Subgroups — #14219758

Order 1792.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3481	C₂	1	1	yes	maximal, characteristic
2	#11740725	C₂	1	1	yes	maximal, characteristic, complemented
3	#11740722	C₂	1	1	yes	maximal, characteristic, complemented
4	#11740578	C₂	1	2	yes	maximal, complemented
5	#11740577	C₂	1	1	yes	maximal, characteristic, complemented
6	#11740576	C₂	1	1	yes	maximal, characteristic, complemented
7	#11740574	C₂	1	1	yes	maximal, characteristic, complemented
8	#11740572	C₂	1	2	yes	maximal, complemented
9	#11740571	C₂	1	1	yes	maximal, characteristic, complemented
10	#11740366	C₂	1	2	yes	maximal, complemented
11	#11740364	C₂	1	2	yes	maximal, complemented
12	#11740363	C₂	1	2	yes	maximal, complemented
13	#11740362	C₂	1	2	yes	maximal, complemented
14	#11739967	C₂	1	1	yes	maximal, characteristic, complemented
15	#11739966	C₂	1	1	yes	maximal, characteristic, complemented
16	#11739964	C₂	1	1	yes	maximal, characteristic, complemented
17	#11739962	C₂	1	1	yes	maximal, characteristic, complemented
18	#11739749	C₂	1	1	yes	maximal, characteristic, complemented
19	#11739748	C₂	1	1	yes	maximal, characteristic, complemented
20	#11739747	C₂	1	2	yes	maximal, complemented
21	D₄×#1136	C₂	1	2	yes	maximal, complemented
22	D₄×#1136	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#89784	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#559	C₄	1	1	yes	characteristic
25	C₇×#554	C₄	1	1	yes	characteristic
26	C₇×#554	C₄	1	1	yes	characteristic
27	C₇×#553	C₄	1	1	yes	characteristic
28	C₇×#553	C₄	1	1	yes	characteristic
29	C₇×#553	C₄	1	2	yes	—
30	C₇×#551	C₄	1	2	yes	—
31	C₇×#551	C₄	1	2	yes	—
32	C₇×#546	C₄	1	2	yes	—
33	C₇×#546	C₄	1	1	yes	characteristic
34	C₇×#546	C₄	1	1	yes	characteristic
35	C₇×D₄²	C₄	1	1	yes	characteristic
36	C₇×#532	C₂²	1	1	yes	characteristic
37	C₇×#529	C₂²	1	1	yes	characteristic
38	C₇×#529	C₂²	1	2	yes	—
39	C₇×#529	C₂²	1	1	yes	characteristic
40	C₇×#525	C₂²	1	2	yes	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₄×C₇×#41	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
46	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
47	C₂×#6511	C₂²	1	2	yes	complemented
48	C₂²×#1136	C₂²	1	2	yes	complemented
49	C₂²×#1136	C₂²	1	2	yes	complemented
50	#90006	C₂²	1	2	yes	complemented
51	#90006	C₂²	1	2	yes	complemented
52	#90006	C₂²	1	2	yes	complemented
53	#89979	C₂²	1	2	yes	complemented
54	#89979	C₂²	1	2	yes	complemented
55	#89979	C₂²	1	2	yes	complemented
56	#89979	C₂²	1	2	yes	complemented
57	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊(C₇⋊C₈)	C₂²	1	2	yes	complemented
59	#89796	C₂²	1	1	yes	characteristic, complemented
60	#89796	C₂²	1	1	yes	characteristic, complemented
61	#89796	C₂²	1	1	yes	characteristic, complemented
62	#89796	C₂²	1	1	yes	characteristic, complemented
63	#89796	C₂²	1	2	yes	complemented
64	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	Q₈×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	#89784	C₂²	1	1	yes	characteristic
67	#89784	C₂²	1	1	yes	characteristic
68	#89784	C₂²	1	1	yes	characteristic
69	#89784	C₂²	1	1	yes	characteristic
70	#89784	C₂²	1	1	yes	characteristic, complemented
71	#89784	C₂²	1	1	yes	characteristic, complemented
72	#89784	C₂²	1	1	yes	characteristic, complemented
73	#89784	C₂²	1	1	yes	characteristic, complemented
74	#89784	C₂²	1	1	yes	characteristic, complemented
75	#89784	C₂²	1	1	yes	characteristic, complemented
76	#89784	C₂²	1	2	yes	complemented
77	#89784	C₂²	1	2	yes	complemented
78	#89784	C₂²	1	2	yes	complemented
79	#89784	C₂²	1	2	yes	complemented
80	#89784	C₂²	1	2	yes	complemented
81	#89784	C₂²	1	2	yes	complemented
82	#89784	C₂²	1	2	yes	complemented
83	#89784	C₂²	1	2	yes	complemented
84	#89783	C₂²	1	1	yes	characteristic
85	#89783	C₂²	1	1	yes	characteristic
86	#89783	C₂²	1	2	yes	—
87	#89783	C₂²	1	2	yes	complemented
88	#89783	C₂²	1	2	yes	complemented
89	#89783	C₂²	1	2	yes	complemented
90	#89783	C₂²	1	2	yes	complemented
91	#89783	C₂²	1	1	yes	characteristic, complemented
92	#89783	C₂²	1	1	yes	characteristic, complemented
93	#89783	C₂²	1	2	yes	complemented
94	#89783	C₂²	1	2	yes	complemented
95	#89783	C₂²	1	2	yes	complemented
96	#89783	C₂²	1	2	yes	complemented
97	#89783	C₂²	1	2	yes	complemented
98	#89783	C₂²	1	2	yes	complemented
99	#89783	C₂²	1	2	yes	complemented
100	#89783	C₂²	1	2	yes	complemented
101	#89783	C₂²	1	2	yes	complemented
102	#89783	C₂²	1	2	yes	complemented
103	#89783	C₂²	1	2	yes	complemented
104	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
105	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
106	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
107	D₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
108	D₄×C₇⋊C₈	C₂²	1	2	yes	complemented
109	D₄×C₇⋊C₈	C₂²	1	2	yes	complemented
110	D₄×C₇⋊C₈	C₂²	1	2	yes	complemented
111	#89772	C₂²	1	2	yes	complemented
112	#89772	C₂²	1	2	yes	complemented
113	#89772	C₂²	1	2	yes	complemented
114	#89772	C₂²	1	2	yes	complemented
115	#89771	C₂²	1	2	yes	complemented
116	#89771	C₂²	1	2	yes	complemented
117	#89769	C₂²	1	2	yes	complemented
118	#89769	C₂²	1	2	yes	complemented
119	#89698	C₂²	1	1	yes	characteristic, complemented
120	#89698	C₂²	1	2	yes	complemented
121	#89698	C₂²	1	2	yes	complemented
122	#89698	C₂²	1	1	yes	characteristic, complemented
123	#89697	C₂²	1	1	yes	characteristic, complemented
124	#89697	C₂²	1	1	yes	characteristic, complemented
125	#89697	C₂²	1	1	yes	characteristic, complemented
