Subgroups — #14219780

Order 1792.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11742906	C₂	1	1	yes	maximal, characteristic
2	C₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
3	#11739966	C₂	1	1	yes	maximal, characteristic, complemented
4	#11737391	C₂	1	2	yes	maximal, complemented
5	#11737385	C₂	1	2	yes	maximal, complemented
6	#11736989	C₂	1	2	yes	maximal, complemented
7	#11736982	C₂	1	2	yes	maximal, complemented
8	#11736936	C₂	1	2	yes	maximal, complemented
9	#11736935	C₂	1	2	yes	maximal, complemented
10	#11736929	C₂	1	2	yes	maximal, complemented
11	#11736927	C₂	1	2	yes	maximal, complemented
12	#11736741	C₂	1	1	yes	maximal, characteristic, complemented
13	#11736740	C₂	1	1	yes	maximal, characteristic, complemented
14	#11736738	C₂	1	1	yes	maximal, characteristic, complemented
15	#11736735	C₂	1	1	yes	maximal, characteristic, complemented
16	#11736734	C₂	1	1	yes	maximal, characteristic, complemented
17	#11736732	C₂	1	1	yes	maximal, characteristic, complemented
18	#11735967	C₂	1	1	yes	maximal, characteristic, complemented
19	M₁₆×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
20	#11735957	C₂	1	1	yes	maximal, characteristic, complemented
21	#11735956	C₂	1	1	yes	maximal, characteristic, complemented
22	#11735903	C₂	1	1	yes	maximal, characteristic, complemented
23	#11735893	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×C₇×#41	C₂²	1	1	yes	characteristic
25	#90524	C₄	1	1	yes	characteristic
26	#90521	C₄	1	1	yes	characteristic
27	C₂×#6470	C₂²	1	2	yes	complemented
28	C₂×D₇×M₁₆	C₂²	1	2	yes	—
29	C₂×#6464	C₂²	1	2	yes	complemented
30	#90273	C₄	1	2	yes	—
31	#90271	C₂²	1	2	yes	—
32	#90253	C₄	1	2	yes	—
33	#90251	C₄	1	2	yes	—
34	#90251	C₄	1	2	yes	—
35	#90239	C₂²	1	2	yes	—
36	#90238	C₂²	1	2	yes	—
37	#90238	C₂²	1	2	yes	—
38	#90226	C₄	1	1	yes	characteristic
39	#90226	C₄	1	1	yes	characteristic
40	#90225	C₄	1	1	yes	characteristic
41	#90225	C₄	1	1	yes	characteristic
42	#90216	C₄	1	1	yes	characteristic
43	#90210	C₄	1	1	yes	characteristic
44	#90170	C₂²	1	1	yes	characteristic
45	#90170	C₂²	1	1	yes	characteristic
46	#90168	C₂²	1	1	yes	characteristic
47	#90168	C₂²	1	1	yes	characteristic
48	C₄×#1157	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₂₈	C₂²	1	1	yes	characteristic
50	C₇×#446	C₂²	1	1	yes	characteristic, complemented
51	C₇×#446	C₂²	1	1	yes	characteristic, complemented
52	C₇×#436	C₂²	1	1	yes	characteristic
53	C₇×#436	C₂²	1	1	yes	characteristic
54	C₇×#435	C₂²	1	1	yes	characteristic
55	C₇×#435	C₂²	1	1	yes	characteristic
56	C₇×#435	C₂²	1	1	yes	characteristic, complemented
57	C₇×#435	C₂²	1	1	yes	characteristic, complemented
58	C₇×#431	C₂²	1	1	yes	characteristic
59	C₇×#431	C₂²	1	1	yes	characteristic, complemented
60	C₇×#431	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
62	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
64	#89901	C₂²	1	2	yes	complemented
65	#89900	C₂²	1	2	yes	—
66	#89900	C₂²	1	2	yes	—
67	#89900	C₂²	1	2	yes	complemented
68	#89899	C₂²	1	2	yes	complemented
69	#89898	C₂²	1	2	yes	—
70	#89883	C₂²	1	2	yes	complemented
71	#89882	C₂²	1	2	yes	complemented
72	C₈×C₂²⋊D₇	C₂²	1	2	yes	complemented
73	#89796	C₂²	1	2	yes	complemented
74	#89784	C₂²	1	2	yes	—
75	#89783	C₂²	1	2	yes	—
76	#89783	C₂²	1	2	yes	complemented
77	#89698	C₂²	1	1	yes	characteristic
78	#89698	C₂²	1	1	yes	characteristic, complemented
79	#89697	C₂²	1	1	yes	characteristic, complemented
80	#89696	C₂²	1	1	yes	characteristic
81	#89696	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊(C₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
83	#89612	C₂²	1	2	yes	complemented
84	#89612	C₂²	1	2	yes	complemented
85	#89611	C₂²	1	2	yes	complemented
86	#89611	C₂²	1	2	yes	complemented
87	#89610	C₂²	1	2	yes	complemented
88	#89608	C₂²	1	2	yes	—
89	#89608	C₂²	1	2	yes	—
90	#89608	C₂²	1	2	yes	complemented
91	#89608	C₂²	1	2	yes	complemented
92	#89607	C₂²	1	2	yes	complemented
93	#89606	C₂²	1	2	yes	complemented
94	D₇×C₄⋊C₈	C₂²	1	2	yes	complemented
95	#89502	C₂²	1	2	yes	complemented
96	#89501	C₂²	1	2	yes	complemented
97	#89500	C₂²	1	2	yes	—
98	#89500	C₂²	1	2	yes	—
99	#89500	C₂²	1	2	yes	complemented
100	#89499	C₂²	1	2	yes	complemented
101	#89499	C₂²	1	2	yes	complemented
102	#89499	C₂²	1	2	yes	complemented
103	#89499	C₂²	1	2	yes	complemented
104	#89498	C₂²	1	2	yes	—
105	(C₂²⋊D₇)⋊C₈	C₂²	1	2	yes	complemented
106	D₇×C₂²⋊C₈	C₂²	1	2	yes	—
107	#89481	C₂²	1	2	yes	complemented
108	#89480	C₂²	1	2	yes	complemented
109	#89479	C₂²	1	2	yes	complemented
110	#89478	C₂²	1	2	yes	—
111	#89478	C₂²	1	2	yes	—
112	#89478	C₂²	1	2	yes	complemented
113	#89478	C₂²	1	2	yes	complemented
114	#89477	C₂²	1	2	yes	complemented
115	#89462	C₂²	1	2	yes	complemented
116	#89461	C₂²	1	2	yes	complemented
