Subgroups — #11743489

Order 896.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	#90400	C₂	1	1	yes	maximal, characteristic, complemented
3	#90398	C₂	1	1	yes	maximal, characteristic, complemented
4	#90396	C₂	1	1	yes	maximal, characteristic, complemented
5	#90395	C₂	1	1	yes	maximal, characteristic, complemented
6	#90375	C₂	1	1	yes	maximal, characteristic, complemented
7	#90370	C₂	1	1	yes	maximal, characteristic, complemented
8	#90367	C₂	1	1	yes	maximal, characteristic, complemented
9	#90367	C₂	1	1	yes	maximal, characteristic, complemented
10	#90354	C₂	1	1	yes	maximal, characteristic, complemented
11	#90351	C₂	1	1	yes	maximal, characteristic, complemented
12	#90344	C₂	1	1	yes	maximal, characteristic, complemented
13	D₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
14	#90329	C₂	1	1	yes	maximal, characteristic, complemented
15	#90320	C₂	1	1	yes	maximal, characteristic, complemented
16	#90312	C₂	1	1	yes	maximal, characteristic, complemented
17	#90311	C₂	1	1	yes	maximal, characteristic, complemented
18	#90304	C₂	1	1	yes	maximal, characteristic, complemented
19	#90303	C₂	1	1	yes	maximal, characteristic, complemented
20	#90300	C₂	1	1	yes	maximal, characteristic, complemented
21	D₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	#90286	C₂	1	1	yes	maximal, characteristic, complemented
23	#90281	C₂	1	1	yes	maximal, characteristic, complemented
24	#90280	C₂	1	1	yes	maximal, characteristic, complemented
25	#90280	C₂	1	1	yes	maximal, characteristic, complemented
26	#90253	C₂	1	1	yes	maximal, characteristic, complemented
27	#90249	C₂	1	1	yes	maximal, characteristic, complemented
28	#90241	C₂	1	1	yes	maximal, characteristic, complemented
29	#90238	C₂	1	1	yes	maximal, characteristic, complemented
30	#90181	C₂	1	1	yes	maximal, characteristic, complemented
31	#90181	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
38	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
41	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₂₈	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
44	C₇×#126	C₂²	1	1	yes	characteristic, complemented
45	C₇×#126	C₂²	1	1	yes	characteristic, complemented
46	C₇×#124	C₂²	1	1	yes	characteristic, complemented
47	C₇×#124	C₂²	1	1	yes	characteristic, complemented
48	C₇×#123	C₂²	1	1	yes	characteristic, complemented
49	C₇×#123	C₂²	1	1	yes	characteristic, complemented
50	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₇×#121	C₂²	1	1	yes	characteristic, complemented
52	C₇×#121	C₂²	1	1	yes	characteristic, complemented
53	C₇×#121	C₂²	1	1	yes	characteristic, complemented
54	C₇×#120	C₂²	1	1	yes	characteristic, complemented
55	C₇×#120	C₂²	1	1	yes	characteristic, complemented
56	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
57	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	#6516	C₂²	1	1	yes	characteristic, complemented
60	#6516	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	#6503	C₂²	1	1	yes	characteristic, complemented
65	#6503	C₂²	1	1	yes	characteristic, complemented
66	#6502	C₂²	1	1	yes	characteristic, complemented
67	#6502	C₂²	1	1	yes	characteristic, complemented
68	#6502	C₂²	1	1	yes	characteristic, complemented
69	#6502	C₂²	1	1	yes	characteristic, complemented
70	#6502	C₂²	1	1	yes	characteristic, complemented
71	#6501	C₂²	1	1	yes	characteristic
72	#6501	C₂²	1	1	yes	characteristic, complemented
73	#6501	C₂²	1	1	yes	characteristic, complemented
