Subgroups — C₂×#22574101 #31764320

Order 17152.

7302 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574101	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864130	C₂	1	2	yes	maximal, complemented
3	C₂×#16864128	C₂	1	2	yes	maximal, complemented
4	C₂×#16864117	C₂	1	2	yes	maximal, complemented
5	C₂×#16864113	C₂	1	2	yes	maximal, complemented
6	C₂×#16864076	C₂	1	2	yes	maximal, complemented
7	C₂×#16864073	C₂	1	2	yes	maximal, complemented
8	C₂×#16864071	C₂	1	2	yes	maximal, complemented
9	C₂×#16864069	C₂	1	2	yes	maximal, complemented
10	C₂×#16864020	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16864017	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16864015	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16863969	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16863962	C₂	1	1	yes	maximal, characteristic
15	C₂×#16863951	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16863933	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16863932	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863928	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16863927	C₂	1	1	yes	maximal, characteristic, 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×#16863864	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#11761628	C₂²	1	1	yes	characteristic
26	C₂²×Q₈×D₆₇	C₂²	1	1	yes	characteristic
27	C₂²×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	#16864130	C₂²	1	32	yes	complemented
29	#16864128	C₂²	1	32	yes	complemented
30	#16864117	C₂²	1	32	yes	complemented
31	#16864113	C₂²	1	32	yes	complemented
32	#16864076	C₂²	1	32	yes	complemented
33	#16864073	C₂²	1	32	yes	complemented
34	#16864071	C₂²	1	32	yes	complemented
35	#16864069	C₂²	1	32	yes	complemented
36	#16864020	C₂²	1	16	yes	complemented
37	#16864017	C₂²	1	16	yes	complemented
38	#16864015	C₂²	1	16	yes	complemented
39	#16863969	C₂²	1	16	yes	complemented
40	#16863962	C₂²	1	16	yes	—
41	#16863951	C₂²	1	16	yes	complemented
42	C₂×#14524043	C₂²	1	1	yes	characteristic, complemented
43	C₂×#14524042	C₂²	1	2	yes	complemented
44	C₂×#14524039	C₂²	1	2	yes	—
45	#16863933	C₂²	1	16	yes	complemented
46	#16863932	C₂²	1	16	yes	complemented
47	#16863928	C₂²	1	16	yes	complemented
48	#16863927	C₂²	1	16	yes	complemented
49	C₂×#14524038	C₂²	1	2	yes	complemented
50	C₂×#14524038	C₂²	1	2	yes	complemented
51	C₂×#14524038	C₂²	1	2	yes	complemented
52	C₂×#14524038	C₂²	1	2	yes	complemented
53	C₂×#14524036	C₂²	1	2	yes	complemented
54	C₂×#14524036	C₂²	1	2	yes	complemented
55	C₂×#14524036	C₂²	1	2	yes	complemented
56	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
57	C₂×#14524034	C₂²	1	1	yes	characteristic, complemented
58	C₂×#14524032	C₂²	1	1	yes	characteristic
59	C₂×#14524032	C₂²	1	2	yes	complemented
60	C₂×#14524031	C₂²	1	1	yes	characteristic
61	C₂×#14524030	C₂²	1	1	yes	characteristic
62	C₂×#14524029	C₂²	1	2	yes	—
63	C₂×#14524029	C₂²	1	2	yes	—
64	C₂×#14524029	C₂²	1	2	yes	—
65	C₂×#14524029	C₂²	1	2	yes	complemented
66	C₂×#14524029	C₂²	1	2	yes	complemented
67	C₂×#14524029	C₂²	1	2	yes	complemented
68	#124×D₆₇	C₂²	1	16	yes	complemented
69	C₂×#14524028	C₂²	1	2	yes	—
70	C₂×#14524028	C₂²	1	2	yes	complemented
71	C₂×#14524028	C₂²	1	2	yes	complemented
72	C₂×#14524027	C₂²	1	2	yes	complemented
73	C₂×#14524027	C₂²	1	2	yes	complemented
74	C₂×#14524025	C₂²	1	2	yes	—
75	C₂×#14524025	C₂²	1	2	yes	complemented
76	C₂×#14524025	C₂²	1	2	yes	complemented
77	C₂×#14524024	C₂²	1	2	yes	complemented
78	C₂×#14524023	C₂²	1	2	yes	—
79	C₂×#14524023	C₂²	1	1	yes	characteristic, complemented
80	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
81	C₂×#14524021	C₂²	1	2	yes	complemented
82	C₂×#14524020	C₂²	1	2	yes	complemented
83	C₂×#14524019	C₂²	1	2	yes	—
84	C₂×#14524019	C₂²	1	1	yes	characteristic, complemented
85	C₂×#14524019	C₂²	1	2	yes	complemented
86	C₂×#14524018	C₂²	1	1	yes	characteristic
87	C₂×#14524017	C₂²	1	1	yes	characteristic
88	C₂×#14524014	C₂²	1	1	yes	characteristic
89	C₂×#14524013	C₂²	1	2	yes	—
90	C₂×#14524011	C₂²	1	2	yes	—
91	#16863872	C₂²	1	16	yes	complemented
92	#16863868	C₂²	1	16	yes	complemented
93	#16863864	C₂²	1	16	yes	complemented
94	C₂×Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×Q₈×Dic₆₇	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
98	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
99	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
100	C₂×#14524008	C₂²	1	1	yes	characteristic, complemented
101	C₂×#14524008	C₂²	1	2	yes	complemented
102	C₂×#14524008	C₂²	1	2	yes	complemented
103	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₂₆₈	C₂²	1	2	yes	complemented
105	C₂×D₄×Dic₆₇	C₂²	1	1	yes	characteristic
106	C₂×D₄×Dic₆₇	C₂²	1	2	yes	complemented
107	C₂×#14524005	C₂²	1	1	yes	characteristic
108	C₂×#14524005	C₂²	1	1	yes	characteristic
109	C₂×#14524005	C₂²	1	1	yes	characteristic
110	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
111	C₂×C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
112	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
113	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
114	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
115	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
118	C₂×#14524002	C₂²	1	2	yes	complemented
119	C₂×#14524001	C₂²	1	1	yes	characteristic
120	C₂×#14524001	C₂²	1	2	yes	—
121	C₂×#14524001	C₂²	1	1	yes	characteristic
122	C₂×#14524001	C₂²	1	2	yes	complemented
123	C₂×#14524000	C₂²	1	1	yes	characteristic
124	C₂×#14524000	C₂²	1	2	yes	—
125	C₂×#14524000	C₂²	1	1	yes	characteristic, complemented
126	C₂×#14524000	C₂²	1	2	yes	complemented
127	C₂×#14523999	C₂²	1	2	yes	complemented
128	C₂²×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
