Subgroups — C₂×#22573765 #31762866

Order 17152.

7954 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573765	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864110	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864091	C₂	1	2	yes	maximal, complemented
6	C₂×#16864084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864082	C₂	1	2	yes	maximal, complemented
8	C₂×#16864080	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864074	C₂	1	2	yes	maximal, complemented
10	C₂×#16864071	C₂	1	2	yes	maximal, complemented
11	C₂×#16864048	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16864039	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863950	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16863928	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863928	C₂	1	2	yes	maximal, complemented
17	C₂×#16863924	C₂	1	2	yes	maximal, complemented
18	C₂×#16863905	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×#11761629	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄×#11761628	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×#11761628	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#117×D₆₇	C₂	1	2	yes	maximal, complemented
24	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×#11761628	C₂²	1	1	yes	characteristic
27	C₂²×#11761628	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
29	C₂³×C₄×D₆₇	C₂²	1	2	yes	—
30	#16864115	C₂²	1	16	yes	complemented
31	#16864110	C₂²	1	16	yes	complemented
32	#16864102	C₂²	1	16	yes	complemented
33	#16864091	C₂²	1	32	yes	complemented
34	#16864084	C₂²	1	16	yes	complemented
35	#16864082	C₂²	1	32	yes	complemented
36	#16864080	C₂²	1	16	yes	complemented
37	#16864074	C₂²	1	32	yes	complemented
38	#16864071	C₂²	1	32	yes	complemented
39	#16864048	C₂²	1	16	yes	complemented
40	#16864043	C₂²	1	16	yes	complemented
41	#16864039	C₂²	1	16	yes	complemented
42	#16863950	C₂²	1	16	yes	complemented
43	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
45	#16863928	C₂²	1	16	yes	complemented
46	#16863928	C₂²	1	32	yes	complemented
47	#16863924	C₂²	1	32	yes	complemented
48	C₂×#14524038	C₂²	1	2	yes	complemented
49	C₂×#14524036	C₂²	1	2	yes	complemented
50	C₂×#14524036	C₂²	1	2	yes	complemented
51	C₂×#14524036	C₂²	1	2	yes	complemented
52	C₂×#14524036	C₂²	1	2	yes	complemented
53	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
54	C₂×#14524034	C₂²	1	2	yes	complemented
55	C₂×#14524033	C₂²	1	2	yes	complemented
56	C₂×#14524033	C₂²	1	2	yes	complemented
57	C₂×#14524030	C₂²	1	1	yes	characteristic
58	C₂×#14524030	C₂²	1	2	yes	complemented
59	C₂×#14524029	C₂²	1	2	yes	complemented
60	#16863905	C₂²	1	32	yes	complemented
61	C₂×#14524028	C₂²	1	2	yes	—
62	C₂×#14524028	C₂²	1	2	yes	complemented
63	C₂×#14524025	C₂²	1	2	yes	—
64	C₂×#14524025	C₂²	1	2	yes	—
65	C₂×#14524025	C₂²	1	2	yes	—
66	C₂×#14524025	C₂²	1	2	yes	complemented
67	C₂×#14524025	C₂²	1	2	yes	complemented
68	C₂×#14524023	C₂²	1	1	yes	characteristic
69	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
70	C₂×#14524023	C₂²	1	2	yes	complemented
71	C₂×#14524021	C₂²	1	2	yes	—
72	C₂×#14524021	C₂²	1	2	yes	complemented
73	C₂×#14524021	C₂²	1	2	yes	complemented
74	C₂×#14524020	C₂²	1	2	yes	complemented
75	C₂×#14524019	C₂²	1	1	yes	characteristic
76	C₂×#14524016	C₂²	1	2	yes	—
77	C₂×#14524016	C₂²	1	2	yes	complemented
78	C₂×#14524015	C₂²	1	2	yes	complemented
79	C₂×#14524014	C₂²	1	1	yes	characteristic
80	C₂×#14524014	C₂²	1	2	yes	—
81	C₂×#14524013	C₂²	1	2	yes	—
82	C₂×#14524011	C₂²	1	2	yes	—
83	C₄×#11761629	C₂²	1	16	yes	complemented
84	C₄×#11761628	C₂²	1	16	yes	complemented
85	C₄×#11761628	C₂²	1	16	yes	complemented
86	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
92	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
94	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
95	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
96	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
97	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
98	C₂×#14524005	C₂²	1	1	yes	characteristic
99	C₂×#14524005	C₂²	1	1	yes	characteristic
100	C₂×#14524005	C₂²	1	2	yes	complemented
101	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
102	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
103	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
104	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
106	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
107	C₂×C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
109	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
110	C₄×D₄×D₆₇	C₂²	1	16	yes	complemented
111	C₂×#14524002	C₂²	1	2	yes	complemented
112	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
113	C₂×#14524002	C₂²	1	1	yes	characteristic, complemented
114	C₂×#14524001	C₂²	1	2	yes	—
115	C₂×#14524001	C₂²	1	2	yes	—
116	C₂×#14524001	C₂²	1	2	yes	complemented
117	C₂×#14524001	C₂²	1	1	yes	characteristic, complemented
118	C₂×#14524000	C₂²	1	1	yes	characteristic
119	C₂×#14524000	C₂²	1	2	yes	—
120	C₂×#14524000	C₂²	1	2	yes	complemented
121	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
122	C₂×#14523999	C₂²	1	2	yes	complemented
123	C₂×#14523999	C₂²	1	2	yes	complemented
124	#117×D₆₇	C₂²	1	32	yes	complemented
125	C₂×C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
127	C₂×C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
128	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
129	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
131	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
133	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
134	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
135	#529×C₆₇	C₂²	1	16	yes	complemented
136	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
137	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
141	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
142	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
144	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
145	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
146	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761629	—	2	8	no	—
149	C₂×#11761629	C₂³	1	8	yes	—
150	C₂×#11761628	—	2	8	no	—
151	C₂×#11761628	—	2	8	no	—
