Subgroups — #11743426

Order 896.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	#90520	C₂	1	1	yes	maximal, characteristic, complemented
3	#90515	C₂	1	1	yes	maximal, characteristic, complemented
4	#90507	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6509	C₂	1	1	yes	maximal, characteristic, complemented
6	#90426	C₂	1	1	yes	maximal, characteristic, complemented
7	#90424	C₂	1	1	yes	maximal, characteristic, complemented
8	#90421	C₂	1	1	yes	maximal, characteristic, complemented
9	#90420	C₂	1	1	yes	maximal, characteristic, complemented
10	#90375	C₂	1	1	yes	maximal, characteristic, complemented
11	#90370	C₂	1	1	yes	maximal, characteristic, complemented
12	#90369	C₂	1	1	yes	maximal, characteristic, complemented
13	#90360	C₂	1	1	yes	maximal, characteristic, complemented
14	#90356	C₂	1	1	yes	maximal, characteristic, complemented
15	#90356	C₂	1	1	yes	maximal, characteristic, complemented
16	#90349	C₂	1	1	yes	maximal, characteristic, complemented
17	#90347	C₂	1	1	yes	maximal, characteristic, complemented
18	#90346	C₂	1	1	yes	maximal, characteristic, complemented
19	#90345	C₂	1	1	yes	maximal, characteristic, complemented
20	D₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
21	#90341	C₂	1	1	yes	maximal, characteristic, complemented
22	#90338	C₂	1	1	yes	maximal, characteristic, complemented
23	#90337	C₂	1	1	yes	maximal, characteristic, complemented
24	#90336	C₂	1	1	yes	maximal, characteristic, complemented
25	#90329	C₂	1	1	yes	maximal, characteristic, complemented
26	#90329	C₂	1	1	yes	maximal, characteristic, complemented
27	#90328	C₂	1	1	yes	maximal, characteristic, complemented
28	#90327	C₂	1	1	yes	maximal, characteristic, complemented
29	#90325	C₂	1	1	yes	maximal, characteristic, complemented
30	#90222	C₂	1	1	yes	maximal, characteristic, complemented
31	#90218	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₇×#41	C₂²	1	1	yes	characteristic
33	C₂²×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
36	C₂×#1157	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
38	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₇×#124	C₂²	1	1	yes	characteristic, complemented
41	C₇×#124	C₂²	1	1	yes	characteristic, complemented
42	C₇×#123	C₂²	1	1	yes	characteristic
43	C₇×#123	C₂²	1	1	yes	characteristic
44	C₇×#123	C₂²	1	1	yes	characteristic, complemented
45	C₇×#123	C₂²	1	1	yes	characteristic, complemented
46	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₇×#117	C₂²	1	1	yes	characteristic, complemented
51	#6510	C₂²	1	1	yes	characteristic
52	#6510	C₂²	1	1	yes	characteristic, complemented
53	#6510	C₂²	1	1	yes	characteristic, complemented
54	#6509	C₂²	1	1	yes	characteristic
55	#6509	C₂²	1	1	yes	characteristic
56	#6509	C₂²	1	1	yes	characteristic
57	#6509	C₂²	1	1	yes	characteristic
58	#6509	C₂²	1	1	yes	characteristic
59	#6509	C₂²	1	1	yes	characteristic, complemented
60	#6509	C₂²	1	1	yes	characteristic, complemented
61	#6509	C₂²	1	1	yes	characteristic, complemented
62	#6509	C₂²	1	1	yes	characteristic, complemented
63	#6509	C₂²	1	1	yes	characteristic, complemented
64	#6509	C₂²	1	1	yes	characteristic, complemented
65	#6509	C₂²	1	1	yes	characteristic, complemented
66	#6509	C₂²	1	1	yes	characteristic, complemented
67	#6509	C₂²	1	1	yes	characteristic, complemented
68	#6507	C₂²	1	1	yes	characteristic, complemented
69	#6507	C₂²	1	1	yes	characteristic, complemented
