Subgroups — C₆₇×#61092 #30740343

Order 17152.

2770 conjugacy classes of subgroups.

The subgroup lattice has 1400 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	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3273	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3269	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#463×C₆₇	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×#3009	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2935	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	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#577×C₆₇	—	2	8	no	—
29	#576×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
31	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#135×C₆₇	C₂²	1	2	yes	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	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
47	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#548×C₆₇	C₂²	1	2	yes	complemented
50	#548×C₆₇	C₂²	1	2	yes	complemented
51	#547×C₆₇	—	2	1	no	—
52	#547×C₆₇	C₂²	1	2	yes	complemented
53	#546×C₆₇	—	2	1	no	—
54	#546×C₆₇	—	2	1	no	—
55	#546×C₆₇	—	2	2	no	—
56	#546×C₆₇	—	2	2	no	—
57	#546×C₆₇	C₂²	1	2	yes	complemented
58	#546×C₆₇	C₂²	1	2	yes	complemented
59	#546×C₆₇	C₂²	1	2	yes	complemented
60	#546×C₆₇	C₂²	1	2	yes	complemented
61	D₄²×C₆₇	—	2	1	no	—
62	D₄²×C₆₇	C₂²	1	2	yes	complemented
63	#537×C₆₇	C₂²	1	1	yes	characteristic
64	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#536×C₆₇	—	2	1	no	—
66	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#535×C₆₇	—	2	1	no	—
68	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#534×C₆₇	—	2	2	no	—
70	#532×C₆₇	—	2	1	no	—
71	#532×C₆₇	C₂²	1	1	yes	characteristic
72	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×#124×C₆₇	—	2	1	no	—
74	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂×#121×C₆₇	—	2	2	no	—
76	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₂×C₄×D₄×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	#495×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	1	yes	characteristic, complemented
91	#464×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#463×C₆₇	C₂²	1	2	yes	complemented
93	#463×C₆₇	C₂²	1	2	yes	complemented
94	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#463×C₆₇	C₂²	1	2	yes	complemented
96	#463×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#463×C₆₇	C₂²	1	2	yes	complemented
98	#462×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#461×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#459×C₆₇	C₂²	1	1	yes	characteristic, 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	#450×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	#447×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	#440×C₆₇	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×D₈×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	C₂×C₄⋊C₈×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, complemented
131	#416×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	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×M₁₆×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	—	2	4	no	—
141	H(5,𝔽₂)×C₆₇	—	2	4	no	—
142	H(5,𝔽₂)×C₆₇	—	4	2	no	—
143	H(5,𝔽₂)×C₆₇	—	4	2	no	—
144	H(5,𝔽₂)×C₆₇	—	4	2	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	1	no	—
149	C₂×#41×C₆₇	—	2	2	no	—
150	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×#41×C₆₇	C₂³	1	2	yes	—
153	C₂×#41×C₆₇	C₂³	1	2	yes	—
154	C₂×#41×C₆₇	C₂³	1	2	yes	—
155	C₂×#41×C₆₇	C₂³	1	2	yes	—
156	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₆₇	—	2	1	no	—
160	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
162	C₂²×D₄×C₆₇	—	2	2	no	—
163	C₂²×D₄×C₆₇	—	2	2	no	—
164	C₂²×D₄×C₆₇	—	2	1	no	—
165	C₂²×D₄×C₆₇	—	2	1	no	—
166	C₂²×D₄×C₆₇	—	2	1	no	—
167	C₂²×D₄×C₆₇	—	2	2	no	—
168	C₂²×D₄×C₆₇	—	2	2	no	—
169	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
171	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
172	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
173	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂³×C₄×C₆₇	—	2	1	no	—
175	#137×C₆₇	—	2	8	no	—
176	#137×C₆₇	—	2	4	no	—
177	#137×C₆₇	—	4	2	no	—
178	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
179	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
180	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
181	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
182	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
183	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	complemented
184	#135×C₆₇	—	2	4	no	—
185	#135×C₆₇	—	2	4	no	—
186	#135×C₆₇	—	2	8	no	—
187	#135×C₆₇	—	2	8	no	—
188	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
191	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
192	C₂×SD₁₆×C₆₇	—	2	4	no	—
193	C₂×SD₁₆×C₆₇	—	2	8	no	—
194	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
198	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
199	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
201	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
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×D₈×C₆₇	—	2	4	no	—
206	C₂×D₈×C₆₇	—	2	8	no	—
207	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×D₈×C₆₇	C₂³	1	2	yes	—
209	C₂×D₈×C₆₇	C₂³	1	2	yes	—
210	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₈×C₆₇	C₂³	1	2	yes	—
212	C₂×D₈×C₆₇	C₂³	1	2	yes	—
213	C₂×D₈×C₆₇	C₂³	1	2	yes	—
214	#131×C₆₇	—	2	4	no	—
215	#131×C₆₇	—	2	4	no	—
216	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
217	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
218	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
221	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
222	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
223	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₄⋊Q₈×C₆₇	—	2	1	no	—
225	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
226	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
227	#127×C₆₇	—	2	1	no	—
228	#127×C₆₇	D₄	1	1	yes	characteristic
229	#127×C₆₇	C₂³	1	1	yes	characteristic
230	#124×C₆₇	—	2	1	no	—
