆₇	1	1	yes	characteristic
783	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#497	C₂²×C₆₇	1	2	yes	complemented
785	#496	C₂²×C₆₇	1	2	yes	complemented
786	#495	C₂²×C₆₇	1	2	yes	complemented
787	#492	C₂²×C₆₇	1	2	yes	complemented
788	#470	C₂²×C₆₇	1	2	yes	complemented
789	#469	C₂²×C₆₇	1	2	yes	complemented
790	#468	C₂²×C₆₇	1	2	yes	complemented
791	#468	C₂²×C₆₇	1	2	yes	complemented
792	#467	C₂²×C₆₇	1	2	yes	complemented
793	#466	C₂²×C₆₇	1	2	yes	complemented
794	#465	C₂²×C₆₇	1	2	yes	complemented
795	#465	C₂²×C₆₇	1	2	yes	complemented
796	#464	C₂²×C₆₇	1	2	yes	complemented
797	#464	C₂²×C₆₇	1	2	yes	complemented
798	#464	C₂²×C₆₇	1	2	yes	complemented
799	#463	C₂²×C₆₇	1	2	yes	complemented
800	#462	C₂²×C₆₇	1	2	yes	complemented
801	#461	C₂²×C₆₇	1	2	yes	complemented
802	#460	C₂²×C₆₇	1	2	yes	complemented
803	#460	C₂²×C₆₇	1	2	yes	complemented
804	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
805	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#452	C₂²×C₆₇	1	2	yes	complemented
807	#452	C₂²×C₆₇	1	2	yes	complemented
808	#452	C₂²×C₆₇	1	2	yes	complemented
809	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
810	#451	C₂²×C₆₇	1	2	yes	complemented
811	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
812	#450	C₂²×C₆₇	1	2	yes	complemented
813	#450	C₂²×C₆₇	1	2	yes	complemented
814	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
816	#449	C₂²×C₆₇	1	2	yes	complemented
817	#448	C₂²×C₆₇	1	2	yes	complemented
818	#448	C₂²×C₆₇	1	2	yes	complemented
819	#448	C₂²×C₆₇	1	2	yes	complemented
820	#448	C₂²×C₆₇	1	2	yes	complemented
821	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
822	#448	C₂²×C₆₇	1	2	yes	complemented
823	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
824	#441	C₂²×C₆₇	1	2	yes	complemented
825	#440	C₂²×C₆₇	1	2	yes	complemented
826	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
827	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
828	#436	C₂²×C₆₇	1	2	yes	complemented
829	#435	C₂²×C₆₇	1	2	yes	complemented
830	#435	C₂²×C₆₇	1	2	yes	complemented
831	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
832	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
834	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
835	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
836	#416	C₂²×C₆₇	1	1	yes	characteristic
837	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
838	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
839	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
840	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
841	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
842	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
843	2₋¹⁺⁴	—	2	4	no	—
844	2₋¹⁺⁴	—	4	2	no	—
845	H(5,𝔽₂)	—	2	4	no	—
846	H(5,𝔽₂)	—	4	2	no	—
847	C₂×#41	—	2	1	no	—
848	C₂×#41	—	2	2	no	—
849	C₂×#41	—	2	1	no	—
850	C₂×#41	—	2	1	no	—
851	C₂×#41	—	2	1	no	—
852	C₂×#41	—	2	4	no	—
853	C₂×#41	—	4	2	no	—
854	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
855	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
856	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
857	C₂×#41	C₂³×C₆₇	1	2	yes	—
858	C₂×#41	C₂³×C₆₇	1	2	yes	—
859	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
860	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
861	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
862	C₂²×Q₈	—	2	1	no	—
863	C₂²×Q₈	—	2	1	no	—