117	#89460	C₂²	1	1	yes	characteristic
118	#89460	C₂²	1	1	yes	characteristic
119	#89460	C₂²	1	1	yes	characteristic
120	#89460	C₂²	1	1	yes	characteristic
121	#89460	C₂²	1	2	yes	complemented
122	#89460	C₂²	1	1	yes	characteristic, complemented
123	#89460	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₂₈	C₂²	1	1	yes	characteristic
125	C₈×D₂₈	C₂²	1	1	yes	characteristic
126	C₈×D₂₈	C₂²	1	1	yes	characteristic
127	C₈×D₂₈	C₂²	1	1	yes	characteristic
128	C₈×D₂₈	C₂²	1	2	yes	complemented
129	C₈×D₂₈	C₂²	1	1	yes	characteristic, complemented
130	C₈×D₂₈	C₂²	1	1	yes	characteristic, complemented
131	#89451	C₂²	1	1	yes	characteristic, complemented
132	#89451	C₂²	1	1	yes	characteristic, complemented
133	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
134	C₈×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
135	#60326	—	7	1	no	maximal, Sylow
136	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
137	C₂×#1157	C₂×C₄	1	1	yes	characteristic
138	C₂×#1157	C₂³	1	2	yes	—
139	C₂×#1157	C₂³	1	2	yes	—
140	C₂²×D₂₈	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₄×D₇	C₂³	1	2	yes	—
142	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
146	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
148	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
149	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
151	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
152	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
153	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
154	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
155	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
156	C₇×#117	C₂×C₄	1	1	yes	characteristic
157	C₇×#117	C₂×C₄	1	1	yes	characteristic
158	C₇×#117	C₂×C₄	1	1	yes	characteristic
159	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
162	#6510	C₂×C₄	1	2	yes	—
163	#6509	C₂×C₄	1	2	yes	—
164	#6503	C₂×C₄	1	2	yes	—
165	#6502	C₂×C₄	1	2	yes	—
166	#6502	C₂×C₄	1	2	yes	—
167	#6501	C₂×C₄	1	2	yes	—
168	#6500	C₂×C₄	1	2	yes	—
169	#6500	C₂×C₄	1	2	yes	—
170	#6493	C₂×C₄	1	1	yes	characteristic
171	#6493	C₂×C₄	1	1	yes	characteristic
172	#6493	C₂×C₄	1	1	yes	characteristic
173	#6493	C₂×C₄	1	1	yes	characteristic
174	#6493	C₂×C₄	1	2	yes	—
175	#6493	C₂×C₄	1	2	yes	—
176	#6493	C₂×C₄	1	1	yes	characteristic
177	#6493	C₂×C₄	1	1	yes	characteristic
178	#6492	C₂×C₄	1	2	yes	—
179	#6492	C₂×C₄	1	2	yes	—
180	C₄×C₂²⋊D₇	C₂×C₄	1	2	yes	—
181	C₄×C₂²⋊D₇	C₂³	1	2	yes	—
182	C₄×C₂²⋊D₇	C₂³	1	2	yes	—
183	C₄×C₂²⋊D₇	C₂³	1	2	yes	—
184	C₂×(C₂×D₇)⋊C₄	C₂×C₄	1	2	yes	—
185	#6489	C₂×C₄	1	1	yes	characteristic
186	C₂×C₄⋊Dic₇	C₂×C₄	1	1	yes	characteristic
187	#6487	C₂×C₄	1	1	yes	characteristic
188	#6487	C₂×C₄	1	1	yes	characteristic
189	C₂×#1136	C₂³	1	2	yes	—
190	C₂×#1136	C₂³	1	2	yes	—
191	C₂²×C₇⋊C₈	C₂³	1	2	yes	—
192	#6470	—	4	4	no	—
193	D₇×M₁₆	—	4	4	no	—
194	#6464	—	4	4	no	—
195	C₂×#1131	C₂³	1	2	yes	—
196	C₂×#1131	C₂³	1	2	yes	—
197	C₂×#1131	C₂³	1	2	yes	—
198	C₂×#1131	C₂³	1	2	yes	—
199	C₂×#1131	C₂³	1	2	yes	—
200	C₂×#1131	C₂³	1	2	yes	—
201	C₂×C₈×D₇	C₂³	1	2	yes	—
202	C₂×C₈×D₇	C₂³	1	2	yes	—
203	C₂×C₈×D₇	C₂³	1	2	yes	—
204	C₂×C₈×D₇	C₂³	1	2	yes	—
205	C₂×C₈×D₇	C₂³	1	2	yes	—
206	C₂×C₈×D₇	C₂³	1	2	yes	—
207	#6461	C₂×C₄	1	2	yes	—
208	#6461	C₂×C₄	1	2	yes	—
209	#6459	C₂×C₄	1	2	yes	—
210	#6459	C₂×C₄	1	2	yes	—
211	#6458	C₂×C₄	1	2	yes	—
212	#6458	C₂×C₄	1	2	yes	—
213	#6457	C₂×C₄	1	2	yes	—
214	#6457	C₂×C₄	1	2	yes	—
215	#6457	C₂×C₄	1	2	yes	—
216	#6457	C₂×C₄	1	2	yes	—
217	#6453	C₂×C₄	1	2	yes	—
218	#6451	C₂×C₄	1	2	yes	—
219	#6448	C₂×C₄	1	2	yes	—
220	#6448	C₂×C₄	1	2	yes	—
221	#6447	C₂×C₄	1	2	yes	—
222	#6447	C₂×C₄	1	2	yes	—
223	#6447	C₂×C₄	1	2	yes	—
224	#6447	C₂×C₄	1	2	yes	—
225	#6446	C₂×C₄	1	2	yes	—
226	#6446	C₂×C₄	1	2	yes	—
227	#6445	C₂×C₄	1	2	yes	—
228	#6445	C₂×C₄	1	2	yes	—
229	#6441	C₂×C₄	1	2	yes	—
230	#6441	C₂×C₄	1	2	yes	—
231	#6439	C₂×C₄	1	2	yes	—
232	#6439	C₂×C₄	1	2	yes	—
233	#6438	C₂×C₄	1	2	yes	—
234	#6438	C₂×C₄	1	2	yes	—
235	#6438	C₂×C₄	1	1	yes	characteristic
236	#6438	C₂×C₄	1	1	yes	characteristic
237	#6437	C₂×C₄	1	1	yes	characteristic
238	#6437	C₂×C₄	1	1	yes	characteristic
239	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
240	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
241	C₄×D₂₈	C₂×C₄	1	2	yes	—
242	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
243	C₄×D₂₈	C₂³	1	2	yes	—
244	C₄×D₂₈	C₂³	1	2	yes	—
245	C₄×D₂₈	C₂³	1	2	yes	—
246	C₄×D₂₈	C₂³	1	1	yes	characteristic
247	C₄×D₂₈	C₂³	1	1	yes	characteristic
248	C₄×D₂₈	C₂³	1	1	yes	characteristic
249	#6435	C₂×C₄	1	2	yes	—
250	#6435	C₂³	1	2	yes	—
251	#6435	C₂³	1	2	yes	—
252	C₄²×D₇	C₂³	1	2	yes	—
253	#6433	C₂×C₄	1	1	yes	characteristic
254	#6433	C₂×C₄	1	1	yes	characteristic