129	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
130	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
131	C₂×C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
132	C₂²×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic
134	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
135	#542×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×#124×C₆₇	C₂²	1	1	yes	characteristic
139	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
140	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
141	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
142	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
143	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
147	C₂⁴×D₆₇	C₂³	1	2	yes	—
148	C₂×#11761628	—	2	8	no	—
149	C₂×#11761628	C₂³	1	8	yes	—
150	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
153	C₂²×Dic₁₃₄	C₂³	1	2	yes	—
154	C₂×Q₈×D₆₇	—	2	8	no	—
155	C₂×Q₈×D₆₇	C₂³	1	8	yes	—
156	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
157	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
158	C₂²×D₂₆₈	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₆₇	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	2	yes	—
164	C₂×D₄×D₆₇	—	2	8	no	—
165	C₂×D₄×D₆₇	C₂³	1	8	yes	—
166	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
167	C₂³×Dic₆₇	C₂³	1	1	yes	characteristic
168	C₂³×Dic₆₇	C₂³	1	2	yes	—
169	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
170	C₂²×C₄×D₆₇	C₂³	1	2	yes	—
171	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
172	C₂²×C₄×D₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
178	#14524043	C₂³	1	8	yes	complemented
179	#14524042	C₂³	1	16	yes	complemented
180	#14524039	C₂³	1	16	yes	—
181	#14524038	C₂³	1	16	yes	complemented
182	#14524038	C₂³	1	16	yes	complemented
183	#14524038	C₂³	1	16	yes	complemented
184	#14524038	C₂³	1	16	yes	complemented
185	#14524036	C₂³	1	16	yes	complemented
186	#14524036	C₂³	1	16	yes	complemented
187	#14524036	C₂³	1	16	yes	complemented
188	#14524034	C₂³	1	8	yes	complemented
189	#14524034	C₂³	1	8	yes	complemented
190	#14524032	C₂³	1	8	yes	—
191	#14524032	C₂³	1	16	yes	complemented
192	#14524031	C₂³	1	8	yes	—
193	#14524030	C₂³	1	8	yes	—
194	#14524029	C₂³	1	16	yes	—
195	#14524029	C₂³	1	16	yes	—
196	#14524029	C₂³	1	16	yes	—
197	#14524029	C₂³	1	16	yes	complemented
198	#14524029	C₂³	1	16	yes	complemented
199	#14524029	C₂³	1	16	yes	complemented
200	#14524028	C₂³	1	16	yes	—
201	#14524028	C₂³	1	16	yes	complemented
202	#14524028	C₂³	1	16	yes	complemented
203	#14524027	C₂³	1	16	yes	complemented
204	#14524027	C₂³	1	16	yes	complemented
205	#14524025	C₂³	1	16	yes	—
206	#14524025	C₂³	1	16	yes	complemented
207	#14524025	C₂³	1	16	yes	complemented
208	#14524024	C₂³	1	16	yes	complemented
209	#14524023	C₂³	1	16	yes	—
210	#14524023	C₂³	1	8	yes	complemented
211	#14524022	C₂³	1	8	yes	complemented
212	#14524021	C₂³	1	16	yes	complemented
213	#14524020	C₂³	1	16	yes	complemented
214	#14524019	C₂³	1	16	yes	—
215	#14524019	C₂³	1	8	yes	complemented
216	#14524019	C₂³	1	16	yes	complemented
217	#14524018	C₂³	1	8	yes	—
218	#14524017	C₂³	1	8	yes	—
219	#14524014	C₂³	1	8	yes	—
220	#14524013	C₂³	1	16	yes	—
221	#14524011	C₂³	1	16	yes	—
222	Q₈×Dic₆₇	C₂³	1	8	yes	complemented
223	Q₈×Dic₆₇	C₂³	1	16	yes	complemented
224	C₄×Dic₁₃₄	C₂³	1	8	yes	complemented
225	C₄×Dic₁₃₄	C₂³	1	16	yes	complemented
226	#14524008	C₂³	1	8	yes	complemented
227	#14524008	C₂³	1	8	yes	complemented
228	#14524008	C₂³	1	16	yes	complemented
229	#14524008	C₂³	1	8	yes	complemented
230	#14524008	C₂³	1	16	yes	complemented
231	C₄×D₂₆₈	C₂³	1	8	yes	—
232	C₄×D₂₆₈	C₂³	1	16	yes	complemented
233	D₄×Dic₆₇	C₂³	1	8	yes	—
234	D₄×Dic₆₇	C₂³	1	16	yes	complemented
235	#14524005	C₂³	1	8	yes	—
236	#14524005	C₂³	1	8	yes	—
237	#14524005	C₂³	1	8	yes	—
238	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	—
239	C₄×C₂²⋊D₆₇	C₂³	1	16	yes	complemented
240	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
241	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	—
242	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	—
243	(C₂²⋊D₆₇)⋊C₄	C₂³	1	16	yes	complemented
244	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
245	(C₂²⋊D₆₇)⋊C₄	C₂³	1	8	yes	complemented
246	#14524002	C₂³	1	16	yes	complemented
247	#14524001	C₂³	1	16	yes	—
248	#14524001	C₂³	1	8	yes	—
249	#14524001	C₂³	1	8	yes	—
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	complemented
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	1	yes	characteristic
258	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
259	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
260	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
261	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
262	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
263	C₂×Dic₆₇⋊C₄	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×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
274	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
275	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
276	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
277	C₂×C₂²⋊Dic₆₇	C₂³	1	2	yes	—
278	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	16	yes	—
279	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
286	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
296	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
297	C₂²⋊C₄×D₆₇	C₂³	1	16	yes	—
298	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
311	C₂×C₄×Dic₆₇	C₂³	1	8	yes	complemented
312	C₄²×D₆₇	C₂³	1	8	yes	—
313	C₄²×D₆₇	C₂³	1	8	yes	complemented
314	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
316	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
