Subgroups — C₂×#22574099 #31764316

Order 17152.

7302 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574099	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16864131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16864129	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16864128	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864120	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16864118	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16864115	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16864073	C₂	1	2	yes	maximal, complemented
10	C₂×#16864071	C₂	1	2	yes	maximal, complemented
11	C₂×#16864071	C₂	1	2	yes	maximal, complemented
12	C₂×#16864070	C₂	1	2	yes	maximal, complemented
13	C₂×#16864016	C₂	1	2	yes	maximal, complemented
14	C₂×#16864012	C₂	1	2	yes	maximal, complemented
15	C₂×#16863971	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863964	C₂	1	1	yes	maximal, characteristic
17	C₂×#16863950	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863929	C₂	1	2	yes	maximal, complemented
19	C₂×#16863924	C₂	1	2	yes	maximal, complemented
20	C₂×#124×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16863872	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863868	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×#11761629	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761629	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	#16864131	C₂²	1	16	yes	complemented
29	#16864131	C₂²	1	16	yes	complemented
30	#16864129	C₂²	1	16	yes	complemented
31	#16864128	C₂²	1	16	yes	complemented
32	#16864120	C₂²	1	16	yes	complemented
33	#16864118	C₂²	1	16	yes	complemented
34	#16864115	C₂²	1	16	yes	complemented
35	#16864073	C₂²	1	32	yes	complemented
36	#16864071	C₂²	1	32	yes	complemented
37	#16864071	C₂²	1	32	yes	complemented
38	#16864070	C₂²	1	32	yes	complemented
39	#16864016	C₂²	1	32	yes	complemented
40	#16864012	C₂²	1	32	yes	complemented
41	#16863971	C₂²	1	16	yes	complemented
42	#16863964	C₂²	1	16	yes	—
43	#16863950	C₂²	1	16	yes	complemented
44	C₂×#14524042	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
46	C₂×#14524041	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14524040	C₂²	1	1	yes	characteristic
48	C₂×#14524039	C₂²	1	1	yes	characteristic
49	#16863929	C₂²	1	32	yes	complemented
50	#16863924	C₂²	1	32	yes	complemented
51	C₂×#14524038	C₂²	1	2	yes	complemented
52	C₂×#14524038	C₂²	1	2	yes	complemented
53	C₂×#14524038	C₂²	1	2	yes	complemented
54	C₂×#14524037	C₂²	1	2	yes	complemented
55	C₂×#14524036	C₂²	1	2	yes	complemented
56	C₂×#14524036	C₂²	1	2	yes	complemented
57	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524033	C₂²	1	1	yes	characteristic, complemented
59	C₂×#14524032	C₂²	1	1	yes	characteristic
60	C₂×#14524032	C₂²	1	1	yes	characteristic
61	C₂×#14524032	C₂²	1	2	yes	complemented
62	C₂×#14524032	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14524031	C₂²	1	1	yes	characteristic
64	C₂×#14524031	C₂²	1	2	yes	complemented
65	C₂×#14524031	C₂²	1	1	yes	characteristic, complemented
66	C₂×#14524030	C₂²	1	1	yes	characteristic
67	C₂×#14524029	C₂²	1	2	yes	—
68	C₂×#14524029	C₂²	1	2	yes	—
69	C₂×#14524029	C₂²	1	2	yes	complemented
70	C₂×#14524029	C₂²	1	2	yes	complemented
71	#124×D₆₇	C₂²	1	16	yes	complemented
72	C₂×#14524028	C₂²	1	2	yes	—
73	C₂×#14524028	C₂²	1	2	yes	—
74	C₂×#14524028	C₂²	1	2	yes	complemented
75	C₂×#14524028	C₂²	1	2	yes	complemented
76	C₂×#14524028	C₂²	1	2	yes	complemented
77	C₂×#14524028	C₂²	1	2	yes	complemented
78	C₂×#14524027	C₂²	1	2	yes	complemented
79	C₂×#14524026	C₂²	1	2	yes	complemented
80	C₂×#14524025	C₂²	1	2	yes	complemented
81	C₂×#14524025	C₂²	1	2	yes	complemented
82	C₂×#14524023	C₂²	1	1	yes	characteristic
83	C₂×#14524023	C₂²	1	2	yes	complemented
84	C₂×#14524021	C₂²	1	1	yes	characteristic
85	C₂×#14524021	C₂²	1	1	yes	characteristic
86	C₂×#14524021	C₂²	1	2	yes	complemented
87	C₂×#14524021	C₂²	1	2	yes	complemented
88	C₂×#14524021	C₂²	1	2	yes	complemented
89	C₂×#14524020	C₂²	1	2	yes	complemented
90	C₂×#14524019	C₂²	1	1	yes	characteristic
91	C₂×#14524016	C₂²	1	2	yes	—
92	C₂×#14524016	C₂²	1	2	yes	—
93	C₂×#14524013	C₂²	1	2	yes	—
94	C₂×#14524013	C₂²	1	2	yes	—
95	#16863872	C₂²	1	16	yes	complemented
96	#16863868	C₂²	1	16	yes	complemented
97	C₄×#11761629	C₂²	1	16	yes	complemented
98	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
101	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
105	C₂×#14524008	C₂²	1	2	yes	complemented
106	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
108	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
109	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
111	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
112	C₂×#14524005	C₂²	1	2	yes	—
113	C₂×#14524005	C₂²	1	1	yes	characteristic
114	C₂×#14524005	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14524005	C₂²	1	2	yes	complemented
116	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
117	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
118	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
119	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
120	C₂×#14524001	C₂²	1	1	yes	characteristic
121	C₂×#14524001	C₂²	1	2	yes	—
122	C₂×#14524001	C₂²	1	2	yes	complemented
123	C₂×#14524001	C₂²	1	2	yes	complemented
124	C₂×#14524000	C₂²	1	1	yes	characteristic
125	C₂×#14524000	C₂²	1	2	yes	—
126	C₂×#14524000	C₂²	1	1	yes	characteristic
127	C₂×#14524000	C₂²	1	2	yes	complemented
128	C₂×#14523999	C₂²	1	2	yes	complemented
129	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
132	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
133	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
134	C₂×C₄²×D₆₇	C₂²	1	2	yes	complemented
135	#556×C₆₇	C₂²	1	16	yes	complemented
136	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