74	#6501	C₂²	1	1	yes	characteristic, complemented
75	#6501	C₂²	1	1	yes	characteristic, complemented
76	#6501	C₂²	1	1	yes	characteristic, complemented
77	#6500	C₂²	1	1	yes	characteristic
78	#6500	C₂²	1	1	yes	characteristic, complemented
79	#6500	C₂²	1	1	yes	characteristic, complemented
80	#6500	C₂²	1	1	yes	characteristic, complemented
81	#6500	C₂²	1	1	yes	characteristic, complemented
82	#6500	C₂²	1	1	yes	characteristic, complemented
83	#6499	C₂²	1	1	yes	characteristic, complemented
84	#6498	C₂²	1	1	yes	characteristic, complemented
85	#6498	C₂²	1	1	yes	characteristic, complemented
86	#6498	C₂²	1	1	yes	characteristic, complemented
87	#6493	C₂²	1	1	yes	characteristic, complemented
88	#6493	C₂²	1	1	yes	characteristic, complemented
89	#6493	C₂²	1	1	yes	characteristic, complemented
90	#6492	C₂²	1	1	yes	characteristic, complemented
91	#6492	C₂²	1	1	yes	characteristic, complemented
92	#6492	C₂²	1	1	yes	characteristic, complemented
93	#6492	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
98	#6487	C₂²	1	1	yes	characteristic, complemented
99	#6461	C₂²	1	1	yes	characteristic, complemented
100	#6461	C₂²	1	1	yes	characteristic, complemented
101	#6460	C₂²	1	1	yes	characteristic, complemented
102	#6459	C₂²	1	1	yes	characteristic, complemented
103	#6459	C₂²	1	1	yes	characteristic, complemented
104	#6459	C₂²	1	1	yes	characteristic, complemented
105	#6458	C₂²	1	1	yes	characteristic, complemented
106	#6458	C₂²	1	1	yes	characteristic, complemented
107	#6458	C₂²	1	1	yes	characteristic, complemented
108	#6458	C₂²	1	1	yes	characteristic, complemented
109	#6457	C₂²	1	1	yes	characteristic, complemented
110	#6457	C₂²	1	1	yes	characteristic, complemented
111	#6457	C₂²	1	1	yes	characteristic, complemented
112	#6457	C₂²	1	1	yes	characteristic, complemented
113	#6457	C₂²	1	1	yes	characteristic, complemented
114	#6456	C₂²	1	1	yes	characteristic, complemented
115	#6456	C₂²	1	1	yes	characteristic, complemented
116	#6455	C₂²	1	1	yes	characteristic, complemented
117	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
118	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	#6453	C₂²	1	1	yes	characteristic, complemented
121	#6452	C₂²	1	1	yes	characteristic, complemented
122	#6452	C₂²	1	1	yes	characteristic, complemented
123	#6449	C₂²	1	1	yes	characteristic, complemented
124	#6449	C₂²	1	1	yes	characteristic, complemented
125	#6449	C₂²	1	1	yes	characteristic, complemented
126	#6448	C₂²	1	1	yes	characteristic, complemented
127	#6448	C₂²	1	1	yes	characteristic, complemented
128	#6447	C₂²	1	1	yes	characteristic
129	#6447	C₂²	1	1	yes	characteristic
130	#6447	C₂²	1	1	yes	characteristic, complemented
131	#6447	C₂²	1	1	yes	characteristic, complemented
132	#6447	C₂²	1	1	yes	characteristic, complemented
133	#6447	C₂²	1	1	yes	characteristic, complemented
134	#6447	C₂²	1	1	yes	characteristic, complemented
135	#6447	C₂²	1	1	yes	characteristic, complemented
136	#6447	C₂²	1	1	yes	characteristic, complemented
137	#6447	C₂²	1	1	yes	characteristic, complemented
138	#6447	C₂²	1	1	yes	characteristic, complemented
139	#6447	C₂²	1	1	yes	characteristic, complemented
140	#6447	C₂²	1	1	yes	characteristic, complemented
141	#6447	C₂²	1	1	yes	characteristic, complemented
142	#6447	C₂²	1	1	yes	characteristic, complemented
143	#6446	C₂²	1	1	yes	characteristic, complemented
144	#6446	C₂²	1	1	yes	characteristic, complemented