317	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
318	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
320	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
321	#126×C₆₇	C₂³	1	16	yes	complemented
322	#124×C₆₇	C₂³	1	8	yes	—
323	#124×C₆₇	C₂³	1	16	yes	complemented
324	#123×C₆₇	C₂³	1	16	yes	complemented
325	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
326	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
327	#121×C₆₇	C₂³	1	8	yes	—
328	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
329	C₄×D₄×C₆₇	C₂³	1	8	yes	—
330	#117×C₆₇	C₂³	1	8	yes	complemented
331	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
336	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
337	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
338	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×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	2	yes	—
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	1	yes	characteristic
353	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
354	C₂³×D₆₇	C₂⁴	1	8	yes	—
355	#11761628	—	2	32	no	—
356	C₂×Dic₁₃₄	—	2	4	no	—
357	C₂×Dic₁₃₄	—	2	8	no	—
358	C₂×Dic₁₃₄	—	2	4	no	—
359	C₂×Dic₁₃₄	—	4	4	no	—
360	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
361	C₂×Dic₁₃₄	C₂⁴	1	4	yes	—
362	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
363	C₂×Dic₁₃₄	C₂⁴	1	8	yes	—
364	Q₈×D₆₇	—	2	32	no	—
365	C₂×D₂₆₈	—	2	4	no	—
366	C₂×D₂₆₈	—	2	4	no	—
367	C₂×D₂₆₈	—	4	4	no	—
368	C₂×D₂₆₈	C₂⁴	1	4	yes	—
369	C₂×D₂₆₈	C₂⁴	1	4	yes	—
370	C₂×D₂₆₈	C₂⁴	1	8	yes	—
371	C₂×C₂²⋊D₆₇	—	2	4	no	—
372	C₂×C₂²⋊D₆₇	—	2	8	no	—
373	C₂×C₂²⋊D₆₇	—	2	4	no	—
374	C₂×C₂²⋊D₆₇	—	4	4	no	—
375	C₂×C₂²⋊D₆₇	—	4	4	no	—
376	C₂×C₂²⋊D₆₇	C₂⁴	1	4	yes	—
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	8	yes	—
381	D₄×D₆₇	—	2	32	no	—
382	C₂²×Dic₆₇	—	4	2	no	—
383	C₂²×Dic₆₇	—	4	2	no	—
384	C₂²×Dic₆₇	—	4	4	no	—
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	1	yes	characteristic
389	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
390	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
391	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₆₇	C₂⁴	1	2	yes	—
393	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
394	C₂²×Dic₆₇	C₂⁴	1	4	yes	—
395	C₂²×Dic₆₇	C₂⁴	1	8	yes	—
396	C₂²×Dic₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×D₆₇	—	2	8	no	—
398	C₂×C₄×D₆₇	—	2	4	no	—
399	C₂×C₄×D₆₇	—	4	2	no	—
400	C₂×C₄×D₆₇	—	4	4	no	—
401	C₂×C₄×D₆₇	—	4	2	no	—
402	C₂×C₄×D₆₇	—	4	2	no	—
403	C₂×C₄×D₆₇	—	4	2	no	—
404	C₂×C₄×D₆₇	—	4	4	no	—
405	C₂×C₄×D₆₇	#41	1	8	yes	—
406	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
407	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
408	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
409	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
410	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
411	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
412	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
413	C₂×C₄×D₆₇	C₂⁴	1	8	yes	—
414	C₂×C₄×D₆₇	C₂⁴	1	4	yes	—
415	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
416	C₄⋊Dic₆₇	C₂⁴	1	4	yes	—
417	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
418	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
419	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
420	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
421	C₄⋊Dic₆₇	C₂⁴	1	8	yes	—
422	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
423	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
424	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
425	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
426	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
427	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
428	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
429	Dic₆₇⋊C₄	C₂⁴	1	4	yes	—
430	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
431	Dic₆₇⋊C₄	C₂⁴	1	8	yes	—
432	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
433	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
434	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
435	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
436	C₂²⋊Dic₆₇	C₂⁴	1	8	yes	—
437	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	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	8	yes	—
443	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
444	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
445	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
446	(C₂×D₆₇)⋊C₄	C₂⁴	1	8	yes	—
447	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	yes	—
448	(C₂×D₆₇)⋊C₄	C₂⁴	1	4	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	C₄×Dic₆₇	C₂⁴	1	4	yes	—
454	C₄×Dic₆₇	C₂⁴	1	4	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	4	yes	—
459	C₄×Dic₆₇	C₂⁴	1	4	yes	—
460	C₄×Dic₆₇	C₂⁴	1	4	yes	—
461	C₄×Dic₆₇	C₂⁴	1	8	yes	—
462	C₄×Dic₆₇	C₂⁴	1	8	yes	—
463	C₄×Dic₆₇	C₂⁴	1	8	yes	—
464	C₄×Dic₆₇	C₂⁴	1	8	yes	—
465	C₄×Dic₆₇	C₂⁴	1	8	yes	—
466	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
467	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
468	C₂×Q₈×C₆₇	—	2	4	no	—
469	C₂×Q₈×C₆₇	—	4	4	no	—
470	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
471	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
472	C₂×D₄×C₆₇	—	2	4	no	—
473	C₂×D₄×C₆₇	—	4	4	no	—
474	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
475	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
476	C₂²×C₄×C₆₇	—	2	4	no	—
477	C₂²×C₄×C₆₇	—	4	4	no	—
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	1	yes	characteristic
483	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
484	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
