Subgroups — #31720972

Order 17152.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573502	C₂	1	1	yes	maximal, characteristic
2	#22569366	C₂	1	2	yes	maximal, complemented
3	#22569362	C₂	1	2	yes	maximal, complemented
4	#22569347	C₂	1	2	yes	maximal, complemented
5	#22569344	C₂	1	2	yes	maximal, complemented
6	#22569336	C₂	1	1	yes	maximal, characteristic, complemented
7	#22569334	C₂	1	1	yes	maximal, characteristic, complemented
8	#22569331	C₂	1	1	yes	maximal, characteristic, complemented
9	#22569328	C₂	1	1	yes	maximal, characteristic, complemented
10	#22569323	C₂	1	1	yes	maximal, characteristic, complemented
11	#22569318	C₂	1	1	yes	maximal, characteristic, complemented
12	#22569317	C₂	1	1	yes	maximal, characteristic, complemented
13	#22569154	C₂	1	2	yes	maximal, complemented
14	#22568950	C₂	1	2	yes	maximal, complemented
15	#22568900	C₂	1	2	yes	maximal, complemented
16	#22568898	C₂	1	2	yes	maximal, complemented
17	#22568876	C₂	1	1	yes	maximal, characteristic, complemented
18	#22568870	C₂	1	1	yes	maximal, characteristic, complemented
19	#22568839	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568778	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568774	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524051	C₂²	1	2	yes	—
25	C₂×#14524049	C₂²	1	2	yes	—
26	C₂²×C₈×D₆₇	C₂²	1	2	yes	—
27	#16863950	C₄	1	1	yes	characteristic
28	#16863950	C₂²	1	1	yes	characteristic
29	#16863949	C₄	1	1	yes	characteristic
30	#16863943	C₄	1	1	yes	characteristic
31	#16863943	C₂²	1	1	yes	characteristic
32	#16863942	C₄	1	1	yes	characteristic
33	#16863933	C₄	1	1	yes	characteristic
34	#16863933	C₂²	1	1	yes	characteristic
35	#16863928	C₄	1	1	yes	characteristic
36	#16863928	C₂²	1	1	yes	characteristic
37	#16863926	C₄	1	1	yes	characteristic
38	#16863926	C₄	1	1	yes	characteristic
39	#16863926	C₂²	1	1	yes	characteristic
40	#16863926	C₂²	1	1	yes	characteristic
41	#16863924	C₄	1	1	yes	characteristic
42	#16863924	C₄	1	1	yes	characteristic
43	#16863924	C₄	1	1	yes	characteristic
44	#16863924	C₄	1	1	yes	characteristic
45	#16863908	C₄	1	1	yes	characteristic
46	#16863905	C₄	1	1	yes	characteristic
47	#16863905	C₄	1	1	yes	characteristic
48	#16863905	C₂²	1	1	yes	characteristic
49	#16863905	C₂²	1	1	yes	characteristic
50	#16863903	C₄	1	1	yes	characteristic
51	C₄×#11761628	C₂²	1	1	yes	characteristic
52	C₄×#11761628	C₂²	1	1	yes	characteristic
53	C₄×#11761628	C₂²	1	1	yes	characteristic
54	C₄×#11761628	C₂²	1	1	yes	characteristic
55	C₄×#11761628	C₂²	1	1	yes	characteristic
56	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
57	#16863527	C₂²	1	2	yes	complemented
58	#16863525	C₂²	1	2	yes	complemented
59	#16863525	C₂²	1	2	yes	complemented
60	#16863524	C₂²	1	2	yes	complemented
61	#16863524	C₂²	1	2	yes	complemented
62	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
63	#16863520	C₂²	1	2	yes	complemented
64	#16863472	C₂²	1	2	yes	complemented
65	#16863471	C₂²	1	2	yes	complemented
66	#16863470	C₂²	1	2	yes	—
67	#16863469	C₂²	1	2	yes	—
68	#16863469	C₂²	1	2	yes	complemented
69	#16863468	C₂²	1	2	yes	—
70	#16863468	C₂²	1	2	yes	complemented
71	#16863467	C₂²	1	2	yes	—
72	#16863466	C₂²	1	2	yes	—
73	#16863466	C₂²	1	2	yes	complemented
74	#16863465	C₂²	1	2	yes	—
75	#16863464	C₂²	1	2	yes	—
76	C₈×D₂₆₈	C₂²	1	2	yes	—
77	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
78	#16863461	C₂²	1	2	yes	—
79	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	—
80	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	—
81	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
82	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	—
83	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	—
84	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	complemented
85	#16863458	C₂²	1	2	yes	complemented
86	#16863455	C₂²	1	2	yes	complemented
87	#16863454	C₂²	1	2	yes	complemented
88	#16863454	C₂²	1	2	yes	complemented
89	#16863453	C₂²	1	1	yes	characteristic
90	#16863453	C₂²	1	1	yes	characteristic, complemented
91	#16863452	C₂²	1	1	yes	characteristic, complemented
92	#16863452	C₂²	1	1	yes	characteristic, complemented
93	#16863451	C₂²	1	2	yes	—
94	#16863449	C₂²	1	1	yes	characteristic, complemented
95	#16863448	C₂²	1	1	yes	characteristic
96	#16863448	C₂²	1	1	yes	characteristic
97	#16863448	C₂²	1	1	yes	characteristic, complemented
98	#16863448	C₂²	1	1	yes	characteristic, complemented
99	#16863446	C₂²	1	2	yes	—
100	#16863424	C₂²	1	2	yes	complemented
101	#16863422	C₂²	1	2	yes	complemented
102	#16863421	C₂²	1	2	yes	—
103	#16863421	C₂²	1	2	yes	—
104	#16863421	C₂²	1	2	yes	complemented
105	#16863421	C₂²	1	2	yes	complemented
106	#16863420	C₂²	1	1	yes	characteristic, complemented
107	#16863418	C₂²	1	1	yes	characteristic
108	#16863418	C₂²	1	1	yes	characteristic
109	#16863418	C₂²	1	1	yes	characteristic, complemented
110	#16863418	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
112	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
113	C₂×Dic₆₇⋊C₈	C₂²	1	2	yes	—
114	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
115	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
116	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
117	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
118	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
119	C₄⋊C₈×D₆₇	C₂²	1	2	yes	—
120	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
122	#16863361	C₂²	1	2	yes	—
123	#16863361	C₂²	1	2	yes	—
124	#16863358	C₂²	1	2	yes	—
125	#16863353	C₂²	1	2	yes	—
126	#16863350	C₂²	1	2	yes	—
127	#16863348	C₂²	1	2	yes	—
128	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
129	#446×C₆₇	C₂²	1	2	yes	complemented
130	#435×C₆₇	C₂²	1	2	yes	—
131	#435×C₆₇	C₂²	1	2	yes	complemented
132	C₈×D₄×C₆₇	C₂²	1	2	yes	—
133	#432×C₆₇	C₂²	1	1	yes	characteristic
134	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
138	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
140	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
141	C₂×#11761628	C₂×C₄	1	1	yes	characteristic
142	C₂×#11761628	C₂³	1	1	yes	characteristic
143	C₂×#11761628	C₂³	1	1	yes	characteristic
144	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
145	C₂²×C₄×D₆₇	C₂×C₄	1	1	yes	characteristic
146	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
147	#14524051	—	4	4	no	—
148	#14524049	—	4	4	no	—
149	C₂×#11761612	C₂³	1	2	yes	—
150	C₂×#11761611	C₂³	1	2	yes	—
151	C₂×#11761611	C₂³	1	2	yes	—
152	C₂×#11761611	C₂³	1	2	yes	—
153	C₂×#11761611	C₂³	1	2	yes	—