255	#6432	C₂×C₄	1	1	yes	characteristic
256	#6432	C₂×C₄	1	1	yes	characteristic
257	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
258	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
266	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
267	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
268	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
269	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
270	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₇×#97	C₂³	1	1	yes	characteristic
272	C₇×#97	C₂³	1	1	yes	characteristic
273	C₇×#97	C₂³	1	1	yes	characteristic
274	C₇×#97	C₂³	1	1	yes	characteristic
275	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
276	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
277	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
278	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
279	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
280	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
281	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
282	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
283	C₂²⋊(C₇⋊C₈)	C₂³	1	2	yes	—
284	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
285	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
286	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
287	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
288	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
289	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
290	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
291	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
292	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
293	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
294	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
295	(C₂×D₇)⋊C₈	C₂³	1	2	yes	—
296	#6389	C₂³	1	2	yes	—
297	#6389	C₂³	1	2	yes	—
298	Dic₇⋊C₈	C₂³	1	2	yes	—
299	Dic₇⋊C₈	C₂³	1	2	yes	—
300	Dic₇⋊C₈	C₂³	1	2	yes	—
301	Dic₇⋊C₈	C₂³	1	2	yes	—
302	C₈×Dic₇	C₂³	1	2	yes	—
303	C₈×Dic₇	C₂³	1	2	yes	—
304	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
305	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
306	C₄⋊(C₇⋊C₈)	C₂³	1	2	yes	—
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	#6377	C₂³	1	2	yes	—
312	#6377	C₂³	1	2	yes	—
313	C₄×C₇⋊C₈	C₂³	1	2	yes	—
314	#3460	—	7	1	no	—
315	#2994	—	7	1	no	—
316	#2993	—	7	1	no	—
317	#2992	—	7	2	no	—
318	#2990	—	7	1	no	—
319	#2989	—	7	1	no	—
320	#2981	—	7	1	no	—
321	#2980	—	7	2	no	—
322	#2979	—	7	1	no	—
323	#2978	—	7	2	no	—
324	#2976	—	7	2	no	—
325	#2974	—	7	1	no	—
326	#2971	—	7	1	no	—
327	#2969	—	7	1	no	—
328	#2967	—	7	2	no	—
329	#2966	—	7	1	no	—
330	#2965	D₇	1	1	yes	characteristic, complemented
331	#2935	—	7	2	no	—
332	#2935	—	7	1	no	—
333	D₄×M₁₆	—	7	1	no	—
334	#2933	—	7	2	no	—
335	#2931	—	7	1	no	—
336	#2930	—	7	2	no	—
337	C₂³×D₇	C₂²×C₄	1	2	yes	—
338	C₇×#41	—	4	2	no	—
339	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
352	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
353	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
354	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
355	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
356	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
357	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
358	C₂×C₂²⋊D₇	C₂²×C₄	1	2	yes	—
359	C₂²×Dic₇	C₂²×C₄	1	2	yes	—
360	#1157	—	4	2	no	—
361	#1157	—	4	2	no	—
362	#1157	—	4	2	no	—
363	#1157	—	4	2	no	—
364	#1157	—	4	2	no	—
365	C₂×D₂₈	—	4	2	no	—
366	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
368	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
369	C₂×D₂₈	C₂²×C₄	1	2	yes	—
370	C₂×D₂₈	C₂²×C₄	1	2	yes	—
371	C₂×D₂₈	C₂²×C₄	1	2	yes	—
372	C₂×D₂₈	C₂²×C₄	1	2	yes	—
373	C₂×D₂₈	C₂²×C₄	1	2	yes	—
374	C₂×C₄×D₇	—	4	2	no	—
375	C₂×C₄×D₇	—	4	2	no	—
376	C₂×C₄×D₇	C₂²×C₄	1	2	yes	—
377	C₂×C₄×D₇	C₂²×C₄	1	2	yes	—
378	C₂×C₄×D₇	C₂²×C₄	1	2	yes	—
379	C₂×C₄×D₇	C₂²×C₄	1	2	yes	—
380	C₂×C₄×D₇	C₂⁴	1	2	yes	—
381	C₂×C₄×D₇	C₂⁴	1	2	yes	—
382	C₂×C₄×D₇	C₂⁴	1	2	yes	—
383	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
384	C₂×Dic₁₄	C₂²×C₄	1	2	yes	—
385	C₂×Dic₁₄	C₂²×C₄	1	2	yes	—
386	C₇×M₁₆	—	2	2	no	—
387	C₇×M₁₆	—	2	2	no	—
388	C₇×M₁₆	—	4	1	no	—
389	C₇×M₁₆	—	4	1	no	—
390	C₂×C₇×C₈	—	2	2	no	—
391	C₂×C₇×C₈	—	4	1	no	—
392	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
393	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
394	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
405	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
409	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
410	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	C₇×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
413	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
