Subgroups — #31720839

Order 17152.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573612	C₂	1	1	yes	maximal, characteristic
2	#22569312	C₂	1	2	yes	maximal, complemented
3	#22569312	C₂	1	2	yes	maximal, complemented
4	#22569309	C₂	1	2	yes	maximal, complemented
5	#22569307	C₂	1	2	yes	maximal, complemented
6	#22569305	C₂	1	2	yes	maximal, complemented
7	#22569302	C₂	1	2	yes	maximal, complemented
8	#22569302	C₂	1	2	yes	maximal, complemented
9	#22569300	C₂	1	2	yes	maximal, complemented
10	#22569158	C₂	1	1	yes	maximal, characteristic, complemented
11	#22569156	C₂	1	1	yes	maximal, characteristic, complemented
12	#22569152	C₂	1	1	yes	maximal, characteristic, complemented
13	#22569148	C₂	1	1	yes	maximal, characteristic, complemented
14	#22569147	C₂	1	1	yes	maximal, characteristic, complemented
15	#22569142	C₂	1	1	yes	maximal, characteristic, complemented
16	#22569141	C₂	1	1	yes	maximal, characteristic, complemented
17	#22568866	C₂	1	1	yes	maximal, characteristic
18	#22568866	C₂	1	1	yes	maximal, characteristic
19	#22568864	C₂	1	1	yes	maximal, characteristic
20	#22568864	C₂	1	1	yes	maximal, characteristic
21	#22568845	C₂	1	1	yes	maximal, characteristic
22	C₂×#16863456	C₂	1	1	yes	maximal, characteristic
23	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	#16864026	C₄	1	1	yes	characteristic
25	#16864026	C₄	1	1	yes	characteristic
26	#16864026	C₄	1	1	yes	characteristic
27	#16864026	C₄	1	1	yes	characteristic
28	#16864025	C₄	1	2	yes	—
29	#16864025	C₄	1	2	yes	—
30	#16864023	C₄	1	1	yes	characteristic
31	#16864023	C₄	1	1	yes	characteristic
32	#16864023	C₄	1	1	yes	characteristic
33	#16864023	C₄	1	1	yes	characteristic
34	#16864021	C₄	1	2	yes	—
35	#16864021	C₄	1	2	yes	—
36	#16863953	C₂²	1	1	yes	characteristic
37	#16863950	C₂²	1	2	yes	—
38	#16863950	C₂²	1	2	yes	—
39	#16863950	C₂²	1	2	yes	—
40	#16863950	C₂²	1	2	yes	—
41	#16863949	C₂²	1	1	yes	characteristic
42	#16863949	C₂²	1	1	yes	characteristic
43	C₂×#14524000	C₂²	1	1	yes	characteristic
44	#117×D₆₇	C₂²	1	1	yes	characteristic
45	#117×D₆₇	C₂²	1	1	yes	characteristic
46	#16863527	C₂²	1	2	yes	complemented
47	#16863527	C₂²	1	2	yes	complemented
48	#16863527	C₂²	1	2	yes	complemented
49	#16863526	C₂²	1	2	yes	complemented
50	#16863526	C₂²	1	2	yes	complemented
51	#16863526	C₂²	1	2	yes	complemented
52	#16863525	C₂²	1	2	yes	complemented
53	#16863525	C₂²	1	2	yes	complemented
54	#16863525	C₂²	1	2	yes	complemented
55	#16863525	C₂²	1	2	yes	complemented
56	#16863525	C₂²	1	2	yes	complemented
57	#16863525	C₂²	1	2	yes	complemented
58	#16863524	C₂²	1	2	yes	complemented
59	#16863524	C₂²	1	2	yes	complemented
60	#16863524	C₂²	1	2	yes	complemented
61	#16863524	C₂²	1	2	yes	complemented
62	#16863524	C₂²	1	2	yes	complemented
63	#16863524	C₂²	1	2	yes	complemented
64	#16863523	C₂²	1	2	yes	complemented
65	#16863523	C₂²	1	2	yes	complemented
66	#16863523	C₂²	1	2	yes	complemented
67	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
68	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
69	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
70	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
71	#16863520	C₂²	1	2	yes	complemented
72	#16863520	C₂²	1	2	yes	complemented
73	#16863520	C₂²	1	2	yes	complemented
74	#16863458	C₂²	1	2	yes	—
75	#16863458	C₂²	1	2	yes	—
76	#16863458	C₂²	1	2	yes	—
77	#16863458	C₂²	1	2	yes	—
78	#16863456	C₂²	1	1	yes	characteristic
79	#16863456	C₂²	1	2	yes	—
80	#16863456	C₂²	1	1	yes	characteristic
81	#16863456	C₂²	1	1	yes	characteristic
82	#16863456	C₂²	1	2	yes	—
83	#16863456	C₂²	1	2	yes	—
84	#16863456	C₂²	1	1	yes	characteristic
85	#16863456	C₂²	1	2	yes	—
86	#16863456	C₂²	1	1	yes	characteristic
87	#16863456	C₂²	1	1	yes	characteristic
88	#16863456	C₂²	1	1	yes	characteristic
89	#16863456	C₂²	1	1	yes	characteristic
90	#16863455	C₂²	1	2	yes	—
91	#16863455	C₂²	1	2	yes	—
92	#16863455	C₂²	1	2	yes	—
93	#16863455	C₂²	1	2	yes	—
94	#16863452	C₂²	1	2	yes	—
95	#16863452	C₂²	1	2	yes	—
96	#16863451	C₂²	1	2	yes	—
97	#16863451	C₂²	1	2	yes	—
98	#16863448	C₂²	1	2	yes	—
99	#16863448	C₂²	1	2	yes	—
100	#16863447	C₂²	1	2	yes	—
101	#16863447	C₂²	1	2	yes	—
102	#16863424	C₂²	1	1	yes	characteristic
103	#16863424	C₂²	1	1	yes	characteristic
104	#16863423	C₂²	1	1	yes	characteristic
105	#16863423	C₂²	1	1	yes	characteristic
106	#16863422	C₂²	1	1	yes	characteristic
107	#16863422	C₂²	1	1	yes	characteristic
108	#16863419	C₂²	1	1	yes	characteristic
109	#16863419	C₂²	1	1	yes	characteristic
110	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