70	#6507	C₂²	1	1	yes	characteristic, complemented
71	#6502	C₂²	1	1	yes	characteristic
72	#6502	C₂²	1	1	yes	characteristic
73	#6502	C₂²	1	1	yes	characteristic
74	#6502	C₂²	1	1	yes	characteristic, complemented
75	#6500	C₂²	1	1	yes	characteristic
76	#6500	C₂²	1	1	yes	characteristic
77	#6498	C₂²	1	1	yes	characteristic
78	#6498	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₇	C₂²	1	1	yes	characteristic
80	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
81	#6493	C₂²	1	1	yes	characteristic
82	#6492	C₂²	1	1	yes	characteristic
83	#6492	C₂²	1	1	yes	characteristic
84	#6492	C₂²	1	1	yes	characteristic
85	#6492	C₂²	1	1	yes	characteristic, complemented
86	#6492	C₂²	1	1	yes	characteristic, complemented
87	#6492	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
90	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
92	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
93	#6489	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
95	#6487	C₂²	1	1	yes	characteristic, complemented
96	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
97	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
98	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	#6461	C₂²	1	1	yes	characteristic, complemented
100	#6461	C₂²	1	1	yes	characteristic, complemented
101	#6461	C₂²	1	1	yes	characteristic, complemented
102	#6461	C₂²	1	1	yes	characteristic, complemented
103	#6461	C₂²	1	1	yes	characteristic, complemented
104	#6461	C₂²	1	1	yes	characteristic, complemented
105	#6460	C₂²	1	1	yes	characteristic
106	#6460	C₂²	1	1	yes	characteristic, complemented
107	#6460	C₂²	1	1	yes	characteristic, complemented
108	#6459	C₂²	1	1	yes	characteristic
109	#6459	C₂²	1	1	yes	characteristic
110	#6459	C₂²	1	1	yes	characteristic
111	#6459	C₂²	1	1	yes	characteristic, complemented
112	#6459	C₂²	1	1	yes	characteristic, complemented
113	#6459	C₂²	1	1	yes	characteristic, complemented
114	#6458	C₂²	1	1	yes	characteristic
115	#6457	C₂²	1	1	yes	characteristic
116	#6457	C₂²	1	1	yes	characteristic
117	#6457	C₂²	1	1	yes	characteristic
118	#6457	C₂²	1	1	yes	characteristic
119	#6457	C₂²	1	1	yes	characteristic, complemented
120	#6457	C₂²	1	1	yes	characteristic, complemented
121	#6456	C₂²	1	1	yes	characteristic
122	#6456	C₂²	1	1	yes	characteristic
123	#6456	C₂²	1	1	yes	characteristic, complemented
124	#6455	C₂²	1	1	yes	characteristic
125	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
126	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
127	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	#6453	C₂²	1	1	yes	characteristic, complemented
129	#6453	C₂²	1	1	yes	characteristic, complemented
130	#6453	C₂²	1	1	yes	characteristic, complemented
131	#6452	C₂²	1	1	yes	characteristic, complemented
132	#6452	C₂²	1	1	yes	characteristic, complemented
133	#6452	C₂²	1	1	yes	characteristic, complemented
134	#6452	C₂²	1	1	yes	characteristic, complemented
135	#6452	C₂²	1	1	yes	characteristic, complemented
136	#6452	C₂²	1	1	yes	characteristic, complemented
137	#6451	C₂²	1	1	yes	characteristic, complemented
138	#6450	C₂²	1	1	yes	characteristic, complemented
139	#6449	C₂²	1	1	yes	characteristic
140	#6449	C₂²	1	1	yes	characteristic, complemented
141	#6449	C₂²	1	1	yes	characteristic, complemented
142	#6449	C₂²	1	1	yes	characteristic, complemented
143	#6448	C₂²	1	1	yes	characteristic