126	#89697	C₂²	1	1	yes	characteristic, complemented
127	#89696	C₂²	1	2	yes	complemented
128	#89696	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
131	C₄×#1136	C₂²	1	1	yes	characteristic, complemented
132	C₄×#1136	C₂²	1	1	yes	characteristic, complemented
133	C₄×#1136	C₂²	1	2	yes	complemented
134	C₂×C₄×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
135	#60324	—	7	1	no	maximal, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
142	C₂³×C₄×C₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₇	C₂³	1	2	yes	—
144	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
145	C₇×#127	C₂×C₄	1	1	yes	characteristic
146	C₇×#126	C₂×C₄	1	2	yes	—
147	C₇×#126	C₂×C₄	1	2	yes	—
148	C₇×#126	C₂×C₄	1	2	yes	—
149	C₇×#126	C₂×C₄	1	2	yes	—
150	C₇×#125	C₂×C₄	1	1	yes	characteristic
151	C₇×#125	C₂×C₄	1	2	yes	—
152	C₇×#125	C₂×C₄	1	1	yes	characteristic
153	C₇×#124	C₂×C₄	1	1	yes	characteristic
154	C₇×#124	C₂×C₄	1	1	yes	characteristic
155	C₇×#124	C₂×C₄	1	2	yes	—
156	C₇×#124	C₂×C₄	1	2	yes	—
157	C₇×#123	C₂×C₄	1	2	yes	—
158	C₇×#123	C₂×C₄	1	2	yes	—
159	C₇×#123	C₂×C₄	1	2	yes	—
160	C₇×#123	C₂×C₄	1	2	yes	—
161	C₇×#123	C₂×C₄	1	2	yes	—
162	C₇×#123	C₂×C₄	1	2	yes	—
163	C₇×#123	C₂×C₄	1	2	yes	—
164	C₇×#123	C₂×C₄	1	2	yes	—
165	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
166	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
167	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
168	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
169	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
170	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
171	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
172	C₇×#121	C₂×C₄	1	2	yes	—
173	C₇×#121	C₂×C₄	1	2	yes	—
174	C₇×#121	C₂×C₄	1	2	yes	—
175	C₇×#121	C₂×C₄	1	2	yes	—
176	C₇×#121	C₂×C₄	1	1	yes	characteristic
177	C₇×#121	C₂×C₄	1	1	yes	characteristic
178	C₇×#121	C₂×C₄	1	2	yes	—
179	C₇×#121	C₂×C₄	1	1	yes	characteristic
180	C₇×#121	C₂×C₄	1	1	yes	characteristic
181	C₇×#121	C₂×C₄	1	2	yes	—
182	C₇×#120	C₂×C₄	1	2	yes	—
183	C₇×#120	C₂×C₄	1	2	yes	—
184	C₇×#120	C₂×C₄	1	2	yes	—
185	C₇×#120	C₂×C₄	1	2	yes	—
186	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
187	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
188	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
189	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
190	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
191	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
192	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
193	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
194	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
195	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
196	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
197	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
198	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
199	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
200	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
201	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
202	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
203	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
204	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
205	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
206	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
207	C₄×C₇×D₄	C₂³	1	2	yes	—
208	C₄×C₇×D₄	C₂³	1	2	yes	—
209	C₄×C₇×D₄	C₂³	1	2	yes	—
210	C₄×C₇×D₄	C₂³	1	2	yes	—
211	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
212	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
213	C₄×C₇×D₄	C₂³	1	2	yes	—
214	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
215	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
216	C₄×C₇×D₄	C₂³	1	2	yes	—
217	C₇×#117	C₂×C₄	1	1	yes	characteristic
218	C₇×#117	C₂×C₄	1	1	yes	characteristic
219	C₇×#117	C₂×C₄	1	2	yes	—
220	C₇×#117	C₂×C₄	1	1	yes	characteristic
221	C₇×#117	C₂×C₄	1	1	yes	characteristic
222	C₇×#117	C₂³	1	2	yes	—
223	C₇×#117	C₂³	1	2	yes	—
224	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
225	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
226	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
227	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
228	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
229	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
230	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇	C₂³	1	2	yes	—
235	#6511	—	4	4	no	—
236	C₂×#1136	—	4	4	no	—
237	C₂×#1136	—	4	4	no	—
238	C₂×#1136	C₂³	1	1	yes	characteristic
239	C₂×#1136	C₂³	1	2	yes	—
240	C₂×#1136	C₂³	1	1	yes	characteristic
241	C₂×#1136	C₂³	1	2	yes	—
242	C₂×#1136	C₂³	1	1	yes	characteristic
243	C₂×#1136	C₂³	1	2	yes	—
244	C₂×#1136	C₂³	1	1	yes	characteristic
245	C₂×#1136	C₂³	1	2	yes	—
246	C₂×#1136	C₂³	1	2	yes	—
247	C₂×#1136	C₂³	1	2	yes	—
248	C₂×#1136	C₂³	1	2	yes	—
249	C₂×#1136	C₂³	1	2	yes	—
250	C₂×#1136	C₂³	1	2	yes	—
251	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
252	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
253	C₂²×C₇⋊C₈	C₂³	1	1	yes	characteristic
254	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
255	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
256	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
257	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
258	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
259	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