111	#16863359	C₂²	1	1	yes	characteristic
112	#16863359	C₂²	1	1	yes	characteristic
113	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
114	C₂×(C₂×D₆₇)⋊C₈	C₂²	1	1	yes	characteristic
115	#16863354	C₂²	1	1	yes	characteristic
116	#16863354	C₂²	1	1	yes	characteristic
117	#16863352	C₂²	1	1	yes	characteristic
118	#16863352	C₂²	1	1	yes	characteristic
119	#16863351	C₂²	1	1	yes	characteristic
120	#16863351	C₂²	1	1	yes	characteristic
121	C₄×#11761612	C₂²	1	1	yes	characteristic
122	C₂×#14523953	C₂²	1	1	yes	characteristic
123	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
124	#533×C₆₇	C₂²	1	1	yes	characteristic
125	#446×C₆₇	C₂²	1	2	yes	complemented
126	#446×C₆₇	C₂²	1	2	yes	complemented
127	#446×C₆₇	C₂²	1	2	yes	complemented
128	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
129	#424×C₆₇	C₂²	1	1	yes	characteristic
130	#424×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
132	#405×C₆₇	C₂²	1	1	yes	characteristic
133	#405×C₆₇	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
135	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
136	C₂×#11761612	C₂³	1	1	yes	characteristic
137	C₂×#11761612	C₂³	1	1	yes	characteristic
138	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
140	#14524043	C₂×C₄	1	1	yes	characteristic
141	#14524043	C₂×C₄	1	1	yes	characteristic
142	#14524042	C₂×C₄	1	1	yes	characteristic
143	#14524042	C₂×C₄	1	1	yes	characteristic
144	#14524042	C₂×C₄	1	1	yes	characteristic
145	#14524042	C₂×C₄	1	1	yes	characteristic
146	#14524042	C₂×C₄	1	2	yes	—
147	#14524042	C₂×C₄	1	2	yes	—
148	#14524042	C₂×C₄	1	2	yes	—
149	#14524042	C₂×C₄	1	2	yes	—
150	#14524041	C₂×C₄	1	2	yes	—
151	#14524041	C₂×C₄	1	2	yes	—
152	#14524041	C₂×C₄	1	2	yes	—
153	#14524041	C₂×C₄	1	2	yes	—
154	#14524035	C₂×C₄	1	1	yes	characteristic
155	#14524035	C₂×C₄	1	1	yes	characteristic
156	#14524034	C₂×C₄	1	1	yes	characteristic
157	#14524034	C₂×C₄	1	1	yes	characteristic
158	#14524034	C₂×C₄	1	1	yes	characteristic
159	#14524034	C₂×C₄	1	1	yes	characteristic
160	#14524033	C₂×C₄	1	2	yes	—
161	#14524033	C₂×C₄	1	2	yes	—
162	#14524033	C₂×C₄	1	2	yes	—
163	#14524033	C₂×C₄	1	2	yes	—
164	#14524033	C₂×C₄	1	2	yes	—
165	#14524033	C₂×C₄	1	2	yes	—
166	#14524033	C₂×C₄	1	2	yes	—
167	#14524033	C₂×C₄	1	2	yes	—
168	#14524023	C₂×C₄	1	2	yes	—
169	#14524023	C₂×C₄	1	2	yes	—
170	#14524023	C₂×C₄	1	2	yes	—
171	#14524023	C₂×C₄	1	2	yes	—
172	#14524022	C₂×C₄	1	2	yes	—
173	#14524022	C₂×C₄	1	2	yes	—
174	#14524021	C₂×C₄	1	2	yes	—
175	#14524021	C₂×C₄	1	2	yes	—
176	#14524021	C₂×C₄	1	2	yes	—
177	#14524021	C₂×C₄	1	2	yes	—
178	#14524021	C₂×C₄	1	2	yes	—
179	#14524021	C₂×C₄	1	2	yes	—
180	#14524021	C₂×C₄	1	2	yes	—
181	#14524021	C₂×C₄	1	2	yes	—
182	#14524020	C₂×C₄	1	2	yes	—
183	#14524020	C₂×C₄	1	2	yes	—
184	#14524020	C₂×C₄	1	2	yes	—
185	#14524020	C₂×C₄	1	2	yes	—
186	#14524019	C₂×C₄	1	2	yes	—
187	#14524019	C₂×C₄	1	2	yes	—
188	#14524019	C₂×C₄	1	2	yes	—
189	#14524019	C₂×C₄	1	2	yes	—
190	C₄×Dic₁₃₄	C₂³	1	2	yes	—
191	C₄×Dic₁₃₄	C₂³	1	2	yes	—
192	C₄×Dic₁₃₄	C₂³	1	2	yes	—
193	C₄×Dic₁₃₄	C₂³	1	2	yes	—
194	C₄×Dic₁₃₄	C₂³	1	2	yes	—
195	C₄×Dic₁₃₄	C₂³	1	2	yes	—
196	#14524002	C₂³	1	1	yes	characteristic
197	#14524002	C₂³	1	1	yes	characteristic
198	#14524001	C₂×C₄	1	1	yes	characteristic
199	#14524001	C₂×C₄	1	1	yes	characteristic
200	#14524001	C₂×C₄	1	1	yes	characteristic
201	#14524001	C₂×C₄	1	1	yes	characteristic
202	#14524000	C₂×C₄	1	1	yes	characteristic
203	#14524000	C₂×C₄	1	1	yes	characteristic
204	#14524000	C₂×C₄	1	1	yes	characteristic
205	#14524000	C₂×C₄	1	1	yes	characteristic
206	#14524000	C₂³	1	2	yes	—
207	#14524000	C₂³	1	2	yes	—
208	#14524000	C₂³	1	1	yes	characteristic
209	#14524000	C₂³	1	1	yes	characteristic
210	#14524000	C₂³	1	1	yes	characteristic
211	#14524000	C₂³	1	1	yes	characteristic
212	#14523999	C₂×C₄	1	2	yes	—
213	#14523999	C₂×C₄	1	2	yes	—
214	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
215	C₂×Dic₆₇⋊C₄	C₂×C₄	1	1	yes	characteristic
216	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
217	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
218	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
219	C₄⋊C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
220	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
221	C₂×(C₂×D₆₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
222	C₂²⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
223	C₂²⋊C₄×D₆₇	C₂×C₄	1	2	yes	—
224	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
225	C₄²×D₆₇	C₂³	1	2	yes	—
226	C₄²×D₆₇	C₂³	1	2	yes	—
227	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
