Subgroups — #31764395

Order 17152.

7286 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573956	C₂	1	4	yes	maximal, complemented
2	#22573949	C₂	1	4	yes	maximal, complemented
3	#22573939	C₂	1	4	yes	maximal, complemented
4	#22573932	C₂	1	4	yes	maximal, complemented
5	#22573921	C₂	1	4	yes	maximal, complemented
6	#22573910	C₂	1	4	yes	maximal, complemented
7	#22573901	C₂	1	4	yes	maximal, complemented
8	#22573892	C₂	1	4	yes	maximal, complemented
9	#22573771	C₂	1	8	yes	maximal, complemented
10	#22573761	C₂	1	8	yes	maximal, complemented
11	#22573612	C₂	1	1	yes	maximal, characteristic, complemented
12	#22573601	C₂	1	1	yes	maximal, characteristic, complemented
13	#22573598	C₂	1	1	yes	maximal, characteristic, complemented
14	#22573594	C₂	1	2	yes	maximal, complemented
15	#22573536	C₂	1	1	yes	maximal, characteristic, complemented
16	#22573505	C₂	1	1	yes	maximal, characteristic, complemented
17	#22573501	C₂	1	2	yes	maximal, complemented
18	#525×D₆₇	C₂	1	2	yes	maximal, complemented
19	#22573408	C₂	1	2	yes	maximal, complemented
20	C₂²×#14524000	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3444	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#41×D₆₇	C₂²	1	2	yes	—
23	C₂³×C₄×D₆₇	C₂²	1	1	yes	characteristic
24	#16864118	C₂²	1	8	yes	complemented
25	#16864113	C₂²	1	8	yes	complemented
26	#16864109	C₂²	1	8	yes	complemented
27	#16864108	C₂²	1	8	yes	complemented
28	#16864105	C₂²	1	8	yes	complemented
29	#16864100	C₂²	1	8	yes	complemented
30	#16864097	C₂²	1	8	yes	complemented
31	#16864095	C₂²	1	8	yes	complemented
32	#16864095	C₂²	1	8	yes	complemented
33	#16864089	C₂²	1	8	yes	complemented
34	#16864087	C₂²	1	8	yes	complemented
35	#16864085	C₂²	1	8	yes	complemented
36	#16864083	C₂²	1	8	yes	complemented
37	#16864082	C₂²	1	8	yes	complemented
38	#16864079	C₂²	1	8	yes	complemented
39	#16864079	C₂²	1	8	yes	complemented
40	#16864078	C₂²	1	8	yes	complemented
41	#16864078	C₂²	1	8	yes	complemented
42	#16864076	C₂²	1	8	yes	complemented
43	#16864075	C₂²	1	8	yes	complemented
44	#16864075	C₂²	1	8	yes	complemented
45	#16864073	C₂²	1	8	yes	complemented
46	#16864071	C₂²	1	8	yes	complemented
47	#16864070	C₂²	1	8	yes	complemented
48	#16864070	C₂²	1	8	yes	complemented
49	#16864069	C₂²	1	8	yes	complemented
50	#16864045	C₂²	1	8	yes	complemented
51	#16864044	C₂²	1	8	yes	complemented
52	#16864041	C₂²	1	8	yes	complemented
53	#16864038	C₂²	1	8	yes	complemented
54	#16864035	C₂²	1	8	yes	complemented
55	#16864034	C₂²	1	8	yes	complemented
56	#16864026	C₂²	1	4	yes	complemented
57	#16864025	C₂²	1	4	yes	complemented
58	#16864023	C₂²	1	4	yes	complemented
59	#16864021	C₂²	1	4	yes	—
60	#16864020	C₂²	1	4	yes	complemented
61	#16864018	C₂²	1	4	yes	complemented
62	#16864015	C₂²	1	4	yes	complemented
63	#16864011	C₂²	1	4	yes	complemented
64	#16864009	C₂²	1	2	yes	complemented
65	#16864007	C₂²	1	2	yes	complemented
66	#16864004	C₂²	1	4	yes	complemented
67	#16864002	C₂²	1	2	yes	complemented
68	#16864000	C₂²	1	2	yes	complemented
69	#16863997	C₂²	1	4	yes	complemented
70	#16863995	C₂²	1	4	yes	complemented
71	#16863991	C₂²	1	4	yes	complemented
72	#16863988	C₂²	1	8	yes	complemented
73	#16863986	C₂²	1	4	yes	complemented
74	#16863983	C₂²	1	4	yes	complemented
75	#16863979	C₂²	1	8	yes	complemented
76	#16863973	C₂²	1	4	yes	complemented
77	#16863971	C₂²	1	2	yes	complemented
78	#16863966	C₂²	1	2	yes	complemented
79	#16863964	C₂²	1	2	yes	complemented
80	#16863959	C₂²	1	2	yes	complemented
81	#16863954	C₂²	1	4	yes	—
82	#16863953	C₂²	1	1	yes	characteristic, complemented
83	#16863953	C₂²	1	2	yes	complemented
84	#16863950	C₂²	1	8	yes	complemented
85	#16863949	C₂²	1	2	yes	complemented
86	#16863948	C₂²	1	4	yes	complemented
87	#16863946	C₂²	1	1	yes	characteristic, complemented
88	#16863946	C₂²	1	2	yes	complemented
89	#16863942	C₂²	1	2	yes	complemented
90	#16863941	C₂²	1	4	yes	complemented
91	#16863933	C₂²	1	8	yes	complemented
92	#16863932	C₂²	1	4	yes	complemented
93	#16863930	C₂²	1	4	yes	complemented
94	#16863930	C₂²	1	4	yes	complemented
95	#16863930	C₂²	1	4	yes	complemented
96	#16863930	C₂²	1	8	yes	complemented
97	#16863927	C₂²	1	4	yes	complemented
98	#16863926	C₂²	1	8	yes	complemented
99	#16863926	C₂²	1	8	yes	complemented
100	#16863924	C₂²	1	8	yes	complemented
101	#16863923	C₂²	1	8	yes	complemented
102	#16863909	C₂²	1	4	yes	—
103	#16863908	C₂²	1	2	yes	complemented
104	#16863907	C₂²	1	4	yes	complemented
105	#16863907	C₂²	1	2	yes	complemented
106	#16863906	C₂²	1	4	yes	—
107	#16863905	C₂²	1	8	yes	—
108	#16863905	C₂²	1	8	yes	complemented
109	#16863904	C₂²	1	4	yes	complemented
110	#16863903	C₂²	1	2	yes	complemented
111	#16863902	C₂²	1	8	yes	complemented
112	#16863902	C₂²	1	4	yes	complemented
113	#123×D₆₇	C₂²	1	4	yes	—
114	C₂²⋊Q₈×D₆₇	C₂²	1	4	yes	complemented
115	#121×D₆₇	C₂²	1	4	yes	complemented
116	#120×D₆₇	C₂²	1	4	yes	—
117	#16863878	C₂²	1	4	yes	complemented
118	#16863875	C₂²	1	8	yes	complemented
119	#16863875	C₂²	1	4	yes	complemented
120	#16863872	C₂²	1	4	yes	complemented
121	#16863868	C₂²	1	8	yes	—
122	#16863868	C₂²	1	4	yes	complemented
123	#41×Dic₆₇	C₂²	1	2	yes	complemented
124	C₄×#11761628	C₂²	1	2	yes	complemented
125	C₄×#11761628	C₂²	1	4	yes	complemented
126	C₄×#11761628	C₂²	1	4	yes	complemented
127	#16863864	C₂²	1	2	yes	complemented
128	#16863864	C₂²	1	4	yes	complemented
129	C₄×#11761627	C₂²	1	8	yes	complemented
130	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
131	C₂×#14524000	C₂²	1	1	yes	characteristic
132	C₂×#14524000	C₂²	1	2	yes	—
133	C₂×#14524000	C₂²	1	1	yes	characteristic
134	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
135	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
136	C₂×#14524000	C₂²	1	2	yes	complemented
137	C₂×#14524000	C₂²	1	4	yes	complemented
138	C₂×#14524000	C₂²	1	4	yes	complemented
139	C₂×#14524000	C₂²	1	4	yes	complemented
140	C₂×#14524000	C₂²	1	4	yes	complemented
141	C₂×#14524000	C₂²	1	4	yes	complemented
142	#117×D₆₇	C₂²	1	2	yes	—
143	#117×D₆₇	C₂²	1	4	yes	complemented
144	C₂²×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
145	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
146	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
147	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
148	#533×C₆₇	C₂²	1	2	yes	complemented
149	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
150	#532×C₆₇	C₂²	1	2	yes	complemented
151	#529×C₆₇	C₂²	1	4	yes	complemented
152	#529×C₆₇	C₂²	1	4	yes	complemented
153	#529×C₆₇	C₂²	1	4	yes	complemented
154	#525×C₆₇	C₂²	1	4	yes	complemented
155	#525×C₆₇	C₂²	1	2	yes	complemented
156	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
157	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
158	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
159	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
160	C₂×#11761629	C₂³	1	2	yes	—
161	C₂×#11761628	C₂³	1	4	yes	—
162	C₂×#11761628	C₂³	1	2	yes	—
163	C₂×#11761628	C₂³	1	4	yes	—
164	C₂×#11761627	C₂³	1	4	yes	—
165	C₂×#11761627	C₂³	1	2	yes	—
166	C₂×#11761627	C₂³	1	8	yes	—
167	#41×D₆₇	—	2	16	no	—
168	C₂×Q₈×D₆₇	C₂³	1	2	yes	—