138	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
139	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
140	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
141	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
142	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
144	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
145	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
146	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761629	—	2	8	no	—
149	C₂×#11761629	C₂³	1	8	yes	—
150	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
151	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
153	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
154	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
155	C₂×Q₈×D₆₇	—	2	8	no	—
156	C₂×Q₈×D₆₇	C₂³	1	8	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×D₂₆₈	C₂³	1	2	yes	—
161	C₂²×D₂₆₈	C₂³	1	2	yes	—
162	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
163	C₂²×C₂²⋊D₆₇	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
169	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
170	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
171	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
173	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
174	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
175	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
176	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
177	#14524042	C₂³	1	8	yes	complemented
178	#14524041	C₂³	1	8	yes	complemented
179	#14524041	C₂³	1	8	yes	complemented
180	#14524040	C₂³	1	8	yes	—
181	#14524039	C₂³	1	8	yes	—
182	#14524038	C₂³	1	16	yes	complemented
183	#14524038	C₂³	1	16	yes	complemented
184	#14524038	C₂³	1	16	yes	complemented
185	#14524037	C₂³	1	16	yes	complemented
186	#14524036	C₂³	1	16	yes	complemented
187	#14524036	C₂³	1	16	yes	complemented
188	#14524033	C₂³	1	8	yes	complemented
189	#14524033	C₂³	1	8	yes	complemented
190	#14524032	C₂³	1	8	yes	—
191	#14524032	C₂³	1	8	yes	—
192	#14524032	C₂³	1	16	yes	complemented
193	#14524032	C₂³	1	8	yes	complemented
194	#14524031	C₂³	1	8	yes	—
195	#14524031	C₂³	1	16	yes	complemented
196	#14524031	C₂³	1	8	yes	complemented
197	#14524030	C₂³	1	8	yes	—
198	#14524029	C₂³	1	16	yes	—
199	#14524029	C₂³	1	16	yes	—
200	#14524029	C₂³	1	16	yes	complemented
201	#14524029	C₂³	1	16	yes	complemented
202	#14524028	C₂³	1	16	yes	—
203	#14524028	C₂³	1	16	yes	—
204	#14524028	C₂³	1	16	yes	complemented
205	#14524028	C₂³	1	16	yes	complemented
206	#14524028	C₂³	1	16	yes	complemented
207	#14524028	C₂³	1	16	yes	complemented
208	#14524027	C₂³	1	16	yes	complemented
209	#14524026	C₂³	1	16	yes	complemented
210	#14524025	C₂³	1	16	yes	complemented
211	#14524025	C₂³	1	16	yes	complemented
212	#14524023	C₂³	1	8	yes	—
213	#14524023	C₂³	1	16	yes	complemented
214	#14524021	C₂³	1	8	yes	—
215	#14524021	C₂³	1	8	yes	—
216	#14524021	C₂³	1	16	yes	complemented
217	#14524021	C₂³	1	16	yes	complemented
218	#14524021	C₂³	1	16	yes	complemented
219	#14524020	C₂³	1	16	yes	complemented
220	#14524019	C₂³	1	8	yes	—
221	#14524016	C₂³	1	16	yes	—
222	#14524016	C₂³	1	16	yes	—
223	#14524013	C₂³	1	16	yes	—
224	#14524013	C₂³	1	16	yes	—
225	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
226	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
227	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
228	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
229	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
230	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
231	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
232	#14524008	C₂³	1	16	yes	complemented
233	#14524008	C₂³	1	8	yes	complemented
234	C₄×D₂₆₈	C₂³	1	16	yes	—
235	C₄×D₂₆₈	C₂³	1	8	yes	—
236	C₄×D₂₆₈	C₂³	1	16	yes	complemented
237	C₄×D₂₆₈	C₂³	1	8	yes	complemented
238	D₄×Dic₆₇	C₂³	1	8	yes	—
239	#14524005	C₂³	1	16	yes	—
240	#14524005	C₂³	1	8	yes	—
241	#14524005	C₂³	1	16	yes	complemented
242	#14524005	C₂³	1	8	yes	complemented
243	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
244	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
245	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
246	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
247	#14524001	C₂³	1	16	yes	—
248	#14524001	C₂³	1	8	yes	—
249	#14524001	C₂³	1	16	yes	complemented
250	#14524001	C₂³	1	16	yes	complemented
251	#14524000	C₂³	1	16	yes	—
252	#14524000	C₂³	1	8	yes	—
253	#14524000	C₂³	1	8	yes	—
254	#14524000	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	1	yes	characteristic
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×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
264	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
269	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
270	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×Dic₆₇⋊C₄	C₂³	1	2	yes	—
272	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
277	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
278	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
279	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
280	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
282	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
283	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
284	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
285	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
288	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
289	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
294	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
299	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
300	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
301	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
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	1	yes	characteristic
310	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