485	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
486	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
487	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
488	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
489	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
490	C₄⋊C₄×C₆₇	C₂⁴	1	4	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	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
495	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
496	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
497	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
498	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
499	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
500	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
501	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
502	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
503	C₄²×C₆₇	C₂⁴	1	4	yes	—
504	C₄²×C₆₇	C₂⁴	1	4	yes	—
505	C₄²×C₆₇	C₂⁴	1	8	yes	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	2	4	no	—
508	C₂³×C₆₇	—	2	4	no	—
509	C₂³×C₆₇	—	2	2	no	—
510	C₂³×C₆₇	—	2	2	no	—
511	C₂³×C₆₇	—	2	4	no	—
512	C₂³×C₆₇	C₂⁵	1	4	yes	—
513	C₂³×C₆₇	C₂⁵	1	2	yes	—
514	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
515	C₂²×D₆₇	—	2	2	no	—
516	C₂²×D₆₇	—	2	2	no	—
517	C₂²×D₆₇	—	2	2	no	—
518	C₂²×D₆₇	—	2	4	no	—
519	C₂²×D₆₇	—	2	2	no	—
520	C₂²×D₆₇	—	2	4	no	—
521	C₂²×D₆₇	—	2	2	no	—
522	C₂²×D₆₇	—	2	4	no	—
523	C₂²×D₆₇	—	2	16	no	—
524	C₂²×D₆₇	—	4	8	no	—
525	C₂²×D₆₇	—	4	8	no	—
526	C₂²×D₆₇	—	8	16	no	—
527	C₂²×D₆₇	C₂×#41	1	4	yes	—
528	C₂²×D₆₇	C₂⁵	1	4	yes	—
529	C₂²×D₆₇	C₂⁵	1	2	yes	—
530	C₂²×D₆₇	C₂⁵	1	2	yes	—
531	Q₈×C₆₇	—	2	8	no	—
532	Q₈×C₆₇	—	4	8	no	—
533	D₄×C₆₇	—	2	8	no	—
534	D₄×C₆₇	—	4	8	no	—
535	C₂×C₄×C₆₇	—	2	2	no	—
536	C₂×C₄×C₆₇	—	2	4	no	—
537	C₂×C₄×C₆₇	—	2	2	no	—
538	C₂×C₄×C₆₇	—	2	4	no	—
539	C₂×C₄×C₆₇	—	2	4	no	—
540	C₂×C₄×C₆₇	—	2	2	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	8	no	—
544	C₂×C₄×C₆₇	—	4	8	no	—
545	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
546	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
547	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
548	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
549	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
550	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
551	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
552	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
553	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
554	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
555	C₂²⋊D₆₇	—	2	8	no	—
556	C₂²⋊D₆₇	—	2	16	no	—
557	C₂²⋊D₆₇	—	2	8	no	—
558	C₂²⋊D₆₇	—	4	8	no	—
559	C₂²⋊D₆₇	—	4	8	no	—
560	C₂×Dic₆₇	—	2	2	no	—
561	C₂×Dic₆₇	—	2	4	no	—
562	C₂×Dic₆₇	—	2	2	no	—
563	C₂×Dic₆₇	—	2	2	no	—
564	C₂×Dic₆₇	—	2	2	no	—
565	C₂×Dic₆₇	—	2	4	no	—
566	C₂×Dic₆₇	—	2	2	no	—
567	C₂×Dic₆₇	—	2	4	no	—
568	C₂×Dic₆₇	—	4	8	no	—
569	C₂×Dic₆₇	—	4	4	no	—
570	C₂×Dic₆₇	—	4	4	no	—
571	C₂×Dic₆₇	C₂×#41	1	4	yes	—
572	C₂×Dic₆₇	C₂⁵	1	2	yes	—
573	C₂×Dic₆₇	C₂⁵	1	2	yes	—
574	C₂×Dic₆₇	C₂⁵	1	2	yes	—
575	C₂×Dic₆₇	C₂⁵	1	2	yes	—
576	C₂×Dic₆₇	C₂⁵	1	4	yes	—
577	C₂×Dic₆₇	C₂⁵	1	4	yes	—
578	C₂×Dic₆₇	C₂⁵	1	2	yes	—
579	C₂×Dic₆₇	C₂⁵	1	4	yes	—
580	C₂×Dic₆₇	C₂⁵	1	2	yes	—
581	D₂₆₈	—	2	8	no	—
582	D₂₆₈	—	2	8	no	—
583	D₂₆₈	—	4	8	no	—
584	C₄×D₆₇	—	2	16	no	—
585	C₄×D₆₇	—	2	8	no	—
586	C₄×D₆₇	—	4	8	no	—
587	C₄×D₆₇	—	4	4	no	—
588	C₄×D₆₇	—	4	4	no	—
589	C₄×D₆₇	—	4	4	no	—
590	C₄×D₆₇	—	4	8	no	—
591	C₄×D₆₇	—	4	4	no	—
592	C₄×D₆₇	C₂×#41	1	16	yes	—
593	Dic₁₃₄	—	2	8	no	—
594	Dic₁₃₄	—	2	16	no	—
595	Dic₁₃₄	—	2	8	no	—
596	Dic₁₃₄	—	4	8	no	—
597	C₂²×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	4	no	—
599	C₂²×C₆₇	—	2	2	no	—
600	C₂²×C₆₇	—	2	4	no	—
601	C₂²×C₆₇	—	2	2	no	—
602	C₂²×C₆₇	—	2	4	no	—
603	C₂²×C₆₇	—	4	8	no	—
604	C₂²×C₆₇	—	4	4	no	—
605	C₂²×C₆₇	C₂²×#41	1	2	yes	—
606	C₂²×C₆₇	#585	1	2	yes	—
607	C₂²×C₆₇	#585	1	2	yes	—
608	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
609	C₂×D₆₇	—	2	2	no	—
610	C₂×D₆₇	—	2	2	no	—
611	C₂×D₆₇	—	2	8	no	—
612	C₂×D₆₇	—	2	2	no	—
613	C₂×D₆₇	—	2	4	no	—
614	C₂×D₆₇	—	2	2	no	—
615	C₂×D₆₇	—	2	4	no	—
616	C₂×D₆₇	—	2	2	no	—
617	C₂×D₆₇	—	2	4	no	—
618	C₂×D₆₇	—	4	4	no	—
619	C₂×D₆₇	—	4	8	no	—
620	C₂×D₆₇	—	8	16	no	—
621	C₂×D₆₇	C₂²×#41	1	4	yes	—
622	C₄×C₆₇	—	2	4	no	—
623	C₄×C₆₇	—	2	2	no	—
624	C₄×C₆₇	—	2	2	no	—
625	C₄×C₆₇	—	2	2	no	—
626	C₄×C₆₇	—	2	2	no	—
627	C₄×C₆₇	—	2	4	no	—
628	C₄×C₆₇	—	2	2	no	—
629	C₄×C₆₇	—	2	4	no	—
630	C₄×C₆₇	C₂²×#41	1	4	yes	—
631	Dic₆₇	—	2	4	no	—
632	Dic₆₇	—	2	2	no	—
633	Dic₆₇	—	2	4	no	—
634	Dic₆₇	—	2	4	no	—
635	Dic₆₇	—	2	2	no	—
636	Dic₆₇	—	2	2	no	—
637	Dic₆₇	—	2	2	no	—
638	Dic₆₇	—	2	2	no	—
639	Dic₆₇	C₂²×#41	1	4	yes	—
640	C₂×#3510	—	67	1	no	maximal, Sylow
641	C₂×C₆₇	—	4	4	no	—
642	C₂×C₆₇	—	4	2	no	—
643	C₂×C₆₇	#3510	1	4	yes	complemented
644	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
645	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
646	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
647	D₆₇	—	2	4	no	—
648	D₆₇	—	4	2	no	—
649	D₆₇	—	4	4	no	—
650	#3510	—	67	32	no	—
651	C₂×#559	—	67	2	no	—
652	C₂×#559	—	67	2	no	—
653	C₂×#556	—	67	2	no	—
654	C₂×#556	—	67	2	no	—
655	C₂×#551	—	67	2	no	—
656	C₂×#551	—	67	2	no	—
657	C₂×#551	—	67	2	no	—
658	C₂×#551	—	67	2	no	—
659	C₂×#542	—	67	1	no	—
660	C₂×#542	—	67	1	no	—
661	C₂×#542	—	67	1	no	—
662	C₂×#542	D₆₇	1	1	yes	characteristic, complemented
663	C₂×#536	—	67	1	no	—
664	C₂×#535	—	67	1	no	—
665	C₂×#533	—	67	1	no	—
666	C₂×#529	—	67	1	no	—
667	C₂×#529	—	67	1	no	—
668	C₂×#529	—	67	1	no	—
669	C₂×#529	—	67	1	no	—
670	C₂²×#124	—	67	1	no	—
671	C₂×#519	—	67	1	no	—
672	C₂×#518	—	67	1	no	—
673	C₂×C₄×#41	—	67	1	no	—