169	C₂×D₄×D₆₇	C₂³	1	4	yes	—
170	C₂×D₄×D₆₇	C₂³	1	2	yes	—
171	C₂×D₄×D₆₇	C₂³	1	8	yes	—
172	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
173	C₂³×Dic₆₇	C₂³	1	2	yes	—
174	C₂²×C₄×D₆₇	—	2	8	no	—
175	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
176	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
178	C₂²×C₄×D₆₇	C₂³	1	4	yes	—
179	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
182	#14524043	C₂³	1	1	yes	characteristic, complemented
183	#14524043	C₂³	1	2	yes	complemented
184	#14524042	C₂³	1	4	yes	complemented
185	#14524042	C₂³	1	8	yes	complemented
186	#14524041	C₂³	1	2	yes	complemented
187	#14524041	C₂³	1	8	yes	complemented
188	#14524040	C₂³	1	1	yes	characteristic, complemented
189	#14524039	C₂³	1	2	yes	complemented
190	#14524038	C₂³	1	8	yes	—
191	#14524038	C₂³	1	8	yes	—
192	#14524038	C₂³	1	8	yes	—
193	#14524038	C₂³	1	8	yes	complemented
194	#14524038	C₂³	1	8	yes	complemented
195	#14524037	C₂³	1	8	yes	—
196	#14524037	C₂³	1	8	yes	complemented
197	#14524037	C₂³	1	8	yes	complemented
198	#14524036	C₂³	1	8	yes	complemented
199	#14524036	C₂³	1	8	yes	complemented
200	#14524036	C₂³	1	8	yes	complemented
201	#14524035	C₂³	1	2	yes	complemented
202	#14524035	C₂³	1	8	yes	complemented
203	#14524035	C₂³	1	4	yes	complemented
204	#14524034	C₂³	1	4	yes	complemented
205	#14524034	C₂³	1	8	yes	complemented
206	#14524033	C₂³	1	8	yes	complemented
207	#14524033	C₂³	1	8	yes	complemented
208	#14524033	C₂³	1	8	yes	complemented
209	#14524033	C₂³	1	8	yes	complemented
210	#14524033	C₂³	1	8	yes	complemented
211	#14524032	C₂³	1	8	yes	—
212	#14524032	C₂³	1	2	yes	complemented
213	#14524031	C₂³	1	8	yes	—
214	#14524031	C₂³	1	2	yes	complemented
215	#14524031	C₂³	1	4	yes	complemented
216	#14524030	C₂³	1	2	yes	complemented
217	#14524029	C₂³	1	8	yes	—
218	#14524029	C₂³	1	8	yes	—
219	#14524029	C₂³	1	8	yes	complemented
220	#14524028	C₂³	1	8	yes	—
221	#14524028	C₂³	1	8	yes	—
222	#14524028	C₂³	1	8	yes	—
223	#14524028	C₂³	1	8	yes	—
224	#14524028	C₂³	1	8	yes	complemented
225	#14524027	C₂³	1	8	yes	—
226	#14524027	C₂³	1	8	yes	—
227	#14524027	C₂³	1	4	yes	—
228	#14524026	C₂³	1	8	yes	—
229	#14524026	C₂³	1	8	yes	—
230	#14524026	C₂³	1	4	yes	—
231	#14524026	C₂³	1	8	yes	complemented
232	#14524025	C₂³	1	8	yes	—
233	#14524025	C₂³	1	8	yes	—
234	#14524025	C₂³	1	8	yes	complemented
235	#14524024	C₂³	1	8	yes	—
236	#14524024	C₂³	1	4	yes	—
237	#14524024	C₂³	1	8	yes	complemented
238	#14524023	C₂³	1	4	yes	—
239	#14524023	C₂³	1	8	yes	—
240	#14524022	C₂³	1	4	yes	—
241	#14524022	C₂³	1	4	yes	—
242	#14524022	C₂³	1	4	yes	—
243	#14524022	C₂³	1	8	yes	complemented
244	#14524021	C₂³	1	8	yes	—
245	#14524021	C₂³	1	8	yes	—
246	#14524021	C₂³	1	8	yes	—
247	#14524021	C₂³	1	8	yes	complemented
248	#14524021	C₂³	1	8	yes	complemented
249	#14524020	C₂³	1	8	yes	—
250	#14524020	C₂³	1	8	yes	—
251	#14524020	C₂³	1	8	yes	—
252	#14524020	C₂³	1	8	yes	complemented
253	#14524020	C₂³	1	8	yes	complemented
254	#14524019	C₂³	1	4	yes	—
255	#14524019	C₂³	1	8	yes	—
256	#14524019	C₂³	1	8	yes	complemented
257	#14524018	C₂³	1	4	yes	—
258	#14524018	C₂³	1	8	yes	—
259	#14524017	C₂³	1	8	yes	—
260	#14524017	C₂³	1	4	yes	—
261	#14524017	C₂³	1	4	yes	—
262	#14524017	C₂³	1	4	yes	—
263	#14524016	C₂³	1	8	yes	—
264	#14524016	C₂³	1	8	yes	—
265	#14524016	C₂³	1	8	yes	complemented
266	#14524015	C₂³	1	8	yes	—
267	#14524015	C₂³	1	8	yes	—
268	#14524015	C₂³	1	8	yes	—
269	#14524015	C₂³	1	8	yes	—
270	#14524015	C₂³	1	8	yes	complemented
271	#14524014	C₂³	1	4	yes	—
272	#14524013	C₂³	1	8	yes	—
273	#14524013	C₂³	1	8	yes	—
274	#14524013	C₂³	1	4	yes	—
275	#14524012	C₂³	1	4	yes	—
276	#14524011	C₂³	1	8	yes	—
277	#14524011	C₂³	1	8	yes	—
278	#14524011	C₂³	1	4	yes	—
279	Q₈×Dic₆₇	C₂³	1	4	yes	complemented
280	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
281	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
282	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
283	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
284	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
285	#14524008	C₂³	1	4	yes	complemented
286	#14524008	C₂³	1	8	yes	complemented
287	#14524008	C₂³	1	8	yes	complemented
288	C₄×D₂₆₈	C₂³	1	8	yes	—
289	C₄×D₂₆₈	C₂³	1	8	yes	—
290	C₄×D₂₆₈	C₂³	1	4	yes	complemented
291	C₄×D₂₆₈	C₂³	1	4	yes	complemented
292	C₄×D₂₆₈	C₂³	1	4	yes	complemented
293	D₄×Dic₆₇	C₂³	1	8	yes	—
294	D₄×Dic₆₇	C₂³	1	8	yes	—
295	D₄×Dic₆₇	C₂³	1	8	yes	—
296	D₄×Dic₆₇	C₂³	1	4	yes	complemented
297	#14524005	C₂³	1	8	yes	—
298	#14524005	C₂³	1	8	yes	—
299	#14524005	C₂³	1	4	yes	complemented
300	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
301	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
302	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
303	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
304	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
305	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
306	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
307	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
308	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
309	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
310	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
311	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
312	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
313	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
314	#14524002	C₂³	1	4	yes	—
315	#14524002	C₂³	1	2	yes	—
316	#14524002	C₂³	1	4	yes	complemented
317	#14524001	C₂³	1	4	yes	—
318	#14524001	C₂³	1	8	yes	—
319	#14524001	C₂³	1	8	yes	complemented
320	#14524000	C₂³	1	2	yes	—
321	#14524000	C₂³	1	2	yes	—
322	#14524000	C₂³	1	4	yes	—
323	#14524000	C₂³	1	2	yes	—
324	#14524000	C₂³	1	2	yes	—
325	#14524000	C₂³	1	4	yes	—
326	#14524000	C₂³	1	8	yes	—
327	#14524000	C₂³	1	4	yes	—
328	#14524000	C₂³	1	4	yes	—
329	#14524000	C₂³	1	4	yes	—
330	#14524000	C₂³	1	4	yes	—
331	#14524000	C₂³	1	4	yes	—
332	#14524000	C₂³	1	4	yes	—
333	#14524000	C₂³	1	4	yes	—
334	#14524000	C₂³	1	4	yes	—
335	#14524000	C₂³	1	2	yes	—
336	#14524000	C₂³	1	2	yes	—
337	#14524000	C₂³	1	4	yes	—
338	#14524000	C₂³	1	4	yes	—
339	#14524000	C₂³	1	2	yes	—
340	#14524000	C₂³	1	4	yes	—
341	#14524000	C₂³	1	2	yes	—
342	#14524000	C₂³	1	8	yes	complemented
343	#14524000	C₂³	1	8	yes	complemented
344	#14524000	C₂³	1	4	yes	complemented
345	#14524000	C₂³	1	4	yes	complemented
346	#14523999	C₂³	1	4	yes	—
347	#14523999	C₂³	1	8	yes	—
348	#14523999	C₂³	1	8	yes	complemented
349	#14523999	C₂³	1	8	yes	complemented
350	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
351	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
352	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
353	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
354	C₂×Dic₆₇⋊C₄	C₂³	1	4	yes	—
355	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
356	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
357	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
358	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
359	C₄⋊C₄×D₆₇	C₂³	1	4	yes	—
360	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