312	C₄²×D₆₇	C₂³	1	8	yes	—
313	C₄²×D₆₇	C₂³	1	16	yes	complemented
314	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
319	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
320	#126×C₆₇	C₂³	1	16	yes	complemented
321	#126×C₆₇	C₂³	1	16	yes	complemented
322	#124×C₆₇	C₂³	1	8	yes	—
323	#124×C₆₇	C₂³	1	8	yes	—
324	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
325	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
326	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
327	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
328	C₄×D₄×C₆₇	C₂³	1	8	yes	—
329	#117×C₆₇	C₂³	1	16	yes	complemented
330	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
338	C₂×C₂²⋊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×C₄²×C₆₇	C₂³	1	2	yes	—
344	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
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	C₂³×D₆₇	—	2	8	no	—
349	C₂³×D₆₇	—	4	4	no	—
350	C₂³×D₆₇	—	4	4	no	—
351	C₂³×D₆₇	C₂⁴	1	2	yes	—
352	C₂³×D₆₇	C₂⁴	1	2	yes	—
353	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
354	C₂³×D₆₇	C₂⁴	1	8	yes	—
355	#11761629	—	2	32	no	—
356	C₂×Dic₁₃₄	—	2	4	no	—
357	C₂×Dic₁₃₄	—	2	8	no	—
358	C₂×Dic₁₃₄	—	4	2	no	—
359	C₂×Dic₁₃₄	—	4	2	no	—
360	C₂×Dic₁₃₄	—	4	2	no	—
361	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
362	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
363	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
364	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
365	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
366	Q₈×D₆₇	—	2	32	no	—
367	C₂×D₂₆₈	—	2	8	no	—
368	C₂×D₂₆₈	—	2	4	no	—
369	C₂×D₂₆₈	—	2	4	no	—
370	C₂×D₂₆₈	—	4	4	no	—
371	C₂×D₂₆₈	—	4	4	no	—
372	C₂×D₂₆₈	C₂⁴	1	8	yes	—
373	C₂×D₂₆₈	C₂⁴	1	4	yes	—
374	C₂×D₂₆₈	C₂⁴	1	4	yes	—
375	C₂×D₂₆₈	C₂⁴	1	8	yes	—
376	C₂×D₂₆₈	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₆₇	—	2	8	no	—
378	C₂×C₂²⋊D₆₇	—	4	4	no	—
379	C₂×C₂²⋊D₆₇	—	4	4	no	—
380	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
381	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
382	C₂×C₂²⋊D₆₇	C₂⁴	1	8	yes	—
383	D₄×D₆₇	—	2	32	no	—
384	C₂²×Dic₆₇	—	4	4	no	—
385	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
386	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
390	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
394	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×D₆₇	—	2	8	no	—
396	C₂×C₄×D₆₇	—	2	8	no	—
397	C₂×C₄×D₆₇	—	4	4	no	—
398	C₂×C₄×D₆₇	—	4	2	no	—
399	C₂×C₄×D₆₇	—	4	4	no	—
400	C₂×C₄×D₆₇	—	4	4	no	—
401	C₂×C₄×D₆₇	—	4	4	no	—
402	C₂×C₄×D₆₇	—	4	2	no	—
403	C₂×C₄×D₆₇	#41	1	8	yes	—
404	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
405	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
406	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
407	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
408	C₂×C₄×D₆₇	C₂⁴	1	8	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	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
414	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
415	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
416	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
417	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
418	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
419	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
420	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
421	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
422	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
423	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
424	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
425	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
426	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
427	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
428	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
429	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
430	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
431	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
432	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
433	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
434	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
435	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
436	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
437	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
438	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
439	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
440	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
441	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
442	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
443	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
444	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
445	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
446	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
447	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
448	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
449	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	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	C₄×Dic₆₇	C₂⁴	1	4	yes	—
456	C₄×Dic₆₇	C₂⁴	1	4	yes	—
457	C₄×Dic₆₇	C₂⁴	1	4	yes	—
458	C₄×Dic₆₇	C₂⁴	1	8	yes	—
459	C₄×Dic₆₇	C₂⁴	1	8	yes	—
460	C₄×Dic₆₇	C₂⁴	1	8	yes	—
461	C₄×Dic₆₇	C₂⁴	1	8	yes	—
462	C₄×Dic₆₇	C₂⁴	1	4	yes	—
463	C₄×Dic₆₇	C₂⁴	1	4	yes	—
464	C₄×Dic₆₇	C₂⁴	1	8	yes	—
465	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
466	C₂×Q₈×C₆₇	—	2	4	no	—
467	C₂×Q₈×C₆₇	—	2	4	no	—
468	C₂×Q₈×C₆₇	—	4	2	no	—
469	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
470	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
471	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
472	C₂×D₄×C₆₇	—	2	4	no	—
473	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