414	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
415	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
416	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
417	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
418	C₄²×C₇	C₂⁴	1	1	yes	characteristic
419	C₄²×C₇	C₂⁴	1	1	yes	characteristic
420	C₄²×C₇	C₂⁴	1	1	yes	characteristic
421	C₄²×C₇	C₂⁴	1	1	yes	characteristic
422	C₂²⋊Dic₇	C₂²×C₄	1	2	yes	—
423	C₂²⋊Dic₇	C₂²×C₄	1	2	yes	—
424	C₂²⋊Dic₇	C₂²×C₄	1	2	yes	—
425	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
426	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
427	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
428	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
429	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
430	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
431	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
432	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
433	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
434	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
435	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
436	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
437	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
438	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
439	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
440	(C₂×D₇)⋊C₄	C₂²×C₄	1	2	yes	—
441	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
442	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
443	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
444	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
445	C₄⋊Dic₇	C₂²×C₄	1	2	yes	—
446	C₄⋊Dic₇	C₂²×C₄	1	2	yes	—
447	C₄⋊Dic₇	C₂²×C₄	1	2	yes	—
448	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
449	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
450	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
451	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
452	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
453	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
454	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
455	Dic₇⋊C₄	C₂²×C₄	1	2	yes	—
456	C₄×Dic₇	C₂²×C₄	1	2	yes	—
457	C₄×Dic₇	C₂²×C₄	1	2	yes	—
458	C₄×Dic₇	C₂⁴	1	2	yes	—
459	#1136	—	4	2	no	—
460	#1136	—	4	2	no	—
461	C₂×C₇⋊C₈	—	4	2	no	—
462	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
463	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
464	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
465	C₂×C₇⋊C₈	C₂⁴	1	2	yes	—
466	#1131	—	2	4	no	—
467	#1131	—	2	4	no	—
468	#1131	—	4	2	no	—
469	#1131	—	4	2	no	—
470	#1131	—	4	2	no	—
471	#1131	—	4	2	no	—
472	C₈×D₇	—	2	4	no	—
473	C₈×D₇	—	4	2	no	—
474	C₈×D₇	—	4	2	no	—
475	C₈×D₇	—	4	2	no	—
476	C₈×D₇	—	4	2	no	—
477	C₈×D₇	—	4	2	no	—
478	C₂×#131	—	7	2	no	—
479	C₂×#131	—	7	2	no	—
480	C₂²×M₁₆	—	7	2	no	—
481	#544	—	7	1	no	—
482	#542	—	7	2	no	—
483	#542	—	7	1	no	—
484	#542	—	7	1	no	—
485	#540	—	7	2	no	—
486	#540	—	7	1	no	—
487	#540	—	7	1	no	—
488	#538	—	7	2	no	—
489	#538	—	7	2	no	—
490	#537	—	7	1	no	—
491	#535	—	7	1	no	—
492	#535	—	7	1	no	—
493	#532	—	7	2	no	—
494	#532	—	7	1	no	—
495	#532	—	7	1	no	—
496	#529	—	7	2	no	—
497	#529	—	7	1	no	—
498	#529	—	7	1	no	—
499	#525	—	7	2	no	—
500	#525	—	7	2	no	—
501	C₄×#41	—	7	1	no	—
502	C₄×#41	C₂×D₇	1	1	yes	characteristic
503	C₂×C₄×D₄	—	7	1	no	—
504	#446	—	7	2	no	—
505	#446	—	7	1	no	—
506	#446	—	7	1	no	—
507	#446	C₂×D₇	1	1	yes	characteristic, complemented
508	#446	C₂×D₇	1	1	yes	characteristic, complemented
509	C₈×Q₈	—	7	1	no	—
510	C₈×Q₈	—	7	1	no	—
511	#436	—	7	2	no	—
512	#436	—	7	2	no	—
513	#436	—	7	2	no	—
514	#436	—	7	2	no	—
515	#436	—	7	2	no	—
516	#436	—	7	2	no	—
517	#436	—	7	2	no	—
518	#436	—	7	1	no	—
519	#436	—	7	1	no	—
520	#436	—	7	1	no	—
521	#436	—	7	1	no	—
522	#436	—	7	1	no	—
523	#436	—	7	1	no	—
524	#436	C₂×D₇	1	1	yes	characteristic
525	#436	C₂×D₇	1	1	yes	characteristic
526	#435	—	7	2	no	—
527	#435	—	7	2	no	—
528	#435	—	7	2	no	—
529	#435	—	7	2	no	—
530	#435	—	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	2	no	—
536	#435	—	7	2	no	—
537	#435	—	7	2	no	—
538	#435	—	7	2	no	—
539	#435	—	7	2	no	—
540	#435	—	7	2	no	—
541	#435	—	7	2	no	—
542	#435	C₂×D₇	1	1	yes	characteristic
543	#435	C₂×D₇	1	1	yes	characteristic
544	#435	C₂×D₇	1	1	yes	characteristic, complemented
545	#435	C₂×D₇	1	1	yes	characteristic, complemented
546	C₈×D₄	—	7	2	no	—
547	C₈×D₄	—	7	2	no	—
548	C₈×D₄	—	7	2	no	—
549	C₈×D₄	—	7	1	no	—
550	C₈×D₄	—	7	1	no	—
551	C₈×D₄	—	7	1	no	—
552	C₈×D₄	—	7	1	no	—
553	C₈×D₄	—	7	2	no	—
554	C₈×D₄	—	7	1	no	—
555	C₈×D₄	—	7	1	no	—
556	#433	—	7	2	no	—
557	#433	—	7	2	no	—
558	#433	—	7	2	no	—
559	#433	—	7	2	no	—