144	#6448	C₂²	1	1	yes	characteristic, complemented
145	#6447	C₂²	1	1	yes	characteristic
146	#6447	C₂²	1	1	yes	characteristic
147	#6447	C₂²	1	1	yes	characteristic, complemented
148	#6447	C₂²	1	1	yes	characteristic, complemented
149	#6446	C₂²	1	1	yes	characteristic
150	#6446	C₂²	1	1	yes	characteristic
151	#6446	C₂²	1	1	yes	characteristic
152	#6446	C₂²	1	1	yes	characteristic, complemented
153	#6446	C₂²	1	1	yes	characteristic, complemented
154	#6446	C₂²	1	1	yes	characteristic, complemented
155	#6445	C₂²	1	1	yes	characteristic
156	#6445	C₂²	1	1	yes	characteristic
157	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
158	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
159	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
160	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
161	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
164	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
165	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
166	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
167	#6442	C₂²	1	1	yes	characteristic, complemented
168	#6442	C₂²	1	1	yes	characteristic, complemented
169	#6442	C₂²	1	1	yes	characteristic, complemented
170	#6442	C₂²	1	1	yes	characteristic, complemented
171	#6441	C₂²	1	1	yes	characteristic, complemented
172	#6441	C₂²	1	1	yes	characteristic, complemented
173	#6441	C₂²	1	1	yes	characteristic, complemented
174	#6441	C₂²	1	1	yes	characteristic, complemented
175	#6441	C₂²	1	1	yes	characteristic, complemented
176	#6441	C₂²	1	1	yes	characteristic, complemented
177	#6440	C₂²	1	1	yes	characteristic, complemented
178	#6440	C₂²	1	1	yes	characteristic, complemented
179	#6439	C₂²	1	1	yes	characteristic, complemented
180	#6439	C₂²	1	1	yes	characteristic, complemented
181	#6438	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₂₈	C₂²	1	1	yes	characteristic
183	#6435	C₂²	1	1	yes	characteristic
184	#6435	C₂²	1	1	yes	characteristic, complemented
185	#6433	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3535	—	7	1	no	maximal, Sylow
188	C₂³×D₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₇×#41	—	4	2	no	—
191	C₂×C₇×Q₈	—	4	2	no	—
192	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
193	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
194	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
195	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
196	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
197	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
198	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
199	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
213	C₂²×Dic₇	C₂³	1	1	yes	characteristic
214	C₂²×Dic₇	C₂³	1	1	yes	characteristic
215	C₂²×Dic₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₇	C₂³	1	1	yes	characteristic
219	#1159	—	4	2	no	—
220	D₄×D₇	—	4	2	no	—
221	#1157	—	4	2	no	—
222	C₂×D₂₈	C₂³	1	1	yes	characteristic
223	C₂×D₂₈	C₂³	1	1	yes	characteristic
224	C₂×D₂₈	C₂³	1	1	yes	characteristic
225	C₂×D₂₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₇	—	4	2	no	—
227	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
239	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
256	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
258	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₄²×C₇	C₂³	1	1	yes	characteristic
264	C₄²×C₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