260	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
261	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
262	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
263	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
264	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
265	C₂²⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
266	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
267	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
268	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
269	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
270	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
271	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
272	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
273	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
274	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
275	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
276	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
277	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
278	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
279	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
280	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
281	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
282	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
283	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
284	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
285	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
286	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
287	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
288	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
289	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
290	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
291	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
292	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
293	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
294	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
295	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
296	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
297	#6377	C₂³	1	1	yes	characteristic
298	#6377	C₂³	1	1	yes	characteristic
299	#6377	C₂³	1	2	yes	—
300	#6377	C₂³	1	1	yes	characteristic
301	#6377	C₂³	1	1	yes	characteristic
302	#6377	C₂³	1	2	yes	—
303	#6377	C₂³	1	2	yes	—
304	#6377	C₂³	1	2	yes	—
305	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
306	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
307	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
308	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
309	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
310	C₄×C₇⋊C₈	C₂³	1	1	yes	characteristic
311	C₄×C₇⋊C₈	C₂³	1	2	yes	—
312	C₄×C₇⋊C₈	C₂³	1	2	yes	—
313	C₄×C₇⋊C₈	C₂³	1	2	yes	—
314	#3481	D₇	1	1	yes	characteristic
315	#2995	—	7	2	no	—
316	#2994	—	7	1	no	—
317	#2993	—	7	1	no	—
318	#2990	—	7	1	no	—
319	#2989	—	7	1	no	—
320	#2981	—	7	1	no	—
321	#2978	—	7	2	no	—
322	#2976	—	7	2	no	—
323	#2975	—	7	1	no	—
324	#2974	—	7	1	no	—
325	#2973	—	7	2	no	—
326	#2971	—	7	1	no	—
327	#2969	—	7	1	no	—
328	#2967	—	7	2	no	—
329	#2966	—	7	1	no	—
330	#2965	—	7	1	no	—
331	#2935	—	7	1	no	—
332	D₄×M₁₆	—	7	2	no	—
333	D₄×M₁₆	—	7	1	no	—
334	#2933	—	7	2	no	—
335	#2930	—	7	2	no	—
336	C₂×#436	—	7	1	no	—
337	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
338	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
339	C₇×#41	—	4	2	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
346	C₂×C₇×D₄	—	4	2	no	—
347	C₂×C₇×D₄	—	4	2	no	—
348	C₂×C₇×D₄	—	4	4	no	—
349	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
350	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
351	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
352	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
353	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
354	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
355	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
356	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
357	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
358	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
359	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
360	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
361	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
362	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
363	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
364	C₂²×C₄×C₇	—	4	2	no	—
365	C₂²×C₄×C₇	—	4	2	no	—
366	C₂²×C₄×C₇	—	4	2	no	—
367	C₂²×C₄×C₇	—	4	2	no	—
368	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
369	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
370	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
371	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
372	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
373	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
374	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
375	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
376	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
378	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
379	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
380	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
381	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
382	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