560	#432	—	7	1	no	—
561	#432	—	7	1	no	—
562	#432	—	7	2	no	—
563	#432	—	7	2	no	—
564	#431	—	7	1	no	—
565	#431	C₂×D₇	1	1	yes	characteristic
566	#431	C₂×D₇	1	1	yes	characteristic, complemented
567	#431	C₂×D₇	1	1	yes	characteristic, complemented
568	#424	—	7	2	no	—
569	#424	—	7	2	no	—
570	#423	—	7	1	no	—
571	#423	—	7	1	no	—
572	C₂×C₄⋊C₈	—	7	1	no	—
573	C₂×C₄⋊C₈	—	7	2	no	—
574	#408	—	7	2	no	—
575	#408	—	7	2	no	—
576	#408	—	7	2	no	—
577	#408	—	7	2	no	—
578	#408	—	7	2	no	—
579	#408	—	7	2	no	—
580	#407	—	7	2	no	—
581	#407	—	7	2	no	—
582	C₂×C₂²⋊C₈	—	7	2	no	—
583	#405	—	7	2	no	—
584	#405	—	7	2	no	—
585	C₄×M₁₆	—	7	2	no	—
586	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
587	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic, complemented
588	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic, complemented
589	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
590	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
591	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
592	C₂²×D₇	—	4	2	no	—
593	C₂²×D₇	—	4	2	no	—
594	C₂²×D₇	—	4	2	no	—
595	C₂²×D₇	C₂³×C₄	1	2	yes	—
596	C₂²×D₇	C₂³×C₄	1	2	yes	—
597	C₂²×D₇	C₂³×C₄	1	2	yes	—
598	C₇×Q₈	—	4	1	no	—
599	C₇×D₄	—	4	1	no	—
600	C₇×D₄	—	4	1	no	—
601	C₇×D₄	—	4	1	no	—
602	C₂×C₄×C₇	—	2	2	no	—
603	C₂×C₄×C₇	—	2	2	no	—
604	C₂×C₄×C₇	—	2	2	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	1	no	—
607	C₂×C₄×C₇	—	2	1	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	1	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	4	1	no	—
612	C₂×C₄×C₇	—	4	1	no	—
613	C₂×C₄×C₇	—	4	1	no	—
614	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
615	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
616	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
617	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
618	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
620	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
622	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
623	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
624	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
625	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
626	C₂²⋊D₇	—	4	2	no	—
627	C₂²⋊D₇	—	4	2	no	—
628	C₂²⋊D₇	—	4	2	no	—
629	C₂²⋊D₇	—	4	2	no	—
630	C₂²⋊D₇	—	4	2	no	—
631	C₂²⋊D₇	—	4	2	no	—
632	C₂²⋊D₇	—	4	2	no	—
633	C₂×Dic₇	—	4	2	no	—
634	C₂×Dic₇	C₂³×C₄	1	2	yes	—
635	C₂×Dic₇	C₂³×C₄	1	2	yes	—
636	C₂×Dic₇	C₂³×C₄	1	2	yes	—
637	C₂×Dic₇	C₂³×C₄	1	2	yes	—
638	C₂×Dic₇	C₂³×C₄	1	2	yes	—
639	D₂₈	—	2	2	no	—
640	D₂₈	—	2	2	no	—
641	D₂₈	—	2	2	no	—
642	D₂₈	—	4	2	no	—
643	D₂₈	—	4	2	no	—
644	D₂₈	—	4	2	no	—
645	D₂₈	—	4	2	no	—
646	D₂₈	—	4	2	no	—
647	C₄×D₇	—	2	2	no	—
648	C₄×D₇	—	2	2	no	—
649	C₄×D₇	—	2	2	no	—
650	C₄×D₇	—	2	2	no	—
651	C₄×D₇	—	2	2	no	—
652	C₄×D₇	—	2	2	no	—
653	C₄×D₇	—	4	2	no	—
654	C₄×D₇	—	4	2	no	—
655	C₄×D₇	—	4	2	no	—
656	C₄×D₇	—	4	2	no	—
657	Dic₁₄	—	2	2	no	—
658	Dic₁₄	—	4	2	no	—
659	Dic₁₄	—	4	2	no	—
660	C₇×C₈	—	2	1	no	—
661	C₇×C₈	—	2	1	no	—
662	C₇×C₈	—	2	1	no	—
663	C₇×C₈	—	2	1	no	—
664	C₇×C₈	—	2	1	no	—
665	C₇×C₈	—	2	1	no	—
666	C₇×C₈	—	2	1	no	—
667	C₇×C₈	H(5,𝔽₂)	1	2	yes	—
668	C₇⋊C₈	—	2	2	no	—
669	C₇⋊C₈	—	2	2	no	—
670	C₇⋊C₈	—	2	2	no	—
671	C₇⋊C₈	—	2	2	no	—
672	C₂×#41	—	7	1	no	—
673	C₂×#41	—	7	2	no	—
674	C₂×#41	—	7	2	no	—
675	C₂×#41	C₄×D₇	1	1	yes	characteristic
676	C₂²×D₄	—	7	1	no	—
677	C₂³×C₄	—	7	2	no	—
678	#131	—	28	4	no	—
679	#131	—	28	4	no	—
680	C₂×M₁₆	—	7	2	no	—
681	C₂×M₁₆	—	7	2	no	—
682	C₂×M₁₆	—	7	2	no	—
683	C₂×M₁₆	—	7	2	no	—
684	C₂×M₁₆	—	7	2	no	—
685	C₂×M₁₆	—	7	2	no	—
686	C₂×M₁₆	—	7	2	no	—
687	C₂×M₁₆	—	7	2	no	—
688	C₂×M₁₆	—	28	4	no	—
689	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
690	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
691	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
692	C₂×M₁₆	C₂²×D₇	1	1	yes	characteristic
693	C₂²×C₈	—	7	2	no	—
694	C₂²×C₈	—	7	2	no	—
695	C₂²×C₈	—	7	2	no	—
696	C₂²×C₈	—	7	2	no	—
697	C₂²×C₈	—	7	2	no	—
698	C₂²×C₈	—	7	2	no	—
699	C₂²×C₈	—	7	2	no	—
700	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
701	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
702	C₄⋊Q₈	—	7	2	no	—
703	C₄⋊Q₈	—	7	1	no	—
704	C₄⋊Q₈	—	7	1	no	—
705	#127	—	7	2	no	—
706	#127	—	7	1	no	—
707	#127	—	7	1	no	—
708	#126	—	7	2	no	—
709	#126	—	7	2	no	—
710	#126	—	7	2	no	—
711	#126	—	7	2	no	—
712	#125	—	7	2	no	—
713	#125	—	7	1	no	—
714	#125	—	7	1	no	—
715	#124	—	7	2	no	—
716	#124	—	7	2	no	—
717	#124	—	7	2	no	—
718	#124	—	7	1	no	—
719	#124	—	7	1	no	—
720	#124	—	7	2	no	—
721	#124	—	7	2	no	—
722	#123	—	7	2	no	—
723	#123	—	7	2	no	—
724	#123	—	7	2	no	—
725	#123	—	7	2	no	—
726	#123	—	7	2	no	—
727	#123	—	7	2	no	—
728	#123	—	7	2	no	—
729	#123	—	7	2	no	—
730	C₂²⋊Q₈	—	7	2	no	—