474	C₂²×C₄×C₆₇	—	4	4	no	—
475	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
478	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
481	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
483	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
484	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
485	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
486	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
487	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
488	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
489	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
490	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
491	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
492	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
493	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
497	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
498	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
499	C₄²×C₆₇	C₂⁴	1	8	yes	—
500	C₄²×C₆₇	C₂⁴	1	8	yes	—
501	C₄²×C₆₇	C₂⁴	1	4	yes	—
502	C₄²×C₆₇	C₂⁴	1	4	yes	—
503	C₄²×C₆₇	C₂⁴	1	4	yes	—
504	C₂³×C₆₇	—	2	4	no	—
505	C₂³×C₆₇	—	2	4	no	—
506	C₂³×C₆₇	—	2	4	no	—
507	C₂³×C₆₇	C₂⁵	1	4	yes	—
508	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
509	C₂²×D₆₇	—	2	2	no	—
510	C₂²×D₆₇	—	2	2	no	—
511	C₂²×D₆₇	—	2	4	no	—
512	C₂²×D₆₇	—	2	4	no	—
513	C₂²×D₆₇	—	2	4	no	—
514	C₂²×D₆₇	—	2	4	no	—
515	C₂²×D₆₇	—	2	4	no	—
516	C₂²×D₆₇	—	2	4	no	—
517	C₂²×D₆₇	—	2	16	no	—
518	C₂²×D₆₇	—	4	8	no	—
519	C₂²×D₆₇	—	4	8	no	—
520	C₂²×D₆₇	—	8	16	no	—
521	C₂²×D₆₇	C₂×#41	1	4	yes	—
522	C₂²×D₆₇	C₂⁵	1	4	yes	—
523	C₂²×D₆₇	C₂⁵	1	4	yes	—
524	C₂²×D₆₇	C₂⁵	1	2	yes	—
525	Q₈×C₆₇	—	2	8	no	—
526	Q₈×C₆₇	—	2	8	no	—
527	Q₈×C₆₇	—	4	4	no	—
528	D₄×C₆₇	—	2	8	no	—
529	C₂×C₄×C₆₇	—	2	4	no	—
530	C₂×C₄×C₆₇	—	2	4	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	4	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	2	2	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	2	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	4	8	no	—
539	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
540	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
541	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
542	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
543	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
544	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
545	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
546	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
547	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
550	C₂²⋊D₆₇	—	2	16	no	—
551	C₂²⋊D₆₇	—	4	8	no	—
552	C₂²⋊D₆₇	—	4	8	no	—
553	C₂×Dic₆₇	—	2	4	no	—
554	C₂×Dic₆₇	—	2	2	no	—
555	C₂×Dic₆₇	—	2	4	no	—
556	C₂×Dic₆₇	—	2	2	no	—
557	C₂×Dic₆₇	—	2	2	no	—
558	C₂×Dic₆₇	—	2	2	no	—
559	C₂×Dic₆₇	—	2	2	no	—
560	C₂×Dic₆₇	—	2	2	no	—
561	C₂×Dic₆₇	—	4	8	no	—
562	C₂×Dic₆₇	C₂×#41	1	4	yes	—
563	C₂×Dic₆₇	C₂⁵	1	4	yes	—
564	C₂×Dic₆₇	C₂⁵	1	2	yes	—
565	C₂×Dic₆₇	C₂⁵	1	2	yes	—
566	C₂×Dic₆₇	C₂⁵	1	2	yes	—
567	C₂×Dic₆₇	C₂⁵	1	4	yes	—
568	C₂×Dic₆₇	C₂⁵	1	2	yes	—
569	C₂×Dic₆₇	C₂⁵	1	2	yes	—
570	C₂×Dic₆₇	C₂⁵	1	2	yes	—
571	C₂×Dic₆₇	C₂⁵	1	2	yes	—
572	D₂₆₈	—	2	16	no	—
573	D₂₆₈	—	2	8	no	—
574	D₂₆₈	—	2	8	no	—
575	D₂₆₈	—	4	8	no	—
576	D₂₆₈	—	4	8	no	—
577	C₄×D₆₇	—	2	16	no	—
578	C₄×D₆₇	—	2	16	no	—
579	C₄×D₆₇	—	4	4	no	—
580	C₄×D₆₇	—	4	8	no	—
581	C₄×D₆₇	—	4	4	no	—
582	C₄×D₆₇	—	4	8	no	—
583	C₄×D₆₇	—	4	8	no	—
584	C₄×D₆₇	—	4	8	no	—
585	C₄×D₆₇	C₂×#41	1	16	yes	—
586	Dic₁₃₄	—	2	8	no	—
587	Dic₁₃₄	—	2	16	no	—
588	Dic₁₃₄	—	4	4	no	—
589	Dic₁₃₄	—	4	4	no	—
590	Dic₁₃₄	—	4	4	no	—
591	C₂²×C₆₇	—	2	4	no	—
592	C₂²×C₆₇	—	2	4	no	—
593	C₂²×C₆₇	—	2	4	no	—
594	C₂²×C₆₇	—	4	8	no	—
595	C₂²×C₆₇	C₂²×#41	1	2	yes	—
596	C₂²×C₆₇	#585	1	2	yes	—
597	C₂²×C₆₇	#585	1	2	yes	—
598	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
599	C₂×D₆₇	—	2	2	no	—
600	C₂×D₆₇	—	2	2	no	—
601	C₂×D₆₇	—	2	8	no	—
602	C₂×D₆₇	—	2	4	no	—
603	C₂×D₆₇	—	2	4	no	—
604	C₂×D₆₇	—	2	4	no	—
605	C₂×D₆₇	—	2	4	no	—
606	C₂×D₆₇	—	2	4	no	—
607	C₂×D₆₇	—	2	4	no	—
608	C₂×D₆₇	—	4	8	no	—
609	C₂×D₆₇	—	4	8	no	—
610	C₂×D₆₇	—	8	16	no	—
611	C₂×D₆₇	C₂²×#41	1	4	yes	—
612	C₄×C₆₇	—	2	4	no	—
613	C₄×C₆₇	—	2	4	no	—
614	C₄×C₆₇	—	2	2	no	—
615	C₄×C₆₇	—	2	2	no	—
616	C₄×C₆₇	—	2	2	no	—
617	C₄×C₆₇	—	2	2	no	—
618	C₄×C₆₇	—	2	4	no	—
619	C₄×C₆₇	—	2	2	no	—
620	C₄×C₆₇	—	2	2	no	—
621	C₄×C₆₇	C₂²×#41	1	4	yes	—
622	Dic₆₇	—	2	4	no	—
623	Dic₆₇	—	2	2	no	—
624	Dic₆₇	—	2	2	no	—
625	Dic₆₇	—	2	2	no	—
626	Dic₆₇	—	2	2	no	—
627	Dic₆₇	—	2	2	no	—
628	Dic₆₇	—	2	2	no	—
629	Dic₆₇	—	2	4	no	—
630	Dic₆₇	C₂²×#41	1	4	yes	—
631	C₂×#3510	—	67	1	no	maximal, Sylow
632	C₂×C₆₇	—	4	4	no	—
633	C₂×C₆₇	#3510	1	4	yes	complemented
634	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
635	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
636	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
637	D₆₇	—	2	4	no	—
638	D₆₇	—	4	4	no	—
639	D₆₇	—	4	4	no	—
640	#3510	—	67	32	no	—
641	C₂×#559	—	67	1	no	—
642	C₂×#559	—	67	1	no	—
643	C₂×#559	—	67	1	no	—
644	C₂×#559	—	67	1	no	—
645	C₂×#556	—	67	1	no	—
646	C₂×#556	—	67	1	no	—
647	C₂×#556	—	67	1	no	—
648	C₂×#556	D₆₇	1	1	yes	characteristic, complemented
649	C₂×#551	—	67	2	no	—
650	C₂×#551	—	67	2	no	—
651	C₂×#551	—	67	2	no	—
652	C₂×#551	—	67	2	no	—
653	C₂×#542	—	67	2	no	—
654	C₂×#542	—	67	2	no	—
655	C₂×#536	—	67	1	no	—
656	C₂×#535	—	67	1	no	—
657	C₂×#533	—	67	1	no	—
658	C₂×#529	—	67	2	no	—
659	C₂×#529	—	67	2	no	—
660	C₂²×#124	—	67	1	no	—
661	C₂×#519	—	67	1	no	—
662	C₂×#518	—	67	1	no	—
663	C₂×C₄×#41	—	67	1	no	—
664	C₆₇	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
665	C₂²×#41	—	67	1	no	—
666	C₂³×Q₈	—	67	1	no	—
667	C₂³×D₄	—	67	1	no	—
668	#559	—	67	16	no	—
669	#559	—	67	16	no	—
670	#559	—	67	16	no	—
671	#559	—	67	16	no	—
672	#556	—	67	16	no	—
673	#556	—	67	16	no	—
674	#556	—	67	16	no	—
675	#556	C₂×D₆₇	1	16	yes	complemented
676	#551	—	67	32	no	—