273	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
313	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#563	—	7	1	no	—
350	#563	—	7	1	no	—
351	#562	—	7	1	no	—
352	#562	—	7	1	no	—
353	#554	—	7	1	no	—
354	#554	—	7	1	no	—
355	#552	—	7	1	no	—
356	#552	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#547	—	7	1	no	—
362	#547	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#544	—	7	1	no	—
366	#543	—	7	1	no	—
367	#542	—	7	1	no	—
368	#542	—	7	1	no	—
369	#539	—	7	1	no	—
370	#539	—	7	1	no	—
371	#539	—	7	1	no	—
372	#539	—	7	1	no	—
373	#539	—	7	1	no	—
374	#538	—	7	1	no	—
375	#536	—	7	1	no	—
376	#536	D₇	1	1	yes	characteristic, complemented
377	#525	—	7	1	no	—
378	C₂×#123	—	7	1	no	—
379	C₂×C₂²⋊Q₈	—	7	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂³×C₇	C₂⁴	1	1	yes	characteristic
383	C₂²×D₇	—	2	2	no	—
384	C₂²×D₇	—	2	2	no	—
385	C₂²×D₇	—	2	2	no	—
386	C₂²×D₇	—	4	1	no	—
387	C₂²×D₇	—	4	1	no	—
388	C₂²×D₇	—	4	1	no	—
389	C₂²×D₇	C₂⁴	1	1	yes	characteristic
390	C₂²×D₇	C₂⁴	1	1	yes	characteristic
391	C₂²×D₇	C₂⁴	1	1	yes	characteristic
392	C₂²×D₇	C₂⁴	1	1	yes	characteristic
393	C₇×Q₈	—	4	1	no	—
394	C₇×Q₈	—	4	1	no	—
395	C₇×Q₈	—	4	1	no	—
396	C₇×Q₈	—	4	1	no	—
397	C₇×Q₈	—	4	1	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	2	2	no	—
400	C₇×D₄	—	4	1	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	4	1	no	—
405	C₂×C₄×C₇	—	4	1	no	—
406	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
408	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
409	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₂²⋊D₇	—	2	2	no	—
419	C₂²⋊D₇	—	2	2	no	—
420	C₂²⋊D₇	—	2	2	no	—
421	C₂²⋊D₇	—	4	1	no	—
422	C₂²⋊D₇	—	4	1	no	—
423	C₂²⋊D₇	—	4	1	no	—
424	C₂²⋊D₇	—	4	1	no	—
425	C₂²⋊D₇	—	4	1	no	—
426	C₂×Dic₇	—	2	2	no	—
427	C₂×Dic₇	—	4	1	no	—
428	C₂×Dic₇	—	4	1	no	—
429	C₂×Dic₇	—	4	1	no	—
430	C₂×Dic₇	—	4	1	no	—
431	C₂×Dic₇	—	4	1	no	—
432	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
433	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
434	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
435	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
436	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
444	D₂₈	—	2	2	no	—
445	D₂₈	—	4	1	no	—
446	D₂₈	—	4	1	no	—
447	D₂₈	—	4	1	no	—
448	C₄×D₇	—	2	2	no	—
449	C₄×D₇	—	4	1	no	—
450	C₄×D₇	—	4	1	no	—
451	C₄×D₇	—	4	1	no	—
452	C₄×D₇	—	4	1	no	—
453	C₄×D₇	—	4	1	no	—
454	C₄×D₇	—	4	1	no	—
455	C₄×D₇	—	4	1	no	—
456	C₄×D₇	—	4	1	no	—
457	C₄×D₇	—	4	1	no	—
458	C₄×D₇	—	4	1	no	—
459	C₄×D₇	—	4	1	no	—
460	Dic₁₄	—	4	1	no	—
461	Dic₁₄	—	4	1	no	—
462	Dic₁₄	—	4	1	no	—
463	Dic₁₄	—	4	1	no	—
464	C₂×#41	—	7	1	no	—
465	C₂×#41	—	7	1	no	—
466	C₂×#41	C₂×D₇	1	1	yes	characteristic
467	C₂²×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
468	C₂²×D₄	—	7	1	no	—
469	C₂³×C₄	—	7	1	no	—
470	C₄⋊Q₈	—	7	1	no	—
471	C₄⋊Q₈	—	7	1	no	—
472	C₄⋊Q₈	—	7	1	no	—
473	C₄⋊Q₈	—	7	1	no	—
474	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
475	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
476	#126	—	7	1	no	—
477	#126	—	7	1	no	—
478	#126	—	7	1	no	—
479	#126	—	7	1	no	—
480	#126	—	7	1	no	—
481	#126	—	7	1	no	—
482	#126	—	7	1	no	—
483	#126	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#125	—	7	1	no	—
489	#125	—	7	1	no	—
490	#125	—	7	1	no	—
491	#125	—	7	1	no	—
492	#125	—	7	1	no	—
493	#125	—	7	1	no	—
494	#125	—	7	1	no	—
495	#125	—	7	1	no	—
496	#125	—	7	1	no	—