674	C₆₇	C₂×#3510	1	1	yes	characteristic, complemented, Sylow
675	C₂²×#41	—	67	1	no	—
676	C₂³×Q₈	—	67	1	no	—
677	C₂³×D₄	—	67	1	no	—
678	#559	—	67	32	no	—
679	#559	—	67	32	no	—
680	#556	—	67	32	no	—
681	#556	—	67	32	no	—
682	#551	—	67	32	no	—
683	#551	—	67	32	no	—
684	#551	—	67	32	no	—
685	#551	—	67	32	no	—
686	#542	—	67	16	no	—
687	#542	—	67	16	no	—
688	#542	—	67	16	no	—
689	#542	C₂×D₆₇	1	16	yes	complemented
690	#536	—	67	16	no	—
691	#535	—	67	16	no	—
692	#533	—	67	16	no	—
693	C₂×C₄⋊Q₈	—	67	2	no	—
694	C₂×C₄⋊Q₈	—	67	1	no	—
695	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
696	C₂×#127	—	67	2	no	—
697	#529	—	67	16	no	—
698	#529	—	67	16	no	—
699	#529	—	67	16	no	—
700	#529	—	67	16	no	—
701	C₂×#126	—	67	2	no	—
702	C₂×#126	—	67	2	no	—
703	C₂×#126	—	67	2	no	—
704	C₂×#126	—	67	2	no	—
705	C₂×#126	—	67	2	no	—
706	C₂×#126	—	67	2	no	—
707	C₂×#126	—	67	2	no	—
708	C₂×#126	C₂×D₆₇	1	2	yes	complemented
709	C₂×#125	—	67	1	no	—
710	C₂×#125	—	67	1	no	—
711	C₂×#124	—	67	1	no	—
712	C₂×#124	—	67	2	no	—
713	C₂×#124	—	67	1	no	—
714	C₂×#124	—	67	16	no	—
715	C₂×#124	—	67	2	no	—
716	C₂×#124	—	67	2	no	—
717	C₂×#124	—	67	2	no	—
718	C₂×#124	—	67	2	no	—
719	C₂×#124	—	67	2	no	—
720	C₂×#124	—	67	2	no	—
721	C₂×#124	—	67	1	no	—
722	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
723	C₂×#124	C₂×D₆₇	1	2	yes	complemented
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	—	67	2	no	—
731	C₂×#123	—	67	2	no	—
732	C₂×#123	—	67	2	no	—
733	C₂×#123	C₂×D₆₇	1	2	yes	complemented
734	C₂×C₂²⋊Q₈	—	67	1	no	—
735	C₂×C₂²⋊Q₈	—	67	2	no	—
736	C₂×C₂²⋊Q₈	—	67	2	no	—
737	C₂×C₂²⋊Q₈	—	67	1	no	—
738	C₂×C₂²⋊Q₈	—	67	1	no	—
739	C₂×C₂²⋊Q₈	—	67	2	no	—
740	C₂×C₂²⋊Q₈	—	67	2	no	—
741	C₂×C₂²⋊Q₈	—	67	2	no	—
742	C₂×C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
743	C₂×C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
744	C₂×#121	—	67	1	no	—
745	C₂×#121	—	67	1	no	—
746	C₂×#121	—	67	1	no	—
747	C₂×#121	C₂×D₆₇	1	1	yes	characteristic
748	C₂×#120	—	67	2	no	—
749	C₂×#120	—	67	2	no	—
750	#519	—	67	16	no	—
751	#518	—	67	16	no	—
752	C₄×#41	—	67	16	no	—
753	C₂×C₄×Q₈	—	67	1	no	—
754	C₂×C₄×Q₈	—	67	2	no	—
755	C₂×C₄×Q₈	—	67	1	no	—
756	C₂×C₄×Q₈	—	67	1	no	—
757	C₂×C₄×Q₈	—	67	1	no	—
758	C₂×C₄×Q₈	—	67	2	no	—
759	C₂×C₄×Q₈	—	67	2	no	—
760	C₂×C₄×Q₈	—	67	1	no	—
761	C₂×C₄×Q₈	—	67	2	no	—
762	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
763	C₂×C₄×D₄	—	67	1	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	1	no	—
770	C₂×C₄×D₄	—	67	1	no	—
771	C₂×C₄×D₄	—	67	1	no	—
772	C₂×C₄×D₄	—	67	1	no	—
773	C₂×C₄×D₄	—	67	1	no	—
774	C₂×C₄×D₄	—	67	2	no	—
775	C₂×C₄×D₄	—	67	2	no	—
776	C₂×C₄×D₄	—	67	1	no	—
777	C₂×C₄×D₄	—	67	2	no	—
778	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
779	C₂×#117	—	67	2	no	—
780	C₂×#117	—	67	1	no	—
781	C₂×#117	—	67	1	no	—
782	C₂×#117	—	67	2	no	—
783	C₂×#117	—	67	2	no	—
784	C₂×#117	—	67	2	no	—
785	C₂×#117	—	67	1	no	—
786	C₂×#117	—	67	1	no	—
787	C₂×#117	—	67	2	no	—
788	C₂×#117	—	67	2	no	—
789	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
790	C₂²×C₂²⋊C₄	—	67	2	no	—
791	C₂²×C₂²⋊C₄	—	67	2	no	—
792	C₂²×C₂²⋊C₄	—	67	2	no	—
793	C₂²×C₂²⋊C₄	—	67	2	no	—
794	C₂²×C₄²	—	67	1	no	—
795	C₂²×C₄²	—	67	1	no	—
796	C₂²×C₄²	—	67	1	no	—
797	C₂⁵	—	67	2	no	—
798	C₂×#41	—	67	8	no	—
799	C₂×#41	—	134	8	no	—
800	C₂²×Q₈	—	67	8	no	—
801	C₂²×Q₈	—	67	2	no	—
802	C₂²×Q₈	—	67	1	no	—
803	C₂²×Q₈	—	67	2	no	—
804	C₂²×Q₈	—	67	1	no	—
805	C₂²×Q₈	—	134	8	no	—
806	C₂²×Q₈	C₂²×D₆₇	1	1	yes	characteristic
807	C₂²×Q₈	C₂²×D₆₇	1	2	yes	—
808	C₂²×D₄	—	67	2	no	—
809	C₂²×D₄	—	67	2	no	—
810	C₂²×D₄	—	67	1	no	—
811	C₂²×D₄	—	67	2	no	—
812	C₂²×D₄	—	67	1	no	—
813	C₂²×D₄	—	67	8	no	—
814	C₂²×D₄	—	67	2	no	—
815	C₂²×D₄	—	67	1	no	—
816	C₂²×D₄	—	67	1	no	—
817	C₂²×D₄	—	134	8	no	—
818	C₂²×D₄	C₂²×D₆₇	1	1	yes	characteristic
819	C₂²×D₄	C₂²×D₆₇	1	2	yes	—
820	C₂³×C₄	—	67	2	no	—
821	C₂³×C₄	—	67	1	no	—
822	C₂³×C₄	—	67	1	no	—
823	C₂³×C₄	—	67	1	no	—
824	C₂³×C₄	—	67	1	no	—
825	C₂³×C₄	—	67	2	no	—
826	C₂³×C₄	—	67	2	no	—
827	C₂³×C₄	—	67	1	no	—
828	C₂³×C₄	—	67	1	no	—
829	C₂³×C₄	—	67	1	no	—
830	C₂³×C₄	—	67	2	no	—
831	C₂³×C₄	—	67	1	no	—
832	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
833	C₂³×C₄	C₂²×D₆₇	1	2	yes	—
834	C₄⋊Q₈	—	67	16	no	—
835	C₄⋊Q₈	—	67	8	no	—
836	C₄⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
837	#127	—	67	16	no	—
838	#126	—	67	16	no	—
839	#126	—	67	16	no	—
840	#126	—	67	16	no	—
841	#126	—	67	16	no	—
842	#126	—	67	16	no	—
843	#126	—	67	16	no	—
844	#126	—	67	16	no	—
845	#126	C₂²×D₆₇	1	16	yes	complemented
846	#125	—	67	8	no	—
847	#125	—	67	8	no	—
848	#124	—	67	8	no	—
849	#124	—	67	16	no	—
850	#124	—	67	8	no	—
851	#124	—	67	16	no	—
852	#124	—	67	16	no	—
853	#124	—	67	16	no	—
854	#124	—	67	16	no	—
855	#124	—	67	16	no	—
856	#124	—	67	16	no	—
857	#124	—	67	8	no	—
858	#124	C₂²×D₆₇	1	8	yes	—
859	#124	C₂²×D₆₇	1	16	yes	complemented
860	#123	—	67	16	no	—
861	#123	—	67	16	no	—
862	#123	—	67	16	no	—
863	#123	—	67	16	no	—
864	#123	—	67	16	no	—
865	#123	—	67	16	no	—
866	#123	—	67	16	no	—
867	#123	—	67	16	no	—
868	#123	—	67	16	no	—
869	#123	C₂²×D₆₇	1	16	yes	complemented
870	C₂²⋊Q₈	—	67	8	no	—
871	C₂²⋊Q₈	—	67	16	no	—
872	C₂²⋊Q₈	—	67	16	no	—
873	C₂²⋊Q₈	—	67	8	no	—
874	C₂²⋊Q₈	—	67	8	no	—
875	C₂²⋊Q₈	—	67	16	no	—
876	C₂²⋊Q₈	—	67	16	no	—
877	C₂²⋊Q₈	—	67	16	no	—
878	C₂²⋊Q₈	C₂²×D₆₇	1	8	yes	complemented
879	C₂²⋊Q₈	C₂²×D₆₇	1	16	yes	complemented
880	#121	—	67	8	no	—
881	#121	—	67	8	no	—
882	#121	—	67	8	no	—
883	#121	C₂²×D₆₇	1	8	yes	—
884	#120	—	67	16	no	—
885	#120	—	67	16	no	—
886	C₄×Q₈	—	67	8	no	—
887	C₄×Q₈	—	67	16	no	—
888	C₄×Q₈	—	67	8	no	—
889	C₄×Q₈	—	67	8	no	—
890	C₄×Q₈	—	67	8	no	—
891	C₄×Q₈	—	67	16	no	—
892	C₄×Q₈	—	67	16	no	—
893	C₄×Q₈	—	67	8	no	—
