Subgroups — #31763865

Order 17152.

7998 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574258	C₂	1	4	yes	maximal, complemented
2	#22574241	C₂	1	4	yes	maximal, complemented
3	#22574149	C₂	1	8	yes	maximal, complemented
4	#22574061	C₂	1	2	yes	maximal, complemented
5	#22574048	C₂	1	4	yes	maximal, complemented
6	#22574012	C₂	1	1	yes	maximal, characteristic, complemented
7	#22573973	C₂	1	1	yes	maximal, characteristic, complemented
8	#22573918	C₂	1	2	yes	maximal, complemented
9	#22573898	C₂	1	4	yes	maximal, complemented
10	#22573844	C₂	1	2	yes	maximal, complemented
11	#22573813	C₂	1	8	yes	maximal, complemented
12	#22573767	C₂	1	4	yes	maximal, complemented
13	D₄×#11761628	C₂	1	4	yes	maximal, complemented
14	#22573631	C₂	1	2	yes	maximal, complemented
15	#22573618	C₂	1	4	yes	maximal, complemented
16	#22573505	C₂	1	2	yes	maximal, complemented
17	C₂×#16863907	C₂	1	4	yes	maximal, complemented
18	C₄×#14524088	C₂	1	2	yes	maximal, complemented
19	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14524088	C₂²	1	2	yes	—
21	C₂²×#11761628	C₂²	1	4	yes	complemented
22	#16864129	C₂²	1	8	yes	complemented
23	#16864116	C₂²	1	4	yes	complemented
24	#16864111	C₂²	1	4	yes	complemented
25	#16864105	C₂²	1	8	yes	complemented
26	#16864103	C₂²	1	4	yes	complemented
27	#16864101	C₂²	1	8	yes	complemented
28	#16864096	C₂²	1	8	yes	complemented
29	#16864095	C₂²	1	16	yes	complemented
30	#16864094	C₂²	1	8	yes	complemented
31	#16864092	C₂²	1	8	yes	complemented
32	#16864086	C₂²	1	8	yes	complemented
33	#16864081	C₂²	1	8	yes	complemented
34	#16864075	C₂²	1	16	yes	complemented
35	#16864072	C₂²	1	16	yes	complemented
36	#16864072	C₂²	1	16	yes	complemented
37	#16864067	C₂²	1	4	yes	complemented
38	D₄×Dic₁₃₄	C₂²	1	4	yes	complemented
39	#16864055	C₂²	1	8	yes	complemented
40	#16864051	C₂²	1	4	yes	complemented
41	#16864050	C₂²	1	4	yes	complemented
42	#16864047	C₂²	1	8	yes	complemented
43	#16864042	C₂²	1	8	yes	complemented
44	#16864041	C₂²	1	8	yes	complemented
45	#16864040	C₂²	1	8	yes	complemented
46	#16864040	C₂²	1	8	yes	complemented
47	#16864036	C₂²	1	16	yes	complemented
48	#16864036	C₂²	1	16	yes	complemented
49	D₄×D₂₆₈	C₂²	1	4	yes	complemented
50	D₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
51	D₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
52	#16864027	C₂²	1	2	yes	complemented
53	#16864022	C₂²	1	4	yes	complemented
54	#16864011	C₂²	1	8	yes	complemented
55	#16863997	C₂²	1	8	yes	complemented
56	#16863993	C₂²	1	8	yes	complemented
57	#16863988	C₂²	1	16	yes	complemented
58	#16863984	C₂²	1	8	yes	complemented
59	#16863984	C₂²	1	8	yes	complemented
60	#16863979	C₂²	1	16	yes	complemented
61	#16863977	C₂²	1	2	yes	complemented
62	#16863963	C₂²	1	4	yes	complemented
63	#16863958	C₂²	1	4	yes	complemented
64	#16863955	C₂²	1	8	yes	complemented
65	#16863953	C₂²	1	2	yes	complemented
66	#16863953	C₂²	1	2	yes	complemented
67	#16863953	C₂²	1	2	yes	complemented
68	#16863946	C₂²	1	2	yes	complemented
69	#16863946	C₂²	1	2	yes	complemented
70	#16863946	C₂²	1	2	yes	complemented
71	#16863943	C₂²	1	8	yes	complemented
72	#16863930	C₂²	1	4	yes	complemented
73	#16863930	C₂²	1	4	yes	complemented
74	#16863930	C₂²	1	4	yes	complemented
75	#16863930	C₂²	1	4	yes	complemented
76	#16863930	C₂²	1	4	yes	complemented
77	#16863930	C₂²	1	4	yes	complemented
78	#16863928	C₂²	1	8	yes	complemented
79	#16863926	C₂²	1	16	yes	complemented
80	#16863907	C₂²	1	4	yes	complemented
81	#16863907	C₂²	1	4	yes	complemented
82	#16863907	C₂²	1	8	yes	complemented
83	#16863907	C₂²	1	4	yes	complemented
84	#16863907	C₂²	1	8	yes	complemented
85	#16863907	C₂²	1	8	yes	complemented
86	#16863907	C₂²	1	8	yes	complemented
87	#16863907	C₂²	1	8	yes	complemented
88	#16863907	C₂²	1	8	yes	complemented
89	#16863907	C₂²	1	8	yes	complemented
90	#16863905	C₂²	1	16	yes	complemented
91	C₂×#14524026	C₂²	1	8	yes	complemented
92	C₂×#14524022	C₂²	1	4	yes	complemented
93	C₂×#14524022	C₂²	1	4	yes	complemented
94	C₂×#14524017	C₂²	1	4	yes	complemented
95	C₂×#14524017	C₂²	1	4	yes	complemented
96	C₂×#14524012	C₂²	1	8	yes	complemented
97	#16863877	C₂²	1	4	yes	complemented
98	#16863875	C₂²	1	8	yes	complemented
99	#16863871	C₂²	1	2	yes	—
100	#16863869	C₂²	1	8	yes	complemented
101	#16863868	C₂²	1	8	yes	complemented
102	C₄×#11761628	C₂²	1	4	yes	complemented
103	C₄×#11761628	C₂²	1	4	yes	complemented
104	C₄×#11761628	C₂²	1	4	yes	complemented
105	C₄×#11761627	C₂²	1	8	yes	complemented
106	C₂×C₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
107	C₂×C₄×C₂²⋊D₆₇	C₂²	1	8	yes	complemented
108	C₄×D₄×D₆₇	C₂²	1	8	yes	complemented
109	C₂×#14524002	C₂²	1	4	yes	complemented
110	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₂⁴×C₄×C₆₇	C₂²	1	2	yes	complemented
112	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
115	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
117	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
118	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
119	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
120	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
122	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
124	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#14524088	—	2	16	no	—
126	C₂×#11761628	—	4	16	no	—
127	C₂×#11761628	C₂³	1	4	yes	—
128	C₂×#11761628	C₂³	1	4	yes	—
129	C₂×#11761628	C₂³	1	4	yes	—
130	C₂×#11761628	C₂³	1	8	yes	—
131	C₂×#11761628	C₂³	1	8	yes	complemented
132	C₂×#11761628	C₂³	1	8	yes	complemented
133	C₂×#11761627	C₂³	1	8	yes	—
134	C₂²×Dic₁₃₄	C₂³	1	4	yes	complemented
135	C₂²×D₂₆₈	C₂³	1	4	yes	complemented
136	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
137	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
138	C₂²×C₂²⋊D₆₇	C₂³	1	8	yes	—
139	C₂×D₄×D₆₇	C₂³	1	8	yes	—
140	C₂²×C₄×D₆₇	C₂³	1	8	yes	complemented
141	#14524043	C₂³	1	2	yes	complemented
142	#14524043	C₂³	1	2	yes	complemented