361	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
362	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
363	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
364	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	—
365	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
366	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
367	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
368	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
369	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
370	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
371	C₂²⋊C₄×D₆₇	C₂³	1	4	yes	—
372	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
373	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
374	C₂²⋊C₄×D₆₇	C₂³	1	8	yes	—
375	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
376	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
377	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
378	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
379	C₂×C₄×Dic₆₇	C₂³	1	4	yes	—
380	C₂×C₄×Dic₆₇	C₂³	1	4	yes	complemented
381	C₄²×D₆₇	C₂³	1	4	yes	—
382	C₄²×D₆₇	C₂³	1	4	yes	complemented
383	C₄²×D₆₇	C₂³	1	4	yes	complemented
384	C₂×#41×C₆₇	C₂³	1	2	yes	—
385	C₂×#41×C₆₇	C₂³	1	4	yes	—
386	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
387	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
388	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
389	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
390	#127×C₆₇	C₂³	1	1	yes	characteristic, complemented
391	#126×C₆₇	C₂³	1	8	yes	complemented
392	#125×C₆₇	C₂³	1	2	yes	complemented
393	#125×C₆₇	C₂³	1	4	yes	complemented
394	#124×C₆₇	C₂³	1	2	yes	complemented
395	#124×C₆₇	C₂³	1	4	yes	complemented
396	#123×C₆₇	C₂³	1	8	yes	—
397	#123×C₆₇	C₂³	1	4	yes	—
398	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
399	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
400	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
401	#121×C₆₇	C₂³	1	4	yes	—
402	#121×C₆₇	C₂³	1	4	yes	—
403	#121×C₆₇	C₂³	1	4	yes	—
404	#120×C₆₇	C₂³	1	4	yes	—
405	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
406	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
407	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
408	C₄×D₄×C₆₇	C₂³	1	8	yes	—
409	C₄×D₄×C₆₇	C₂³	1	8	yes	—
410	C₄×D₄×C₆₇	C₂³	1	8	yes	—
411	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
412	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
413	C₄×D₄×C₆₇	C₂³	1	4	yes	complemented
414	#117×C₆₇	C₂³	1	4	yes	—
415	#117×C₆₇	C₂³	1	2	yes	—
416	#117×C₆₇	C₂³	1	8	yes	complemented
417	#117×C₆₇	C₂³	1	4	yes	complemented
418	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
419	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
420	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
421	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
422	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
423	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
424	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
425	C₂×C₄²×C₆₇	C₂³	1	4	yes	complemented
426	C₂³×D₆₇	—	2	4	no	—
427	C₂³×D₆₇	—	4	4	no	—
428	C₂³×D₆₇	C₂⁴	1	4	yes	—
429	C₂³×D₆₇	C₂⁴	1	4	yes	—
430	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
431	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
432	#11761629	—	2	8	no	—
433	#11761628	—	2	8	no	—
434	#11761628	—	2	16	no	—
435	#11761628	—	4	8	no	—
436	#11761627	—	2	16	no	—
437	#11761627	—	2	8	no	—
438	#11761627	—	4	16	no	—
439	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
440	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
441	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
442	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
443	Q₈×D₆₇	—	2	8	no	—
444	C₂×D₂₆₈	C₂⁴	1	4	yes	—
445	C₂×D₂₆₈	C₂⁴	1	2	yes	—
446	C₂×D₂₆₈	C₂⁴	1	8	yes	—
447	C₂×D₂₆₈	C₂⁴	1	4	yes	—
448	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
449	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
450	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
451	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
452	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
453	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
454	D₄×D₆₇	—	2	16	no	—
455	D₄×D₆₇	—	2	8	no	—
456	D₄×D₆₇	—	4	16	no	—
457	C₂²×Dic₆₇	—	2	4	no	—
458	C₂²×Dic₆₇	—	4	4	no	—
459	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
460	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
461	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
462	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
463	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
464	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
465	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
466	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
467	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
468	C₂×C₄×D₆₇	—	2	4	no	—
469	C₂×C₄×D₆₇	—	2	4	no	—
470	C₂×C₄×D₆₇	—	2	4	no	—
471	C₂×C₄×D₆₇	—	2	16	no	—
472	C₂×C₄×D₆₇	—	2	16	no	—
473	C₂×C₄×D₆₇	—	2	16	no	—
474	C₂×C₄×D₆₇	#41	1	8	yes	complemented
475	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
476	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
477	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
478	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
479	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
480	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
481	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
482	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
483	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
484	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
485	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
486	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
487	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
488	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
489	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
490	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
491	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
492	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
493	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
494	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
495	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
496	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
497	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
498	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
499	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
500	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
501	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
502	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
503	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
504	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
505	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
506	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
507	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
508	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