677	#551	—	67	32	no	—
678	#551	—	67	32	no	—
679	#551	—	67	32	no	—
680	#542	—	67	32	no	—
681	#542	—	67	32	no	—
682	#536	—	67	16	no	—
683	#535	—	67	16	no	—
684	#533	—	67	16	no	—
685	C₂×C₄⋊Q₈	—	67	1	no	—
686	C₂×C₄⋊Q₈	—	67	1	no	—
687	C₂×C₄⋊Q₈	—	67	1	no	—
688	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
689	C₂×#127	—	67	1	no	—
690	C₂×#127	—	67	1	no	—
691	#529	—	67	32	no	—
692	#529	—	67	32	no	—
693	C₂×#126	—	67	2	no	—
694	C₂×#126	—	67	2	no	—
695	C₂×#126	—	67	2	no	—
696	C₂×#126	—	67	2	no	—
697	C₂×#126	—	67	2	no	—
698	C₂×#126	—	67	2	no	—
699	C₂×#126	C₂×D₆₇	1	2	yes	complemented
700	C₂×#126	C₂×D₆₇	1	2	yes	complemented
701	C₂×#125	—	67	1	no	—
702	C₂×#125	—	67	1	no	—
703	C₂×#124	—	67	1	no	—
704	C₂×#124	—	67	1	no	—
705	C₂×#124	—	67	1	no	—
706	C₂×#124	—	67	2	no	—
707	C₂×#124	—	67	1	no	—
708	C₂×#124	—	67	16	no	—
709	C₂×#124	—	67	2	no	—
710	C₂×#124	—	67	2	no	—
711	C₂×#124	—	67	2	no	—
712	C₂×#124	—	67	2	no	—
713	C₂×#124	—	67	1	no	—
714	C₂×#124	—	67	1	no	—
715	C₂×#124	—	67	2	no	—
716	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
717	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
718	C₂×#123	—	67	2	no	—
719	C₂×#123	—	67	2	no	—
720	C₂×#123	—	67	2	no	—
721	C₂×#123	—	67	2	no	—
722	C₂×#123	—	67	2	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×C₂²⋊Q₈	—	67	1	no	—
729	C₂×C₂²⋊Q₈	—	67	2	no	—
730	C₂×C₂²⋊Q₈	—	67	2	no	—
731	C₂×C₂²⋊Q₈	—	67	1	no	—
732	C₂×C₂²⋊Q₈	—	67	1	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	2	no	—
737	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
738	C₂×#121	—	67	2	no	—
739	C₂×#121	—	67	2	no	—
740	C₂×#120	—	67	2	no	—
741	C₂×#120	—	67	2	no	—
742	#519	—	67	16	no	—
743	#518	—	67	16	no	—
744	C₄×#41	—	67	16	no	—
745	C₂×C₄×Q₈	—	67	1	no	—
746	C₂×C₄×Q₈	—	67	1	no	—
747	C₂×C₄×Q₈	—	67	2	no	—
748	C₂×C₄×Q₈	—	67	1	no	—
749	C₂×C₄×Q₈	—	67	2	no	—
750	C₂×C₄×Q₈	—	67	1	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	C₂×D₆₇	1	1	yes	characteristic, complemented
755	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
756	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
757	C₂×C₄×D₄	—	67	1	no	—
758	C₂×C₄×D₄	—	67	2	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	2	no	—
764	C₂×C₄×D₄	—	67	2	no	—
765	C₂×C₄×D₄	—	67	2	no	—
766	C₂×C₄×D₄	—	67	2	no	—
767	C₂×C₄×D₄	—	67	1	no	—
768	C₂×C₄×D₄	—	67	1	no	—
769	C₂×C₄×D₄	—	67	2	no	—
770	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
771	C₂×#117	—	67	1	no	—
772	C₂×#117	—	67	2	no	—
773	C₂×#117	—	67	2	no	—
774	C₂×#117	—	67	2	no	—
775	C₂×#117	—	67	2	no	—
776	C₂×#117	—	67	1	no	—
777	C₂×#117	—	67	1	no	—
778	C₂×#117	—	67	2	no	—
779	C₂×#117	—	67	2	no	—
780	C₂×#117	C₂×D₆₇	1	2	yes	complemented
781	C₂²×C₂²⋊C₄	—	67	2	no	—
782	C₂²×C₂²⋊C₄	—	67	2	no	—
783	C₂²×C₂²⋊C₄	—	67	2	no	—
784	C₂²×C₂²⋊C₄	—	67	2	no	—
785	C₂²×C₄²	—	67	1	no	—
786	C₂²×C₄²	—	67	2	no	—
787	C₂⁵	—	67	2	no	—
788	C₂×#41	—	67	8	no	—
789	C₂×#41	—	134	8	no	—
790	C₂²×Q₈	—	67	8	no	—
791	C₂²×Q₈	—	67	1	no	—
792	C₂²×Q₈	—	67	1	no	—
793	C₂²×Q₈	—	67	1	no	—
794	C₂²×Q₈	—	67	2	no	—
795	C₂²×Q₈	—	67	1	no	—
796	C₂²×Q₈	—	134	8	no	—
797	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
798	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
799	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
800	C₂²×D₄	—	67	2	no	—
801	C₂²×D₄	—	67	2	no	—
802	C₂²×D₄	—	67	2	no	—
803	C₂²×D₄	—	67	8	no	—
804	C₂²×D₄	—	67	2	no	—
805	C₂²×D₄	—	67	2	no	—
806	C₂²×D₄	—	67	2	no	—
807	C₂²×D₄	—	67	1	no	—
808	C₂²×D₄	—	67	1	no	—
809	C₂²×D₄	—	134	8	no	—
810	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
811	C₂³×C₄	—	67	2	no	—
812	C₂³×C₄	—	67	1	no	—
813	C₂³×C₄	—	67	1	no	—
814	C₂³×C₄	—	67	2	no	—
815	C₂³×C₄	—	67	2	no	—
816	C₂³×C₄	—	67	2	no	—
817	C₂³×C₄	—	67	2	no	—
818	C₂³×C₄	—	67	1	no	—
819	C₂³×C₄	—	67	2	no	—
820	C₂³×C₄	—	67	2	no	—
821	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
822	C₄⋊Q₈	—	67	8	no	—
823	C₄⋊Q₈	—	67	8	no	—
824	C₄⋊Q₈	—	67	8	no	—
825	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
826	#127	—	67	8	no	—
827	#127	—	67	8	no	—
828	#126	—	67	16	no	—
829	#126	—	67	16	no	—
830	#126	—	67	16	no	—
831	#126	—	67	16	no	—
832	#126	—	67	16	no	—
833	#126	—	67	16	no	—
834	#126	C₂²×D₆₇	1	16	yes	complemented
835	#126	C₂²×D₆₇	1	16	yes	complemented
836	#125	—	67	8	no	—
837	#125	—	67	8	no	—
838	#124	—	67	8	no	—
839	#124	—	67	8	no	—
840	#124	—	67	8	no	—
841	#124	—	67	16	no	—
842	#124	—	67	8	no	—
843	#124	—	67	16	no	—
844	#124	—	67	16	no	—
845	#124	—	67	16	no	—
846	#124	—	67	16	no	—
847	#124	—	67	8	no	—
848	#124	—	67	8	no	—
849	#124	—	67	16	no	—
850	#124	C₂²×D₆₇	1	8	yes	—
851	#124	C₂²×D₆₇	1	8	yes	—
852	#123	—	67	16	no	—
853	#123	—	67	16	no	—
854	#123	—	67	16	no	—
855	#123	—	67	16	no	—
856	#123	—	67	16	no	—
857	#123	—	67	16	no	—
858	#123	—	67	16	no	—
859	#123	—	67	16	no	—
860	#123	—	67	16	no	—
861	#123	—	67	16	no	—
862	C₂²⋊Q₈	—	67	8	no	—
863	C₂²⋊Q₈	—	67	16	no	—
864	C₂²⋊Q₈	—	67	16	no	—
865	C₂²⋊Q₈	—	67	8	no	—
866	C₂²⋊Q₈	—	67	8	no	—
867	C₂²⋊Q₈	—	67	8	no	—
868	C₂²⋊Q₈	—	67	16	no	—
869	C₂²⋊Q₈	—	67	16	no	—
870	C₂²⋊Q₈	—	67	16	no	—
871	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
872	#121	—	67	16	no	—
873	#121	—	67	16	no	—
874	#120	—	67	16	no	—
875	#120	—	67	16	no	—
876	C₄×Q₈	—	67	8	no	—
877	C₄×Q₈	—	67	8	no	—
878	C₄×Q₈	—	67	16	no	—
879	C₄×Q₈	—	67	8	no	—
880	C₄×Q₈	—	67	16	no	—
881	C₄×Q₈	—	67	8	no	—
882	C₄×Q₈	—	67	8	no	—
883	C₄×Q₈	—	67	8	no	—
884	C₄×Q₈	—	67	8	no	—
885	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
886	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
887	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
888	C₄×D₄	—	67	8	no	—
889	C₄×D₄	—	67	16	no	—
890	C₄×D₄	—	67	16	no	—
891	C₄×D₄	—	67	16	no	—
892	C₄×D₄	—	67	8	no	—
893	C₄×D₄	—	67	8	no	—
894	C₄×D₄	—	67	16	no	—
895	C₄×D₄	—	67	16	no	—
896	C₄×D₄	—	67	16	no	—
897	C₄×D₄	—	67	16	no	—
898	C₄×D₄	—	67	8	no	—
899	C₄×D₄	—	67	8	no	—
900	C₄×D₄	—	67	16	no	—