152	C₂×#11761628	C₂³	1	8	yes	—
153	C₂×#11761628	C₂³	1	8	yes	—
154	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
157	C₂²×D₂₆₈	C₂³	1	2	yes	—
158	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
159	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
160	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
161	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
165	C₂×D₄×D₆₇	—	2	8	no	—
166	C₂×D₄×D₆₇	C₂³	1	8	yes	—
167	C₂³×Dic₆₇	C₂³	1	2	yes	—
168	C₂²×C₄×D₆₇	—	2	16	no	—
169	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
171	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
172	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
173	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
176	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
177	C₂²×C₄×D₆₇	C₂³	1	16	yes	—
178	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
179	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
180	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
181	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
182	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
183	#14524042	C₂³	1	8	yes	complemented
184	#14524041	C₂³	1	8	yes	complemented
185	#14524038	C₂³	1	16	yes	complemented
186	#14524036	C₂³	1	16	yes	complemented
187	#14524036	C₂³	1	16	yes	complemented
188	#14524036	C₂³	1	16	yes	complemented
189	#14524036	C₂³	1	16	yes	complemented
190	#14524034	C₂³	1	8	yes	complemented
191	#14524034	C₂³	1	16	yes	complemented
192	#14524033	C₂³	1	16	yes	complemented
193	#14524033	C₂³	1	16	yes	complemented
194	#14524030	C₂³	1	8	yes	—
195	#14524030	C₂³	1	16	yes	complemented
196	#14524029	C₂³	1	16	yes	complemented
197	#14524028	C₂³	1	16	yes	—
198	#14524028	C₂³	1	16	yes	complemented
199	#14524025	C₂³	1	16	yes	—
200	#14524025	C₂³	1	16	yes	—
201	#14524025	C₂³	1	16	yes	—
202	#14524025	C₂³	1	16	yes	complemented
203	#14524025	C₂³	1	16	yes	complemented
204	#14524023	C₂³	1	8	yes	—
205	#14524023	C₂³	1	8	yes	complemented
206	#14524023	C₂³	1	16	yes	complemented
207	#14524021	C₂³	1	16	yes	—
208	#14524021	C₂³	1	16	yes	complemented
209	#14524021	C₂³	1	16	yes	complemented
210	#14524020	C₂³	1	16	yes	complemented
211	#14524019	C₂³	1	8	yes	—
212	#14524016	C₂³	1	16	yes	—
213	#14524016	C₂³	1	16	yes	complemented
214	#14524015	C₂³	1	16	yes	complemented
215	#14524014	C₂³	1	8	yes	—
216	#14524014	C₂³	1	16	yes	—
217	#14524013	C₂³	1	16	yes	—
218	#14524011	C₂³	1	16	yes	—
219	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
220	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
221	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
222	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
223	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
224	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
225	C₄×D₂₆₈	C₂³	1	8	yes	—
226	C₄×D₂₆₈	C₂³	1	8	yes	—
227	C₄×D₂₆₈	C₂³	1	8	yes	—
228	C₄×D₂₆₈	C₂³	1	8	yes	—
229	C₄×D₂₆₈	C₂³	1	16	yes	complemented
230	D₄×Dic₆₇	C₂³	1	8	yes	—
231	#14524005	C₂³	1	8	yes	—
232	#14524005	C₂³	1	8	yes	—
233	#14524005	C₂³	1	16	yes	complemented
234	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
235	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	—
236	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
237	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
238	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
239	C₄×C₂²⋊D₆₇	C₂³	1	8	yes	complemented
240	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
241	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
242	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
243	#14524002	C₂³	1	8	yes	complemented
244	#14524002	C₂³	1	16	yes	complemented
245	#14524002	C₂³	1	8	yes	complemented
246	#14524001	C₂³	1	16	yes	—
247	#14524001	C₂³	1	16	yes	—
248	#14524001	C₂³	1	16	yes	complemented
249	#14524001	C₂³	1	8	yes	complemented
250	#14524000	C₂³	1	8	yes	—
251	#14524000	C₂³	1	16	yes	—
252	#14524000	C₂³	1	16	yes	complemented
253	#14524000	C₂³	1	8	yes	complemented
254	#14523999	C₂³	1	16	yes	complemented
255	#14523999	C₂³	1	16	yes	complemented
256	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
264	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
265	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
268	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
269	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
272	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
273	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
274	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
275	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
276	C₄⋊C₄×D₆₇	C₂³	1	8	yes	—
277	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
278	C₄⋊C₄×D₆₇	C₂³	1	16	yes	complemented
279	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
280	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
281	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
282	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
285	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
291	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
292	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
293	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
296	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
297	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
298	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
299	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
300	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
301	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
306	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
307	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
308	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
309	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
310	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₄²×D₆₇	C₂³	1	8	yes	—
313	C₄²×D₆₇	C₂³	1	16	yes	complemented
314	C₄²×D₆₇	C₂³	1	16	yes	complemented
315	C₄²×D₆₇	C₂³	1	8	yes	complemented
316	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
319	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
322	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
