Subgroups — #3568×D₆₇ #31763257

Order 17152.

6726 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574906	C₂	1	3	yes	maximal, complemented
2	#22574905	C₂	1	3	yes	maximal, complemented
3	#22574904	C₂	1	6	yes	maximal, complemented
4	#22574903	C₂	1	1	yes	maximal, characteristic, complemented
5	#22574902	C₂	1	6	yes	maximal, complemented
6	#22574901	C₂	1	6	yes	maximal, complemented
7	#22574900	C₂	1	6	yes	maximal, complemented
8	#563×D₆₇	C₂	1	3	yes	maximal, complemented
9	H(3,𝔽₄)×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#556×D₆₇	C₂	1	6	yes	maximal, complemented
11	#551×D₆₇	C₂	1	6	yes	maximal, complemented
12	#542×D₆₇	C₂	1	6	yes	maximal, complemented
13	#538×D₆₇	C₂	1	6	yes	maximal, complemented
14	#529×D₆₇	C₂	1	3	yes	maximal, complemented
15	C₆₇×#3568	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864150	C₂²	1	3	yes	complemented
17	#16864150	C₂²	1	3	yes	complemented
18	#16864149	C₂²	1	6	yes	complemented
19	#16864148	C₂²	1	6	yes	complemented
20	#16864148	C₂²	1	6	yes	complemented
21	#16864147	C₂²	1	6	yes	complemented
22	#16864147	C₂²	1	6	yes	complemented
23	#16864146	C₂²	1	3	yes	complemented
24	#16864145	C₂²	1	6	yes	complemented
25	#16864139	C₂²	1	6	yes	complemented
26	#16864138	C₂²	1	6	yes	complemented
27	#16864138	C₂²	1	3	yes	complemented
28	#16864120	C₂²	1	6	yes	complemented
29	#16864119	C₂²	1	6	yes	complemented
30	#16864118	C₂²	1	6	yes	complemented
31	#16864118	C₂²	1	6	yes	complemented
32	#16864117	C₂²	1	6	yes	complemented
33	#16864117	C₂²	1	6	yes	complemented
34	#16864116	C₂²	1	6	yes	complemented
35	#16864115	C₂²	1	6	yes	complemented
36	#16864115	C₂²	1	6	yes	complemented
37	#16864114	C₂²	1	6	yes	complemented
38	#16864114	C₂²	1	6	yes	complemented
39	#16864113	C₂²	1	6	yes	complemented
40	#16864113	C₂²	1	6	yes	complemented
41	#16864113	C₂²	1	6	yes	complemented
42	#16864113	C₂²	1	6	yes	complemented
43	#16864077	C₂²	1	6	yes	complemented
44	#16864076	C₂²	1	6	yes	complemented
45	#16864075	C₂²	1	6	yes	complemented
46	#16864075	C₂²	1	6	yes	complemented
47	#16864074	C₂²	1	6	yes	complemented
48	#16864073	C₂²	1	6	yes	complemented
49	#16864073	C₂²	1	6	yes	complemented
50	#16864072	C₂²	1	6	yes	complemented
51	#16864072	C₂²	1	6	yes	complemented
52	#16864071	C₂²	1	6	yes	complemented
53	#16864071	C₂²	1	6	yes	complemented
54	#16864070	C₂²	1	6	yes	complemented
55	#16864070	C₂²	1	6	yes	complemented
56	#16864069	C₂²	1	6	yes	complemented
57	#16864069	C₂²	1	6	yes	complemented
58	#16864020	C₂²	1	6	yes	complemented
59	#16864019	C₂²	1	6	yes	complemented
60	#16864018	C₂²	1	6	yes	complemented
61	#16864017	C₂²	1	6	yes	complemented
62	#16864016	C₂²	1	6	yes	complemented
63	#16864016	C₂²	1	6	yes	complemented
64	#16864015	C₂²	1	6	yes	complemented
65	#16864014	C₂²	1	6	yes	complemented
66	#16864014	C₂²	1	6	yes	complemented
67	#16864013	C₂²	1	6	yes	complemented
68	#16864012	C₂²	1	6	yes	complemented
69	#16864012	C₂²	1	6	yes	complemented
70	#16864011	C₂²	1	6	yes	complemented
71	#16864010	C₂²	1	6	yes	complemented
72	#16864010	C₂²	1	6	yes	complemented
73	#16863986	C₂²	1	6	yes	complemented
74	#16863985	C₂²	1	6	yes	complemented
75	#16863985	C₂²	1	6	yes	complemented
76	#16863984	C₂²	1	6	yes	complemented
77	#16863983	C₂²	1	6	yes	complemented
78	#16863982	C₂²	1	6	yes	complemented
79	#16863982	C₂²	1	6	yes	complemented
80	#16863981	C₂²	1	6	yes	complemented
81	#16863981	C₂²	1	6	yes	complemented
82	#16863980	C₂²	1	6	yes	complemented
83	#16863980	C₂²	1	6	yes	complemented
84	#16863979	C₂²	1	6	yes	complemented
85	#16863979	C₂²	1	6	yes	complemented
86	#16863978	C₂²	1	6	yes	complemented
87	#16863978	C₂²	1	6	yes	complemented
88	C₄⋊Q₈×D₆₇	C₂²	1	6	yes	complemented
89	#16863933	C₂²	1	3	yes	complemented
90	#16863932	C₂²	1	3	yes	complemented
91	#16863931	C₂²	1	3	yes	complemented
92	#16863930	C₂²	1	3	yes	complemented
93	#16863929	C₂²	1	6	yes	complemented
94	#16863928	C₂²	1	3	yes	complemented
95	#16863927	C₂²	1	3	yes	complemented
96	#16863926	C₂²	1	6	yes	complemented
97	#16863925	C₂²	1	3	yes	complemented
98	#16863924	C₂²	1	6	yes	complemented
99	#16863923	C₂²	1	6	yes	complemented
100	#126×D₆₇	C₂²	1	6	yes	complemented
101	#126×D₆₇	C₂²	1	6	yes	complemented
102	#126×D₆₇	C₂²	1	2	yes	complemented
103	#126×D₆₇	C₂²	1	6	yes	complemented
104	#126×D₆₇	C₂²	1	6	yes	complemented
105	#125×D₆₇	C₂²	1	3	yes	complemented
106	#124×D₆₇	C₂²	1	3	yes	—
107	#124×D₆₇	C₂²	1	6	yes	—
108	#124×D₆₇	C₂²	1	6	yes	—
109	#124×D₆₇	C₂²	1	6	yes	complemented
110	#123×D₆₇	C₂²	1	6	yes	—
111	#123×D₆₇	C₂²	1	6	yes	—
112	#123×D₆₇	C₂²	1	6	yes	complemented
113	C₂²⋊Q₈×D₆₇	C₂²	1	6	yes	complemented
114	C₂²⋊Q₈×D₆₇	C₂²	1	6	yes	complemented
115	C₂²⋊Q₈×D₆₇	C₂²	1	3	yes	complemented
116	C₂²⋊Q₈×D₆₇	C₂²	1	6	yes	complemented
117	#121×D₆₇	C₂²	1	6	yes	—
118	#121×D₆₇	C₂²	1	3	yes	—
119	#120×D₆₇	C₂²	1	6	yes	—
120	#120×D₆₇	C₂²	1	2	yes	complemented
121	C₄×Q₈×D₆₇	C₂²	1	6	yes	complemented
122	C₄×Q₈×D₆₇	C₂²	1	3	yes	complemented
123	C₄×D₄×D₆₇	C₂²	1	3	yes	—
124	C₄×D₄×D₆₇	C₂²	1	6	yes	—
125	C₄×D₄×D₆₇	C₂²	1	6	yes	complemented
126	#117×D₆₇	C₂²	1	6	yes	complemented
127	#117×D₆₇	C₂²	1	6	yes	complemented
128	C₂×C₂²⋊C₄×D₆₇	C₂²	1	6	yes	complemented
129	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
130	#563×C₆₇	C₂²	1	3	yes	complemented
131	H(3,𝔽₄)×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#556×C₆₇	C₂²	1	6	yes	complemented
133	#551×C₆₇	C₂²	1	6	yes	complemented
134	#542×C₆₇	C₂²	1	6	yes	complemented
135	#538×C₆₇	C₂²	1	6	yes	complemented
136	#529×C₆₇	C₂²	1	3	yes	complemented
137	C₂⁴×D₆₇	C₂³	1	2	yes	—
138	C₂×Q₈×D₆₇	C₂³	1	6	yes	—
139	C₂×Q₈×D₆₇	C₂³	1	3	yes	—
140	C₂×D₄×D₆₇	C₂³	1	3	yes	—
141	C₂×D₄×D₆₇	C₂³	1	6	yes	—
142	C₂×D₄×D₆₇	C₂³	1	6	yes	—
143	C₂²×C₄×D₆₇	C₂³	1	3	yes	—
144	C₂²×C₄×D₆₇	C₂³	1	6	yes	—
145	C₂²×C₄×D₆₇	C₂³	1	6	yes	—
146	#14524043	C₂³	1	6	yes	complemented
147	#14524042	C₂³	1	6	yes	complemented
148	#14524042	C₂³	1	6	yes	complemented
149	#14524042	C₂³	1	6	yes	complemented
150	#14524042	C₂³	1	6	yes	complemented
151	#14524041	C₂³	1	6	yes	complemented
152	#14524041	C₂³	1	6	yes	complemented
153	#14524038	C₂³	1	6	yes	complemented
154	#14524038	C₂³	1	6	yes	complemented
155	#14524038	C₂³	1	6	yes	complemented