901	C₄×D₄	C₂²×D₆₇	1	8	yes	—
902	#117	—	67	8	no	—
903	#117	—	67	16	no	—
904	#117	—	67	16	no	—
905	#117	—	67	16	no	—
906	#117	—	67	16	no	—
907	#117	—	67	8	no	—
908	#117	—	67	8	no	—
909	#117	—	67	16	no	—
910	#117	—	67	16	no	—
911	#117	C₂²×D₆₇	1	16	yes	complemented
912	C₂×C₄⋊C₄	—	67	1	no	—
913	C₂×C₄⋊C₄	—	67	1	no	—
914	C₂×C₄⋊C₄	—	67	1	no	—
915	C₂×C₄⋊C₄	—	67	1	no	—
916	C₂×C₄⋊C₄	—	67	1	no	—
917	C₂×C₄⋊C₄	—	67	1	no	—
918	C₂×C₄⋊C₄	—	67	2	no	—
919	C₂×C₄⋊C₄	—	67	1	no	—
920	C₂×C₄⋊C₄	—	67	1	no	—
921	C₂×C₄⋊C₄	—	67	2	no	—
922	C₂×C₄⋊C₄	—	67	2	no	—
923	C₂×C₄⋊C₄	—	67	2	no	—
924	C₂×C₄⋊C₄	—	67	2	no	—
925	C₂×C₄⋊C₄	—	67	2	no	—
926	C₂×C₄⋊C₄	—	67	1	no	—
927	C₂×C₄⋊C₄	—	67	1	no	—
928	C₂×C₄⋊C₄	—	67	1	no	—
929	C₂×C₄⋊C₄	—	67	1	no	—
930	C₂×C₄⋊C₄	—	67	1	no	—
931	C₂×C₄⋊C₄	—	67	1	no	—
932	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
934	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
935	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
936	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
937	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
938	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	—	67	2	no	—
941	C₂×C₂²⋊C₄	—	67	2	no	—
942	C₂×C₂²⋊C₄	—	67	2	no	—
943	C₂×C₂²⋊C₄	—	67	2	no	—
944	C₂×C₂²⋊C₄	—	67	1	no	—
945	C₂×C₂²⋊C₄	—	67	1	no	—
946	C₂×C₂²⋊C₄	—	67	2	no	—
947	C₂×C₂²⋊C₄	—	67	2	no	—
948	C₂×C₂²⋊C₄	—	67	2	no	—
949	C₂×C₂²⋊C₄	—	67	2	no	—
950	C₂×C₂²⋊C₄	—	67	16	no	—
951	C₂×C₂²⋊C₄	—	67	2	no	—
952	C₂×C₂²⋊C₄	—	67	2	no	—
953	C₂×C₂²⋊C₄	—	67	1	no	—
954	C₂×C₂²⋊C₄	—	67	1	no	—
955	C₂×C₂²⋊C₄	—	67	2	no	—
956	C₂×C₂²⋊C₄	—	67	2	no	—
957	C₂×C₂²⋊C₄	—	67	2	no	—
958	C₂×C₂²⋊C₄	—	67	2	no	—
959	C₂×C₂²⋊C₄	—	67	2	no	—
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	16	no	—
964	C₂×C₂²⋊C₄	—	67	16	no	—
965	C₂×C₂²⋊C₄	—	67	16	no	—
966	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
967	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
968	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
969	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
970	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
971	C₂×C₄²	—	67	2	no	—
972	C₂×C₄²	—	67	2	no	—
973	C₂×C₄²	—	67	2	no	—
974	C₂×C₄²	—	67	2	no	—
975	C₂×C₄²	—	67	2	no	—
976	C₂×C₄²	—	67	1	no	—
977	C₂×C₄²	—	67	1	no	—
978	C₂×C₄²	—	67	1	no	—
979	C₂×C₄²	—	67	1	no	—
980	C₂×C₄²	—	67	1	no	—
981	C₂×C₄²	—	67	8	no	—
982	C₂×C₄²	—	67	16	no	—
983	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
984	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
985	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
986	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
987	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
988	C₂⁴	—	268	4	no	—
989	C₂⁴	—	268	4	no	—
990	C₂⁴	—	67	8	no	—
991	C₂⁴	—	67	1	no	—
992	C₂⁴	—	67	2	no	—
993	C₂⁴	—	67	2	no	—
994	C₂⁴	—	134	8	no	—
995	C₂⁴	C₂³×D₆₇	1	2	yes	—
996	#41	—	134	32	no	—
997	C₂×Q₈	—	2	4	no	—
998	C₂×Q₈	—	2	4	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	—	268	2	no	—
1001	C₂×Q₈	—	268	2	no	—
1002	C₂×Q₈	—	268	2	no	—
1003	C₂×Q₈	—	67	4	no	—
1004	C₂×Q₈	—	67	4	no	—
1005	C₂×Q₈	—	67	4	no	—
1006	C₂×Q₈	—	67	8	no	—
1007	C₂×Q₈	—	67	4	no	—
1008	C₂×Q₈	—	134	8	no	—
1009	C₂×Q₈	—	134	32	no	—
1010	C₂×Q₈	—	134	4	no	—
1011	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1012	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1013	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1014	C₂×D₄	—	2	4	no	—
1015	C₂×D₄	—	268	4	no	—
1016	C₂×D₄	—	268	4	no	—
1017	C₂×D₄	—	268	4	no	—
1018	C₂×D₄	—	268	4	no	—
1019	C₂×D₄	—	67	8	no	—
1020	C₂×D₄	—	67	8	no	—
1021	C₂×D₄	—	67	8	no	—
1022	C₂×D₄	—	67	8	no	—
1023	C₂×D₄	—	67	8	no	—
1024	C₂×D₄	—	67	8	no	—
1025	C₂×D₄	—	67	4	no	—
1026	C₂×D₄	—	67	4	no	—
1027	C₂×D₄	—	134	8	no	—
1028	C₂×D₄	—	134	32	no	—
1029	C₂×D₄	—	134	8	no	—
1030	C₂×D₄	—	134	4	no	—
1031	C₂×D₄	—	134	4	no	—
1032	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1033	C₂²×C₄	—	4	4	no	—
1034	C₂²×C₄	—	268	4	no	—
1035	C₂²×C₄	—	268	4	no	—
1036	C₂²×C₄	—	268	2	no	—
1037	C₂²×C₄	—	268	4	no	—
1038	C₂²×C₄	—	268	2	no	—
1039	C₂²×C₄	—	268	4	no	—
1040	C₂²×C₄	—	268	4	no	—
1041	C₂²×C₄	—	67	8	no	—
1042	C₂²×C₄	—	67	4	no	—
1043	C₂²×C₄	—	67	4	no	—
1044	C₂²×C₄	—	67	8	no	—
1045	C₂²×C₄	—	67	8	no	—
1046	C₂²×C₄	—	67	8	no	—
1047	C₂²×C₄	—	67	8	no	—
1048	C₂²×C₄	—	67	1	no	—
1049	C₂²×C₄	—	67	8	no	—
1050	C₂²×C₄	—	67	4	no	—
1051	C₂²×C₄	—	67	1	no	—
1052	C₂²×C₄	—	67	2	no	—
1053	C₂²×C₄	—	67	1	no	—
1054	C₂²×C₄	—	67	1	no	—
1055	C₂²×C₄	—	67	2	no	—
1056	C₂²×C₄	—	67	1	no	—
1057	C₂²×C₄	—	67	1	no	—
1058	C₂²×C₄	—	67	1	no	—
1059	C₂²×C₄	—	67	8	no	—
1060	C₂²×C₄	—	67	8	no	—
1061	C₂²×C₄	—	134	8	no	—
1062	C₂²×C₄	—	134	8	no	—
1063	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1064	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1065	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1066	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1067	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1068	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1069	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1070	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1071	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1072	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1073	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	—	67	4	no	—
1075	C₄⋊C₄	—	67	4	no	—
1076	C₄⋊C₄	—	67	4	no	—
1077	C₄⋊C₄	—	67	4	no	—
1078	C₄⋊C₄	—	67	4	no	—
1079	C₄⋊C₄	—	67	4	no	—
1080	C₄⋊C₄	—	67	8	no	—
1081	C₄⋊C₄	—	67	4	no	—
1082	C₄⋊C₄	—	67	4	no	—
1083	C₄⋊C₄	—	67	8	no	—
1084	C₄⋊C₄	—	67	8	no	—
1085	C₄⋊C₄	—	67	8	no	—
1086	C₄⋊C₄	—	67	8	no	—
1087	C₄⋊C₄	—	67	8	no	—
1088	C₄⋊C₄	—	67	4	no	—
1089	C₄⋊C₄	—	67	4	no	—
1090	C₄⋊C₄	—	67	4	no	—
1091	C₄⋊C₄	—	67	4	no	—
1092	C₄⋊C₄	—	67	4	no	—
1093	C₄⋊C₄	—	67	4	no	—