864	C₂²×Q₈	—	2	1	no	—
865	C₂²×Q₈	—	2	1	no	—
866	C₂²×Q₈	—	2	4	no	—
867	C₂²×Q₈	—	4	2	no	—
868	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
869	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
871	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
872	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
873	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₂²×D₄	—	2	1	no	—
875	C₂²×D₄	—	2	1	no	—
876	C₂²×D₄	—	2	1	no	—
877	C₂²×D₄	—	2	2	no	—
878	C₂²×D₄	—	2	2	no	—
879	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
880	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
881	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
882	C₂³×C₄	—	2	1	no	—
883	C₂³×C₄	—	2	1	no	—
884	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
885	#137	—	2	4	no	—
886	#137	—	2	4	no	—
887	#137	—	2	8	no	—
888	#137	—	2	8	no	—
889	#137	—	2	8	no	—
890	#137	—	2	4	no	—
891	#137	D₄×C₆₇	1	8	yes	complemented
892	AGL(1,ℤ/8)	—	2	8	no	—
893	AGL(1,ℤ/8)	—	2	4	no	—
894	#135	—	2	4	no	—
895	#135	—	2	8	no	—
896	#135	—	4	2	no	—
897	C₂×Q₁₆	—	2	8	no	—
898	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
899	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
900	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
901	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
902	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
903	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
904	C₂×SD₁₆	—	2	4	no	—
905	C₂×SD₁₆	—	2	8	no	—
906	C₂×SD₁₆	—	2	8	no	—
907	C₂×SD₁₆	—	4	2	no	—
908	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
909	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
910	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
911	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
912	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
913	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
914	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
915	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
916	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
917	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
918	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
919	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
920	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
921	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
922	C₂×D₈	C₂³×C₆₇	1	2	yes	—
923	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
924	#131	—	2	4	no	—
925	C₂×M₁₆	—	2	4	no	—
926	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
927	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
928	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
929	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
930	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
931	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
932	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
933	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
934	C₄⋊Q₈	—	2	1	no	—
935	C₄⋊Q₈	—	2	2	no	—
936	C₄⋊Q₈	—	2	2	no	—
937	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
938	#127	—	2	2	no	—
939	#127	C₂³×C₆₇	1	2	yes	—
940	#124	—	2	1	no	—
941	#124	—	2	2	no	—
942	#124	—	2	2	no	—
943	#124	—	2	2	no	—
944	#124	C₂³×C₆₇	1	2	yes	—
945	#124	C₂³×C₆₇	1	2	yes	—
946	#123	—	2	2	no	—
947	#123	—	2	1	no	—
948	#123	—	2	2	no	—
949	#123	—	2	2	no	—
950	#123	D₄×C₆₇	1	2	yes	—
951	C₂²⋊Q₈	—	2	1	no	—