894	C₄×Q₈	—	67	16	no	—
895	C₄×Q₈	C₂²×D₆₇	1	8	yes	complemented
896	C₄×D₄	—	67	8	no	—
897	C₄×D₄	—	67	16	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	8	no	—
904	C₄×D₄	—	67	8	no	—
905	C₄×D₄	—	67	8	no	—
906	C₄×D₄	—	67	8	no	—
907	C₄×D₄	—	67	16	no	—
908	C₄×D₄	—	67	16	no	—
909	C₄×D₄	—	67	8	no	—
910	C₄×D₄	—	67	16	no	—
911	C₄×D₄	C₂²×D₆₇	1	8	yes	—
912	#117	—	67	16	no	—
913	#117	—	67	8	no	—
914	#117	—	67	8	no	—
915	#117	—	67	16	no	—
916	#117	—	67	16	no	—
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	C₂²×D₆₇	1	8	yes	complemented
923	C₂×C₄⋊C₄	—	67	2	no	—
924	C₂×C₄⋊C₄	—	67	2	no	—
925	C₂×C₄⋊C₄	—	67	1	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	2	no	—
932	C₂×C₄⋊C₄	—	67	2	no	—
933	C₂×C₄⋊C₄	—	67	2	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	2	no	—
940	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
943	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
944	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	2	no	—
951	C₂×C₂²⋊C₄	—	67	2	no	—
952	C₂×C₂²⋊C₄	—	67	1	no	—
953	C₂×C₂²⋊C₄	—	67	1	no	—
954	C₂×C₂²⋊C₄	—	67	2	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	16	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	1	no	—
964	C₂×C₂²⋊C₄	—	67	1	no	—
965	C₂×C₂²⋊C₄	—	67	2	no	—
966	C₂×C₂²⋊C₄	—	67	2	no	—
967	C₂×C₂²⋊C₄	—	67	2	no	—
968	C₂×C₂²⋊C₄	—	67	2	no	—
969	C₂×C₂²⋊C₄	—	67	16	no	—
970	C₂×C₂²⋊C₄	—	67	16	no	—
971	C₂×C₂²⋊C₄	—	67	16	no	—
972	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
973	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
974	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
975	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
976	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
979	C₂×C₄²	—	67	1	no	—
980	C₂×C₄²	—	67	2	no	—
981	C₂×C₄²	—	67	2	no	—
982	C₂×C₄²	—	67	2	no	—
983	C₂×C₄²	—	67	1	no	—
984	C₂×C₄²	—	67	1	no	—
985	C₂×C₄²	—	67	1	no	—
986	C₂×C₄²	—	67	1	no	—
987	C₂×C₄²	—	67	2	no	—
988	C₂×C₄²	—	67	2	no	—
989	C₂×C₄²	—	67	1	no	—
990	C₂×C₄²	—	67	1	no	—
991	C₂×C₄²	—	67	8	no	—
992	C₂×C₄²	—	67	1	no	—
993	C₂×C₄²	—	67	8	no	—
994	C₂×C₄²	—	67	8	no	—
995	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
996	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
997	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
998	C₂⁴	—	268	4	no	—
999	C₂⁴	—	268	4	no	—
1000	C₂⁴	—	67	8	no	—
1001	C₂⁴	—	67	1	no	—
1002	C₂⁴	—	67	2	no	—
1003	C₂⁴	—	67	1	no	—
1004	C₂⁴	—	134	8	no	—
1005	C₂⁴	C₂³×D₆₇	1	2	yes	—
1006	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
1007	#41	—	134	32	no	—
1008	C₂×Q₈	—	2	4	no	—
1009	C₂×Q₈	—	4	4	no	—
1010	C₂×Q₈	—	268	4	no	—
1011	C₂×Q₈	—	67	8	no	—
1012	C₂×Q₈	—	67	4	no	—
1013	C₂×Q₈	—	67	8	no	—
1014	C₂×Q₈	—	67	4	no	—
1015	C₂×Q₈	—	134	8	no	—
1016	C₂×Q₈	—	134	4	no	—
1017	C₂×Q₈	—	134	32	no	—
1018	C₂×Q₈	—	134	4	no	—
1019	C₂×Q₈	C₂³×D₆₇	1	4	yes	—
1020	C₂×Q₈	C₂³×D₆₇	1	8	yes	—
1021	C₂×D₄	—	2	4	no	—
1022	C₂×D₄	—	4	4	no	—
1023	C₂×D₄	—	268	4	no	—
1024	C₂×D₄	—	268	4	no	—
1025	C₂×D₄	—	268	4	no	—
1026	C₂×D₄	—	67	8	no	—
1027	C₂×D₄	—	67	8	no	—
1028	C₂×D₄	—	67	4	no	—
1029	C₂×D₄	—	67	8	no	—
1030	C₂×D₄	—	67	4	no	—
1031	C₂×D₄	—	67	8	no	—
1032	C₂×D₄	—	67	4	no	—
1033	C₂×D₄	—	67	4	no	—
1034	C₂×D₄	—	134	4	no	—
1035	C₂×D₄	—	134	32	no	—
1036	C₂×D₄	—	134	8	no	—
1037	C₂×D₄	—	134	4	no	—
1038	C₂×D₄	—	134	4	no	—
1039	C₂×D₄	—	134	4	no	—
1040	C₂×D₄	C₂³×D₆₇	1	4	yes	—
1041	C₂×D₄	C₂³×D₆₇	1	8	yes	—
1042	C₂²×C₄	—	2	4	no	—
1043	C₂²×C₄	—	4	4	no	—
1044	C₂²×C₄	—	268	2	no	—
1045	C₂²×C₄	—	268	4	no	—
1046	C₂²×C₄	—	268	2	no	—
1047	C₂²×C₄	—	268	2	no	—
1048	C₂²×C₄	—	268	4	no	—
1049	C₂²×C₄	—	268	2	no	—
1050	C₂²×C₄	—	268	2	no	—
1051	C₂²×C₄	—	268	2	no	—
1052	C₂²×C₄	—	268	4	no	—
1053	C₂²×C₄	—	67	4	no	—
1054	C₂²×C₄	—	67	4	no	—
1055	C₂²×C₄	—	67	8	no	—
1056	C₂²×C₄	—	67	4	no	—
1057	C₂²×C₄	—	67	4	no	—
1058	C₂²×C₄	—	67	4	no	—
1059	C₂²×C₄	—	67	4	no	—
1060	C₂²×C₄	—	67	8	no	—
1061	C₂²×C₄	—	67	8	no	—
1062	C₂²×C₄	—	67	1	no	—
1063	C₂²×C₄	—	67	8	no	—
1064	C₂²×C₄	—	67	4	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	2	no	—
1073	C₂²×C₄	—	67	4	no	—
1074	C₂²×C₄	—	67	8	no	—
1075	C₂²×C₄	—	134	8	no	—
1076	C₂²×C₄	—	134	4	no	—
1077	C₂²×C₄	C₂³×D₆₇	1	4	yes	—
1078	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1079	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1080	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1081	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1082	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1083	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1084	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1085	C₂²×C₄	C₂³×D₆₇	1	2	yes	—
1086	C₂²×C₄	C₂³×D₆₇	1	8	yes	—
1087	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1088	C₄⋊C₄	—	67	8	no	—
1089	C₄⋊C₄	—	67	8	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	—	67	4	no	—
1095	C₄⋊C₄	—	67	4	no	—
1096	C₄⋊C₄	—	67	8	no	—
1097	C₄⋊C₄	—	67	8	no	—
1098	C₄⋊C₄	—	67	8	no	—
1099	C₄⋊C₄	—	67	8	no	—
1100	C₄⋊C₄	—	67	8	no	—
1101	C₄⋊C₄	—	67	8	no	—
1102	C₄⋊C₄	—	67	8	no	—
1103	C₄⋊C₄	—	67	8	no	—
1104	C₄⋊C₄	—	67	8	no	—
1105	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1106	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1107	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1108	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1109	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1110	C₄⋊C₄	C₂³×D₆₇	1	4	yes	—
1111	C₄⋊C₄	C₂³×D₆₇	1	8	yes	—
1112	C₂²⋊C₄	—	67	8	no	—
1113	C₂²⋊C₄	—	67	8	no	—
1114	C₂²⋊C₄	—	67	8	no	—
1115	C₂²⋊C₄	—	67	8	no	—
1116	C₂²⋊C₄	—	67	8	no	—
1117	C₂²⋊C₄	—	67	4	no	—
1118	C₂²⋊C₄	—	67	4	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	—	67	8	no	—
1125	C₂²⋊C₄	—	67	8	no	—
1126	C₂²⋊C₄	—	67	8	no	—
1127	C₂²⋊C₄	—	67	4	no	—