156	#14524038	C₂³	1	6	yes	complemented
157	#14524038	C₂³	1	6	yes	complemented
158	#14524038	C₂³	1	6	yes	complemented
159	#14524038	C₂³	1	6	yes	complemented
160	#14524038	C₂³	1	6	yes	complemented
161	#14524038	C₂³	1	6	yes	complemented
162	#14524038	C₂³	1	6	yes	complemented
163	#14524038	C₂³	1	6	yes	complemented
164	#14524038	C₂³	1	6	yes	complemented
165	#14524038	C₂³	1	6	yes	complemented
166	#14524037	C₂³	1	2	yes	complemented
167	#14524037	C₂³	1	6	yes	complemented
168	#14524037	C₂³	1	6	yes	complemented
169	#14524037	C₂³	1	6	yes	complemented
170	#14524037	C₂³	1	6	yes	complemented
171	#14524036	C₂³	1	6	yes	complemented
172	#14524036	C₂³	1	6	yes	complemented
173	#14524036	C₂³	1	6	yes	complemented
174	#14524036	C₂³	1	6	yes	complemented
175	#14524036	C₂³	1	6	yes	complemented
176	#14524036	C₂³	1	6	yes	complemented
177	#14524036	C₂³	1	6	yes	complemented
178	#14524036	C₂³	1	6	yes	complemented
179	#14524036	C₂³	1	6	yes	complemented
180	#14524036	C₂³	1	6	yes	complemented
181	#14524036	C₂³	1	6	yes	complemented
182	#14524036	C₂³	1	6	yes	complemented
183	#14524036	C₂³	1	6	yes	complemented
184	#14524035	C₂³	1	3	yes	complemented
185	#14524034	C₂³	1	3	yes	complemented
186	#14524034	C₂³	1	3	yes	complemented
187	#14524033	C₂³	1	6	yes	complemented
188	#14524033	C₂³	1	6	yes	complemented
189	#14524032	C₂³	1	6	yes	—
190	#14524032	C₂³	1	6	yes	—
191	#14524032	C₂³	1	3	yes	—
192	#14524032	C₂³	1	6	yes	complemented
193	#14524031	C₂³	1	6	yes	—
194	#14524031	C₂³	1	6	yes	—
195	#14524031	C₂³	1	3	yes	—
196	#14524031	C₂³	1	6	yes	complemented
197	#14524030	C₂³	1	6	yes	—
198	#14524030	C₂³	1	6	yes	—
199	#14524030	C₂³	1	3	yes	—
200	#14524030	C₂³	1	6	yes	complemented
201	#14524029	C₂³	1	6	yes	—
202	#14524029	C₂³	1	6	yes	—
203	#14524029	C₂³	1	6	yes	—
204	#14524029	C₂³	1	6	yes	—
205	#14524029	C₂³	1	6	yes	—
206	#14524029	C₂³	1	6	yes	—
207	#14524029	C₂³	1	6	yes	—
208	#14524029	C₂³	1	6	yes	—
209	#14524029	C₂³	1	6	yes	—
210	#14524029	C₂³	1	6	yes	—
211	#14524029	C₂³	1	6	yes	complemented
212	#14524029	C₂³	1	6	yes	complemented
213	#14524029	C₂³	1	6	yes	complemented
214	#14524029	C₂³	1	6	yes	complemented
215	#14524028	C₂³	1	6	yes	—
216	#14524028	C₂³	1	6	yes	—
217	#14524028	C₂³	1	6	yes	—
218	#14524028	C₂³	1	6	yes	—
219	#14524028	C₂³	1	6	yes	complemented
220	#14524028	C₂³	1	6	yes	complemented
221	#14524027	C₂³	1	6	yes	—
222	#14524027	C₂³	1	6	yes	—
223	#14524027	C₂³	1	6	yes	complemented
224	#14524026	C₂³	1	6	yes	—
225	#14524026	C₂³	1	6	yes	—
226	#14524026	C₂³	1	6	yes	complemented
227	#14524025	C₂³	1	6	yes	—
228	#14524025	C₂³	1	6	yes	—
229	#14524025	C₂³	1	6	yes	—
230	#14524025	C₂³	1	6	yes	—
231	#14524025	C₂³	1	6	yes	complemented
232	#14524025	C₂³	1	6	yes	complemented
233	#14524024	C₂³	1	6	yes	—
234	#14524024	C₂³	1	6	yes	—
235	#14524024	C₂³	1	6	yes	complemented
236	#14524023	C₂³	1	6	yes	complemented
237	#14524023	C₂³	1	3	yes	complemented
238	#14524023	C₂³	1	6	yes	complemented
239	#14524023	C₂³	1	6	yes	complemented
240	#14524022	C₂³	1	3	yes	complemented
241	#14524022	C₂³	1	6	yes	complemented
242	#14524022	C₂³	1	6	yes	complemented
243	#14524022	C₂³	1	6	yes	complemented
244	#14524021	C₂³	1	6	yes	complemented
245	#14524021	C₂³	1	6	yes	complemented
246	#14524021	C₂³	1	6	yes	complemented
247	#14524021	C₂³	1	6	yes	complemented
248	#14524021	C₂³	1	6	yes	complemented
249	#14524021	C₂³	1	6	yes	complemented
250	#14524021	C₂³	1	6	yes	complemented
251	#14524020	C₂³	1	6	yes	complemented
252	#14524020	C₂³	1	6	yes	complemented
253	#14524020	C₂³	1	6	yes	complemented
254	#14524020	C₂³	1	6	yes	complemented
255	#14524020	C₂³	1	6	yes	complemented
256	#14524020	C₂³	1	6	yes	complemented
257	#14524020	C₂³	1	6	yes	complemented
258	#14524019	C₂³	1	3	yes	complemented
259	#14524019	C₂³	1	6	yes	complemented
260	#14524019	C₂³	1	6	yes	complemented
261	#14524019	C₂³	1	6	yes	complemented
262	#14524018	C₂³	1	6	yes	—
263	#14524018	C₂³	1	3	yes	—
264	#14524017	C₂³	1	6	yes	—
265	#14524017	C₂³	1	3	yes	—
266	#14524016	C₂³	1	6	yes	—
267	#14524016	C₂³	1	6	yes	—
268	#14524016	C₂³	1	6	yes	—
269	#14524015	C₂³	1	6	yes	—
270	#14524015	C₂³	1	6	yes	—
271	#14524015	C₂³	1	6	yes	—
272	#14524014	C₂³	1	6	yes	—
273	#14524014	C₂³	1	3	yes	—
274	#14524013	C₂³	1	6	yes	—
275	#14524013	C₂³	1	6	yes	—
276	#14524013	C₂³	1	6	yes	—
277	#14524013	C₂³	1	6	yes	complemented
278	#14524012	C₂³	1	6	yes	—
279	#14524012	C₂³	1	2	yes	complemented
280	#14524011	C₂³	1	6	yes	—
281	#14524011	C₂³	1	6	yes	—
282	#14524011	C₂³	1	6	yes	—
283	#14524011	C₂³	1	6	yes	complemented
284	Q₈×Dic₆₇	C₂³	1	6	yes	complemented
285	Q₈×Dic₆₇	C₂³	1	3	yes	complemented
286	C₄×Dic₁₃₄	C₂³	1	6	yes	complemented
287	C₄×Dic₁₃₄	C₂³	1	6	yes	complemented
288	C₄×Dic₁₃₄	C₂³	1	6	yes	complemented
289	C₄×Dic₁₃₄	C₂³	1	3	yes	complemented
290	C₄×Dic₁₃₄	C₂³	1	6	yes	complemented
291	#14524008	C₂³	1	6	yes	complemented
292	#14524008	C₂³	1	6	yes	complemented
293	#14524008	C₂³	1	6	yes	complemented
294	#14524008	C₂³	1	3	yes	complemented
295	#14524008	C₂³	1	6	yes	complemented
296	C₄×D₂₆₈	C₂³	1	3	yes	—
297	C₄×D₂₆₈	C₂³	1	6	yes	—
298	C₄×D₂₆₈	C₂³	1	6	yes	complemented
299	D₄×Dic₆₇	C₂³	1	3	yes	—
300	D₄×Dic₆₇	C₂³	1	6	yes	—
301	D₄×Dic₆₇	C₂³	1	6	yes	complemented
302	#14524005	C₂³	1	3	yes	—
303	#14524005	C₂³	1	6	yes	—
304	#14524005	C₂³	1	6	yes	complemented
305	C₄×C₂²⋊D₆₇	C₂³	1	6	yes	—
306	C₄×C₂²⋊D₆₇	C₂³	1	6	yes	—
307	C₄×C₂²⋊D₆₇	C₂³	1	6	yes	—
308	C₄×C₂²⋊D₆₇	C₂³	1	6	yes	complemented
309	C₄×C₂²⋊D₆₇	C₂³	1	6	yes	complemented
310	(C₂²⋊D₆₇)⋊C₄	C₂³	1	6	yes	—
311	(C₂²⋊D₆₇)⋊C₄	C₂³	1	6	yes	—
312	(C₂²⋊D₆₇)⋊C₄	C₂³	1	6	yes	—
313	(C₂²⋊D₆₇)⋊C₄	C₂³	1	6	yes	complemented
314	(C₂²⋊D₆₇)⋊C₄	C₂³	1	6	yes	complemented
315	#14524002	C₂³	1	6	yes	complemented
316	#14524002	C₂³	1	6	yes	complemented
317	#14524001	C₂³	1	6	yes	complemented
318	#14524001	C₂³	1	6	yes	complemented
319	#14524001	C₂³	1	6	yes	complemented
320	#14524001	C₂³	1	6	yes	complemented
321	#14524000	C₂³	1	6	yes	complemented
322	#14524000	C₂³	1	6	yes	complemented
323	#14524000	C₂³	1	6	yes	complemented
324	#14524000	C₂³	1	6	yes	complemented
325	#14523999	C₂³	1	6	yes	complemented
326	#14523999	C₂³	1	6	yes	complemented