228	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
229	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
230	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
231	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
232	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
233	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
234	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
235	Dic₆₇⋊C₈	C₂³	1	2	yes	—
236	Dic₆₇⋊C₈	C₂³	1	2	yes	—
237	Dic₆₇⋊C₈	C₂³	1	2	yes	—
238	Dic₆₇⋊C₈	C₂³	1	2	yes	—
239	Dic₆₇⋊C₈	C₂³	1	2	yes	—
240	Dic₆₇⋊C₈	C₂³	1	2	yes	—
241	Dic₆₇⋊C₈	C₂³	1	2	yes	—
242	Dic₆₇⋊C₈	C₂³	1	2	yes	—
243	Dic₆₇⋊C₈	C₂³	1	2	yes	—
244	Dic₆₇⋊C₈	C₂³	1	2	yes	—
245	Dic₆₇⋊C₈	C₂³	1	2	yes	—
246	Dic₆₇⋊C₈	C₂³	1	2	yes	—
247	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
248	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
249	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
250	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
251	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
252	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
253	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
254	(C₂×D₆₇)⋊C₈	C₂³	1	1	yes	characteristic
255	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
256	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
257	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
258	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
259	#14523954	C₂³	1	2	yes	—
260	#14523954	C₂³	1	2	yes	—
261	#14523954	C₂³	1	2	yes	—
262	#14523953	C₂³	1	1	yes	characteristic
263	#14523953	C₂³	1	2	yes	—
264	#14523953	C₂³	1	1	yes	characteristic
265	#14523953	C₂³	1	2	yes	—
266	#14523953	C₂³	1	2	yes	—
267	#14523953	C₂³	1	1	yes	characteristic
268	#14523953	C₂³	1	2	yes	—
269	#14523953	C₂³	1	1	yes	characteristic
270	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
271	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
272	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
273	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
274	C₈×Dic₆₇	C₂³	1	2	yes	—
275	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
276	C₈×Dic₆₇	C₂³	1	2	yes	—
277	C₈×Dic₆₇	C₂³	1	2	yes	—
278	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
279	C₈×Dic₆₇	C₂³	1	2	yes	—
280	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
281	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
286	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
287	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
288	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
289	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
290	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
291	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
292	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
297	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
298	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
299	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
301	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
302	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
304	#97×C₆₇	C₂³	1	2	yes	—
305	#97×C₆₇	C₂³	1	2	yes	—
306	#97×C₆₇	C₂³	1	2	yes	—
307	C₄×C₈×C₆₇	C₂³	1	2	yes	—
308	C₄×C₈×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	2	yes	—
310	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
311	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
312	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
313	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
314	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
315	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
316	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
317	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
318	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
319	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
320	C₂×C₄×D₆₇	—	2	2	no	—
321	C₂×C₄×D₆₇	—	2	2	no	—
322	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
325	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
326	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
327	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
328	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
330	#11761612	—	2	2	no	—
331	#11761612	—	2	2	no	—
332	C₂×C₆₇⋊C₈	—	2	2	no	—
333	C₂×C₆₇⋊C₈	—	2	2	no	—
334	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
335	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
336	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