323	#126×C₆₇	C₂³	1	16	yes	complemented
324	#125×C₆₇	C₂³	1	8	yes	complemented
325	#124×C₆₇	C₂³	1	8	yes	—
326	#123×C₆₇	C₂³	1	16	yes	complemented
327	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
328	#121×C₆₇	C₂³	1	8	yes	—
329	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
330	C₄×D₄×C₆₇	C₂³	1	8	yes	—
331	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
332	#117×C₆₇	C₂³	1	16	yes	complemented
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
340	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
341	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
342	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
343	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
344	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
349	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
350	C₂³×D₆₇	—	2	8	no	—
351	C₂³×D₆₇	—	2	8	no	—
352	C₂³×D₆₇	—	4	4	no	—
353	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
354	C₂³×D₆₇	C₂⁴	1	8	yes	—
355	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
356	C₂³×D₆₇	C₂⁴	1	2	yes	—
357	#11761629	—	2	32	no	—
358	#11761628	—	2	32	no	—
359	#11761628	—	2	32	no	—
360	C₂×Dic₁₃₄	—	2	4	no	—
361	C₂×Dic₁₃₄	—	2	4	no	—
362	C₂×Dic₁₃₄	—	4	4	no	—
363	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
364	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
365	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
366	C₂×D₂₆₈	—	2	4	no	—
367	C₂×D₂₆₈	—	2	8	no	—
368	C₂×D₂₆₈	#41	1	8	yes	complemented
369	C₂×D₂₆₈	C₂⁴	1	8	yes	—
370	C₂×D₂₆₈	C₂⁴	1	4	yes	—
371	C₂×D₂₆₈	C₂⁴	1	4	yes	—
372	C₂×C₂²⋊D₆₇	—	2	8	no	—
373	C₂×C₂²⋊D₆₇	—	2	4	no	—
374	C₂×C₂²⋊D₆₇	—	2	8	no	—
375	C₂×C₂²⋊D₆₇	—	2	4	no	—
376	C₂×C₂²⋊D₆₇	—	4	4	no	—
377	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
378	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
379	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
380	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
381	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
382	D₄×D₆₇	—	2	32	no	—
383	C₂²×Dic₆₇	—	2	8	no	—
384	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
385	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
389	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
393	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×D₆₇	—	2	8	no	—
395	C₂×C₄×D₆₇	—	2	8	no	—
396	C₂×C₄×D₆₇	—	2	8	no	—
397	C₂×C₄×D₆₇	—	2	8	no	—
398	C₂×C₄×D₆₇	—	2	4	no	—
399	C₂×C₄×D₆₇	—	2	4	no	—
400	C₂×C₄×D₆₇	—	2	4	no	—
401	C₂×C₄×D₆₇	—	2	8	no	—
402	C₂×C₄×D₆₇	—	2	64	no	—
403	C₂×C₄×D₆₇	—	4	2	no	—
404	C₂×C₄×D₆₇	—	4	4	no	—
405	C₂×C₄×D₆₇	—	4	4	no	—
406	C₂×C₄×D₆₇	—	4	2	no	—
407	C₂×C₄×D₆₇	#41	1	8	yes	complemented
408	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
409	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
410	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
411	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
412	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
413	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
414	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
415	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
416	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
417	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
418	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
419	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
420	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
421	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
422	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
423	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
424	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
425	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
426	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
427	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
428	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
429	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
430	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
431	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
432	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
433	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
434	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
435	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
436	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
437	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
438	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
439	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
440	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
441	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
442	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
443	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
444	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
445	C₂²⋊Dic₆₇	C₂⁴	1	4	yes	—
446	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
447	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
448	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
449	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
450	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
451	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
452	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
453	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
454	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
455	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
456	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
457	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
458	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
459	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
460	C₄×Dic₆₇	C₂⁴	1	4	yes	—
461	C₄×Dic₆₇	C₂⁴	1	4	yes	—
462	C₄×Dic₆₇	C₂⁴	1	4	yes	—
463	C₄×Dic₆₇	C₂⁴	1	4	yes	—
464	C₄×Dic₆₇	C₂⁴	1	8	yes	—
465	C₄×Dic₆₇	C₂⁴	1	8	yes	—
466	C₄×Dic₆₇	C₂⁴	1	8	yes	—
467	C₄×Dic₆₇	C₂⁴	1	8	yes	—
468	C₄×Dic₆₇	C₂⁴	1	8	yes	—
469	C₄×Dic₆₇	C₂⁴	1	4	yes	—
470	C₄×Dic₆₇	C₂⁴	1	4	yes	—
471	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
472	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
473	C₂×Q₈×C₆₇	—	2	4	no	—
474	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