509	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
510	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
511	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
512	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
513	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
514	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
515	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
516	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
517	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
518	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
519	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
520	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
521	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
522	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
523	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
524	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
525	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
526	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
527	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
528	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
529	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
530	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
531	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
532	C₄×Dic₆₇	C₂⁴	1	4	yes	—
533	C₄×Dic₆₇	C₂⁴	1	8	yes	—
534	C₄×Dic₆₇	C₂⁴	1	2	yes	—
535	C₄×Dic₆₇	C₂⁴	1	8	yes	—
536	C₄×Dic₆₇	C₂⁴	1	8	yes	—
537	C₄×Dic₆₇	C₂⁴	1	4	yes	—
538	C₄×Dic₆₇	C₂⁴	1	4	yes	—
539	C₄×Dic₆₇	C₂⁴	1	2	yes	—
540	C₄×Dic₆₇	C₂⁴	1	2	yes	—
541	C₄×Dic₆₇	C₂⁴	1	2	yes	—
542	C₄×Dic₆₇	C₂⁴	1	8	yes	—
543	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
544	#41×C₆₇	—	2	8	no	—
545	#41×C₆₇	—	4	8	no	—
546	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
547	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
548	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
549	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
550	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
551	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
552	C₂²×C₄×C₆₇	—	2	4	no	—
553	C₂²×C₄×C₆₇	—	4	4	no	—
554	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
555	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
556	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
557	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
558	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
559	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
560	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
561	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
562	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
563	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
564	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
565	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
566	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
567	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
568	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
569	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
570	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
571	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
572	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
573	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
574	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
575	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
576	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
577	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
578	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
579	C₄²×C₆₇	C₂⁴	1	2	yes	—
580	C₄²×C₆₇	C₂⁴	1	2	yes	—
581	C₄²×C₆₇	C₂⁴	1	2	yes	—
582	C₄²×C₆₇	C₂⁴	1	2	yes	—
583	C₄²×C₆₇	C₂⁴	1	2	yes	—
584	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
585	C₄²×C₆₇	C₂⁴	1	2	yes	—
586	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
587	C₄²×C₆₇	C₂⁴	1	4	yes	—
588	C₄²×C₆₇	C₂⁴	1	8	yes	—
589	C₂³×C₆₇	—	2	2	no	—
590	C₂³×C₆₇	—	2	4	no	—
591	C₂³×C₆₇	C₂⁵	1	4	yes	—
592	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
593	C₂³×C₆₇	C₂⁵	1	2	yes	—
594	C₂²×D₆₇	—	2	2	no	—
595	C₂²×D₆₇	—	2	8	no	—
596	C₂²×D₆₇	—	2	8	no	—
597	C₂²×D₆₇	—	2	8	no	—
598	C₂²×D₆₇	—	4	2	no	—
599	C₂²×D₆₇	—	4	4	no	—
600	C₂²×D₆₇	—	4	2	no	—
601	C₂²×D₆₇	—	4	8	no	—
602	C₂²×D₆₇	—	4	16	no	—
603	C₂²×D₆₇	C₂×#41	1	4	yes	—
604	C₂²×D₆₇	C₂⁵	1	2	yes	—
605	C₂²×D₆₇	C₂⁵	1	4	yes	—
606	C₂²×D₆₇	C₂⁵	1	2	yes	—
607	Q₈×C₆₇	—	2	4	no	—
608	Q₈×C₆₇	—	4	4	no	—
609	D₄×C₆₇	—	2	8	no	—
610	D₄×C₆₇	—	2	16	no	—
611	D₄×C₆₇	—	2	4	no	—
612	D₄×C₆₇	—	4	4	no	—
613	C₂×C₄×C₆₇	—	2	2	no	—
614	C₂×C₄×C₆₇	—	2	4	no	—
615	C₂×C₄×C₆₇	—	2	4	no	—
616	C₂×C₄×C₆₇	—	2	4	no	—
617	C₂×C₄×C₆₇	—	2	4	no	—
618	C₂×C₄×C₆₇	—	2	8	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	—	4	2	no	—
623	C₂×C₄×C₆₇	—	4	8	no	—
624	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
625	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
626	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
627	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
628	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
629	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
630	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
631	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
632	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
633	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
634	C₂²⋊D₆₇	—	2	8	no	—
635	C₂²⋊D₆₇	—	2	16	no	—
636	C₂²⋊D₆₇	—	2	8	no	—
637	C₂²⋊D₆₇	—	2	8	no	—
638	C₂²⋊D₆₇	—	4	8	no	—
639	C₂²⋊D₆₇	—	4	8	no	—
640	C₂×Dic₆₇	—	2	2	no	—
641	C₂×Dic₆₇	—	2	8	no	—
642	C₂×Dic₆₇	—	2	8	no	—
643	C₂×Dic₆₇	—	2	8	no	—
644	C₂×Dic₆₇	—	4	2	no	—
645	C₂×Dic₆₇	—	4	4	no	—
646	C₂×Dic₆₇	—	4	2	no	—
647	C₂×Dic₆₇	—	4	8	no	—
648	C₂×Dic₆₇	C₂×#41	1	4	yes	—
649	C₂×Dic₆₇	C₂⁵	1	4	yes	—
650	C₂×Dic₆₇	C₂⁵	1	4	yes	—
651	C₂×Dic₆₇	C₂⁵	1	4	yes	—
652	C₂×Dic₆₇	C₂⁵	1	8	yes	—
653	C₂×Dic₆₇	C₂⁵	1	2	yes	—
654	C₂×Dic₆₇	C₂⁵	1	2	yes	—
655	D₂₆₈	—	2	8	no	—
656	D₂₆₈	—	2	4	no	—
657	D₂₆₈	—	4	8	no	—
658	D₂₆₈	—	4	4	no	—
659	C₄×D₆₇	—	2	8	no	—
660	C₄×D₆₇	—	2	8	no	—
661	C₄×D₆₇	—	2	4	no	—
662	C₄×D₆₇	—	2	4	no	—
663	C₄×D₆₇	—	2	8	no	—
664	C₄×D₆₇	—	2	8	no	—
665	C₄×D₆₇	—	2	8	no	—
666	C₄×D₆₇	—	4	8	no	—
667	C₄×D₆₇	—	4	8	no	—
668	C₄×D₆₇	—	4	8	no	—
669	C₄×D₆₇	C₂×#41	1	8	yes	—
670	C₄×D₆₇	C₂×#41	1	8	yes	—
671	Dic₁₃₄	—	2	4	no	—
672	Dic₁₃₄	—	2	8	no	—
673	Dic₁₃₄	—	4	8	no	—
674	Dic₁₃₄	—	4	4	no	—
675	C₂²×C₆₇	—	2	8	no	—
676	C₂²×C₆₇	—	2	2	no	—
677	C₂²×C₆₇	—	2	2	no	—
678	C₂²×C₆₇	—	2	2	no	—
679	C₂²×C₆₇	—	2	4	no	—
680	C₂²×C₆₇	—	2	8	no	—
681	C₂²×C₆₇	C₂²×#41	1	2	yes	—
682	C₂²×C₆₇	#585	1	4	yes	—
683	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
684	C₂×D₆₇	—	2	4	no	—
685	C₂×D₆₇	—	2	2	no	—
686	C₂×D₆₇	—	2	4	no	—
687	C₂×D₆₇	—	2	8	no	—
688	C₂×D₆₇	—	2	4	no	—
689	C₂×D₆₇	—	4	4	no	—
690	C₂×D₆₇	—	4	16	no	—
691	C₂×D₆₇	—	4	4	no	—
692	C₂×D₆₇	—	8	8	no	—
693	C₂×D₆₇	C₂²×#41	1	4	yes	—
694	C₄×C₆₇	—	2	4	no	—
695	C₄×C₆₇	—	2	2	no	—
696	C₄×C₆₇	—	2	2	no	—
697	C₄×C₆₇	—	2	8	no	—
698	C₄×C₆₇	—	2	2	no	—