143	#14524043	C₂³	1	2	yes	complemented
144	#14524042	C₂³	1	8	yes	complemented
145	#14524040	C₂³	1	2	yes	complemented
146	#14524039	C₂³	1	8	yes	—
147	#14524038	C₂³	1	16	yes	complemented
148	#14524037	C₂³	1	8	yes	complemented
149	#14524037	C₂³	1	8	yes	complemented
150	#14524036	C₂³	1	16	yes	complemented
151	#14524036	C₂³	1	16	yes	complemented
152	#14524035	C₂³	1	4	yes	complemented
153	#14524035	C₂³	1	4	yes	complemented
154	#14524035	C₂³	1	4	yes	complemented
155	#14524034	C₂³	1	8	yes	complemented
156	#14524033	C₂³	1	16	yes	complemented
157	#14524031	C₂³	1	4	yes	complemented
158	#14524031	C₂³	1	4	yes	complemented
159	#14524031	C₂³	1	4	yes	complemented
160	#14524030	C₂³	1	8	yes	—
161	#14524029	C₂³	1	16	yes	complemented
162	#14524029	C₂³	1	16	yes	complemented
163	#14524028	C₂³	1	16	yes	complemented
164	#14524027	C₂³	1	16	yes	complemented
165	#14524026	C₂³	1	8	yes	—
166	#14524026	C₂³	1	16	yes	—
167	#14524026	C₂³	1	8	yes	—
168	#14524026	C₂³	1	8	yes	—
169	#14524026	C₂³	1	16	yes	complemented
170	#14524026	C₂³	1	16	yes	complemented
171	#14524025	C₂³	1	16	yes	complemented
172	#14524025	C₂³	1	16	yes	complemented
173	#14524024	C₂³	1	16	yes	—
174	#14524023	C₂³	1	8	yes	complemented
175	#14524022	C₂³	1	4	yes	—
176	#14524022	C₂³	1	8	yes	—
177	#14524022	C₂³	1	4	yes	—
178	#14524022	C₂³	1	4	yes	—
179	#14524022	C₂³	1	4	yes	—
180	#14524022	C₂³	1	8	yes	—
181	#14524022	C₂³	1	4	yes	—
182	#14524022	C₂³	1	4	yes	—
183	#14524022	C₂³	1	8	yes	complemented
184	#14524022	C₂³	1	8	yes	complemented
185	#14524022	C₂³	1	8	yes	complemented
186	#14524022	C₂³	1	8	yes	complemented
187	#14524021	C₂³	1	16	yes	complemented
188	#14524020	C₂³	1	16	yes	complemented
189	#14524020	C₂³	1	16	yes	complemented
190	#14524018	C₂³	1	8	yes	complemented
191	#14524017	C₂³	1	4	yes	—
192	#14524017	C₂³	1	4	yes	—
193	#14524017	C₂³	1	4	yes	—
194	#14524017	C₂³	1	8	yes	—
195	#14524017	C₂³	1	4	yes	—
196	#14524017	C₂³	1	4	yes	—
197	#14524017	C₂³	1	8	yes	—
198	#14524017	C₂³	1	4	yes	—
199	#14524017	C₂³	1	8	yes	complemented
200	#14524017	C₂³	1	8	yes	complemented
201	#14524017	C₂³	1	8	yes	complemented
202	#14524017	C₂³	1	8	yes	complemented
203	#14524016	C₂³	1	16	yes	complemented
204	#14524016	C₂³	1	16	yes	complemented
205	#14524015	C₂³	1	16	yes	—
206	#14524015	C₂³	1	16	yes	—
207	#14524014	C₂³	1	8	yes	—
208	#14524014	C₂³	1	8	yes	—
209	#14524013	C₂³	1	16	yes	complemented
210	#14524012	C₂³	1	16	yes	—
211	#14524012	C₂³	1	16	yes	—
212	#14524012	C₂³	1	8	yes	—
213	#14524012	C₂³	1	16	yes	—
214	#14524011	C₂³	1	16	yes	—
215	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
216	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
217	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
218	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
219	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
220	C₄×Dic₁₃₄	C₂³	1	4	yes	complemented
221	#14524008	C₂³	1	8	yes	complemented
222	C₄×D₂₆₈	C₂³	1	4	yes	complemented
223	C₄×D₂₆₈	C₂³	1	4	yes	complemented
224	C₄×D₂₆₈	C₂³	1	4	yes	complemented
225	C₄×D₂₆₈	C₂³	1	4	yes	complemented
226	C₄×D₂₆₈	C₂³	1	4	yes	complemented
227	C₄×D₂₆₈	C₂³	1	4	yes	complemented
228	D₄×Dic₆₇	C₂³	1	8	yes	—
229	D₄×Dic₆₇	C₂³	1	8	yes	—
230	#14524005	C₂³	1	8	yes	complemented
231	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
232	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
233	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
234	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
235	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
236	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
237	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
238	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
239	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
240	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
241	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
242	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
243	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
244	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
245	#14524002	C₂³	1	4	yes	—
246	#14524002	C₂³	1	4	yes	—
247	#14524002	C₂³	1	8	yes	—
248	#14524002	C₂³	1	4	yes	—
249	#14524002	C₂³	1	8	yes	complemented
250	#14524002	C₂³	1	8	yes	complemented
251	#14524001	C₂³	1	8	yes	complemented
252	#14524000	C₂³	1	8	yes	complemented
253	#14524000	C₂³	1	8	yes	complemented
254	#14524000	C₂³	1	8	yes	complemented
255	#14523999	C₂³	1	16	yes	complemented
256	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	complemented
257	C₂×C₄⋊Dic₆₇	C₂³	1	4	yes	complemented
258	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
259	C₂×Dic₆₇⋊C₄	C₂³	1	8	yes	complemented
260	C₄⋊C₄×D₆₇	C₂³	1	8	yes	complemented
261	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
262	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
263	C₂×C₂²⋊Dic₆₇	C₂³	1	8	yes	—
264	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
265	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	8	yes	complemented
266	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	complemented
267	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
268	C₄²×D₆₇	C₂³	1	8	yes	complemented
269	C₂⁵×C₆₇	C₂³	1	2	yes	—
270	C₂²×D₄×C₆₇	—	2	8	no	—
271	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
272	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
273	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
274	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
275	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂³×C₄×C₆₇	—	4	8	no	—
277	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
278	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
280	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
282	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
283	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