475	C₂×D₄×C₆₇	—	2	4	no	—
476	C₂×D₄×C₆₇	—	4	4	no	—
477	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
478	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
479	C₂²×C₄×C₆₇	—	2	8	no	—
480	C₂²×C₄×C₆₇	—	2	4	no	—
481	C₂²×C₄×C₆₇	—	2	4	no	—
482	C₂²×C₄×C₆₇	—	4	2	no	—
483	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
487	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
488	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
489	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
490	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
491	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
492	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
493	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
494	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
495	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
496	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
497	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
499	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
500	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
501	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
502	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
503	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
504	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
505	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
506	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
507	C₄²×C₆₇	C₂⁴	1	4	yes	—
508	C₄²×C₆₇	C₂⁴	1	4	yes	—
509	C₄²×C₆₇	C₂⁴	1	4	yes	—
510	C₄²×C₆₇	C₂⁴	1	4	yes	—
511	C₄²×C₆₇	C₂⁴	1	8	yes	—
512	C₂³×C₆₇	—	2	4	no	—
513	C₂³×C₆₇	—	2	2	no	—
514	C₂³×C₆₇	—	2	2	no	—
515	C₂³×C₆₇	—	2	4	no	—
516	C₂³×C₆₇	—	2	2	no	—
517	C₂³×C₆₇	—	2	4	no	—
518	C₂³×C₆₇	C₂⁵	1	4	yes	—
519	C₂³×C₆₇	C₂⁵	1	2	yes	—
520	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
521	C₂²×D₆₇	—	2	4	no	—
522	C₂²×D₆₇	—	2	2	no	—
523	C₂²×D₆₇	—	2	4	no	—
524	C₂²×D₆₇	—	2	2	no	—
525	C₂²×D₆₇	—	2	2	no	—
526	C₂²×D₆₇	—	2	2	no	—
527	C₂²×D₆₇	—	2	2	no	—
528	C₂²×D₆₇	—	2	16	no	—
529	C₂²×D₆₇	—	2	16	no	—
530	C₂²×D₆₇	—	4	8	no	—
531	C₂²×D₆₇	—	4	32	no	—
532	C₂²×D₆₇	C₂×#41	1	4	yes	—
533	C₂²×D₆₇	C₂×#41	1	8	yes	—
534	C₂²×D₆₇	C₂⁵	1	2	yes	—
535	C₂²×D₆₇	C₂⁵	1	2	yes	—
536	C₂²×D₆₇	C₂⁵	1	4	yes	—
537	Q₈×C₆₇	—	2	8	no	—
538	D₄×C₆₇	—	2	8	no	—
539	D₄×C₆₇	—	4	8	no	—
540	C₂×C₄×C₆₇	—	2	2	no	—
541	C₂×C₄×C₆₇	—	2	4	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	4	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	4	no	—
547	C₂×C₄×C₆₇	—	2	16	no	—
548	C₂×C₄×C₆₇	—	2	8	no	—
549	C₂×C₄×C₆₇	—	2	8	no	—
550	C₂×C₄×C₆₇	—	4	4	no	—
551	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
552	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
553	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
554	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
555	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
556	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
557	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
558	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
559	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
560	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
561	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
562	C₂²⋊D₆₇	—	2	16	no	—
563	C₂²⋊D₆₇	—	2	8	no	—
564	C₂²⋊D₆₇	—	2	16	no	—
565	C₂²⋊D₆₇	—	2	8	no	—
566	C₂²⋊D₆₇	—	4	8	no	—
567	C₂×Dic₆₇	—	2	2	no	—
568	C₂×Dic₆₇	—	2	4	no	—
569	C₂×Dic₆₇	—	2	2	no	—
570	C₂×Dic₆₇	—	2	4	no	—
571	C₂×Dic₆₇	—	2	2	no	—
572	C₂×Dic₆₇	—	2	2	no	—
573	C₂×Dic₆₇	—	2	4	no	—
574	C₂×Dic₆₇	—	2	2	no	—
575	C₂×Dic₆₇	—	2	16	no	—
576	C₂×Dic₆₇	C₂×#41	1	4	yes	—
577	C₂×Dic₆₇	C₂⁵	1	4	yes	—
578	C₂×Dic₆₇	C₂⁵	1	2	yes	—
579	C₂×Dic₆₇	C₂⁵	1	2	yes	—
580	C₂×Dic₆₇	C₂⁵	1	2	yes	—
581	C₂×Dic₆₇	C₂⁵	1	4	yes	—
582	C₂×Dic₆₇	C₂⁵	1	2	yes	—
583	C₂×Dic₆₇	C₂⁵	1	4	yes	—
584	C₂×Dic₆₇	C₂⁵	1	2	yes	—
585	C₂×Dic₆₇	C₂⁵	1	2	yes	—
586	D₂₆₈	—	2	8	no	—
587	D₂₆₈	—	2	16	no	—
588	D₂₆₈	C₂×#41	1	16	yes	complemented
589	C₄×D₆₇	—	2	16	no	—
590	C₄×D₆₇	—	2	16	no	—
591	C₄×D₆₇	—	2	16	no	—
592	C₄×D₆₇	—	2	16	no	—
593	C₄×D₆₇	—	2	8	no	—
594	C₄×D₆₇	—	2	8	no	—
595	C₄×D₆₇	—	2	8	no	—
596	C₄×D₆₇	—	2	16	no	—
597	C₄×D₆₇	—	4	4	no	—
598	C₄×D₆₇	—	4	8	no	—
599	C₄×D₆₇	—	4	8	no	—
600	C₄×D₆₇	—	4	4	no	—
601	C₄×D₆₇	C₂×#41	1	16	yes	complemented
602	Dic₁₃₄	—	2	8	no	—
603	Dic₁₃₄	—	2	8	no	—
604	Dic₁₃₄	—	4	8	no	—
605	C₂²×C₆₇	—	2	4	no	—
606	C₂²×C₆₇	—	2	2	no	—
607	C₂²×C₆₇	—	2	2	no	—
608	C₂²×C₆₇	—	2	4	no	—
609	C₂²×C₆₇	—	2	4	no	—
610	C₂²×C₆₇	—	2	2	no	—
611	C₂²×C₆₇	—	4	8	no	—
612	C₂²×C₆₇	—	4	4	no	—
613	C₂²×C₆₇	C₂²×#41	1	2	yes	—
614	C₂²×C₆₇	C₂²×#41	1	2	yes	—
615	C₂²×C₆₇	#585	1	2	yes	—
616	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
617	C₂×D₆₇	—	2	4	no	—
618	C₂×D₆₇	—	2	2	no	—
619	C₂×D₆₇	—	2	4	no	—
620	C₂×D₆₇	—	2	2	no	—
621	C₂×D₆₇	—	2	8	no	—
622	C₂×D₆₇	—	2	16	no	—
623	C₂×D₆₇	—	2	2	no	—
624	C₂×D₆₇	—	2	2	no	—
625	C₂×D₆₇	—	2	2	no	—
626	C₂×D₆₇	—	4	32	no	—
627	C₂×D₆₇	—	4	4	no	—
628	C₂×D₆₇	C₂²×#41	1	4	yes	—
629	C₂×D₆₇	C₂²×#41	1	8	yes	—
630	C₄×C₆₇	—	2	2	no	—
631	C₄×C₆₇	—	2	2	no	—
632	C₄×C₆₇	—	2	4	no	—
633	C₄×C₆₇	—	2	4	no	—
634	C₄×C₆₇	—	2	4	no	—
635	C₄×C₆₇	—	2	2	no	—
636	C₄×C₆₇	—	2	2	no	—
637	C₄×C₆₇	C₂²×#41	1	4	yes	—
638	C₄×C₆₇	C₂²×#41	1	4	yes	—
639	Dic₆₇	—	2	4	no	—
640	Dic₆₇	—	2	2	no	—
641	Dic₆₇	—	2	2	no	—
642	Dic₆₇	—	2	4	no	—
643	Dic₆₇	—	2	2	no	—
644	Dic₆₇	—	2	2	no	—
645	Dic₆₇	—	2	4	no	—
646	Dic₆₇	—	2	2	no	—
647	Dic₆₇	C₂²×#41	1	4	yes	—
648	C₂×#3475	—	67	1	no	maximal, Sylow
649	C₂×C₆₇	—	4	4	no	—
650	C₂×C₆₇	—	4	2	no	—
651	C₂×C₆₇	#3475	1	4	yes	complemented
652	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
653	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
654	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
655	D₆₇	—	2	4	no	—
656	D₆₇	—	2	8	no	—
657	D₆₇	—	4	2	no	—
658	#3475	—	67	32	no	—
659	C₂×#556	—	67	1	no	—
660	C₂×#555	—	67	1	no	—
661	C₂×#554	—	67	1	no	—
662	C₂×#553	—	67	2	no	—
663	C₂×#552	—	67	2	no	—
664	C₂×#552	—	67	1	no	—
665	C₂×#552	—	67	1	no	—
666	C₂×#551	—	67	2	no	—
667	C₂×#551	—	67	2	no	—
668	C₂×#547	—	67	1	no	—
669	C₂×#546	—	67	1	no	—
670	C₂×#546	—	67	1	no	—
671	C₂×#533	—	67	1	no	—
672	C₂×#529	—	67	1	no	—
673	C₂×#529	—	67	2	no	—
674	C₂×#529	—	67	2	no	—