154	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
156	C₂×C₈×D₆₇	—	4	4	no	—
157	C₂×C₈×D₆₇	C₂³	1	2	yes	—
158	C₂×C₈×D₆₇	C₂³	1	2	yes	—
159	C₂×C₈×D₆₇	C₂³	1	2	yes	—
160	C₂×C₈×D₆₇	C₂³	1	2	yes	—
161	C₂×C₈×D₆₇	C₂³	1	2	yes	—
162	C₂×C₈×D₆₇	C₂³	1	2	yes	—
163	#14524042	C₂×C₄	1	1	yes	characteristic
164	#14524042	C₂×C₄	1	1	yes	characteristic
165	#14524041	C₂×C₄	1	1	yes	characteristic
166	#14524039	C₂×C₄	1	1	yes	characteristic
167	#14524038	C₂×C₄	1	1	yes	characteristic
168	#14524038	C₂×C₄	1	1	yes	characteristic
169	#14524038	C₂×C₄	1	1	yes	characteristic
170	#14524038	C₂×C₄	1	1	yes	characteristic
171	#14524036	C₂×C₄	1	1	yes	characteristic
172	#14524036	C₂×C₄	1	1	yes	characteristic
173	#14524036	C₂×C₄	1	1	yes	characteristic
174	#14524036	C₂×C₄	1	1	yes	characteristic
175	#14524034	C₂×C₄	1	1	yes	characteristic
176	#14524034	C₂×C₄	1	1	yes	characteristic
177	#14524033	C₂×C₄	1	1	yes	characteristic
178	#14524033	C₂×C₄	1	1	yes	characteristic
179	#14524033	C₂×C₄	1	1	yes	characteristic
180	#14524033	C₂×C₄	1	1	yes	characteristic
181	#14524032	C₂×C₄	1	1	yes	characteristic
182	#14524030	C₂×C₄	1	1	yes	characteristic
183	#14524029	C₂×C₄	1	1	yes	characteristic
184	#14524029	C₂×C₄	1	1	yes	characteristic
185	#14524029	C₂×C₄	1	1	yes	characteristic
186	#14524029	C₂×C₄	1	1	yes	characteristic
187	#14524028	C₂×C₄	1	1	yes	characteristic
188	#14524028	C₂×C₄	1	1	yes	characteristic
189	#14524028	C₂×C₄	1	1	yes	characteristic
190	#14524028	C₂×C₄	1	1	yes	characteristic
191	#14524027	C₂×C₄	1	1	yes	characteristic
192	#14524027	C₂×C₄	1	1	yes	characteristic
193	#14524025	C₂×C₄	1	1	yes	characteristic
194	#14524025	C₂×C₄	1	1	yes	characteristic
195	#14524025	C₂×C₄	1	1	yes	characteristic
196	#14524025	C₂×C₄	1	1	yes	characteristic
197	#14524024	C₂×C₄	1	1	yes	characteristic
198	#14524024	C₂×C₄	1	1	yes	characteristic
199	#14524023	C₂×C₄	1	1	yes	characteristic
200	#14524023	C₂×C₄	1	1	yes	characteristic
201	#14524021	C₂×C₄	1	1	yes	characteristic
202	#14524021	C₂×C₄	1	1	yes	characteristic
203	#14524021	C₂×C₄	1	1	yes	characteristic
204	#14524021	C₂×C₄	1	1	yes	characteristic
205	#14524020	C₂×C₄	1	1	yes	characteristic
206	#14524020	C₂×C₄	1	1	yes	characteristic
207	#14524020	C₂×C₄	1	1	yes	characteristic
208	#14524020	C₂×C₄	1	1	yes	characteristic
209	#14524019	C₂×C₄	1	1	yes	characteristic
210	#14524019	C₂×C₄	1	1	yes	characteristic
211	#14524018	C₂×C₄	1	1	yes	characteristic
212	#14524018	C₂×C₄	1	1	yes	characteristic
213	#14524016	C₂×C₄	1	1	yes	characteristic
214	#14524016	C₂×C₄	1	1	yes	characteristic
215	#14524016	C₂×C₄	1	1	yes	characteristic
216	#14524016	C₂×C₄	1	1	yes	characteristic
217	#14524015	C₂×C₄	1	1	yes	characteristic
218	#14524015	C₂×C₄	1	1	yes	characteristic
219	#14524015	C₂×C₄	1	1	yes	characteristic
220	#14524015	C₂×C₄	1	1	yes	characteristic
221	#14524014	C₂×C₄	1	1	yes	characteristic
222	#14524014	C₂×C₄	1	1	yes	characteristic
223	#14524013	C₂×C₄	1	1	yes	characteristic
224	#14524013	C₂×C₄	1	1	yes	characteristic
225	#14524011	C₂×C₄	1	1	yes	characteristic
226	#14524011	C₂×C₄	1	1	yes	characteristic
227	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
228	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
229	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
230	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
231	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
232	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
233	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
234	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
235	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
236	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
237	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
238	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
239	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
240	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
241	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
242	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
243	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
244	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
245	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
246	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
247	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
248	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
249	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
250	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
251	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
252	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
253	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
254	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
255	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
256	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
257	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
258	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
259	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
260	C₄×C₂²⋊D₆₇	C₂×C₄	1	1	yes	characteristic
261	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
262	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
263	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
264	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
265	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
266	C₄×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
267	#14524002	C₂×C₄	1	1	yes	characteristic
268	#14524002	C₂×C₄	1	1	yes	characteristic
269	#14524002	C₂×C₄	1	1	yes	characteristic
270	#14524002	C₂³	1	1	yes	characteristic
271	#14524002	C₂³	1	1	yes	characteristic
272	#14524000	C₂×C₄	1	1	yes	characteristic
273	#14524000	C₂×C₄	1	1	yes	characteristic
274	#14524000	C₂×C₄	1	1	yes	characteristic
275	#14524000	C₂×C₄	1	1	yes	characteristic
276	#14524000	C₂×C₄	1	1	yes	characteristic
277	#14524000	C₂×C₄	1	1	yes	characteristic
278	#14524000	C₂³	1	1	yes	characteristic
279	#14524000	C₂³	1	1	yes	characteristic
280	#14524000	C₂³	1	1	yes	characteristic
281	#14524000	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
283	C₂×C₄×Dic₆₇	C₂×C₄	1	1	yes	characteristic
284	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
285	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
286	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
287	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
288	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
289	C₄²×D₆₇	C₂³	1	1	yes	characteristic