386	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
388	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
391	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
393	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
394	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
395	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
398	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
400	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
402	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
403	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
405	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
406	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
407	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
408	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
409	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
411	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
413	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
414	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
415	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
416	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
417	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
418	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
419	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
420	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
421	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
422	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
423	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
424	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
425	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
426	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
427	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
428	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
429	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
430	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
431	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
432	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
433	C₇×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
434	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
435	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
436	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
437	C₄²×C₇	C₂²×C₄	1	2	yes	—
438	C₄²×C₇	C₂²×C₄	1	2	yes	—
439	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
440	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
441	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
442	C₄²×C₇	C₂⁴	1	1	yes	characteristic
443	C₄²×C₇	C₂⁴	1	1	yes	characteristic
444	C₄²×C₇	C₂⁴	1	1	yes	characteristic
445	C₄²×C₇	C₂⁴	1	1	yes	characteristic
446	C₄²×C₇	C₂⁴	1	2	yes	—
447	#1136	—	2	2	no	—
448	#1136	—	2	4	no	—
449	#1136	—	2	4	no	—
450	#1136	—	2	2	no	—
451	#1136	—	4	2	no	—
452	#1136	—	4	2	no	—
453	#1136	—	4	2	no	—
454	#1136	—	4	2	no	—
455	#1136	—	4	1	no	—
456	#1136	—	4	2	no	—
457	#1136	—	4	2	no	—
458	#1136	—	4	1	no	—
459	#1136	—	4	2	no	—
460	C₂×C₇⋊C₈	—	2	2	no	—
461	C₂×C₇⋊C₈	—	2	4	no	—
462	C₂×C₇⋊C₈	—	4	2	no	—
463	C₂×C₇⋊C₈	—	4	1	no	—
464	C₂×C₇⋊C₈	—	4	2	no	—
465	C₂×C₇⋊C₈	—	4	2	no	—
466	C₂×C₇⋊C₈	—	4	2	no	—
467	C₂×C₇⋊C₈	—	4	2	no	—
468	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
469	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
470	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
471	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
472	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
473	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
474	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
475	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
476	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
477	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
478	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
479	C₂×C₇⋊C₈	C₂⁴	1	1	yes	characteristic
480	C₂×#131	—	7	2	no	—
481	C₂²×M₁₆	—	7	2	no	—
482	C₂²×M₁₆	—	7	2	no	—
483	#559	Dic₇	1	1	yes	characteristic
484	#554	Dic₇	1	1	yes	characteristic
485	#554	Dic₇	1	1	yes	characteristic
486	#553	Dic₇	1	1	yes	characteristic
487	#553	Dic₇	1	1	yes	characteristic
488	#553	Dic₇	1	2	yes	—
489	#551	Dic₇	1	2	yes	—
490	#551	Dic₇	1	2	yes	—
491	#546	Dic₇	1	2	yes	—
492	#546	Dic₇	1	1	yes	characteristic
493	#546	Dic₇	1	1	yes	characteristic
494	D₄²	Dic₇	1	1	yes	characteristic
495	#532	C₂×D₇	1	1	yes	characteristic
496	#529	C₂×D₇	1	1	yes	characteristic
497	#529	C₂×D₇	1	2	yes	—
498	#529	C₂×D₇	1	1	yes	characteristic
499	#525	C₂×D₇	1	2	yes	—
500	#525	C₂×D₇	1	2	yes	—
501	C₄×#41	C₂×D₇	1	1	yes	characteristic
502	C₄×#41	C₂×D₇	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂×D₇	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂×D₇	1	2	yes	—
505	C₂×C₄×D₄	C₂×D₇	1	1	yes	characteristic
506	#446	—	7	1	no	—
507	#446	—	7	1	no	—
508	#446	—	7	1	no	—
509	#446	—	7	2	no	—
510	#446	—	7	1	no	—
511	C₈×Q₈	—	7	1	no	—
512	C₈×Q₈	—	7	1	no	—
513	#436	—	7	2	no	—
514	#436	—	7	1	no	—
515	#436	—	7	1	no	—
516	#436	—	7	1	no	—
517	#436	—	7	2	no	—
518	#436	—	7	1	no	—
519	#436	—	7	1	no	—
520	#436	—	7	2	no	—
521	#436	—	7	2	no	—
522	#436	—	7	2	no	—
523	#436	—	7	1	no	—
524	#436	—	7	2	no	—
525	#436	—	7	1	no	—
526	#436	—	7	1	no	—
527	#436	—	7	1	no	—
528	#436	—	7	2	no	—
529	#436	—	7	1	no	—
530	#436	—	7	2	no	—
531	#435	—	7	2	no	—
532	#435	—	7	2	no	—
533	#435	—	7	2	no	—