497	#125	—	7	1	no	—
498	#124	—	7	1	no	—
499	#124	—	7	1	no	—
500	#124	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	C₂×D₇	1	1	yes	characteristic, complemented
505	#124	C₂×D₇	1	1	yes	characteristic, complemented
506	#123	—	7	1	no	—
507	#123	—	7	1	no	—
508	#123	—	7	1	no	—
509	#123	—	7	1	no	—
510	#123	—	7	1	no	—
511	#123	—	7	1	no	—
512	#123	—	7	1	no	—
513	#123	—	7	1	no	—
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	—	7	1	no	—
524	#123	—	7	1	no	—
525	#123	—	7	1	no	—
526	#123	—	7	1	no	—
527	#123	—	7	1	no	—
528	#123	—	7	1	no	—
529	#123	—	7	1	no	—
530	#123	C₂×D₇	1	1	yes	characteristic
531	#123	C₂×D₇	1	1	yes	characteristic
532	#123	C₂×D₇	1	1	yes	characteristic, complemented
533	#123	C₂×D₇	1	1	yes	characteristic, complemented
534	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	—	7	1	no	—
539	C₂²⋊Q₈	—	7	1	no	—
540	C₂²⋊Q₈	—	7	1	no	—
541	C₂²⋊Q₈	—	7	1	no	—
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	—	7	1	no	—
554	C₂²⋊Q₈	—	7	1	no	—
555	C₂²⋊Q₈	—	7	1	no	—
556	C₂²⋊Q₈	—	7	1	no	—
557	C₂²⋊Q₈	—	7	1	no	—
558	C₂²⋊Q₈	—	7	1	no	—
559	C₂²⋊Q₈	—	7	1	no	—
560	C₂²⋊Q₈	—	7	1	no	—
561	C₂²⋊Q₈	—	7	1	no	—
562	C₂²⋊Q₈	—	7	1	no	—
563	C₂²⋊Q₈	—	7	1	no	—
564	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
565	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
566	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
567	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	—	7	1	no	—
578	#120	—	7	1	no	—
579	#120	—	7	1	no	—
580	#120	—	7	1	no	—
581	#120	—	7	1	no	—
582	C₄×Q₈	—	7	1	no	—
583	C₄×Q₈	—	7	1	no	—
584	C₄×D₄	—	7	1	no	—
585	C₄×D₄	—	7	1	no	—
586	C₄×D₄	—	7	1	no	—
587	C₄×D₄	—	7	1	no	—
588	C₄×D₄	—	7	1	no	—
589	C₄×D₄	—	7	1	no	—
590	C₄×D₄	—	7	1	no	—
591	C₄×D₄	—	7	1	no	—
592	C₄×D₄	—	7	1	no	—
593	C₄×D₄	—	7	1	no	—
594	C₄×D₄	—	7	1	no	—
595	C₄×D₄	—	7	1	no	—
596	C₄×D₄	—	7	1	no	—
597	C₄×D₄	—	7	1	no	—
598	#117	—	7	1	no	—
599	#117	—	7	1	no	—
600	#117	—	7	1	no	—
601	#117	—	7	1	no	—
602	#117	—	7	1	no	—
603	#117	—	7	1	no	—
604	#117	C₂×D₇	1	1	yes	characteristic, complemented
605	C₂×C₄⋊C₄	—	7	1	no	—
606	C₂×C₄⋊C₄	—	7	1	no	—
607	C₂×C₄⋊C₄	—	7	1	no	—
608	C₂×C₄⋊C₄	—	7	1	no	—
609	C₂×C₄⋊C₄	—	7	1	no	—
610	C₂×C₄⋊C₄	—	7	1	no	—
611	C₂×C₄⋊C₄	—	7	1	no	—
612	C₂×C₂²⋊C₄	—	7	1	no	—
613	C₂×C₂²⋊C₄	—	7	1	no	—
614	C₂×C₂²⋊C₄	—	7	1	no	—
615	C₂×C₂²⋊C₄	—	7	1	no	—
616	C₂×C₂²⋊C₄	—	7	1	no	—
617	C₂×C₂²⋊C₄	—	7	1	no	—
618	C₂×C₂²⋊C₄	—	7	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	—	2	1	no	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	H(5,𝔽₂)	1	2	yes	—
628	C₂²×C₇	C₂⁵	1	1	yes	characteristic
629	C₂×D₇	—	2	1	no	—
630	C₂×D₇	—	2	1	no	—
631	C₂×D₇	—	2	1	no	—
632	C₂×D₇	—	2	1	no	—
633	C₂×D₇	—	2	1	no	—
634	C₂×D₇	—	2	1	no	—
635	C₂×D₇	—	2	1	no	—
636	C₂×D₇	—	2	1	no	—
637	C₂×D₇	—	2	1	no	—
638	C₂×D₇	—	2	1	no	—
639	C₂×D₇	—	2	1	no	—
640	C₂×D₇	—	4	4	no	—
641	C₂×D₇	—	8	2	no	—
642	C₂×D₇	2₋¹⁺⁴	1	2	yes	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	1	no	—
652	C₄×C₇	—	2	1	no	—
653	C₄×C₇	—	2	1	no	—
654	C₄×C₇	—	2	1	no	—
655	Dic₇	—	2	1	no	—
656	Dic₇	—	2	1	no	—
657	Dic₇	—	2	1	no	—
658	Dic₇	—	2	1	no	—
659	Dic₇	—	2	1	no	—
660	Dic₇	—	2	1	no	—
661	Dic₇	—	2	1	no	—
662	Dic₇	—	2	1	no	—
663	Dic₇	—	2	1	no	—
664	Dic₇	—	2	1	no	—
665	Dic₇	—	2	1	no	—
666	Dic₇	—	2	1	no	—
667	C₂⁴	—	7	1	no	—
668	C₂⁴	—	7	1	no	—
669	#41	—	4	2	no	—
670	#41	—	28	2	no	—
671	#41	—	28	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	7	1	no	—