699	C₄×C₆₇	—	2	2	no	—
700	C₄×C₆₇	—	2	2	no	—
701	C₄×C₆₇	C₂²×#41	1	2	yes	—
702	C₄×C₆₇	C₂²×#41	1	2	yes	—
703	Dic₆₇	—	2	4	no	—
704	Dic₆₇	—	2	2	no	—
705	Dic₆₇	—	2	8	no	—
706	Dic₆₇	—	2	4	no	—
707	Dic₆₇	—	2	4	no	—
708	Dic₆₇	C₂²×#41	1	4	yes	—
709	#62814	—	67	1	no	maximal, Sylow
710	C₂×C₆₇	—	2	2	no	—
711	C₂×C₆₇	—	2	4	no	—
712	C₂×C₆₇	—	4	4	no	—
713	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
714	C₂×C₆₇	C₂×#585	1	2	yes	—
715	D₆₇	—	2	4	no	—
716	D₆₇	—	4	2	no	—
717	D₆₇	—	4	4	no	—
718	#3495	—	67	4	no	—
719	#3495	—	67	4	no	—
720	#3494	—	67	4	no	—
721	#3494	—	67	4	no	—
722	#3493	—	67	4	no	—
723	#3492	—	67	4	no	—
724	#3491	—	67	4	no	—
725	#3490	—	67	4	no	—
726	#3475	—	67	8	no	—
727	#3475	—	67	8	no	—
728	#3458	—	67	1	no	—
729	#3455	—	67	1	no	—
730	#3455	—	67	1	no	—
731	#3455	—	67	2	no	—
732	#3449	—	67	1	no	—
733	#3444	—	67	1	no	—
734	#3444	—	67	2	no	—
735	#3444	D₆₇	1	1	yes	characteristic, complemented
736	C₂×#525	—	67	2	no	—
737	#3428	—	67	2	no	—
738	C₂²×#117	—	67	1	no	—
739	C₆₇	#62814	1	1	yes	characteristic, complemented, Sylow
740	C₂²×#41	—	67	2	no	—
741	C₂⁴×C₄	—	67	1	no	—
742	#556	—	67	8	no	—
743	#556	—	67	8	no	—
744	#555	—	67	8	no	—
745	#555	—	67	8	no	—
746	#554	—	67	8	no	—
747	#554	—	67	8	no	—
748	#553	—	67	8	no	—
749	#553	—	67	8	no	—
750	#553	—	67	8	no	—
751	#553	—	67	8	no	—
752	#552	—	67	8	no	—
753	#552	—	67	8	no	—
754	#552	—	67	8	no	—
755	#552	—	67	8	no	—
756	#552	—	67	8	no	—
757	#552	—	67	8	no	—
758	#552	—	67	8	no	—
759	#552	—	67	8	no	—
760	#551	—	67	8	no	—
761	#551	—	67	8	no	—
762	#551	—	67	8	no	—
763	#551	—	67	8	no	—
764	#551	—	67	8	no	—
765	#551	—	67	8	no	—
766	#551	—	67	8	no	—
767	#551	—	67	8	no	—
768	#547	—	67	8	no	—
769	#547	—	67	8	no	—
770	#546	—	67	8	no	—
771	#546	—	67	8	no	—
772	#546	—	67	8	no	—
773	#546	—	67	8	no	—
774	#544	—	67	4	no	—
775	#544	—	67	4	no	—
776	#544	—	67	4	no	—
777	#543	—	67	4	no	—
778	#542	—	67	4	no	—
779	#542	—	67	4	no	—
780	#542	—	67	4	no	—
781	#542	—	67	4	no	—
782	#541	—	67	2	no	—
783	#541	—	67	2	no	—
784	#541	—	67	4	no	—
785	#540	—	67	2	no	—
786	#540	—	67	2	no	—
787	#540	—	67	4	no	—
788	#539	—	67	4	no	—
789	#539	—	67	4	no	—
790	#539	—	67	8	no	—
791	#538	—	67	4	no	—
792	#538	—	67	4	no	—
793	#538	—	67	8	no	—
794	#537	—	67	4	no	—
795	#536	—	67	2	no	—
796	#536	—	67	2	no	—
797	#535	—	67	2	no	—
798	#535	—	67	2	no	—
799	#534	—	67	4	no	—
800	#533	—	67	4	no	—
801	#533	—	67	8	no	—
802	#533	—	67	2	no	—
803	#533	—	67	1	no	—
804	#533	—	67	2	no	—
805	#533	C₂×D₆₇	1	1	yes	characteristic, complemented
806	#533	C₂×D₆₇	1	2	yes	complemented
807	#532	—	67	2	no	—
808	#532	—	67	4	no	—
809	#532	—	67	1	no	—
810	#532	—	67	2	no	—
811	#532	C₂×D₆₇	1	1	yes	characteristic, complemented
812	#532	C₂×D₆₇	1	2	yes	complemented
813	#529	—	67	8	no	—
814	#529	—	67	4	no	—
815	#529	—	67	4	no	—
816	#529	—	67	8	no	—
817	#529	—	67	8	no	—
818	#529	—	67	8	no	—
819	#529	—	67	8	no	—
820	#529	—	67	4	no	—
821	#529	—	67	4	no	—
822	#529	—	67	4	no	—
823	#529	—	67	8	no	—
824	#529	C₂×D₆₇	1	4	yes	complemented
825	#529	C₂×D₆₇	1	4	yes	complemented
826	#529	C₂×D₆₇	1	4	yes	complemented
827	#525	—	67	2	no	—
828	#525	—	67	2	no	—
829	#525	—	67	4	no	—
830	#525	—	67	4	no	—
831	#525	—	67	4	no	—
832	#525	—	67	4	no	—
833	#525	—	67	4	no	—
834	#525	—	67	8	no	—
835	#525	—	67	8	no	—
836	#525	—	67	8	no	—
837	#525	—	67	2	no	—
838	#525	C₂×D₆₇	1	2	yes	complemented
839	#525	C₂×D₆₇	1	4	yes	complemented
840	C₂×#123	—	67	4	no	—
841	C₂×C₂²⋊Q₈	—	67	4	no	—
842	C₂×#121	—	67	4	no	—
843	C₂×#120	—	67	4	no	—
844	#520	—	67	4	no	—
845	#520	—	67	8	no	—
846	#520	—	67	4	no	—
847	#519	—	67	4	no	—
848	#518	—	67	8	no	—
849	#518	—	67	4	no	—
850	C₄×#41	—	67	2	no	—
851	C₄×#41	—	67	8	no	—
852	C₄×#41	—	67	2	no	—
853	C₄×#41	—	67	4	no	—
854	C₄×#41	—	67	2	no	—
855	C₄×#41	—	67	4	no	—
856	C₄×#41	—	67	4	no	—
857	C₄×#41	C₂×D₆₇	1	2	yes	complemented
858	C₄×#41	C₂×D₆₇	1	4	yes	complemented
859	C₂×C₄×D₄	—	67	8	no	—
860	C₂×#117	—	67	2	no	—
861	C₂×#117	—	67	4	no	—
862	C₂×#117	—	67	1	no	—
863	C₂×#117	—	67	1	no	—
864	C₂×#117	—	67	2	no	—
865	C₂×#117	—	67	1	no	—
866	C₂×#117	—	67	1	no	—
867	C₂×#117	—	67	4	no	—
868	C₂×#117	—	67	4	no	—
869	C₂×#117	—	67	2	no	—
870	C₂×#117	—	67	4	no	—
871	C₂×#117	—	67	4	no	—
872	C₂×#117	—	67	4	no	—
873	C₂²×C₄⋊C₄	—	67	2	no	—
874	C₂²×C₂²⋊C₄	—	67	2	no	—
875	C₂²×C₄²	—	67	1	no	—
876	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
877	C₂⁵	—	67	1	no	—
878	C₂×#41	—	67	2	no	—
879	C₂×#41	—	67	8	no	—
880	C₂×#41	—	67	2	no	—
881	C₂×#41	—	67	4	no	—
882	C₂×#41	—	67	4	no	—
883	C₂×#41	—	67	4	no	—
884	C₂×#41	—	67	2	no	—
885	C₂×#41	—	134	16	no	—
886	C₂×#41	C₂²×D₆₇	1	2	yes	—
887	C₂×#41	C₂²×D₆₇	1	4	yes	—
888	C₂²×Q₈	—	67	2	no	—
889	C₂²×D₄	—	67	8	no	—
890	C₂²×D₄	—	67	4	no	—
891	C₂²×D₄	—	67	2	no	—
892	C₂³×C₄	—	67	2	no	—
893	C₂³×C₄	—	67	1	no	—
894	C₂³×C₄	—	67	1	no	—
895	C₂³×C₄	—	67	4	no	—
896	C₂³×C₄	—	67	4	no	—
897	C₂³×C₄	—	67	4	no	—
898	C₂³×C₄	—	67	1	no	—
899	C₂³×C₄	—	67	1	no	—
900	C₂³×C₄	—	67	1	no	—
901	C₂³×C₄	—	134	8	no	—
902	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
903	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
904	C₄⋊Q₈	—	67	2	no	—
905	C₄⋊Q₈	—	67	8	no	—
906	C₄⋊Q₈	—	67	4	no	—
907	C₄⋊Q₈	—	67	8	no	—
908	C₄⋊Q₈	—	67	1	no	—
909	C₄⋊Q₈	—	67	2	no	—
910	C₄⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic, complemented
911	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	complemented
912	#127	—	67	2	no	—
913	#127	—	67	1	no	—
914	#127	C₂²×D₆₇	1	1	yes	characteristic, complemented
915	#126	—	67	8	no	—
916	#126	—	67	8	no	—
917	#126	—	67	8	no	—
918	#126	—	67	8	no	—
919	#126	—	67	8	no	—
920	#126	—	67	8	no	—
921	#126	—	67	8	no	—
922	#126	—	67	8	no	—
923	#126	—	67	8	no	—
924	#126	—	67	8	no	—
925	#126	—	67	8	no	—
926	#126	C₂²×D₆₇	1	8	yes	complemented
927	#125	—	67	4	no	—
928	#125	—	67	8	no	—
929	#125	—	67	8	no	—
930	#125	—	67	8	no	—
931	#125	—	67	8	no	—
932	#125	—	67	8	no	—
933	#125	—	67	8	no	—
934	#125	—	67	2	no	—
935	#125	—	67	4	no	—
936	#125	—	67	8	no	—
937	#125	C₂²×D₆₇	1	2	yes	complemented
938	#125	C₂²×D₆₇	1	4	yes	complemented
939	#124	—	67	2	no	—
940	#124	—	67	8	no	—
941	#124	—	67	2	no	—
942	#124	—	67	8	no	—
943	#124	—	67	8	no	—
944	#124	—	67	8	no	—
945	#124	—	67	2	no	—
946	#124	—	67	4	no	—
947	#124	—	67	8	no	—
948	#124	C₂²×D₆₇	1	2	yes	complemented
949	#124	C₂²×D₆₇	1	4	yes	complemented
950	#123	—	67	4	no	—
951	#123	—	67	8	no	—
952	#123	—	67	8	no	—
953	#123	—	67	4	no	—
954	#123	—	67	8	no	—
955	#123	—	67	8	no	—
956	#123	—	67	8	no	—
957	#123	—	67	8	no	—
958	#123	—	67	8	no	—
959	#123	—	67	8	no	—
960	#123	—	67	8	no	—
961	#123	—	67	8	no	—
962	#123	—	67	4	no	—
963	#123	—	67	8	no	—
964	#123	—	67	8	no	—
965	#123	—	67	8	no	—
966	#123	—	67	8	no	—
967	#123	—	67	8	no	—
968	#123	C₂²×D₆₇	1	4	yes	—
969	#123	C₂²×D₆₇	1	8	yes	—
970	C₂²⋊Q₈	—	67	4	no	—
971	C₂²⋊Q₈	—	67	8	no	—
972	C₂²⋊Q₈	—	67	8	no	—
973	C₂²⋊Q₈	—	67	4	no	—
974	C₂²⋊Q₈	—	67	4	no	—
975	C₂²⋊Q₈	—	67	4	no	—
976	C₂²⋊Q₈	—	67	8	no	—
977	C₂²⋊Q₈	—	67	4	no	—
978	C₂²⋊Q₈	—	67	8	no	—
979	C₂²⋊Q₈	—	67	8	no	—
980	C₂²⋊Q₈	—	67	8	no	—
981	C₂²⋊Q₈	—	67	8	no	—
982	C₂²⋊Q₈	—	67	8	no	—
983	C₂²⋊Q₈	—	67	8	no	—