952	C₂²⋊Q₈	—	2	2	no	—
953	C₂²⋊Q₈	—	2	2	no	—
954	C₂²⋊Q₈	—	2	1	no	—
955	C₂²⋊Q₈	—	2	1	no	—
956	C₂²⋊Q₈	—	2	2	no	—
957	C₂²⋊Q₈	—	2	2	no	—
958	C₂²⋊Q₈	—	2	2	no	—
959	C₂²⋊Q₈	—	2	2	no	—
960	C₂²⋊Q₈	—	2	2	no	—
961	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
962	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
963	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
964	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
965	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
966	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
967	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
968	#121	—	2	1	no	—
969	#121	—	2	2	no	—
970	#121	—	2	2	no	—
971	#121	—	2	2	no	—
972	#121	—	2	2	no	—
973	#121	—	2	1	no	—
974	#121	—	2	1	no	—
975	#121	—	2	1	no	—
976	#121	—	2	1	no	—
977	#121	—	2	2	no	—
978	#121	—	2	2	no	—
979	#121	—	2	2	no	—
980	#121	—	2	2	no	—
981	#121	D₄×C₆₇	1	1	yes	characteristic
982	#121	D₄×C₆₇	1	1	yes	characteristic
983	#121	C₂³×C₆₇	1	2	yes	—
984	#121	C₂³×C₆₇	1	2	yes	—
985	#121	C₂³×C₆₇	1	1	yes	characteristic
986	#121	C₂³×C₆₇	1	1	yes	characteristic
987	#121	C₂³×C₆₇	1	2	yes	—
988	#120	—	2	1	no	—
989	#120	—	2	2	no	—
990	#120	—	2	2	no	—
991	#120	—	2	2	no	—
992	#120	—	2	2	no	—
993	#120	D₄×C₆₇	1	2	yes	—
994	C₄×Q₈	—	2	1	no	—
995	C₄×Q₈	—	2	1	no	—
996	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
997	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
998	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
999	C₄×D₄	—	2	2	no	—
1000	C₄×D₄	—	2	2	no	—
1001	C₄×D₄	—	2	1	no	—
1002	C₄×D₄	—	2	1	no	—
1003	C₄×D₄	—	2	2	no	—
1004	C₄×D₄	—	2	2	no	—
1005	C₄×D₄	—	2	2	no	—
1006	C₄×D₄	—	2	2	no	—
1007	C₄×D₄	—	2	2	no	—
1008	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1009	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1010	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1011	#117	—	2	1	no	—
1012	#117	—	2	2	no	—
1013	#117	C₂³×C₆₇	1	1	yes	characteristic
1014	#117	C₂³×C₆₇	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	—	2	1	no	—
1016	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	—	2	1	no	—
1018	C₂×C₂²⋊C₄	—	2	2	no	—
1019	#107	C₂³×C₆₇	1	2	yes	—
1020	#106	C₂³×C₆₇	1	2	yes	—
1021	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1022	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1023	#103	C₂³×C₆₇	1	2	yes	—
1024	#103	C₂³×C₆₇	1	2	yes	—
1025	#103	C₂³×C₆₇	1	2	yes	—
1026	#103	C₂³×C₆₇	1	2	yes	—
1027	#103	C₂³×C₆₇	1	1	yes	characteristic
1028	#103	C₂³×C₆₇	1	1	yes	characteristic
1029	#103	C₂³×C₆₇	1	1	yes	characteristic
1030	#103	C₂³×C₆₇	1	1	yes	characteristic
1031	#103	C₂³×C₆₇	1	2	yes	—
1032	#102	C₂³×C₆₇	1	1	yes	characteristic
1033	#102	C₂³×C₆₇	1	1	yes	characteristic
1034	#102	C₂³×C₆₇	1	1	yes	characteristic
1035	#102	C₂³×C₆₇	1	1	yes	characteristic
1036	#102	C₂³×C₆₇	1	2	yes	—
1037	#102	C₂³×C₆₇	1	2	yes	—
1038	#102	C₂³×C₆₇	1	2	yes	—
1039	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1040	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1041	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1042	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1043	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1044	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1045	#97	C₂³×C₆₇	1	2	yes	—
1046	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1047	C₂⁴	—	2	1	no	—
1048	C₂⁴	—	2	2	no	—
1049	C₂⁴	—	2	1	no	—