674	C₂×Q₈	—	7	1	no	—
675	C₂×Q₈	—	7	1	no	—
676	C₂×Q₈	—	7	1	no	—
677	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
678	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
679	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
680	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
681	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
682	C₂×D₄	—	7	1	no	—
683	C₂×D₄	—	7	1	no	—
684	C₂×D₄	—	7	1	no	—
685	C₂×D₄	—	7	1	no	—
686	C₂×D₄	—	7	1	no	—
687	C₂×D₄	—	7	1	no	—
688	C₂×D₄	—	7	1	no	—
689	C₂×D₄	—	7	1	no	—
690	C₂×D₄	—	7	1	no	—
691	C₂×D₄	—	7	1	no	—
692	C₂×D₄	—	7	1	no	—
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	28	2	no	—
695	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
696	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
697	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
698	C₂²×C₄	—	7	1	no	—
699	C₂²×C₄	—	7	1	no	—
700	C₂²×C₄	—	7	1	no	—
701	C₂²×C₄	—	7	1	no	—
702	C₂²×C₄	—	7	1	no	—
703	C₂²×C₄	—	7	1	no	—
704	C₂²×C₄	—	7	1	no	—
705	C₂²×C₄	—	7	1	no	—
706	C₂²×C₄	—	7	1	no	—
707	C₂²×C₄	—	7	1	no	—
708	C₂²×C₄	—	7	1	no	—
709	C₂²×C₄	—	7	1	no	—
710	C₂²×C₄	—	7	1	no	—
711	C₂²×C₄	—	7	1	no	—
712	C₂²×C₄	—	7	1	no	—
713	C₂²×C₄	—	7	1	no	—
714	C₂²×C₄	—	7	1	no	—
715	C₂²×C₄	—	7	1	no	—
716	C₂²×C₄	—	28	2	no	—
717	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
720	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
721	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
722	C₄⋊C₄	—	7	1	no	—
723	C₄⋊C₄	—	7	1	no	—
724	C₄⋊C₄	—	7	1	no	—
725	C₄⋊C₄	—	7	1	no	—
726	C₄⋊C₄	—	7	1	no	—
727	C₄⋊C₄	—	7	1	no	—
728	C₄⋊C₄	—	7	1	no	—
729	C₄⋊C₄	—	7	1	no	—
730	C₄⋊C₄	—	7	1	no	—
731	C₄⋊C₄	—	7	1	no	—
732	C₄⋊C₄	—	7	1	no	—
733	C₄⋊C₄	—	7	1	no	—
734	C₄⋊C₄	—	7	1	no	—
735	C₄⋊C₄	—	7	1	no	—
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	—	7	1	no	—
739	C₄⋊C₄	—	7	1	no	—
740	C₄⋊C₄	—	7	1	no	—
741	C₄⋊C₄	—	7	1	no	—
742	C₄⋊C₄	—	7	1	no	—
743	C₄⋊C₄	—	7	1	no	—
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	—	7	1	no	—
757	C₄⋊C₄	—	7	1	no	—
758	C₄⋊C₄	—	7	1	no	—
759	C₄⋊C₄	—	7	1	no	—
760	C₄⋊C₄	—	7	1	no	—
761	C₄⋊C₄	—	7	1	no	—
762	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₂²⋊C₄	—	7	1	no	—
773	C₂²⋊C₄	—	7	1	no	—
774	C₂²⋊C₄	—	7	1	no	—
775	C₂²⋊C₄	—	7	1	no	—
776	C₂²⋊C₄	—	7	1	no	—
777	C₂²⋊C₄	—	7	1	no	—
778	C₂²⋊C₄	—	7	1	no	—
779	C₂²⋊C₄	—	7	1	no	—
780	C₂²⋊C₄	—	7	1	no	—
781	C₂²⋊C₄	—	7	1	no	—
782	C₂²⋊C₄	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	—	7	1	no	—
801	C₂²⋊C₄	—	7	1	no	—
802	C₂²⋊C₄	—	7	1	no	—
803	C₂²⋊C₄	—	7	1	no	—
804	C₂²⋊C₄	—	7	1	no	—
805	C₂²⋊C₄	—	7	1	no	—
806	C₂²⋊C₄	—	7	1	no	—
807	C₂²⋊C₄	—	7	1	no	—
808	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
809	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
810	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
818	C₄²	—	7	1	no	—
819	C₄²	—	7	1	no	—
820	C₄²	—	7	1	no	—
821	C₄²	—	7	1	no	—
822	C₄²	—	7	1	no	—
823	C₄²	—	7	1	no	—
824	C₄²	—	7	1	no	—
825	C₄²	—	7	1	no	—
826	C₄²	C₂²×D₇	1	1	yes	characteristic
827	C₄²	C₂²×D₇	1	1	yes	characteristic
828	C₂×C₇	—	2	2	no	—
829	C₂×C₇	—	4	1	no	—
830	C₂×C₇	—	4	1	no	—
831	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
832	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
833	C₂×C₇	#585	1	1	yes	characteristic
834	D₇	—	2	2	no	—
835	D₇	—	4	1	no	—
836	D₇	—	4	1	no	—
837	D₇	—	4	1	no	—
838	C₂³	—	7	1	no	—
839	C₂³	—	7	1	no	—
840	C₂³	—	7	1	no	—