1128	C₂²⋊C₄	—	67	4	no	—
1129	C₂²⋊C₄	—	67	8	no	—
1130	C₂²⋊C₄	—	67	8	no	—
1131	C₂²⋊C₄	—	67	8	no	—
1132	C₂²⋊C₄	—	67	8	no	—
1133	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1134	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1135	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1136	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1137	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1138	C₂²⋊C₄	C₂³×D₆₇	1	4	yes	—
1139	C₂²⋊C₄	C₂³×D₆₇	1	8	yes	—
1140	C₄²	—	67	4	no	—
1141	C₄²	—	67	4	no	—
1142	C₄²	—	67	4	no	—
1143	C₄²	—	67	4	no	—
1144	C₄²	—	67	4	no	—
1145	C₄²	—	67	4	no	—
1146	C₄²	—	67	4	no	—
1147	C₄²	—	67	4	no	—
1148	C₄²	—	67	8	no	—
1149	C₄²	—	67	8	no	—
1150	C₄²	—	67	8	no	—
1151	C₄²	—	67	8	no	—
1152	C₄²	—	67	8	no	—
1153	C₄²	C₂³×D₆₇	1	4	yes	—
1154	C₄²	C₂³×D₆₇	1	4	yes	—
1155	C₄²	C₂³×D₆₇	1	8	yes	—
1156	C₂³	—	2	2	no	—
1157	C₂³	—	2	4	no	—
1158	C₂³	—	2	4	no	—
1159	C₂³	—	2	2	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	4	no	—
1162	C₂³	—	268	8	no	—
1163	C₂³	—	268	8	no	—
1164	C₂³	—	536	16	no	—
1165	C₂³	—	67	4	no	—
1166	C₂³	—	67	2	no	—
1167	C₂³	—	67	4	no	—
1168	C₂³	—	67	2	no	—
1169	C₂³	—	134	16	no	—
1170	C₂³	—	134	2	no	—
1171	C₂³	—	134	4	no	—
1172	C₂³	—	134	2	no	—
1173	C₂³	—	134	4	no	—
1174	C₂³	—	134	2	no	—
1175	C₂³	—	134	4	no	—
1176	C₂³	—	134	2	no	—
1177	C₂³	—	134	2	no	—
1178	C₂³	C₂⁴×D₆₇	1	4	yes	—
1179	C₂³	C₂⁴×D₆₇	1	2	yes	—
1180	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
1181	Q₈	—	2	8	no	—
1182	Q₈	—	4	8	no	—
1183	Q₈	—	268	8	no	—
1184	Q₈	—	134	16	no	—
1185	Q₈	—	134	8	no	—
1186	Q₈	—	134	8	no	—
1187	D₄	—	2	8	no	—
1188	D₄	—	4	8	no	—
1189	D₄	—	268	8	no	—
1190	D₄	—	268	8	no	—
1191	D₄	—	268	8	no	—
1192	D₄	—	134	8	no	—
1193	D₄	—	134	16	no	—
1194	D₄	—	134	8	no	—
1195	D₄	—	134	8	no	—
1196	D₄	—	134	8	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	4	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	4	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	4	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	8	no	—
1206	C₂×C₄	—	4	8	no	—
1207	C₂×C₄	—	268	4	no	—
1208	C₂×C₄	—	268	8	no	—
1209	C₂×C₄	—	268	4	no	—
1210	C₂×C₄	—	268	4	no	—
1211	C₂×C₄	—	268	8	no	—
1212	C₂×C₄	—	268	4	no	—
1213	C₂×C₄	—	268	4	no	—
1214	C₂×C₄	—	268	4	no	—
1215	C₂×C₄	—	268	8	no	—
1216	C₂×C₄	—	67	4	no	—
1217	C₂×C₄	—	67	2	no	—
1218	C₂×C₄	—	67	16	no	—
1219	C₂×C₄	—	67	2	no	—
1220	C₂×C₄	—	67	2	no	—
1221	C₂×C₄	—	67	2	no	—
1222	C₂×C₄	—	67	2	no	—
1223	C₂×C₄	—	67	4	no	—
1224	C₂×C₄	—	67	4	no	—
1225	C₂×C₄	—	67	2	no	—
1226	C₂×C₄	—	67	4	no	—
1227	C₂×C₄	—	134	16	no	—
1228	C₂×C₄	—	134	2	no	—
1229	C₂×C₄	—	134	4	no	—
1230	C₂×C₄	—	134	2	no	—
1231	C₂×C₄	—	134	2	no	—
1232	C₂×C₄	—	134	2	no	—
1233	C₂×C₄	—	134	2	no	—
1234	C₂×C₄	—	134	4	no	—
1235	C₂×C₄	—	134	4	no	—
1236	C₂×C₄	—	134	8	no	—
1237	C₂×C₄	#41×D₆₇	1	4	yes	—
1238	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1239	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1240	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1241	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1242	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1243	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1244	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1245	C₂×C₄	C₂⁴×D₆₇	1	4	yes	—
1246	C₂×C₄	C₂⁴×D₆₇	1	2	yes	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	4	no	—
1249	C₂²	—	2	4	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	2	2	no	—
1252	C₂²	—	2	4	no	—
1253	C₂²	—	4	8	no	—
1254	C₂²	—	4	4	no	—
1255	C₂²	—	268	8	no	—
1256	C₂²	—	268	4	no	—
1257	C₂²	—	536	16	no	—
1258	C₂²	—	67	4	no	—
1259	C₂²	—	134	2	no	—
1260	C₂²	—	134	4	no	—
1261	C₂²	—	134	2	no	—
1262	C₂²	—	134	4	no	—
1263	C₂²	—	134	2	no	—
1264	C₂²	—	134	4	no	—
1265	C₂²	—	134	8	no	—
1266	C₂²	—	134	2	no	—
1267	C₂²	—	134	2	no	—
1268	C₂²	C₂×#41×D₆₇	1	2	yes	—
1269	C₂²	#16864231	1	2	yes	—
1270	C₂²	#16864233	1	2	yes	—
1271	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
1272	C₄	—	2	2	no	—
1273	C₄	—	2	4	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	4	no	—
1276	C₄	—	2	2	no	—
1277	C₄	—	2	4	no	—
1278	C₄	—	2	2	no	—
1279	C₄	—	2	2	no	—
1280	C₄	—	67	4	no	—
1281	C₄	—	134	2	no	—
1282	C₄	—	134	4	no	—
1283	C₄	—	134	2	no	—
1284	C₄	—	134	2	no	—
1285	C₄	—	134	2	no	—
1286	C₄	—	134	2	no	—
1287	C₄	—	134	4	no	—
1288	C₄	—	134	4	no	—
1289	C₄	C₂×#41×D₆₇	1	4	yes	—
1290	C₂	—	4	4	no	—
1291	C₂	—	4	2	no	—
1292	C₂	—	268	4	no	—
1293	C₂	—	268	2	no	—
1294	C₂	—	134	4	no	—
1295	C₂	#22574101	1	4	yes	direct product factor
1296	C₂	C₂²×#41×D₆₇	1	1	yes	characteristic
1297	C₂	C₂×#16864231	1	1	yes	characteristic
1298	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×#542×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
prime radical	C₂×#16863962	C₂
hypercenter	C₂×#542	D₆₇
hypocenter	C₆₇	C₂×#3510
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #22574101	C₂	direct (N × H)
2. C₂×#16864130	C₂	semidirect
3. C₂×#16864128	C₂	semidirect
4. C₂×#16864117	C₂	semidirect
5. C₂×#16864113	C₂	semidirect
6. C₂×#16864076	C₂	semidirect
7. C₂×#16864073	C₂	semidirect
8. C₂×#16864071	C₂	semidirect
9. C₂×#16864069	C₂	semidirect
10. C₂×#16864020	C₂	semidirect
11. C₂×#16864017	C₂	semidirect
12. C₂×#16864015	C₂	semidirect
13. C₂×#16863969	C₂	semidirect
15. C₂×#16863951	C₂	semidirect
16. C₂×#16863933	C₂	semidirect
17. C₂×#16863932	C₂	semidirect
18. C₂×#16863928	C₂	semidirect
19. C₂×#16863927	C₂	semidirect
20. C₂×#124×D₆₇	C₂	semidirect
21. C₂×#16863872	C₂	semidirect
22. C₂×#16863868	C₂	semidirect
23. C₂×#16863864	C₂	semidirect
24. C₂×#542×C₆₇	C₂	semidirect
28. #16864130	C₂²	semidirect
29. #16864128	C₂²	semidirect
30. #16864117	C₂²	semidirect
31. #16864113	C₂²	semidirect
32. #16864076	C₂²	semidirect