290	C₄²×D₆₇	C₂³	1	1	yes	characteristic
291	C₄²×D₆₇	C₂³	1	1	yes	characteristic
292	C₄²×D₆₇	C₂³	1	1	yes	characteristic
293	C₄²×D₆₇	C₂³	1	1	yes	characteristic
294	C₄²×D₆₇	C₂³	1	1	yes	characteristic
295	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
296	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
297	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
298	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
299	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
300	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
301	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
302	Dic₆₇⋊C₈	C₂³	1	2	yes	—
303	Dic₆₇⋊C₈	C₂³	1	2	yes	—
304	Dic₆₇⋊C₈	C₂³	1	2	yes	—
305	Dic₆₇⋊C₈	C₂³	1	2	yes	—
306	Dic₆₇⋊C₈	C₂³	1	2	yes	—
307	Dic₆₇⋊C₈	C₂³	1	2	yes	—
308	Dic₆₇⋊C₈	C₂³	1	2	yes	—
309	Dic₆₇⋊C₈	C₂³	1	2	yes	—
310	Dic₆₇⋊C₈	C₂³	1	2	yes	—
311	Dic₆₇⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
313	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
314	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
315	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
316	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
317	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
318	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
319	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
320	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
321	#14523954	C₂³	1	2	yes	—
322	#14523954	C₂³	1	2	yes	—
323	#14523953	C₂³	1	2	yes	—
324	#14523953	C₂³	1	2	yes	—
325	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
326	C₈×Dic₆₇	C₂³	1	2	yes	—
327	C₈×Dic₆₇	C₂³	1	2	yes	—
328	C₈×Dic₆₇	C₂³	1	2	yes	—
329	C₈×Dic₆₇	C₂³	1	2	yes	—
330	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
331	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
332	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
333	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
334	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
335	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
337	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
338	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
339	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
342	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
343	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
344	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
348	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
349	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
350	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
351	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
352	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
353	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
354	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
355	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
356	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
357	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
358	#97×C₆₇	C₂³	1	2	yes	—
359	#97×C₆₇	C₂³	1	2	yes	—
360	C₄×C₈×C₆₇	C₂³	1	2	yes	—
361	C₂³×D₆₇	C₂²×C₄	1	1	yes	characteristic
362	#11761628	—	2	4	no	—
363	#11761628	—	2	4	no	—
364	#11761628	—	2	2	no	—
365	#11761628	—	2	2	no	—
366	#11761628	—	2	2	no	—
367	#11761628	—	2	2	no	—
368	#11761628	—	4	2	no	—
369	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
370	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
371	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
372	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
373	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
374	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
375	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
376	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
377	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
378	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
379	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
380	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
381	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
382	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
383	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
384	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
385	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
386	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
387	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
388	C₂×C₂²⋊D₆₇	C₂²×C₄	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
392	C₂×C₄×D₆₇	—	2	4	no	—
393	C₂×C₄×D₆₇	—	2	2	no	—
394	C₂×C₄×D₆₇	—	2	2	no	—
395	C₂×C₄×D₆₇	—	4	2	no	—
396	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
397	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
403	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
405	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
408	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
409	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
410	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×D₆₇	C₂⁴	1	1	yes	characteristic
414	#11761612	—	4	2	no	—
415	#11761611	—	2	4	no	—
416	#11761611	—	2	4	no	—
417	#11761611	—	4	2	no	—
418	#11761611	—	4	2	no	—
419	C₂×C₆₇⋊C₈	—	4	2	no	—
420	C₂×C₆₇⋊C₈	—	4	2	no	—
421	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
422	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
423	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
424	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
425	C₈×D₆₇	—	2	4	no	—
426	C₈×D₆₇	—	2	4	no	—
427	C₈×D₆₇	—	4	2	no	—
428	C₈×D₆₇	—	4	2	no	—
429	C₈×D₆₇	—	4	2	no	—
430	C₈×D₆₇	—	4	2	no	—
431	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
432	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
433	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
434	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
435	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
436	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
437	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
438	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
439	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
440	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
441	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
442	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
443	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
444	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
445	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