1094	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1095	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1096	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1097	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1098	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1099	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1100	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1101	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1102	C₂²⋊C₄	—	67	8	no	—
1103	C₂²⋊C₄	—	67	8	no	—
1104	C₂²⋊C₄	—	67	8	no	—
1105	C₂²⋊C₄	—	67	8	no	—
1106	C₂²⋊C₄	—	67	4	no	—
1107	C₂²⋊C₄	—	67	4	no	—
1108	C₂²⋊C₄	—	67	8	no	—
1109	C₂²⋊C₄	—	67	8	no	—
1110	C₂²⋊C₄	—	67	8	no	—
1111	C₂²⋊C₄	—	67	8	no	—
1112	C₂²⋊C₄	—	67	8	no	—
1113	C₂²⋊C₄	—	67	8	no	—
1114	C₂²⋊C₄	—	67	4	no	—
1115	C₂²⋊C₄	—	67	4	no	—
1116	C₂²⋊C₄	—	67	8	no	—
1117	C₂²⋊C₄	—	67	8	no	—
1118	C₂²⋊C₄	—	67	8	no	—
1119	C₂²⋊C₄	—	67	8	no	—
1120	C₂²⋊C₄	—	67	8	no	—
1121	C₂²⋊C₄	—	67	8	no	—
1122	C₂²⋊C₄	—	67	8	no	—
1123	C₂²⋊C₄	—	67	8	no	—
1124	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1125	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1126	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1127	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1128	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1129	C₄²	—	67	4	no	—
1130	C₄²	—	67	8	no	—
1131	C₄²	—	67	8	no	—
1132	C₄²	—	67	4	no	—
1133	C₄²	—	67	4	no	—
1134	C₄²	—	67	8	no	—
1135	C₄²	—	67	8	no	—
1136	C₄²	—	67	8	no	—
1137	C₄²	—	67	4	no	—
1138	C₄²	—	67	4	no	—
1139	C₄²	C₂³×D₆₇	1	8	yes	—
1140	C₄²	C₂³×D₆₇	1	4	yes	—
1141	C₄²	C₂³×D₆₇	1	8	yes	—
1142	C₄²	C₂³×D₆₇	1	4	yes	—
1143	C₄²	C₂³×D₆₇	1	4	yes	—
1144	C₂³	—	2	4	no	—
1145	C₂³	—	2	4	no	—
1146	C₂³	—	2	4	no	—
1147	C₂³	—	268	8	no	—
1148	C₂³	—	268	8	no	—
1149	C₂³	—	536	16	no	—
1150	C₂³	—	67	4	no	—
1151	C₂³	—	67	2	no	—
1152	C₂³	—	67	4	no	—
1153	C₂³	—	67	4	no	—
1154	C₂³	—	134	16	no	—
1155	C₂³	—	134	4	no	—
1156	C₂³	—	134	4	no	—
1157	C₂³	—	134	4	no	—
1158	C₂³	—	134	4	no	—
1159	C₂³	—	134	4	no	—
1160	C₂³	—	134	4	no	—
1161	C₂³	—	134	2	no	—
1162	C₂³	—	134	2	no	—
1163	C₂³	C₂⁴×D₆₇	1	4	yes	—
1164	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1165	Q₈	—	2	8	no	—
1166	Q₈	—	2	8	no	—
1167	Q₈	—	4	4	no	—
1168	Q₈	—	268	4	no	—
1169	Q₈	—	268	4	no	—
1170	Q₈	—	268	4	no	—
1171	Q₈	—	134	16	no	—
1172	Q₈	—	134	8	no	—
1173	D₄	—	2	8	no	—
1174	D₄	—	268	8	no	—
1175	D₄	—	268	8	no	—
1176	D₄	—	268	8	no	—
1177	D₄	—	268	8	no	—
1178	D₄	—	134	16	no	—
1179	D₄	—	134	16	no	—
1180	D₄	—	134	8	no	—
1181	D₄	—	134	8	no	—
1182	C₂×C₄	—	2	4	no	—
1183	C₂×C₄	—	2	4	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	4	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	4	8	no	—
1192	C₂×C₄	—	268	8	no	—
1193	C₂×C₄	—	268	8	no	—
1194	C₂×C₄	—	268	4	no	—
1195	C₂×C₄	—	268	8	no	—
1196	C₂×C₄	—	268	4	no	—
1197	C₂×C₄	—	268	8	no	—
1198	C₂×C₄	—	268	8	no	—
1199	C₂×C₄	—	67	4	no	—
1200	C₂×C₄	—	67	2	no	—
1201	C₂×C₄	—	67	16	no	—
1202	C₂×C₄	—	67	2	no	—
1203	C₂×C₄	—	67	4	no	—
1204	C₂×C₄	—	67	2	no	—
1205	C₂×C₄	—	67	2	no	—
1206	C₂×C₄	—	67	4	no	—
1207	C₂×C₄	—	67	2	no	—
1208	C₂×C₄	—	67	2	no	—
1209	C₂×C₄	—	67	2	no	—
1210	C₂×C₄	—	134	16	no	—
1211	C₂×C₄	—	134	16	no	—
1212	C₂×C₄	—	134	4	no	—
1213	C₂×C₄	—	134	2	no	—
1214	C₂×C₄	—	134	2	no	—
1215	C₂×C₄	—	134	2	no	—
1216	C₂×C₄	—	134	4	no	—
1217	C₂×C₄	—	134	2	no	—
1218	C₂×C₄	—	134	2	no	—
1219	C₂×C₄	—	134	2	no	—
1220	C₂×C₄	#41×D₆₇	1	4	yes	—
1221	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1222	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1223	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1224	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1225	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1226	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1227	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1228	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1229	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1230	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	4	no	—
1234	C₂²	—	4	8	no	—
1235	C₂²	—	268	8	no	—
1236	C₂²	—	268	8	no	—
1237	C₂²	—	536	16	no	—
1238	C₂²	—	67	4	no	—
1239	C₂²	—	134	4	no	—
1240	C₂²	—	134	4	no	—
1241	C₂²	—	134	4	no	—
1242	C₂²	—	134	4	no	—
1243	C₂²	—	134	4	no	—
1244	C₂²	—	134	4	no	—
1245	C₂²	—	134	8	no	—
1246	C₂²	—	134	2	no	—
1247	C₂²	—	134	2	no	—
1248	C₂²	C₂×#41×D₆₇	1	2	yes	—
1249	C₂²	#16864232	1	2	yes	—
1250	C₂²	#16864233	1	2	yes	—
1251	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1252	C₄	—	2	4	no	—
1253	C₄	—	2	4	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	2	4	no	—
1256	C₄	—	2	2	no	—
1257	C₄	—	2	2	no	—
1258	C₄	—	2	2	no	—
1259	C₄	—	2	2	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	67	4	no	—
1262	C₄	—	134	4	no	—
1263	C₄	—	134	2	no	—
1264	C₄	—	134	2	no	—
1265	C₄	—	134	2	no	—
1266	C₄	—	134	4	no	—
1267	C₄	—	134	2	no	—
1268	C₄	—	134	2	no	—
1269	C₄	—	134	2	no	—
1270	C₄	C₂×#41×D₆₇	1	4	yes	—
1271	C₂	—	4	4	no	—
1272	C₂	—	268	4	no	—
1273	C₂	—	268	4	no	—
1274	C₂	—	134	4	no	—
1275	C₂	#22574099	1	4	yes	direct product factor
1276	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1277	C₂	C₂×#16864232	1	1	yes	characteristic
1278	C₂	C₂×#16864233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×#556×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#16863964	C₂
hypercenter	C₂×#556	D₆₇
hypocenter	C₆₇	C₂×#3510
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#556

Complements

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

N	H ≅ G/N	type
1. #22574099	C₂	direct (N × H)
2. C₂×#16864131	C₂	semidirect
3. C₂×#16864131	C₂	semidirect
4. C₂×#16864129	C₂	semidirect
5. C₂×#16864128	C₂	semidirect
6. C₂×#16864120	C₂	semidirect
7. C₂×#16864118	C₂	semidirect
8. C₂×#16864115	C₂	semidirect
9. C₂×#16864073	C₂	semidirect
10. C₂×#16864071	C₂	semidirect
11. C₂×#16864071	C₂	semidirect
12. C₂×#16864070	C₂	semidirect
13. C₂×#16864016	C₂	semidirect
14. C₂×#16864012	C₂	semidirect
15. C₂×#16863971	C₂	semidirect