145	#6446	C₂²	1	1	yes	characteristic, complemented
146	#6446	C₂²	1	1	yes	characteristic, complemented
147	#6446	C₂²	1	1	yes	characteristic, complemented
148	#6446	C₂²	1	1	yes	characteristic, complemented
149	#6446	C₂²	1	1	yes	characteristic, complemented
150	#6446	C₂²	1	1	yes	characteristic, complemented
151	#6446	C₂²	1	1	yes	characteristic, complemented
152	#6446	C₂²	1	1	yes	characteristic, complemented
153	#6446	C₂²	1	1	yes	characteristic, complemented
154	#6445	C₂²	1	1	yes	characteristic
155	#6445	C₂²	1	1	yes	characteristic, complemented
156	#6445	C₂²	1	1	yes	characteristic, complemented
157	#6445	C₂²	1	1	yes	characteristic, complemented
158	#6445	C₂²	1	1	yes	characteristic, complemented
159	#6445	C₂²	1	1	yes	characteristic, complemented
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	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
167	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
169	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
170	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
171	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
172	#6442	C₂²	1	1	yes	characteristic, complemented
173	#6442	C₂²	1	1	yes	characteristic, complemented
174	#6442	C₂²	1	1	yes	characteristic, complemented
175	#6442	C₂²	1	1	yes	characteristic, complemented
176	#6441	C₂²	1	1	yes	characteristic, complemented
177	#6441	C₂²	1	1	yes	characteristic, complemented
178	#6441	C₂²	1	1	yes	characteristic, complemented
179	#6438	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
184	#6435	C₂²	1	1	yes	characteristic, complemented
185	#6435	C₂²	1	1	yes	characteristic, complemented
186	#6433	C₂²	1	1	yes	characteristic, complemented
187	#3534	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂³×D₇	C₂³	1	1	yes	characteristic
191	C₂³×D₇	C₂³	1	1	yes	characteristic
192	C₂³×D₇	C₂³	1	1	yes	characteristic
193	C₂³×D₇	C₂³	1	1	yes	characteristic
194	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
195	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
196	C₂×C₇×D₄	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	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
201	C₂×C₇×D₄	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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₇	—	4	2	no	—
207	C₂×C₂²⋊D₇	—	4	2	no	—
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	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
228	C₂²×Dic₇	C₂³	1	1	yes	characteristic
229	C₂²×Dic₇	C₂³	1	1	yes	characteristic
230	C₂²×Dic₇	C₂³	1	1	yes	characteristic
231	#1161	—	4	2	no	—
232	D₄×D₇	—	4	2	no	—
233	D₄×D₇	—	4	2	no	—
234	D₄×D₇	—	4	2	no	—
235	D₄×D₇	—	4	2	no	—
236	D₄×D₇	—	4	2	no	—
237	#1157	—	4	2	no	—
238	#1157	—	4	2	no	—
239	C₂×D₂₈	—	4	2	no	—
240	C₂×D₂₈	C₂³	1	1	yes	characteristic
241	C₂×D₂₈	C₂³	1	1	yes	characteristic
242	C₂×D₂₈	C₂³	1	1	yes	characteristic
243	C₂×D₂₈	C₂³	1	1	yes	characteristic
244	C₂×D₂₈	C₂³	1	1	yes	characteristic
245	C₂×D₂₈	C₂³	1	1	yes	characteristic
246	C₂×D₂₈	C₂³	1	1	yes	characteristic
247	C₂×D₂₈	C₂³	1	1	yes	characteristic
248	C₂×D₂₈	C₂³	1	1	yes	characteristic
249	C₂×D₂₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₇	—	4	2	no	—
251	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
252	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
253	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