534	#435	—	7	2	no	—
535	#435	—	7	1	no	—
536	#435	—	7	2	no	—
537	#435	—	7	2	no	—
538	#435	—	7	2	no	—
539	#435	—	7	1	no	—
540	#435	—	7	2	no	—
541	#435	—	7	2	no	—
542	#435	—	7	2	no	—
543	#435	—	7	2	no	—
544	#435	—	7	2	no	—
545	#435	—	7	1	no	—
546	#435	—	7	1	no	—
547	#435	—	7	2	no	—
548	#435	—	7	2	no	—
549	#435	—	7	2	no	—
550	#435	—	7	2	no	—
551	C₈×D₄	—	7	2	no	—
552	C₈×D₄	—	7	2	no	—
553	C₈×D₄	—	7	1	no	—
554	C₈×D₄	—	7	2	no	—
555	C₈×D₄	—	7	1	no	—
556	C₈×D₄	—	7	1	no	—
557	C₈×D₄	—	7	1	no	—
558	#433	—	7	2	no	—
559	#433	—	7	2	no	—
560	#433	—	7	2	no	—
561	#433	—	7	2	no	—
562	#432	—	7	1	no	—
563	#432	—	7	2	no	—
564	#432	—	7	2	no	—
565	#432	—	7	1	no	—
566	#431	—	7	1	no	—
567	#431	—	7	1	no	—
568	#431	—	7	1	no	—
569	#431	—	7	1	no	—
570	#424	—	7	2	no	—
571	#424	—	7	2	no	—
572	#423	—	7	2	no	—
573	#423	—	7	1	no	—
574	C₂×C₄⋊C₈	—	7	1	no	—
575	C₂×C₄⋊C₈	—	7	1	no	—
576	#408	—	7	2	no	—
577	#408	—	7	2	no	—
578	#408	—	7	2	no	—
579	#407	—	7	2	no	—
580	#407	—	7	2	no	—
581	#407	—	7	2	no	—
582	#407	—	7	2	no	—
583	C₂×C₂²⋊C₈	—	7	2	no	—
584	C₂×C₂²⋊C₈	—	7	2	no	—
585	#405	—	7	2	no	—
586	#405	—	7	2	no	—
587	C₄×M₁₆	—	7	1	no	—
588	C₄×M₁₆	—	7	2	no	—
589	C₄×M₁₆	—	7	1	no	—
590	C₂×C₄×C₈	—	7	1	no	—
591	C₂³×C₇	—	2	4	no	—
592	C₂³×C₇	—	4	2	no	—
593	C₂³×C₇	—	4	2	no	—
594	C₂³×C₇	—	4	2	no	—
595	C₂³×C₇	—	4	2	no	—
596	C₂³×C₇	—	4	2	no	—
597	C₂³×C₇	C₂³×C₄	1	2	yes	—
598	C₂³×C₇	C₂³×C₄	1	2	yes	—
599	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
600	C₂³×C₇	C₂³×C₄	1	2	yes	—
601	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
602	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	4	2	no	—
605	C₇×Q₈	—	4	1	no	—
606	C₇×D₄	—	2	2	no	—
607	C₇×D₄	—	2	4	no	—
608	C₇×D₄	—	2	2	no	—
609	C₇×D₄	—	2	2	no	—
610	C₇×D₄	—	2	2	no	—
611	C₇×D₄	—	2	2	no	—
612	C₇×D₄	—	4	2	no	—
613	C₇×D₄	—	4	2	no	—
614	C₇×D₄	—	4	2	no	—
615	C₇×D₄	—	4	2	no	—
616	C₇×D₄	—	4	2	no	—
617	C₇×D₄	—	4	2	no	—
618	C₇×D₄	—	4	2	no	—
619	C₇×D₄	—	4	1	no	—
620	C₇×D₄	—	4	2	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	2	2	no	—
624	C₂×C₄×C₇	—	2	2	no	—
625	C₂×C₄×C₇	—	2	1	no	—
626	C₂×C₄×C₇	—	2	2	no	—
627	C₂×C₄×C₇	—	2	1	no	—
628	C₂×C₄×C₇	—	2	2	no	—
629	C₂×C₄×C₇	—	2	1	no	—
630	C₂×C₄×C₇	—	2	2	no	—
631	C₂×C₄×C₇	—	2	1	no	—
632	C₂×C₄×C₇	—	2	2	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	2	no	—
635	C₂×C₄×C₇	—	2	2	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	4	2	no	—
638	C₂×C₄×C₇	—	4	2	no	—
639	C₂×C₄×C₇	—	4	2	no	—
640	C₂×C₄×C₇	—	4	2	no	—
641	C₂×C₄×C₇	—	4	2	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	—	4	2	no	—
644	C₂×C₄×C₇	—	4	1	no	—
645	C₂×C₄×C₇	—	4	1	no	—
646	C₂×C₄×C₇	—	4	2	no	—
647	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
648	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
649	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
650	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
651	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
653	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
654	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
655	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
657	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
658	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
660	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
661	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
662	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
663	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
664	C₇⋊C₈	—	2	2	no	—
665	C₇⋊C₈	—	2	1	no	—
666	C₇⋊C₈	—	2	2	no	—
667	C₇⋊C₈	—	2	1	no	—
668	C₇⋊C₈	—	2	2	no	—
669	C₇⋊C₈	—	2	1	no	—
670	C₇⋊C₈	—	2	1	no	—
671	C₇⋊C₈	—	2	2	no	—
672	C₇⋊C₈	—	2	1	no	—
673	C₇⋊C₈	—	2	1	no	—
674	C₇⋊C₈	—	2	1	no	—
675	C₇⋊C₈	H(5,𝔽₂)	1	2	yes	—
676	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
677	C₂×#41	C₂×Dic₇	1	1	yes	characteristic
678	C₂×#41	C₂²×D₇	1	2	yes	—
679	C₂²×D₄	C₂×Dic₇	1	1	yes	characteristic
680	C₂²×D₄	C₂×Dic₇	1	1	yes	characteristic
681	C₂²×D₄	C₂×Dic₇	1	2	yes	—
682	C₂³×C₄	C₂²×D₇	1	2	yes	—
683	C₂³×C₄	C₂²×D₇	1	2	yes	—
684	#131	—	28	4	no	—
685	C₂×M₁₆	—	7	2	no	—
686	C₂×M₁₆	—	7	1	no	—
687	C₂×M₁₆	—	7	2	no	—
688	C₂×M₁₆	—	7	1	no	—
689	C₂×M₁₆	—	7	2	no	—
690	C₂×M₁₆	—	7	2	no	—
691	C₂×M₁₆	—	7	2	no	—
692	C₂×M₁₆	—	7	2	no	—
693	C₂×M₁₆	—	7	2	no	—
694	C₂×M₁₆	—	7	1	no	—
695	C₂×M₁₆	—	7	2	no	—
696	C₂×M₁₆	—	7	1	no	—
697	C₂×M₁₆	—	7	2	no	—
698	C₂×M₁₆	—	28	4	no	—
699	C₂×M₁₆	—	28	4	no	—
700	C₂²×C₈	—	7	1	no	—
701	C₂²×C₈	—	7	2	no	—
702	C₂²×C₈	—	7	2	no	—
703	C₂²×C₈	—	7	2	no	—
704	C₂²×C₈	—	7	2	no	—
705	C₂²×C₈	—	7	2	no	—
706	C₂²×C₈	—	7	1	no	—
707	C₂²×C₈	—	7	2	no	—
708	C₄⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
709	#127	C₂×Dic₇	1	1	yes	characteristic
710	#126	C₂×Dic₇	1	2	yes	—
711	#126	C₂×Dic₇	1	2	yes	—
712	#126	C₂×Dic₇	1	2	yes	—
713	#126	C₂×Dic₇	1	2	yes	—
714	#125	C₂×Dic₇	1	1	yes	characteristic
715	#125	C₂×Dic₇	1	2	yes	—
716	#125	C₂×Dic₇	1	1	yes	characteristic
717	#124	C₂×Dic₇	1	1	yes	characteristic
718	#124	C₂×Dic₇	1	1	yes	characteristic
719	#124	C₂×Dic₇	1	2	yes	—
720	#124	C₂×Dic₇	1	2	yes	—
721	#123	C₂×Dic₇	1	2	yes	—
722	#123	C₂×Dic₇	1	2	yes	—
723	#123	C₂×Dic₇	1	2	yes	—
724	#123	C₂×Dic₇	1	2	yes	—
725	#123	C₂×Dic₇	1	2	yes	—
726	#123	C₂×Dic₇	1	2	yes	—
727	#123	C₂×Dic₇	1	2	yes	—
728	#123	C₂×Dic₇	1	2	yes	—
729	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
730	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
731	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
732	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