327	#14523999	C₂³	1	6	yes	complemented
328	#14523999	C₂³	1	6	yes	complemented
329	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
330	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
331	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
332	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
333	C₄⋊C₄×D₆₇	C₂³	1	3	yes	—
334	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
335	C₄⋊C₄×D₆₇	C₂³	1	3	yes	—
336	C₄⋊C₄×D₆₇	C₂³	1	6	yes	—
337	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	complemented
338	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	6	yes	complemented
339	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	6	yes	complemented
340	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
341	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
342	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
343	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
344	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
345	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
346	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
347	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
348	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	—
349	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	complemented
350	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	complemented
351	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	complemented
352	C₂²⋊C₄×D₆₇	C₂³	1	6	yes	complemented
353	C₂×C₄×Dic₆₇	C₂³	1	3	yes	complemented
354	C₄²×D₆₇	C₂³	1	3	yes	—
355	C₄²×D₆₇	C₂³	1	1	yes	characteristic
356	C₄²×D₆₇	C₂³	1	6	yes	—
357	C₄²×D₆₇	C₂³	1	6	yes	—
358	C₄²×D₆₇	C₂³	1	2	yes	—
359	C₄²×D₆₇	C₂³	1	3	yes	complemented
360	C₄²×D₆₇	C₂³	1	1	yes	characteristic, complemented
361	C₄⋊Q₈×C₆₇	C₂³	1	6	yes	complemented
362	#126×C₆₇	C₂³	1	2	yes	complemented
363	#126×C₆₇	C₂³	1	6	yes	complemented
364	#126×C₆₇	C₂³	1	6	yes	complemented
365	#126×C₆₇	C₂³	1	6	yes	complemented
366	#126×C₆₇	C₂³	1	6	yes	complemented
367	#125×C₆₇	C₂³	1	3	yes	complemented
368	#124×C₆₇	C₂³	1	6	yes	—
369	#124×C₆₇	C₂³	1	6	yes	—
370	#124×C₆₇	C₂³	1	3	yes	—
371	#124×C₆₇	C₂³	1	6	yes	complemented
372	#123×C₆₇	C₂³	1	6	yes	—
373	#123×C₆₇	C₂³	1	6	yes	—
374	#123×C₆₇	C₂³	1	6	yes	complemented
375	C₂²⋊Q₈×C₆₇	C₂³	1	3	yes	complemented
376	C₂²⋊Q₈×C₆₇	C₂³	1	6	yes	complemented
377	C₂²⋊Q₈×C₆₇	C₂³	1	6	yes	complemented
378	C₂²⋊Q₈×C₆₇	C₂³	1	6	yes	complemented
379	#121×C₆₇	C₂³	1	6	yes	—
380	#121×C₆₇	C₂³	1	3	yes	—
381	#120×C₆₇	C₂³	1	6	yes	—
382	#120×C₆₇	C₂³	1	2	yes	complemented
383	C₄×Q₈×C₆₇	C₂³	1	6	yes	complemented
384	C₄×Q₈×C₆₇	C₂³	1	3	yes	complemented
385	C₄×D₄×C₆₇	C₂³	1	3	yes	—
386	C₄×D₄×C₆₇	C₂³	1	6	yes	—
387	C₄×D₄×C₆₇	C₂³	1	6	yes	complemented
388	#117×C₆₇	C₂³	1	6	yes	complemented
389	#117×C₆₇	C₂³	1	6	yes	complemented
390	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	complemented
391	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic, complemented
392	C₂³×D₆₇	—	4	12	no	—
393	C₂³×D₆₇	C₂⁴	1	6	yes	—
394	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
395	C₂³×D₆₇	C₂⁴	1	6	yes	—
396	C₂×Dic₁₃₄	C₂⁴	1	6	yes	—
397	C₂×Dic₁₃₄	C₂⁴	1	6	yes	—
398	C₂×Dic₁₃₄	C₂⁴	1	6	yes	—
399	C₂×Dic₁₃₄	C₂⁴	1	6	yes	—
400	C₂×Dic₁₃₄	C₂⁴	1	3	yes	—
401	Q₈×D₆₇	—	4	12	no	—
402	Q₈×D₆₇	—	4	6	no	—
403	C₂×D₂₆₈	C₂⁴	1	6	yes	—
404	C₂×D₂₆₈	C₂⁴	1	3	yes	—
405	C₂×D₂₆₈	C₂⁴	1	6	yes	—
406	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
407	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
408	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
409	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
410	C₂×C₂²⋊D₆₇	C₂⁴	1	6	yes	—
411	D₄×D₆₇	—	4	12	no	—
412	D₄×D₆₇	—	4	6	no	—
413	D₄×D₆₇	—	4	12	no	—
414	C₂²×Dic₆₇	C₂⁴	1	3	yes	—
415	C₂²×Dic₆₇	C₂⁴	1	6	yes	—
416	C₂²×Dic₆₇	C₂⁴	1	6	yes	—
417	C₂×C₄×D₆₇	—	4	12	no	—
418	C₂×C₄×D₆₇	—	4	6	no	—
419	C₂×C₄×D₆₇	—	4	12	no	—
420	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
421	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
422	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
423	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
424	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
425	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
426	C₂×C₄×D₆₇	C₂⁴	1	3	yes	—
427	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
428	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
429	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
430	C₂×C₄×D₆₇	C₂⁴	1	6	yes	—
431	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
432	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
433	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
434	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
435	C₄⋊Dic₆₇	C₂⁴	1	3	yes	—
436	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
437	C₄⋊Dic₆₇	C₂⁴	1	3	yes	—
438	C₄⋊Dic₆₇	C₂⁴	1	6	yes	—
439	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
440	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
441	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
442	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
443	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
444	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
445	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
446	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
447	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
448	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
449	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
450	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
451	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
452	Dic₆₇⋊C₄	C₂⁴	1	6	yes	—
453	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
454	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
455	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
456	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
457	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
458	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
459	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
460	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
461	C₂²⋊Dic₆₇	C₂⁴	1	6	yes	—