984	C₂²⋊Q₈	—	67	8	no	—
985	C₂²⋊Q₈	—	67	8	no	—
986	C₂²⋊Q₈	—	67	8	no	—
987	C₂²⋊Q₈	—	67	8	no	—
988	C₂²⋊Q₈	—	67	8	no	—
989	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	—
990	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	—
991	C₂²⋊Q₈	C₂²×D₆₇	1	4	yes	—
992	#121	—	67	4	no	—
993	#121	—	67	8	no	—
994	#121	—	67	8	no	—
995	#121	—	67	8	no	—
996	#121	—	67	8	no	—
997	#121	—	67	8	no	—
998	#121	—	67	4	no	—
999	#121	—	67	4	no	—
1000	#121	—	67	4	no	—
1001	#121	—	67	8	no	—
1002	#121	—	67	4	no	—
1003	#121	—	67	8	no	—
1004	#121	—	67	8	no	—
1005	#121	—	67	8	no	—
1006	#121	—	67	8	no	—
1007	#121	C₂²×D₆₇	1	4	yes	—
1008	#121	C₂²×D₆₇	1	4	yes	—
1009	#121	C₂²×D₆₇	1	4	yes	—
1010	#120	—	67	4	no	—
1011	#120	—	67	4	no	—
1012	#120	—	67	8	no	—
1013	#120	—	67	8	no	—
1014	#120	—	67	4	no	—
1015	#120	—	67	8	no	—
1016	#120	—	67	8	no	—
1017	#120	C₂²×D₆₇	1	4	yes	—
1018	C₄×Q₈	—	67	4	no	—
1019	C₄×Q₈	—	67	4	no	—
1020	C₄×Q₈	—	67	8	no	—
1021	C₄×Q₈	—	67	8	no	—
1022	C₄×Q₈	—	67	4	no	—
1023	C₄×Q₈	—	67	8	no	—
1024	C₄×Q₈	—	67	8	no	—
1025	C₄×Q₈	—	67	4	no	—
1026	C₄×Q₈	—	67	4	no	—
1027	C₄×Q₈	C₂²×D₆₇	1	4	yes	complemented
1028	C₄×Q₈	C₂²×D₆₇	1	4	yes	complemented
1029	C₄×Q₈	C₂²×D₆₇	1	4	yes	complemented
1030	C₄×D₄	—	67	8	no	—
1031	C₄×D₄	—	67	8	no	—
1032	C₄×D₄	—	67	4	no	—
1033	C₄×D₄	—	67	8	no	—
1034	C₄×D₄	—	67	8	no	—
1035	C₄×D₄	—	67	8	no	—
1036	C₄×D₄	—	67	8	no	—
1037	C₄×D₄	—	67	8	no	—
1038	C₄×D₄	—	67	8	no	—
1039	C₄×D₄	—	67	8	no	—
1040	C₄×D₄	—	67	8	no	—
1041	C₄×D₄	—	67	8	no	—
1042	C₄×D₄	—	67	4	no	—
1043	C₄×D₄	—	67	8	no	—
1044	C₄×D₄	—	67	8	no	—
1045	C₄×D₄	—	67	8	no	—
1046	C₄×D₄	—	67	8	no	—
1047	C₄×D₄	—	67	8	no	—
1048	C₄×D₄	—	67	8	no	—
1049	C₄×D₄	—	67	8	no	—
1050	C₄×D₄	—	67	8	no	—
1051	C₄×D₄	—	67	8	no	—
1052	C₄×D₄	—	67	4	no	—
1053	C₄×D₄	—	67	8	no	—
1054	C₄×D₄	—	67	4	no	—
1055	C₄×D₄	—	67	4	no	—
1056	C₄×D₄	C₂²×D₆₇	1	8	yes	—
1057	C₄×D₄	C₂²×D₆₇	1	8	yes	—
1058	C₄×D₄	C₂²×D₆₇	1	8	yes	—
1059	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1060	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1061	C₄×D₄	C₂²×D₆₇	1	4	yes	complemented
1062	#117	—	67	2	no	—
1063	#117	—	67	4	no	—
1064	#117	—	67	4	no	—
1065	#117	—	67	4	no	—
1066	#117	—	67	8	no	—
1067	#117	—	67	8	no	—
1068	#117	—	67	4	no	—
1069	#117	—	67	8	no	—
1070	#117	—	67	8	no	—
1071	#117	—	67	8	no	—
1072	#117	—	67	2	no	—
1073	#117	—	67	2	no	—
1074	#117	—	67	4	no	—
1075	#117	—	67	4	no	—
1076	#117	—	67	4	no	—
1077	#117	—	67	4	no	—
1078	#117	—	67	2	no	—
1079	#117	—	67	2	no	—
1080	#117	—	67	2	no	—
1081	#117	—	67	2	no	—
1082	#117	—	67	2	no	—
1083	#117	—	67	2	no	—
1084	#117	—	67	4	no	—
1085	#117	—	67	4	no	—
1086	#117	—	67	4	no	—
1087	#117	—	67	4	no	—
1088	#117	—	67	4	no	—
1089	#117	—	67	4	no	—
1090	#117	—	67	4	no	—
1091	#117	—	67	4	no	—
1092	#117	—	67	4	no	—
1093	#117	—	67	4	no	—
1094	#117	—	67	4	no	—
1095	#117	—	67	8	no	—
1096	#117	—	67	8	no	—
1097	#117	—	67	8	no	—
1098	#117	C₂²×D₆₇	1	2	yes	—
1099	#117	C₂²×D₆₇	1	4	yes	—
1100	#117	C₂²×D₆₇	1	4	yes	complemented
1101	#117	C₂²×D₆₇	1	8	yes	complemented
1102	C₂×C₄⋊C₄	—	67	2	no	—
1103	C₂×C₄⋊C₄	—	67	2	no	—
1104	C₂×C₄⋊C₄	—	67	2	no	—
1105	C₂×C₄⋊C₄	—	67	2	no	—
1106	C₂×C₄⋊C₄	—	67	4	no	—
1107	C₂×C₄⋊C₄	—	67	4	no	—
1108	C₂×C₄⋊C₄	—	67	4	no	—
1109	C₂×C₄⋊C₄	—	67	4	no	—
1110	C₂×C₄⋊C₄	—	67	8	no	—
1111	C₂×C₄⋊C₄	—	67	4	no	—
1112	C₂×C₄⋊C₄	—	67	8	no	—
1113	C₂×C₄⋊C₄	—	67	8	no	—
1114	C₂×C₂²⋊C₄	—	67	2	no	—
1115	C₂×C₂²⋊C₄	—	67	2	no	—
1116	C₂×C₂²⋊C₄	—	67	2	no	—
1117	C₂×C₂²⋊C₄	—	67	2	no	—
1118	C₂×C₂²⋊C₄	—	67	4	no	—
1119	C₂×C₂²⋊C₄	—	67	4	no	—
1120	C₂×C₂²⋊C₄	—	67	4	no	—
1121	C₂×C₂²⋊C₄	—	67	4	no	—
1122	C₂×C₂²⋊C₄	—	67	8	no	—
1123	C₂×C₂²⋊C₄	—	67	4	no	—
1124	C₂×C₂²⋊C₄	—	67	8	no	—
1125	C₂×C₂²⋊C₄	—	67	8	no	—
1126	C₂×C₂²⋊C₄	—	67	8	no	—
1127	C₂×C₄²	—	67	1	no	—
1128	C₂×C₄²	—	67	4	no	—
1129	C₂×C₄²	—	67	2	no	—
1130	C₂×C₄²	—	67	4	no	—
1131	C₂×C₄²	—	67	1	no	—
1132	C₂×C₄²	—	67	4	no	—
1133	C₂×C₄²	—	67	4	no	—
1134	C₂×C₄²	—	67	4	no	—
1135	C₂×C₄²	—	67	4	no	—
1136	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1137	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1138	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1139	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1140	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1141	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1142	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1143	C₂×C₄²	C₂²×D₆₇	1	4	yes	complemented
1144	C₂⁴	—	268	4	no	—
1145	C₂⁴	—	67	1	no	—
1146	C₂⁴	—	67	4	no	—
1147	C₂⁴	—	67	1	no	—
1148	C₂⁴	—	67	4	no	—
1149	C₂⁴	—	134	4	no	—
1150	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1151	#41	—	2	8	no	—
1152	#41	—	4	8	no	—
1153	#41	—	268	8	no	—
1154	#41	—	268	16	no	—
1155	#41	—	134	16	no	—
1156	#41	—	134	16	no	—
1157	#41	—	134	8	no	—
1158	#41	—	134	8	no	—
1159	#41	—	134	8	no	—
1160	C₂×Q₈	—	67	8	no	—
1161	C₂×Q₈	—	67	4	no	—
1162	C₂×Q₈	—	67	4	no	—
1163	C₂×Q₈	—	67	2	no	—
1164	C₂×Q₈	—	134	8	no	—
1165	C₂×Q₈	C₂³×D₆₇	1	2	yes	—
1166	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1167	C₂×D₄	—	268	16	no	—
1168	C₂×D₄	—	67	8	no	—
1169	C₂×D₄	—	67	8	no	—
1170	C₂×D₄	—	67	4	no	—
1171	C₂×D₄	—	67	4	no	—
1172	C₂×D₄	—	67	8	no	—
1173	C₂×D₄	—	67	4	no	—
1174	C₂×D₄	—	67	8	no	—
1175	C₂×D₄	—	67	4	no	—
1176	C₂×D₄	—	67	4	no	—
1177	C₂×D₄	—	67	2	no	—
1178	C₂×D₄	—	134	8	no	—
1179	C₂×D₄	—	134	16	no	—
1180	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1181	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1182	C₂×D₄	C₂³×D₆₇	1	2	yes	—
1183	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1184	C₂²×C₄	—	2	4	no	—
1185	C₂²×C₄	—	4	4	no	—
1186	C₂²×C₄	—	268	4	no	—
1187	C₂²×C₄	—	67	2	no	—
1188	C₂²×C₄	—	67	4	no	—
1189	C₂²×C₄	—	67	2	no	—
1190	C₂²×C₄	—	67	8	no	—
1191	C₂²×C₄	—	67	8	no	—
1192	C₂²×C₄	—	67	8	no	—
1193	C₂²×C₄	—	67	8	no	—
1194	C₂²×C₄	—	67	1	no	—
1195	C₂²×C₄	—	67	8	no	—
1196	C₂²×C₄	—	67	2	no	—
1197	C₂²×C₄	—	67	2	no	—
1198	C₂²×C₄	—	67	4	no	—
1199	C₂²×C₄	—	67	4	no	—
1200	C₂²×C₄	—	67	1	no	—
1201	C₂²×C₄	—	67	4	no	—
1202	C₂²×C₄	—	67	4	no	—
1203	C₂²×C₄	—	67	4	no	—
1204	C₂²×C₄	—	67	4	no	—
1205	C₂²×C₄	—	67	4	no	—
1206	C₂²×C₄	—	67	2	no	—
1207	C₂²×C₄	—	67	4	no	—
1208	C₂²×C₄	—	67	2	no	—
1209	C₂²×C₄	—	134	4	no	—
1210	C₂²×C₄	—	134	16	no	—
1211	C₂²×C₄	—	134	16	no	—
1212	C₂²×C₄	—	134	16	no	—
1213	C₂²×C₄	—	134	4	no	—
1214	C₂²×C₄	—	134	4	no	—
1215	C₂²×C₄	—	134	4	no	—
1216	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1217	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1219	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1220	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1221	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1222	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1223	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1224	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1225	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1226	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1227	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1228	C₄⋊C₄	—	67	4	no	—
1229	C₄⋊C₄	—	67	4	no	—
1230	C₄⋊C₄	—	67	8	no	—
1231	C₄⋊C₄	—	67	4	no	—
1232	C₄⋊C₄	—	67	4	no	—