675	C₂×#529	D₆₇	1	1	yes	characteristic, complemented
676	C₂×#525	—	67	2	no	—
677	C₂×C₄×#41	—	67	1	no	—
678	C₂×C₄×#41	—	67	1	no	—
679	C₂×C₄×#41	—	67	1	no	—
680	C₂²×C₄×D₄	—	67	1	no	—
681	C₂²×#117	—	67	2	no	—
682	C₆₇	C₂×#3475	1	1	yes	characteristic, complemented, Sylow
683	C₂²×#41	—	67	1	no	—
684	C₂²×#41	—	67	1	no	—
685	C₂²×#41	—	67	1	no	—
686	C₂³×D₄	—	67	1	no	—
687	C₂⁴×C₄	—	67	2	no	—
688	#556	—	67	16	no	—
689	#555	—	67	16	no	—
690	#554	—	67	16	no	—
691	#553	—	67	32	no	—
692	#552	—	67	32	no	—
693	#552	—	67	16	no	—
694	#552	—	67	16	no	—
695	#551	—	67	32	no	—
696	#551	—	67	32	no	—
697	#547	—	67	16	no	—
698	#546	—	67	16	no	—
699	#546	—	67	16	no	—
700	#533	—	67	16	no	—
701	C₂×C₄⋊Q₈	—	67	1	no	—
702	C₂×C₄⋊Q₈	—	67	1	no	—
703	#529	—	67	16	no	—
704	#529	—	67	32	no	—
705	#529	—	67	32	no	—
706	#529	C₂×D₆₇	1	16	yes	complemented
707	C₂×#126	—	67	2	no	—
708	C₂×#126	—	67	2	no	—
709	C₂×#126	—	67	2	no	—
710	C₂×#126	—	67	2	no	—
711	C₂×#126	—	67	2	no	—
712	C₂×#126	C₂×D₆₇	1	2	yes	complemented
713	C₂×#125	—	67	2	no	—
714	C₂×#125	—	67	2	no	—
715	C₂×#125	—	67	1	no	—
716	C₂×#125	—	67	2	no	—
717	C₂×#125	C₂×D₆₇	1	1	yes	characteristic, complemented
718	C₂×#124	—	67	1	no	—
719	C₂×#124	—	67	2	no	—
720	C₂×#124	—	67	2	no	—
721	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
722	#525	—	67	32	no	—
723	C₂×#123	—	67	2	no	—
724	C₂×#123	—	67	2	no	—
725	C₂×#123	—	67	2	no	—
726	C₂×#123	—	67	2	no	—
727	C₂×#123	—	67	2	no	—
728	C₂×#123	—	67	2	no	—
729	C₂×#123	—	67	2	no	—
730	C₂×#123	C₂×D₆₇	1	2	yes	complemented
731	C₂×C₂²⋊Q₈	—	67	1	no	—
732	C₂×C₂²⋊Q₈	—	67	2	no	—
733	C₂×C₂²⋊Q₈	—	67	1	no	—
734	C₂×C₂²⋊Q₈	—	67	2	no	—
735	C₂×C₂²⋊Q₈	—	67	2	no	—
736	C₂×C₂²⋊Q₈	—	67	1	no	—
737	C₂×C₂²⋊Q₈	—	67	2	no	—
738	C₂×C₂²⋊Q₈	—	67	2	no	—
739	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
740	C₂×#121	—	67	2	no	—
741	C₂×#121	—	67	2	no	—
742	C₂×#121	—	67	1	no	—
743	C₂×#121	—	67	2	no	—
744	C₂×#121	—	67	2	no	—
745	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
746	C₂×#120	—	67	2	no	—
747	C₂×#120	—	67	2	no	—
748	C₄×#41	—	67	16	no	—
749	C₄×#41	—	67	16	no	—
750	C₄×#41	—	67	16	no	—
751	C₂×C₄×Q₈	—	67	1	no	—
752	C₂×C₄×Q₈	—	67	1	no	—
753	C₂×C₄×Q₈	—	67	1	no	—
754	C₂×C₄×Q₈	—	67	1	no	—
755	C₂×C₄×Q₈	—	67	1	no	—
756	C₂×C₄×Q₈	—	67	2	no	—
757	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
758	C₂×C₄×D₄	—	67	1	no	—
759	C₂×C₄×D₄	—	67	2	no	—
760	C₂×C₄×D₄	—	67	2	no	—
761	C₂×C₄×D₄	—	67	1	no	—
762	C₂×C₄×D₄	—	67	1	no	—
763	C₂×C₄×D₄	—	67	1	no	—
764	C₂×C₄×D₄	—	67	2	no	—
765	C₂×C₄×D₄	—	67	1	no	—
766	C₂×C₄×D₄	—	67	2	no	—
767	C₂×C₄×D₄	—	67	16	no	—
768	C₂×C₄×D₄	—	67	1	no	—
769	C₂×C₄×D₄	—	67	1	no	—
770	C₂×C₄×D₄	—	67	2	no	—
771	C₂×C₄×D₄	—	67	2	no	—
772	C₂×C₄×D₄	—	67	1	no	—
773	C₂×C₄×D₄	—	67	2	no	—
774	C₂×C₄×D₄	—	67	1	no	—
775	C₂×C₄×D₄	—	67	1	no	—
776	C₂×C₄×D₄	—	67	1	no	—
777	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
778	C₂×C₄×D₄	C₂×D₆₇	1	2	yes	complemented
779	C₂×#117	—	67	2	no	—
780	C₂×#117	—	67	1	no	—
781	C₂×#117	—	67	1	no	—
782	C₂×#117	—	67	32	no	—
783	C₂×#117	—	67	2	no	—
784	C₂×#117	—	67	2	no	—
785	C₂×#117	—	67	2	no	—
786	C₂×#117	—	67	1	no	—
787	C₂×#117	—	67	2	no	—
788	C₂×#117	—	67	2	no	—
789	C₂×#117	—	67	1	no	—
790	C₂×#117	—	67	2	no	—
791	C₂×#117	—	67	1	no	—
792	C₂×#117	—	67	2	no	—
793	C₂×#117	C₂×D₆₇	1	2	yes	complemented
794	C₂²×C₄⋊C₄	—	67	2	no	—
795	C₂²×C₄⋊C₄	—	67	2	no	—
796	C₂²×C₄⋊C₄	—	67	1	no	—
797	C₂²×C₂²⋊C₄	—	67	2	no	—
798	C₂²×C₂²⋊C₄	—	67	2	no	—
799	C₂²×C₂²⋊C₄	—	67	2	no	—
800	C₂²×C₄²	—	67	2	no	—
801	C₂²×C₄²	—	67	2	no	—
802	C₂²×C₄²	—	67	1	no	—
803	C₂²×C₄²	—	67	1	no	—
804	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic, complemented
805	C₂⁵	—	67	2	no	—
806	C₂×#41	—	67	8	no	—
807	C₂×#41	—	67	8	no	—
808	C₂×#41	—	67	8	no	—
809	C₂×#41	—	134	8	no	—
810	C₂×#41	—	134	8	no	—
811	C₂×#41	—	134	8	no	—
812	C₂²×Q₈	—	67	2	no	—
813	C₂²×Q₈	—	67	1	no	—
814	C₂²×Q₈	—	67	1	no	—
815	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
816	C₂²×D₄	—	67	2	no	—
817	C₂²×D₄	—	67	1	no	—
818	C₂²×D₄	—	67	2	no	—
819	C₂²×D₄	—	67	1	no	—
820	C₂²×D₄	—	67	2	no	—
821	C₂²×D₄	—	67	8	no	—
822	C₂²×D₄	—	67	1	no	—
823	C₂²×D₄	—	67	1	no	—
824	C₂²×D₄	—	67	2	no	—
825	C₂²×D₄	—	134	8	no	—
826	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
827	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
828	C₂³×C₄	—	67	1	no	—
829	C₂³×C₄	—	67	2	no	—
830	C₂³×C₄	—	67	2	no	—
831	C₂³×C₄	—	67	1	no	—
832	C₂³×C₄	—	67	1	no	—
833	C₂³×C₄	—	67	2	no	—
834	C₂³×C₄	—	67	2	no	—
835	C₂³×C₄	—	67	2	no	—
836	C₂³×C₄	—	67	2	no	—
837	C₂³×C₄	—	67	2	no	—
838	C₂³×C₄	—	67	1	no	—
839	C₂³×C₄	—	67	16	no	—
840	C₂³×C₄	—	67	1	no	—
841	C₂³×C₄	—	67	1	no	—
842	C₂³×C₄	—	67	2	no	—
843	C₂³×C₄	—	134	16	no	—
844	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
845	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
846	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
847	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
848	C₄⋊Q₈	—	67	8	no	—
849	C₄⋊Q₈	—	67	8	no	—
850	#126	—	67	16	no	—
851	#126	—	67	16	no	—
852	#126	—	67	16	no	—
853	#126	—	67	16	no	—
854	#126	—	67	16	no	—
855	#126	C₂²×D₆₇	1	16	yes	complemented
856	#125	—	67	16	no	—
857	#125	—	67	16	no	—
858	#125	—	67	8	no	—
859	#125	—	67	16	no	—
860	#125	C₂²×D₆₇	1	8	yes	complemented
861	#124	—	67	8	no	—
862	#124	—	67	16	no	—
863	#124	—	67	16	no	—
864	#124	C₂²×D₆₇	1	8	yes	—
865	#123	—	67	16	no	—
866	#123	—	67	16	no	—
867	#123	—	67	16	no	—
868	#123	—	67	16	no	—
869	#123	—	67	16	no	—
870	#123	—	67	16	no	—
871	#123	—	67	16	no	—
872	#123	C₂²×D₆₇	1	16	yes	complemented
873	C₂²⋊Q₈	—	67	8	no	—
874	C₂²⋊Q₈	—	67	16	no	—
875	C₂²⋊Q₈	—	67	8	no	—
876	C₂²⋊Q₈	—	67	16	no	—
877	C₂²⋊Q₈	—	67	16	no	—
878	C₂²⋊Q₈	—	67	8	no	—
879	C₂²⋊Q₈	—	67	16	no	—
880	C₂²⋊Q₈	—	67	16	no	—
881	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
882	#121	—	67	16	no	—
883	#121	—	67	16	no	—
884	#121	—	67	8	no	—
885	#121	—	67	16	no	—
886	#121	—	67	16	no	—
887	#121	C₂²×D₆₇	1	8	yes	—
888	#120	—	67	16	no	—
889	#120	—	67	16	no	—
890	C₄×Q₈	—	67	8	no	—
891	C₄×Q₈	—	67	8	no	—
892	C₄×Q₈	—	67	8	no	—
893	C₄×Q₈	—	67	8	no	—
894	C₄×Q₈	—	67	8	no	—
895	C₄×Q₈	—	67	16	no	—
896	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
897	C₄×D₄	—	67	8	no	—
898	C₄×D₄	—	67	16	no	—