337	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
338	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
339	C₂×C₆₇⋊C₈	C₂⁴	1	1	yes	characteristic
340	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
341	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
342	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
343	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
344	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
345	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
346	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
347	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
348	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
349	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
350	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
351	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
352	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
353	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
354	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
355	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
356	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
357	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
358	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
359	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
360	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
361	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
362	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
363	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
364	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
365	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
366	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
367	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
368	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
369	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
370	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
371	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
372	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
373	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
374	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
376	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
377	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
378	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
379	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
380	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
381	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
382	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
383	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
384	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
385	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
386	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
389	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
390	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
391	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
392	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
393	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
394	C₄×Dic₆₇	C₂⁴	1	2	yes	—
395	C₄×Dic₆₇	C₂⁴	1	2	yes	—
396	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
398	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
399	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	M₁₆×C₆₇	—	2	2	no	—
404	M₁₆×C₆₇	—	2	2	no	—
405	C₂×C₈×C₆₇	—	2	2	no	—
406	C₂×C₈×C₆₇	—	2	2	no	—
407	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
412	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
425	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
426	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
427	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
429	C₄²×C₆₇	C₂⁴	1	2	yes	—
430	C₄²×C₆₇	C₂⁴	1	2	yes	—
431	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
432	C₂²×D₆₇	—	2	2	no	—
433	C₂²×D₆₇	—	4	1	no	—
434	C₂²×D₆₇	—	4	1	no	—
435	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
436	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
437	Q₈×C₆₇	—	4	2	no	—
438	Q₈×C₆₇	—	4	2	no	—
439	C₂×C₄×C₆₇	—	4	1	no	—
440	C₂×C₄×C₆₇	—	4	1	no	—
441	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
442	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
444	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
445	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
451	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
452	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