231	#124×C₆₇	—	2	1	no	—
232	#124×C₆₇	—	2	2	no	—
233	#124×C₆₇	—	2	2	no	—
234	#124×C₆₇	—	2	1	no	—
235	#124×C₆₇	—	2	1	no	—
236	#124×C₆₇	D₄	1	1	yes	characteristic
237	#124×C₆₇	D₄	1	1	yes	characteristic
238	#124×C₆₇	C₂³	1	2	yes	—
239	#124×C₆₇	C₂³	1	2	yes	—
240	#124×C₆₇	C₂³	1	1	yes	characteristic
241	#124×C₆₇	C₂³	1	1	yes	characteristic
242	#123×C₆₇	—	2	2	no	—
243	#123×C₆₇	—	2	2	no	—
244	#123×C₆₇	—	2	2	no	—
245	#123×C₆₇	—	2	2	no	—
246	#123×C₆₇	—	2	2	no	—
247	#123×C₆₇	—	2	2	no	—
248	#123×C₆₇	—	2	2	no	—
249	C₂²⋊Q₈×C₆₇	—	2	1	no	—
250	C₂²⋊Q₈×C₆₇	—	2	1	no	—
251	C₂²⋊Q₈×C₆₇	—	2	2	no	—
252	C₂²⋊Q₈×C₆₇	—	2	2	no	—
253	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
257	#121×C₆₇	—	2	2	no	—
258	#121×C₆₇	—	2	2	no	—
259	#121×C₆₇	—	2	2	no	—
260	#121×C₆₇	—	2	2	no	—
261	#121×C₆₇	—	2	2	no	—
262	#121×C₆₇	—	2	1	no	—
263	#121×C₆₇	—	2	1	no	—
264	#121×C₆₇	—	2	1	no	—
265	#121×C₆₇	—	2	1	no	—
266	#121×C₆₇	—	2	2	no	—
267	#121×C₆₇	—	2	2	no	—
268	#121×C₆₇	—	2	2	no	—
269	#121×C₆₇	—	2	2	no	—
270	#121×C₆₇	—	2	2	no	—
271	#121×C₆₇	D₄	1	2	yes	—
272	#121×C₆₇	D₄	1	2	yes	—
273	#121×C₆₇	C₂³	1	2	yes	—
274	#121×C₆₇	C₂³	1	2	yes	—
275	#121×C₆₇	C₂³	1	2	yes	—
276	#121×C₆₇	C₂³	1	2	yes	—
277	#120×C₆₇	—	2	2	no	—
278	#120×C₆₇	—	2	2	no	—
279	#120×C₆₇	—	2	2	no	—
280	#120×C₆₇	—	2	2	no	—
281	#120×C₆₇	—	2	2	no	—
282	#120×C₆₇	—	2	2	no	—
283	#120×C₆₇	—	2	2	no	—
284	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₆₇	—	2	1	no	—
287	C₄×D₄×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	—	2	2	no	—
289	C₄×D₄×C₆₇	—	2	2	no	—
290	C₄×D₄×C₆₇	—	2	1	no	—
291	C₄×D₄×C₆₇	—	2	1	no	—
292	C₄×D₄×C₆₇	—	2	1	no	—
293	C₄×D₄×C₆₇	—	2	1	no	—
294	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₆₇	C₂³	1	2	yes	—
296	C₄×D₄×C₆₇	C₂³	1	2	yes	—
297	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₆₇	C₂³	1	2	yes	—
299	C₄×D₄×C₆₇	C₂³	1	2	yes	—
300	#117×C₆₇	—	2	1	no	—
301	#117×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
306	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
307	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
308	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂×C₄²×C₆₇	—	2	1	no	—
312	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
313	#107×C₆₇	C₂³	1	2	yes	—
314	#106×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	1	yes	characteristic
322	#103×C₆₇	C₂³	1	1	yes	characteristic
323	#103×C₆₇	C₂³	1	2	yes	—
324	#103×C₆₇	C₂³	1	1	yes	characteristic
325	#103×C₆₇	C₂³	1	1	yes	characteristic
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	1	yes	characteristic
331	#102×C₆₇	C₂³	1	1	yes	characteristic
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	1	yes	characteristic
334	#102×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	—	2	2	no	—
345	C₂⁴×C₆₇	—	2	2	no	—
346	#41×C₆₇	—	2	2	no	—
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	2	no	—
349	#41×C₆₇	—	2	2	no	—
350	#41×C₆₇	—	2	2	no	—
351	#41×C₆₇	—	2	4	no	—
352	#41×C₆₇	—	2	4	no	—
353	#41×C₆₇	—	2	4	no	—
354	#41×C₆₇	—	2	4	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	2	2	no	—
357	#41×C₆₇	—	2	2	no	—
358	#41×C₆₇	—	2	2	no	—
359	#41×C₆₇	—	4	2	no	—
360	#41×C₆₇	—	4	2	no	—
361	#41×C₆₇	—	4	2	no	—
362	#41×C₆₇	—	4	2	no	—
363	#41×C₆₇	—	4	4	no	—
364	#41×C₆₇	—	4	4	no	—
365	#41×C₆₇	—	4	8	no	—
366	#41×C₆₇	—	4	4	no	—
367	#41×C₆₇	—	4	4	no	—
368	#41×C₆₇	C₂×D₄	1	4	yes	complemented
369	C₂×Q₈×C₆₇	—	2	2	no	—
370	C₂×Q₈×C₆₇	—	2	1	no	—
371	C₂×Q₈×C₆₇	—	2	4	no	—
372	C₂×Q₈×C₆₇	—	2	2	no	—
373	C₂×Q₈×C₆₇	—	2	2	no	—
374	C₂×Q₈×C₆₇	—	4	2	no	—
375	C₂×Q₈×C₆₇	—	4	4	no	—
376	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
379	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₆₇	—	2	1	no	—
383	C₂×D₄×C₆₇	—	2	4	no	—
384	C₂×D₄×C₆₇	—	2	4	no	—
385	C₂×D₄×C₆₇	—	2	4	no	—
386	C₂×D₄×C₆₇	—	2	2	no	—
387	C₂×D₄×C₆₇	—	2	2	no	—
388	C₂×D₄×C₆₇	—	2	2	no	—
389	C₂×D₄×C₆₇	—	2	1	no	—
390	C₂×D₄×C₆₇	—	2	1	no	—
391	C₂×D₄×C₆₇	—	2	2	no	—
392	C₂×D₄×C₆₇	—	2	2	no	—
393	C₂×D₄×C₆₇	—	2	2	no	—
394	C₂×D₄×C₆₇	—	2	2	no	—
395	C₂×D₄×C₆₇	—	2	2	no	—
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	—	2	2	no	—
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	2	2	no	—
400	C₂×D₄×C₆₇	—	2	2	no	—
401	C₂×D₄×C₆₇	—	2	2	no	—
402	C₂×D₄×C₆₇	—	2	1	no	—
403	C₂×D₄×C₆₇	—	2	1	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	2	no	—
406	C₂×D₄×C₆₇	—	4	2	no	—
407	C₂×D₄×C₆₇	—	4	2	no	—
408	C₂×D₄×C₆₇	—	4	2	no	—
409	C₂×D₄×C₆₇	—	4	4	no	—
410	C₂×D₄×C₆₇	—	4	8	no	—
411	C₂×D₄×C₆₇	—	4	4	no	—
412	C₂×D₄×C₆₇	—	4	4	no	—
413	C₂×D₄×C₆₇	—	4	8	no	—
414	C₂×D₄×C₆₇	—	4	8	no	—
415	C₂×D₄×C₆₇	—	8	4	no	—
416	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
417	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
418	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
419	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
420	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
421	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
422	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
424	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
428	C₂²×C₄×C₆₇	—	2	1	no	—
429	C₂²×C₄×C₆₇	—	2	1	no	—
430	C₂²×C₄×C₆₇	—	2	2	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	2	no	—
435	C₂²×C₄×C₆₇	—	2	2	no	—
436	C₂²×C₄×C₆₇	—	2	1	no	—
437	C₂²×C₄×C₆₇	—	2	1	no	—
438	C₂²×C₄×C₆₇	—	2	2	no	—
439	C₂²×C₄×C₆₇	—	2	1	no	—
440	C₂²×C₄×C₆₇	—	2	1	no	—
441	C₂²×C₄×C₆₇	—	2	2	no	—
442	C₂²×C₄×C₆₇	—	8	2	no	—
443	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
446	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
447	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	Q₁₆×C₆₇	—	2	2	no	—
449	Q₁₆×C₆₇	—	2	2	no	—
450	Q₁₆×C₆₇	—	2	4	no	—
451	Q₁₆×C₆₇	—	4	2	no	—
452	SD₁₆×C₆₇	—	2	2	no	—
453	SD₁₆×C₆₇	—	2	2	no	—
454	SD₁₆×C₆₇	—	2	4	no	—
455	SD₁₆×C₆₇	—	2	4	no	—
456	SD₁₆×C₆₇	—	2	2	no	—
457	SD₁₆×C₆₇	—	2	2	no	—
458	SD₁₆×C₆₇	—	2	4	no	—
459	SD₁₆×C₆₇	—	2	4	no	—
460	SD₁₆×C₆₇	—	4	2	no	—
461	SD₁₆×C₆₇	—	4	2	no	—
462	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
463	D₈×C₆₇	—	2	2	no	—
464	D₈×C₆₇	—	2	4	no	—
465	D₈×C₆₇	—	2	4	no	—
466	D₈×C₆₇	—	2	2	no	—
467	D₈×C₆₇	—	2	4	no	—