1050	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1051	#41	—	2	2	no	—
1052	#41	—	2	2	no	—
1053	#41	—	2	2	no	—
1054	#41	—	2	4	no	—
1055	#41	—	2	4	no	—
1056	#41	—	2	2	no	—
1057	#41	—	2	2	no	—
1058	#41	—	2	2	no	—
1059	#41	—	2	2	no	—
1060	#41	—	2	2	no	—
1061	#41	—	2	2	no	—
1062	#41	—	4	4	no	—
1063	#41	—	4	1	no	—
1064	#41	—	4	1	no	—
1065	#41	—	4	2	no	—
1066	#41	—	4	2	no	—
1067	#41	—	4	4	no	—
1068	#41	—	4	8	no	—
1069	#41	—	4	4	no	—
1070	#41	—	4	4	no	—
1071	#41	C₂×D₄×C₆₇	1	4	yes	—
1072	C₂×Q₈	—	2	1	no	—
1073	C₂×Q₈	—	2	1	no	—
1074	C₂×Q₈	—	2	2	no	—
1075	C₂×Q₈	—	2	2	no	—
1076	C₂×Q₈	—	2	1	no	—
1077	C₂×Q₈	—	2	2	no	—
1078	C₂×Q₈	—	2	2	no	—
1079	C₂×Q₈	—	2	4	no	—
1080	C₂×Q₈	—	2	4	no	—
1081	C₂×Q₈	—	2	2	no	—
1082	C₂×Q₈	—	2	4	no	—
1083	C₂×Q₈	—	2	2	no	—
1084	C₂×Q₈	—	2	2	no	—
1085	C₂×Q₈	—	4	4	no	—
1086	C₂×Q₈	—	4	2	no	—
1087	C₂×Q₈	—	4	2	no	—
1088	C₂×Q₈	—	4	1	no	—
1089	C₂×Q₈	—	4	2	no	—
1090	C₂×Q₈	—	4	4	no	—
1091	C₂×Q₈	—	4	4	no	—
1092	C₂×Q₈	—	4	4	no	—
1093	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1094	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
1095	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1096	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1097	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1098	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1099	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₂×D₄	—	2	1	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	4	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	2	1	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	1	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	2	no	—
1111	C₂×D₄	—	2	1	no	—
1112	C₂×D₄	—	2	2	no	—
1113	C₂×D₄	—	2	2	no	—
1114	C₂×D₄	—	2	2	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	2	no	—
1117	C₂×D₄	—	2	1	no	—
1118	C₂×D₄	—	2	2	no	—
1119	C₂×D₄	—	2	2	no	—
1120	C₂×D₄	—	2	2	no	—
1121	C₂×D₄	—	4	1	no	—
1122	C₂×D₄	—	4	2	no	—
1123	C₂×D₄	—	4	4	no	—
1124	C₂×D₄	—	4	8	no	—
1125	C₂×D₄	—	4	4	no	—
1126	C₂×D₄	—	8	4	no	—
1127	C₂×D₄	—	8	2	no	—
1128	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1129	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1130	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1131	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1132	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1133	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1134	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1135	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	2	1	no	—
1145	C₂²×C₄	—	2	1	no	—
1146	C₂²×C₄	—	2	1	no	—
1147	C₂²×C₄	—	2	1	no	—
1148	C₂²×C₄	—	2	2	no	—
1149	C₂²×C₄	—	2	2	no	—
1150	C₂²×C₄	—	2	1	no	—
1151	C₂²×C₄	—	2	1	no	—
1152	C₂²×C₄	—	2	2	no	—
1153	C₂²×C₄	—	4	4	no	—
1154	C₂²×C₄	—	4	4	no	—
1155	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1156	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1157	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1158	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1159	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1160	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1161	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1162	Q₁₆	—	2	4	no	—
1163	Q₁₆	—	2	4	no	—
1164	Q₁₆	—	2	2	no	—
1165	Q₁₆	—	2	4	no	—
1166	Q₁₆	—	4	1	no	—
1167	Q₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1168	SD₁₆	—	2	4	no	—
1169	SD₁₆	—	2	4	no	—
1170	SD₁₆	—	2	4	no	—
1171	SD₁₆	—	2	2	no	—