733	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
734	C₂²⋊Q₈	C₂×Dic₇	1	1	yes	characteristic
735	C₂²⋊Q₈	C₂×Dic₇	1	2	yes	—
736	#121	C₂×Dic₇	1	2	yes	—
737	#121	C₂×Dic₇	1	2	yes	—
738	#121	C₂×Dic₇	1	2	yes	—
739	#121	C₂×Dic₇	1	2	yes	—
740	#121	C₂×Dic₇	1	1	yes	characteristic
741	#121	C₂×Dic₇	1	1	yes	characteristic
742	#121	C₂×Dic₇	1	2	yes	—
743	#121	C₂×Dic₇	1	1	yes	characteristic
744	#121	C₂×Dic₇	1	1	yes	characteristic
745	#121	C₂×Dic₇	1	2	yes	—
746	#120	C₂×Dic₇	1	2	yes	—
747	#120	C₂×Dic₇	1	2	yes	—
748	#120	C₂×Dic₇	1	2	yes	—
749	#120	C₂×Dic₇	1	2	yes	—
750	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
751	C₄×Q₈	C₂×Dic₇	1	1	yes	characteristic
752	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
753	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
754	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
755	C₄×D₄	C₂×Dic₇	1	2	yes	—
756	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
757	C₄×D₄	C₂×Dic₇	1	2	yes	—
758	C₄×D₄	C₂×Dic₇	1	2	yes	—
759	C₄×D₄	C₂×Dic₇	1	2	yes	—
760	C₄×D₄	C₂×Dic₇	1	2	yes	—
761	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
762	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
763	C₄×D₄	C₂×Dic₇	1	2	yes	—
764	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
765	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
766	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
767	C₄×D₄	C₂×Dic₇	1	1	yes	characteristic
768	C₄×D₄	C₂×Dic₇	1	2	yes	—
769	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
770	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
771	C₄×D₄	C₂²×D₇	1	2	yes	—
772	C₄×D₄	C₂²×D₇	1	2	yes	—
773	C₄×D₄	C₂²×D₇	1	2	yes	—
774	C₄×D₄	C₂²×D₇	1	2	yes	—
775	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
776	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
777	C₄×D₄	C₂²×D₇	1	2	yes	—
778	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
779	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
780	C₄×D₄	C₂²×D₇	1	2	yes	—
781	#117	C₂×Dic₇	1	1	yes	characteristic
782	#117	C₂×Dic₇	1	1	yes	characteristic
783	#117	C₂×Dic₇	1	2	yes	—
784	#117	C₂×Dic₇	1	1	yes	characteristic
785	#117	C₂×Dic₇	1	1	yes	characteristic
786	#117	C₂²×D₇	1	2	yes	—
787	#117	C₂²×D₇	1	2	yes	—
788	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂×Dic₇	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂×Dic₇	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂×Dic₇	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂×Dic₇	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂×Dic₇	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂×Dic₇	1	2	yes	—
795	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
796	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
797	C₂×C₄²	C₂²×D₇	1	2	yes	—
798	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
799	C₄⋊C₈	—	7	1	no	—
800	C₄⋊C₈	—	7	1	no	—
801	C₄⋊C₈	—	7	1	no	—
802	C₄⋊C₈	—	7	2	no	—
803	C₄⋊C₈	—	7	2	no	—
804	C₄⋊C₈	—	7	1	no	—
805	C₄⋊C₈	—	7	2	no	—
806	C₄⋊C₈	—	7	2	no	—
807	C₄⋊C₈	—	7	2	no	—
808	C₄⋊C₈	—	7	1	no	—
809	C₄⋊C₈	—	7	1	no	—
810	C₄⋊C₈	—	7	2	no	—
811	C₄⋊C₈	—	7	1	no	—
812	C₄⋊C₈	—	7	1	no	—
813	C₄⋊C₈	—	7	1	no	—
814	C₄⋊C₈	—	7	1	no	—
815	C₄⋊C₈	—	7	2	no	—
816	C₂²⋊C₈	—	7	1	no	—
817	C₂²⋊C₈	—	7	2	no	—
818	C₂²⋊C₈	—	7	2	no	—
819	C₂²⋊C₈	—	7	2	no	—
820	C₂²⋊C₈	—	7	2	no	—
821	C₂²⋊C₈	—	7	2	no	—
822	C₂²⋊C₈	—	7	2	no	—
823	C₂²⋊C₈	—	7	2	no	—
824	C₂²⋊C₈	—	7	1	no	—
825	C₂²⋊C₈	—	7	1	no	—
826	C₂²⋊C₈	—	7	2	no	—
827	C₂²⋊C₈	—	7	1	no	—
828	C₂²⋊C₈	—	7	2	no	—
829	C₂²⋊C₈	—	7	2	no	—
830	C₂²⋊C₈	—	7	2	no	—
831	C₂²⋊C₈	—	7	2	no	—
832	C₂²⋊C₈	—	7	2	no	—
833	C₂²⋊C₈	—	7	2	no	—
834	C₂²⋊C₈	—	7	1	no	—
835	C₂²⋊C₈	—	7	1	no	—
836	C₂²⋊C₈	—	7	2	no	—
837	#97	—	7	1	no	—
838	#97	—	7	1	no	—
839	#97	—	7	2	no	—
840	#97	—	7	1	no	—
841	#97	—	7	1	no	—
842	#97	—	7	2	no	—
843	#97	—	7	2	no	—
844	#97	—	7	2	no	—
845	C₄×C₈	—	7	1	no	—
846	C₄×C₈	—	7	1	no	—
847	C₄×C₈	—	7	1	no	—
848	C₄×C₈	—	7	1	no	—
849	C₄×C₈	—	7	2	no	—
850	C₄×C₈	—	7	1	no	—
851	C₄×C₈	—	7	1	no	—
852	C₄×C₈	—	7	2	no	—
853	C₄×C₈	—	7	2	no	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	1	no	—
857	C₂²×C₇	—	2	2	no	—
858	C₂²×C₇	—	2	2	no	—
859	C₂²×C₇	—	2	2	no	—
860	C₂²×C₇	—	2	1	no	—
861	C₂²×C₇	—	2	1	no	—
862	C₂²×C₇	—	2	1	no	—
863	C₂²×C₇	—	2	1	no	—
864	C₂²×C₇	—	2	2	no	—
865	C₂²×C₇	—	2	1	no	—
866	C₂²×C₇	—	2	2	no	—
867	C₂²×C₇	—	2	2	no	—
868	C₂²×C₇	—	2	2	no	—
869	C₂²×C₇	—	2	2	no	—
870	C₂²×C₇	—	2	2	no	—
871	C₂²×C₇	—	8	4	no	—
872	C₂²×C₇	—	8	4	no	—
873	C₂²×C₇	#568	1	2	yes	—
874	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	2	no	—
877	C₄×C₇	—	2	1	no	—
878	C₄×C₇	—	2	2	no	—
879	C₄×C₇	—	2	2	no	—
880	C₄×C₇	—	2	1	no	—
881	C₄×C₇	—	2	1	no	—
882	C₄×C₇	—	2	1	no	—
883	C₄×C₇	—	2	1	no	—
884	C₄×C₇	—	2	1	no	—
885	C₄×C₇	—	2	1	no	—
886	C₄×C₇	—	2	1	no	—
887	C₄×C₇	—	2	2	no	—
888	C₄×C₇	—	2	1	no	—
889	C₄×C₇	—	2	2	no	—
890	C₄×C₇	#568	1	2	yes	—
891	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
892	C₄×C₇	#585	1	1	yes	characteristic
893	C₂⁴	C₂²×Dic₇	1	2	yes	—
894	C₂⁴	C₂²×Dic₇	1	2	yes	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
900	C₂×Q₈	C₂²×Dic₇	1	1	yes	characteristic
901	C₂×Q₈	C₂²×Dic₇	1	2	yes	—
902	C₂×D₄	—	4	2	no	—
903	C₂×D₄	—	4	2	no	—
904	C₂×D₄	—	4	4	no	—
905	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
906	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
907	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
908	C₂×D₄	C₂²×Dic₇	1	2	yes	—
909	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