446	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
447	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
448	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
449	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
450	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
451	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
452	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
453	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
454	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
455	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
456	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
457	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
458	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
459	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
460	Dic₆₇⋊C₄	C₂²×C₄	1	1	yes	characteristic
461	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
462	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
463	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
467	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
469	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
471	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
472	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
473	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
474	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
475	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
476	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
477	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
478	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
479	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
480	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
481	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
482	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
483	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
484	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
485	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
486	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
487	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
488	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
489	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
490	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	1	yes	characteristic
491	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
492	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
493	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
494	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
495	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
496	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
497	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
498	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
499	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
500	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
501	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
502	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
503	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
504	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
505	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
506	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
507	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
508	C₄×Dic₆₇	C₂⁴	1	1	yes	characteristic
509	#41×C₆₇	—	4	2	no	—
510	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
511	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
512	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
513	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
514	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
515	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
516	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
517	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
518	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
519	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
520	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
522	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
523	M₁₆×C₆₇	—	4	2	no	—
524	C₂×C₈×C₆₇	—	4	2	no	—
525	C₂×C₈×C₆₇	—	4	2	no	—
526	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
527	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
528	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
529	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
530	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
531	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
532	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
533	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
534	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
535	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
536	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
537	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
538	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
539	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
540	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
541	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
542	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
543	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
544	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
545	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
546	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
547	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
548	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
549	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
550	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
551	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
552	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
553	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
554	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
555	C₂²×D₆₇	—	2	2	no	—
556	C₂²×D₆₇	—	2	2	no	—
557	C₂²×D₆₇	—	2	2	no	—
558	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
559	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
560	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
561	C₂²×D₆₇	C₂³×C₄	1	1	yes	characteristic
562	Q₈×C₆₇	—	4	1	no	—
563	D₄×C₆₇	—	2	2	no	—
564	D₄×C₆₇	—	2	2	no	—
565	D₄×C₆₇	—	4	1	no	—
566	C₂×C₄×C₆₇	—	2	2	no	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	2	no	—
569	C₂×C₄×C₆₇	—	2	2	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	4	1	no	—