462	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
463	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
464	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
465	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
466	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
467	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
468	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
469	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
470	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
471	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
472	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
473	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
474	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
475	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
476	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
477	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
478	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
479	(C₂×D₆₇)⋊C₄	C₂⁴	1	6	yes	—
480	C₄×Dic₆₇	C₂⁴	1	3	yes	—
481	C₄×Dic₆₇	C₂⁴	1	3	yes	—
482	C₄×Dic₆₇	C₂⁴	1	3	yes	—
483	C₄×Dic₆₇	C₂⁴	1	3	yes	—
484	C₄×Dic₆₇	C₂⁴	1	6	yes	—
485	C₄×Dic₆₇	C₂⁴	1	6	yes	—
486	C₄×Dic₆₇	C₂⁴	1	6	yes	—
487	C₄×Dic₆₇	C₂⁴	1	6	yes	—
488	C₄×Dic₆₇	C₂⁴	1	6	yes	—
489	C₄×Dic₆₇	C₂⁴	1	6	yes	—
490	C₄×Dic₆₇	C₂⁴	1	6	yes	—
491	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
492	C₂×Q₈×C₆₇	C₂⁴	1	6	yes	—
493	C₂×Q₈×C₆₇	C₂⁴	1	3	yes	—
494	C₂×D₄×C₆₇	C₂⁴	1	3	yes	—
495	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
496	C₂×D₄×C₆₇	C₂⁴	1	6	yes	—
497	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
498	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
499	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
500	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
501	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
502	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
503	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
504	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
505	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
506	C₄⋊C₄×C₆₇	C₂⁴	1	3	yes	—
507	C₄⋊C₄×C₆₇	C₂⁴	1	6	yes	—
508	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
509	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
510	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
511	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
512	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
513	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
514	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
515	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
516	C₂²⋊C₄×C₆₇	C₂⁴	1	6	yes	—
517	C₄²×C₆₇	C₂⁴	1	3	yes	—
518	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
519	C₄²×C₆₇	C₂⁴	1	6	yes	—
520	C₄²×C₆₇	C₂⁴	1	6	yes	—
521	C₄²×C₆₇	C₂⁴	1	2	yes	—
522	C₂³×C₆₇	—	4	6	no	—
523	C₂³×C₆₇	C₂⁵	1	6	yes	—
524	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
525	C₂²×D₆₇	—	2	6	no	—
526	C₂²×D₆₇	—	2	12	no	—
527	C₂²×D₆₇	—	2	12	no	—
528	C₂²×D₆₇	—	2	12	no	—
529	C₂²×D₆₇	—	4	6	no	—
530	C₂²×D₆₇	—	4	6	no	—
531	C₂²×D₆₇	—	4	6	no	—
532	C₂²×D₆₇	—	8	16	no	—
533	C₂²×D₆₇	C₂⁵	1	6	yes	—
534	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
535	C₂²×D₆₇	C₂⁵	1	1	yes	characteristic
536	Q₈×C₆₇	—	4	3	no	—
537	Q₈×C₆₇	—	4	6	no	—
538	D₄×C₆₇	—	4	6	no	—
539	D₄×C₆₇	—	4	6	no	—
540	D₄×C₆₇	—	4	3	no	—
541	C₂×C₄×C₆₇	—	4	6	no	—
542	C₂×C₄×C₆₇	—	4	6	no	—
543	C₂×C₄×C₆₇	—	4	3	no	—
544	C₂×C₄×C₆₇	C₂⁵	1	3	yes	—
545	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
546	C₂×C₄×C₆₇	C₂⁵	1	3	yes	—
547	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
549	C₂²⋊D₆₇	—	4	6	no	—
550	C₂²⋊D₆₇	—	4	6	no	—
551	C₂²⋊D₆₇	—	4	6	no	—
552	C₂²⋊D₆₇	—	4	6	no	—
553	C₂²⋊D₆₇	—	4	6	no	—
554	C₂×Dic₆₇	—	4	6	no	—
555	C₂×Dic₆₇	—	4	6	no	—
556	C₂×Dic₆₇	—	4	3	no	—
557	C₂×Dic₆₇	C₂⁵	1	3	yes	—
558	C₂×Dic₆₇	C₂⁵	1	6	yes	—
559	C₂×Dic₆₇	C₂⁵	1	3	yes	—
560	C₂×Dic₆₇	C₂⁵	1	6	yes	—
561	C₂×Dic₆₇	C₂⁵	1	6	yes	—
562	D₂₆₈	—	4	6	no	—
563	D₂₆₈	—	4	6	no	—
564	D₂₆₈	—	4	3	no	—
565	C₄×D₆₇	—	2	6	no	—
566	C₄×D₆₇	—	2	12	no	—
567	C₄×D₆₇	—	2	6	no	—
568	C₄×D₆₇	—	2	12	no	—
569	C₄×D₆₇	—	2	12	no	—
570	C₄×D₆₇	—	4	6	no	—
571	C₄×D₆₇	—	4	6	no	—
572	C₄×D₆₇	—	4	6	no	—
573	C₄×D₆₇	—	4	3	no	—
574	C₄×D₆₇	—	4	6	no	—
575	C₄×D₆₇	—	4	3	no	—
576	Dic₁₃₄	—	4	3	no	—
577	Dic₁₃₄	—	4	6	no	—
578	Dic₁₃₄	—	4	6	no	—
579	Dic₁₃₄	—	4	6	no	—
580	Dic₁₃₄	—	4	6	no	—
581	C₂²×C₆₇	—	2	3	no	—
582	C₂²×C₆₇	—	2	6	no	—
583	C₂²×C₆₇	—	2	6	no	—
584	C₂²×C₆₇	—	2	6	no	—
585	C₂²×C₆₇	—	8	4	no	—
586	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
587	C₂×D₆₇	—	2	3	no	—
588	C₂×D₆₇	—	2	6	no	—
589	C₂×D₆₇	—	2	6	no	—
590	C₂×D₆₇	—	2	6	no	—
591	C₂×D₆₇	—	4	4	no	—
592	C₂×D₆₇	—	4	24	no	—
593	C₂×D₆₇	—	8	12	no	—
594	C₂×D₆₇	#585	1	6	yes	—
595	C₄×C₆₇	—	2	6	no	—
596	C₄×C₆₇	—	2	6	no	—
597	C₄×C₆₇	—	2	3	no	—
598	C₄×C₆₇	—	2	6	no	—
599	C₄×C₆₇	—	2	3	no	—
600	Dic₆₇	—	2	6	no	—
601	Dic₆₇	—	2	6	no	—
602	Dic₆₇	—	2	3	no	—
603	Dic₆₇	—	2	6	no	—
604	Dic₆₇	—	2	3	no	—
605	C₂×#3568	—	67	1	no	maximal, Sylow
606	C₂×C₆₇	—	4	6	no	—
607	C₂×C₆₇	—	4	1	no	—
608	C₂×C₆₇	C₂×#585	1	3	yes	—
609	D₆₇	—	4	1	no	—
610	D₆₇	—	4	6	no	—
611	D₆₇	#3568	1	4	yes	direct product factor
612	#3568	—	67	3	no	—
613	#3568	—	67	1	no	—
614	#3568	—	67	6	no	—
615	#3568	—	67	6	no	—
616	#3568	—	67	6	no	—
617	#3568	—	67	6	no	—
618	#3568	—	67	3	no	—
619	#3568	D₆₇	1	1	yes	characteristic, direct product factor
620	C₂×#563	—	67	3	no	—
621	C₂×H(3,𝔽₄)	—	67	1	no	—
622	C₂×#556	—	67	6	no	—
623	C₂×#551	—	67	6	no	—
624	C₂×#542	—	67	6	no	—
625	C₂×#538	—	67	6	no	—
626	C₂×#529	—	67	3	no	—
627	C₆₇	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
628	#563	—	67	6	no	—
629	#563	—	67	6	no	—
630	#563	—	67	6	no	—
631	#563	—	67	3	no	—
632	#563	—	67	3	no	—
633	#563	—	67	3	no	—
634	#563	—	67	6	no	—
635	#563	—	67	6	no	—
636	#563	—	67	6	no	—
637	#563	C₂×D₆₇	1	3	yes	complemented
638	H(3,𝔽₄)	—	67	6	no	—
639	H(3,𝔽₄)	—	67	3	no	—
640	H(3,𝔽₄)	—	67	6	no	—
641	H(3,𝔽₄)	C₂×D₆₇	1	1	yes	characteristic, complemented
642	#556	—	67	6	no	—
643	#556	—	67	6	no	—
644	#556	—	67	6	no	—
645	#556	—	67	6	no	—
646	#556	—	67	6	no	—
647	#556	—	67	6	no	—
648	#556	—	67	6	no	—
649	#556	—	67	6	no	—