284	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
285	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
286	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
287	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
288	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
289	C₄×D₄×C₆₇	C₂³	1	4	yes	—
290	C₄×D₄×C₆₇	C₂³	1	4	yes	—
291	C₄×D₄×C₆₇	C₂³	1	4	yes	—
292	C₄×D₄×C₆₇	C₂³	1	8	yes	—
293	C₄×D₄×C₆₇	C₂³	1	4	yes	—
294	C₄×D₄×C₆₇	C₂³	1	4	yes	—
295	C₄×D₄×C₆₇	C₂³	1	4	yes	—
296	C₄×D₄×C₆₇	C₂³	1	8	yes	—
297	C₄×D₄×C₆₇	C₂³	1	4	yes	—
298	C₄×D₄×C₆₇	C₂³	1	8	yes	—
299	C₄×D₄×C₆₇	C₂³	1	4	yes	—
300	C₄×D₄×C₆₇	C₂³	1	8	yes	—
301	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
303	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
305	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
306	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
307	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
308	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
309	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
310	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
311	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
312	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
315	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
316	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
318	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
320	C₂³×D₆₇	C₂⁴	1	8	yes	—
321	#11761628	—	2	16	no	—
322	#11761628	—	2	16	no	—
323	#11761628	—	4	16	no	—
324	#11761628	—	4	16	no	—
325	#11761628	—	4	16	no	—
326	#11761628	—	4	8	no	—
327	#11761627	—	2	32	no	—
328	C₂×Dic₁₃₄	—	4	8	no	—
329	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
330	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
331	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
332	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
333	C₂×D₂₆₈	—	4	8	no	—
334	C₂×D₂₆₈	C₂⁴	1	4	yes	—
335	C₂×D₂₆₈	C₂⁴	1	4	yes	—
336	C₂×D₂₆₈	C₂⁴	1	4	yes	—
337	C₂×D₂₆₈	C₂⁴	1	8	yes	—
338	C₂×C₂²⋊D₆₇	—	2	32	no	—
339	C₂×C₂²⋊D₆₇	—	4	16	no	—
340	C₂×C₂²⋊D₆₇	—	4	16	no	—
341	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
342	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
343	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
344	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
345	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
346	C₂×C₂²⋊D₆₇	C₂⁴	1	16	yes	—
347	D₄×D₆₇	—	2	32	no	—
348	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
349	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
350	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
351	C₂×C₄×D₆₇	—	4	16	no	—
352	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
353	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
354	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
355	C₂×C₄×D₆₇	C₂⁴	1	16	yes	—
356	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
357	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
358	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
359	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
360	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
361	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
362	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
363	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
364	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
365	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
366	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
367	Dic₆₇⋊C₄	C₂⁴	1	16	yes	—
368	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
369	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
370	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
371	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
372	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
373	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
374	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
375	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
376	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
377	C₂²⋊Dic₆₇	C₂⁴	1	16	yes	—
378	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
379	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
380	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
381	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
382	(C₂×D₆₇)⋊C₄	C₂⁴	1	16	yes	—
383	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
384	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
385	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
386	C₄×Dic₆₇	C₂⁴	1	8	yes	—
387	C₄×Dic₆₇	C₂⁴	1	8	yes	—
388	C₄×Dic₆₇	C₂⁴	1	8	yes	—
389	C₄×Dic₆₇	C₂⁴	1	16	yes	—
390	C₂⁴×C₆₇	—	2	8	no	—
391	C₂⁴×C₆₇	—	4	4	no	—
392	C₂⁴×C₆₇	—	4	4	no	—
393	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
395	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
396	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
397	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
398	C₂×D₄×C₆₇	—	2	8	no	—
399	C₂×D₄×C₆₇	—	2	16	no	—
400	C₂×D₄×C₆₇	—	2	16	no	—
401	C₂×D₄×C₆₇	—	2	4	no	—
402	C₂×D₄×C₆₇	#41	1	8	yes	complemented
403	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
404	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
405	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
406	C₂²×C₄×C₆₇	—	2	4	no	—
407	C₂²×C₄×C₆₇	—	2	4	no	—
408	C₂²×C₄×C₆₇	—	2	16	no	—
409	C₂²×C₄×C₆₇	—	4	4	no	—
410	C₂²×C₄×C₆₇	—	4	8	no	—
411	C₂²×C₄×C₆₇	—	4	4	no	—
412	C₂²×C₄×C₆₇	—	4	8	no	—
413	C₂²×C₄×C₆₇	—	4	4	no	—
414	C₂²×C₄×C₆₇	—	4	4	no	—
415	C₂²×C₄×C₆₇	—	4	8	no	—
416	C₂²×C₄×C₆₇	—	4	4	no	—
417	C₂²×C₄×C₆₇	—	4	2	no	—
418	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
428	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
429	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
430	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