254	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
255	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
256	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
257	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
258	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
259	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
260	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
261	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
262	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
263	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
264	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
265	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
266	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
267	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
268	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
269	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
277	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
278	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
279	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
280	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
281	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
282	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
283	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
284	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
285	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
286	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
287	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
288	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
289	C₄²×C₇	C₂³	1	1	yes	characteristic
290	C₄²×C₇	C₂³	1	1	yes	characteristic
291	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
292	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
293	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
294	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
295	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
296	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
297	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
298	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
299	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
300	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
301	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
302	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
303	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
306	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
307	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
308	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
309	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
310	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
311	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
312	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
313	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
314	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
315	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
316	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
317	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
318	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
319	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
320	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
321	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
322	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
323	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
324	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
325	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
326	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
327	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
328	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
329	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
330	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
331	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
332	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
333	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
334	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
342	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
343	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
344	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
345	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
346	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
347	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
348	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
349	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
350	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
351	C₄×Dic₇	C₂³	1	1	yes	characteristic
352	C₄×Dic₇	C₂³	1	1	yes	characteristic
353	C₄×Dic₇	C₂³	1	1	yes	characteristic
354	C₄×Dic₇	C₂³	1	1	yes	characteristic
355	#562	—	7	1	no	—
356	#562	—	7	1	no	—
357	#560	—	7	1	no	—
358	#560	—	7	1	no	—
359	#553	—	7	1	no	—
360	#553	—	7	1	no	—
361	#551	—	7	1	no	—
362	#551	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#546	—	7	1	no	—
366	#546	—	7	1	no	—
367	#546	—	7	1	no	—
368	#546	—	7	1	no	—
369	D₄²	—	7	1	no	—
370	D₄²	—	7	1	no	—
371	#540	—	7	1	no	—
372	#540	—	7	1	no	—
373	#539	—	7	1	no	—
374	#539	—	7	1	no	—
375	#539	—	7	1	no	—
376	#538	—	7	1	no	—
377	#538	—	7	1	no	—
378	#538	D₇	1	1	yes	characteristic, complemented
379	#537	—	7	1	no	—
380	#534	—	7	1	no	—
381	#534	—	7	1	no	—
382	#534	—	7	1	no	—
383	#525	—	7	1	no	—
384	C₂×#123	—	7	1	no	—
385	C₂×#121	—	7	1	no	—
386	C₂³×C₇	—	4	1	no	—
387	C₂³×C₇	—	4	1	no	—
388	C₂³×C₇	—	4	1	no	—
389	C₂³×C₇	C₂⁴	1	1	yes	characteristic
390	C₂³×C₇	C₂⁴	1	1	yes	characteristic
391	C₂³×C₇	C₂⁴	1	1	yes	characteristic
392	C₂³×C₇	C₂⁴	1	1	yes	characteristic
393	C₂³×C₇	C₂⁴	1	1	yes	characteristic
394	C₂²×D₇	—	2	2	no	—
395	C₂²×D₇	—	2	2	no	—
396	C₂²×D₇	—	2	2	no	—
397	C₂²×D₇	—	2	2	no	—
398	C₂²×D₇	—	2	2	no	—
399	C₂²×D₇	—	4	1	no	—
400	C₂²×D₇	—	4	1	no	—
401	C₂²×D₇	—	4	1	no	—
402	C₂²×D₇	—	4	1	no	—
403	C₂²×D₇	—	4	1	no	—
404	C₂²×D₇	—	4	1	no	—
405	C₂²×D₇	—	4	1	no	—
406	C₂²×D₇	—	4	1	no	—
407	C₂²×D₇	—	4	1	no	—
408	C₂²×D₇	—	4	1	no	—
409	C₂²×D₇	C₂⁴	1	1	yes	characteristic
410	C₂²×D₇	C₂⁴	1	1	yes	characteristic
411	C₂²×D₇	C₂⁴	1	1	yes	characteristic
412	C₂²×D₇	C₂⁴	1	1	yes	characteristic
413	C₂²×D₇	C₂⁴	1	1	yes	characteristic
414	C₂²×D₇	C₂⁴	1	1	yes	characteristic
415	C₇×Q₈	—	4	1	no	—
416	C₇×D₄	—	4	1	no	—
417	C₇×D₄	—	4	1	no	—
418	C₇×D₄	—	4	1	no	—
419	C₇×D₄	—	4	1	no	—
420	C₇×D₄	—	4	1	no	—
421	C₇×D₄	—	4	1	no	—
422	C₇×D₄	—	4	1	no	—
423	C₂×C₄×C₇	—	4	1	no	—
424	C₂×C₄×C₇	—	4	1	no	—
425	C₂×C₄×C₇	—	4	1	no	—
426	C₂×C₄×C₇	—	4	1	no	—
427	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
430	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