899	C₄×D₄	—	67	16	no	—
900	C₄×D₄	—	67	8	no	—
901	C₄×D₄	—	67	8	no	—
902	C₄×D₄	—	67	8	no	—
903	C₄×D₄	—	67	16	no	—
904	C₄×D₄	—	67	8	no	—
905	C₄×D₄	—	67	16	no	—
906	C₄×D₄	—	67	8	no	—
907	C₄×D₄	—	67	8	no	—
908	C₄×D₄	—	67	16	no	—
909	C₄×D₄	—	67	16	no	—
910	C₄×D₄	—	67	8	no	—
911	C₄×D₄	—	67	16	no	—
912	C₄×D₄	—	67	8	no	—
913	C₄×D₄	—	67	8	no	—
914	C₄×D₄	—	67	8	no	—
915	C₄×D₄	C₂²×D₆₇	1	8	yes	—
916	C₄×D₄	C₂²×D₆₇	1	16	yes	complemented
917	#117	—	67	16	no	—
918	#117	—	67	8	no	—
919	#117	—	67	8	no	—
920	#117	—	67	16	no	—
921	#117	—	67	16	no	—
922	#117	—	67	16	no	—
923	#117	—	67	8	no	—
924	#117	—	67	16	no	—
925	#117	—	67	16	no	—
926	#117	—	67	8	no	—
927	#117	—	67	16	no	—
928	#117	—	67	8	no	—
929	#117	—	67	16	no	—
930	#117	C₂²×D₆₇	1	16	yes	complemented
931	C₂×C₄⋊C₄	—	67	1	no	—
932	C₂×C₄⋊C₄	—	67	1	no	—
933	C₂×C₄⋊C₄	—	67	1	no	—
934	C₂×C₄⋊C₄	—	67	2	no	—
935	C₂×C₄⋊C₄	—	67	2	no	—
936	C₂×C₄⋊C₄	—	67	2	no	—
937	C₂×C₄⋊C₄	—	67	2	no	—
938	C₂×C₄⋊C₄	—	67	2	no	—
939	C₂×C₄⋊C₄	—	67	1	no	—
940	C₂×C₄⋊C₄	—	67	1	no	—
941	C₂×C₄⋊C₄	—	67	1	no	—
942	C₂×C₄⋊C₄	—	67	2	no	—
943	C₂×C₄⋊C₄	—	67	2	no	—
944	C₂×C₄⋊C₄	—	67	2	no	—
945	C₂×C₄⋊C₄	—	67	1	no	—
946	C₂×C₄⋊C₄	—	67	1	no	—
947	C₂×C₄⋊C₄	—	67	2	no	—
948	C₂×C₄⋊C₄	—	67	2	no	—
949	C₂×C₄⋊C₄	—	67	2	no	—
950	C₂×C₄⋊C₄	—	67	2	no	—
951	C₂×C₄⋊C₄	—	67	16	no	—
952	C₂×C₄⋊C₄	—	67	16	no	—
953	C₂×C₄⋊C₄	—	67	8	no	—
954	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
955	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
956	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
959	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
960	C₂×C₂²⋊C₄	—	67	2	no	—
961	C₂×C₂²⋊C₄	—	67	2	no	—
962	C₂×C₂²⋊C₄	—	67	2	no	—
963	C₂×C₂²⋊C₄	—	67	1	no	—
964	C₂×C₂²⋊C₄	—	67	2	no	—
965	C₂×C₂²⋊C₄	—	67	1	no	—
966	C₂×C₂²⋊C₄	—	67	2	no	—
967	C₂×C₂²⋊C₄	—	67	1	no	—
968	C₂×C₂²⋊C₄	—	67	1	no	—
969	C₂×C₂²⋊C₄	—	67	2	no	—
970	C₂×C₂²⋊C₄	—	67	2	no	—
971	C₂×C₂²⋊C₄	—	67	2	no	—
972	C₂×C₂²⋊C₄	—	67	2	no	—
973	C₂×C₂²⋊C₄	—	67	2	no	—
974	C₂×C₂²⋊C₄	—	67	2	no	—
975	C₂×C₂²⋊C₄	—	67	1	no	—
976	C₂×C₂²⋊C₄	—	67	2	no	—
977	C₂×C₂²⋊C₄	—	67	1	no	—
978	C₂×C₂²⋊C₄	—	67	2	no	—
979	C₂×C₂²⋊C₄	—	67	16	no	—
980	C₂×C₂²⋊C₄	—	67	16	no	—
981	C₂×C₂²⋊C₄	—	67	16	no	—
982	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
983	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
984	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
985	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
986	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
987	C₂×C₄²	—	67	2	no	—
988	C₂×C₄²	—	67	2	no	—
989	C₂×C₄²	—	67	2	no	—
990	C₂×C₄²	—	67	2	no	—
991	C₂×C₄²	—	67	1	no	—
992	C₂×C₄²	—	67	1	no	—
993	C₂×C₄²	—	67	1	no	—
994	C₂×C₄²	—	67	1	no	—
995	C₂×C₄²	—	67	1	no	—
996	C₂×C₄²	—	67	1	no	—
997	C₂×C₄²	—	67	2	no	—
998	C₂×C₄²	—	67	16	no	—
999	C₂×C₄²	—	67	16	no	—
1000	C₂×C₄²	—	67	8	no	—
1001	C₂×C₄²	—	67	8	no	—
1002	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1003	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1004	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1005	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
1006	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
1007	C₂×C₄²	C₂²×D₆₇	1	8	yes	complemented
1008	C₂⁴	—	268	4	no	—
1009	C₂⁴	—	67	8	no	—
1010	C₂⁴	—	67	1	no	—
1011	C₂⁴	—	67	2	no	—
1012	C₂⁴	—	67	1	no	—
1013	C₂⁴	—	134	8	no	—
1014	C₂⁴	—	134	8	no	—
1015	C₂⁴	C₂³×D₆₇	1	2	yes	—
1016	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1017	#41	—	134	32	no	—
1018	#41	—	134	32	no	—
1019	#41	—	134	32	no	—
1020	C₂×Q₈	—	2	4	no	—
1021	C₂×Q₈	—	268	4	no	—
1022	C₂×Q₈	—	67	8	no	—
1023	C₂×Q₈	—	67	4	no	—
1024	C₂×Q₈	—	67	4	no	—
1025	C₂×Q₈	—	134	4	no	—
1026	C₂×Q₈	—	134	4	no	—
1027	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1028	C₂×D₄	—	2	4	no	—
1029	C₂×D₄	—	4	4	no	—
1030	C₂×D₄	—	268	4	no	—
1031	C₂×D₄	—	67	8	no	—
1032	C₂×D₄	—	67	4	no	—
1033	C₂×D₄	—	67	8	no	—
1034	C₂×D₄	—	67	4	no	—
1035	C₂×D₄	—	67	8	no	—
1036	C₂×D₄	—	67	8	no	—
1037	C₂×D₄	—	67	4	no	—
1038	C₂×D₄	—	67	4	no	—
1039	C₂×D₄	—	67	8	no	—
1040	C₂×D₄	—	134	4	no	—
1041	C₂×D₄	—	134	8	no	—
1042	C₂×D₄	—	134	4	no	—
1043	C₂×D₄	—	134	32	no	—
1044	C₂×D₄	—	134	8	no	—
1045	C₂×D₄	—	134	4	no	—
1046	C₂×D₄	—	134	8	no	—
1047	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1048	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1049	C₂²×C₄	—	2	8	no	—
1050	C₂²×C₄	—	2	4	no	—
1051	C₂²×C₄	—	2	4	no	—
1052	C₂²×C₄	—	4	2	no	—
1053	C₂²×C₄	—	268	2	no	—
1054	C₂²×C₄	—	268	4	no	—
1055	C₂²×C₄	—	268	2	no	—
1056	C₂²×C₄	—	268	4	no	—
1057	C₂²×C₄	—	67	4	no	—
1058	C₂²×C₄	—	67	8	no	—
1059	C₂²×C₄	—	67	8	no	—
1060	C₂²×C₄	—	67	4	no	—
1061	C₂²×C₄	—	67	1	no	—
1062	C₂²×C₄	—	67	8	no	—
1063	C₂²×C₄	—	67	4	no	—
1064	C₂²×C₄	—	67	2	no	—
1065	C₂²×C₄	—	67	1	no	—
1066	C₂²×C₄	—	67	1	no	—
1067	C₂²×C₄	—	67	1	no	—
1068	C₂²×C₄	—	67	1	no	—
1069	C₂²×C₄	—	67	2	no	—
1070	C₂²×C₄	—	67	2	no	—
1071	C₂²×C₄	—	67	1	no	—
1072	C₂²×C₄	—	67	8	no	—
1073	C₂²×C₄	—	67	8	no	—
1074	C₂²×C₄	—	67	8	no	—
1075	C₂²×C₄	—	67	8	no	—
1076	C₂²×C₄	—	67	4	no	—
1077	C₂²×C₄	—	67	4	no	—
1078	C₂²×C₄	—	67	4	no	—
1079	C₂²×C₄	—	67	8	no	—
1080	C₂²×C₄	—	67	8	no	—
1081	C₂²×C₄	—	134	8	no	—
1082	C₂²×C₄	—	134	64	no	—
1083	C₂²×C₄	—	134	8	no	—
1084	C₂²×C₄	—	134	8	no	—
1085	C₂²×C₄	—	134	8	no	—
1086	C₂²×C₄	—	134	8	no	—
1087	C₂²×C₄	—	134	8	no	—
1088	C₂²×C₄	—	134	4	no	—
1089	C₂²×C₄	—	134	4	no	—
1090	C₂²×C₄	—	134	4	no	—
1091	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1092	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1093	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1094	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1095	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1096	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1097	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1098	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1099	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1100	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1101	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1102	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1104	C₄⋊C₄	—	67	4	no	—
1105	C₄⋊C₄	—	67	4	no	—
1106	C₄⋊C₄	—	67	4	no	—
1107	C₄⋊C₄	—	67	8	no	—
1108	C₄⋊C₄	—	67	8	no	—
1109	C₄⋊C₄	—	67	8	no	—