431	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
432	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
434	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
436	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
437	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
439	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
440	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
441	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
442	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
451	C₄²×C₆₇	C₂⁴	1	2	yes	—
452	C₄²×C₆₇	C₂⁴	1	2	yes	—
453	C₄²×C₆₇	C₂⁴	1	2	yes	—
454	C₄²×C₆₇	C₂⁴	1	2	yes	—
455	C₄²×C₆₇	C₂⁴	1	2	yes	—
456	C₄²×C₆₇	C₂⁴	1	2	yes	—
457	C₄²×C₆₇	C₂⁴	1	2	yes	—
458	C₄²×C₆₇	C₂⁴	1	2	yes	—
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	2	8	no	—
463	C₂³×C₆₇	—	2	8	no	—
464	C₂³×C₆₇	—	2	4	no	—
465	C₂³×C₆₇	—	2	8	no	—
466	C₂³×C₆₇	—	2	8	no	—
467	C₂³×C₆₇	—	4	2	no	—
468	C₂³×C₆₇	—	4	4	no	—
469	C₂³×C₆₇	—	4	2	no	—
470	C₂³×C₆₇	—	4	2	no	—
471	C₂³×C₆₇	—	4	4	no	—
472	C₂³×C₆₇	—	4	2	no	—
473	C₂³×C₆₇	—	4	32	no	—
474	C₂³×C₆₇	C₂×#41	1	8	yes	complemented
475	C₂³×C₆₇	C₂⁵	1	4	yes	—
476	C₂³×C₆₇	C₂⁵	1	4	yes	—
477	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
478	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
479	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
480	C₂²×D₆₇	—	2	16	no	—
481	C₂²×D₆₇	—	4	8	no	—
482	C₂²×D₆₇	—	4	8	no	—
483	C₂²×D₆₇	C₂⁵	1	8	yes	—
484	D₄×C₆₇	—	2	16	no	—
485	D₄×C₆₇	—	2	8	no	—
486	D₄×C₆₇	C₂×#41	1	16	yes	complemented
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	8	no	—
490	C₂×C₄×C₆₇	—	2	4	no	—
491	C₂×C₄×C₆₇	—	2	4	no	—
492	C₂×C₄×C₆₇	—	2	4	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	8	no	—
498	C₂×C₄×C₆₇	—	2	8	no	—
499	C₂×C₄×C₆₇	—	2	8	no	—
500	C₂×C₄×C₆₇	—	2	8	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	4	no	—
503	C₂×C₄×C₆₇	—	4	4	no	—
504	C₂×C₄×C₆₇	—	4	4	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	4	4	no	—
507	C₂×C₄×C₆₇	—	4	4	no	—
508	C₂×C₄×C₆₇	—	4	1	no	—
509	C₂×C₄×C₆₇	—	4	2	no	—
510	C₂×C₄×C₆₇	—	4	1	no	—
511	C₂×C₄×C₆₇	C₂×#41	1	4	yes	complemented
512	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	complemented
513	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
514	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
515	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
516	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
518	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
519	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
520	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
521	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
522	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
523	C₂²⋊D₆₇	—	2	32	no	—
524	C₂²⋊D₆₇	—	2	16	no	—
525	C₂²⋊D₆₇	—	2	16	no	—
526	C₂²⋊D₆₇	—	2	16	no	—
527	C₂²⋊D₆₇	—	4	16	no	—
528	C₂²⋊D₆₇	—	4	16	no	—
529	C₂×Dic₆₇	—	2	16	no	—
530	C₂×Dic₆₇	—	4	8	no	—
531	C₂×Dic₆₇	—	4	8	no	—
532	C₂×Dic₆₇	C₂⁵	1	8	yes	—
533	C₂×Dic₆₇	C₂⁵	1	8	yes	—
534	C₂×Dic₆₇	C₂⁵	1	8	yes	—
535	D₂₆₈	—	2	8	no	—
536	D₂₆₈	—	2	8	no	—
537	D₂₆₈	—	4	8	no	—
538	D₂₆₈	—	4	4	no	—
539	C₄×D₆₇	—	2	16	no	—
540	C₄×D₆₇	—	2	16	no	—
541	C₄×D₆₇	—	4	16	no	—
542	C₄×D₆₇	—	4	8	no	—
543	Dic₁₃₄	—	2	8	no	—
544	Dic₁₃₄	—	2	8	no	—
545	Dic₁₃₄	—	4	8	no	—
546	Dic₁₃₄	—	4	4	no	—
547	C₂²×C₆₇	—	2	8	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	4	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	2	1	no	—
553	C₂²×C₆₇	—	2	4	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	2	1	no	—
556	C₂²×C₆₇	—	2	4	no	—
557	C₂²×C₆₇	—	2	4	no	—
558	C₂²×C₆₇	—	2	4	no	—
559	C₂²×C₆₇	—	4	8	no	—
560	C₂²×C₆₇	—	4	16	no	—
561	C₂²×C₆₇	—	4	16	no	—
562	C₂²×C₆₇	—	4	8	no	—
563	C₂²×C₆₇	C₂²×#41	1	8	yes	—
564	C₂²×C₆₇	C₂²×#41	1	2	yes	—
565	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
566	C₂²×C₆₇	#585	1	2	yes	—
567	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
568	C₂×D₆₇	—	2	8	no	—
569	C₂×D₆₇	—	2	8	no	—
570	C₂×D₆₇	—	2	8	no	—
571	C₂×D₆₇	—	8	16	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	4	no	—
574	C₄×C₆₇	—	2	4	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	1	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	2	no	—
579	C₄×C₆₇	C₂²×#41	1	4	yes	—
580	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
581	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
582	Dic₆₇	—	2	8	no	—
583	Dic₆₇	—	2	8	no	—
584	Dic₆₇	—	2	8	no	—
585	#62773	—	67	1	no	maximal, Sylow
586	C₂×C₆₇	—	2	8	no	—
587	C₂×C₆₇	—	2	2	no	—
588	C₂×C₆₇	—	2	2	no	—
589	C₂×C₆₇	—	2	2	no	—
590	C₂×C₆₇	—	4	4	no	—
591	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
592	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
594	D₆₇	—	4	8	no	—
595	#3520	—	67	4	no	—
596	#3519	—	67	4	no	—
597	#3513	—	67	8	no	—
598	#3506	—	67	2	no	—
599	#3505	—	67	4	no	—
600	#3501	—	67	1	no	—
601	#3496	—	67	1	no	—
602	#3492	—	67	2	no	—
603	#3490	—	67	4	no	—
604	#3484	—	67	2	no	—
605	#3481	—	67	8	no	—
606	#3475	—	67	4	no	—
607	D₄×#41	—	67	4	no	—
608	#3460	—	67	2	no	—
609	#3459	—	67	4	no	—
610	#3444	—	67	2	no	—
611	C₂×#525	—	67	4	no	—
612	C₄×H(5,𝔽₂)	—	67	2	no	—
613	C₂²×C₄×D₄	D₆₇	1	1	yes	characteristic, complemented
614	C₆₇	#62773	1	1	yes	characteristic, complemented, Sylow
615	C₂×H(5,𝔽₂)	—	67	2	no	—
616	C₂²×#41	—	67	4	no	—
617	C₂³×D₄	C₂×D₆₇	1	1	yes	characteristic
618	C₂⁴×C₄	C₂×D₆₇	1	2	yes	complemented
619	#559	—	67	8	no	—
620	#556	—	67	4	no	—
621	#555	—	67	4	no	—
622	#554	—	67	4	no	—
623	#554	—	67	8	no	—
624	#554	—	67	8	no	—
625	#553	—	67	8	no	—
626	#553	—	67	16	no	—
627	#553	—	67	8	no	—
628	#553	—	67	8	no	—
629	#552	—	67	8	no	—
630	#552	—	67	8	no	—
631	#551	—	67	16	no	—
632	#551	—	67	16	no	—
633	#551	—	67	16	no	—
634	#550	—	67	4	no	—
635	D₄×Q₈	—	67	4	no	—
636	#548	—	67	8	no	—
637	#547	—	67	4	no	—
638	#547	—	67	4	no	—
639	#547	—	67	8	no	—
640	#546	—	67	8	no	—
641	#546	—	67	8	no	—
642	#546	—	67	8	no	—
643	#546	—	67	8	no	—