1172	SD₁₆	—	2	2	no	—
1173	SD₁₆	—	2	4	no	—
1174	SD₁₆	—	2	4	no	—
1175	SD₁₆	—	2	4	no	—
1176	SD₁₆	—	4	2	no	—
1177	SD₁₆	—	4	2	no	—
1178	SD₁₆	—	4	1	no	—
1179	SD₁₆	—	4	1	no	—
1180	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1181	D₈	—	2	2	no	—
1182	D₈	—	2	4	no	—
1183	D₈	—	4	1	no	—
1184	M₁₆	—	2	2	no	—
1185	M₁₆	—	2	4	no	—
1186	M₁₆	—	2	4	no	—
1187	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1188	C₂×C₈	—	2	2	no	—
1189	C₂×C₈	—	2	2	no	—
1190	C₂×C₈	—	2	4	no	—
1191	C₂×C₈	—	2	4	no	—
1192	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1193	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1194	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1195	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1196	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1197	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1198	C₄⋊C₄	—	2	1	no	—
1199	C₄⋊C₄	—	2	2	no	—
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	2	2	no	—
1204	C₄⋊C₄	—	2	2	no	—
1205	C₄⋊C₄	—	2	2	no	—
1206	C₄⋊C₄	—	2	2	no	—
1207	C₄⋊C₄	—	2	1	no	—
1208	C₄⋊C₄	—	2	1	no	—
1209	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1210	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1211	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1212	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1213	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1214	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1215	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1216	C₂²⋊C₄	—	2	2	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	—	2	1	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	2	2	no	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	2	2	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	1	no	—
1231	C₂²⋊C₄	—	2	1	no	—
1232	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1233	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1234	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1235	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1236	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1237	C₄²	—	2	2	no	—
1238	C₄²	—	2	2	no	—
1239	C₄²	—	2	2	no	—
1240	C₄²	—	2	1	no	—
1241	C₄²	C₂⁴×C₆₇	1	2	yes	—
1242	C₂³	—	2	2	no	—
1243	C₂³	—	2	2	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	2	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	4	1	no	—
1249	C₂³	—	4	2	no	—
1250	C₂³	—	4	4	no	—
1251	C₂³	—	4	2	no	—
1252	C₂³	—	4	2	no	—
1253	C₂³	—	8	1	no	—
1254	C₂³	—	8	1	no	—
1255	C₂³	—	8	2	no	—
1256	C₂³	—	8	1	no	—
1257	C₂³	—	8	2	no	—
1258	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1259	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1260	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1261	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1262	Q₈	—	2	4	no	—
1263	Q₈	—	2	2	no	—
1264	Q₈	—	2	2	no	—
1265	Q₈	—	2	1	no	—
1266	Q₈	—	2	1	no	—
1267	Q₈	—	2	2	no	—
1268	Q₈	—	2	1	no	—
1269	Q₈	—	2	2	no	—
1270	Q₈	—	2	1	no	—
1271	Q₈	—	2	1	no	—
1272	Q₈	—	4	4	no	—
1273	Q₈	—	4	4	no	—
1274	Q₈	—	4	4	no	—
1275	Q₈	—	4	2	no	—
1276	Q₈	—	4	2	no	—
1277	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
1278	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1279	D₄	—	2	4	no	—
1280	D₄	—	2	4	no	—
1281	D₄	—	2	4	no	—
1282	D₄	—	2	2	no	—
1283	D₄	—	2	1	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	2	1	no	—
1286	D₄	—	2	1	no	—
1287	D₄	—	2	1	no	—
1288	D₄	—	2	1	no	—