1110	C₄⋊C₄	—	67	8	no	—
1111	C₄⋊C₄	—	67	8	no	—
1112	C₄⋊C₄	—	67	4	no	—
1113	C₄⋊C₄	—	67	4	no	—
1114	C₄⋊C₄	—	67	4	no	—
1115	C₄⋊C₄	—	67	8	no	—
1116	C₄⋊C₄	—	67	8	no	—
1117	C₄⋊C₄	—	67	8	no	—
1118	C₄⋊C₄	—	67	4	no	—
1119	C₄⋊C₄	—	67	4	no	—
1120	C₄⋊C₄	—	67	8	no	—
1121	C₄⋊C₄	—	67	8	no	—
1122	C₄⋊C₄	—	67	8	no	—
1123	C₄⋊C₄	—	67	8	no	—
1124	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1125	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1126	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1127	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1129	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1130	C₂²⋊C₄	—	67	8	no	—
1131	C₂²⋊C₄	—	67	8	no	—
1132	C₂²⋊C₄	—	67	8	no	—
1133	C₂²⋊C₄	—	67	4	no	—
1134	C₂²⋊C₄	—	67	8	no	—
1135	C₂²⋊C₄	—	67	4	no	—
1136	C₂²⋊C₄	—	67	8	no	—
1137	C₂²⋊C₄	—	67	4	no	—
1138	C₂²⋊C₄	—	67	4	no	—
1139	C₂²⋊C₄	—	67	8	no	—
1140	C₂²⋊C₄	—	67	8	no	—
1141	C₂²⋊C₄	—	67	8	no	—
1142	C₂²⋊C₄	—	67	8	no	—
1143	C₂²⋊C₄	—	67	8	no	—
1144	C₂²⋊C₄	—	67	8	no	—
1145	C₂²⋊C₄	—	67	4	no	—
1146	C₂²⋊C₄	—	67	8	no	—
1147	C₂²⋊C₄	—	67	4	no	—
1148	C₂²⋊C₄	—	67	8	no	—
1149	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1150	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1151	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1152	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1153	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1154	C₄²	—	67	4	no	—
1155	C₄²	—	67	8	no	—
1156	C₄²	—	67	8	no	—
1157	C₄²	—	67	4	no	—
1158	C₄²	—	67	8	no	—
1159	C₄²	—	67	8	no	—
1160	C₄²	—	67	8	no	—
1161	C₄²	—	67	4	no	—
1162	C₄²	—	67	4	no	—
1163	C₄²	—	67	4	no	—
1164	C₄²	—	67	4	no	—
1165	C₄²	C₂³×D₆₇	1	4	yes	—
1166	C₄²	C₂³×D₆₇	1	4	yes	—
1167	C₄²	C₂³×D₆₇	1	8	yes	—
1168	C₄²	C₂³×D₆₇	1	4	yes	—
1169	C₄²	C₂³×D₆₇	1	4	yes	—
1170	C₂³	—	2	4	no	—
1171	C₂³	—	2	2	no	—
1172	C₂³	—	2	2	no	—
1173	C₂³	—	2	4	no	—
1174	C₂³	—	2	2	no	—
1175	C₂³	—	2	4	no	—
1176	C₂³	—	268	8	no	—
1177	C₂³	—	268	32	no	—
1178	C₂³	—	67	4	no	—
1179	C₂³	—	67	8	no	—
1180	C₂³	—	67	2	no	—
1181	C₂³	—	67	4	no	—
1182	C₂³	—	67	2	no	—
1183	C₂³	—	134	16	no	—
1184	C₂³	—	134	16	no	—
1185	C₂³	—	134	2	no	—
1186	C₂³	—	134	2	no	—
1187	C₂³	—	134	2	no	—
1188	C₂³	—	134	4	no	—
1189	C₂³	—	134	2	no	—
1190	C₂³	—	134	4	no	—
1191	C₂³	—	134	2	no	—
1192	C₂³	C₂⁴×D₆₇	1	4	yes	—
1193	C₂³	C₂⁴×D₆₇	1	2	yes	—
1194	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1195	Q₈	—	2	8	no	—
1196	Q₈	—	268	8	no	—
1197	Q₈	—	134	8	no	—
1198	Q₈	—	134	8	no	—
1199	D₄	—	2	8	no	—
1200	D₄	—	4	8	no	—
1201	D₄	—	268	8	no	—
1202	D₄	—	67	16	no	—
1203	D₄	—	134	8	no	—
1204	D₄	—	134	16	no	—
1205	D₄	—	134	8	no	—
1206	D₄	—	134	16	no	—
1207	D₄	—	134	8	no	—
1208	D₄	—	134	16	no	—
1209	C₂×C₄	—	2	4	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	4	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	4	no	—
1216	C₂×C₄	—	2	16	no	—
1217	C₂×C₄	—	2	8	no	—
1218	C₂×C₄	—	2	8	no	—
1219	C₂×C₄	—	4	4	no	—
1220	C₂×C₄	—	268	4	no	—
1221	C₂×C₄	—	268	8	no	—
1222	C₂×C₄	—	268	4	no	—
1223	C₂×C₄	—	268	8	no	—
1224	C₂×C₄	—	67	4	no	—
1225	C₂×C₄	—	67	2	no	—
1226	C₂×C₄	—	67	16	no	—
1227	C₂×C₄	—	67	2	no	—
1228	C₂×C₄	—	67	4	no	—
1229	C₂×C₄	—	67	2	no	—
1230	C₂×C₄	—	67	2	no	—
1231	C₂×C₄	—	67	4	no	—
1232	C₂×C₄	—	67	2	no	—
1233	C₂×C₄	—	67	4	no	—
1234	C₂×C₄	—	67	2	no	—
1235	C₂×C₄	—	134	16	no	—
1236	C₂×C₄	—	134	16	no	—
1237	C₂×C₄	—	134	16	no	—
1238	C₂×C₄	—	134	16	no	—
1239	C₂×C₄	—	134	16	no	—
1240	C₂×C₄	—	134	4	no	—
1241	C₂×C₄	—	134	2	no	—
1242	C₂×C₄	—	134	2	no	—
1243	C₂×C₄	—	134	2	no	—
1244	C₂×C₄	—	134	4	no	—
1245	C₂×C₄	—	134	2	no	—
1246	C₂×C₄	—	134	4	no	—
1247	C₂×C₄	—	134	2	no	—
1248	C₂×C₄	—	134	16	no	—
1249	C₂×C₄	—	134	8	no	—
1250	C₂×C₄	—	134	8	no	—
1251	C₂×C₄	—	134	8	no	—
1252	C₂×C₄	#41×D₆₇	1	4	yes	—
1253	C₂×C₄	#41×D₆₇	1	4	yes	—
1254	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1255	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1256	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1257	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1258	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1259	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1260	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1261	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1262	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1263	C₂²	—	2	4	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	4	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	2	4	no	—
1269	C₂²	—	4	8	no	—
1270	C₂²	—	4	4	no	—
1271	C₂²	—	268	32	no	—
1272	C₂²	—	268	4	no	—
1273	C₂²	—	67	4	no	—
1274	C₂²	—	67	8	no	—
1275	C₂²	—	134	2	no	—
1276	C₂²	—	134	2	no	—
1277	C₂²	—	134	2	no	—
1278	C₂²	—	134	4	no	—
1279	C₂²	—	134	2	no	—
1280	C₂²	—	134	4	no	—
1281	C₂²	—	134	2	no	—
1282	C₂²	—	134	8	no	—
1283	C₂²	—	134	16	no	—
1284	C₂²	C₂×#41×D₆₇	1	2	yes	—
1285	C₂²	C₂×#41×D₆₇	1	2	yes	—
1286	C₂²	#16864232	1	2	yes	—
1287	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1288	C₄	—	2	4	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	4	no	—
1292	C₄	—	2	2	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	4	no	—
1295	C₄	—	67	4	no	—
1296	C₄	—	134	4	no	—
1297	C₄	—	134	2	no	—
1298	C₄	—	134	2	no	—
1299	C₄	—	134	2	no	—
1300	C₄	—	134	4	no	—
1301	C₄	—	134	2	no	—
1302	C₄	—	134	4	no	—
1303	C₄	—	134	2	no	—
1304	C₄	C₂×#41×D₆₇	1	4	yes	—
1305	C₄	C₂×#41×D₆₇	1	4	yes	—
1306	C₂	—	4	4	no	—
1307	C₂	—	4	2	no	—
1308	C₂	—	268	2	no	—
1309	C₂	—	134	4	no	—
1310	C₂	—	134	8	no	—
1311	C₂	#22573765	1	4	yes	direct product factor
1312	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1313	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1314	C₂	C₂×#16864232	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#529×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×#529	D₆₇
hypocenter	C₆₇	C₂×#3475
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #22573765	C₂	direct (N × H)
2. C₂×#16864115	C₂	semidirect
3. C₂×#16864110	C₂	semidirect
4. C₂×#16864102	C₂	semidirect
5. C₂×#16864091	C₂	semidirect
6. C₂×#16864084	C₂	semidirect
7. C₂×#16864082	C₂	semidirect
8. C₂×#16864080	C₂	semidirect
9. C₂×#16864074	C₂	semidirect
10. C₂×#16864071	C₂	semidirect
11. C₂×#16864048	C₂	semidirect
12. C₂×#16864043	C₂	semidirect
13. C₂×#16864039	C₂	semidirect