453	C₂×Dic₆₇	—	2	2	no	—
454	C₂×Dic₆₇	—	4	1	no	—
455	C₂×Dic₆₇	—	4	1	no	—
456	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
457	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
458	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
459	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
460	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
461	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
462	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
463	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
464	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
465	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
466	C₄×D₆₇	—	2	2	no	—
467	C₄×D₆₇	—	2	2	no	—
468	C₄×D₆₇	—	2	1	no	—
469	C₄×D₆₇	—	2	1	no	—
470	C₄×D₆₇	—	2	1	no	—
471	C₄×D₆₇	—	2	1	no	—
472	C₄×D₆₇	—	4	2	no	—
473	C₄×D₆₇	—	4	2	no	—
474	C₄×D₆₇	—	4	2	no	—
475	C₄×D₆₇	—	4	2	no	—
476	Dic₁₃₄	—	4	2	no	—
477	Dic₁₃₄	—	4	2	no	—
478	Dic₁₃₄	—	4	2	no	—
479	Dic₁₃₄	—	4	2	no	—
480	Dic₁₃₄	—	4	2	no	—
481	Dic₁₃₄	—	4	2	no	—
482	C₈×C₆₇	—	2	1	no	—
483	C₈×C₆₇	—	2	1	no	—
484	C₈×C₆₇	—	2	1	no	—
485	C₈×C₆₇	—	2	1	no	—
486	C₈×C₆₇	—	2	2	no	—
487	C₈×C₆₇	—	2	2	no	—
488	C₆₇⋊C₈	—	2	1	no	—
489	C₆₇⋊C₈	—	2	1	no	—
490	C₆₇⋊C₈	—	2	1	no	—
491	C₆₇⋊C₈	—	2	1	no	—
492	C₆₇⋊C₈	—	2	2	no	—
493	C₆₇⋊C₈	—	2	2	no	—
494	C₂²×C₆₇	—	2	1	no	—
495	C₂²×C₆₇	—	2	1	no	—
496	C₂²×C₆₇	#519	1	2	yes	—
497	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
498	C₂×D₆₇	—	2	1	no	—
499	C₂×D₆₇	—	2	1	no	—
500	C₂×D₆₇	—	2	1	no	—
501	C₂×D₆₇	—	2	1	no	—
502	C₂×D₆₇	—	2	1	no	—
503	C₂×D₆₇	—	2	1	no	—
504	C₂×D₆₇	—	8	2	no	—
505	C₄×C₆₇	—	2	1	no	—
506	C₄×C₆₇	—	2	1	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	—	2	2	no	—
510	C₄×C₆₇	—	2	2	no	—
511	C₄×C₆₇	—	2	1	no	—
512	C₄×C₆₇	—	2	1	no	—
513	C₄×C₆₇	#519	1	2	yes	—
514	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	Dic₆₇	—	2	1	no	—
517	Dic₆₇	—	2	1	no	—
518	Dic₆₇	—	2	2	no	—
519	Dic₆₇	—	2	2	no	—
520	Dic₆₇	—	2	2	no	—
521	Dic₆₇	—	2	2	no	—
522	Dic₆₇	—	2	1	no	—
523	Dic₆₇	—	2	1	no	—
524	Dic₆₇	—	2	1	no	—
525	Dic₆₇	—	2	1	no	—
526	#60252	—	67	1	no	maximal, Sylow
527	C₂×C₆₇	—	2	2	no	—
528	C₂×C₆₇	C₂×#519	1	1	yes	characteristic
529	C₂×C₆₇	#3573	1	1	yes	characteristic
530	C₂×C₆₇	#3573	1	1	yes	characteristic
531	D₆₇	—	4	1	no	—
532	D₆₇	—	4	1	no	—
533	#3458	—	67	1	no	—
534	#2987	—	67	2	no	—
535	#2987	—	67	2	no	—
536	#2986	—	67	2	no	—
537	#2986	—	67	2	no	—
538	#2985	—	67	2	no	—
539	#2985	—	67	2	no	—
540	#2985	—	67	2	no	—
541	#2985	—	67	2	no	—
542	#2962	—	67	1	no	—
543	#2962	—	67	1	no	—
544	#2962	—	67	1	no	—
545	#2962	D₆₇	1	1	yes	characteristic, complemented
546	#2961	—	67	1	no	—
547	#2961	—	67	1	no	—
548	#2960	—	67	1	no	—
549	#2960	—	67	1	no	—
550	#2924	—	67	1	no	—
551	#2924	—	67	1	no	—
552	#2924	—	67	1	no	—
553	#2924	—	67	1	no	—
554	#2921	—	67	1	no	—
555	C₂×#433	—	67	1	no	—
556	C₆₇	#60252	1	1	yes	characteristic, complemented, Sylow
557	#544	—	67	1	no	—
558	#544	—	67	1	no	—
559	#544	—	67	1	no	—
560	#544	—	67	1	no	—
561	#544	—	67	1	no	—
562	#544	—	67	1	no	—
563	#544	—	67	1	no	—
564	#544	—	67	1	no	—
565	#544	—	67	2	no	—
566	#544	—	67	2	no	—
567	#543	—	67	2	no	—
568	#543	—	67	2	no	—
569	#533	—	67	2	no	—
570	#533	—	67	2	no	—
571	#533	—	67	2	no	—
572	#533	—	67	2	no	—
573	#533	—	67	1	no	—
574	#533	—	67	1	no	—
575	#533	—	67	1	no	—
576	#533	C₂×D₆₇	1	1	yes	characteristic
577	C₂×#117	—	67	1	no	—
578	C₂×#117	—	67	1	no	—
579	C₂×#117	—	67	1	no	—
580	#446	—	67	2	no	—
581	#446	—	67	2	no	—
582	#446	—	67	2	no	—
583	#446	—	67	2	no	—
584	#446	—	67	2	no	—
585	#446	—	67	2	no	—
586	#446	—	67	2	no	—
587	#446	—	67	2	no	—
588	#446	—	67	2	no	—
589	#446	—	67	2	no	—
590	#446	—	67	2	no	—
591	#446	—	67	2	no	—
592	#446	—	67	2	no	—
593	#446	—	67	2	no	—
594	#446	—	67	2	no	—
595	#446	—	67	2	no	—
596	#446	—	67	2	no	—
597	#446	—	67	2	no	—
598	#446	—	67	2	no	—
599	#446	—	67	2	no	—
600	#446	—	67	2	no	—
601	#446	C₂×D₆₇	1	2	yes	complemented
602	#446	C₂×D₆₇	1	2	yes	complemented
603	#446	C₂×D₆₇	1	2	yes	complemented
604	C₈×Q₈	—	67	2	no	—
605	C₈×Q₈	—	67	2	no	—
606	C₈×Q₈	—	67	2	no	—
607	C₈×Q₈	—	67	2	no	—
608	C₈×Q₈	—	67	2	no	—
609	C₈×Q₈	—	67	2	no	—
610	C₈×Q₈	—	67	2	no	—
611	C₈×Q₈	C₂×D₆₇	1	2	yes	complemented
612	#433	—	67	1	no	—
613	#433	—	67	1	no	—
614	#433	—	67	1	no	—
615	#433	—	67	1	no	—
616	#433	—	67	1	no	—
617	#433	—	67	1	no	—
618	#433	—	67	1	no	—
619	#433	—	67	1	no	—
620	#433	—	67	2	no	—
621	#433	—	67	2	no	—
622	#433	—	67	2	no	—
623	#433	—	67	2	no	—
624	#433	—	67	2	no	—
625	#433	—	67	2	no	—
626	#433	—	67	2	no	—
627	#433	—	67	2	no	—