431	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
432	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
433	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
434	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
435	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
437	C₂²⋊D₇	—	2	2	no	—
438	C₂²⋊D₇	—	2	2	no	—
439	C₂²⋊D₇	—	2	2	no	—
440	C₂²⋊D₇	—	2	2	no	—
441	C₂²⋊D₇	—	2	2	no	—
442	C₂²⋊D₇	—	4	1	no	—
443	C₂²⋊D₇	—	4	1	no	—
444	C₂²⋊D₇	—	4	1	no	—
445	C₂²⋊D₇	—	4	1	no	—
446	C₂²⋊D₇	—	4	1	no	—
447	C₂²⋊D₇	—	4	1	no	—
448	C₂²⋊D₇	—	4	1	no	—
449	C₂²⋊D₇	—	4	1	no	—
450	C₂²⋊D₇	—	4	1	no	—
451	C₂²⋊D₇	—	4	1	no	—
452	C₂²⋊D₇	—	4	1	no	—
453	C₂²⋊D₇	—	4	1	no	—
454	C₂²⋊D₇	—	4	1	no	—
455	C₂²⋊D₇	—	4	1	no	—
456	C₂²⋊D₇	—	4	1	no	—
457	C₂×Dic₇	—	4	1	no	—
458	C₂×Dic₇	—	4	1	no	—
459	C₂×Dic₇	—	4	1	no	—
460	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
461	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
462	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
463	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
464	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
465	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
466	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
467	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
468	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
469	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
470	D₂₈	—	2	2	no	—
471	D₂₈	—	2	2	no	—
472	D₂₈	—	2	2	no	—
473	D₂₈	—	2	2	no	—
474	D₂₈	—	2	2	no	—
475	D₂₈	—	4	1	no	—
476	D₂₈	—	4	1	no	—
477	D₂₈	—	4	1	no	—
478	D₂₈	—	4	1	no	—
479	D₂₈	—	4	1	no	—
480	C₄×D₇	—	2	2	no	—
481	C₄×D₇	—	2	2	no	—
482	C₄×D₇	—	2	2	no	—
483	C₄×D₇	—	4	1	no	—
484	C₄×D₇	—	4	1	no	—
485	C₄×D₇	—	4	1	no	—
486	C₄×D₇	—	4	1	no	—
487	C₄×D₇	—	4	1	no	—
488	C₄×D₇	—	4	1	no	—
489	C₄×D₇	—	4	1	no	—
490	C₄×D₇	—	4	1	no	—
491	C₄×D₇	—	4	1	no	—
492	C₄×D₇	—	4	1	no	—
493	C₄×D₇	—	4	1	no	—
494	C₄×D₇	—	4	1	no	—
495	C₄×D₇	—	4	1	no	—
496	Dic₁₄	—	4	1	no	—
497	Dic₁₄	—	4	1	no	—
498	C₂×#41	—	7	1	no	—
499	C₂×#41	—	7	1	no	—
500	C₂×#41	—	7	1	no	—
501	C₂²×D₄	—	7	1	no	—
502	C₂²×D₄	—	7	1	no	—
503	C₂²×D₄	—	7	1	no	—
504	C₂²×D₄	—	7	1	no	—
505	C₂²×D₄	—	7	1	no	—
506	C₂²×D₄	—	7	1	no	—
507	C₂²×D₄	—	7	1	no	—
508	C₂²×D₄	—	7	1	no	—
509	C₂³×C₄	—	7	1	no	—
510	#127	—	7	1	no	—
511	#127	—	7	1	no	—
512	#126	—	7	1	no	—
513	#126	—	7	1	no	—
514	#126	—	7	1	no	—
515	#126	—	7	1	no	—
516	#126	—	7	1	no	—
517	#126	—	7	1	no	—
518	#126	C₂×D₇	1	1	yes	characteristic, complemented
519	#126	C₂×D₇	1	1	yes	characteristic, complemented
520	#125	—	7	1	no	—
521	#125	—	7	1	no	—
522	#125	—	7	1	no	—
523	#125	—	7	1	no	—
524	#124	—	7	1	no	—
525	#124	—	7	1	no	—
526	#124	—	7	1	no	—
527	#124	—	7	1	no	—
528	#124	C₂×D₇	1	1	yes	characteristic, complemented
529	#124	C₂×D₇	1	1	yes	characteristic, complemented
530	#123	—	7	1	no	—
531	#123	—	7	1	no	—
532	#123	—	7	1	no	—
533	#123	—	7	1	no	—
534	#123	—	7	1	no	—
535	#123	—	7	1	no	—
536	#123	—	7	1	no	—
537	#123	—	7	1	no	—
538	#123	—	7	1	no	—
539	#123	—	7	1	no	—
540	#123	—	7	1	no	—
541	#123	—	7	1	no	—
542	#123	—	7	1	no	—
543	#123	—	7	1	no	—
544	#123	—	7	1	no	—
545	#123	—	7	1	no	—
546	#123	—	7	1	no	—
547	#123	—	7	1	no	—
548	#123	—	7	1	no	—
549	#123	—	7	1	no	—
550	#123	—	7	1	no	—
551	#123	—	7	1	no	—
552	#123	—	7	1	no	—
553	#123	—	7	1	no	—
554	#123	—	7	1	no	—
555	#123	—	7	1	no	—
556	#123	C₂×D₇	1	1	yes	characteristic, complemented
557	#123	C₂×D₇	1	1	yes	characteristic, complemented