644	#546	—	67	16	no	—
645	#546	—	67	16	no	—
646	D₄²	—	67	8	no	—
647	D₄²	—	67	8	no	—
648	D₄²	—	67	4	no	—
649	#544	—	67	2	no	—
650	#543	—	67	4	no	—
651	#542	—	67	8	no	—
652	#540	—	67	8	no	—
653	#539	—	67	16	no	—
654	#539	—	67	8	no	—
655	#538	—	67	16	no	—
656	#538	—	67	8	no	—
657	#538	—	67	8	no	—
658	#537	—	67	2	no	—
659	#535	—	67	4	no	—
660	#534	—	67	8	no	—
661	#534	—	67	4	no	—
662	#533	—	67	2	no	—
663	#533	—	67	2	no	—
664	#533	—	67	2	no	—
665	#532	—	67	8	no	—
666	#532	—	67	2	no	—
667	#532	—	67	2	no	—
668	#532	—	67	2	no	—
669	#529	—	67	16	no	—
670	#529	—	67	8	no	—
671	#529	—	67	4	no	—
672	#529	—	67	4	no	—
673	#529	—	67	4	no	—
674	#529	—	67	4	no	—
675	#529	—	67	4	no	—
676	#529	—	67	4	no	—
677	#525	—	67	4	no	—
678	#525	—	67	8	no	—
679	#525	—	67	8	no	—
680	#525	—	67	8	no	—
681	#525	—	67	8	no	—
682	#525	—	67	8	no	—
683	#525	—	67	8	no	—
684	#525	—	67	8	no	—
685	#525	—	67	4	no	—
686	#525	—	67	4	no	—
687	#525	—	67	16	no	—
688	C₂×#123	—	67	8	no	—
689	C₂×C₂²⋊Q₈	—	67	4	no	—
690	C₂×C₂²⋊Q₈	—	67	4	no	—
691	C₂×#121	—	67	4	no	—
692	C₂×#121	—	67	4	no	—
693	C₂×#120	—	67	8	no	—
694	#520	—	67	8	no	—
695	#520	—	67	4	no	—
696	#518	—	67	2	no	—
697	#518	—	67	8	no	—
698	#518	—	67	8	no	—
699	C₄×#41	—	67	8	no	—
700	C₄×#41	—	67	4	no	—
701	C₄×#41	—	67	4	no	—
702	C₄×#41	—	67	4	no	—
703	C₂×C₄×D₄	—	67	8	no	—
704	C₂×C₄×D₄	—	67	8	no	—
705	C₂×C₄×D₄	—	67	8	no	—
706	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
707	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
708	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
709	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
710	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
711	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
712	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
713	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
714	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
715	C₂×C₄×D₄	C₂×D₆₇	1	4	yes	complemented
716	C₂×#117	—	67	4	no	—
717	C₂²×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
718	C₂²×C₂²⋊C₄	C₂×D₆₇	1	2	yes	complemented
719	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
720	C₂⁵	C₂²×D₆₇	1	2	yes	—
721	H(5,𝔽₂)	—	134	16	no	—
722	C₂×#41	—	268	16	no	—
723	C₂×#41	—	67	8	no	—
724	C₂×#41	—	67	4	no	—
725	C₂×#41	—	67	8	no	—
726	C₂×#41	—	67	8	no	—
727	C₂×#41	—	67	8	no	—
728	C₂×#41	—	67	4	no	—
729	C₂×#41	—	67	4	no	—
730	C₂²×Q₈	—	67	4	no	—
731	C₂²×D₄	—	2	8	no	—
732	C₂²×D₄	—	67	8	no	—
733	C₂²×D₄	—	67	8	no	—
734	C₂²×D₄	—	67	8	no	—
735	C₂²×D₄	—	67	8	no	—
736	C₂²×D₄	—	67	4	no	—
737	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
738	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
739	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
740	C₂²×D₄	C₂²×D₆₇	1	4	yes	—
741	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
742	C₂³×C₄	—	4	8	no	—
743	C₂³×C₄	—	67	8	no	—
744	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
745	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
746	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
747	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
748	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
749	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
750	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
751	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
752	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
753	C₂³×C₄	C₂²×D₆₇	1	4	yes	—
754	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
755	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
756	C₄⋊Q₈	—	67	8	no	—
757	C₄⋊Q₈	—	67	2	no	—
758	C₄⋊Q₈	—	67	2	no	—
759	C₄⋊Q₈	—	67	2	no	—
760	#127	—	67	8	no	—
761	#127	—	67	2	no	—
762	#126	—	67	16	no	—
763	#126	—	67	16	no	—
764	#126	—	67	16	no	—
765	#126	—	67	8	no	—
766	#126	—	67	8	no	—
767	#125	—	67	16	no	—
768	#125	—	67	8	no	—
769	#125	—	67	4	no	—
770	#125	—	67	4	no	—
771	#125	—	67	4	no	—
772	#124	—	67	8	no	—
773	#124	—	67	16	no	—
774	#124	—	67	16	no	—
775	#124	—	67	4	no	—
776	#124	—	67	4	no	—
777	#124	—	67	4	no	—
778	#123	—	67	16	no	—
779	#123	—	67	8	no	—
780	#123	—	67	16	no	—
781	#123	—	67	16	no	—
782	#123	—	67	16	no	—
783	#123	—	67	8	no	—
784	#123	—	67	8	no	—
785	#123	—	67	16	no	—
786	#123	—	67	16	no	—
787	#123	—	67	16	no	—
788	#123	—	67	16	no	—
789	C₂²⋊Q₈	—	67	4	no	—
790	C₂²⋊Q₈	—	67	4	no	—
791	C₂²⋊Q₈	—	67	8	no	—
792	C₂²⋊Q₈	—	67	8	no	—
793	C₂²⋊Q₈	—	67	8	no	—
794	C₂²⋊Q₈	—	67	8	no	—
795	C₂²⋊Q₈	—	67	8	no	—
796	C₂²⋊Q₈	—	67	8	no	—
797	C₂²⋊Q₈	—	67	4	no	—
798	C₂²⋊Q₈	—	67	4	no	—
799	C₂²⋊Q₈	—	67	4	no	—
800	C₂²⋊Q₈	—	67	4	no	—
801	C₂²⋊Q₈	—	67	16	no	—
802	C₂²⋊Q₈	—	67	8	no	—
803	C₂²⋊Q₈	—	67	16	no	—
804	C₂²⋊Q₈	—	67	16	no	—
805	#121	—	67	16	no	—
806	#121	—	67	16	no	—
807	#121	—	67	8	no	—
808	#121	—	67	8	no	—
809	#121	—	67	4	no	—
810	#121	—	67	4	no	—
811	#121	—	67	8	no	—
812	#121	—	67	8	no	—
813	#121	—	67	8	no	—
814	#121	—	67	8	no	—
815	#121	—	67	8	no	—
816	#121	—	67	8	no	—
817	#121	—	67	4	no	—
818	#121	—	67	4	no	—
819	#121	—	67	4	no	—
820	#121	—	67	4	no	—
821	#121	—	67	8	no	—
822	#121	—	67	16	no	—
823	#121	—	67	16	no	—
824	#120	—	67	8	no	—
825	#120	—	67	16	no	—
826	#120	—	67	16	no	—
827	#120	—	67	16	no	—
828	#120	—	67	16	no	—
829	#120	—	67	16	no	—
830	C₄×Q₈	—	67	8	no	—
831	C₄×Q₈	—	67	4	no	—
832	C₄×Q₈	—	67	4	no	—
833	C₄×Q₈	—	67	4	no	—
834	C₄×Q₈	—	67	4	no	—
835	C₄×Q₈	—	67	4	no	—
836	C₄×Q₈	—	67	4	no	—
837	C₄×D₄	—	67	8	no	—
838	C₄×D₄	—	67	8	no	—
839	C₄×D₄	—	67	8	no	—
840	C₄×D₄	—	67	8	no	—
841	C₄×D₄	—	67	16	no	—
842	C₄×D₄	—	67	16	no	—
843	C₄×D₄	—	67	16	no	—
844	C₄×D₄	—	67	16	no	—
845	C₄×D₄	—	67	16	no	—
846	C₄×D₄	—	67	16	no	—
847	C₄×D₄	—	67	8	no	—
848	C₄×D₄	—	67	8	no	—
849	C₄×D₄	—	67	8	no	—
850	C₄×D₄	—	67	8	no	—
851	C₄×D₄	—	67	8	no	—
852	C₄×D₄	—	67	16	no	—
853	C₄×D₄	—	67	16	no	—
854	C₄×D₄	—	67	4	no	—
855	C₄×D₄	—	67	4	no	—
856	C₄×D₄	—	67	4	no	—
857	C₄×D₄	—	67	4	no	—
858	C₄×D₄	—	67	4	no	—