650	#556	—	67	6	no	—
651	#556	—	67	6	no	—
652	#556	—	67	6	no	—
653	#556	—	67	6	no	—
654	#556	—	67	6	no	—
655	#556	—	67	6	no	—
656	#556	—	67	6	no	—
657	#556	C₂×D₆₇	1	6	yes	complemented
658	#551	—	67	6	no	—
659	#551	—	67	6	no	—
660	#551	—	67	6	no	—
661	#551	—	67	6	no	—
662	#551	—	67	6	no	—
663	#551	—	67	6	no	—
664	#551	—	67	6	no	—
665	#551	—	67	6	no	—
666	#551	—	67	6	no	—
667	#551	—	67	6	no	—
668	#551	—	67	6	no	—
669	#551	—	67	6	no	—
670	#551	—	67	6	no	—
671	#551	—	67	6	no	—
672	#551	—	67	6	no	—
673	#551	C₂×D₆₇	1	6	yes	complemented
674	#542	—	67	6	no	—
675	#542	—	67	6	no	—
676	#542	—	67	6	no	—
677	#542	—	67	6	no	—
678	#542	—	67	6	no	—
679	#542	—	67	6	no	—
680	#542	—	67	6	no	—
681	#542	—	67	6	no	—
682	#542	—	67	6	no	—
683	#542	—	67	6	no	—
684	#542	—	67	6	no	—
685	#542	—	67	6	no	—
686	#542	—	67	6	no	—
687	#542	—	67	6	no	—
688	#542	—	67	6	no	—
689	#542	C₂×D₆₇	1	6	yes	complemented
690	#538	—	67	6	no	—
691	#538	—	67	6	no	—
692	#538	—	67	6	no	—
693	#538	—	67	6	no	—
694	#538	—	67	6	no	—
695	#538	—	67	6	no	—
696	#538	—	67	6	no	—
697	#538	—	67	6	no	—
698	#538	—	67	6	no	—
699	#538	—	67	6	no	—
700	#538	—	67	6	no	—
701	#538	—	67	6	no	—
702	#538	—	67	6	no	—
703	#538	—	67	6	no	—
704	#538	—	67	6	no	—
705	#538	C₂×D₆₇	1	6	yes	complemented
706	C₂×C₄⋊Q₈	—	67	6	no	—
707	#529	—	67	6	no	—
708	#529	—	67	3	no	—
709	#529	—	67	3	no	—
710	#529	—	67	6	no	—
711	#529	—	67	3	no	—
712	#529	—	67	3	no	—
713	#529	—	67	3	no	—
714	#529	—	67	3	no	—
715	#529	—	67	6	no	—
716	#529	—	67	6	no	—
717	#529	—	67	3	no	—
718	#529	C₂×D₆₇	1	3	yes	complemented
719	C₂×#126	—	67	6	no	—
720	C₂×#126	—	67	6	no	—
721	C₂×#126	—	67	6	no	—
722	C₂×#126	—	67	2	no	—
723	C₂×#126	—	67	6	no	—
724	C₂×#125	—	67	3	no	—
725	C₂×#124	—	67	3	no	—
726	C₂×#124	—	67	6	no	—
727	C₂×#124	—	67	6	no	—
728	C₂×#124	—	67	6	no	—
729	C₂×#123	—	67	6	no	—
730	C₂×#123	—	67	6	no	—
731	C₂×#123	—	67	6	no	—
732	C₂×C₂²⋊Q₈	—	67	3	no	—
733	C₂×C₂²⋊Q₈	—	67	6	no	—
734	C₂×C₂²⋊Q₈	—	67	6	no	—
735	C₂×C₂²⋊Q₈	—	67	6	no	—
736	C₂×#121	—	67	3	no	—
737	C₂×#121	—	67	6	no	—
738	C₂×#120	—	67	6	no	—
739	C₂×#120	—	67	2	no	—
740	C₂×C₄×Q₈	—	67	3	no	—
741	C₂×C₄×Q₈	—	67	6	no	—
742	C₂×C₄×D₄	—	67	3	no	—
743	C₂×C₄×D₄	—	67	6	no	—
744	C₂×C₄×D₄	—	67	6	no	—
745	C₂×#117	—	67	6	no	—
746	C₂×#117	—	67	6	no	—
747	C₂²×C₂²⋊C₄	—	67	6	no	—
748	C₂²×C₄²	—	67	1	no	—
749	C₂⁵	—	67	2	no	—
750	C₂²×Q₈	—	67	6	no	—
751	C₂²×Q₈	—	67	3	no	—
752	C₂²×D₄	—	67	3	no	—
753	C₂²×D₄	—	67	6	no	—
754	C₂²×D₄	—	67	6	no	—
755	C₂³×C₄	—	67	6	no	—
756	C₂³×C₄	—	67	6	no	—
757	C₂³×C₄	—	67	3	no	—
758	C₄⋊Q₈	—	67	6	no	—
759	C₄⋊Q₈	—	67	6	no	—
760	C₄⋊Q₈	—	67	6	no	—
761	C₄⋊Q₈	—	67	6	no	—
762	C₄⋊Q₈	—	67	6	no	—
763	C₄⋊Q₈	—	67	6	no	—
764	C₄⋊Q₈	—	67	6	no	—
765	C₄⋊Q₈	C₂²×D₆₇	1	6	yes	complemented
766	#126	—	67	6	no	—
767	#126	—	67	6	no	—
768	#126	—	67	6	no	—
769	#126	—	67	6	no	—
770	#126	—	67	6	no	—
771	#126	—	67	6	no	—
772	#126	—	67	6	no	—
773	#126	—	67	6	no	—
774	#126	—	67	6	no	—
775	#126	—	67	6	no	—
776	#126	—	67	6	no	—
777	#126	—	67	6	no	—
778	#126	—	67	6	no	—
779	#126	—	67	6	no	—
780	#126	—	67	6	no	—
781	#126	—	67	6	no	—
782	#126	—	67	6	no	—
783	#126	—	67	6	no	—
784	#126	—	67	6	no	—
785	#126	—	67	6	no	—
786	#126	—	67	6	no	—
787	#126	—	67	6	no	—
788	#126	—	67	6	no	—
789	#126	—	67	6	no	—
790	#126	—	67	6	no	—
791	#126	—	67	6	no	—
792	#126	—	67	6	no	—
793	#126	—	67	6	no	—
794	#126	—	67	6	no	—
795	#126	—	67	2	no	—
796	#126	—	67	6	no	—
797	#126	C₂²×D₆₇	1	6	yes	complemented
798	#126	C₂²×D₆₇	1	6	yes	complemented
799	#126	C₂²×D₆₇	1	6	yes	complemented
800	#126	C₂²×D₆₇	1	2	yes	complemented
801	#126	C₂²×D₆₇	1	6	yes	complemented
802	#125	—	67	6	no	—
803	#125	—	67	6	no	—
804	#125	—	67	3	no	—
805	#125	—	67	3	no	—
806	#125	—	67	3	no	—
807	#125	C₂²×D₆₇	1	3	yes	complemented
808	#124	—	67	3	no	—
809	#124	—	67	6	no	—
810	#124	—	67	6	no	—
811	#124	—	67	6	no	—
812	#124	—	67	3	no	—
813	#124	—	67	6	no	—
814	#124	—	67	6	no	—
815	#124	—	67	6	no	—
816	#124	—	67	6	no	—
817	#124	—	67	6	no	—
818	#124	—	67	6	no	—
819	#124	—	67	6	no	—
820	#124	—	67	6	no	—
821	#124	—	67	6	no	—
822	#124	—	67	6	no	—
823	#124	—	67	6	no	—
824	#124	—	67	6	no	—
825	#124	—	67	6	no	—
826	#124	—	67	6	no	—
827	#124	—	67	6	no	—
828	#124	—	67	6	no	—
829	#124	—	67	6	no	—
830	#124	—	67	3	no	—
831	#124	—	67	6	no	—
832	#124	—	67	6	no	—
833	#124	—	67	6	no	—
834	#124	C₂²×D₆₇	1	3	yes	—
835	#124	C₂²×D₆₇	1	6	yes	—
836	#124	C₂²×D₆₇	1	6	yes	—
837	#124	C₂²×D₆₇	1	6	yes	complemented
838	#123	—	67	6	no	—
839	#123	—	67	6	no	—
840	#123	—	67	6	no	—
841	#123	—	67	6	no	—
842	#123	—	67	6	no	—
843	#123	—	67	6	no	—
844	#123	—	67	6	no	—
845	#123	—	67	6	no	—
846	#123	—	67	6	no	—
847	#123	—	67	6	no	—
848	#123	—	67	6	no	—
849	#123	—	67	6	no	—
850	#123	—	67	6	no	—
851	#123	—	67	6	no	—
852	#123	—	67	6	no	—
853	#123	—	67	6	no	—
854	#123	—	67	6	no	—
855	#123	—	67	6	no	—
856	#123	—	67	6	no	—
857	#123	—	67	6	no	—
858	#123	—	67	6	no	—
859	#123	C₂²×D₆₇	1	6	yes	—
860	#123	C₂²×D₆₇	1	6	yes	—
861	#123	C₂²×D₆₇	1	6	yes	complemented
862	C₂²⋊Q₈	—	67	3	no	—
863	C₂²⋊Q₈	—	67	6	no	—
864	C₂²⋊Q₈	—	67	6	no	—
865	C₂²⋊Q₈	—	67	6	no	—
866	C₂²⋊Q₈	—	67	3	no	—
867	C₂²⋊Q₈	—	67	6	no	—
868	C₂²⋊Q₈	—	67	6	no	—
869	C₂²⋊Q₈	—	67	6	no	—
870	C₂²⋊Q₈	—	67	6	no	—
871	C₂²⋊Q₈	—	67	3	no	—
872	C₂²⋊Q₈	—	67	6	no	—
873	C₂²⋊Q₈	—	67	6	no	—
874	C₂²⋊Q₈	—	67	6	no	—
875	C₂²⋊Q₈	—	67	6	no	—
876	C₂²⋊Q₈	—	67	6	no	—
877	C₂²⋊Q₈	—	67	6	no	—
878	C₂²⋊Q₈	—	67	6	no	—
879	C₂²⋊Q₈	—	67	6	no	—
880	C₂²⋊Q₈	—	67	6	no	—
881	C₂²⋊Q₈	—	67	6	no	—
882	C₂²⋊Q₈	—	67	6	no	—
883	C₂²⋊Q₈	—	67	6	no	—
884	C₂²⋊Q₈	—	67	6	no	—
885	C₂²⋊Q₈	—	67	6	no	—
886	C₂²⋊Q₈	—	67	6	no	—
887	C₂²⋊Q₈	—	67	6	no	—
888	C₂²⋊Q₈	C₂²×D₆₇	1	3	yes	complemented
889	C₂²⋊Q₈	C₂²×D₆₇	1	6	yes	complemented
890	C₂²⋊Q₈	C₂²×D₆₇	1	6	yes	complemented
891	C₂²⋊Q₈	C₂²×D₆₇	1	6	yes	complemented
892	#121	—	67	3	no	—
893	#121	—	67	6	no	—
894	#121	—	67	6	no	—
895	#121	—	67	6	no	—
896	#121	—	67	6	no	—
897	#121	—	67	3	no	—
898	#121	—	67	6	no	—
899	#121	—	67	3	no	—
900	#121	—	67	6	no	—
901	#121	—	67	6	no	—
902	#121	—	67	6	no	—
903	#121	—	67	6	no	—
904	#121	C₂²×D₆₇	1	3	yes	—
905	#121	C₂²×D₆₇	1	6	yes	—
906	#120	—	67	2	no	—
907	#120	—	67	6	no	—
908	#120	—	67	6	no	—
909	#120	—	67	6	no	—