910	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
911	C₂×D₄	C₂²×Dic₇	1	1	yes	characteristic
912	C₂×D₄	C₂²×Dic₇	1	2	yes	—
913	C₂×D₄	C₂²×Dic₇	1	2	yes	—
914	C₂×D₄	C₂²×Dic₇	1	2	yes	—
915	C₂×D₄	C₂²×Dic₇	1	2	yes	—
916	C₂×D₄	C₂²×Dic₇	1	2	yes	—
917	C₂×D₄	C₂²×Dic₇	1	2	yes	—
918	C₂×D₄	C₂²×Dic₇	1	2	yes	—
919	C₂×D₄	C₂²×Dic₇	1	2	yes	—
920	C₂²×C₄	—	4	2	no	—
921	C₂²×C₄	—	4	2	no	—
922	C₂²×C₄	—	4	2	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
925	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
926	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
927	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
928	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
929	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
930	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
931	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
932	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
933	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
934	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
935	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
936	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
937	C₂²×C₄	C₂²×Dic₇	1	2	yes	—
938	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
939	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
940	C₂²×C₄	C₂³×D₇	1	2	yes	—
941	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₇	1	2	yes	—
943	C₂²×C₄	C₂³×D₇	1	2	yes	—
944	M₁₆	—	14	2	no	—
945	M₁₆	—	14	4	no	—
946	M₁₆	—	14	4	no	—
947	M₁₆	—	14	2	no	—
948	M₁₆	—	28	1	no	—
949	M₁₆	—	28	2	no	—
950	M₁₆	—	28	2	no	—
951	M₁₆	—	28	1	no	—
952	M₁₆	—	28	2	no	—
953	M₁₆	—	28	2	no	—
954	M₁₆	—	28	2	no	—
955	M₁₆	—	28	2	no	—
956	M₁₆	—	28	2	no	—
957	C₂×C₈	—	7	1	no	—
958	C₂×C₈	—	7	1	no	—
959	C₂×C₈	—	7	1	no	—
960	C₂×C₈	—	7	1	no	—
961	C₂×C₈	—	7	2	no	—
962	C₂×C₈	—	7	1	no	—
963	C₂×C₈	—	7	1	no	—
964	C₂×C₈	—	7	1	no	—
965	C₂×C₈	—	7	1	no	—
966	C₂×C₈	—	7	2	no	—
967	C₂×C₈	—	7	2	no	—
968	C₂×C₈	—	7	2	no	—
969	C₂×C₈	—	14	2	no	—
970	C₂×C₈	—	14	4	no	—
971	C₂×C₈	—	28	2	no	—
972	C₂×C₈	—	28	1	no	—
973	C₂×C₈	—	28	2	no	—
974	C₂×C₈	—	28	2	no	—
975	C₂×C₈	—	28	2	no	—
976	C₂×C₈	—	28	2	no	—
977	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
979	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
980	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
983	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
984	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
985	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
986	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
989	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
994	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
995	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
996	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
997	C₄⋊C₄	C₂²×Dic₇	1	2	yes	—
998	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
999	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1000	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
1001	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1002	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1003	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1004	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1005	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1006	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1007	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1008	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1009	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1010	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1011	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1012	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1013	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
1016	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
1017	C₂²⋊C₄	C₂²×Dic₇	1	1	yes	characteristic
1018	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1019	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1020	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1021	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1022	C₂²⋊C₄	C₂²×Dic₇	1	2	yes	—
1023	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1024	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1025	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1026	C₄²	C₂²×Dic₇	1	2	yes	—
1027	C₄²	C₂²×Dic₇	1	2	yes	—
1028	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1029	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1030	C₄²	C₂²×Dic₇	1	1	yes	characteristic
1031	C₄²	C₂³×D₇	1	1	yes	characteristic
1032	C₄²	C₂³×D₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₇	1	2	yes	—
1034	C₄²	C₂³×D₇	1	1	yes	characteristic
1035	C₄²	C₂³×D₇	1	1	yes	characteristic
1036	C₂×C₇	—	2	2	no	—
1037	C₂×C₇	—	4	1	no	—
1038	C₂×C₇	—	4	2	no	—
1039	C₂×C₇	—	4	2	no	—
1040	C₂×C₇	—	4	1	no	—
1041	C₂×C₇	—	4	2	no	—
1042	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1043	C₂×C₇	C₂×#568	1	1	yes	characteristic
1044	C₂×C₇	C₂×#568	1	1	yes	characteristic
1045	C₂³	—	2	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	C₂³×Dic₇	1	2	yes	—
1052	C₂³	C₂³×Dic₇	1	2	yes	—
1053	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1054	C₂³	C₂³×Dic₇	1	2	yes	—
1055	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1056	C₂³	C₂³×Dic₇	1	1	yes	characteristic