628	#433	—	67	2	no	—
629	#433	—	67	2	no	—
630	#433	—	67	2	no	—
631	#433	—	67	2	no	—
632	#432	—	67	2	no	—
633	#432	—	67	2	no	—
634	#432	—	67	2	no	—
635	#432	—	67	2	no	—
636	#431	—	67	2	no	—
637	#431	—	67	2	no	—
638	#431	—	67	2	no	—
639	#431	—	67	2	no	—
640	#424	—	67	1	no	—
641	#424	—	67	1	no	—
642	#424	—	67	1	no	—
643	#424	—	67	1	no	—
644	#424	—	67	1	no	—
645	#424	—	67	1	no	—
646	#424	C₂×D₆₇	1	1	yes	characteristic
647	#424	C₂×D₆₇	1	1	yes	characteristic
648	#423	—	67	1	no	—
649	#423	—	67	1	no	—
650	C₂×C₄⋊C₈	—	67	1	no	—
651	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
652	#407	—	67	1	no	—
653	#407	—	67	1	no	—
654	C₂×C₂²⋊C₈	—	67	1	no	—
655	C₂×C₂²⋊C₈	—	67	1	no	—
656	#405	—	67	1	no	—
657	#405	—	67	1	no	—
658	#405	—	67	1	no	—
659	#405	—	67	1	no	—
660	#405	—	67	1	no	—
661	#405	—	67	1	no	—
662	#405	C₂×D₆₇	1	1	yes	characteristic
663	#405	C₂×D₆₇	1	1	yes	characteristic
664	C₄×M₁₆	—	67	1	no	—
665	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
666	C₂×#97	—	67	1	no	—
667	C₂×C₄×C₈	—	67	1	no	—
668	C₂³×C₄	—	67	1	no	—
669	C₂×M₁₆	—	67	1	no	—
670	C₂×M₁₆	—	67	1	no	—
671	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
672	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
673	C₂²×C₈	—	67	1	no	—
674	C₂²×C₈	—	67	1	no	—
675	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
676	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
677	C₄⋊Q₈	—	67	2	no	—
678	C₄⋊Q₈	—	67	2	no	—
679	C₄⋊Q₈	—	67	2	no	—
680	C₄⋊Q₈	—	67	2	no	—
681	C₄⋊Q₈	—	67	2	no	—
682	C₄⋊Q₈	—	67	2	no	—
683	C₄⋊Q₈	—	67	2	no	—
684	C₄⋊Q₈	—	67	2	no	—
685	C₄⋊Q₈	—	67	1	no	—
686	C₄⋊Q₈	—	67	1	no	—
687	C₄⋊Q₈	—	67	1	no	—
688	C₄⋊Q₈	—	67	1	no	—
689	C₄⋊Q₈	—	67	1	no	—
690	C₄⋊Q₈	—	67	1	no	—
691	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
692	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
693	#125	—	67	2	no	—
694	#125	—	67	2	no	—
695	#125	—	67	2	no	—
696	#125	—	67	2	no	—
697	#125	—	67	2	no	—
698	#125	—	67	2	no	—
699	#125	—	67	2	no	—
700	#125	—	67	2	no	—
701	#125	—	67	1	no	—
702	#125	—	67	1	no	—
703	#125	—	67	1	no	—
704	#125	—	67	1	no	—
705	#125	—	67	1	no	—
706	#125	—	67	1	no	—
707	#125	C₄×D₆₇	1	1	yes	characteristic
708	#125	C₄×D₆₇	1	1	yes	characteristic
709	C₂²⋊Q₈	—	67	2	no	—
710	C₂²⋊Q₈	—	67	2	no	—
711	C₂²⋊Q₈	—	67	2	no	—
712	C₂²⋊Q₈	—	67	2	no	—
713	C₂²⋊Q₈	—	67	2	no	—
714	C₂²⋊Q₈	—	67	2	no	—
715	C₂²⋊Q₈	—	67	2	no	—
716	C₂²⋊Q₈	—	67	2	no	—
717	C₂²⋊Q₈	—	67	2	no	—
718	C₂²⋊Q₈	—	67	2	no	—
719	C₂²⋊Q₈	—	67	2	no	—
720	C₂²⋊Q₈	—	67	2	no	—
721	C₂²⋊Q₈	—	67	2	no	—
722	C₂²⋊Q₈	—	67	2	no	—
723	C₂²⋊Q₈	—	67	2	no	—
724	C₂²⋊Q₈	—	67	2	no	—
725	C₂²⋊Q₈	—	67	2	no	—
726	C₂²⋊Q₈	—	67	2	no	—
727	C₂²⋊Q₈	—	67	2	no	—
728	C₂²⋊Q₈	—	67	2	no	—
729	C₂²⋊Q₈	—	67	2	no	—
730	C₂²⋊Q₈	—	67	2	no	—
731	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
732	C₂²⋊Q₈	C₄×D₆₇	1	2	yes	—
733	C₄×Q₈	—	67	2	no	—
734	C₄×Q₈	—	67	2	no	—
735	C₄×Q₈	—	67	2	no	—
736	C₄×Q₈	—	67	2	no	—
737	C₄×Q₈	—	67	2	no	—
738	C₄×Q₈	—	67	2	no	—
739	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
740	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
741	#117	—	67	1	no	—
742	#117	—	67	1	no	—
743	#117	—	67	1	no	—
744	#117	—	67	1	no	—
745	#117	—	67	1	no	—
746	#117	—	67	1	no	—
747	#117	—	67	2	no	—
748	#117	—	67	2	no	—
749	#117	—	67	1	no	—
750	#117	—	67	1	no	—
751	#117	—	67	1	no	—
752	#117	—	67	1	no	—
753	#117	—	67	1	no	—
754	#117	—	67	1	no	—
755	#117	—	67	2	no	—
756	#117	—	67	2	no	—
757	#117	—	67	1	no	—
758	#117	—	67	1	no	—
759	#117	C₂²×D₆₇	1	1	yes	characteristic
760	#117	C₂²×D₆₇	1	1	yes	characteristic
761	C₂×C₄⋊C₄	—	67	1	no	—
762	C₂×C₄⋊C₄	—	67	1	no	—
763	C₂×C₄⋊C₄	—	67	1	no	—
764	C₂×C₄⋊C₄	—	67	1	no	—
765	C₂×C₄⋊C₄	—	67	1	no	—
766	C₂×C₄⋊C₄	—	67	1	no	—
767	C₂×C₂²⋊C₄	—	67	1	no	—
768	C₂×C₂²⋊C₄	—	67	1	no	—
769	C₂×C₂²⋊C₄	—	67	2	no	—
770	C₂×C₂²⋊C₄	—	67	2	no	—
771	C₂×C₄²	—	67	1	no	—
772	C₂×C₄²	—	67	2	no	—
773	C₂×C₄²	—	67	2	no	—
774	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
775	C₄⋊C₈	—	67	2	no	—
776	C₄⋊C₈	—	67	2	no	—
777	C₄⋊C₈	—	67	2	no	—
778	C₄⋊C₈	—	67	2	no	—
779	C₄⋊C₈	—	67	2	no	—
780	C₄⋊C₈	—	67	2	no	—
781	C₄⋊C₈	—	67	2	no	—
782	C₄⋊C₈	—	67	2	no	—
783	C₄⋊C₈	—	67	2	no	—
784	C₄⋊C₈	—	67	2	no	—
785	C₄⋊C₈	—	67	2	no	—
786	C₄⋊C₈	—	67	2	no	—
787	C₄⋊C₈	—	67	1	no	—
788	C₄⋊C₈	—	67	1	no	—
789	C₄⋊C₈	—	67	1	no	—
790	C₄⋊C₈	—	67	1	no	—
791	C₄⋊C₈	—	67	2	no	—
792	C₄⋊C₈	—	67	2	no	—
793	C₄⋊C₈	—	67	2	no	—
794	C₄⋊C₈	—	67	2	no	—
795	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
796	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
797	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