910	#120	—	67	6	no	—
911	#120	—	67	6	no	—
912	#120	—	67	6	no	—
913	#120	—	67	6	no	—
914	#120	—	67	6	no	—
915	#120	—	67	6	no	—
916	#120	C₂²×D₆₇	1	6	yes	—
917	#120	C₂²×D₆₇	1	2	yes	complemented
918	C₄×Q₈	—	67	3	no	—
919	C₄×Q₈	—	67	6	no	—
920	C₄×Q₈	—	67	3	no	—
921	C₄×Q₈	—	67	6	no	—
922	C₄×Q₈	—	67	6	no	—
923	C₄×Q₈	—	67	6	no	—
924	C₄×Q₈	—	67	6	no	—
925	C₄×Q₈	—	67	6	no	—
926	C₄×Q₈	—	67	3	no	—
927	C₄×Q₈	—	67	6	no	—
928	C₄×Q₈	—	67	6	no	—
929	C₄×Q₈	—	67	6	no	—
930	C₄×Q₈	C₂²×D₆₇	1	3	yes	complemented
931	C₄×Q₈	C₂²×D₆₇	1	6	yes	complemented
932	C₄×D₄	—	67	6	no	—
933	C₄×D₄	—	67	3	no	—
934	C₄×D₄	—	67	6	no	—
935	C₄×D₄	—	67	6	no	—
936	C₄×D₄	—	67	6	no	—
937	C₄×D₄	—	67	6	no	—
938	C₄×D₄	—	67	6	no	—
939	C₄×D₄	—	67	6	no	—
940	C₄×D₄	—	67	6	no	—
941	C₄×D₄	—	67	3	no	—
942	C₄×D₄	—	67	6	no	—
943	C₄×D₄	—	67	6	no	—
944	C₄×D₄	—	67	6	no	—
945	C₄×D₄	—	67	6	no	—
946	C₄×D₄	—	67	6	no	—
947	C₄×D₄	—	67	6	no	—
948	C₄×D₄	—	67	6	no	—
949	C₄×D₄	—	67	3	no	—
950	C₄×D₄	—	67	6	no	—
951	C₄×D₄	C₂²×D₆₇	1	3	yes	—
952	C₄×D₄	C₂²×D₆₇	1	6	yes	—
953	C₄×D₄	C₂²×D₆₇	1	6	yes	complemented
954	#117	—	67	6	no	—
955	#117	—	67	6	no	—
956	#117	—	67	6	no	—
957	#117	—	67	6	no	—
958	#117	—	67	6	no	—
959	#117	—	67	6	no	—
960	#117	—	67	6	no	—
961	#117	—	67	6	no	—
962	#117	—	67	6	no	—
963	#117	—	67	6	no	—
964	#117	—	67	6	no	—
965	#117	—	67	6	no	—
966	#117	—	67	6	no	—
967	#117	—	67	6	no	—
968	#117	C₂²×D₆₇	1	6	yes	complemented
969	#117	C₂²×D₆₇	1	6	yes	complemented
970	C₂×C₄⋊C₄	—	67	6	no	—
971	C₂×C₄⋊C₄	—	67	6	no	—
972	C₂×C₄⋊C₄	—	67	6	no	—
973	C₂×C₄⋊C₄	—	67	6	no	—
974	C₂×C₄⋊C₄	—	67	3	no	—
975	C₂×C₄⋊C₄	—	67	6	no	—
976	C₂×C₄⋊C₄	—	67	3	no	—
977	C₂×C₄⋊C₄	—	67	6	no	—
978	C₂×C₂²⋊C₄	—	67	6	no	—
979	C₂×C₂²⋊C₄	—	67	6	no	—
980	C₂×C₂²⋊C₄	—	67	6	no	—
981	C₂×C₂²⋊C₄	—	67	6	no	—
982	C₂×C₂²⋊C₄	—	67	6	no	—
983	C₂×C₂²⋊C₄	—	67	6	no	—
984	C₂×C₂²⋊C₄	—	67	6	no	—
985	C₂×C₂²⋊C₄	—	67	6	no	—
986	C₂×C₂²⋊C₄	—	67	6	no	—
987	C₂×C₂²⋊C₄	—	67	6	no	—
988	C₂×C₂²⋊C₄	—	67	6	no	—
989	C₂×C₂²⋊C₄	—	67	6	no	—
990	C₂×C₂²⋊C₄	—	67	6	no	—
991	C₂×C₂²⋊C₄	—	67	6	no	—
992	C₂×C₂²⋊C₄	—	67	6	no	—
993	C₂×C₂²⋊C₄	—	67	6	no	—
994	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	complemented
995	C₂×C₄²	—	67	3	no	—
996	C₂×C₄²	—	67	6	no	—
997	C₂×C₄²	—	67	3	no	—
998	C₂×C₄²	—	67	6	no	—
999	C₂×C₄²	—	67	2	no	—
1000	C₂×C₄²	—	67	1	no	—
1001	C₂×C₄²	—	67	1	no	—
1002	C₂×C₄²	—	67	3	no	—
1003	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic, complemented
1004	C₂⁴	—	268	12	no	—
1005	C₂⁴	—	67	6	no	—
1006	C₂⁴	—	67	6	no	—
1007	C₂⁴	—	67	1	no	—
1008	C₂⁴	C₂³×D₆₇	1	2	yes	—
1009	C₂×Q₈	—	268	12	no	—
1010	C₂×Q₈	—	268	6	no	—
1011	C₂×Q₈	—	67	6	no	—
1012	C₂×Q₈	—	67	6	no	—
1013	C₂×Q₈	—	67	6	no	—
1014	C₂×Q₈	—	67	3	no	—
1015	C₂×Q₈	—	67	6	no	—
1016	C₂×Q₈	C₂³×D₆₇	1	6	yes	—
1017	C₂×Q₈	C₂³×D₆₇	1	3	yes	—
1018	C₂×D₄	—	268	12	no	—
1019	C₂×D₄	—	268	6	no	—
1020	C₂×D₄	—	268	12	no	—
1021	C₂×D₄	—	67	6	no	—
1022	C₂×D₄	—	67	6	no	—
1023	C₂×D₄	—	67	6	no	—
1024	C₂×D₄	—	67	6	no	—
1025	C₂×D₄	—	67	6	no	—
1026	C₂×D₄	—	67	3	no	—
1027	C₂×D₄	—	67	6	no	—
1028	C₂×D₄	—	67	6	no	—
1029	C₂×D₄	C₂³×D₆₇	1	3	yes	—
1030	C₂×D₄	C₂³×D₆₇	1	6	yes	—
1031	C₂×D₄	C₂³×D₆₇	1	6	yes	—
1032	C₂²×C₄	—	268	12	no	—
1033	C₂²×C₄	—	268	6	no	—
1034	C₂²×C₄	—	268	12	no	—
1035	C₂²×C₄	—	67	3	no	—
1036	C₂²×C₄	—	67	6	no	—
1037	C₂²×C₄	—	67	6	no	—
1038	C₂²×C₄	—	67	3	no	—
1039	C₂²×C₄	—	67	3	no	—
1040	C₂²×C₄	—	67	6	no	—
1041	C₂²×C₄	—	67	6	no	—
1042	C₂²×C₄	—	67	6	no	—
1043	C₂²×C₄	—	67	6	no	—
1044	C₂²×C₄	—	67	3	no	—
1045	C₂²×C₄	—	67	6	no	—
1046	C₂²×C₄	—	67	6	no	—
1047	C₂²×C₄	—	67	3	no	—
1048	C₂²×C₄	—	67	6	no	—
1049	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
1050	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
1051	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
1052	C₄⋊C₄	—	67	6	no	—
1053	C₄⋊C₄	—	67	6	no	—
1054	C₄⋊C₄	—	67	6	no	—
1055	C₄⋊C₄	—	67	6	no	—
1056	C₄⋊C₄	—	67	6	no	—
1057	C₄⋊C₄	—	67	6	no	—
1058	C₄⋊C₄	—	67	6	no	—
1059	C₄⋊C₄	—	67	6	no	—
1060	C₄⋊C₄	—	67	6	no	—
1061	C₄⋊C₄	—	67	6	no	—
1062	C₄⋊C₄	—	67	6	no	—
1063	C₄⋊C₄	—	67	6	no	—
1064	C₄⋊C₄	—	67	6	no	—
1065	C₄⋊C₄	—	67	3	no	—
1066	C₄⋊C₄	—	67	6	no	—
1067	C₄⋊C₄	—	67	6	no	—
1068	C₄⋊C₄	—	67	6	no	—
1069	C₄⋊C₄	—	67	6	no	—
1070	C₄⋊C₄	—	67	3	no	—
1071	C₄⋊C₄	—	67	6	no	—
1072	C₄⋊C₄	—	67	6	no	—
1073	C₄⋊C₄	—	67	6	no	—
1074	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1075	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1076	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1077	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1078	C₄⋊C₄	C₂³×D₆₇	1	3	yes	—
1079	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1080	C₄⋊C₄	C₂³×D₆₇	1	3	yes	—
1081	C₄⋊C₄	C₂³×D₆₇	1	6	yes	—
1082	C₂²⋊C₄	—	67	6	no	—
1083	C₂²⋊C₄	—	67	6	no	—
1084	C₂²⋊C₄	—	67	6	no	—
1085	C₂²⋊C₄	—	67	6	no	—
1086	C₂²⋊C₄	—	67	6	no	—
1087	C₂²⋊C₄	—	67	6	no	—
1088	C₂²⋊C₄	—	67	6	no	—
1089	C₂²⋊C₄	—	67	6	no	—
1090	C₂²⋊C₄	—	67	6	no	—
1091	C₂²⋊C₄	—	67	6	no	—
1092	C₂²⋊C₄	—	67	6	no	—
1093	C₂²⋊C₄	—	67	6	no	—
1094	C₂²⋊C₄	—	67	6	no	—
1095	C₂²⋊C₄	—	67	6	no	—
1096	C₂²⋊C₄	—	67	6	no	—
1097	C₂²⋊C₄	—	67	6	no	—
1098	C₂²⋊C₄	—	67	6	no	—
1099	C₂²⋊C₄	—	67	6	no	—
1100	C₂²⋊C₄	—	67	6	no	—
1101	C₂²⋊C₄	—	67	6	no	—
1102	C₂²⋊C₄	—	67	6	no	—
1103	C₂²⋊C₄	—	67	6	no	—
1104	C₂²⋊C₄	—	67	6	no	—
1105	C₂²⋊C₄	—	67	6	no	—
1106	C₂²⋊C₄	—	67	6	no	—
1107	C₂²⋊C₄	—	67	6	no	—
1108	C₂²⋊C₄	—	67	6	no	—
1109	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1110	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1111	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1112	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1113	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1114	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1115	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1116	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1117	C₂²⋊C₄	C₂³×D₆₇	1	6	yes	—
1118	C₄²	—	67	3	no	—
1119	C₄²	—	67	3	no	—
1120	C₄²	—	67	3	no	—
1121	C₄²	—	67	3	no	—
1122	C₄²	—	67	6	no	—
1123	C₄²	—	67	6	no	—
1124	C₄²	—	67	6	no	—
1125	C₄²	—	67	6	no	—
1126	C₄²	—	67	6	no	—
1127	C₄²	—	67	6	no	—
1128	C₄²	—	67	6	no	—
1129	C₄²	C₂³×D₆₇	1	3	yes	—
1130	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1131	C₄²	C₂³×D₆₇	1	6	yes	—