731	C₂²⋊Q₈	—	7	1	no	—
732	C₂²⋊Q₈	—	7	1	no	—
733	C₂²⋊Q₈	—	7	2	no	—
734	C₂²⋊Q₈	—	7	2	no	—
735	C₂²⋊Q₈	—	7	2	no	—
736	C₂²⋊Q₈	—	7	2	no	—
737	#121	—	7	2	no	—
738	#121	—	7	2	no	—
739	#121	—	7	2	no	—
740	#121	—	7	1	no	—
741	#121	—	7	1	no	—
742	#121	—	7	1	no	—
743	#121	—	7	1	no	—
744	#121	—	7	1	no	—
745	#121	—	7	1	no	—
746	#121	—	7	2	no	—
747	#121	—	7	2	no	—
748	#121	—	7	2	no	—
749	#121	—	7	2	no	—
750	#121	—	7	2	no	—
751	#121	—	7	2	no	—
752	#121	—	7	2	no	—
753	#121	—	7	2	no	—
754	#120	—	7	2	no	—
755	#120	—	7	2	no	—
756	#120	—	7	2	no	—
757	#120	—	7	2	no	—
758	C₄×Q₈	—	7	1	no	—
759	C₄×Q₈	—	7	1	no	—
760	C₄×Q₈	C₄×D₇	1	1	yes	characteristic
761	C₄×Q₈	C₂²×D₇	1	1	yes	characteristic
762	C₄×D₄	—	7	2	no	—
763	C₄×D₄	—	7	2	no	—
764	C₄×D₄	—	7	2	no	—
765	C₄×D₄	—	7	2	no	—
766	C₄×D₄	—	7	2	no	—
767	C₄×D₄	—	7	1	no	—
768	C₄×D₄	—	7	1	no	—
769	C₄×D₄	—	7	1	no	—
770	C₄×D₄	—	7	1	no	—
771	C₄×D₄	—	7	1	no	—
772	C₄×D₄	—	7	2	no	—
773	C₄×D₄	—	7	1	no	—
774	C₄×D₄	—	7	2	no	—
775	C₄×D₄	—	7	2	no	—
776	C₄×D₄	C₄×D₇	1	1	yes	characteristic
777	C₄×D₄	C₄×D₇	1	1	yes	characteristic
778	C₄×D₄	C₄×D₇	1	1	yes	characteristic
779	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
780	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
781	C₄×D₄	C₂²×D₇	1	1	yes	characteristic
782	#117	—	7	1	no	—
783	#117	—	7	2	no	—
784	#117	—	7	2	no	—
785	#117	—	7	2	no	—
786	#117	C₄×D₇	1	1	yes	characteristic
787	#117	C₄×D₇	1	1	yes	characteristic
788	#117	C₄×D₇	1	1	yes	characteristic
789	C₂×C₄⋊C₄	—	7	1	no	—
790	C₂×C₂²⋊C₄	—	7	2	no	—
791	C₂×C₄²	—	7	2	no	—
792	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
793	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
794	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
795	C₄⋊C₈	—	7	2	no	—
796	C₄⋊C₈	—	7	2	no	—
797	C₄⋊C₈	—	7	2	no	—
798	C₄⋊C₈	—	7	2	no	—
799	C₄⋊C₈	—	7	1	no	—
800	C₄⋊C₈	—	7	1	no	—
801	C₄⋊C₈	—	7	2	no	—
802	C₄⋊C₈	—	7	2	no	—
803	C₄⋊C₈	—	7	1	no	—
804	C₄⋊C₈	—	7	2	no	—
805	C₄⋊C₈	—	7	1	no	—
806	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
807	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
808	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
809	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
810	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
811	C₄⋊C₈	C₂²×D₇	1	1	yes	characteristic
812	C₂²⋊C₈	—	7	2	no	—
813	C₂²⋊C₈	—	7	2	no	—
814	C₂²⋊C₈	—	7	2	no	—
815	C₂²⋊C₈	—	7	2	no	—
816	C₂²⋊C₈	—	7	2	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	2	no	—
825	C₂²⋊C₈	—	7	2	no	—
826	C₂²⋊C₈	—	7	2	no	—
827	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
828	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
829	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
830	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
831	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
832	C₂²⋊C₈	C₂²×D₇	1	1	yes	characteristic
833	#97	—	7	2	no	—
834	#97	—	7	2	no	—
835	#97	—	7	2	no	—
836	#97	—	7	2	no	—
837	#97	C₂²×D₇	1	1	yes	characteristic
838	#97	C₂²×D₇	1	1	yes	characteristic
839	#97	C₂²×D₇	1	1	yes	characteristic
840	#97	C₂²×D₇	1	1	yes	characteristic
841	C₄×C₈	—	7	2	no	—
842	C₄×C₈	—	7	2	no	—
843	C₄×C₈	—	7	2	no	—
844	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
845	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
846	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
847	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
848	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
849	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
850	C₂²×C₇	—	2	1	no	—
851	C₂²×C₇	—	2	1	no	—
852	C₂²×C₇	—	2	1	no	—
853	C₂²×C₇	—	2	1	no	—
854	C₂²×C₇	—	2	1	no	—
855	C₂²×C₇	—	2	1	no	—
856	C₂²×C₇	—	2	1	no	—
857	C₂²×C₇	—	2	1	no	—
858	C₂²×C₇	—	2	1	no	—
859	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
860	C₂×D₇	—	2	2	no	—
861	C₂×D₇	—	2	2	no	—
862	C₂×D₇	—	2	2	no	—
863	C₂×D₇	—	2	2	no	—
864	C₂×D₇	—	2	2	no	—
865	C₂×D₇	—	2	2	no	—
866	C₂×D₇	—	2	2	no	—
867	C₂×D₇	—	2	2	no	—
868	C₂×D₇	—	2	2	no	—
869	C₂×D₇	—	8	4	no	—
870	C₄×C₇	—	2	1	no	—
871	C₄×C₇	—	2	1	no	—
872	C₄×C₇	—	2	1	no	—
873	C₄×C₇	—	2	1	no	—
874	C₄×C₇	—	2	1	no	—
875	C₄×C₇	—	2	1	no	—
876	C₄×C₇	—	2	1	no	—
877	C₄×C₇	—	2	1	no	—
878	C₄×C₇	—	2	1	no	—
879	C₄×C₇	—	2	1	no	—
880	C₄×C₇	#568	1	2	yes	—
881	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
882	C₄×C₇	#585	1	1	yes	characteristic
883	Dic₇	—	2	2	no	—
884	Dic₇	—	2	2	no	—
885	Dic₇	—	2	2	no	—
886	Dic₇	—	2	2	no	—
887	Dic₇	—	2	2	no	—
888	C₂⁴	—	7	2	no	—
889	#41	—	4	2	no	—
890	#41	—	28	2	no	—
891	#41	—	28	2	no	—
892	#41	—	28	2	no	—
893	#41	—	28	2	no	—
894	#41	—	28	2	no	—
895	C₂×Q₈	—	7	1	no	—
896	C₂×Q₈	—	7	2	no	—
897	C₂×Q₈	—	7	2	no	—
898	C₂×Q₈	C₂×C₄×D₇	1	1	yes	characteristic
899	C₂×D₄	—	7	2	no	—
900	C₂×D₄	—	7	2	no	—