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	—	7	1	no	—
565	C₂²⋊Q₈	—	7	1	no	—
566	C₂²⋊Q₈	—	7	1	no	—
567	C₂²⋊Q₈	—	7	1	no	—
568	C₂²⋊Q₈	—	7	1	no	—
569	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
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	#121	—	7	1	no	—
579	#121	—	7	1	no	—
580	#121	—	7	1	no	—
581	#121	—	7	1	no	—
582	#121	—	7	1	no	—
583	#121	—	7	1	no	—
584	#121	—	7	1	no	—
585	#121	—	7	1	no	—
586	#121	—	7	1	no	—
587	#121	—	7	1	no	—
588	#121	—	7	1	no	—
589	#121	—	7	1	no	—
590	#121	—	7	1	no	—
591	#121	—	7	1	no	—
592	#121	—	7	1	no	—
593	#121	—	7	1	no	—
594	#121	—	7	1	no	—
595	#121	—	7	1	no	—
596	#121	—	7	1	no	—
597	#121	—	7	1	no	—
598	#121	—	7	1	no	—
599	#121	—	7	1	no	—
600	#121	—	7	1	no	—
601	#121	—	7	1	no	—
602	#121	—	7	1	no	—
603	#121	C₂×D₇	1	1	yes	characteristic, complemented
604	#121	C₂×D₇	1	1	yes	characteristic, complemented
605	#121	C₂×D₇	1	1	yes	characteristic, complemented
606	#120	—	7	1	no	—
607	#120	—	7	1	no	—
608	#120	—	7	1	no	—
609	#120	—	7	1	no	—
610	#120	—	7	1	no	—
611	#120	—	7	1	no	—
612	#120	—	7	1	no	—
613	#120	—	7	1	no	—
614	#120	—	7	1	no	—
615	#120	—	7	1	no	—
616	#120	—	7	1	no	—
617	#120	—	7	1	no	—
618	#120	—	7	1	no	—
619	#120	—	7	1	no	—
620	#120	C₂×D₇	1	1	yes	characteristic, complemented
621	#120	C₂×D₇	1	1	yes	characteristic, complemented
622	C₄×D₄	—	7	1	no	—
623	C₄×D₄	—	7	1	no	—
624	C₄×D₄	—	7	1	no	—
625	C₄×D₄	—	7	1	no	—
626	C₄×D₄	—	7	1	no	—
627	C₄×D₄	—	7	1	no	—
628	C₄×D₄	—	7	1	no	—
629	C₄×D₄	—	7	1	no	—
630	C₄×D₄	—	7	1	no	—
631	C₄×D₄	—	7	1	no	—
632	C₄×D₄	—	7	1	no	—
633	C₄×D₄	—	7	1	no	—
634	C₄×D₄	—	7	1	no	—
635	C₄×D₄	—	7	1	no	—
636	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
637	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
638	#117	—	7	1	no	—
639	#117	—	7	1	no	—
640	#117	—	7	1	no	—
641	C₂×C₄⋊C₄	—	7	1	no	—
642	C₂×C₄⋊C₄	—	7	1	no	—
643	C₂×C₄⋊C₄	—	7	1	no	—
644	C₂×C₂²⋊C₄	—	7	1	no	—
645	C₂×C₂²⋊C₄	—	7	1	no	—
646	C₂×C₂²⋊C₄	—	7	1	no	—
647	C₂×C₂²⋊C₄	—	7	1	no	—
648	C₂×C₂²⋊C₄	—	7	1	no	—
649	C₂×C₂²⋊C₄	—	7	1	no	—
650	C₂×C₂²⋊C₄	—	7	1	no	—
651	C₂×C₂²⋊C₄	—	7	1	no	—
652	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
653	C₂²×C₇	—	2	1	no	—
654	C₂²×C₇	—	2	1	no	—
655	C₂²×C₇	—	2	1	no	—
656	C₂²×C₇	—	2	1	no	—
657	C₂²×C₇	—	2	1	no	—
658	C₂²×C₇	—	2	1	no	—
659	C₂²×C₇	—	2	1	no	—
660	C₂²×C₇	—	2	1	no	—
661	C₂²×C₇	—	2	1	no	—
662	C₂²×C₇	—	2	1	no	—
663	C₂²×C₇	—	2	1	no	—
664	C₂²×C₇	—	2	1	no	—
665	C₂²×C₇	—	2	1	no	—
666	C₂²×C₇	—	2	1	no	—
667	C₂²×C₇	—	2	1	no	—
668	C₂²×C₇	—	8	2	no	—
669	C₂²×C₇	C₂⁵	1	1	yes	characteristic
670	C₂×D₇	—	2	1	no	—
671	C₂×D₇	—	2	1	no	—
672	C₂×D₇	—	2	1	no	—
673	C₂×D₇	—	2	1	no	—
674	C₂×D₇	—	2	1	no	—
675	C₂×D₇	—	2	1	no	—
676	C₂×D₇	—	2	1	no	—
677	C₂×D₇	—	2	1	no	—
678	C₂×D₇	—	2	1	no	—
679	C₂×D₇	—	2	1	no	—
680	C₂×D₇	—	2	1	no	—
681	C₂×D₇	—	2	1	no	—
682	C₂×D₇	—	2	1	no	—
683	C₂×D₇	—	2	1	no	—
684	C₂×D₇	—	2	1	no	—
685	C₂×D₇	—	2	1	no	—
686	C₂×D₇	—	4	4	no	—
687	C₂×D₇	—	8	2	no	—
688	C₂×D₇	—	8	2	no	—
689	C₂×D₇	—	8	2	no	—
690	C₂×D₇	—	8	2	no	—
691	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
692	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
693	C₄×C₇	—	2	1	no	—
694	C₄×C₇	—	2	1	no	—
695	C₄×C₇	—	2	1	no	—
696	C₄×C₇	—	2	1	no	—
697	C₄×C₇	—	2	1	no	—
698	C₄×C₇	—	2	1	no	—
699	C₄×C₇	—	2	1	no	—
700	C₄×C₇	—	2	1	no	—
701	C₄×C₇	—	2	1	no	—
702	C₄×C₇	—	2	1	no	—
703	Dic₇	—	2	1	no	—
704	Dic₇	—	2	1	no	—
705	Dic₇	—	2	1	no	—