577	C₂×C₄×C₆₇	—	4	1	no	—
578	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
582	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
583	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
585	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
586	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
587	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
588	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
589	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
590	C₂²⋊D₆₇	—	2	2	no	—
591	C₂²⋊D₆₇	—	2	2	no	—
592	C₂²⋊D₆₇	—	2	2	no	—
593	C₂²⋊D₆₇	—	2	2	no	—
594	C₂²⋊D₆₇	—	2	2	no	—
595	C₂²⋊D₆₇	—	2	2	no	—
596	C₂²⋊D₆₇	—	2	2	no	—
597	C₂²⋊D₆₇	—	2	2	no	—
598	C₂²⋊D₆₇	—	2	2	no	—
599	C₂²⋊D₆₇	—	2	2	no	—
600	C₂×Dic₆₇	—	2	2	no	—
601	C₂×Dic₆₇	—	2	2	no	—
602	C₂×Dic₆₇	—	2	2	no	—
603	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
604	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
605	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
606	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
607	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
608	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
609	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
610	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
611	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
612	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
613	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
614	C₂×Dic₆₇	C₂³×C₄	1	1	yes	characteristic
615	D₂₆₈	—	2	2	no	—
616	D₂₆₈	—	2	2	no	—
617	D₂₆₈	—	2	2	no	—
618	D₂₆₈	—	2	2	no	—
619	D₂₆₈	—	4	1	no	—
620	C₄×D₆₇	—	2	2	no	—
621	C₄×D₆₇	—	2	2	no	—
622	C₄×D₆₇	—	2	2	no	—
623	C₄×D₆₇	—	2	2	no	—
624	C₄×D₆₇	—	2	2	no	—
625	C₄×D₆₇	—	2	1	no	—
626	C₄×D₆₇	—	2	1	no	—
627	C₄×D₆₇	—	2	1	no	—
628	C₄×D₆₇	—	2	1	no	—
629	C₄×D₆₇	—	2	1	no	—
630	C₄×D₆₇	—	2	1	no	—
631	C₄×D₆₇	—	2	2	no	—
632	C₄×D₆₇	—	2	2	no	—
633	C₄×D₆₇	—	4	1	no	—
634	C₄×D₆₇	—	4	1	no	—
635	C₄×D₆₇	—	4	1	no	—
636	C₄×D₆₇	—	4	1	no	—
637	C₄×D₆₇	—	4	1	no	—
638	C₄×D₆₇	—	4	1	no	—
639	C₄×D₆₇	#131	1	4	yes	complemented
640	C₄×D₆₇	H(5,𝔽₂)	1	2	yes	—
641	C₄×D₆₇	2₋¹⁺⁴	1	2	yes	—
642	Dic₁₃₄	—	2	2	no	—
643	Dic₁₃₄	—	2	2	no	—
644	Dic₁₃₄	—	2	2	no	—
645	Dic₁₃₄	—	2	2	no	—
646	Dic₁₃₄	—	4	1	no	—
647	C₈×C₆₇	—	2	2	no	—
648	C₈×C₆₇	—	2	2	no	—
649	C₈×C₆₇	—	2	2	no	—
650	C₈×C₆₇	—	2	2	no	—
651	C₆₇⋊C₈	—	2	2	no	—
652	C₆₇⋊C₈	—	2	2	no	—
653	C₆₇⋊C₈	—	2	2	no	—
654	C₆₇⋊C₈	—	2	2	no	—
655	C₂²×C₆₇	—	2	1	no	—
656	C₂²×C₆₇	—	2	1	no	—
657	C₂²×C₆₇	—	2	1	no	—
658	C₂²×C₆₇	—	2	1	no	—
659	C₂²×C₆₇	—	2	1	no	—
660	C₂²×C₆₇	—	2	1	no	—
661	C₂²×C₆₇	—	2	1	no	—
662	C₂²×C₆₇	—	2	1	no	—
663	C₂²×C₆₇	#568	1	2	yes	—
664	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
665	C₂×D₆₇	—	2	8	no	—
666	C₂×D₆₇	—	2	1	no	—
667	C₂×D₆₇	—	2	1	no	—
668	C₂×D₆₇	—	2	1	no	—
669	C₂×D₆₇	—	2	1	no	—
670	C₂×D₆₇	—	2	1	no	—
671	C₂×D₆₇	—	2	1	no	—
672	C₂×D₆₇	—	2	1	no	—
673	C₂×D₆₇	—	2	1	no	—
674	C₂×D₆₇	—	2	1	no	—
675	C₂×D₆₇	—	2	1	no	—
676	C₂×D₆₇	#520	1	2	yes	—
677	C₂×D₆₇	C₂×#131	1	2	yes	—
678	C₄×C₆₇	—	2	1	no	—
679	C₄×C₆₇	—	2	1	no	—
680	C₄×C₆₇	—	2	1	no	—
681	C₄×C₆₇	—	2	1	no	—
682	C₄×C₆₇	—	2	1	no	—
683	C₄×C₆₇	—	2	1	no	—
684	C₄×C₆₇	—	2	1	no	—
685	C₄×C₆₇	—	2	1	no	—
686	C₄×C₆₇	—	2	1	no	—
687	C₄×C₆₇	—	2	1	no	—
688	C₄×C₆₇	C₂×#131	1	2	yes	—
689	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
690	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	Dic₆₇	—	2	1	no	—
692	Dic₆₇	—	2	1	no	—
693	Dic₆₇	—	2	1	no	—
694	Dic₆₇	—	2	1	no	—
695	Dic₆₇	—	2	1	no	—
696	Dic₆₇	—	2	1	no	—
697	Dic₆₇	—	2	1	no	—
698	Dic₆₇	—	2	1	no	—
699	Dic₆₇	—	2	1	no	—
700	Dic₆₇	—	2	1	no	—
701	Dic₆₇	#520	1	2	yes	—
702	Dic₆₇	C₂×#131	1	2	yes	—
703	#60265	—	67	1	no	maximal, Sylow
704	C₂×C₆₇	—	2	2	no	—
705	C₂×C₆₇	—	4	1	no	—
706	C₂×C₆₇	—	4	1	no	—
707	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
708	C₂×C₆₇	C₂²×#131	1	1	yes	characteristic
709	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
710	D₆₇	—	2	2	no	—
711	D₆₇	—	2	2	no	—
712	D₆₇	—	4	1	no	—
713	D₆₇	—	4	1	no	—
714	#3444	—	67	1	no	—
715	#2994	—	67	2	no	—
716	#2994	—	67	2	no	—
717	#2992	—	67	2	no	—
718	#2992	—	67	2	no	—
719	#2990	—	67	1	no	—
720	#2990	—	67	1	no	—
721	#2990	—	67	1	no	—
722	#2990	D₆₇	1	1	yes	characteristic, complemented
723	#2989	—	67	1	no	—
724	#2989	—	67	1	no	—
725	#2988	—	67	1	no	—
726	#2988	—	67	1	no	—
727	#2962	—	67	2	no	—
728	#2935	—	67	2	no	—
729	#2929	—	67	2	no	—
730	#2929	—	67	2	no	—
731	#2925	—	67	1	no	—
732	#2925	—	67	1	no	—
733	#2920	—	67	1	no	—
734	#2906	—	67	1	no	—
735	#2906	—	67	1	no	—
736	C₂²×C₄⋊C₈	—	67	1	no	—
737	C₆₇	#60265	1	1	yes	characteristic, complemented, Sylow
738	C₂×#131	—	67	2	no	—
739	C₂×#131	—	67	2	no	—
740	C₂³×C₈	—	67	2	no	—
741	#533	—	67	1	no	—
742	#533	—	67	1	no	—
743	#533	—	67	1	no	—
744	#532	—	67	1	no	—
745	#532	—	67	1	no	—
746	#532	—	67	1	no	—
747	#529	—	67	1	no	—
748	#529	—	67	1	no	—
749	#529	—	67	1	no	—
750	#529	—	67	1	no	—
751	#529	—	67	1	no	—
752	#529	—	67	1	no	—
753	#529	—	67	1	no	—
754	#529	—	67	1	no	—
755	#529	—	67	1	no	—
756	#529	—	67	1	no	—
757	#529	—	67	1	no	—
758	#529	—	67	1	no	—
759	#525	—	67	1	no	—
760	#525	—	67	1	no	—
761	#525	—	67	1	no	—
762	#525	—	67	1	no	—
763	#525	—	67	1	no	—
764	#525	—	67	1	no	—
765	C₄×#41	—	67	1	no	—
766	C₄×#41	—	67	1	no	—
767	C₄×#41	—	67	1	no	—
768	C₄×#41	—	67	1	no	—
769	C₄×#41	—	67	1	no	—
770	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
771	C₂²×C₄²	—	67	1	no	—
772	#446	—	67	2	no	—
773	#446	—	67	2	no	—
774	#446	—	67	2	no	—
775	#446	—	67	2	no	—
776	#446	—	67	2	no	—
777	#446	C₂×D₆₇	1	2	yes	complemented
778	C₈×Q₈	—	67	2	no	—
779	C₈×Q₈	—	67	2	no	—
780	#436	—	67	2	no	—
781	#436	—	67	2	no	—
782	#435	—	67	2	no	—
783	#435	—	67	2	no	—
784	#435	—	67	2	no	—
785	#435	—	67	2	no	—
786	#435	—	67	2	no	—
787	#435	—	67	2	no	—
788	#435	—	67	2	no	—
789	#435	—	67	2	no	—
790	#435	—	67	2	no	—
791	#435	—	67	2	no	—
792	#435	C₂×D₆₇	1	2	yes	—
793	#435	C₂×D₆₇	1	2	yes	complemented
794	C₈×D₄	—	67	2	no	—
795	C₈×D₄	—	67	2	no	—
796	C₈×D₄	—	67	2	no	—
797	C₈×D₄	—	67	2	no	—
798	C₈×D₄	—	67	2	no	—
799	C₈×D₄	—	67	2	no	—
800	C₈×D₄	—	67	2	no	—
801	C₈×D₄	—	67	2	no	—
802	C₈×D₄	—	67	2	no	—
803	C₈×D₄	C₂×D₆₇	1	2	yes	—
804	#433	—	67	2	no	—
805	#433	—	67	2	no	—
806	#433	—	67	2	no	—
807	#433	—	67	2	no	—
808	#432	—	67	1	no	—
809	#432	—	67	1	no	—
810	#432	—	67	1	no	—
811	#432	—	67	1	no	—
812	#432	—	67	2	no	—
813	#432	C₂×D₆₇	1	1	yes	characteristic
814	#432	C₂×D₆₇	1	1	yes	characteristic, complemented
815	#431	—	67	1	no	—
816	#431	—	67	1	no	—
817	#431	—	67	1	no	—