901	C₂×D₄	—	7	2	no	—
902	C₂×D₄	—	7	2	no	—
903	C₂×D₄	—	7	2	no	—
904	C₂×D₄	—	7	2	no	—
905	C₂×D₄	—	7	2	no	—
906	C₂×D₄	—	7	1	no	—
907	C₂×D₄	—	7	1	no	—
908	C₂×D₄	—	7	1	no	—
909	C₂×D₄	—	7	2	no	—
910	C₂×D₄	—	7	2	no	—
911	C₂×D₄	—	7	2	no	—
912	C₂×D₄	—	7	2	no	—
913	C₂×D₄	—	7	2	no	—
914	C₂×D₄	—	28	2	no	—
915	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
916	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
917	C₂×D₄	C₂×C₄×D₇	1	1	yes	characteristic
918	C₂²×C₄	—	7	2	no	—
919	C₂²×C₄	—	7	2	no	—
920	C₂²×C₄	—	7	2	no	—
921	C₂²×C₄	—	7	2	no	—
922	C₂²×C₄	—	7	2	no	—
923	C₂²×C₄	—	7	2	no	—
924	C₂²×C₄	—	7	2	no	—
925	C₂²×C₄	—	7	2	no	—
926	C₂²×C₄	—	28	2	no	—
927	C₂²×C₄	—	28	2	no	—
928	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
929	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
930	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
931	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
932	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
933	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
935	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
936	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
937	M₁₆	—	2	2	no	—
938	M₁₆	—	2	2	no	—
939	M₁₆	—	4	1	no	—
940	M₁₆	—	4	1	no	—
941	M₁₆	—	14	4	no	—
942	M₁₆	—	14	4	no	—
943	M₁₆	—	28	2	no	—
944	M₁₆	—	28	2	no	—
945	M₁₆	—	28	2	no	—
946	M₁₆	—	28	2	no	—
947	M₁₆	—	28	2	no	—
948	M₁₆	—	28	2	no	—
949	C₂×C₈	—	2	2	no	—
950	C₂×C₈	—	4	1	no	—
951	C₂×C₈	—	7	2	no	—
952	C₂×C₈	—	7	2	no	—
953	C₂×C₈	—	7	2	no	—
954	C₂×C₈	—	7	2	no	—
955	C₂×C₈	—	14	4	no	—
956	C₂×C₈	—	28	2	no	—
957	C₂×C₈	—	28	2	no	—
958	C₂×C₈	—	28	2	no	—
959	C₂×C₈	—	28	2	no	—
960	C₂×C₈	—	28	2	no	—
961	C₂×C₈	—	28	2	no	—
962	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
967	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
968	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
969	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
970	C₄⋊C₄	—	7	2	no	—
971	C₄⋊C₄	—	7	2	no	—
972	C₄⋊C₄	—	7	2	no	—
973	C₄⋊C₄	—	7	2	no	—
974	C₄⋊C₄	—	7	2	no	—
975	C₄⋊C₄	—	7	2	no	—
976	C₄⋊C₄	—	7	2	no	—
977	C₄⋊C₄	—	7	2	no	—
978	C₄⋊C₄	—	7	2	no	—
979	C₄⋊C₄	—	7	1	no	—
980	C₄⋊C₄	—	7	1	no	—
981	C₄⋊C₄	—	7	1	no	—
982	C₄⋊C₄	—	7	1	no	—
983	C₄⋊C₄	—	7	2	no	—
984	C₄⋊C₄	—	7	2	no	—
985	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
991	C₂²⋊C₄	—	7	2	no	—
992	C₂²⋊C₄	—	7	2	no	—
993	C₂²⋊C₄	—	7	2	no	—
994	C₂²⋊C₄	—	7	2	no	—
995	C₂²⋊C₄	—	7	2	no	—
996	C₂²⋊C₄	—	7	2	no	—
997	C₂²⋊C₄	—	7	2	no	—
998	C₂²⋊C₄	—	7	2	no	—
999	C₂²⋊C₄	—	7	2	no	—
1000	C₂²⋊C₄	—	7	2	no	—
1001	C₂²⋊C₄	—	7	2	no	—
1002	C₂²⋊C₄	—	7	2	no	—
1003	C₂²⋊C₄	—	7	2	no	—
1004	C₂²⋊C₄	—	7	2	no	—
1005	C₂²⋊C₄	—	7	2	no	—
1006	C₂²⋊C₄	—	7	2	no	—
1007	C₂²⋊C₄	—	7	2	no	—
1008	C₂²⋊C₄	—	7	2	no	—
1009	C₂²⋊C₄	—	7	2	no	—
1010	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1013	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1014	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1015	C₂²⋊C₄	C₂×C₄×D₇	1	1	yes	characteristic
1016	C₄²	—	7	2	no	—
1017	C₄²	—	7	2	no	—
1018	C₄²	—	7	2	no	—
1019	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1020	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1021	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1022	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1023	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
1025	C₄²	C₂³×D₇	1	1	yes	characteristic
1026	C₄²	C₂³×D₇	1	1	yes	characteristic
1027	C₄²	C₂³×D₇	1	1	yes	characteristic
1028	C₄²	C₂³×D₇	1	1	yes	characteristic
1029	C₂×C₇	—	4	1	no	—
1030	C₂×C₇	—	4	1	no	—
1031	C₂×C₇	—	4	1	no	—
1032	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1033	C₂×C₇	C₂×#568	1	1	yes	characteristic
1034	C₂×C₇	#3573	1	1	yes	characteristic
1035	D₇	—	4	2	no	—
1036	D₇	—	4	2	no	—
1037	D₇	—	4	2	no	—
1038	C₂³	—	7	2	no	—
1039	C₂³	—	7	2	no	—
1040	C₂³	—	7	2	no	—
1041	C₂³	—	28	2	no	—
1042	C₂³	—	28	2	no	—
1043	C₂³	—	28	2	no	—
1044	C₂³	C₂²×C₄×D₇	1	1	yes	characteristic
1045	C₂³	C₂²×C₄×D₇	1	1	yes	characteristic
1046	C₂³	C₂²×C₄×D₇	1	1	yes	characteristic
1047	Q₈	—	4	1	no	—
1048	Q₈	—	14	2	no	—
1049	Q₈	—	28	2	no	—
1050	Q₈	—	28	2	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	4	1	no	—
1054	D₄	—	14	2	no	—
1055	D₄	—	14	2	no	—
1056	D₄	—	14	2	no	—
1057	D₄	—	28	2	no	—
1058	D₄	—	28	2	no	—
1059	D₄	—	28	2	no	—
1060	D₄	—	28	2	no	—
1061	D₄	—	28	2	no	—
1062	D₄	—	28	2	no	—
1063	D₄	—	28	2	no	—
1064	D₄	—	28	2	no	—
1065	D₄	—	28	2	no	—
1066	D₄	—	28	2	no	—
1067	D₄	—	28	2	no	—
1068	D₄	—	28	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	7	2	no	—
1082	C₂×C₄	—	7	2	no	—
1083	C₂×C₄	—	7	2	no	—
1084	C₂×C₄	—	7	2	no	—
1085	C₂×C₄	—	7	2	no	—
1086	C₂×C₄	—	14	2	no	—
1087	C₂×C₄	—	14	2	no	—
1088	C₂×C₄	—	14	2	no	—
1089	C₂×C₄	—	14	2	no	—