17. C₂×#16863950	C₂	semidirect
18. C₂×#16863929	C₂	semidirect
19. C₂×#16863924	C₂	semidirect
20. C₂×#124×D₆₇	C₂	semidirect
21. C₂×#16863872	C₂	semidirect
22. C₂×#16863868	C₂	semidirect
23. C₂×C₄×#11761629	C₂	semidirect
24. C₂×#556×C₆₇	C₂	semidirect
28. #16864131	C₂²	semidirect
29. #16864131	C₂²	semidirect
30. #16864129	C₂²	semidirect
31. #16864128	C₂²	semidirect
32. #16864120	C₂²	semidirect
33. #16864118	C₂²	semidirect
34. #16864115	C₂²	semidirect
35. #16864073	C₂²	semidirect
36. #16864071	C₂²	semidirect
37. #16864071	C₂²	semidirect
38. #16864070	C₂²	semidirect
39. #16864016	C₂²	semidirect
40. #16864012	C₂²	semidirect
41. #16863971	C₂²	semidirect
43. #16863950	C₂²	semidirect
44. C₂×#14524042	C₂²	semidirect
45. C₂×#14524041	C₂²	semidirect
46. C₂×#14524041	C₂²	semidirect
49. #16863929	C₂²	semidirect
50. #16863924	C₂²	semidirect
51. C₂×#14524038	C₂²	semidirect
52. C₂×#14524038	C₂²	semidirect
53. C₂×#14524038	C₂²	semidirect
54. C₂×#14524037	C₂²	semidirect
55. C₂×#14524036	C₂²	semidirect
56. C₂×#14524036	C₂²	semidirect
57. C₂×#14524033	C₂²	semidirect
58. C₂×#14524033	C₂²	semidirect
61. C₂×#14524032	C₂²	semidirect
62. C₂×#14524032	C₂²	semidirect
64. C₂×#14524031	C₂²	semidirect
65. C₂×#14524031	C₂²	semidirect
69. C₂×#14524029	C₂²	semidirect
70. C₂×#14524029	C₂²	semidirect
71. #124×D₆₇	C₂²	semidirect
74. C₂×#14524028	C₂²	semidirect
75. C₂×#14524028	C₂²	semidirect
76. C₂×#14524028	C₂²	semidirect
77. C₂×#14524028	C₂²	semidirect
78. C₂×#14524027	C₂²	semidirect
79. C₂×#14524026	C₂²	semidirect
80. C₂×#14524025	C₂²	semidirect
81. C₂×#14524025	C₂²	semidirect
83. C₂×#14524023	C₂²	semidirect
86. C₂×#14524021	C₂²	semidirect
87. C₂×#14524021	C₂²	semidirect
88. C₂×#14524021	C₂²	semidirect
89. C₂×#14524020	C₂²	semidirect
95. #16863872	C₂²	semidirect
96. #16863868	C₂²	semidirect
97. C₄×#11761629	C₂²	semidirect
98. C₂×Q₈×Dic₆₇	C₂²	semidirect
99. C₂×Q₈×Dic₆₇	C₂²	semidirect
100. C₂×C₄×Dic₁₃₄	C₂²	semidirect
101. C₂×C₄×Dic₁₃₄	C₂²	semidirect
102. C₂×C₄×Dic₁₃₄	C₂²	semidirect
103. C₂×C₄×Dic₁₃₄	C₂²	semidirect
104. C₂×C₄×Dic₁₃₄	C₂²	semidirect
105. C₂×#14524008	C₂²	semidirect
106. C₂×#14524008	C₂²	semidirect
109. C₂×C₄×D₂₆₈	C₂²	semidirect
110. C₂×C₄×D₂₆₈	C₂²	semidirect
114. C₂×#14524005	C₂²	semidirect
115. C₂×#14524005	C₂²	semidirect
117. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
119. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
122. C₂×#14524001	C₂²	semidirect
123. C₂×#14524001	C₂²	semidirect
127. C₂×#14524000	C₂²	semidirect
128. C₂×#14523999	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. #556×C₆₇	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
137. C₂×#126×C₆₇	C₂²	semidirect
138. C₂×#126×C₆₇	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
143. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
146. C₂×#117×C₆₇	C₂²	semidirect
177. #14524042	C₂³	semidirect
178. #14524041	C₂³	semidirect
179. #14524041	C₂³	semidirect
182. #14524038	C₂³	semidirect
183. #14524038	C₂³	semidirect
184. #14524038	C₂³	semidirect
185. #14524037	C₂³	semidirect
186. #14524036	C₂³	semidirect
187. #14524036	C₂³	semidirect
188. #14524033	C₂³	semidirect
189. #14524033	C₂³	semidirect
192. #14524032	C₂³	semidirect
193. #14524032	C₂³	semidirect
195. #14524031	C₂³	semidirect
196. #14524031	C₂³	semidirect
200. #14524029	C₂³	semidirect
201. #14524029	C₂³	semidirect
204. #14524028	C₂³	semidirect
205. #14524028	C₂³	semidirect
206. #14524028	C₂³	semidirect
207. #14524028	C₂³	semidirect
208. #14524027	C₂³	semidirect
209. #14524026	C₂³	semidirect
210. #14524025	C₂³	semidirect
211. #14524025	C₂³	semidirect
213. #14524023	C₂³	semidirect
216. #14524021	C₂³	semidirect
217. #14524021	C₂³	semidirect
218. #14524021	C₂³	semidirect
219. #14524020	C₂³	semidirect
225. Q₈×Dic₆₇	C₂³	semidirect
226. Q₈×Dic₆₇	C₂³	semidirect
227. C₄×Dic₁₃₄	C₂³	semidirect
228. C₄×Dic₁₃₄	C₂³	semidirect
229. C₄×Dic₁₃₄	C₂³	semidirect
230. C₄×Dic₁₃₄	C₂³	semidirect
231. C₄×Dic₁₃₄	C₂³	semidirect
232. #14524008	C₂³	semidirect
233. #14524008	C₂³	semidirect
236. C₄×D₂₆₈	C₂³	semidirect
237. C₄×D₂₆₈	C₂³	semidirect
241. #14524005	C₂³	semidirect
242. #14524005	C₂³	semidirect
244. C₄×C₂²⋊D₆₇	C₂³	semidirect
246. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
249. #14524001	C₂³	semidirect
250. #14524001	C₂³	semidirect
254. #14524000	C₂³	semidirect
255. #14523999	C₂³	semidirect
313. C₄²×D₆₇	C₂³	semidirect
319. C₄⋊Q₈×C₆₇	C₂³	semidirect
320. #126×C₆₇	C₂³	semidirect
321. #126×C₆₇	C₂³	semidirect
324. C₂²⋊Q₈×C₆₇	C₂³	semidirect
325. C₄×Q₈×C₆₇	C₂³	semidirect
326. C₄×Q₈×C₆₇	C₂³	semidirect
327. C₄×Q₈×C₆₇	C₂³	semidirect
329. #117×C₆₇	C₂³	semidirect
633. C₂×C₆₇	#3510	semidirect
648. C₂×#556	D₆₇	semidirect
664. C₆₇	C₂×#3510	semidirect
675. #556	C₂×D₆₇	semidirect
688. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
699. C₂×#126	C₂×D₆₇	semidirect
700. C₂×#126	C₂×D₆₇	semidirect
737. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
754. C₂×C₄×Q₈	C₂×D₆₇	semidirect
755. C₂×C₄×Q₈	C₂×D₆₇	semidirect
756. C₂×C₄×Q₈	C₂×D₆₇	semidirect
780. C₂×#117	C₂×D₆₇	semidirect
825. C₄⋊Q₈	C₂²×D₆₇	semidirect
834. #126	C₂²×D₆₇	semidirect
835. #126	C₂²×D₆₇	semidirect
871. C₂²⋊Q₈	C₂²×D₆₇	semidirect
885. C₄×Q₈	C₂²×D₆₇	semidirect
886. C₄×Q₈	C₂²×D₆₇	semidirect
887. C₄×Q₈	C₂²×D₆₇	semidirect
911. #117	C₂²×D₆₇	semidirect
1275. C₂	#22574099	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574099	2
C₂×#16864131	2
C₂×#16864129	2
C₂×#16864128	2
C₂×#16864120	2
C₂×#16864118	2
C₂×#16864115	2
C₂×#16864073	2
C₂×#16864071	2
C₂×#16864070	2
C₂×#16864016	2
C₂×#16864012	2
C₂×#16863971	2
C₂×#16863964	2
C₂×#16863950	2
C₂×#16863929	2
C₂×#16863924	2
C₂×#124×D₆₇	2
C₂×#16863872	2
C₂×#16863868	2
C₂×C₄×#11761629	2
C₂×#556×C₆₇	2
C₂×#3510	67

Subgroups — C2×#22574099 #31764316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574099 #31764316