818	#431	—	67	1	no	—
819	#431	—	67	1	no	—
820	#431	—	67	2	no	—
821	#431	C₂×D₆₇	1	1	yes	characteristic, complemented
822	#424	—	67	2	no	—
823	#424	—	67	2	no	—
824	#424	—	67	2	no	—
825	#424	—	67	2	no	—
826	#424	—	67	2	no	—
827	#424	—	67	2	no	—
828	#423	—	67	1	no	—
829	#423	—	67	1	no	—
830	#423	—	67	1	no	—
831	#423	—	67	1	no	—
832	#423	—	67	1	no	—
833	#423	C₂×D₆₇	1	1	yes	characteristic, complemented
834	C₂×C₄⋊C₈	—	67	2	no	—
835	C₂×C₄⋊C₈	—	67	1	no	—
836	C₂×C₄⋊C₈	—	67	1	no	—
837	C₂×C₄⋊C₈	—	67	1	no	—
838	C₂×C₄⋊C₈	—	67	1	no	—
839	C₂×C₄⋊C₈	—	67	2	no	—
840	C₂×C₄⋊C₈	—	67	1	no	—
841	C₂×C₄⋊C₈	—	67	1	no	—
842	C₂×C₄⋊C₈	—	67	2	no	—
843	C₂×C₄⋊C₈	—	67	1	no	—
844	C₂×C₄⋊C₈	—	67	1	no	—
845	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
846	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
847	#408	—	67	2	no	—
848	#408	—	67	2	no	—
849	#407	—	67	2	no	—
850	#405	—	67	2	no	—
851	#405	—	67	2	no	—
852	C₄×M₁₆	—	67	2	no	—
853	C₂×#41	—	67	1	no	—
854	C₂×#41	—	67	1	no	—
855	C₂×#41	—	67	1	no	—
856	C₂×#41	—	67	1	no	—
857	C₂×#41	—	67	1	no	—
858	C₂×#41	C₄×D₆₇	1	1	yes	characteristic
859	C₂³×C₄	—	67	1	no	—
860	C₂³×C₄	—	67	1	no	—
861	C₂³×C₄	—	67	1	no	—
862	#131	—	268	4	no	—
863	#131	—	268	4	no	—
864	C₂×M₁₆	—	67	2	no	—
865	C₂×M₁₆	—	67	2	no	—
866	C₂×M₁₆	—	67	2	no	—
867	C₂×M₁₆	—	67	2	no	—
868	C₂×M₁₆	—	67	2	no	—
869	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
870	C₂²×C₈	—	268	4	no	—
871	C₂²×C₈	—	67	2	no	—
872	C₂²×C₈	—	67	2	no	—
873	C₂²×C₈	—	67	2	no	—
874	C₂²×C₈	—	67	2	no	—
875	C₂²×C₈	—	67	2	no	—
876	C₂²×C₈	—	67	2	no	—
877	C₂²×C₈	—	67	2	no	—
878	C₂²×C₈	—	67	2	no	—
879	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
880	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
881	C₄⋊Q₈	—	67	1	no	—
882	C₄⋊Q₈	—	67	1	no	—
883	C₄⋊Q₈	—	67	1	no	—
884	#127	—	67	1	no	—
885	#126	—	67	1	no	—
886	#126	—	67	1	no	—
887	#126	—	67	1	no	—
888	#126	—	67	1	no	—
889	#126	—	67	1	no	—
890	#126	—	67	1	no	—
891	#126	—	67	1	no	—
892	#126	—	67	1	no	—
893	#125	—	67	1	no	—
894	#125	—	67	1	no	—
895	#125	—	67	1	no	—
896	#125	—	67	1	no	—
897	#125	—	67	1	no	—
898	#125	—	67	1	no	—
899	#124	—	67	1	no	—
900	#124	—	67	1	no	—
901	#124	—	67	1	no	—
902	#124	—	67	1	no	—
903	#124	—	67	1	no	—
904	#124	—	67	1	no	—
905	#123	—	67	1	no	—
906	#123	—	67	1	no	—
907	#123	—	67	1	no	—
908	#123	—	67	1	no	—
909	#123	—	67	1	no	—
910	#123	—	67	1	no	—
911	#123	—	67	1	no	—
912	#123	—	67	1	no	—
913	#123	—	67	1	no	—
914	#123	—	67	1	no	—
915	#123	—	67	1	no	—
916	#123	—	67	1	no	—
917	C₂²⋊Q₈	—	67	1	no	—
918	C₂²⋊Q₈	—	67	1	no	—
919	C₂²⋊Q₈	—	67	1	no	—
920	C₂²⋊Q₈	—	67	1	no	—
921	C₂²⋊Q₈	—	67	1	no	—
922	C₂²⋊Q₈	—	67	1	no	—
923	C₂²⋊Q₈	—	67	1	no	—
924	C₂²⋊Q₈	—	67	1	no	—
925	C₂²⋊Q₈	—	67	1	no	—
926	C₂²⋊Q₈	—	67	1	no	—
927	C₂²⋊Q₈	—	67	1	no	—
928	C₂²⋊Q₈	—	67	1	no	—
929	#121	—	67	1	no	—
930	#121	—	67	1	no	—
931	#121	—	67	1	no	—
932	#121	—	67	1	no	—
933	#121	—	67	1	no	—
934	#121	—	67	1	no	—
935	#121	—	67	1	no	—
936	#121	—	67	1	no	—
937	#121	—	67	1	no	—
938	#121	—	67	1	no	—
939	#121	—	67	1	no	—
940	#121	—	67	1	no	—
941	#120	—	67	1	no	—
942	#120	—	67	1	no	—
943	#120	—	67	1	no	—
944	#120	—	67	1	no	—
945	C₄×Q₈	—	67	1	no	—
946	C₄×Q₈	—	67	1	no	—
947	C₄×Q₈	—	67	1	no	—
948	C₄×Q₈	—	67	1	no	—
949	C₄×Q₈	—	67	1	no	—
950	C₄×Q₈	—	67	1	no	—
951	C₄×Q₈	—	67	1	no	—
952	C₄×Q₈	—	67	1	no	—
953	C₄×Q₈	—	67	1	no	—
954	C₄×Q₈	—	67	1	no	—
955	C₄×Q₈	C₄×D₆₇	1	1	yes	characteristic
956	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
957	C₄×D₄	—	67	1	no	—
958	C₄×D₄	—	67	1	no	—
959	C₄×D₄	—	67	1	no	—
960	C₄×D₄	—	67	1	no	—
961	C₄×D₄	—	67	1	no	—
962	C₄×D₄	—	67	1	no	—
963	C₄×D₄	—	67	1	no	—
964	C₄×D₄	—	67	1	no	—
965	C₄×D₄	—	67	1	no	—
966	C₄×D₄	—	67	1	no	—
967	C₄×D₄	—	67	1	no	—
968	C₄×D₄	—	67	1	no	—
969	C₄×D₄	—	67	1	no	—
970	C₄×D₄	—	67	1	no	—
971	C₄×D₄	—	67	1	no	—
972	C₄×D₄	—	67	1	no	—
973	C₄×D₄	—	67	1	no	—
974	C₄×D₄	—	67	1	no	—
975	C₄×D₄	—	67	1	no	—
976	C₄×D₄	—	67	1	no	—
977	C₄×D₄	—	67	1	no	—
978	C₄×D₄	—	67	1	no	—
979	C₄×D₄	—	67	1	no	—
980	C₄×D₄	—	67	1	no	—
981	C₄×D₄	—	67	1	no	—
982	C₄×D₄	—	67	1	no	—
983	C₄×D₄	—	67	1	no	—
984	C₄×D₄	—	67	1	no	—
985	C₄×D₄	—	67	1	no	—
986	C₄×D₄	—	67	1	no	—
987	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
988	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
989	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
990	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
991	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
992	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
993	#117	—	67	1	no	—
994	#117	—	67	1	no	—
995	#117	—	67	1	no	—
996	#117	—	67	1	no	—
997	#117	—	67	1	no	—
998	#117	—	67	1	no	—
999	#117	—	67	1	no	—
1000	#117	—	67	1	no	—
1001	#117	—	67	1	no	—
1002	#117	—	67	1	no	—
1003	#117	—	67	1	no	—
1004	#117	—	67	1	no	—
1005	#117	—	67	1	no	—
1006	#117	—	67	1	no	—
1007	#117	—	67	1	no	—
1008	#117	C₄×D₆₇	1	1	yes	characteristic
1009	#117	C₄×D₆₇	1	1	yes	characteristic
1010	#117	C₄×D₆₇	1	1	yes	characteristic
1011	C₂×C₄²	—	67	1	no	—
1012	C₂×C₄²	—	67	1	no	—
1013	C₂×C₄²	—	67	1	no	—
1014	C₂×C₄²	—	67	1	no	—
1015	C₂×C₄²	—	67	1	no	—
1016	C₂×C₄²	—	67	1	no	—
1017	C₂×C₄²	—	67	1	no	—
1018	C₂×C₄²	—	67	1	no	—
1019	C₂×C₄²	—	67	1	no	—
1020	C₂×C₄²	—	67	1	no	—
1021	C₂×C₄²	—	67	1	no	—
1022	C₂×C₄²	—	67	1	no	—
1023	C₂×C₄²	—	67	1	no	—
1024	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1027	C₄⋊C₈	—	67	2	no	—
1028	C₄⋊C₈	—	67	2	no	—
1029	C₄⋊C₈	—	67	2	no	—
1030	C₄⋊C₈	—	67	2	no	—
1031	C₄⋊C₈	—	67	2	no	—
1032	C₄⋊C₈	—	67	2	no	—
1033	C₄⋊C₈	—	67	2	no	—
1034	C₄⋊C₈	—	67	2	no	—
1035	C₄⋊C₈	—	67	2	no	—
1036	C₄⋊C₈	—	67	2	no	—
1037	C₄⋊C₈	—	67	1	no	—
1038	C₄⋊C₈	—	67	1	no	—
1039	C₄⋊C₈	—	67	2	no	—
1040	C₄⋊C₈	—	67	1	no	—
1041	C₄⋊C₈	—	67	2	no	—
1042	C₄⋊C₈	—	67	2	no	—
1043	C₄⋊C₈	—	67	1	no	—
1044	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
1045	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
1046	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
1047	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
1048	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
1049	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
1050	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
1051	C₂²⋊C₈	—	67	2	no	—
1052	C₂²⋊C₈	—	67	2	no	—
1053	C₂²⋊C₈	—	67	2	no	—
1054	C₂²⋊C₈	—	67	2	no	—
1055	C₂²⋊C₈	—	67	2	no	—
1056	C₂²⋊C₈	—	67	2	no	—
1057	C₂²⋊C₈	—	67	2	no	—
1058	C₂²⋊C₈	—	67	2	no	—
1059	C₂²⋊C₈	—	67	2	no	—
1060	C₂²⋊C₈	C₂²×D₆₇	1	2	yes	—
1061	C₂²⋊C₈	C₂²×D₆₇	1	2	yes	—
1062	C₂²⋊C₈	C₂²×D₆₇	1	2	yes	—
1063	#97	—	67	2	no	—