798	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
799	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
800	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
801	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
802	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
803	C₂²⋊C₈	—	67	1	no	—
804	C₂²⋊C₈	—	67	1	no	—
805	C₂²⋊C₈	—	67	1	no	—
806	C₂²⋊C₈	—	67	1	no	—
807	C₂²⋊C₈	—	67	1	no	—
808	C₂²⋊C₈	—	67	1	no	—
809	C₂²⋊C₈	—	67	1	no	—
810	C₂²⋊C₈	—	67	1	no	—
811	C₂²⋊C₈	—	67	2	no	—
812	C₂²⋊C₈	—	67	2	no	—
813	C₂²⋊C₈	—	67	2	no	—
814	C₂²⋊C₈	—	67	2	no	—
815	#97	—	67	1	no	—
816	#97	—	67	1	no	—
817	#97	—	67	1	no	—
818	#97	—	67	1	no	—
819	#97	—	67	2	no	—
820	#97	—	67	2	no	—
821	#97	—	67	2	no	—
822	#97	—	67	2	no	—
823	#97	—	67	2	no	—
824	#97	—	67	2	no	—
825	#97	—	67	2	no	—
826	#97	C₂²×D₆₇	1	2	yes	—
827	#97	C₂²×D₆₇	1	2	yes	—
828	#97	C₂²×D₆₇	1	2	yes	—
829	C₄×C₈	—	67	1	no	—
830	C₄×C₈	—	67	1	no	—
831	C₄×C₈	—	67	1	no	—
832	C₄×C₈	—	67	1	no	—
833	C₄×C₈	—	67	2	no	—
834	C₄×C₈	—	67	2	no	—
835	C₄×C₈	—	67	2	no	—
836	C₄×C₈	—	67	2	no	—
837	C₄×C₈	—	67	2	no	—
838	C₄×C₈	—	67	2	no	—
839	C₄×C₈	—	67	2	no	—
840	C₄×C₈	C₂²×D₆₇	1	2	yes	—
841	C₄×C₈	C₂²×D₆₇	1	2	yes	—
842	C₄×C₈	C₂²×D₆₇	1	2	yes	—
843	C₂⁴	—	67	1	no	—
844	C₂×Q₈	—	67	2	no	—
845	C₂×Q₈	—	67	2	no	—
846	C₂×Q₈	—	67	2	no	—
847	C₂×Q₈	—	67	2	no	—
848	C₂×Q₈	—	67	2	no	—
849	C₂×Q₈	—	67	2	no	—
850	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
851	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
852	C₂²×C₄	—	67	1	no	—
853	C₂²×C₄	—	67	1	no	—
854	C₂²×C₄	—	67	2	no	—
855	C₂²×C₄	—	67	2	no	—
856	C₂²×C₄	—	67	2	no	—
857	C₂²×C₄	—	67	2	no	—
858	C₂²×C₄	—	67	1	no	—
859	C₂²×C₄	—	67	1	no	—
860	C₂²×C₄	—	67	1	no	—
861	C₂²×C₄	—	67	1	no	—
862	C₂²×C₄	—	67	1	no	—
863	C₂²×C₄	—	134	2	no	—
864	C₂²×C₄	—	134	2	no	—
865	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
866	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
867	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	2	no	—
870	M₁₆	—	134	2	no	—
871	M₁₆	—	134	2	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	2	no	—
874	C₂×C₈	—	67	1	no	—
875	C₂×C₈	—	67	2	no	—
876	C₂×C₈	—	67	2	no	—
877	C₂×C₈	—	67	1	no	—
878	C₂×C₈	—	67	1	no	—
879	C₂×C₈	—	67	1	no	—
880	C₂×C₈	—	134	2	no	—
881	C₂×C₈	—	134	2	no	—
882	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₆₇	1	2	yes	—
884	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₆₇	1	2	yes	—
887	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
888	C₄⋊C₄	—	67	2	no	—
889	C₄⋊C₄	—	67	2	no	—
890	C₄⋊C₄	—	67	2	no	—
891	C₄⋊C₄	—	67	2	no	—
892	C₄⋊C₄	—	67	1	no	—
893	C₄⋊C₄	—	67	1	no	—
894	C₄⋊C₄	—	67	1	no	—
895	C₄⋊C₄	—	67	1	no	—
896	C₄⋊C₄	—	67	1	no	—
897	C₄⋊C₄	—	67	1	no	—
898	C₄⋊C₄	—	67	1	no	—
899	C₄⋊C₄	—	67	1	no	—
900	C₄⋊C₄	—	67	1	no	—
901	C₄⋊C₄	—	67	1	no	—
902	C₄⋊C₄	—	67	1	no	—
903	C₄⋊C₄	—	67	1	no	—
904	C₄⋊C₄	—	67	2	no	—
905	C₄⋊C₄	—	67	2	no	—
906	C₄⋊C₄	—	67	2	no	—
907	C₄⋊C₄	—	67	2	no	—
908	C₄⋊C₄	—	67	2	no	—
909	C₄⋊C₄	—	67	2	no	—
910	C₄⋊C₄	—	67	2	no	—
911	C₄⋊C₄	—	67	2	no	—
912	C₄⋊C₄	—	67	2	no	—
913	C₄⋊C₄	—	67	2	no	—
914	C₄⋊C₄	—	67	2	no	—
915	C₄⋊C₄	—	67	2	no	—
916	C₄⋊C₄	—	67	2	no	—
917	C₄⋊C₄	—	67	2	no	—
918	C₄⋊C₄	—	67	2	no	—
919	C₄⋊C₄	—	67	2	no	—
920	C₄⋊C₄	—	67	2	no	—
921	C₄⋊C₄	—	67	2	no	—
922	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
923	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
925	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
927	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
928	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
929	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
930	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
931	C₄⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
932	C₂²⋊C₄	—	67	2	no	—
933	C₂²⋊C₄	—	67	2	no	—
934	C₂²⋊C₄	—	67	2	no	—
935	C₂²⋊C₄	—	67	2	no	—
936	C₂²⋊C₄	—	67	2	no	—
937	C₂²⋊C₄	—	67	2	no	—
938	C₂²⋊C₄	—	67	1	no	—
939	C₂²⋊C₄	—	67	1	no	—
940	C₂²⋊C₄	—	67	1	no	—
941	C₂²⋊C₄	—	67	1	no	—
942	C₂²⋊C₄	—	67	1	no	—
943	C₂²⋊C₄	—	67	1	no	—
944	C₂²⋊C₄	—	67	1	no	—
945	C₂²⋊C₄	—	67	1	no	—
946	C₂²⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
947	C₂²⋊C₄	C₂×C₄×D₆₇	1	2	yes	—
948	C₄²	—	67	2	no	—
949	C₄²	—	67	2	no	—
950	C₄²	—	67	2	no	—
951	C₄²	—	67	2	no	—
952	C₄²	—	67	1	no	—
953	C₄²	—	67	1	no	—
954	C₄²	—	67	1	no	—
955	C₄²	—	67	1	no	—
956	C₄²	—	67	2	no	—
957	C₄²	—	67	2	no	—
958	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
959	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
960	C₄²	C₂³×D₆₇	1	1	yes	characteristic
961	C₄²	C₂³×D₆₇	1	2	yes	—