468	D₈×C₆₇	—	4	2	no	—
469	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
470	M₁₆×C₆₇	—	2	2	no	—
471	M₁₆×C₆₇	—	2	4	no	—
472	M₁₆×C₆₇	—	2	4	no	—
473	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
474	C₂×C₈×C₆₇	—	2	2	no	—
475	C₂×C₈×C₆₇	—	2	2	no	—
476	C₂×C₈×C₆₇	—	2	4	no	—
477	C₂×C₈×C₆₇	—	2	4	no	—
478	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
479	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
480	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
481	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
482	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
483	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
484	C₄⋊C₄×C₆₇	—	2	1	no	—
485	C₄⋊C₄×C₆₇	—	2	2	no	—
486	C₄⋊C₄×C₆₇	—	2	2	no	—
487	C₄⋊C₄×C₆₇	—	2	1	no	—
488	C₄⋊C₄×C₆₇	—	2	1	no	—
489	C₄⋊C₄×C₆₇	—	2	1	no	—
490	C₄⋊C₄×C₆₇	—	2	2	no	—
491	C₄⋊C₄×C₆₇	—	2	2	no	—
492	C₄⋊C₄×C₆₇	—	2	1	no	—
493	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
494	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
495	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
498	C₂²⋊C₄×C₆₇	—	2	2	no	—
499	C₂²⋊C₄×C₆₇	—	2	2	no	—
500	C₂²⋊C₄×C₆₇	—	2	2	no	—
501	C₂²⋊C₄×C₆₇	—	2	2	no	—
502	C₂²⋊C₄×C₆₇	—	2	1	no	—
503	C₂²⋊C₄×C₆₇	—	2	1	no	—
504	C₂²⋊C₄×C₆₇	—	2	1	no	—
505	C₂²⋊C₄×C₆₇	—	2	2	no	—
506	C₂²⋊C₄×C₆₇	—	2	2	no	—
507	C₂²⋊C₄×C₆₇	—	2	2	no	—
508	C₂²⋊C₄×C₆₇	—	2	2	no	—
509	C₂²⋊C₄×C₆₇	—	2	2	no	—
510	C₂²⋊C₄×C₆₇	—	2	2	no	—
511	C₂²⋊C₄×C₆₇	—	2	2	no	—
512	C₂²⋊C₄×C₆₇	—	2	2	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	2	no	—
515	C₂²⋊C₄×C₆₇	—	2	1	no	—
516	C₂²⋊C₄×C₆₇	—	2	1	no	—
517	C₂²⋊C₄×C₆₇	—	2	1	no	—
518	C₂²⋊C₄×C₆₇	—	2	1	no	—
519	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
520	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
521	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
522	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
523	C₄²×C₆₇	—	2	1	no	—
524	C₄²×C₆₇	—	2	1	no	—
525	C₄²×C₆₇	—	2	1	no	—
526	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
527	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
528	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
529	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
530	C₂³×C₆₇	—	2	1	no	—
531	C₂³×C₆₇	—	2	2	no	—
532	C₂³×C₆₇	—	2	4	no	—
533	C₂³×C₆₇	—	2	2	no	—
534	C₂³×C₆₇	—	2	1	no	—
535	C₂³×C₆₇	—	2	1	no	—
536	C₂³×C₆₇	—	4	4	no	—
537	C₂³×C₆₇	—	4	4	no	—
538	C₂³×C₆₇	—	4	4	no	—
539	C₂³×C₆₇	—	4	2	no	—
540	C₂³×C₆₇	—	8	1	no	—
541	C₂³×C₆₇	—	8	1	no	—
542	C₂³×C₆₇	—	8	2	no	—
543	C₂³×C₆₇	—	8	2	no	—
544	C₂³×C₆₇	—	8	1	no	—
545	C₂³×C₆₇	—	8	1	no	—
546	C₂³×C₆₇	—	8	2	no	—
547	C₂³×C₆₇	—	8	2	no	—
548	C₂³×C₆₇	—	8	2	no	—
549	C₂³×C₆₇	—	8	2	no	—
550	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
551	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
552	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
553	Q₈×C₆₇	—	2	2	no	—
554	Q₈×C₆₇	—	2	2	no	—
555	Q₈×C₆₇	—	2	1	no	—
556	Q₈×C₆₇	—	2	2	no	—
557	Q₈×C₆₇	—	2	1	no	—
558	Q₈×C₆₇	—	2	1	no	—
559	Q₈×C₆₇	—	2	1	no	—
560	Q₈×C₆₇	—	2	2	no	—
561	Q₈×C₆₇	—	2	1	no	—
562	Q₈×C₆₇	—	4	4	no	—
563	Q₈×C₆₇	—	4	2	no	—
564	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
565	D₄×C₆₇	—	2	4	no	—
566	D₄×C₆₇	—	2	4	no	—
567	D₄×C₆₇	—	2	4	no	—
568	D₄×C₆₇	—	2	4	no	—
569	D₄×C₆₇	—	2	2	no	—
570	D₄×C₆₇	—	2	2	no	—
571	D₄×C₆₇	—	2	2	no	—
572	D₄×C₆₇	—	2	1	no	—
573	D₄×C₆₇	—	2	1	no	—
574	D₄×C₆₇	—	2	2	no	—
575	D₄×C₆₇	—	2	1	no	—
576	D₄×C₆₇	—	2	1	no	—
577	D₄×C₆₇	—	2	2	no	—
578	D₄×C₆₇	—	2	1	no	—
579	D₄×C₆₇	—	4	2	no	—
580	D₄×C₆₇	—	4	2	no	—
581	D₄×C₆₇	—	4	4	no	—
582	D₄×C₆₇	—	4	4	no	—
583	D₄×C₆₇	—	4	4	no	—
584	D₄×C₆₇	—	4	4	no	—
585	D₄×C₆₇	—	4	2	no	—
586	D₄×C₆₇	—	4	4	no	—
587	D₄×C₆₇	—	4	4	no	—
588	D₄×C₆₇	—	4	4	no	—
589	D₄×C₆₇	—	4	2	no	—
590	D₄×C₆₇	—	4	2	no	—
591	D₄×C₆₇	—	4	2	no	—
592	D₄×C₆₇	—	8	1	no	—
593	D₄×C₆₇	—	8	2	no	—
594	D₄×C₆₇	—	8	2	no	—
595	D₄×C₆₇	—	8	2	no	—
596	D₄×C₆₇	—	8	2	no	—
597	D₄×C₆₇	C₂²×D₄	1	2	yes	—
598	D₄×C₆₇	C₂²×D₄	1	4	yes	—
599	C₂×C₄×C₆₇	—	2	1	no	—
600	C₂×C₄×C₆₇	—	2	4	no	—
601	C₂×C₄×C₆₇	—	2	2	no	—
602	C₂×C₄×C₆₇	—	2	2	no	—
603	C₂×C₄×C₆₇	—	2	2	no	—
604	C₂×C₄×C₆₇	—	2	2	no	—
605	C₂×C₄×C₆₇	—	2	1	no	—
606	C₂×C₄×C₆₇	—	2	1	no	—
607	C₂×C₄×C₆₇	—	2	2	no	—
608	C₂×C₄×C₆₇	—	2	2	no	—
609	C₂×C₄×C₆₇	—	2	1	no	—
610	C₂×C₄×C₆₇	—	2	1	no	—
611	C₂×C₄×C₆₇	—	4	1	no	—
612	C₂×C₄×C₆₇	—	4	1	no	—
613	C₂×C₄×C₆₇	—	4	4	no	—
614	C₂×C₄×C₆₇	—	4	4	no	—
615	C₂×C₄×C₆₇	—	4	4	no	—
616	C₂×C₄×C₆₇	—	4	4	no	—
617	C₂×C₄×C₆₇	—	4	4	no	—
618	C₂×C₄×C₆₇	—	4	4	no	—
619	C₂×C₄×C₆₇	—	4	2	no	—
620	C₂×C₄×C₆₇	—	4	2	no	—
621	C₂×C₄×C₆₇	—	4	2	no	—
622	C₂×C₄×C₆₇	—	8	1	no	—
623	C₂×C₄×C₆₇	—	8	1	no	—
624	C₂×C₄×C₆₇	—	8	2	no	—
625	C₂×C₄×C₆₇	—	8	1	no	—
626	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
627	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
631	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
632	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
633	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
634	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
635	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
636	C₈×C₆₇	—	2	1	no	—
637	C₈×C₆₇	—	2	1	no	—
638	C₈×C₆₇	—	2	1	no	—
639	C₈×C₆₇	—	2	1	no	—
640	C₈×C₆₇	—	2	2	no	—
641	C₈×C₆₇	C₂²×D₄	1	4	yes	—
642	C₂²×C₆₇	—	2	1	no	—
643	C₂²×C₆₇	—	2	1	no	—
644	C₂²×C₆₇	—	2	2	no	—
645	C₂²×C₆₇	—	2	2	no	—
646	C₂²×C₆₇	—	2	2	no	—
647	C₂²×C₆₇	—	2	2	no	—
648	C₂²×C₆₇	—	2	2	no	—
649	C₂²×C₆₇	—	2	2	no	—
650	C₂²×C₆₇	—	2	2	no	—
651	C₂²×C₆₇	—	2	4	no	—
652	C₂²×C₆₇	—	4	1	no	—
653	C₂²×C₆₇	—	4	2	no	—
654	C₂²×C₆₇	—	4	2	no	—
655	C₂²×C₆₇	—	4	1	no	—
656	C₂²×C₆₇	—	4	1	no	—
657	C₂²×C₆₇	—	4	1	no	—
658	C₂²×C₆₇	—	4	2	no	—
659	C₂²×C₆₇	—	4	1	no	—
660	C₂²×C₆₇	—	4	1	no	—
661	C₂²×C₆₇	—	4	2	no	—
662	C₂²×C₆₇	—	4	2	no	—
663	C₂²×C₆₇	—	4	1	no	—
664	C₂²×C₆₇	—	4	1	no	—
665	C₂²×C₆₇	—	8	4	no	—
666	C₂²×C₆₇	—	16	2	no	—
667	C₂²×C₆₇	—	16	4	no	—
668	C₂²×C₆₇	—	16	4	no	—
669	C₂²×C₆₇	—	16	4	no	—
670	C₂²×C₆₇	D₄²	1	2	yes	—
671	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
672	C₄×C₆₇	—	2	1	no	—
673	C₄×C₆₇	—	2	1	no	—
674	C₄×C₆₇	—	2	1	no	—
675	C₄×C₆₇	—	2	1	no	—
676	C₄×C₆₇	—	2	2	no	—