859	C₄×D₄	—	67	4	no	—
860	C₄×D₄	C₂²×D₆₇	1	4	yes	—
861	C₄×D₄	C₂²×D₆₇	1	4	yes	—
862	C₄×D₄	C₂²×D₆₇	1	4	yes	—
863	C₄×D₄	C₂²×D₆₇	1	4	yes	—
864	C₄×D₄	C₂²×D₆₇	1	8	yes	—
865	C₄×D₄	C₂²×D₆₇	1	4	yes	—
866	C₄×D₄	C₂²×D₆₇	1	8	yes	—
867	C₄×D₄	C₂²×D₆₇	1	4	yes	—
868	C₄×D₄	C₂²×D₆₇	1	8	yes	—
869	C₄×D₄	C₂²×D₆₇	1	4	yes	—
870	C₄×D₄	C₂²×D₆₇	1	8	yes	—
871	C₄×D₄	C₂²×D₆₇	1	4	yes	—
872	#117	—	67	4	no	—
873	#117	—	67	8	no	—
874	#117	—	67	8	no	—
875	#117	—	67	8	no	—
876	#117	—	67	4	no	—
877	#117	—	67	4	no	—
878	#117	—	67	8	no	—
879	#117	—	67	16	no	—
880	#117	—	67	8	no	—
881	#117	—	67	8	no	—
882	#117	—	67	8	no	—
883	C₂×C₄⋊C₄	—	67	4	no	—
884	C₂×C₄⋊C₄	—	67	4	no	—
885	C₂×C₄⋊C₄	—	67	8	no	—
886	C₂×C₄⋊C₄	—	67	8	no	—
887	C₂×C₄⋊C₄	—	67	8	no	—
888	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
891	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
892	C₂×C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
893	C₂×C₂²⋊C₄	—	67	8	no	—
894	C₂×C₂²⋊C₄	—	67	8	no	—
895	C₂×C₂²⋊C₄	—	67	8	no	—
896	C₂×C₂²⋊C₄	—	67	8	no	—
897	C₂×C₂²⋊C₄	—	67	8	no	—
898	C₂×C₂²⋊C₄	—	67	16	no	—
899	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
900	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
901	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
902	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
903	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	—
904	C₂×C₂²⋊C₄	C₂²×D₆₇	1	8	yes	—
905	C₂×C₄²	—	67	8	no	—
906	C₂×C₄²	—	67	8	no	—
907	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
908	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
909	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
910	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
911	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
912	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
913	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
914	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
915	C₂⁴	—	2	8	no	—
916	C₂⁴	—	4	4	no	—
917	C₂⁴	—	4	4	no	—
918	C₂⁴	—	67	8	no	—
919	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
920	C₂⁴	C₂³×D₆₇	1	4	yes	—
921	C₂⁴	C₂³×D₆₇	1	4	yes	—
922	C₂⁴	C₂³×D₆₇	1	2	yes	—
923	C₂⁴	C₂³×D₆₇	1	2	yes	—
924	#41	—	268	16	no	—
925	#41	—	268	16	no	—
926	#41	—	268	8	no	—
927	#41	—	268	16	no	—
928	#41	—	134	32	no	—
929	#41	—	134	16	no	—
930	#41	—	134	16	no	—
931	C₂×Q₈	—	268	8	no	—
932	C₂×Q₈	—	67	4	no	—
933	C₂×Q₈	—	67	8	no	—
934	C₂×Q₈	—	67	4	no	—
935	C₂×Q₈	—	67	4	no	—
936	C₂×D₄	—	2	8	no	—
937	C₂×D₄	—	2	16	no	—
938	C₂×D₄	—	2	16	no	—
939	C₂×D₄	—	2	4	no	—
940	C₂×D₄	—	268	8	no	—
941	C₂×D₄	—	268	16	no	—
942	C₂×D₄	—	268	16	no	—
943	C₂×D₄	—	67	16	no	—
944	C₂×D₄	—	67	16	no	—
945	C₂×D₄	—	67	8	no	—
946	C₂×D₄	—	67	16	no	—
947	C₂×D₄	—	67	8	no	—
948	C₂×D₄	—	67	8	no	—
949	C₂×D₄	—	67	4	no	—
950	C₂×D₄	—	67	8	no	—
951	C₂×D₄	—	67	4	no	—
952	C₂×D₄	—	67	4	no	—
953	C₂×D₄	—	134	32	no	—
954	C₂×D₄	—	134	32	no	—
955	C₂×D₄	#11761628	1	8	yes	complemented
956	C₂×D₄	C₂³×D₆₇	1	8	yes	—
957	C₂×D₄	C₂³×D₆₇	1	4	yes	—
958	C₂×D₄	C₂³×D₆₇	1	4	yes	—
959	C₂²×C₄	—	2	4	no	—
960	C₂²×C₄	—	2	4	no	—
961	C₂²×C₄	—	2	16	no	—
962	C₂²×C₄	—	4	4	no	—
963	C₂²×C₄	—	4	8	no	—
964	C₂²×C₄	—	4	4	no	—
965	C₂²×C₄	—	4	8	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	—	4	4	no	—
968	C₂²×C₄	—	4	8	no	—
969	C₂²×C₄	—	4	4	no	—
970	C₂²×C₄	—	4	2	no	—
971	C₂²×C₄	—	268	16	no	—
972	C₂²×C₄	—	67	8	no	—
973	C₂²×C₄	—	67	8	no	—
974	C₂²×C₄	—	67	8	no	—
975	C₂²×C₄	—	67	16	no	—
976	C₂²×C₄	—	67	8	no	—
977	C₂²×C₄	—	67	8	no	—
978	C₂²×C₄	—	67	8	no	—
979	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
980	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
981	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
982	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
984	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
985	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
986	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
987	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
988	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
989	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
990	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
991	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
992	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
993	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
994	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
995	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
996	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
997	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
998	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
999	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1000	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1001	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1002	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1003	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1005	C₄⋊C₄	—	67	4	no	—
1006	C₄⋊C₄	—	67	4	no	—
1007	C₄⋊C₄	—	67	4	no	—
1008	C₄⋊C₄	—	67	16	no	—
1009	C₄⋊C₄	—	67	8	no	—
1010	C₄⋊C₄	—	67	8	no	—
1011	C₄⋊C₄	—	67	8	no	—
1012	C₄⋊C₄	—	67	8	no	—
1013	C₄⋊C₄	—	67	16	no	—
1014	C₄⋊C₄	—	67	4	no	—
1015	C₄⋊C₄	—	67	8	no	—
1016	C₄⋊C₄	—	67	8	no	—
1017	C₄⋊C₄	—	67	8	no	—
1018	C₄⋊C₄	—	67	8	no	—
1019	C₄⋊C₄	—	67	4	no	—
1020	C₄⋊C₄	—	67	4	no	—
1021	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1022	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1023	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1024	C₂²⋊C₄	—	67	8	no	—
1025	C₂²⋊C₄	—	67	8	no	—
1026	C₂²⋊C₄	—	67	16	no	—
1027	C₂²⋊C₄	—	67	8	no	—
1028	C₂²⋊C₄	—	67	16	no	—
1029	C₂²⋊C₄	—	67	16	no	—
1030	C₂²⋊C₄	—	67	16	no	—
1031	C₂²⋊C₄	—	67	8	no	—
1032	C₂²⋊C₄	—	67	8	no	—
1033	C₂²⋊C₄	—	67	8	no	—
1034	C₂²⋊C₄	—	67	16	no	—
1035	C₂²⋊C₄	—	67	8	no	—
1036	C₂²⋊C₄	—	67	8	no	—
1037	C₂²⋊C₄	—	67	8	no	—