1132	C₄²	C₂³×D₆₇	1	6	yes	—
1133	C₄²	C₂³×D₆₇	1	2	yes	—
1134	C₂³	—	4	6	no	—
1135	C₂³	—	268	6	no	—
1136	C₂³	—	268	6	no	—
1137	C₂³	—	268	6	no	—
1138	C₂³	—	536	16	no	—
1139	C₂³	—	67	1	no	—
1140	C₂³	—	67	6	no	—
1141	C₂³	—	67	1	no	—
1142	C₂³	—	134	6	no	—
1143	C₂³	—	134	12	no	—
1144	C₂³	—	134	12	no	—
1145	C₂³	—	134	12	no	—
1146	C₂³	C₂⁴×D₆₇	1	6	yes	—
1147	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1148	Q₈	—	4	6	no	—
1149	Q₈	—	4	3	no	—
1150	Q₈	—	268	6	no	—
1151	Q₈	—	268	6	no	—
1152	Q₈	—	268	3	no	—
1153	Q₈	—	268	6	no	—
1154	Q₈	—	268	6	no	—
1155	D₄	—	4	6	no	—
1156	D₄	—	4	3	no	—
1157	D₄	—	4	6	no	—
1158	D₄	—	268	6	no	—
1159	D₄	—	268	3	no	—
1160	D₄	—	268	6	no	—
1161	D₄	—	268	6	no	—
1162	D₄	—	268	6	no	—
1163	D₄	—	268	6	no	—
1164	D₄	—	268	6	no	—
1165	D₄	—	268	6	no	—
1166	C₂×C₄	—	4	6	no	—
1167	C₂×C₄	—	4	3	no	—
1168	C₂×C₄	—	4	6	no	—
1169	C₂×C₄	—	268	6	no	—
1170	C₂×C₄	—	268	3	no	—
1171	C₂×C₄	—	268	6	no	—
1172	C₂×C₄	—	268	6	no	—
1173	C₂×C₄	—	268	3	no	—
1174	C₂×C₄	—	268	6	no	—
1175	C₂×C₄	—	268	6	no	—
1176	C₂×C₄	—	268	3	no	—
1177	C₂×C₄	—	268	6	no	—
1178	C₂×C₄	—	67	3	no	—
1179	C₂×C₄	—	67	6	no	—
1180	C₂×C₄	—	67	3	no	—
1181	C₂×C₄	—	67	6	no	—
1182	C₂×C₄	—	67	6	no	—
1183	C₂×C₄	—	134	6	no	—
1184	C₂×C₄	—	134	12	no	—
1185	C₂×C₄	—	134	6	no	—
1186	C₂×C₄	—	134	12	no	—
1187	C₂×C₄	—	134	12	no	—
1188	C₂×C₄	C₂⁴×D₆₇	1	3	yes	—
1189	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
1190	C₂×C₄	C₂⁴×D₆₇	1	3	yes	—
1191	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
1192	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
1193	C₂²	—	2	3	no	—
1194	C₂²	—	2	6	no	—
1195	C₂²	—	2	6	no	—
1196	C₂²	—	2	6	no	—
1197	C₂²	—	8	4	no	—
1198	C₂²	—	268	24	no	—
1199	C₂²	—	268	4	no	—
1200	C₂²	—	536	12	no	—
1201	C₂²	—	67	6	no	—
1202	C₂²	—	134	3	no	—
1203	C₂²	—	134	6	no	—
1204	C₂²	—	134	6	no	—
1205	C₂²	—	134	6	no	—
1206	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1207	C₄	—	2	3	no	—
1208	C₄	—	2	6	no	—
1209	C₄	—	2	3	no	—
1210	C₄	—	2	6	no	—
1211	C₄	—	2	6	no	—
1212	C₄	—	134	3	no	—
1213	C₄	—	134	6	no	—
1214	C₄	—	134	3	no	—
1215	C₄	—	134	6	no	—
1216	C₄	—	134	6	no	—
1217	C₂	—	4	6	no	—
1218	C₂	—	4	1	no	—
1219	C₂	—	268	6	no	—
1220	C₂	—	268	1	no	—
1221	C₂	—	67	4	no	—
1222	C₂	#585×D₆₇	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Fitting	C₆₇×#3568	C₂
hypercenter	#3568	D₆₇
hypocenter	C₆₇	C₂×#3568
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #3568

Complements

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

N	H ≅ G/N	type
1. #22574906	C₂	semidirect
2. #22574905	C₂	semidirect
3. #22574904	C₂	semidirect
4. #22574903	C₂	semidirect
5. #22574902	C₂	semidirect
6. #22574901	C₂	semidirect
7. #22574900	C₂	semidirect
8. #563×D₆₇	C₂	semidirect
9. H(3,𝔽₄)×D₆₇	C₂	semidirect
10. #556×D₆₇	C₂	semidirect
11. #551×D₆₇	C₂	semidirect
12. #542×D₆₇	C₂	semidirect
13. #538×D₆₇	C₂	semidirect
14. #529×D₆₇	C₂	semidirect
15. C₆₇×#3568	C₂	semidirect
16. #16864150	C₂²	semidirect
17. #16864150	C₂²	semidirect
18. #16864149	C₂²	semidirect
19. #16864148	C₂²	semidirect
20. #16864148	C₂²	semidirect
21. #16864147	C₂²	semidirect
22. #16864147	C₂²	semidirect
23. #16864146	C₂²	semidirect
24. #16864145	C₂²	semidirect
25. #16864139	C₂²	semidirect
26. #16864138	C₂²	semidirect
27. #16864138	C₂²	semidirect
28. #16864120	C₂²	semidirect
29. #16864119	C₂²	semidirect
30. #16864118	C₂²	semidirect
31. #16864118	C₂²	semidirect
32. #16864117	C₂²	semidirect
33. #16864117	C₂²	semidirect
34. #16864116	C₂²	semidirect
35. #16864115	C₂²	semidirect
36. #16864115	C₂²	semidirect
37. #16864114	C₂²	semidirect
38. #16864114	C₂²	semidirect
39. #16864113	C₂²	semidirect
40. #16864113	C₂²	semidirect
41. #16864113	C₂²	semidirect
42. #16864113	C₂²	semidirect
43. #16864077	C₂²	semidirect
44. #16864076	C₂²	semidirect
45. #16864075	C₂²	semidirect
46. #16864075	C₂²	semidirect
47. #16864074	C₂²	semidirect
48. #16864073	C₂²	semidirect
49. #16864073	C₂²	semidirect
50. #16864072	C₂²	semidirect
51. #16864072	C₂²	semidirect
52. #16864071	C₂²	semidirect
53. #16864071	C₂²	semidirect
54. #16864070	C₂²	semidirect
55. #16864070	C₂²	semidirect
56. #16864069	C₂²	semidirect
57. #16864069	C₂²	semidirect
58. #16864020	C₂²	semidirect
59. #16864019	C₂²	semidirect
60. #16864018	C₂²	semidirect
61. #16864017	C₂²	semidirect
62. #16864016	C₂²	semidirect
63. #16864016	C₂²	semidirect
64. #16864015	C₂²	semidirect
65. #16864014	C₂²	semidirect
66. #16864014	C₂²	semidirect
67. #16864013	C₂²	semidirect
68. #16864012	C₂²	semidirect
69. #16864012	C₂²	semidirect
70. #16864011	C₂²	semidirect
71. #16864010	C₂²	semidirect
72. #16864010	C₂²	semidirect
73. #16863986	C₂²	semidirect
74. #16863985	C₂²	semidirect
75. #16863985	C₂²	semidirect
76. #16863984	C₂²	semidirect
77. #16863983	C₂²	semidirect
78. #16863982	C₂²	semidirect
79. #16863982	C₂²	semidirect
80. #16863981	C₂²	semidirect
81. #16863981	C₂²	semidirect
82. #16863980	C₂²	semidirect
83. #16863980	C₂²	semidirect
84. #16863979	C₂²	semidirect
85. #16863979	C₂²	semidirect
86. #16863978	C₂²	semidirect
87. #16863978	C₂²	semidirect
88. C₄⋊Q₈×D₆₇	C₂²	semidirect
89. #16863933	C₂²	semidirect
90. #16863932	C₂²	semidirect
91. #16863931	C₂²	semidirect
92. #16863930	C₂²	semidirect
93. #16863929	C₂²	semidirect
94. #16863928	C₂²	semidirect
95. #16863927	C₂²	semidirect
96. #16863926	C₂²	semidirect
97. #16863925	C₂²	semidirect
98. #16863924	C₂²	semidirect
99. #16863923	C₂²	semidirect
100. #126×D₆₇	C₂²	semidirect
101. #126×D₆₇	C₂²	semidirect
102. #126×D₆₇	C₂²	semidirect
103. #126×D₆₇	C₂²	semidirect
104. #126×D₆₇	C₂²	semidirect
105. #125×D₆₇	C₂²	semidirect
109. #124×D₆₇	C₂²	semidirect
112. #123×D₆₇	C₂²	semidirect
113. C₂²⋊Q₈×D₆₇	C₂²	semidirect
114. C₂²⋊Q₈×D₆₇	C₂²	semidirect
115. C₂²⋊Q₈×D₆₇	C₂²	semidirect
116. C₂²⋊Q₈×D₆₇	C₂²	semidirect
120. #120×D₆₇	C₂²	semidirect
121. C₄×Q₈×D₆₇	C₂²	semidirect
122. C₄×Q₈×D₆₇	C₂²	semidirect
125. C₄×D₄×D₆₇	C₂²	semidirect
126. #117×D₆₇	C₂²	semidirect
127. #117×D₆₇	C₂²	semidirect
128. C₂×C₂²⋊C₄×D₆₇	C₂²	semidirect
129. C₂×C₄²×D₆₇	C₂²	semidirect
130. #563×C₆₇	C₂²	semidirect
131. H(3,𝔽₄)×C₆₇	C₂²	semidirect
132. #556×C₆₇	C₂²	semidirect
133. #551×C₆₇	C₂²	semidirect