677	C₄×C₆₇	—	2	2	no	—
678	C₄×C₆₇	—	2	2	no	—
679	C₄×C₆₇	—	4	1	no	—
680	C₄×C₆₇	—	4	2	no	—
681	C₄×C₆₇	—	4	1	no	—
682	C₄×C₆₇	—	4	1	no	—
683	C₄×C₆₇	—	4	1	no	—
684	C₄×C₆₇	—	4	2	no	—
685	C₄×C₆₇	D₄²	1	2	yes	—
686	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
688	#61092	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
689	C₂×C₆₇	—	2	2	no	—
690	C₂×C₆₇	—	4	2	no	—
691	C₂×C₆₇	—	4	2	no	—
692	C₂×C₆₇	—	4	4	no	—
693	C₂×C₆₇	—	4	2	no	—
694	C₂×C₆₇	—	8	1	no	—
695	C₂×C₆₇	—	8	1	no	—
696	C₂×C₆₇	—	8	2	no	—
697	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
698	C₂×C₆₇	#3584	1	1	yes	characteristic
699	C₂×C₆₇	#3585	1	1	yes	characteristic
700	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
701	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
702	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
703	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
704	#3282	C₂×C₆₇	1	2	yes	complemented
705	#3280	C₂×C₆₇	1	2	yes	complemented
706	#3275	C₂×C₆₇	1	2	yes	complemented
707	#3273	C₂×C₆₇	1	2	yes	complemented
708	#3269	C₂×C₆₇	1	2	yes	complemented
709	#3267	C₂×C₆₇	1	2	yes	complemented
710	#3265	C₂×C₆₇	1	2	yes	complemented
711	#3264	C₂×C₆₇	1	2	yes	complemented
712	#3153	C₂×C₆₇	1	1	yes	characteristic, complemented
713	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
714	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
715	#3035	C₂×C₆₇	1	1	yes	characteristic, complemented
716	C₂×#463	C₂×C₆₇	1	1	yes	characteristic, complemented
717	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
718	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
721	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
722	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
723	C₆₇	#61092	1	1	yes	characteristic, direct product factor, Sylow
724	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
726	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#577	—	2	8	no	—
729	#576	—	2	8	no	—
730	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
731	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
732	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
734	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
736	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
737	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
738	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
739	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
740	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
742	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
743	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
745	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
746	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
747	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	#548	C₂²×C₆₇	1	2	yes	complemented
750	#548	C₂²×C₆₇	1	2	yes	complemented
751	#547	—	2	1	no	—
752	#547	C₂²×C₆₇	1	2	yes	complemented
753	#546	—	2	1	no	—
754	#546	—	2	1	no	—
755	#546	—	2	2	no	—
756	#546	—	2	2	no	—
757	#546	C₂²×C₆₇	1	2	yes	complemented
758	#546	C₂²×C₆₇	1	2	yes	complemented
759	#546	C₂²×C₆₇	1	2	yes	complemented
760	#546	C₂²×C₆₇	1	2	yes	complemented
761	D₄²	—	2	1	no	—
762	D₄²	C₂²×C₆₇	1	2	yes	complemented
763	#537	C₂²×C₆₇	1	1	yes	characteristic
764	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	#536	—	2	1	no	—
766	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
767	#535	—	2	1	no	—
768	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
769	#534	—	2	2	no	—
770	#532	—	2	1	no	—
771	#532	C₂²×C₆₇	1	1	yes	characteristic
772	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	C₂×#124	—	2	1	no	—
774	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	C₂×#121	—	2	2	no	—
776	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
777	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	#497	C₂²×C₆₇	1	2	yes	complemented
779	#496	C₂²×C₆₇	1	2	yes	complemented
780	#495	C₂²×C₆₇	1	2	yes	complemented
781	#495	C₂²×C₆₇	1	2	yes	complemented
782	#470	C₂²×C₆₇	1	2	yes	complemented
783	#469	C₂²×C₆₇	1	2	yes	complemented
784	#468	C₂²×C₆₇	1	2	yes	complemented
785	#468	C₂²×C₆₇	1	2	yes	complemented
786	#467	C₂²×C₆₇	1	2	yes	complemented
787	#466	C₂²×C₆₇	1	2	yes	complemented
788	#465	C₂²×C₆₇	1	2	yes	complemented
789	#465	C₂²×C₆₇	1	2	yes	complemented
790	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	#464	C₂²×C₆₇	1	1	yes	characteristic, complemented
792	#463	C₂²×C₆₇	1	2	yes	complemented
793	#463	C₂²×C₆₇	1	2	yes	complemented
794	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
795	#463	C₂²×C₆₇	1	2	yes	complemented
796	#463	C₂²×C₆₇	1	1	yes	characteristic, complemented
797	#463	C₂²×C₆₇	1	2	yes	complemented
798	#462	C₂²×C₆₇	1	1	yes	characteristic, complemented
799	#461	C₂²×C₆₇	1	1	yes	characteristic, complemented
800	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
801	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
802	#452	C₂²×C₆₇	1	2	yes	complemented
803	#452	C₂²×C₆₇	1	2	yes	complemented
804	#452	C₂²×C₆₇	1	2	yes	complemented
805	#452	C₂²×C₆₇	1	2	yes	complemented
806	#451	C₂²×C₆₇	1	2	yes	complemented
807	#450	C₂²×C₆₇	1	2	yes	complemented
808	#450	C₂²×C₆₇	1	2	yes	complemented
809	#450	C₂²×C₆₇	1	2	yes	complemented
810	#449	C₂²×C₆₇	1	2	yes	complemented
811	#449	C₂²×C₆₇	1	2	yes	complemented
812	#449	C₂²×C₆₇	1	2	yes	complemented
813	#449	C₂²×C₆₇	1	2	yes	complemented
814	#448	C₂²×C₆₇	1	2	yes	complemented
815	#447	C₂²×C₆₇	1	2	yes	complemented
816	#447	C₂²×C₆₇	1	2	yes	complemented
817	#447	C₂²×C₆₇	1	2	yes	complemented
818	#442	C₂²×C₆₇	1	2	yes	complemented
819	#440	C₂²×C₆₇	1	2	yes	complemented
820	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
821	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
822	#436	C₂²×C₆₇	1	2	yes	complemented
823	#435	C₂²×C₆₇	1	2	yes	complemented
824	#435	C₂²×C₆₇	1	2	yes	complemented
825	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
826	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
827	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
828	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