33. #16864073	C₂²	semidirect
34. #16864071	C₂²	semidirect
35. #16864069	C₂²	semidirect
36. #16864020	C₂²	semidirect
37. #16864017	C₂²	semidirect
38. #16864015	C₂²	semidirect
39. #16863969	C₂²	semidirect
41. #16863951	C₂²	semidirect
42. C₂×#14524043	C₂²	semidirect
43. C₂×#14524042	C₂²	semidirect
45. #16863933	C₂²	semidirect
46. #16863932	C₂²	semidirect
47. #16863928	C₂²	semidirect
48. #16863927	C₂²	semidirect
49. C₂×#14524038	C₂²	semidirect
50. C₂×#14524038	C₂²	semidirect
51. C₂×#14524038	C₂²	semidirect
52. C₂×#14524038	C₂²	semidirect
53. C₂×#14524036	C₂²	semidirect
54. C₂×#14524036	C₂²	semidirect
55. C₂×#14524036	C₂²	semidirect
56. C₂×#14524034	C₂²	semidirect
57. C₂×#14524034	C₂²	semidirect
59. C₂×#14524032	C₂²	semidirect
65. C₂×#14524029	C₂²	semidirect
66. C₂×#14524029	C₂²	semidirect
67. C₂×#14524029	C₂²	semidirect
68. #124×D₆₇	C₂²	semidirect
70. C₂×#14524028	C₂²	semidirect
71. C₂×#14524028	C₂²	semidirect
72. C₂×#14524027	C₂²	semidirect
73. C₂×#14524027	C₂²	semidirect
75. C₂×#14524025	C₂²	semidirect
76. C₂×#14524025	C₂²	semidirect
77. C₂×#14524024	C₂²	semidirect
79. C₂×#14524023	C₂²	semidirect
80. C₂×#14524022	C₂²	semidirect
81. C₂×#14524021	C₂²	semidirect
82. C₂×#14524020	C₂²	semidirect
84. C₂×#14524019	C₂²	semidirect
85. C₂×#14524019	C₂²	semidirect
91. #16863872	C₂²	semidirect
92. #16863868	C₂²	semidirect
93. #16863864	C₂²	semidirect
94. C₂×Q₈×Dic₆₇	C₂²	semidirect
95. C₂×Q₈×Dic₆₇	C₂²	semidirect
96. C₂×C₄×Dic₁₃₄	C₂²	semidirect
97. C₂×C₄×Dic₁₃₄	C₂²	semidirect
98. C₂×#14524008	C₂²	semidirect
99. C₂×#14524008	C₂²	semidirect
100. C₂×#14524008	C₂²	semidirect
101. C₂×#14524008	C₂²	semidirect
102. C₂×#14524008	C₂²	semidirect
104. C₂×C₄×D₂₆₈	C₂²	semidirect
106. C₂×D₄×Dic₆₇	C₂²	semidirect
111. C₂×C₄×C₂²⋊D₆₇	C₂²	semidirect
115. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
116. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
117. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
118. C₂×#14524002	C₂²	semidirect
122. C₂×#14524001	C₂²	semidirect
125. C₂×#14524000	C₂²	semidirect
126. C₂×#14524000	C₂²	semidirect
127. C₂×#14523999	C₂²	semidirect
132. C₂²×C₄×Dic₆₇	C₂²	semidirect
134. C₂×C₄²×D₆₇	C₂²	semidirect
135. #542×C₆₇	C₂²	semidirect
136. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
137. C₂×#126×C₆₇	C₂²	semidirect
139. C₂×#124×C₆₇	C₂²	semidirect
140. C₂×#123×C₆₇	C₂²	semidirect
141. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
142. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
144. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
146. C₂×#117×C₆₇	C₂²	semidirect
178. #14524043	C₂³	semidirect
179. #14524042	C₂³	semidirect
181. #14524038	C₂³	semidirect
182. #14524038	C₂³	semidirect
183. #14524038	C₂³	semidirect
184. #14524038	C₂³	semidirect
185. #14524036	C₂³	semidirect
186. #14524036	C₂³	semidirect
187. #14524036	C₂³	semidirect
188. #14524034	C₂³	semidirect
189. #14524034	C₂³	semidirect
191. #14524032	C₂³	semidirect
197. #14524029	C₂³	semidirect
198. #14524029	C₂³	semidirect
199. #14524029	C₂³	semidirect
201. #14524028	C₂³	semidirect
202. #14524028	C₂³	semidirect
203. #14524027	C₂³	semidirect
204. #14524027	C₂³	semidirect
206. #14524025	C₂³	semidirect
207. #14524025	C₂³	semidirect
208. #14524024	C₂³	semidirect
210. #14524023	C₂³	semidirect
211. #14524022	C₂³	semidirect
212. #14524021	C₂³	semidirect
213. #14524020	C₂³	semidirect
215. #14524019	C₂³	semidirect
216. #14524019	C₂³	semidirect
222. Q₈×Dic₆₇	C₂³	semidirect
223. Q₈×Dic₆₇	C₂³	semidirect
224. C₄×Dic₁₃₄	C₂³	semidirect
225. C₄×Dic₁₃₄	C₂³	semidirect
226. #14524008	C₂³	semidirect
227. #14524008	C₂³	semidirect
228. #14524008	C₂³	semidirect
229. #14524008	C₂³	semidirect
230. #14524008	C₂³	semidirect
232. C₄×D₂₆₈	C₂³	semidirect
234. D₄×Dic₆₇	C₂³	semidirect
239. C₄×C₂²⋊D₆₇	C₂³	semidirect
243. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
244. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
245. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
246. #14524002	C₂³	semidirect
250. #14524001	C₂³	semidirect
253. #14524000	C₂³	semidirect
254. #14524000	C₂³	semidirect
255. #14523999	C₂³	semidirect
311. C₂×C₄×Dic₆₇	C₂³	semidirect
313. C₄²×D₆₇	C₂³	semidirect
320. C₄⋊Q₈×C₆₇	C₂³	semidirect
321. #126×C₆₇	C₂³	semidirect
323. #124×C₆₇	C₂³	semidirect
324. #123×C₆₇	C₂³	semidirect
325. C₂²⋊Q₈×C₆₇	C₂³	semidirect
326. C₂²⋊Q₈×C₆₇	C₂³	semidirect
328. C₄×Q₈×C₆₇	C₂³	semidirect
330. #117×C₆₇	C₂³	semidirect
643. C₂×C₆₇	#3510	semidirect
662. C₂×#542	D₆₇	semidirect
674. C₆₇	C₂×#3510	semidirect
689. #542	C₂×D₆₇	semidirect
695. C₂×C₄⋊Q₈	C₂×D₆₇	semidirect
708. C₂×#126	C₂×D₆₇	semidirect
723. C₂×#124	C₂×D₆₇	semidirect
733. C₂×#123	C₂×D₆₇	semidirect
742. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
743. C₂×C₂²⋊Q₈	C₂×D₆₇	semidirect
762. C₂×C₄×Q₈	C₂×D₆₇	semidirect
789. C₂×#117	C₂×D₆₇	semidirect
836. C₄⋊Q₈	C₂²×D₆₇	semidirect
845. #126	C₂²×D₆₇	semidirect
859. #124	C₂²×D₆₇	semidirect
869. #123	C₂²×D₆₇	semidirect
878. C₂²⋊Q₈	C₂²×D₆₇	semidirect
879. C₂²⋊Q₈	C₂²×D₆₇	semidirect
895. C₄×Q₈	C₂²×D₆₇	semidirect
922. #117	C₂²×D₆₇	semidirect
1295. C₂	#22574101	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574101	2
C₂×#16864130	2
C₂×#16864128	2
C₂×#16864117	2
C₂×#16864113	2
C₂×#16864076	2
C₂×#16864073	2
C₂×#16864071	2
C₂×#16864069	2
C₂×#16864020	2
C₂×#16864017	2
C₂×#16864015	2
C₂×#16863969	2
C₂×#16863962	2
C₂×#16863951	2
C₂×#16863933	2
C₂×#16863932	2
C₂×#16863928	2
C₂×#16863927	2
C₂×#124×D₆₇	2
C₂×#16863872	2
C₂×#16863868	2
C₂×#16863864	2
C₂×#542×C₆₇	2
C₂×#3510	67

Subgroups — C2×#22574101 #31764320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574101 #31764320