1090	C₂×C₄	—	14	2	no	—
1091	C₂×C₄	—	14	2	no	—
1092	C₂×C₄	—	28	2	no	—
1093	C₂×C₄	—	28	2	no	—
1094	C₂×C₄	—	28	2	no	—
1095	C₂×C₄	—	28	2	no	—
1096	C₂×C₄	—	28	2	no	—
1097	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1098	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1099	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1106	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₇	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	14	2	no	—
1117	C₈	—	14	2	no	—
1118	C₈	—	14	2	no	—
1119	C₈	—	14	2	no	—
1120	C₈	#6553	1	2	yes	—
1121	C₇	#60326	1	1	yes	characteristic, complemented, Sylow
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	14	2	no	—
1132	C₂²	—	14	2	no	—
1133	C₂²	—	14	2	no	—
1134	C₂²	—	14	2	no	—
1135	C₂²	—	14	2	no	—
1136	C₂²	—	14	2	no	—
1137	C₂²	—	14	2	no	—
1138	C₂²	—	14	2	no	—
1139	C₂²	—	14	2	no	—
1140	C₂²	—	56	4	no	—
1141	C₂²	C₂³×C₄×D₇	1	1	yes	characteristic
1142	C₄	—	2	1	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	1	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	14	2	no	—
1153	C₄	—	14	2	no	—
1154	C₄	—	14	2	no	—
1155	C₄	—	14	2	no	—
1156	C₄	—	14	2	no	—
1157	C₄	#90436	1	2	yes	—
1158	C₄	C₂×#6553	1	1	yes	characteristic
1159	C₄	#90616	1	1	yes	characteristic
1160	C₂	—	4	1	no	—
1161	C₂	—	4	1	no	—
1162	C₂	—	4	1	no	—
1163	C₂	—	28	2	no	—
1164	C₂	—	28	2	no	—
1165	C₂	—	28	2	no	—
1166	C₂	C₄×#6553	1	1	yes	characteristic
1167	C₂	C₂×#90436	1	1	yes	characteristic
1168	C₂	#11744228	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇
commutator, socle	C₂²×C₇	C₂⁴×C₄
Fitting	C₇×#2965	C₂
prime radical	#11742906	C₂
cosocle	C₂×C₄×C₇	C₂⁵
hypercenter	#2965	D₇
hypocenter	C₇	#60326
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ #2965

Complements

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

N	H ≅ G/N	type
2. C₇×#2965	C₂	semidirect
3. #11739966	C₂	semidirect
4. #11737391	C₂	semidirect
5. #11737385	C₂	semidirect
6. #11736989	C₂	semidirect
7. #11736982	C₂	semidirect
8. #11736936	C₂	semidirect
9. #11736935	C₂	semidirect
10. #11736929	C₂	semidirect
11. #11736927	C₂	semidirect
12. #11736741	C₂	semidirect
13. #11736740	C₂	semidirect
14. #11736738	C₂	semidirect
15. #11736735	C₂	semidirect
16. #11736734	C₂	semidirect
17. #11736732	C₂	semidirect
18. #11735967	C₂	semidirect
19. M₁₆×D₂₈	C₂	semidirect
20. #11735957	C₂	semidirect
21. #11735956	C₂	semidirect
22. #11735903	C₂	semidirect
23. #11735893	C₂	semidirect
27. C₂×#6470	C₂²	semidirect
29. C₂×#6464	C₂²	semidirect
50. C₇×#446	C₂²	semidirect
51. C₇×#446	C₂²	semidirect
56. C₇×#435	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
59. C₇×#431	C₂²	semidirect
60. C₇×#431	C₂²	semidirect
62. C₄×C₇×M₁₆	C₂²	semidirect
63. C₂×C₄×C₇×C₈	C₂²	semidirect
64. #89901	C₂²	semidirect
67. #89900	C₂²	semidirect
68. #89899	C₂²	semidirect
70. #89883	C₂²	semidirect
71. #89882	C₂²	semidirect
72. C₈×C₂²⋊D₇	C₂²	semidirect
73. #89796	C₂²	semidirect
76. #89783	C₂²	semidirect
78. #89698	C₂²	semidirect
79. #89697	C₂²	semidirect
81. #89696	C₂²	semidirect
82. C₂×C₄⋊(C₇⋊C₈)	C₂²	semidirect
83. #89612	C₂²	semidirect
84. #89612	C₂²	semidirect
85. #89611	C₂²	semidirect
86. #89611	C₂²	semidirect
87. #89610	C₂²	semidirect
90. #89608	C₂²	semidirect
91. #89608	C₂²	semidirect
92. #89607	C₂²	semidirect
93. #89606	C₂²	semidirect
94. D₇×C₄⋊C₈	C₂²	semidirect
95. #89502	C₂²	semidirect
96. #89501	C₂²	semidirect
99. #89500	C₂²	semidirect
100. #89499	C₂²	semidirect
101. #89499	C₂²	semidirect
102. #89499	C₂²	semidirect
103. #89499	C₂²	semidirect
105. (C₂²⋊D₇)⋊C₈	C₂²	semidirect
107. #89481	C₂²	semidirect
108. #89480	C₂²	semidirect
109. #89479	C₂²	semidirect
112. #89478	C₂²	semidirect
113. #89478	C₂²	semidirect
114. #89477	C₂²	semidirect
115. #89462	C₂²	semidirect
116. #89461	C₂²	semidirect
121. #89460	C₂²	semidirect
122. #89460	C₂²	semidirect
123. #89460	C₂²	semidirect
128. C₈×D₂₈	C₂²	semidirect
129. C₈×D₂₈	C₂²	semidirect
130. C₈×D₂₈	C₂²	semidirect
131. #89451	C₂²	semidirect
132. #89451	C₂²	semidirect
133. C₈×Dic₁₄	C₂²	semidirect
134. C₈×Dic₁₄	C₂²	semidirect
330. #2965	D₇	semidirect
507. #446	C₂×D₇	semidirect
508. #446	C₂×D₇	semidirect
544. #435	C₂×D₇	semidirect
545. #435	C₂×D₇	semidirect
566. #431	C₂×D₇	semidirect
567. #431	C₂×D₇	semidirect
587. C₄×M₁₆	C₂×D₇	semidirect
588. C₂×C₄×C₈	C₂×D₇	semidirect
1121. C₇	#60326	semidirect

Maximal subgroups

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

subgroup	index
#11742906	2
C₇×#2965	2
#11739966	2
#11737391	2
#11737385	2
#11736989	2
#11736982	2
#11736936	2
#11736935	2
#11736929	2
#11736927	2
#11736741	2
#11736740	2
#11736738	2
#11736735	2
#11736734	2
#11736732	2
#11735967	2
M₁₆×D₂₈	2
#11735957	2
#11735956	2
#11735903	2
#11735893	2
#60326	7