829	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
831	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
832	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
834	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
835	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
836	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
837	2₋¹⁺⁴	—	2	4	no	—
838	2₋¹⁺⁴	—	4	2	no	—
839	H(5,𝔽₂)	—	2	4	no	—
840	H(5,𝔽₂)	—	2	4	no	—
841	H(5,𝔽₂)	—	2	4	no	—
842	H(5,𝔽₂)	—	4	2	no	—
843	H(5,𝔽₂)	—	4	2	no	—
844	H(5,𝔽₂)	—	4	2	no	—
845	C₂×#41	—	2	1	no	—
846	C₂×#41	—	2	1	no	—
847	C₂×#41	—	2	1	no	—
848	C₂×#41	—	2	1	no	—
849	C₂×#41	—	2	2	no	—
850	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
852	C₂×#41	C₂³×C₆₇	1	2	yes	—
853	C₂×#41	C₂³×C₆₇	1	2	yes	—
854	C₂×#41	C₂³×C₆₇	1	2	yes	—
855	C₂×#41	C₂³×C₆₇	1	2	yes	—
856	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
857	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
858	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
859	C₂²×Q₈	—	2	1	no	—
860	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
862	C₂²×D₄	—	2	2	no	—
863	C₂²×D₄	—	2	2	no	—
864	C₂²×D₄	—	2	1	no	—
865	C₂²×D₄	—	2	1	no	—
866	C₂²×D₄	—	2	1	no	—
867	C₂²×D₄	—	2	2	no	—
868	C₂²×D₄	—	2	2	no	—
869	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
871	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
872	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
873	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
874	C₂³×C₄	—	2	1	no	—
875	#137	—	2	8	no	—
876	#137	—	2	4	no	—
877	#137	—	4	2	no	—
878	AGL(1,ℤ/8)	—	2	8	no	—
879	AGL(1,ℤ/8)	—	2	8	no	—
880	AGL(1,ℤ/8)	—	2	8	no	—
881	AGL(1,ℤ/8)	—	2	4	no	—
882	AGL(1,ℤ/8)	—	4	2	no	—
883	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
884	#135	—	2	4	no	—
885	#135	—	2	4	no	—
886	#135	—	2	8	no	—
887	#135	—	2	8	no	—
888	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
889	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
891	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
892	C₂×SD₁₆	—	2	4	no	—
893	C₂×SD₁₆	—	2	8	no	—
894	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
895	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
896	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
897	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
898	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
899	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
900	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
901	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
902	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
903	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
904	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
905	C₂×D₈	—	2	4	no	—
906	C₂×D₈	—	2	8	no	—
907	C₂×D₈	C₂³×C₆₇	1	2	yes	—
908	C₂×D₈	C₂³×C₆₇	1	2	yes	—
909	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
910	C₂×D₈	C₂³×C₆₇	1	2	yes	—
911	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
912	C₂×D₈	C₂³×C₆₇	1	2	yes	—
913	C₂×D₈	C₂³×C₆₇	1	2	yes	—
914	#131	—	2	4	no	—
915	#131	—	2	4	no	—
916	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
917	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
918	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
919	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
920	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
921	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
922	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
923	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
924	C₄⋊Q₈	—	2	1	no	—
925	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
926	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
927	#127	—	2	1	no	—
928	#127	D₄×C₆₇	1	1	yes	characteristic
929	#127	C₂³×C₆₇	1	1	yes	characteristic
930	#124	—	2	1	no	—
931	#124	—	2	1	no	—
932	#124	—	2	2	no	—
933	#124	—	2	2	no	—
934	#124	—	2	1	no	—
935	#124	—	2	1	no	—
936	#124	D₄×C₆₇	1	1	yes	characteristic
937	#124	D₄×C₆₇	1	1	yes	characteristic
938	#124	C₂³×C₆₇	1	2	yes	—
939	#124	C₂³×C₆₇	1	2	yes	—
940	#124	C₂³×C₆₇	1	1	yes	characteristic
941	#124	C₂³×C₆₇	1	1	yes	characteristic
942	#123	—	2	2	no	—
943	#123	—	2	2	no	—
944	#123	—	2	2	no	—
945	#123	—	2	2	no	—
946	#123	—	2	2	no	—
947	#123	—	2	2	no	—
948	#123	—	2	2	no	—
949	C₂²⋊Q₈	—	2	1	no	—
950	C₂²⋊Q₈	—	2	1	no	—
951	C₂²⋊Q₈	—	2	2	no	—
952	C₂²⋊Q₈	—	2	2	no	—
953	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
954	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
955	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
956	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
957	#121	—	2	2	no	—
958	#121	—	2	2	no	—
959	#121	—	2	2	no	—
960	#121	—	2	2	no	—
961	#121	—	2	2	no	—
962	#121	—	2	1	no	—
963	#121	—	2	1	no	—
964	#121	—	2	1	no	—
965	#121	—	2	1	no	—
966	#121	—	2	2	no	—
967	#121	—	2	2	no	—
968	#121	—	2	2	no	—
969	#121	—	2	2	no	—
970	#121	—	2	2	no	—
971	#121	D₄×C₆₇	1	2	yes	—
972	#121	D₄×C₆₇	1	2	yes	—
973	#121	C₂³×C₆₇	1	2	yes	—
974	#121	C₂³×C₆₇	1	2	yes	—
975	#121	C₂³×C₆₇	1	2	yes	—
976	#121	C₂³×C₆₇	1	2	yes	—
977	#120	—	2	2	no	—
978	#120	—	2	2	no	—
979	#120	—	2	2	no	—
980	#120	—	2	2	no	—
981	#120	—	2	2	no	—
982	#120	—	2	2	no	—
983	#120	—	2	2	no	—
984	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
985	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
986	C₄×D₄	—	2	1	no	—
987	C₄×D₄	—	2	1	no	—
988	C₄×D₄	—	2	2	no	—
989	C₄×D₄	—	2	2	no	—
990	C₄×D₄	—	2	1	no	—
991	C₄×D₄	—	2	1	no	—
992	C₄×D₄	—	2	1	no	—
993	C₄×D₄	—	2	1	no	—
994	C₄×D₄	C₂³×C₆₇	1	2	yes	—
995	C₄×D₄	C₂³×C₆₇	1	2	yes	—
996	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
997	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
998	C₄×D₄	C₂³×C₆₇	1	2	yes	—
999	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1000	#117	—	2	1	no	—
1001	#117	C₂³×C₆₇	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	—	2	2	no	—
1003	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	—	2	1	no	—
1005	C₂×C₂²⋊C₄	—	2	1	no	—
1006	C₂×C₂²⋊C₄	—	2	1	no	—
1007	C₂×C₂²⋊C₄	—	2	2	no	—