841	C₂³	—	7	1	no	—
842	C₂³	—	14	2	no	—
843	C₂³	—	14	2	no	—
844	C₂³	—	14	2	no	—
845	C₂³	—	28	1	no	—
846	C₂³	—	28	1	no	—
847	C₂³	—	28	1	no	—
848	C₂³	C₂³×D₇	1	1	yes	characteristic
849	C₂³	C₂³×D₇	1	1	yes	characteristic
850	C₂³	C₂³×D₇	1	1	yes	characteristic
851	Q₈	—	4	1	no	—
852	Q₈	—	4	1	no	—
853	Q₈	—	4	1	no	—
854	Q₈	—	4	1	no	—
855	Q₈	—	4	1	no	—
856	Q₈	—	28	1	no	—
857	Q₈	—	28	1	no	—
858	Q₈	—	28	1	no	—
859	Q₈	—	28	1	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	4	1	no	—
863	D₄	—	14	2	no	—
864	D₄	—	14	2	no	—
865	D₄	—	14	2	no	—
866	D₄	—	14	2	no	—
867	D₄	—	28	1	no	—
868	D₄	—	28	1	no	—
869	D₄	—	28	1	no	—
870	D₄	—	28	1	no	—
871	D₄	—	28	1	no	—
872	D₄	—	28	1	no	—
873	D₄	—	28	1	no	—
874	D₄	—	28	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	7	1	no	—
881	C₂×C₄	—	7	1	no	—
882	C₂×C₄	—	7	1	no	—
883	C₂×C₄	—	7	1	no	—
884	C₂×C₄	—	7	1	no	—
885	C₂×C₄	—	7	1	no	—
886	C₂×C₄	—	7	1	no	—
887	C₂×C₄	—	7	1	no	—
888	C₂×C₄	—	7	1	no	—
889	C₂×C₄	—	7	1	no	—
890	C₂×C₄	—	7	1	no	—
891	C₂×C₄	—	7	1	no	—
892	C₂×C₄	—	14	2	no	—
893	C₂×C₄	—	14	2	no	—
894	C₂×C₄	—	28	1	no	—
895	C₂×C₄	—	28	1	no	—
896	C₂×C₄	—	28	1	no	—
897	C₂×C₄	—	28	1	no	—
898	C₂×C₄	—	28	1	no	—
899	C₂×C₄	—	28	1	no	—
900	C₂×C₄	—	28	1	no	—
901	C₂×C₄	—	28	1	no	—
902	C₂×C₄	—	28	1	no	—
903	C₂×C₄	—	28	1	no	—
904	C₂×C₄	—	28	1	no	—
905	C₂×C₄	—	28	1	no	—
906	C₂×C₄	—	28	1	no	—
907	C₂×C₄	—	28	1	no	—
908	C₂×C₄	—	28	1	no	—
909	C₂×C₄	—	28	1	no	—
910	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
922	C₇	#3535	1	1	yes	characteristic, complemented, Sylow
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	7	2	no	—
932	C₂²	—	14	1	no	—
933	C₂²	—	14	1	no	—
934	C₂²	—	14	1	no	—
935	C₂²	—	14	1	no	—
936	C₂²	—	14	1	no	—
937	C₂²	—	14	1	no	—
938	C₂²	—	14	1	no	—
939	C₂²	—	14	1	no	—
940	C₂²	—	14	1	no	—
941	C₂²	—	14	1	no	—
942	C₂²	—	14	1	no	—
943	C₂²	—	28	4	no	—
944	C₂²	—	56	2	no	—
945	C₂²	#6548	1	2	yes	—
946	C₂²	C₂⁴×D₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	14	1	no	—
960	C₄	—	14	1	no	—
961	C₄	—	14	1	no	—
962	C₄	—	14	1	no	—
963	C₄	—	14	1	no	—
964	C₄	—	14	1	no	—
965	C₄	—	14	1	no	—
966	C₄	—	14	1	no	—
967	C₄	—	14	1	no	—
968	C₄	—	14	1	no	—
969	C₄	—	14	1	no	—
970	C₄	—	14	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	14	2	no	—
975	C₂	—	28	1	no	—
976	C₂	—	28	1	no	—
977	C₂	—	28	1	no	—
978	C₂	C₂×#6548	1	1	yes	characteristic
979	C₂	D₇×2₋¹⁺⁴	1	1	yes	characteristic
980	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#536	C₂
hypercenter	#536	D₇
hypocenter	C₇	#3535
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₇×#536	C₂	semidirect
2. #90520	C₂	semidirect
3. #90515	C₂	semidirect
4. #90507	C₂	semidirect
5. C₂×#6509	C₂	semidirect
6. #90426	C₂	semidirect
7. #90424	C₂	semidirect
8. #90421	C₂	semidirect
9. #90420	C₂	semidirect
10. #90375	C₂	semidirect
11. #90370	C₂	semidirect
12. #90369	C₂	semidirect
13. #90360	C₂	semidirect
14. #90356	C₂	semidirect
15. #90356	C₂	semidirect
16. #90349	C₂	semidirect
17. #90347	C₂	semidirect
18. #90346	C₂	semidirect
19. #90345	C₂	semidirect
20. D₇×#123	C₂	semidirect
21. #90341	C₂	semidirect
22. #90338	C₂	semidirect
23. #90337	C₂	semidirect
24. #90336	C₂	semidirect
25. #90329	C₂	semidirect
26. #90329	C₂	semidirect
27. #90328	C₂	semidirect
28. #90327	C₂	semidirect
29. #90325	C₂	semidirect
30. #90222	C₂	semidirect
31. #90218	C₂	semidirect
33. C₂²×C₇×Q₈	C₂²	semidirect
34. C₂×#1159	C₂²	semidirect