134. #542×C₆₇	C₂²	semidirect
135. #538×C₆₇	C₂²	semidirect
136. #529×C₆₇	C₂²	semidirect
146. #14524043	C₂³	semidirect
147. #14524042	C₂³	semidirect
148. #14524042	C₂³	semidirect
149. #14524042	C₂³	semidirect
150. #14524042	C₂³	semidirect
151. #14524041	C₂³	semidirect
152. #14524041	C₂³	semidirect
153. #14524038	C₂³	semidirect
154. #14524038	C₂³	semidirect
155. #14524038	C₂³	semidirect
156. #14524038	C₂³	semidirect
157. #14524038	C₂³	semidirect
158. #14524038	C₂³	semidirect
159. #14524038	C₂³	semidirect
160. #14524038	C₂³	semidirect
161. #14524038	C₂³	semidirect
162. #14524038	C₂³	semidirect
163. #14524038	C₂³	semidirect
164. #14524038	C₂³	semidirect
165. #14524038	C₂³	semidirect
166. #14524037	C₂³	semidirect
167. #14524037	C₂³	semidirect
168. #14524037	C₂³	semidirect
169. #14524037	C₂³	semidirect
170. #14524037	C₂³	semidirect
171. #14524036	C₂³	semidirect
172. #14524036	C₂³	semidirect
173. #14524036	C₂³	semidirect
174. #14524036	C₂³	semidirect
175. #14524036	C₂³	semidirect
176. #14524036	C₂³	semidirect
177. #14524036	C₂³	semidirect
178. #14524036	C₂³	semidirect
179. #14524036	C₂³	semidirect
180. #14524036	C₂³	semidirect
181. #14524036	C₂³	semidirect
182. #14524036	C₂³	semidirect
183. #14524036	C₂³	semidirect
184. #14524035	C₂³	semidirect
185. #14524034	C₂³	semidirect
186. #14524034	C₂³	semidirect
187. #14524033	C₂³	semidirect
188. #14524033	C₂³	semidirect
192. #14524032	C₂³	semidirect
196. #14524031	C₂³	semidirect
200. #14524030	C₂³	semidirect
211. #14524029	C₂³	semidirect
212. #14524029	C₂³	semidirect
213. #14524029	C₂³	semidirect
214. #14524029	C₂³	semidirect
219. #14524028	C₂³	semidirect
220. #14524028	C₂³	semidirect
223. #14524027	C₂³	semidirect
226. #14524026	C₂³	semidirect
231. #14524025	C₂³	semidirect
232. #14524025	C₂³	semidirect
235. #14524024	C₂³	semidirect
236. #14524023	C₂³	semidirect
237. #14524023	C₂³	semidirect
238. #14524023	C₂³	semidirect
239. #14524023	C₂³	semidirect
240. #14524022	C₂³	semidirect
241. #14524022	C₂³	semidirect
242. #14524022	C₂³	semidirect
243. #14524022	C₂³	semidirect
244. #14524021	C₂³	semidirect
245. #14524021	C₂³	semidirect
246. #14524021	C₂³	semidirect
247. #14524021	C₂³	semidirect
248. #14524021	C₂³	semidirect
249. #14524021	C₂³	semidirect
250. #14524021	C₂³	semidirect
251. #14524020	C₂³	semidirect
252. #14524020	C₂³	semidirect
253. #14524020	C₂³	semidirect
254. #14524020	C₂³	semidirect
255. #14524020	C₂³	semidirect
256. #14524020	C₂³	semidirect
257. #14524020	C₂³	semidirect
258. #14524019	C₂³	semidirect
259. #14524019	C₂³	semidirect
260. #14524019	C₂³	semidirect
261. #14524019	C₂³	semidirect
277. #14524013	C₂³	semidirect
279. #14524012	C₂³	semidirect
283. #14524011	C₂³	semidirect
284. Q₈×Dic₆₇	C₂³	semidirect
285. Q₈×Dic₆₇	C₂³	semidirect
286. C₄×Dic₁₃₄	C₂³	semidirect
287. C₄×Dic₁₃₄	C₂³	semidirect
288. C₄×Dic₁₃₄	C₂³	semidirect
289. C₄×Dic₁₃₄	C₂³	semidirect
290. C₄×Dic₁₃₄	C₂³	semidirect
291. #14524008	C₂³	semidirect
292. #14524008	C₂³	semidirect
293. #14524008	C₂³	semidirect
294. #14524008	C₂³	semidirect
295. #14524008	C₂³	semidirect
298. C₄×D₂₆₈	C₂³	semidirect
301. D₄×Dic₆₇	C₂³	semidirect
304. #14524005	C₂³	semidirect
308. C₄×C₂²⋊D₆₇	C₂³	semidirect
309. C₄×C₂²⋊D₆₇	C₂³	semidirect
313. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
314. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
315. #14524002	C₂³	semidirect
316. #14524002	C₂³	semidirect
317. #14524001	C₂³	semidirect
318. #14524001	C₂³	semidirect
319. #14524001	C₂³	semidirect
320. #14524001	C₂³	semidirect
321. #14524000	C₂³	semidirect
322. #14524000	C₂³	semidirect
323. #14524000	C₂³	semidirect
324. #14524000	C₂³	semidirect
325. #14523999	C₂³	semidirect
326. #14523999	C₂³	semidirect
327. #14523999	C₂³	semidirect
328. #14523999	C₂³	semidirect
337. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
338. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
339. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
349. C₂²⋊C₄×D₆₇	C₂³	semidirect
350. C₂²⋊C₄×D₆₇	C₂³	semidirect
351. C₂²⋊C₄×D₆₇	C₂³	semidirect
352. C₂²⋊C₄×D₆₇	C₂³	semidirect
353. C₂×C₄×Dic₆₇	C₂³	semidirect
359. C₄²×D₆₇	C₂³	semidirect
360. C₄²×D₆₇	C₂³	semidirect
361. C₄⋊Q₈×C₆₇	C₂³	semidirect
362. #126×C₆₇	C₂³	semidirect
363. #126×C₆₇	C₂³	semidirect
364. #126×C₆₇	C₂³	semidirect
365. #126×C₆₇	C₂³	semidirect
366. #126×C₆₇	C₂³	semidirect
367. #125×C₆₇	C₂³	semidirect
371. #124×C₆₇	C₂³	semidirect
374. #123×C₆₇	C₂³	semidirect
375. C₂²⋊Q₈×C₆₇	C₂³	semidirect
376. C₂²⋊Q₈×C₆₇	C₂³	semidirect
377. C₂²⋊Q₈×C₆₇	C₂³	semidirect
378. C₂²⋊Q₈×C₆₇	C₂³	semidirect
382. #120×C₆₇	C₂³	semidirect
383. C₄×Q₈×C₆₇	C₂³	semidirect
384. C₄×Q₈×C₆₇	C₂³	semidirect
387. C₄×D₄×C₆₇	C₂³	semidirect
388. #117×C₆₇	C₂³	semidirect
389. #117×C₆₇	C₂³	semidirect
390. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
391. C₂×C₄²×C₆₇	C₂³	semidirect
611. D₆₇	#3568	direct (N × H)
619. #3568	D₆₇	direct (N × H)
627. C₆₇	C₂×#3568	semidirect
637. #563	C₂×D₆₇	semidirect
641. H(3,𝔽₄)	C₂×D₆₇	semidirect
657. #556	C₂×D₆₇	semidirect
673. #551	C₂×D₆₇	semidirect
689. #542	C₂×D₆₇	semidirect
705. #538	C₂×D₆₇	semidirect
718. #529	C₂×D₆₇	semidirect
765. C₄⋊Q₈	C₂²×D₆₇	semidirect
797. #126	C₂²×D₆₇	semidirect
798. #126	C₂²×D₆₇	semidirect
799. #126	C₂²×D₆₇	semidirect
800. #126	C₂²×D₆₇	semidirect
801. #126	C₂²×D₆₇	semidirect
807. #125	C₂²×D₆₇	semidirect
837. #124	C₂²×D₆₇	semidirect
861. #123	C₂²×D₆₇	semidirect
888. C₂²⋊Q₈	C₂²×D₆₇	semidirect
889. C₂²⋊Q₈	C₂²×D₆₇	semidirect
890. C₂²⋊Q₈	C₂²×D₆₇	semidirect
891. C₂²⋊Q₈	C₂²×D₆₇	semidirect
917. #120	C₂²×D₆₇	semidirect
930. C₄×Q₈	C₂²×D₆₇	semidirect
931. C₄×Q₈	C₂²×D₆₇	semidirect
953. C₄×D₄	C₂²×D₆₇	semidirect
968. #117	C₂²×D₆₇	semidirect
969. #117	C₂²×D₆₇	semidirect
994. C₂×C₂²⋊C₄	C₂²×D₆₇	semidirect
1003. 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
#22574906	2
#22574905	2
#22574904	2
#22574903	2
#22574902	2
#22574901	2
#22574900	2
#563×D₆₇	2
H(3,𝔽₄)×D₆₇	2
#556×D₆₇	2
#551×D₆₇	2
#542×D₆₇	2
#538×D₆₇	2
#529×D₆₇	2
C₆₇×#3568	2
C₂×#3568	67

Subgroups — #3568×D67 #31763257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3568×D₆₇ #31763257