1008	C₂×C₂²⋊C₄	—	2	2	no	—
1009	C₂×C₂²⋊C₄	—	2	2	no	—
1010	C₂×C₂²⋊C₄	—	2	2	no	—
1011	C₂×C₄²	—	2	1	no	—
1012	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
1013	#107	C₂³×C₆₇	1	2	yes	—
1014	#106	C₂³×C₆₇	1	2	yes	—
1015	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1016	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1017	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1018	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1019	#103	C₂³×C₆₇	1	2	yes	—
1020	#103	C₂³×C₆₇	1	2	yes	—
1021	#103	C₂³×C₆₇	1	1	yes	characteristic
1022	#103	C₂³×C₆₇	1	1	yes	characteristic
1023	#103	C₂³×C₆₇	1	1	yes	characteristic
1024	#103	C₂³×C₆₇	1	1	yes	characteristic
1025	#103	C₂³×C₆₇	1	2	yes	—
1026	#102	C₂³×C₆₇	1	2	yes	—
1027	#102	C₂³×C₆₇	1	2	yes	—
1028	#102	C₂³×C₆₇	1	1	yes	characteristic
1029	#102	C₂³×C₆₇	1	1	yes	characteristic
1030	#102	C₂³×C₆₇	1	1	yes	characteristic
1031	#102	C₂³×C₆₇	1	1	yes	characteristic
1032	#102	C₂³×C₆₇	1	2	yes	—
1033	#102	C₂³×C₆₇	1	2	yes	—
1034	#102	C₂³×C₆₇	1	2	yes	—
1035	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1036	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1037	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1038	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1039	#97	C₂³×C₆₇	1	2	yes	—
1040	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1041	C₂⁴	—	2	1	no	—
1042	C₂⁴	—	2	2	no	—
1043	C₂⁴	—	2	1	no	—
1044	C₂⁴	—	2	2	no	—
1045	C₂⁴	—	2	2	no	—
1046	#41	—	2	2	no	—
1047	#41	—	2	2	no	—
1048	#41	—	2	2	no	—
1049	#41	—	2	2	no	—
1050	#41	—	2	2	no	—
1051	#41	—	2	4	no	—
1052	#41	—	2	4	no	—
1053	#41	—	2	4	no	—
1054	#41	—	2	4	no	—
1055	#41	—	2	2	no	—
1056	#41	—	2	2	no	—
1057	#41	—	2	2	no	—
1058	#41	—	2	2	no	—
1059	#41	—	4	2	no	—
1060	#41	—	4	2	no	—
1061	#41	—	4	2	no	—
1062	#41	—	4	2	no	—
1063	#41	—	4	4	no	—
1064	#41	—	4	4	no	—
1065	#41	—	4	8	no	—
1066	#41	—	4	4	no	—
1067	#41	—	4	4	no	—
1068	#41	C₂×D₄×C₆₇	1	4	yes	complemented
1069	C₂×Q₈	—	2	2	no	—
1070	C₂×Q₈	—	2	1	no	—
1071	C₂×Q₈	—	2	4	no	—
1072	C₂×Q₈	—	2	2	no	—
1073	C₂×Q₈	—	2	2	no	—
1074	C₂×Q₈	—	4	2	no	—
1075	C₂×Q₈	—	4	4	no	—
1076	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1077	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1078	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1079	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1080	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1081	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1082	C₂×D₄	—	2	1	no	—
1083	C₂×D₄	—	2	4	no	—
1084	C₂×D₄	—	2	4	no	—
1085	C₂×D₄	—	2	4	no	—
1086	C₂×D₄	—	2	2	no	—
1087	C₂×D₄	—	2	2	no	—
1088	C₂×D₄	—	2	2	no	—
1089	C₂×D₄	—	2	1	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	2	no	—
1092	C₂×D₄	—	2	2	no	—
1093	C₂×D₄	—	2	2	no	—
1094	C₂×D₄	—	2	2	no	—
1095	C₂×D₄	—	2	2	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	2	2	no	—
1098	C₂×D₄	—	2	1	no	—
1099	C₂×D₄	—	2	2	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	1	no	—
1103	C₂×D₄	—	2	1	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	4	2	no	—
1107	C₂×D₄	—	4	2	no	—
1108	C₂×D₄	—	4	2	no	—
1109	C₂×D₄	—	4	4	no	—
1110	C₂×D₄	—	4	8	no	—
1111	C₂×D₄	—	4	4	no	—
1112	C₂×D₄	—	4	4	no	—
1113	C₂×D₄	—	4	8	no	—
1114	C₂×D₄	—	4	8	no	—
1115	C₂×D₄	—	8	4	no	—
1116	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1117	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1118	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1119	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1120	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
1121	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1122	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1123	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1124	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1125	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1126	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	2	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	2	no	—
1133	C₂²×C₄	—	2	2	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	2	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	8	2	no	—
1143	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1144	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1146	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1147	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1148	Q₁₆	—	2	2	no	—
1149	Q₁₆	—	2	2	no	—
1150	Q₁₆	—	2	4	no	—
1151	Q₁₆	—	4	2	no	—
1152	SD₁₆	—	2	2	no	—
1153	SD₁₆	—	2	2	no	—
1154	SD₁₆	—	2	4	no	—
1155	SD₁₆	—	2	4	no	—
1156	SD₁₆	—	2	2	no	—
1157	SD₁₆	—	2	2	no	—
1158	SD₁₆	—	2	4	no	—
1159	SD₁₆	—	2	4	no	—
1160	SD₁₆	—	4	2	no	—
1161	SD₁₆	—	4	2	no	—
1162	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1163	D₈	—	2	2	no	—
1164	D₈	—	2	4	no	—
1165	D₈	—	2	4	no	—
1166	D₈	—	2	2	no	—
1167	D₈	—	2	4	no	—
1168	D₈	—	4	2	no	—
1169	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
1170	M₁₆	—	2	2	no	—
1171	M₁₆	—	2	4	no	—
1172	M₁₆	—	2	4	no	—
1173	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1174	C₂×C₈	—	2	2	no	—
1175	C₂×C₈	—	2	2	no	—
1176	C₂×C₈	—	2	4	no	—
1177	C₂×C₈	—	2	4	no	—
1178	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1179	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1180	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1181	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1182	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1183	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1184	C₄⋊C₄	—	2	1	no	—
1185	C₄⋊C₄	—	2	2	no	—
1186	C₄⋊C₄	—	2	2	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	2	1	no	—
1189	C₄⋊C₄	—	2	1	no	—
1190	C₄⋊C₄	—	2	2	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	1	no	—
1193	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1194	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1195	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1196	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1197	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	1	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	2	no	—
1214	C₂²⋊C₄	—	2	2	no	—