38. C₇×C₄⋊Q₈	C₂²	semidirect
39. C₇×C₄⋊Q₈	C₂²	semidirect
40. C₇×#124	C₂²	semidirect
41. C₇×#124	C₂²	semidirect
44. C₇×#123	C₂²	semidirect
45. C₇×#123	C₂²	semidirect
46. C₇×C₂²⋊Q₈	C₂²	semidirect
47. C₇×C₂²⋊Q₈	C₂²	semidirect
48. C₇×C₂²⋊Q₈	C₂²	semidirect
49. C₇×C₂²⋊Q₈	C₂²	semidirect
50. C₇×#117	C₂²	semidirect
52. #6510	C₂²	semidirect
53. #6510	C₂²	semidirect
59. #6509	C₂²	semidirect
60. #6509	C₂²	semidirect
61. #6509	C₂²	semidirect
62. #6509	C₂²	semidirect
63. #6509	C₂²	semidirect
64. #6509	C₂²	semidirect
65. #6509	C₂²	semidirect
66. #6509	C₂²	semidirect
67. #6509	C₂²	semidirect
68. #6507	C₂²	semidirect
69. #6507	C₂²	semidirect
70. #6507	C₂²	semidirect
74. #6502	C₂²	semidirect
78. #6498	C₂²	semidirect
80. D₄×Dic₇	C₂²	semidirect
85. #6492	C₂²	semidirect
86. #6492	C₂²	semidirect
87. #6492	C₂²	semidirect
89. C₄×C₂²⋊D₇	C₂²	semidirect
93. #6489	C₂²	semidirect
94. C₂×C₄⋊Dic₇	C₂²	semidirect
95. #6487	C₂²	semidirect
96. C₂×Dic₇⋊C₄	C₂²	semidirect
97. C₂×Dic₇⋊C₄	C₂²	semidirect
98. C₂×Dic₇⋊C₄	C₂²	semidirect
99. #6461	C₂²	semidirect
100. #6461	C₂²	semidirect
101. #6461	C₂²	semidirect
102. #6461	C₂²	semidirect
103. #6461	C₂²	semidirect
104. #6461	C₂²	semidirect
106. #6460	C₂²	semidirect
107. #6460	C₂²	semidirect
111. #6459	C₂²	semidirect
112. #6459	C₂²	semidirect
113. #6459	C₂²	semidirect
119. #6457	C₂²	semidirect
120. #6457	C₂²	semidirect
123. #6456	C₂²	semidirect
127. D₇×C₄⋊C₄	C₂²	semidirect
128. #6453	C₂²	semidirect
129. #6453	C₂²	semidirect
130. #6453	C₂²	semidirect
131. #6452	C₂²	semidirect
132. #6452	C₂²	semidirect
133. #6452	C₂²	semidirect
134. #6452	C₂²	semidirect
135. #6452	C₂²	semidirect
136. #6452	C₂²	semidirect
137. #6451	C₂²	semidirect
138. #6450	C₂²	semidirect
140. #6449	C₂²	semidirect
141. #6449	C₂²	semidirect
142. #6449	C₂²	semidirect
144. #6448	C₂²	semidirect
147. #6447	C₂²	semidirect
148. #6447	C₂²	semidirect
152. #6446	C₂²	semidirect
153. #6446	C₂²	semidirect
154. #6446	C₂²	semidirect
160. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
161. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
162. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
167. #6442	C₂²	semidirect
168. #6442	C₂²	semidirect
169. #6442	C₂²	semidirect
170. #6442	C₂²	semidirect
171. #6441	C₂²	semidirect
172. #6441	C₂²	semidirect
173. #6441	C₂²	semidirect
174. #6441	C₂²	semidirect
175. #6441	C₂²	semidirect
176. #6441	C₂²	semidirect
177. #6440	C₂²	semidirect
178. #6440	C₂²	semidirect
179. #6439	C₂²	semidirect
180. #6439	C₂²	semidirect
181. #6438	C₂²	semidirect
184. #6435	C₂²	semidirect
185. #6433	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
376. #536	D₇	semidirect
467. C₂²×Q₈	C₂×D₇	semidirect
474. C₄⋊Q₈	C₂×D₇	semidirect
475. C₄⋊Q₈	C₂×D₇	semidirect
504. #124	C₂×D₇	semidirect
505. #124	C₂×D₇	semidirect
532. #123	C₂×D₇	semidirect
533. #123	C₂×D₇	semidirect
564. C₂²⋊Q₈	C₂×D₇	semidirect
565. C₂²⋊Q₈	C₂×D₇	semidirect
566. C₂²⋊Q₈	C₂×D₇	semidirect
567. C₂²⋊Q₈	C₂×D₇	semidirect
604. #117	C₂×D₇	semidirect
922. C₇	#3535	semidirect

Maximal subgroups

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

subgroup	index
C₇×#536	2
#90520	2
#90515	2
#90507	2
C₂×#6509	2
#90426	2
#90424	2
#90421	2
#90420	2
#90375	2
#90370	2
#90369	2
#90360	2
#90356	2
#90349	2
#90347	2
#90346	2
#90345	2
D₇×#123	2
#90341	2
#90338	2
#90337	2
#90336	2
#90329	2
#90328	2
#90327	2
#90325	2
#90222	2
#90218	2
#3535	7