1064	#97	—	67	2	no	—
1065	#97	—	67	2	no	—
1066	#97	—	67	2	no	—
1067	#97	C₂²×D₆₇	1	2	yes	—
1068	#97	C₂²×D₆₇	1	2	yes	—
1069	C₄×C₈	—	67	2	no	—
1070	C₄×C₈	—	67	2	no	—
1071	C₄×C₈	—	67	2	no	—
1072	C₄×C₈	—	67	2	no	—
1073	C₄×C₈	—	67	2	no	—
1074	C₄×C₈	C₂²×D₆₇	1	2	yes	—
1075	C₂⁴	—	67	1	no	—
1076	#41	—	4	2	no	—
1077	#41	—	268	2	no	—
1078	#41	—	134	2	no	—
1079	#41	—	134	2	no	—
1080	#41	—	134	4	no	—
1081	#41	—	134	4	no	—
1082	#41	—	134	2	no	—
1083	#41	—	134	2	no	—
1084	C₂×Q₈	—	67	1	no	—
1085	C₂×Q₈	—	67	1	no	—
1086	C₂×Q₈	—	67	1	no	—
1087	C₂×Q₈	—	67	1	no	—
1088	C₂×Q₈	—	67	1	no	—
1089	C₂×Q₈	C₂×C₄×D₆₇	1	1	yes	characteristic
1090	C₂×D₄	—	67	1	no	—
1091	C₂×D₄	—	67	1	no	—
1092	C₂×D₄	—	67	1	no	—
1093	C₂×D₄	—	67	1	no	—
1094	C₂×D₄	—	67	1	no	—
1095	C₂×D₄	—	67	1	no	—
1096	C₂×D₄	—	67	1	no	—
1097	C₂×D₄	—	67	1	no	—
1098	C₂×D₄	—	67	1	no	—
1099	C₂×D₄	—	67	1	no	—
1100	C₂×D₄	—	67	1	no	—
1101	C₂×D₄	—	67	1	no	—
1102	C₂×D₄	—	67	1	no	—
1103	C₂×D₄	—	67	1	no	—
1104	C₂×D₄	—	67	1	no	—
1105	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1106	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1107	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1108	C₂²×C₄	—	268	2	no	—
1109	C₂²×C₄	—	67	1	no	—
1110	C₂²×C₄	—	67	1	no	—
1111	C₂²×C₄	—	67	1	no	—
1112	C₂²×C₄	—	67	1	no	—
1113	C₂²×C₄	—	67	1	no	—
1114	C₂²×C₄	—	67	1	no	—
1115	C₂²×C₄	—	67	1	no	—
1116	C₂²×C₄	—	67	1	no	—
1117	C₂²×C₄	—	67	1	no	—
1118	C₂²×C₄	—	67	1	no	—
1119	C₂²×C₄	—	67	1	no	—
1120	C₂²×C₄	—	67	1	no	—
1121	C₂²×C₄	—	67	1	no	—
1122	C₂²×C₄	—	67	1	no	—
1123	C₂²×C₄	—	67	1	no	—
1124	C₂²×C₄	—	67	1	no	—
1125	C₂²×C₄	—	67	1	no	—
1126	C₂²×C₄	—	67	1	no	—
1127	C₂²×C₄	—	67	1	no	—
1128	C₂²×C₄	—	67	1	no	—
1129	C₂²×C₄	—	67	1	no	—
1130	C₂²×C₄	—	134	2	no	—
1131	C₂²×C₄	—	134	4	no	—
1132	C₂²×C₄	—	134	2	no	—
1133	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1134	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1135	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1136	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1137	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1138	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1139	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1140	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1141	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1142	M₁₆	—	4	2	no	—
1143	M₁₆	—	268	2	no	—
1144	M₁₆	—	268	2	no	—
1145	M₁₆	—	268	2	no	—
1146	M₁₆	—	134	4	no	—
1147	M₁₆	—	134	4	no	—
1148	C₂×C₈	—	4	2	no	—
1149	C₂×C₈	—	4	2	no	—
1150	C₂×C₈	—	268	2	no	—
1151	C₂×C₈	—	268	2	no	—
1152	C₂×C₈	—	268	2	no	—
1153	C₂×C₈	—	268	2	no	—
1154	C₂×C₈	—	268	2	no	—
1155	C₂×C₈	—	268	2	no	—
1156	C₂×C₈	—	67	2	no	—
1157	C₂×C₈	—	67	2	no	—
1158	C₂×C₈	—	67	2	no	—
1159	C₂×C₈	—	67	2	no	—
1160	C₂×C₈	—	134	4	no	—
1161	C₂×C₈	—	134	4	no	—
1162	C₂×C₈	C₂³×D₆₇	1	2	yes	—
1163	C₂×C₈	C₂³×D₆₇	1	2	yes	—
1164	C₂×C₈	C₂³×D₆₇	1	2	yes	—
1165	C₂×C₈	C₂³×D₆₇	1	2	yes	—
1166	C₄⋊C₄	—	67	1	no	—
1167	C₄⋊C₄	—	67	1	no	—
1168	C₄⋊C₄	—	67	1	no	—
1169	C₄⋊C₄	—	67	1	no	—
1170	C₄⋊C₄	—	67	1	no	—
1171	C₄⋊C₄	—	67	1	no	—
1172	C₄⋊C₄	—	67	1	no	—
1173	C₄⋊C₄	—	67	1	no	—
1174	C₄⋊C₄	—	67	1	no	—
1175	C₄⋊C₄	—	67	1	no	—
1176	C₄⋊C₄	—	67	1	no	—
1177	C₄⋊C₄	—	67	1	no	—
1178	C₄⋊C₄	—	67	1	no	—
1179	C₄⋊C₄	—	67	1	no	—
1180	C₄⋊C₄	—	67	1	no	—
1181	C₄⋊C₄	—	67	1	no	—
1182	C₄⋊C₄	—	67	1	no	—
1183	C₄⋊C₄	—	67	1	no	—
1184	C₄⋊C₄	—	67	1	no	—
1185	C₄⋊C₄	—	67	1	no	—
1186	C₄⋊C₄	—	67	1	no	—
1187	C₄⋊C₄	—	67	1	no	—
1188	C₄⋊C₄	—	67	1	no	—
1189	C₄⋊C₄	—	67	1	no	—
1190	C₄⋊C₄	—	67	1	no	—
1191	C₄⋊C₄	—	67	1	no	—
1192	C₄⋊C₄	—	67	1	no	—
1193	C₄⋊C₄	—	67	1	no	—
1194	C₄⋊C₄	—	67	1	no	—
1195	C₄⋊C₄	—	67	1	no	—
1196	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1197	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1198	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1199	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1200	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1201	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1202	C₂²⋊C₄	—	67	1	no	—
1203	C₂²⋊C₄	—	67	1	no	—
1204	C₂²⋊C₄	—	67	1	no	—
1205	C₂²⋊C₄	—	67	1	no	—
1206	C₂²⋊C₄	—	67	1	no	—
1207	C₂²⋊C₄	—	67	1	no	—
1208	C₂²⋊C₄	—	67	1	no	—
1209	C₂²⋊C₄	—	67	1	no	—
1210	C₂²⋊C₄	—	67	1	no	—
1211	C₂²⋊C₄	—	67	1	no	—
1212	C₂²⋊C₄	—	67	1	no	—
1213	C₂²⋊C₄	—	67	1	no	—
1214	C₂²⋊C₄	—	67	1	no	—
1215	C₂²⋊C₄	—	67	1	no	—
1216	C₂²⋊C₄	—	67	1	no	—
1217	C₂²⋊C₄	—	67	1	no	—
1218	C₂²⋊C₄	—	67	1	no	—
1219	C₂²⋊C₄	—	67	1	no	—
1220	C₂²⋊C₄	—	67	1	no	—
1221	C₂²⋊C₄	—	67	1	no	—
1222	C₂²⋊C₄	—	67	1	no	—
1223	C₂²⋊C₄	—	67	1	no	—
1224	C₂²⋊C₄	—	67	1	no	—
1225	C₂²⋊C₄	—	67	1	no	—
1226	C₂²⋊C₄	—	67	1	no	—
1227	C₂²⋊C₄	—	67	1	no	—
1228	C₂²⋊C₄	—	67	1	no	—
1229	C₂²⋊C₄	—	67	1	no	—
1230	C₂²⋊C₄	—	67	1	no	—
1231	C₂²⋊C₄	—	67	1	no	—
1232	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1233	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1234	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1235	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1236	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1237	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1238	C₄²	—	67	1	no	—
1239	C₄²	—	67	1	no	—
1240	C₄²	—	67	1	no	—
1241	C₄²	—	67	1	no	—
1242	C₄²	—	67	1	no	—
1243	C₄²	—	67	1	no	—
1244	C₄²	—	67	1	no	—
1245	C₄²	—	67	1	no	—
1246	C₄²	—	67	1	no	—
1247	C₄²	—	67	1	no	—
1248	C₄²	—	67	1	no	—
1249	C₄²	—	67	1	no	—
1250	C₄²	—	67	1	no	—
1251	C₄²	—	67	1	no	—
1252	C₄²	—	67	1	no	—
1253	C₄²	—	67	1	no	—
1254	C₄²	—	67	1	no	—
1255	C₄²	—	67	1	no	—
1256	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1257	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1258	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1259	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1260	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1261	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1262	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1263	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1264	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1265	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1266	C₂³	—	67	1	no	—
1267	C₂³	—	67	1	no	—
1268	C₂³	—	67	1	no	—
1269	C₂³	—	67	1	no	—
1270	C₂³	—	134	2	no	—
1271	C₂³	—	134	2	no	—
1272	C₂³	—	134	2	no	—
1273	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1274	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1275	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1276	Q₈	—	4	1	no	—
1277	Q₈	—	268	1	no	—
1278	Q₈	—	134	2	no	—
1279	Q₈	—	134	2	no	—
1280	Q₈	—	134	2	no	—
1281	Q₈	—	134	2	no	—