1215	C₂²⋊C₄	—	2	1	no	—
1216	C₂²⋊C₄	—	2	1	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1220	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1221	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1222	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1223	C₄²	—	2	1	no	—
1224	C₄²	—	2	1	no	—
1225	C₄²	—	2	1	no	—
1226	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1227	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1228	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1229	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1230	C₂³	—	2	1	no	—
1231	C₂³	—	2	2	no	—
1232	C₂³	—	2	4	no	—
1233	C₂³	—	2	2	no	—
1234	C₂³	—	2	1	no	—
1235	C₂³	—	2	1	no	—
1236	C₂³	—	4	4	no	—
1237	C₂³	—	4	4	no	—
1238	C₂³	—	4	4	no	—
1239	C₂³	—	4	2	no	—
1240	C₂³	—	8	1	no	—
1241	C₂³	—	8	1	no	—
1242	C₂³	—	8	2	no	—
1243	C₂³	—	8	2	no	—
1244	C₂³	—	8	1	no	—
1245	C₂³	—	8	1	no	—
1246	C₂³	—	8	2	no	—
1247	C₂³	—	8	2	no	—
1248	C₂³	—	8	2	no	—
1249	C₂³	—	8	2	no	—
1250	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1251	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1252	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1253	Q₈	—	2	2	no	—
1254	Q₈	—	2	2	no	—
1255	Q₈	—	2	1	no	—
1256	Q₈	—	2	2	no	—
1257	Q₈	—	2	1	no	—
1258	Q₈	—	2	1	no	—
1259	Q₈	—	2	1	no	—
1260	Q₈	—	2	2	no	—
1261	Q₈	—	2	1	no	—
1262	Q₈	—	4	4	no	—
1263	Q₈	—	4	2	no	—
1264	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1265	D₄	—	2	4	no	—
1266	D₄	—	2	4	no	—
1267	D₄	—	2	4	no	—
1268	D₄	—	2	4	no	—
1269	D₄	—	2	2	no	—
1270	D₄	—	2	2	no	—
1271	D₄	—	2	2	no	—
1272	D₄	—	2	1	no	—
1273	D₄	—	2	1	no	—
1274	D₄	—	2	2	no	—
1275	D₄	—	2	1	no	—
1276	D₄	—	2	1	no	—
1277	D₄	—	2	2	no	—
1278	D₄	—	2	1	no	—
1279	D₄	—	4	2	no	—
1280	D₄	—	4	2	no	—
1281	D₄	—	4	4	no	—
1282	D₄	—	4	4	no	—
1283	D₄	—	4	4	no	—
1284	D₄	—	4	4	no	—
1285	D₄	—	4	2	no	—
1286	D₄	—	4	4	no	—
1287	D₄	—	4	4	no	—
1288	D₄	—	4	4	no	—
1289	D₄	—	4	2	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	4	2	no	—
1292	D₄	—	8	1	no	—
1293	D₄	—	8	2	no	—
1294	D₄	—	8	2	no	—
1295	D₄	—	8	2	no	—
1296	D₄	—	8	2	no	—
1297	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1298	D₄	C₂²×D₄×C₆₇	1	4	yes	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	4	no	—
1301	C₂×C₄	—	2	2	no	—
1302	C₂×C₄	—	2	2	no	—
1303	C₂×C₄	—	2	2	no	—
1304	C₂×C₄	—	2	2	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	4	1	no	—
1312	C₂×C₄	—	4	1	no	—
1313	C₂×C₄	—	4	4	no	—
1314	C₂×C₄	—	4	4	no	—
1315	C₂×C₄	—	4	4	no	—
1316	C₂×C₄	—	4	4	no	—
1317	C₂×C₄	—	4	4	no	—
1318	C₂×C₄	—	4	4	no	—
1319	C₂×C₄	—	4	2	no	—
1320	C₂×C₄	—	4	2	no	—
1321	C₂×C₄	—	4	2	no	—
1322	C₂×C₄	—	8	2	no	—
1323	C₂×C₄	—	8	1	no	—
1324	C₂×C₄	—	8	1	no	—
1325	C₂×C₄	—	8	1	no	—
1326	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1327	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1328	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1329	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1330	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1331	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1332	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1333	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1334	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1335	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1336	C₈	—	2	1	no	—
1337	C₈	—	2	1	no	—
1338	C₈	—	2	1	no	—
1339	C₈	—	2	1	no	—
1340	C₈	—	2	2	no	—
1341	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1342	C₂²	—	2	1	no	—
1343	C₂²	—	2	1	no	—
1344	C₂²	—	2	2	no	—
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	2	2	no	—
1348	C₂²	—	2	2	no	—
1349	C₂²	—	2	2	no	—
1350	C₂²	—	2	2	no	—
1351	C₂²	—	2	4	no	—
1352	C₂²	—	4	1	no	—
1353	C₂²	—	4	2	no	—
1354	C₂²	—	4	2	no	—
1355	C₂²	—	4	1	no	—
1356	C₂²	—	4	1	no	—
1357	C₂²	—	4	1	no	—
1358	C₂²	—	4	2	no	—
1359	C₂²	—	4	1	no	—
1360	C₂²	—	4	1	no	—
1361	C₂²	—	4	2	no	—
1362	C₂²	—	4	2	no	—
1363	C₂²	—	4	1	no	—
1364	C₂²	—	4	1	no	—
1365	C₂²	—	8	4	no	—
1366	C₂²	—	16	2	no	—
1367	C₂²	—	16	4	no	—
1368	C₂²	—	16	4	no	—
1369	C₂²	—	16	4	no	—
1370	C₂²	D₄²×C₆₇	1	2	yes	—
1371	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1372	C₄	—	2	1	no	—
1373	C₄	—	2	1	no	—
1374	C₄	—	2	1	no	—
1375	C₄	—	2	1	no	—
1376	C₄	—	2	2	no	—
1377	C₄	—	2	2	no	—
1378	C₄	—	2	2	no	—
1379	C₄	—	4	1	no	—
1380	C₄	—	4	2	no	—
1381	C₄	—	4	1	no	—
1382	C₄	—	4	1	no	—
1383	C₄	—	4	1	no	—
1384	C₄	—	4	2	no	—
1385	C₄	D₄²×C₆₇	1	2	yes	—
1386	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1387	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1388	C₂	—	2	2	no	—
1389	C₂	—	4	2	no	—
1390	C₂	—	4	2	no	—
1391	C₂	—	4	4	no	—
1392	C₂	—	4	2	no	—
1393	C₂	—	8	1	no	—
1394	C₂	—	8	1	no	—
1395	C₂	—	8	2	no	—
1396	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1397	C₂	C₆₇×#3584	1	1	yes	characteristic
1398	C₂	C₆₇×#3585	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 ◁ #532×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. C₂×#576×C₆₇	C₂	semidirect
3. C₆₇×#3500	C₂	semidirect
4. C₆₇×#3496	C₂	semidirect
5. C₆₇×#3282	C₂	semidirect
6. C₆₇×#3280	C₂	semidirect
7. C₆₇×#3275	C₂	semidirect
8. C₆₇×#3273	C₂	semidirect
9. C₆₇×#3269	C₂	semidirect
10. C₆₇×#3267	C₂	semidirect
11. C₆₇×#3265	C₂	semidirect
12. C₆₇×#3264	C₂	semidirect
13. C₆₇×#3153	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₆₇×#3062	C₂	semidirect
16. C₆₇×#3035	C₂	semidirect
17. C₂×#463×C₆₇	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3012	C₂	semidirect
20. C₆₇×#3009	C₂	semidirect
21. C₆₇×#3008	C₂	semidirect
22. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
23. C₆₇×#2935	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
26. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
27. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
38. C₂×AGL(1,ℤ/8)×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. C₂²×SD₁₆×C₆₇	C₂²	semidirect
44. C₂²×SD₁₆×C₆₇	C₂²	semidirect
46. C₂²×D₈×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
48. C₂×#131×C₆₇	C₂²	semidirect
49. #548×C₆₇	C₂²	semidirect
50. #548×C₆₇	C₂²	semidirect
52. #547×C₆₇	C₂²	semidirect