1057	Q₈	—	2	2	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	2	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	4	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	1	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1102	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1103	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1104	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1105	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1106	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1107	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1108	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1109	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1110	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1111	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1112	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1113	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1114	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1115	C₂×C₄	C₂³×Dic₇	1	2	yes	—
1116	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
1117	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
1118	C₈	—	7	2	no	—
1119	C₈	—	14	2	no	—
1120	C₈	—	14	1	no	—
1121	C₈	—	14	1	no	—
1122	C₈	—	14	2	no	—
1123	C₈	—	14	2	no	—
1124	C₈	—	14	1	no	—
1125	C₈	—	14	1	no	—
1126	C₈	—	14	1	no	—
1127	C₈	—	14	1	no	—
1128	C₈	—	14	2	no	—
1129	C₈	—	14	1	no	—
1130	C₇	#60324	1	1	yes	characteristic, complemented, Sylow
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	8	4	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	#90510	1	2	yes	—
1151	C₂²	C₂⁴×Dic₇	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	#90510	1	2	yes	—
1168	C₄	D₇×H(5,𝔽₂)	1	1	yes	characteristic
1169	C₄	#90618	1	1	yes	characteristic
1170	C₂	—	2	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	C₂×#90510	1	1	yes	characteristic
1177	C₂	C₂×#90510	1	1	yes	characteristic
1178	C₂	Dic₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇
commutator, socle	C₂²×C₇	C₂⁴×C₄
Fitting, prime radical	C₇×#3481	C₂
cosocle	C₂×C₄×C₇	C₂⁵
hypercenter	#3481	D₇
hypocenter	C₇	#60324
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #3481

Complements

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

N	H ≅ G/N	type
2. #11740725	C₂	semidirect
3. #11740722	C₂	semidirect
4. #11740578	C₂	semidirect
5. #11740577	C₂	semidirect
6. #11740576	C₂	semidirect
7. #11740574	C₂	semidirect
8. #11740572	C₂	semidirect
9. #11740571	C₂	semidirect
10. #11740366	C₂	semidirect
11. #11740364	C₂	semidirect
12. #11740363	C₂	semidirect
13. #11740362	C₂	semidirect
14. #11739967	C₂	semidirect
15. #11739966	C₂	semidirect
16. #11739964	C₂	semidirect
17. #11739962	C₂	semidirect
18. #11739749	C₂	semidirect
19. #11739748	C₂	semidirect
20. #11739747	C₂	semidirect
21. D₄×#1136	C₂	semidirect
22. D₄×#1136	C₂	semidirect
23. C₂×#89784	C₂	semidirect
47. C₂×#6511	C₂²	semidirect
48. C₂²×#1136	C₂²	semidirect
49. C₂²×#1136	C₂²	semidirect
50. #90006	C₂²	semidirect
51. #90006	C₂²	semidirect
52. #90006	C₂²	semidirect
53. #89979	C₂²	semidirect
54. #89979	C₂²	semidirect
55. #89979	C₂²	semidirect
56. #89979	C₂²	semidirect
57. C₂×C₂²⋊(C₇⋊C₈)	C₂²	semidirect
58. C₂×C₂²⋊(C₇⋊C₈)	C₂²	semidirect
59. #89796	C₂²	semidirect
60. #89796	C₂²	semidirect
61. #89796	C₂²	semidirect
62. #89796	C₂²	semidirect
63. #89796	C₂²	semidirect
64. Q₈×C₇⋊C₈	C₂²	semidirect
65. Q₈×C₇⋊C₈	C₂²	semidirect
70. #89784	C₂²	semidirect
71. #89784	C₂²	semidirect
72. #89784	C₂²	semidirect
73. #89784	C₂²	semidirect
74. #89784	C₂²	semidirect
75. #89784	C₂²	semidirect
76. #89784	C₂²	semidirect
77. #89784	C₂²	semidirect
78. #89784	C₂²	semidirect
79. #89784	C₂²	semidirect
80. #89784	C₂²	semidirect
81. #89784	C₂²	semidirect
82. #89784	C₂²	semidirect
83. #89784	C₂²	semidirect
87. #89783	C₂²	semidirect
88. #89783	C₂²	semidirect
89. #89783	C₂²	semidirect
90. #89783	C₂²	semidirect
91. #89783	C₂²	semidirect
92. #89783	C₂²	semidirect
93. #89783	C₂²	semidirect
94. #89783	C₂²	semidirect
95. #89783	C₂²	semidirect
96. #89783	C₂²	semidirect
97. #89783	C₂²	semidirect
98. #89783	C₂²	semidirect
99. #89783	C₂²	semidirect
100. #89783	C₂²	semidirect
101. #89783	C₂²	semidirect
102. #89783	C₂²	semidirect
103. #89783	C₂²	semidirect
104. D₄×C₇⋊C₈	C₂²	semidirect
105. D₄×C₇⋊C₈	C₂²	semidirect
106. D₄×C₇⋊C₈	C₂²	semidirect
107. D₄×C₇⋊C₈	C₂²	semidirect
108. D₄×C₇⋊C₈	C₂²	semidirect
109. D₄×C₇⋊C₈	C₂²	semidirect
110. D₄×C₇⋊C₈	C₂²	semidirect
111. #89772	C₂²	semidirect
112. #89772	C₂²	semidirect
113. #89772	C₂²	semidirect
114. #89772	C₂²	semidirect
115. #89771	C₂²	semidirect
116. #89771	C₂²	semidirect
117. #89769	C₂²	semidirect
118. #89769	C₂²	semidirect
119. #89698	C₂²	semidirect
120. #89698	C₂²	semidirect
121. #89698	C₂²	semidirect
122. #89698	C₂²	semidirect
123. #89697	C₂²	semidirect
124. #89697	C₂²	semidirect
125. #89697	C₂²	semidirect
126. #89697	C₂²	semidirect
127. #89696	C₂²	semidirect
128. #89696	C₂²	semidirect
129. C₂×C₄⋊(C₇⋊C₈)	C₂²	semidirect
130. C₂×C₄⋊(C₇⋊C₈)	C₂²	semidirect
131. C₄×#1136	C₂²	semidirect
132. C₄×#1136	C₂²	semidirect
133. C₄×#1136	C₂²	semidirect
134. C₂×C₄×C₇⋊C₈	C₂²	semidirect
1130. C₇	#60324	semidirect

Maximal subgroups

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

subgroup	index
C₇×#3481	2
#11740725	2
#11740722	2
#11740578	2
#11740577	2
#11740576	2
#11740574	2
#11740572	2
#11740571	2
#11740366	2
#11740364	2
#11740363	2
#11740362	2
#11739967	2
#11739966	2
#11739964	2
#11739962	2
#11739749	2
#11739748	2
#11739747	2
D₄×#1136	2
C₂×#89784	2
#60324	7