1038	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1039	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1040	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1041	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1042	C₄²	—	67	16	no	—
1043	C₄²	—	67	8	no	—
1044	C₄²	—	67	8	no	—
1045	C₄²	—	67	8	no	—
1046	C₄²	C₂³×D₆₇	1	2	yes	—
1047	C₄²	C₂³×D₆₇	1	2	yes	—
1048	C₄²	C₂³×D₆₇	1	2	yes	—
1049	C₄²	C₂³×D₆₇	1	2	yes	—
1050	C₄²	C₂³×D₆₇	1	2	yes	—
1051	C₄²	C₂³×D₆₇	1	2	yes	—
1052	C₄²	C₂³×D₆₇	1	2	yes	—
1053	C₄²	C₂³×D₆₇	1	2	yes	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	8	no	—
1058	C₂³	—	2	8	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	8	no	—
1061	C₂³	—	2	8	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	2	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	4	no	—
1067	C₂³	—	4	2	no	—
1068	C₂³	—	4	32	no	—
1069	C₂³	—	268	8	no	—
1070	C₂³	—	268	8	no	—
1071	C₂³	—	67	8	no	—
1072	C₂³	—	134	16	no	—
1073	C₂³	C₂×#11761628	1	8	yes	complemented
1074	C₂³	C₂⁴×D₆₇	1	4	yes	—
1075	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1076	C₂³	C₂⁴×D₆₇	1	4	yes	—
1077	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1078	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1079	Q₈	—	268	8	no	—
1080	Q₈	—	268	4	no	—
1081	Q₈	—	134	8	no	—
1082	Q₈	—	134	8	no	—
1083	D₄	—	2	16	no	—
1084	D₄	—	2	8	no	—
1085	D₄	—	268	8	no	—
1086	D₄	—	268	4	no	—
1087	D₄	—	268	16	no	—
1088	D₄	—	268	16	no	—
1089	D₄	—	134	16	no	—
1090	D₄	—	134	32	no	—
1091	D₄	—	134	16	no	—
1092	D₄	—	134	16	no	—
1093	D₄	—	134	8	no	—
1094	D₄	—	134	8	no	—
1095	D₄	C₂×#11761628	1	16	yes	complemented
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	8	no	—
1099	C₂×C₄	—	2	4	no	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	4	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	8	no	—
1107	C₂×C₄	—	2	8	no	—
1108	C₂×C₄	—	2	8	no	—
1109	C₂×C₄	—	2	8	no	—
1110	C₂×C₄	—	4	4	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	4	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	268	16	no	—
1121	C₂×C₄	—	268	8	no	—
1122	C₂×C₄	—	268	8	no	—
1123	C₂×C₄	—	268	8	no	—
1124	C₂×C₄	—	67	8	no	—
1125	C₂×C₄	—	67	8	no	—
1126	C₂×C₄	—	67	8	no	—
1127	C₂×C₄	—	134	16	no	—
1128	C₂×C₄	—	134	16	no	—
1129	C₂×C₄	—	134	16	no	—
1130	C₂×C₄	C₂×#11761628	1	4	yes	complemented
1131	C₂×C₄	#14524088	1	4	yes	complemented
1132	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1133	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1134	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1135	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1136	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1137	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1138	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1139	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1140	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1141	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1142	C₂²	—	2	8	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	4	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	4	no	—
1151	C₂²	—	2	4	no	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	4	8	no	—
1155	C₂²	—	4	16	no	—
1156	C₂²	—	4	16	no	—
1157	C₂²	—	4	8	no	—
1158	C₂²	—	536	16	no	—
1159	C₂²	—	134	8	no	—
1160	C₂²	—	134	8	no	—
1161	C₂²	—	134	8	no	—
1162	C₂²	C₂²×#11761628	1	2	yes	—
1163	C₂²	C₂²×#11761628	1	8	yes	—
1164	C₂²	C₂×#14524088	1	2	yes	—
1165	C₂²	#16864232	1	2	yes	—
1166	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1167	C₄	—	2	2	no	—
1168	C₄	—	2	1	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	4	no	—
1171	C₄	—	2	4	no	—
1172	C₄	—	2	2	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	134	8	no	—
1175	C₄	—	134	8	no	—
1176	C₄	—	134	8	no	—
1177	C₄	C₂²×#11761628	1	4	yes	—
1178	C₄	C₂×#14524088	1	2	yes	—
1179	C₄	C₂×#14524088	1	2	yes	—
1180	C₂	—	2	2	no	—
1181	C₂	—	2	2	no	—
1182	C₂	—	2	2	no	—
1183	C₂	—	2	8	no	—
1184	C₂	—	4	4	no	—
1185	C₂	—	268	8	no	—
1186	C₂	C₂³×#11761628	1	1	yes	characteristic
1187	C₂	C₂²×#14524088	1	1	yes	characteristic
1188	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₆₇
commutator, socle, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂²×C₄×D₄×C₆₇	C₂
hypercenter	C₂²×C₄×D₄	D₆₇
hypocenter	C₆₇	#62773
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #22574258	C₂	semidirect
2. #22574241	C₂	semidirect
3. #22574149	C₂	semidirect
4. #22574061	C₂	semidirect
5. #22574048	C₂	semidirect
6. #22574012	C₂	semidirect
7. #22573973	C₂	semidirect
8. #22573918	C₂	semidirect
9. #22573898	C₂	semidirect
10. #22573844	C₂	semidirect
11. #22573813	C₂	semidirect
12. #22573767	C₂	semidirect
13. D₄×#11761628	C₂	semidirect
14. #22573631	C₂	semidirect
15. #22573618	C₂	semidirect
16. #22573505	C₂	semidirect
17. C₂×#16863907	C₂	semidirect
18. C₄×#14524088	C₂	semidirect
19. C₂²×C₄×D₄×C₆₇	C₂	semidirect
21. C₂²×#11761628	C₂²	semidirect
22. #16864129	C₂²	semidirect
23. #16864116	C₂²	semidirect
24. #16864111	C₂²	semidirect
25. #16864105	C₂²	semidirect
26. #16864103	C₂²	semidirect
27. #16864101	C₂²	semidirect
28. #16864096	C₂²	semidirect
29. #16864095	C₂²	semidirect
30. #16864094	C₂²	semidirect
31. #16864092	C₂²	semidirect
32. #16864086	C₂²	semidirect
33. #16864081	C₂²	semidirect
34. #16864075	C₂²	semidirect
35. #16864072	C₂²	semidirect
36. #16864072	C₂²	semidirect
37. #16864067	C₂²	semidirect
38. D₄×Dic₁₃₄	C₂²	semidirect
39. #16864055	C₂²	semidirect
40. #16864051	C₂²	semidirect
41. #16864050	C₂²	semidirect
42. #16864047	C₂²	semidirect
43. #16864042	C₂²	semidirect
44. #16864041	C₂²	semidirect
45. #16864040	C₂²	semidirect
46. #16864040	C₂²	semidirect
47. #16864036	C₂²	semidirect
48. #16864036	C₂²	semidirect
49. D₄×D₂₆₈	C₂²	semidirect
50. D₄×C₂²⋊D₆₇	C₂²	semidirect
51. D₄×C₂²⋊D₆₇	C₂²	semidirect
52. #16864027	C₂²	semidirect
53. #16864022	C₂²	semidirect
54. #16864011	C₂²	semidirect
55. #16863997	C₂²	semidirect
56. #16863993	C₂²	semidirect