1233	C₄⋊C₄	—	67	4	no	—
1234	C₄⋊C₄	—	67	4	no	—
1235	C₄⋊C₄	—	67	4	no	—
1236	C₄⋊C₄	—	67	4	no	—
1237	C₄⋊C₄	—	67	4	no	—
1238	C₄⋊C₄	—	67	8	no	—
1239	C₄⋊C₄	—	67	8	no	—
1240	C₄⋊C₄	—	67	8	no	—
1241	C₄⋊C₄	—	67	8	no	—
1242	C₄⋊C₄	—	67	8	no	—
1243	C₄⋊C₄	—	67	8	no	—
1244	C₄⋊C₄	—	67	8	no	—
1245	C₄⋊C₄	—	67	8	no	—
1246	C₄⋊C₄	—	67	8	no	—
1247	C₄⋊C₄	—	67	8	no	—
1248	C₄⋊C₄	—	67	8	no	—
1249	C₄⋊C₄	—	67	4	no	—
1250	C₄⋊C₄	—	67	4	no	—
1251	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1252	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1253	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1254	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1255	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1256	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1257	C₂²⋊C₄	—	67	4	no	—
1258	C₂²⋊C₄	—	67	8	no	—
1259	C₂²⋊C₄	—	67	8	no	—
1260	C₂²⋊C₄	—	67	8	no	—
1261	C₂²⋊C₄	—	67	8	no	—
1262	C₂²⋊C₄	—	67	4	no	—
1263	C₂²⋊C₄	—	67	4	no	—
1264	C₂²⋊C₄	—	67	8	no	—
1265	C₂²⋊C₄	—	67	4	no	—
1266	C₂²⋊C₄	—	67	4	no	—
1267	C₂²⋊C₄	—	67	4	no	—
1268	C₂²⋊C₄	—	67	4	no	—
1269	C₂²⋊C₄	—	67	4	no	—
1270	C₂²⋊C₄	—	67	4	no	—
1271	C₂²⋊C₄	—	67	8	no	—
1272	C₂²⋊C₄	—	67	8	no	—
1273	C₂²⋊C₄	—	67	8	no	—
1274	C₂²⋊C₄	—	67	8	no	—
1275	C₂²⋊C₄	—	67	8	no	—
1276	C₂²⋊C₄	—	67	8	no	—
1277	C₂²⋊C₄	—	67	8	no	—
1278	C₂²⋊C₄	—	67	8	no	—
1279	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1280	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1281	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1282	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1283	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1284	C₄²	—	67	4	no	—
1285	C₄²	—	67	2	no	—
1286	C₄²	—	67	4	no	—
1287	C₄²	—	67	2	no	—
1288	C₄²	—	67	8	no	—
1289	C₄²	—	67	8	no	—
1290	C₄²	—	67	8	no	—
1291	C₄²	—	67	8	no	—
1292	C₄²	—	67	2	no	—
1293	C₄²	—	67	2	no	—
1294	C₄²	—	67	4	no	—
1295	C₄²	C₂³×D₆₇	1	2	yes	—
1296	C₄²	C₂³×D₆₇	1	2	yes	—
1297	C₄²	C₂³×D₆₇	1	2	yes	—
1298	C₄²	C₂³×D₆₇	1	2	yes	—
1299	C₄²	C₂³×D₆₇	1	2	yes	—
1300	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1301	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1302	C₄²	C₂³×D₆₇	1	8	yes	—
1303	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1304	C₄²	C₂³×D₆₇	1	4	yes	—
1305	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1306	C₄²	C₂³×D₆₇	1	2	yes	—
1307	C₂³	—	2	2	no	—
1308	C₂³	—	2	4	no	—
1309	C₂³	—	268	16	no	—
1310	C₂³	—	268	2	no	—
1311	C₂³	—	268	4	no	—
1312	C₂³	—	268	2	no	—
1313	C₂³	—	268	8	no	—
1314	C₂³	—	67	4	no	—
1315	C₂³	—	67	2	no	—
1316	C₂³	—	67	2	no	—
1317	C₂³	—	67	4	no	—
1318	C₂³	—	134	8	no	—
1319	C₂³	—	134	8	no	—
1320	C₂³	—	134	2	no	—
1321	C₂³	—	134	8	no	—
1322	C₂³	C₂⁴×D₆₇	1	4	yes	—
1323	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1324	C₂³	C₂⁴×D₆₇	1	2	yes	—
1325	Q₈	—	2	4	no	—
1326	Q₈	—	4	4	no	—
1327	Q₈	—	268	4	no	—
1328	Q₈	—	268	8	no	—
1329	Q₈	—	134	8	no	—
1330	Q₈	—	134	4	no	—
1331	D₄	—	2	8	no	—
1332	D₄	—	2	16	no	—
1333	D₄	—	2	4	no	—
1334	D₄	—	4	4	no	—
1335	D₄	—	268	8	no	—
1336	D₄	—	268	4	no	—
1337	D₄	—	268	8	no	—
1338	D₄	—	268	8	no	—
1339	D₄	—	134	8	no	—
1340	D₄	—	134	8	no	—
1341	D₄	—	134	8	no	—
1342	D₄	—	134	8	no	—
1343	D₄	—	134	16	no	—
1344	D₄	—	134	4	no	—
1345	C₂×C₄	—	2	2	no	—
1346	C₂×C₄	—	2	4	no	—
1347	C₂×C₄	—	2	4	no	—
1348	C₂×C₄	—	2	4	no	—
1349	C₂×C₄	—	2	4	no	—
1350	C₂×C₄	—	2	8	no	—
1351	C₂×C₄	—	4	2	no	—
1352	C₂×C₄	—	4	2	no	—
1353	C₂×C₄	—	4	2	no	—
1354	C₂×C₄	—	4	2	no	—
1355	C₂×C₄	—	4	8	no	—
1356	C₂×C₄	—	268	8	no	—
1357	C₂×C₄	—	268	8	no	—
1358	C₂×C₄	—	268	8	no	—
1359	C₂×C₄	—	268	2	no	—
1360	C₂×C₄	—	268	4	no	—
1361	C₂×C₄	—	268	2	no	—
1362	C₂×C₄	—	268	8	no	—
1363	C₂×C₄	—	67	4	no	—
1364	C₂×C₄	—	67	2	no	—
1365	C₂×C₄	—	67	8	no	—
1366	C₂×C₄	—	67	8	no	—
1367	C₂×C₄	—	67	4	no	—
1368	C₂×C₄	—	67	4	no	—
1369	C₂×C₄	—	67	8	no	—
1370	C₂×C₄	—	67	4	no	—
1371	C₂×C₄	—	67	2	no	—
1372	C₂×C₄	—	134	8	no	—
1373	C₂×C₄	—	134	8	no	—
1374	C₂×C₄	—	134	8	no	—
1375	C₂×C₄	—	134	8	no	—
1376	C₂×C₄	—	134	8	no	—
1377	C₂×C₄	—	134	8	no	—
1378	C₂×C₄	—	134	2	no	—
1379	C₂×C₄	—	134	8	no	—
1380	C₂×C₄	—	134	4	no	—
1381	C₂×C₄	—	134	4	no	—
1382	C₂×C₄	—	134	8	no	—
1383	C₂×C₄	#41×D₆₇	1	4	yes	—
1384	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1385	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1386	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1387	C₂×C₄	C₂⁴×D₆₇	1	8	yes	—
1388	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1389	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1390	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1391	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1392	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1393	C₂²	—	2	8	no	—
1394	C₂²	—	2	2	no	—
1395	C₂²	—	2	2	no	—
1396	C₂²	—	2	2	no	—
1397	C₂²	—	2	4	no	—
1398	C₂²	—	2	8	no	—
1399	C₂²	—	268	4	no	—
1400	C₂²	—	268	16	no	—
1401	C₂²	—	268	4	no	—
1402	C₂²	—	536	8	no	—
1403	C₂²	—	67	4	no	—
1404	C₂²	—	134	2	no	—
1405	C₂²	—	134	4	no	—
1406	C₂²	—	134	8	no	—
1407	C₂²	—	134	4	no	—
1408	C₂²	—	134	4	no	—
1409	C₂²	C₂×#41×D₆₇	1	2	yes	—
1410	C₂²	#16864232	1	4	yes	—
1411	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1412	C₄	—	2	2	no	—
1413	C₄	—	2	4	no	—
1414	C₄	—	2	2	no	—
1415	C₄	—	2	2	no	—
1416	C₄	—	2	2	no	—
1417	C₄	—	2	2	no	—
1418	C₄	—	2	8	no	—
1419	C₄	—	67	4	no	—
1420	C₄	—	134	2	no	—
1421	C₄	—	134	4	no	—
1422	C₄	—	134	4	no	—
1423	C₄	—	134	8	no	—
1424	C₄	—	134	4	no	—
1425	C₄	C₂×#41×D₆₇	1	2	yes	—
1426	C₄	C₂×#41×D₆₇	1	2	yes	—
1427	C₂	—	2	2	no	—
1428	C₂	—	2	4	no	—
1429	C₂	—	4	4	no	—
1430	C₂	—	268	2	no	—
1431	C₂	—	268	4	no	—
1432	C₂	—	134	4	no	—
1433	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1434	C₂	C₂×#16864232	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₆₇×#3444	C₂
hypercenter	#3444	D₆₇
hypocenter	C₆₇	#62814
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #22573956	C₂	semidirect
2. #22573949	C₂	semidirect
3. #22573939	C₂	semidirect
4. #22573932	C₂	semidirect
5. #22573921	C₂	semidirect
6. #22573910	C₂	semidirect
7. #22573901	C₂	semidirect
8. #22573892	C₂	semidirect
9. #22573771	C₂	semidirect
10. #22573761	C₂	semidirect
11. #22573612	C₂	semidirect
12. #22573601	C₂	semidirect
13. #22573598	C₂	semidirect
14. #22573594	C₂	semidirect
15. #22573536	C₂	semidirect
16. #22573505	C₂	semidirect
17. #22573501	C₂	semidirect
18. #525×D₆₇	C₂	semidirect
19. #22573408	C₂	semidirect
20. C₂²×#14524000	C₂	semidirect
21. C₆₇×#3444	C₂	semidirect
24. #16864118	C₂²	semidirect
25. #16864113	C₂²	semidirect
26. #16864109	C₂²	semidirect
27. #16864108	C₂²	semidirect
28. #16864105	C₂²	semidirect
29. #16864100	C₂²	semidirect
30. #16864097	C₂²	semidirect
31. #16864095	C₂²	semidirect
32. #16864095	C₂²	semidirect
33. #16864089	C₂²	semidirect
34. #16864087	C₂²	semidirect
35. #16864085	C₂²	semidirect
36. #16864083	C₂²	semidirect
37. #16864082	C₂²	semidirect
38. #16864079	C₂²	semidirect
39. #16864079	C₂²	semidirect
40. #16864078	C₂²	semidirect
41. #16864078	C₂²	semidirect
42. #16864076	C₂²	semidirect
43. #16864075	C₂²	semidirect
44. #16864075	C₂²	semidirect
45. #16864073	C₂²	semidirect
46. #16864071	C₂²	semidirect
47. #16864070	C₂²	semidirect