962	C₄²	C₂³×D₆₇	1	2	yes	—
963	C₄²	C₂³×D₆₇	1	1	yes	characteristic
964	C₂³	—	268	1	no	—
965	C₂³	—	268	1	no	—
966	C₂³	—	67	1	no	—
967	C₂³	—	67	1	no	—
968	C₂³	—	134	2	no	—
969	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	268	2	no	—
973	Q₈	—	268	2	no	—
974	Q₈	—	268	2	no	—
975	Q₈	—	268	2	no	—
976	Q₈	—	268	2	no	—
977	Q₈	—	268	2	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	268	2	no	—
981	C₂×C₄	—	268	2	no	—
982	C₂×C₄	—	268	2	no	—
983	C₂×C₄	—	268	2	no	—
984	C₂×C₄	—	268	1	no	—
985	C₂×C₄	—	268	1	no	—
986	C₂×C₄	—	67	1	no	—
987	C₂×C₄	—	67	1	no	—
988	C₂×C₄	—	67	2	no	—
989	C₂×C₄	—	67	2	no	—
990	C₂×C₄	—	67	1	no	—
991	C₂×C₄	—	67	1	no	—
992	C₂×C₄	—	67	2	no	—
993	C₂×C₄	—	67	2	no	—
994	C₂×C₄	—	67	1	no	—
995	C₂×C₄	—	67	1	no	—
996	C₂×C₄	—	134	2	no	—
997	C₂×C₄	—	134	2	no	—
998	C₂×C₄	—	134	2	no	—
999	C₂×C₄	—	134	1	no	—
1000	C₂×C₄	—	134	1	no	—
1001	C₂×C₄	—	134	1	no	—
1002	C₂×C₄	—	134	1	no	—
1003	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1004	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1005	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1006	C₂×C₄	C₂²×C₄×D₆₇	1	2	yes	—
1007	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1008	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1009	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1010	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1011	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1012	C₂×C₄	#14524090	1	2	yes	—
1013	C₂×C₄	#14524091	1	2	yes	—
1014	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₈	—	134	2	no	—
1022	C₈	—	134	1	no	—
1023	C₈	—	134	1	no	—
1024	C₈	—	134	1	no	—
1025	C₈	—	134	1	no	—
1026	C₈	—	134	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	536	2	no	—
1030	C₂²	—	134	1	no	—
1031	C₂²	—	134	1	no	—
1032	C₂²	—	134	1	no	—
1033	C₂²	—	134	1	no	—
1034	C₂²	—	134	1	no	—
1035	C₂²	—	134	1	no	—
1036	C₂²	#16863872	1	2	yes	—
1037	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	134	2	no	—
1047	C₄	—	134	2	no	—
1048	C₄	—	134	1	no	—
1049	C₄	—	134	1	no	—
1050	C₄	—	134	2	no	—
1051	C₄	—	134	2	no	—
1052	C₄	—	134	1	no	—
1053	C₄	—	134	1	no	—
1054	C₄	—	134	1	no	—
1055	C₄	—	134	1	no	—
1056	C₄	#16863872	1	2	yes	—
1057	C₄	C₂×#14524090	1	1	yes	characteristic
1058	C₄	C₂×#14524091	1	1	yes	characteristic
1059	C₂	—	2	2	no	—
1060	C₂	—	268	1	no	—
1061	C₂	—	268	1	no	—
1062	C₂	C₂×#16863872	1	1	yes	characteristic
1063	C₂	#22574920	1	1	yes	characteristic
1064	C₂	#22574922	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₆₇×#2962	C₂
prime radical	C₂³×D₆₇	C₂²×C₄
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2962	D₆₇
hypocenter	C₆₇	#60252
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #22569312	C₂	semidirect
3. #22569312	C₂	semidirect
4. #22569309	C₂	semidirect
5. #22569307	C₂	semidirect
6. #22569305	C₂	semidirect
7. #22569302	C₂	semidirect
8. #22569302	C₂	semidirect
9. #22569300	C₂	semidirect
10. #22569158	C₂	semidirect
11. #22569156	C₂	semidirect
12. #22569152	C₂	semidirect
13. #22569148	C₂	semidirect
14. #22569147	C₂	semidirect
15. #22569142	C₂	semidirect
16. #22569141	C₂	semidirect
23. C₆₇×#2962	C₂	semidirect
46. #16863527	C₂²	semidirect
47. #16863527	C₂²	semidirect
48. #16863527	C₂²	semidirect
49. #16863526	C₂²	semidirect
50. #16863526	C₂²	semidirect
51. #16863526	C₂²	semidirect
52. #16863525	C₂²	semidirect
53. #16863525	C₂²	semidirect
54. #16863525	C₂²	semidirect
55. #16863525	C₂²	semidirect
56. #16863525	C₂²	semidirect
57. #16863525	C₂²	semidirect
58. #16863524	C₂²	semidirect
59. #16863524	C₂²	semidirect
60. #16863524	C₂²	semidirect
61. #16863524	C₂²	semidirect
62. #16863524	C₂²	semidirect
63. #16863524	C₂²	semidirect
64. #16863523	C₂²	semidirect
65. #16863523	C₂²	semidirect
66. #16863523	C₂²	semidirect
67. Q₈×C₆₇⋊C₈	C₂²	semidirect
68. C₈×Dic₁₃₄	C₂²	semidirect
69. C₈×Dic₁₃₄	C₂²	semidirect
70. C₈×Dic₁₃₄	C₂²	semidirect
71. #16863520	C₂²	semidirect
72. #16863520	C₂²	semidirect
73. #16863520	C₂²	semidirect
125. #446×C₆₇	C₂²	semidirect
126. #446×C₆₇	C₂²	semidirect
127. #446×C₆₇	C₂²	semidirect
128. C₈×Q₈×C₆₇	C₂²	semidirect
545. #2962	D₆₇	semidirect
556. C₆₇	#60252	semidirect
601. #446	C₂×D₆₇	semidirect
602. #446	C₂×D₆₇	semidirect
603. #446	C₂×D₆₇	semidirect
611. C₈×Q₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573612	2
#22569312	2
#22569309	2
#22569307	2
#22569305	2
#22569302	2
#22569300	2
#22569158	2
#22569156	2
#22569152	2
#22569148	2
#22569147	2
#22569142	2
#22569141	2
#22568866	2
#22568864	2
#22568845	2
C₂×#16863456	2
C₆₇×#2962	2
#60252	67