57. #16863988	C₂²	semidirect
58. #16863984	C₂²	semidirect
59. #16863984	C₂²	semidirect
60. #16863979	C₂²	semidirect
61. #16863977	C₂²	semidirect
62. #16863963	C₂²	semidirect
63. #16863958	C₂²	semidirect
64. #16863955	C₂²	semidirect
65. #16863953	C₂²	semidirect
66. #16863953	C₂²	semidirect
67. #16863953	C₂²	semidirect
68. #16863946	C₂²	semidirect
69. #16863946	C₂²	semidirect
70. #16863946	C₂²	semidirect
71. #16863943	C₂²	semidirect
72. #16863930	C₂²	semidirect
73. #16863930	C₂²	semidirect
74. #16863930	C₂²	semidirect
75. #16863930	C₂²	semidirect
76. #16863930	C₂²	semidirect
77. #16863930	C₂²	semidirect
78. #16863928	C₂²	semidirect
79. #16863926	C₂²	semidirect
80. #16863907	C₂²	semidirect
81. #16863907	C₂²	semidirect
82. #16863907	C₂²	semidirect
83. #16863907	C₂²	semidirect
84. #16863907	C₂²	semidirect
85. #16863907	C₂²	semidirect
86. #16863907	C₂²	semidirect
87. #16863907	C₂²	semidirect
88. #16863907	C₂²	semidirect
89. #16863907	C₂²	semidirect
90. #16863905	C₂²	semidirect
91. C₂×#14524026	C₂²	semidirect
92. C₂×#14524022	C₂²	semidirect
93. C₂×#14524022	C₂²	semidirect
94. C₂×#14524017	C₂²	semidirect
95. C₂×#14524017	C₂²	semidirect
96. C₂×#14524012	C₂²	semidirect
97. #16863877	C₂²	semidirect
98. #16863875	C₂²	semidirect
100. #16863869	C₂²	semidirect
101. #16863868	C₂²	semidirect
102. C₄×#11761628	C₂²	semidirect
103. C₄×#11761628	C₂²	semidirect
104. C₄×#11761628	C₂²	semidirect
105. C₄×#11761627	C₂²	semidirect
106. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
108. C₄×D₄×D₆₇	C₂²	semidirect
109. C₂×#14524002	C₂²	semidirect
111. C₂⁴×C₄×C₆₇	C₂²	semidirect
114. C₂×C₄×D₄×C₆₇	C₂²	semidirect
115. C₂×C₄×D₄×C₆₇	C₂²	semidirect
116. C₂×C₄×D₄×C₆₇	C₂²	semidirect
117. C₂×C₄×D₄×C₆₇	C₂²	semidirect
118. C₂×C₄×D₄×C₆₇	C₂²	semidirect
119. C₂×C₄×D₄×C₆₇	C₂²	semidirect
120. C₂×C₄×D₄×C₆₇	C₂²	semidirect
121. C₂×C₄×D₄×C₆₇	C₂²	semidirect
122. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
123. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
124. C₂²×C₄²×C₆₇	C₂²	semidirect
131. C₂×#11761628	C₂³	semidirect
132. C₂×#11761628	C₂³	semidirect
134. C₂²×Dic₁₃₄	C₂³	semidirect
135. C₂²×D₂₆₈	C₂³	semidirect
140. C₂²×C₄×D₆₇	C₂³	semidirect
141. #14524043	C₂³	semidirect
142. #14524043	C₂³	semidirect
143. #14524043	C₂³	semidirect
144. #14524042	C₂³	semidirect
145. #14524040	C₂³	semidirect
147. #14524038	C₂³	semidirect
148. #14524037	C₂³	semidirect
149. #14524037	C₂³	semidirect
150. #14524036	C₂³	semidirect
151. #14524036	C₂³	semidirect
152. #14524035	C₂³	semidirect
153. #14524035	C₂³	semidirect
154. #14524035	C₂³	semidirect
155. #14524034	C₂³	semidirect
156. #14524033	C₂³	semidirect
157. #14524031	C₂³	semidirect
158. #14524031	C₂³	semidirect
159. #14524031	C₂³	semidirect
161. #14524029	C₂³	semidirect
162. #14524029	C₂³	semidirect
163. #14524028	C₂³	semidirect
164. #14524027	C₂³	semidirect
169. #14524026	C₂³	semidirect
170. #14524026	C₂³	semidirect
171. #14524025	C₂³	semidirect
172. #14524025	C₂³	semidirect
174. #14524023	C₂³	semidirect
183. #14524022	C₂³	semidirect
184. #14524022	C₂³	semidirect
185. #14524022	C₂³	semidirect
186. #14524022	C₂³	semidirect
187. #14524021	C₂³	semidirect
188. #14524020	C₂³	semidirect
189. #14524020	C₂³	semidirect
190. #14524018	C₂³	semidirect
199. #14524017	C₂³	semidirect
200. #14524017	C₂³	semidirect
201. #14524017	C₂³	semidirect
202. #14524017	C₂³	semidirect
203. #14524016	C₂³	semidirect
204. #14524016	C₂³	semidirect
209. #14524013	C₂³	semidirect
215. C₄×Dic₁₃₄	C₂³	semidirect
216. C₄×Dic₁₃₄	C₂³	semidirect
217. C₄×Dic₁₃₄	C₂³	semidirect
218. C₄×Dic₁₃₄	C₂³	semidirect
219. C₄×Dic₁₃₄	C₂³	semidirect
220. C₄×Dic₁₃₄	C₂³	semidirect
221. #14524008	C₂³	semidirect
222. C₄×D₂₆₈	C₂³	semidirect
223. C₄×D₂₆₈	C₂³	semidirect
224. C₄×D₂₆₈	C₂³	semidirect
225. C₄×D₂₆₈	C₂³	semidirect
226. C₄×D₂₆₈	C₂³	semidirect
227. C₄×D₂₆₈	C₂³	semidirect
230. #14524005	C₂³	semidirect
239. C₄×C₂²⋊D₆₇	C₂³	semidirect
240. C₄×C₂²⋊D₆₇	C₂³	semidirect
241. C₄×C₂²⋊D₆₇	C₂³	semidirect
242. C₄×C₂²⋊D₆₇	C₂³	semidirect
243. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
244. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
249. #14524002	C₂³	semidirect
250. #14524002	C₂³	semidirect
251. #14524001	C₂³	semidirect
252. #14524000	C₂³	semidirect
253. #14524000	C₂³	semidirect
254. #14524000	C₂³	semidirect
255. #14523999	C₂³	semidirect
256. C₂×C₄⋊Dic₆₇	C₂³	semidirect
257. C₂×C₄⋊Dic₆₇	C₂³	semidirect
258. C₂×Dic₆₇⋊C₄	C₂³	semidirect
259. C₂×Dic₆₇⋊C₄	C₂³	semidirect
260. C₄⋊C₄×D₆₇	C₂³	semidirect
264. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
265. C₂×(C₂×D₆₇)⋊C₄	C₂³	semidirect
266. C₂²⋊C₄×D₆₇	C₂³	semidirect
267. C₂×C₄×Dic₆₇	C₂³	semidirect
268. C₄²×D₆₇	C₂³	semidirect
402. C₂×D₄×C₆₇	#41	semidirect
474. C₂³×C₆₇	C₂×#41	semidirect
486. D₄×C₆₇	C₂×#41	semidirect
511. C₂×C₄×C₆₇	C₂×#41	semidirect
512. C₂×C₄×C₆₇	H(5,𝔽₂)	semidirect
613. C₂²×C₄×D₄	D₆₇	semidirect
614. C₆₇	#62773	semidirect
618. C₂⁴×C₄	C₂×D₆₇	semidirect
708. C₂×C₄×D₄	C₂×D₆₇	semidirect
709. C₂×C₄×D₄	C₂×D₆₇	semidirect
710. C₂×C₄×D₄	C₂×D₆₇	semidirect
711. C₂×C₄×D₄	C₂×D₆₇	semidirect
712. C₂×C₄×D₄	C₂×D₆₇	semidirect
713. C₂×C₄×D₄	C₂×D₆₇	semidirect
714. C₂×C₄×D₄	C₂×D₆₇	semidirect
715. C₂×C₄×D₄	C₂×D₆₇	semidirect
717. C₂²×C₄⋊C₄	C₂×D₆₇	semidirect
718. C₂²×C₂²⋊C₄	C₂×D₆₇	semidirect
719. C₂²×C₄²	C₂×D₆₇	semidirect
955. C₂×D₄	#11761628	semidirect
1073. C₂³	C₂×#11761628	semidirect
1095. D₄	C₂×#11761628	semidirect
1130. C₂×C₄	C₂×#11761628	semidirect
1131. C₂×C₄	#14524088	semidirect

Maximal subgroups

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

subgroup	index
#22574258	2
#22574241	2
#22574149	2
#22574061	2
#22574048	2
#22574012	2
#22573973	2
#22573918	2
#22573898	2
#22573844	2
#22573813	2
#22573767	2
D₄×#11761628	2
#22573631	2
#22573618	2
#22573505	2
C₂×#16863907	2
C₄×#14524088	2
C₂²×C₄×D₄×C₆₇	2
#62773	67