14. C₂×#16863950	C₂	semidirect
15. C₂×#16863928	C₂	semidirect
16. C₂×#16863928	C₂	semidirect
17. C₂×#16863924	C₂	semidirect
18. C₂×#16863905	C₂	semidirect
19. C₂×C₄×#11761629	C₂	semidirect
20. C₂×C₄×#11761628	C₂	semidirect
21. C₂×C₄×#11761628	C₂	semidirect
22. C₂×C₄×D₄×D₆₇	C₂	semidirect
23. C₂×#117×D₆₇	C₂	semidirect
24. C₂×#529×C₆₇	C₂	semidirect
30. #16864115	C₂²	semidirect
31. #16864110	C₂²	semidirect
32. #16864102	C₂²	semidirect
33. #16864091	C₂²	semidirect
34. #16864084	C₂²	semidirect
35. #16864082	C₂²	semidirect
36. #16864080	C₂²	semidirect
37. #16864074	C₂²	semidirect
38. #16864071	C₂²	semidirect
39. #16864048	C₂²	semidirect
40. #16864043	C₂²	semidirect
41. #16864039	C₂²	semidirect
42. #16863950	C₂²	semidirect
43. C₂×#14524042	C₂²	semidirect
44. C₂×#14524041	C₂²	semidirect
45. #16863928	C₂²	semidirect
46. #16863928	C₂²	semidirect
47. #16863924	C₂²	semidirect
48. C₂×#14524038	C₂²	semidirect
49. C₂×#14524036	C₂²	semidirect
50. C₂×#14524036	C₂²	semidirect
51. C₂×#14524036	C₂²	semidirect
52. C₂×#14524036	C₂²	semidirect
53. C₂×#14524034	C₂²	semidirect
54. C₂×#14524034	C₂²	semidirect
55. C₂×#14524033	C₂²	semidirect
56. C₂×#14524033	C₂²	semidirect
58. C₂×#14524030	C₂²	semidirect
59. C₂×#14524029	C₂²	semidirect
60. #16863905	C₂²	semidirect
62. C₂×#14524028	C₂²	semidirect
66. C₂×#14524025	C₂²	semidirect
67. C₂×#14524025	C₂²	semidirect
69. C₂×#14524023	C₂²	semidirect
70. C₂×#14524023	C₂²	semidirect
72. C₂×#14524021	C₂²	semidirect
73. C₂×#14524021	C₂²	semidirect
74. C₂×#14524020	C₂²	semidirect
77. C₂×#14524016	C₂²	semidirect
78. C₂×#14524015	C₂²	semidirect
83. C₄×#11761629	C₂²	semidirect
84. C₄×#11761628	C₂²	semidirect
85. C₄×#11761628	C₂²	semidirect
86. C₂×Q₈×Dic₆₇	C₂²	semidirect
87. C₂×C₄×Dic₁₃₄	C₂²	semidirect
88. C₂×C₄×Dic₁₃₄	C₂²	semidirect
89. C₂×C₄×Dic₁₃₄	C₂²	semidirect
90. C₂×C₄×Dic₁₃₄	C₂²	semidirect
91. C₂×C₄×Dic₁₃₄	C₂²	semidirect
96. C₂×C₄×D₂₆₈	C₂²	semidirect
100. C₂×#14524005	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
105. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
106. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
107. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
108. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
110. C₄×D₄×D₆₇	C₂²	semidirect
111. C₂×#14524002	C₂²	semidirect
112. C₂×#14524002	C₂²	semidirect
113. C₂×#14524002	C₂²	semidirect
116. C₂×#14524001	C₂²	semidirect
117. C₂×#14524001	C₂²	semidirect
120. C₂×#14524000	C₂²	semidirect
121. C₂×#14524000	C₂²	semidirect
122. C₂×#14523999	C₂²	semidirect
123. C₂×#14523999	C₂²	semidirect
124. #117×D₆₇	C₂²	semidirect
126. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
127. C₂×C₄⋊C₄×D₆₇	C₂²	semidirect
132. C₂×C₄²×D₆₇	C₂²	semidirect
133. C₂×C₄²×D₆₇	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. #529×C₆₇	C₂²	semidirect
136. C₂×#126×C₆₇	C₂²	semidirect
137. C₂×#125×C₆₇	C₂²	semidirect
139. C₂×#123×C₆₇	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×D₄×C₆₇	C₂²	semidirect
145. C₂×#117×C₆₇	C₂²	semidirect
146. C₂²×C₄²×C₆₇	C₂²	semidirect
183. #14524042	C₂³	semidirect
184. #14524041	C₂³	semidirect
185. #14524038	C₂³	semidirect
186. #14524036	C₂³	semidirect
187. #14524036	C₂³	semidirect
188. #14524036	C₂³	semidirect
189. #14524036	C₂³	semidirect
190. #14524034	C₂³	semidirect
191. #14524034	C₂³	semidirect
192. #14524033	C₂³	semidirect
193. #14524033	C₂³	semidirect
195. #14524030	C₂³	semidirect
196. #14524029	C₂³	semidirect
198. #14524028	C₂³	semidirect
202. #14524025	C₂³	semidirect
203. #14524025	C₂³	semidirect
205. #14524023	C₂³	semidirect
206. #14524023	C₂³	semidirect
208. #14524021	C₂³	semidirect
209. #14524021	C₂³	semidirect
210. #14524020	C₂³	semidirect
213. #14524016	C₂³	semidirect
214. #14524015	C₂³	semidirect
219. Q₈×Dic₆₇	C₂³	semidirect
220. C₄×Dic₁₃₄	C₂³	semidirect
221. C₄×Dic₁₃₄	C₂³	semidirect
222. C₄×Dic₁₃₄	C₂³	semidirect
223. C₄×Dic₁₃₄	C₂³	semidirect
224. C₄×Dic₁₃₄	C₂³	semidirect
229. C₄×D₂₆₈	C₂³	semidirect
233. #14524005	C₂³	semidirect
237. C₄×C₂²⋊D₆₇	C₂³	semidirect
238. C₄×C₂²⋊D₆₇	C₂³	semidirect
239. C₄×C₂²⋊D₆₇	C₂³	semidirect
240. C₄×C₂²⋊D₆₇	C₂³	semidirect
241. C₄×C₂²⋊D₆₇	C₂³	semidirect
243. #14524002	C₂³	semidirect
244. #14524002	C₂³	semidirect
245. #14524002	C₂³	semidirect
248. #14524001	C₂³	semidirect
249. #14524001	C₂³	semidirect
252. #14524000	C₂³	semidirect
253. #14524000	C₂³	semidirect
254. #14523999	C₂³	semidirect
255. #14523999	C₂³	semidirect
277. C₄⋊C₄×D₆₇	C₂³	semidirect
278. C₄⋊C₄×D₆₇	C₂³	semidirect
313. C₄²×D₆₇	C₂³	semidirect
314. C₄²×D₆₇	C₂³	semidirect
315. C₄²×D₆₇	C₂³	semidirect
323. #126×C₆₇	C₂³	semidirect
324. #125×C₆₇	C₂³	semidirect
326. #123×C₆₇	C₂³	semidirect
327. C₂²⋊Q₈×C₆₇	C₂³	semidirect
329. C₄×Q₈×C₆₇	C₂³	semidirect
331. C₄×D₄×C₆₇	C₂³	semidirect
332. #117×C₆₇	C₂³	semidirect
349. C₂×C₄²×C₆₇	C₂³	semidirect
368. C₂×D₂₆₈	#41	semidirect
407. C₂×C₄×D₆₇	#41	semidirect
588. D₂₆₈	C₂×#41	semidirect
601. C₄×D₆₇	C₂×#41	semidirect
651. C₂×C₆₇	#3475	semidirect
675. C₂×#529	D₆₇	semidirect
682. C₆₇	C₂×#3475	semidirect
706. #529	C₂×D₆₇	semidirect
712. C₂×#126	C₂×D₆₇	semidirect
717. C₂×#125	C₂×D₆₇	semidirect
730. C₂×#123	C₂×D₆₇	semidirect
739. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
757. C₂×C₄×Q₈	C₂×D₆₇	semidirect
778. C₂×C₄×D₄	C₂×D₆₇	semidirect
793. C₂×#117	C₂×D₆₇	semidirect
804. C₂²×C₄²	C₂×D₆₇	semidirect
855. #126	C₂²×D₆₇	semidirect
860. #125	C₂²×D₆₇	semidirect
872. #123	C₂²×D₆₇	semidirect
881. C₂²⋊Q₈	C₂²×D₆₇	semidirect
896. C₄×Q₈	C₂²×D₆₇	semidirect
916. C₄×D₄	C₂²×D₆₇	semidirect
930. #117	C₂²×D₆₇	semidirect
1007. C₂×C₄²	C₂²×D₆₇	semidirect
1311. C₂	#22573765	direct (N × H)

Maximal subgroups

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

subgroup	index
#22573765	2
C₂×#16864115	2
C₂×#16864110	2
C₂×#16864102	2
C₂×#16864091	2
C₂×#16864084	2
C₂×#16864082	2
C₂×#16864080	2
C₂×#16864074	2
C₂×#16864071	2
C₂×#16864048	2
C₂×#16864043	2
C₂×#16864039	2
C₂×#16863950	2
C₂×#16863928	2
C₂×#16863924	2
C₂×#16863905	2
C₂×C₄×#11761629	2
C₂×C₄×#11761628	2
C₂×C₄×D₄×D₆₇	2
C₂×#117×D₆₇	2
C₂×#529×C₆₇	2
C₂×#3475	67

Subgroups — C2×#22573765 #31762866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22573765 #31762866