48. #16864070	C₂²	semidirect
49. #16864069	C₂²	semidirect
50. #16864045	C₂²	semidirect
51. #16864044	C₂²	semidirect
52. #16864041	C₂²	semidirect
53. #16864038	C₂²	semidirect
54. #16864035	C₂²	semidirect
55. #16864034	C₂²	semidirect
56. #16864026	C₂²	semidirect
57. #16864025	C₂²	semidirect
58. #16864023	C₂²	semidirect
60. #16864020	C₂²	semidirect
61. #16864018	C₂²	semidirect
62. #16864015	C₂²	semidirect
63. #16864011	C₂²	semidirect
64. #16864009	C₂²	semidirect
65. #16864007	C₂²	semidirect
66. #16864004	C₂²	semidirect
67. #16864002	C₂²	semidirect
68. #16864000	C₂²	semidirect
69. #16863997	C₂²	semidirect
70. #16863995	C₂²	semidirect
71. #16863991	C₂²	semidirect
72. #16863988	C₂²	semidirect
73. #16863986	C₂²	semidirect
74. #16863983	C₂²	semidirect
75. #16863979	C₂²	semidirect
76. #16863973	C₂²	semidirect
77. #16863971	C₂²	semidirect
78. #16863966	C₂²	semidirect
79. #16863964	C₂²	semidirect
80. #16863959	C₂²	semidirect
82. #16863953	C₂²	semidirect
83. #16863953	C₂²	semidirect
84. #16863950	C₂²	semidirect
85. #16863949	C₂²	semidirect
86. #16863948	C₂²	semidirect
87. #16863946	C₂²	semidirect
88. #16863946	C₂²	semidirect
89. #16863942	C₂²	semidirect
90. #16863941	C₂²	semidirect
91. #16863933	C₂²	semidirect
92. #16863932	C₂²	semidirect
93. #16863930	C₂²	semidirect
94. #16863930	C₂²	semidirect
95. #16863930	C₂²	semidirect
96. #16863930	C₂²	semidirect
97. #16863927	C₂²	semidirect
98. #16863926	C₂²	semidirect
99. #16863926	C₂²	semidirect
100. #16863924	C₂²	semidirect
101. #16863923	C₂²	semidirect
103. #16863908	C₂²	semidirect
104. #16863907	C₂²	semidirect
105. #16863907	C₂²	semidirect
108. #16863905	C₂²	semidirect
109. #16863904	C₂²	semidirect
110. #16863903	C₂²	semidirect
111. #16863902	C₂²	semidirect
112. #16863902	C₂²	semidirect
114. C₂²⋊Q₈×D₆₇	C₂²	semidirect
115. #121×D₆₇	C₂²	semidirect
117. #16863878	C₂²	semidirect
118. #16863875	C₂²	semidirect
119. #16863875	C₂²	semidirect
120. #16863872	C₂²	semidirect
122. #16863868	C₂²	semidirect
123. #41×Dic₆₇	C₂²	semidirect
124. C₄×#11761628	C₂²	semidirect
125. C₄×#11761628	C₂²	semidirect
126. C₄×#11761628	C₂²	semidirect
127. #16863864	C₂²	semidirect
128. #16863864	C₂²	semidirect
129. C₄×#11761627	C₂²	semidirect
130. C₄×D₄×D₆₇	C₂²	semidirect
134. C₂×#14524000	C₂²	semidirect
135. C₂×#14524000	C₂²	semidirect
136. C₂×#14524000	C₂²	semidirect
137. C₂×#14524000	C₂²	semidirect
138. C₂×#14524000	C₂²	semidirect
139. C₂×#14524000	C₂²	semidirect
140. C₂×#14524000	C₂²	semidirect
141. C₂×#14524000	C₂²	semidirect
143. #117×D₆₇	C₂²	semidirect
144. C₂²×Dic₆₇⋊C₄	C₂²	semidirect
146. C₂²×C₄×Dic₆₇	C₂²	semidirect
147. #533×C₆₇	C₂²	semidirect
148. #533×C₆₇	C₂²	semidirect
149. #532×C₆₇	C₂²	semidirect
150. #532×C₆₇	C₂²	semidirect
151. #529×C₆₇	C₂²	semidirect
152. #529×C₆₇	C₂²	semidirect
153. #529×C₆₇	C₂²	semidirect
154. #525×C₆₇	C₂²	semidirect
155. #525×C₆₇	C₂²	semidirect
156. C₄×#41×C₆₇	C₂²	semidirect
157. C₄×#41×C₆₇	C₂²	semidirect
158. C₂²×C₄²×C₆₇	C₂²	semidirect
182. #14524043	C₂³	semidirect
183. #14524043	C₂³	semidirect
184. #14524042	C₂³	semidirect
185. #14524042	C₂³	semidirect
186. #14524041	C₂³	semidirect
187. #14524041	C₂³	semidirect
188. #14524040	C₂³	semidirect
189. #14524039	C₂³	semidirect
193. #14524038	C₂³	semidirect
194. #14524038	C₂³	semidirect
196. #14524037	C₂³	semidirect
197. #14524037	C₂³	semidirect
198. #14524036	C₂³	semidirect
199. #14524036	C₂³	semidirect
200. #14524036	C₂³	semidirect
201. #14524035	C₂³	semidirect
202. #14524035	C₂³	semidirect
203. #14524035	C₂³	semidirect
204. #14524034	C₂³	semidirect
205. #14524034	C₂³	semidirect
206. #14524033	C₂³	semidirect
207. #14524033	C₂³	semidirect
208. #14524033	C₂³	semidirect
209. #14524033	C₂³	semidirect
210. #14524033	C₂³	semidirect
212. #14524032	C₂³	semidirect
214. #14524031	C₂³	semidirect
215. #14524031	C₂³	semidirect
216. #14524030	C₂³	semidirect
219. #14524029	C₂³	semidirect
224. #14524028	C₂³	semidirect
231. #14524026	C₂³	semidirect
234. #14524025	C₂³	semidirect
237. #14524024	C₂³	semidirect
243. #14524022	C₂³	semidirect
247. #14524021	C₂³	semidirect
248. #14524021	C₂³	semidirect
252. #14524020	C₂³	semidirect
253. #14524020	C₂³	semidirect
256. #14524019	C₂³	semidirect
265. #14524016	C₂³	semidirect
270. #14524015	C₂³	semidirect
279. Q₈×Dic₆₇	C₂³	semidirect
280. C₄×Dic₁₃₄	C₂³	semidirect
281. C₄×Dic₁₃₄	C₂³	semidirect
282. C₄×Dic₁₃₄	C₂³	semidirect
283. C₄×Dic₁₃₄	C₂³	semidirect
284. C₄×Dic₁₃₄	C₂³	semidirect
285. #14524008	C₂³	semidirect
286. #14524008	C₂³	semidirect
287. #14524008	C₂³	semidirect
290. C₄×D₂₆₈	C₂³	semidirect
291. C₄×D₂₆₈	C₂³	semidirect
292. C₄×D₂₆₈	C₂³	semidirect
296. D₄×Dic₆₇	C₂³	semidirect
299. #14524005	C₂³	semidirect
305. C₄×C₂²⋊D₆₇	C₂³	semidirect
306. C₄×C₂²⋊D₆₇	C₂³	semidirect
312. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
313. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
316. #14524002	C₂³	semidirect
319. #14524001	C₂³	semidirect
342. #14524000	C₂³	semidirect
343. #14524000	C₂³	semidirect
344. #14524000	C₂³	semidirect
345. #14524000	C₂³	semidirect
348. #14523999	C₂³	semidirect
349. #14523999	C₂³	semidirect
358. C₂×Dic₆₇⋊C₄	C₂³	semidirect
361. C₄⋊C₄×D₆₇	C₂³	semidirect
380. C₂×C₄×Dic₆₇	C₂³	semidirect
382. C₄²×D₆₇	C₂³	semidirect
383. C₄²×D₆₇	C₂³	semidirect
388. C₄⋊Q₈×C₆₇	C₂³	semidirect
389. C₄⋊Q₈×C₆₇	C₂³	semidirect
390. #127×C₆₇	C₂³	semidirect
391. #126×C₆₇	C₂³	semidirect
392. #125×C₆₇	C₂³	semidirect
393. #125×C₆₇	C₂³	semidirect
394. #124×C₆₇	C₂³	semidirect
395. #124×C₆₇	C₂³	semidirect
405. C₄×Q₈×C₆₇	C₂³	semidirect
406. C₄×Q₈×C₆₇	C₂³	semidirect
407. C₄×Q₈×C₆₇	C₂³	semidirect
411. C₄×D₄×C₆₇	C₂³	semidirect
412. C₄×D₄×C₆₇	C₂³	semidirect
413. C₄×D₄×C₆₇	C₂³	semidirect
416. #117×C₆₇	C₂³	semidirect
417. #117×C₆₇	C₂³	semidirect
425. C₂×C₄²×C₆₇	C₂³	semidirect
474. C₂×C₄×D₆₇	#41	semidirect
735. #3444	D₆₇	semidirect
739. C₆₇	#62814	semidirect
805. #533	C₂×D₆₇	semidirect
806. #533	C₂×D₆₇	semidirect
811. #532	C₂×D₆₇	semidirect
812. #532	C₂×D₆₇	semidirect
824. #529	C₂×D₆₇	semidirect
825. #529	C₂×D₆₇	semidirect
826. #529	C₂×D₆₇	semidirect
838. #525	C₂×D₆₇	semidirect
839. #525	C₂×D₆₇	semidirect
857. C₄×#41	C₂×D₆₇	semidirect
858. C₄×#41	C₂×D₆₇	semidirect
876. C₂²×C₄²	C₂×D₆₇	semidirect
910. C₄⋊Q₈	C₂²×D₆₇	semidirect
911. C₄⋊Q₈	C₂²×D₆₇	semidirect
914. #127	C₂²×D₆₇	semidirect
926. #126	C₂²×D₆₇	semidirect
937. #125	C₂²×D₆₇	semidirect
938. #125	C₂²×D₆₇	semidirect
948. #124	C₂²×D₆₇	semidirect
949. #124	C₂²×D₆₇	semidirect
1027. C₄×Q₈	C₂²×D₆₇	semidirect
1028. C₄×Q₈	C₂²×D₆₇	semidirect
1029. C₄×Q₈	C₂²×D₆₇	semidirect
1059. C₄×D₄	C₂²×D₆₇	semidirect
1060. C₄×D₄	C₂²×D₆₇	semidirect
1061. C₄×D₄	C₂²×D₆₇	semidirect
1100. #117	C₂²×D₆₇	semidirect
1101. #117	C₂²×D₆₇	semidirect
1143. C₂×C₄²	C₂²×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573956	2
#22573949	2
#22573939	2
#22573932	2
#22573921	2
#22573910	2
#22573901	2
#22573892	2
#22573771	2
#22573761	2
#22573612	2
#22573601	2
#22573598	2
#22573594	2
#22573536	2
#22573505	2
#22573501	2
#525×D₆₇	2
#22573408	2
C₂²×#14524000	2
C₆₇×#3444	2
#62814	67