1289	D₄	—	2	2	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	4	4	no	—
1292	D₄	—	4	2	no	—
1293	D₄	—	4	4	no	—
1294	D₄	—	4	2	no	—
1295	D₄	—	4	4	no	—
1296	D₄	—	4	2	no	—
1297	D₄	—	4	2	no	—
1298	D₄	—	4	2	no	—
1299	D₄	—	4	2	no	—
1300	D₄	—	4	4	no	—
1301	D₄	—	4	2	no	—
1302	D₄	—	4	2	no	—
1303	D₄	—	8	2	no	—
1304	D₄	—	8	2	no	—
1305	D₄	—	8	2	no	—
1306	D₄	—	8	2	no	—
1307	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	4	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	2	no	—
1312	C₂×C₄	—	2	2	no	—
1313	C₂×C₄	—	2	2	no	—
1314	C₂×C₄	—	2	4	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	2	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	2	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	2	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	2	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	4	2	no	—
1328	C₂×C₄	—	4	4	no	—
1329	C₂×C₄	—	4	4	no	—
1330	C₂×C₄	—	4	2	no	—
1331	C₂×C₄	—	4	4	no	—
1332	C₂×C₄	—	4	4	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	4	4	no	—
1335	C₂×C₄	—	4	2	no	—
1336	C₂×C₄	—	4	2	no	—
1337	C₂×C₄	—	4	2	no	—
1338	C₂×C₄	—	8	2	no	—
1339	C₂×C₄	—	8	1	no	—
1340	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1341	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1342	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1343	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1344	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1345	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1346	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1347	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1348	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1349	C₈	—	2	1	no	—
1350	C₈	—	2	1	no	—
1351	C₈	—	2	2	no	—
1352	C₈	—	2	1	no	—
1353	C₈	—	2	1	no	—
1354	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1355	C₂²	—	2	1	no	—
1356	C₂²	—	2	1	no	—
1357	C₂²	—	2	1	no	—
1358	C₂²	—	2	1	no	—
1359	C₂²	—	2	2	no	—
1360	C₂²	—	2	1	no	—
1361	C₂²	—	2	1	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	2	1	no	—
1364	C₂²	—	2	2	no	—
1365	C₂²	—	2	2	no	—
1366	C₂²	—	4	4	no	—
1367	C₂²	—	4	1	no	—
1368	C₂²	—	4	1	no	—
1369	C₂²	—	4	2	no	—
1370	C₂²	—	4	1	no	—
1371	C₂²	—	4	1	no	—
1372	C₂²	—	4	1	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	2	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	2	no	—
1378	C₂²	—	8	4	no	—
1379	C₂²	—	16	2	no	—
1380	C₂²	—	16	4	no	—
1381	C₂²	D₄²×C₆₇	1	2	yes	—
1382	C₂²	#577×C₆₇	1	2	yes	complemented
1383	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1384	C₄	—	2	2	no	—
1385	C₄	—	2	2	no	—
1386	C₄	—	2	1	no	—
1387	C₄	—	2	1	no	—
1388	C₄	—	2	2	no	—
1389	C₄	—	2	4	no	—
1390	C₄	—	2	2	no	—
1391	C₄	—	4	2	no	—
1392	C₄	—	4	1	no	—
1393	C₄	—	4	1	no	—
1394	C₄	—	4	1	no	—
1395	C₄	—	4	1	no	—
1396	C₄	—	4	2	no	—
1397	C₄	D₄²×C₆₇	1	2	yes	—
1398	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1399	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1400	C₂	—	2	2	no	—
1401	C₂	—	2	2	no	—
1402	C₂	—	4	1	no	—
1403	C₂	—	4	2	no	—
1404	C₂	—	4	2	no	—
1405	C₂	—	8	1	no	—
1406	C₂	—	8	2	no	—
1407	C₂	—	8	1	no	—
1408	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1409	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1410	C₂	C₆₇×#3586	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×#137×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3486	C₂	semidirect
5. C₆₇×#3285	C₂	semidirect
6. D₄×SD₁₆×C₆₇	C₂	semidirect