1282	D₄	—	2	2	no	—
1283	D₄	—	2	2	no	—
1284	D₄	—	4	1	no	—
1285	D₄	—	268	1	no	—
1286	D₄	—	134	2	no	—
1287	D₄	—	134	2	no	—
1288	D₄	—	134	2	no	—
1289	D₄	—	134	2	no	—
1290	D₄	—	134	2	no	—
1291	D₄	—	134	2	no	—
1292	D₄	—	134	2	no	—
1293	D₄	—	134	2	no	—
1294	D₄	—	134	2	no	—
1295	D₄	—	134	2	no	—
1296	D₄	—	134	2	no	—
1297	D₄	—	134	2	no	—
1298	D₄	—	134	2	no	—
1299	D₄	—	134	2	no	—
1300	C₂×C₄	—	2	2	no	—
1301	C₂×C₄	—	2	2	no	—
1302	C₂×C₄	—	2	2	no	—
1303	C₂×C₄	—	2	2	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	4	1	no	—
1311	C₂×C₄	—	4	1	no	—
1312	C₂×C₄	—	268	1	no	—
1313	C₂×C₄	—	268	1	no	—
1314	C₂×C₄	—	268	1	no	—
1315	C₂×C₄	—	268	1	no	—
1316	C₂×C₄	—	268	1	no	—
1317	C₂×C₄	—	268	1	no	—
1318	C₂×C₄	—	67	1	no	—
1319	C₂×C₄	—	67	1	no	—
1320	C₂×C₄	—	67	4	no	—
1321	C₂×C₄	—	67	2	no	—
1322	C₂×C₄	—	67	2	no	—
1323	C₂×C₄	—	67	1	no	—
1324	C₂×C₄	—	67	1	no	—
1325	C₂×C₄	—	67	1	no	—
1326	C₂×C₄	—	67	1	no	—
1327	C₂×C₄	—	67	1	no	—
1328	C₂×C₄	—	67	1	no	—
1329	C₂×C₄	—	67	1	no	—
1330	C₂×C₄	—	67	1	no	—
1331	C₂×C₄	—	67	1	no	—
1332	C₂×C₄	—	67	1	no	—
1333	C₂×C₄	—	134	2	no	—
1334	C₂×C₄	—	134	2	no	—
1335	C₂×C₄	—	134	2	no	—
1336	C₂×C₄	—	134	2	no	—
1337	C₂×C₄	—	134	2	no	—
1338	C₂×C₄	—	134	2	no	—
1339	C₂×C₄	—	134	2	no	—
1340	C₂×C₄	—	134	2	no	—
1341	C₂×C₄	—	134	2	no	—
1342	C₂×C₄	—	134	2	no	—
1343	C₂×C₄	—	134	1	no	—
1344	C₂×C₄	—	134	1	no	—
1345	C₂×C₄	—	134	1	no	—
1346	C₂×C₄	—	134	1	no	—
1347	C₂×C₄	—	134	1	no	—
1348	C₂×C₄	—	134	1	no	—
1349	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1350	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1351	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1352	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1353	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1354	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1355	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1356	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1357	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1358	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1359	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1360	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1361	C₈	—	2	2	no	—
1362	C₈	—	2	2	no	—
1363	C₈	—	2	2	no	—
1364	C₈	—	2	2	no	—
1365	C₈	—	134	2	no	—
1366	C₈	—	134	2	no	—
1367	C₈	—	134	2	no	—
1368	C₈	—	134	2	no	—
1369	C₂²	—	2	1	no	—
1370	C₂²	—	2	1	no	—
1371	C₂²	—	2	1	no	—
1372	C₂²	—	2	1	no	—
1373	C₂²	—	2	1	no	—
1374	C₂²	—	2	1	no	—
1375	C₂²	—	2	1	no	—
1376	C₂²	—	2	1	no	—
1377	C₂²	—	67	2	no	—
1378	C₂²	—	67	2	no	—
1379	C₂²	—	134	8	no	—
1380	C₂²	—	134	1	no	—
1381	C₂²	—	134	1	no	—
1382	C₂²	—	134	1	no	—
1383	C₂²	—	134	1	no	—
1384	C₂²	—	134	1	no	—
1385	C₂²	—	134	1	no	—
1386	C₂²	—	134	1	no	—
1387	C₂²	—	134	1	no	—
1388	C₂²	—	134	1	no	—
1389	C₂²	—	134	1	no	—
1390	C₂²	#16864162	1	2	yes	—
1391	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1392	C₄	—	2	1	no	—
1393	C₄	—	2	1	no	—
1394	C₄	—	2	1	no	—
1395	C₄	—	2	1	no	—
1396	C₄	—	2	1	no	—
1397	C₄	—	2	1	no	—
1398	C₄	—	2	1	no	—
1399	C₄	—	2	1	no	—
1400	C₄	—	2	1	no	—
1401	C₄	—	2	1	no	—
1402	C₄	—	67	2	no	—
1403	C₄	—	67	2	no	—
1404	C₄	—	134	1	no	—
1405	C₄	—	134	1	no	—
1406	C₄	—	134	1	no	—
1407	C₄	—	134	1	no	—
1408	C₄	—	134	1	no	—
1409	C₄	—	134	1	no	—
1410	C₄	—	134	1	no	—
1411	C₄	—	134	1	no	—
1412	C₄	—	134	1	no	—
1413	C₄	—	134	1	no	—
1414	C₄	#131×D₆₇	1	2	yes	—
1415	C₄	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1416	C₄	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic
1417	C₂	—	2	2	no	—
1418	C₂	—	4	1	no	—
1419	C₂	—	4	1	no	—
1420	C₂	—	268	1	no	—
1421	C₂	—	268	1	no	—
1422	C₂	—	134	2	no	—
1423	C₂	—	134	2	no	—
1424	C₂	#520×D₆₇	1	1	yes	characteristic
1425	C₂	C₂×#131×D₆₇	1	1	yes	characteristic
1426	C₂	C₂×#16864162	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₆₇×#2990	C₂
prime radical	#22573502	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	#2990	D₆₇
hypocenter	C₆₇	#60265
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #2990

Complements

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

N	H ≅ G/N	type
2. #22569366	C₂	semidirect
3. #22569362	C₂	semidirect
4. #22569347	C₂	semidirect
5. #22569344	C₂	semidirect
6. #22569336	C₂	semidirect
7. #22569334	C₂	semidirect
8. #22569331	C₂	semidirect
9. #22569328	C₂	semidirect
10. #22569323	C₂	semidirect
11. #22569318	C₂	semidirect
12. #22569317	C₂	semidirect
13. #22569154	C₂	semidirect
14. #22568950	C₂	semidirect
15. #22568900	C₂	semidirect
16. #22568898	C₂	semidirect
17. #22568876	C₂	semidirect
18. #22568870	C₂	semidirect
19. #22568839	C₂	semidirect
20. #22568778	C₂	semidirect
21. #22568774	C₂	semidirect
22. C₂×C₄⋊C₈×D₆₇	C₂	semidirect
23. C₆₇×#2990	C₂	semidirect
57. #16863527	C₂²	semidirect
58. #16863525	C₂²	semidirect
59. #16863525	C₂²	semidirect
60. #16863524	C₂²	semidirect
61. #16863524	C₂²	semidirect
62. C₈×Dic₁₃₄	C₂²	semidirect
63. #16863520	C₂²	semidirect
64. #16863472	C₂²	semidirect
65. #16863471	C₂²	semidirect
68. #16863469	C₂²	semidirect
70. #16863468	C₂²	semidirect
73. #16863466	C₂²	semidirect
81. C₈×C₂²⋊D₆₇	C₂²	semidirect
84. (C₂²⋊D₆₇)⋊C₈	C₂²	semidirect
85. #16863458	C₂²	semidirect
86. #16863455	C₂²	semidirect
87. #16863454	C₂²	semidirect
88. #16863454	C₂²	semidirect
90. #16863453	C₂²	semidirect
91. #16863452	C₂²	semidirect
92. #16863452	C₂²	semidirect
94. #16863449	C₂²	semidirect
97. #16863448	C₂²	semidirect
98. #16863448	C₂²	semidirect
100. #16863424	C₂²	semidirect
101. #16863422	C₂²	semidirect
104. #16863421	C₂²	semidirect
105. #16863421	C₂²	semidirect
106. #16863420	C₂²	semidirect
109. #16863418	C₂²	semidirect
110. #16863418	C₂²	semidirect
112. C₂×C₄⋊(C₆₇⋊C₈)	C₂²	semidirect
120. C₄⋊C₈×D₆₇	C₂²	semidirect
121. C₄⋊C₈×D₆₇	C₂²	semidirect
129. #446×C₆₇	C₂²	semidirect
131. #435×C₆₇	C₂²	semidirect
134. #432×C₆₇	C₂²	semidirect
135. #431×C₆₇	C₂²	semidirect
136. #423×C₆₇	C₂²	semidirect
138. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
639. C₄×D₆₇	#131	semidirect
722. #2990	D₆₇	semidirect
737. C₆₇	#60265	semidirect
777. #446	C₂×D₆₇	semidirect
793. #435	C₂×D₆₇	semidirect
814. #432	C₂×D₆₇	semidirect
821. #431	C₂×D₆₇	semidirect
833. #423	C₂×D₆₇	semidirect
846. C₂×C₄⋊C₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573502	2
#22569366	2
#22569362	2
#22569347	2
#22569344	2
#22569336	2
#22569334	2
#22569331	2
#22569328	2
#22569323	2
#22569318	2
#22569317	2
#22569154	2
#22568950	2
#22568900	2
#22568898	2
#22568876	2
#22568870	2
#22568839	2
#22568778	2
#22568774	2
C₂×C₄⋊C₈×D₆₇	2
C₆₇×#2990	2
#60265	67