57. #546×C₆₇	C₂²	semidirect
58. #546×C₆₇	C₂²	semidirect
59. #546×C₆₇	C₂²	semidirect
60. #546×C₆₇	C₂²	semidirect
62. D₄²×C₆₇	C₂²	semidirect
64. #537×C₆₇	C₂²	semidirect
66. #536×C₆₇	C₂²	semidirect
68. #535×C₆₇	C₂²	semidirect
72. #532×C₆₇	C₂²	semidirect
74. C₂×#124×C₆₇	C₂²	semidirect
76. C₄×#41×C₆₇	C₂²	semidirect
77. C₂×C₄×D₄×C₆₇	C₂²	semidirect
78. #497×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #495×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. #463×C₆₇	C₂²	semidirect
93. #463×C₆₇	C₂²	semidirect
94. #463×C₆₇	C₂²	semidirect
95. #463×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. #450×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. #447×C₆₇	C₂²	semidirect
116. #447×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #442×C₆₇	C₂²	semidirect
119. #440×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. C₄×D₈×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. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
128. #418×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #416×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#103×C₆₇	C₂²	semidirect
133. C₂×#102×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
135. #408×C₆₇	C₂²	semidirect
136. C₄×M₁₆×C₆₇	C₂²	semidirect
183. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
368. #41×C₆₇	C₂×D₄	semidirect
462. SD₁₆×C₆₇	C₂×D₄	semidirect
469. D₈×C₆₇	C₂×D₄	semidirect
473. M₁₆×C₆₇	C₂×D₄	semidirect
688. #61092	C₆₇	direct (N × H)
700. C₂×#577	C₂×C₆₇	semidirect
701. C₂×#576	C₂×C₆₇	semidirect
702. #3500	C₂×C₆₇	semidirect
703. #3496	C₂×C₆₇	semidirect
704. #3282	C₂×C₆₇	semidirect
705. #3280	C₂×C₆₇	semidirect
706. #3275	C₂×C₆₇	semidirect
707. #3273	C₂×C₆₇	semidirect
708. #3269	C₂×C₆₇	semidirect
709. #3267	C₂×C₆₇	semidirect
710. #3265	C₂×C₆₇	semidirect
711. #3264	C₂×C₆₇	semidirect
712. #3153	C₂×C₆₇	semidirect
713. #3063	C₂×C₆₇	semidirect
714. #3062	C₂×C₆₇	semidirect
715. #3035	C₂×C₆₇	semidirect
716. C₂×#463	C₂×C₆₇	semidirect
717. #3013	C₂×C₆₇	semidirect
718. #3012	C₂×C₆₇	semidirect
719. #3009	C₂×C₆₇	semidirect
720. #3008	C₂×C₆₇	semidirect
721. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
722. #2935	C₂×C₆₇	semidirect
723. C₆₇	#61092	direct (N × H)
724. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
726. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
727. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
730. C₂×#137	C₂²×C₆₇	semidirect
731. C₂×#137	C₂²×C₆₇	semidirect
732. C₂×#137	C₂²×C₆₇	semidirect
734. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
735. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
736. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
737. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
738. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
739. C₂×#135	C₂²×C₆₇	semidirect
740. C₂×#135	C₂²×C₆₇	semidirect
741. C₂×#135	C₂²×C₆₇	semidirect
742. C₂×#135	C₂²×C₆₇	semidirect
743. C₂²×SD₁₆	C₂²×C₆₇	semidirect
744. C₂²×SD₁₆	C₂²×C₆₇	semidirect
746. C₂²×D₈	C₂²×C₆₇	semidirect
747. C₂×#131	C₂²×C₆₇	semidirect
748. C₂×#131	C₂²×C₆₇	semidirect
749. #548	C₂²×C₆₇	semidirect
750. #548	C₂²×C₆₇	semidirect
752. #547	C₂²×C₆₇	semidirect
757. #546	C₂²×C₆₇	semidirect
758. #546	C₂²×C₆₇	semidirect
759. #546	C₂²×C₆₇	semidirect
760. #546	C₂²×C₆₇	semidirect
762. D₄²	C₂²×C₆₇	semidirect
764. #537	C₂²×C₆₇	semidirect
766. #536	C₂²×C₆₇	semidirect
768. #535	C₂²×C₆₇	semidirect
772. #532	C₂²×C₆₇	semidirect
774. C₂×#124	C₂²×C₆₇	semidirect
776. C₄×#41	C₂²×C₆₇	semidirect
777. C₂×C₄×D₄	C₂²×C₆₇	semidirect
778. #497	C₂²×C₆₇	semidirect
779. #496	C₂²×C₆₇	semidirect
780. #495	C₂²×C₆₇	semidirect
781. #495	C₂²×C₆₇	semidirect
782. #470	C₂²×C₆₇	semidirect
783. #469	C₂²×C₆₇	semidirect
784. #468	C₂²×C₆₇	semidirect
785. #468	C₂²×C₆₇	semidirect
786. #467	C₂²×C₆₇	semidirect
787. #466	C₂²×C₆₇	semidirect
788. #465	C₂²×C₆₇	semidirect
789. #465	C₂²×C₆₇	semidirect
790. #464	C₂²×C₆₇	semidirect
791. #464	C₂²×C₆₇	semidirect
792. #463	C₂²×C₆₇	semidirect
793. #463	C₂²×C₆₇	semidirect
794. #463	C₂²×C₆₇	semidirect
795. #463	C₂²×C₆₇	semidirect
796. #463	C₂²×C₆₇	semidirect
797. #463	C₂²×C₆₇	semidirect
798. #462	C₂²×C₆₇	semidirect
799. #461	C₂²×C₆₇	semidirect
800. #460	C₂²×C₆₇	semidirect
801. #459	C₂²×C₆₇	semidirect
802. #452	C₂²×C₆₇	semidirect
803. #452	C₂²×C₆₇	semidirect
804. #452	C₂²×C₆₇	semidirect
805. #452	C₂²×C₆₇	semidirect
806. #451	C₂²×C₆₇	semidirect
807. #450	C₂²×C₆₇	semidirect
808. #450	C₂²×C₆₇	semidirect
809. #450	C₂²×C₆₇	semidirect
810. #449	C₂²×C₆₇	semidirect
811. #449	C₂²×C₆₇	semidirect
812. #449	C₂²×C₆₇	semidirect
813. #449	C₂²×C₆₇	semidirect
814. #448	C₂²×C₆₇	semidirect
815. #447	C₂²×C₆₇	semidirect
816. #447	C₂²×C₆₇	semidirect
817. #447	C₂²×C₆₇	semidirect
818. #442	C₂²×C₆₇	semidirect
819. #440	C₂²×C₆₇	semidirect
820. C₄×SD₁₆	C₂²×C₆₇	semidirect
821. C₄×D₈	C₂²×C₆₇	semidirect
822. #436	C₂²×C₆₇	semidirect
823. #435	C₂²×C₆₇	semidirect
824. #435	C₂²×C₆₇	semidirect
825. C₈×D₄	C₂²×C₆₇	semidirect
826. #428	C₂²×C₆₇	semidirect
827. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
828. #418	C₂²×C₆₇	semidirect
829. #417	C₂²×C₆₇	semidirect
830. #416	C₂²×C₆₇	semidirect
831. #416	C₂²×C₆₇	semidirect
832. C₂×#103	C₂²×C₆₇	semidirect
833. C₂×#102	C₂²×C₆₇	semidirect
834. #408	C₂²×C₆₇	semidirect
835. #408	C₂²×C₆₇	semidirect
836. C₄×M₁₆	C₂²×C₆₇	semidirect
883. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
1068. #41	C₂×D₄×C₆₇	semidirect
1162. SD₁₆	C₂×D₄×C₆₇	semidirect
1169. D₈	C₂×D₄×C₆₇	semidirect
1173. M₁₆	C₂×D₄×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
C₂×#576×C₆₇	2
C₆₇×#3500	2
C₆₇×#3496	2
C₆₇×#3282	2
C₆₇×#3280	2
C₆₇×#3275	2
C₆₇×#3273	2
C₆₇×#3269	2
C₆₇×#3267	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3153	2
C₆₇×#3063	2
C₆₇×#3062	2
C₆₇×#3035	2
C₂×#463×C₆₇	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3009	2
C₆₇×#3008	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2935	2
#61092	67

Subgroups — C67×#61092 #30740343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61092 #30740343