7. C₆₇×#3278	C₂	semidirect
8. C₆₇×#3275	C₂	semidirect
9. C₆₇×#3271	C₂	semidirect
10. C₆₇×#3270	C₂	semidirect
11. C₆₇×#3266	C₂	semidirect
12. C₆₇×#3265	C₂	semidirect
13. C₆₇×#3154	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₆₇×#3055	C₂	semidirect
16. C₆₇×#3046	C₂	semidirect
17. C₆₇×#3043	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3009	C₂	semidirect
20. C₆₇×#3002	C₂	semidirect
21. C₂×#448×C₆₇	C₂	semidirect
22. C₆₇×#2947	C₂	semidirect
23. C₆₇×#2933	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
27. C₂³×Q₈×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×#137×C₆₇	C₂²	semidirect
35. C₂×#137×C₆₇	C₂²	semidirect
36. C₂×#137×C₆₇	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
38. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
40. C₂×#135×C₆₇	C₂²	semidirect
41. C₂×#135×C₆₇	C₂²	semidirect
42. C₂²×Q₁₆×C₆₇	C₂²	semidirect
43. C₂²×SD₁₆×C₆₇	C₂²	semidirect
44. C₂²×SD₁₆×C₆₇	C₂²	semidirect
45. C₂²×SD₁₆×C₆₇	C₂²	semidirect
46. C₂²×SD₁₆×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
48. C₂²×M₁₆×C₆₇	C₂²	semidirect
52. D₄×Q₈×C₆₇	C₂²	semidirect
53. D₄×Q₈×C₆₇	C₂²	semidirect
57. #548×C₆₇	C₂²	semidirect
58. #548×C₆₇	C₂²	semidirect
66. #536×C₆₇	C₂²	semidirect
67. #536×C₆₇	C₂²	semidirect
73. #525×C₆₇	C₂²	semidirect
77. #519×C₆₇	C₂²	semidirect
78. #497×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #492×C₆₇	C₂²	semidirect
82. #470×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #467×C₆₇	C₂²	semidirect
87. #466×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #464×C₆₇	C₂²	semidirect
92. #464×C₆₇	C₂²	semidirect
93. #463×C₆₇	C₂²	semidirect
94. #462×C₆₇	C₂²	semidirect
95. #461×C₆₇	C₂²	semidirect
96. #460×C₆₇	C₂²	semidirect
97. #460×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #451×C₆₇	C₂²	semidirect
104. #451×C₆₇	C₂²	semidirect
105. #450×C₆₇	C₂²	semidirect
106. #450×C₆₇	C₂²	semidirect
107. #450×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #448×C₆₇	C₂²	semidirect
112. #448×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×C₆₇	C₂²	semidirect
116. #448×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #441×C₆₇	C₂²	semidirect
119. #440×C₆₇	C₂²	semidirect
120. C₄×Q₁₆×C₆₇	C₂²	semidirect
121. C₄×SD₁₆×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #424×C₆₇	C₂²	semidirect
128. #418×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. C₂×#103×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
135. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
136. #405×C₆₇	C₂²	semidirect
185. #137×C₆₇	D₄	semidirect
388. C₂×Q₈×C₆₇	C₂×D₄	semidirect
461. Q₁₆×C₆₇	C₂×D₄	semidirect
474. SD₁₆×C₆₇	C₂×D₄	semidirect
481. M₁₆×C₆₇	C₂×D₄	semidirect
676. C₂²×C₆₇	#577	semidirect
694. #61075	C₆₇	direct (N × H)
706. C₂×#577	C₂×C₆₇	semidirect
707. C₂²×#137	C₂×C₆₇	semidirect
708. #3488	C₂×C₆₇	semidirect
709. #3486	C₂×C₆₇	semidirect
710. #3285	C₂×C₆₇	semidirect
711. D₄×SD₁₆	C₂×C₆₇	semidirect
712. #3278	C₂×C₆₇	semidirect
713. #3275	C₂×C₆₇	semidirect
714. #3271	C₂×C₆₇	semidirect
715. #3270	C₂×C₆₇	semidirect
716. #3266	C₂×C₆₇	semidirect
717. #3265	C₂×C₆₇	semidirect
718. #3154	C₂×C₆₇	semidirect
719. #3063	C₂×C₆₇	semidirect
720. #3055	C₂×C₆₇	semidirect
721. #3046	C₂×C₆₇	semidirect
722. #3043	C₂×C₆₇	semidirect
723. #3013	C₂×C₆₇	semidirect
724. #3009	C₂×C₆₇	semidirect
725. #3002	C₂×C₆₇	semidirect
726. C₂×#448	C₂×C₆₇	semidirect
727. #2947	C₂×C₆₇	semidirect
728. #2933	C₂×C₆₇	semidirect
729. C₆₇	#61075	direct (N × H)
730. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
733. C₂³×Q₈	C₂²×C₆₇	semidirect
738. C₂×#137	C₂²×C₆₇	semidirect
739. C₂×#137	C₂²×C₆₇	semidirect
740. C₂×#137	C₂²×C₆₇	semidirect
741. C₂×#137	C₂²×C₆₇	semidirect
742. C₂×#137	C₂²×C₆₇	semidirect
743. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
744. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
746. C₂×#135	C₂²×C₆₇	semidirect
747. C₂×#135	C₂²×C₆₇	semidirect
748. C₂²×Q₁₆	C₂²×C₆₇	semidirect
749. C₂²×SD₁₆	C₂²×C₆₇	semidirect
750. C₂²×SD₁₆	C₂²×C₆₇	semidirect
751. C₂²×SD₁₆	C₂²×C₆₇	semidirect
752. C₂²×SD₁₆	C₂²×C₆₇	semidirect
753. C₂×#131	C₂²×C₆₇	semidirect
754. C₂²×M₁₆	C₂²×C₆₇	semidirect
758. D₄×Q₈	C₂²×C₆₇	semidirect
759. D₄×Q₈	C₂²×C₆₇	semidirect
763. #548	C₂²×C₆₇	semidirect
764. #548	C₂²×C₆₇	semidirect
772. #536	C₂²×C₆₇	semidirect
773. #536	C₂²×C₆₇	semidirect
779. #525	C₂²×C₆₇	semidirect
783. #519	C₂²×C₆₇	semidirect
784. #497	C₂²×C₆₇	semidirect
785. #496	C₂²×C₆₇	semidirect
786. #495	C₂²×C₆₇	semidirect
787. #492	C₂²×C₆₇	semidirect
788. #470	C₂²×C₆₇	semidirect
789. #469	C₂²×C₆₇	semidirect
790. #468	C₂²×C₆₇	semidirect
791. #468	C₂²×C₆₇	semidirect
792. #467	C₂²×C₆₇	semidirect
793. #466	C₂²×C₆₇	semidirect
794. #465	C₂²×C₆₇	semidirect
795. #465	C₂²×C₆₇	semidirect
796. #464	C₂²×C₆₇	semidirect
797. #464	C₂²×C₆₇	semidirect
798. #464	C₂²×C₆₇	semidirect
799. #463	C₂²×C₆₇	semidirect
800. #462	C₂²×C₆₇	semidirect
801. #461	C₂²×C₆₇	semidirect
802. #460	C₂²×C₆₇	semidirect
803. #460	C₂²×C₆₇	semidirect
804. #452	C₂²×C₆₇	semidirect
805. #452	C₂²×C₆₇	semidirect
806. #452	C₂²×C₆₇	semidirect
807. #452	C₂²×C₆₇	semidirect
808. #452	C₂²×C₆₇	semidirect
809. #451	C₂²×C₆₇	semidirect
810. #451	C₂²×C₆₇	semidirect
811. #450	C₂²×C₆₇	semidirect
812. #450	C₂²×C₆₇	semidirect
813. #450	C₂²×C₆₇	semidirect
814. #449	C₂²×C₆₇	semidirect
815. #449	C₂²×C₆₇	semidirect
816. #449	C₂²×C₆₇	semidirect
817. #448	C₂²×C₆₇	semidirect
818. #448	C₂²×C₆₇	semidirect
819. #448	C₂²×C₆₇	semidirect
820. #448	C₂²×C₆₇	semidirect
821. #448	C₂²×C₆₇	semidirect
822. #448	C₂²×C₆₇	semidirect
823. #447	C₂²×C₆₇	semidirect
824. #441	C₂²×C₆₇	semidirect
825. #440	C₂²×C₆₇	semidirect
826. C₄×Q₁₆	C₂²×C₆₇	semidirect
827. C₄×SD₁₆	C₂²×C₆₇	semidirect
828. #436	C₂²×C₆₇	semidirect
829. #435	C₂²×C₆₇	semidirect
830. #435	C₂²×C₆₇	semidirect
831. C₈×D₄	C₂²×C₆₇	semidirect
832. #428	C₂²×C₆₇	semidirect
833. #424	C₂²×C₆₇	semidirect
834. #418	C₂²×C₆₇	semidirect
835. #417	C₂²×C₆₇	semidirect
837. #416	C₂²×C₆₇	semidirect
838. C₂×#103	C₂²×C₆₇	semidirect
839. C₂×#103	C₂²×C₆₇	semidirect
840. #408	C₂²×C₆₇	semidirect
841. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
842. #405	C₂²×C₆₇	semidirect
891. #137	D₄×C₆₇	semidirect
1094. C₂×Q₈	C₂×D₄×C₆₇	semidirect
1167. Q₁₆	C₂×D₄×C₆₇	semidirect
1180. SD₁₆	C₂×D₄×C₆₇	semidirect
1187. M₁₆	C₂×D₄×C₆₇	semidirect
1382. 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×#137×C₆₇	2
C₆₇×#3488	2
C₆₇×#3486	2
C₆₇×#3285	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3278	2
C₆₇×#3275	2
C₆₇×#3271	2
C₆₇×#3270	2
C₆₇×#3266	2
C₆₇×#3265	2
C₆₇×#3154	2
C₆₇×#3063	2
C₆₇×#3055	2
C₆₇×#3046	2
C₆₇×#3043	2
C₆₇×#3013	2
C₆₇×#3009	2
C₆₇×#3002	2
C₂×#448×C₆₇	2
C₆₇×#2947	2
C₆₇×#2933	2
#61075	67

Subgroups — C67×#61075 #30740326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61075 #30740326