706	Dic₇	—	2	1	no	—
707	Dic₇	—	2	1	no	—
708	Dic₇	—	2	1	no	—
709	Dic₇	—	2	1	no	—
710	Dic₇	—	2	1	no	—
711	Dic₇	—	2	1	no	—
712	Dic₇	—	2	1	no	—
713	C₂⁴	—	7	1	no	—
714	C₂⁴	—	7	1	no	—
715	C₂⁴	—	7	1	no	—
716	C₂⁴	—	7	1	no	—
717	C₂⁴	—	7	1	no	—
718	C₂⁴	C₂²×D₇	1	1	yes	characteristic
719	#41	—	28	2	no	—
720	#41	—	28	2	no	—
721	#41	—	28	2	no	—
722	C₂×Q₈	—	7	1	no	—
723	C₂×Q₈	—	7	1	no	—
724	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
725	C₂×D₄	—	7	1	no	—
726	C₂×D₄	—	7	1	no	—
727	C₂×D₄	—	7	1	no	—
728	C₂×D₄	—	7	1	no	—
729	C₂×D₄	—	7	1	no	—
730	C₂×D₄	—	7	1	no	—
731	C₂×D₄	—	7	1	no	—
732	C₂×D₄	—	7	1	no	—
733	C₂×D₄	—	7	1	no	—
734	C₂×D₄	—	7	1	no	—
735	C₂×D₄	—	7	1	no	—
736	C₂×D₄	—	7	1	no	—
737	C₂×D₄	—	7	1	no	—
738	C₂×D₄	—	7	1	no	—
739	C₂×D₄	—	7	1	no	—
740	C₂×D₄	—	7	1	no	—
741	C₂×D₄	—	7	1	no	—
742	C₂×D₄	—	7	1	no	—
743	C₂×D₄	—	7	1	no	—
744	C₂×D₄	—	7	1	no	—
745	C₂×D₄	—	7	1	no	—
746	C₂×D₄	—	7	1	no	—
747	C₂×D₄	—	7	1	no	—
748	C₂×D₄	—	7	1	no	—
749	C₂×D₄	—	7	1	no	—
750	C₂×D₄	—	7	1	no	—
751	C₂×D₄	—	7	1	no	—
752	C₂×D₄	—	7	1	no	—
753	C₂×D₄	—	7	1	no	—
754	C₂×D₄	—	7	1	no	—
755	C₂×D₄	—	28	2	no	—
756	C₂×D₄	—	28	2	no	—
757	C₂×D₄	—	28	2	no	—
758	C₂×D₄	—	28	2	no	—
759	C₂×D₄	—	28	2	no	—
760	C₂×D₄	—	28	2	no	—
761	C₂×D₄	—	28	2	no	—
762	C₂×D₄	—	28	2	no	—
763	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
764	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
765	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
766	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
767	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
768	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
769	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
770	C₂²×C₄	—	7	1	no	—
771	C₂²×C₄	—	7	1	no	—
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	—	28	2	no	—
790	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
791	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
792	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
793	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
794	C₄⋊C₄	—	7	1	no	—
795	C₄⋊C₄	—	7	1	no	—
796	C₄⋊C₄	—	7	1	no	—
797	C₄⋊C₄	—	7	1	no	—
798	C₄⋊C₄	—	7	1	no	—
799	C₄⋊C₄	—	7	1	no	—
800	C₄⋊C₄	—	7	1	no	—
801	C₄⋊C₄	—	7	1	no	—
802	C₄⋊C₄	—	7	1	no	—
803	C₄⋊C₄	—	7	1	no	—
804	C₄⋊C₄	—	7	1	no	—
805	C₄⋊C₄	—	7	1	no	—
806	C₄⋊C₄	—	7	1	no	—
807	C₄⋊C₄	—	7	1	no	—
808	C₄⋊C₄	—	7	1	no	—
809	C₄⋊C₄	—	7	1	no	—
810	C₄⋊C₄	—	7	1	no	—
811	C₄⋊C₄	—	7	1	no	—
812	C₄⋊C₄	—	7	1	no	—
813	C₄⋊C₄	—	7	1	no	—
814	C₄⋊C₄	—	7	1	no	—
815	C₄⋊C₄	—	7	1	no	—
816	C₄⋊C₄	—	7	1	no	—
817	C₄⋊C₄	—	7	1	no	—
818	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
819	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
820	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
821	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
822	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
823	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
824	C₂²⋊C₄	—	7	1	no	—
825	C₂²⋊C₄	—	7	1	no	—
826	C₂²⋊C₄	—	7	1	no	—
827	C₂²⋊C₄	—	7	1	no	—
828	C₂²⋊C₄	—	7	1	no	—
829	C₂²⋊C₄	—	7	1	no	—
830	C₂²⋊C₄	—	7	1	no	—
831	C₂²⋊C₄	—	7	1	no	—
832	C₂²⋊C₄	—	7	1	no	—
833	C₂²⋊C₄	—	7	1	no	—
834	C₂²⋊C₄	—	7	1	no	—
835	C₂²⋊C₄	—	7	1	no	—
836	C₂²⋊C₄	—	7	1	no	—
837	C₂²⋊C₄	—	7	1	no	—
838	C₂²⋊C₄	—	7	1	no	—
839	C₂²⋊C₄	—	7	1	no	—
840	C₂²⋊C₄	—	7	1	no	—
841	C₂²⋊C₄	—	7	1	no	—
842	C₂²⋊C₄	—	7	1	no	—
843	C₂²⋊C₄	—	7	1	no	—
844	C₂²⋊C₄	—	7	1	no	—
845	C₂²⋊C₄	—	7	1	no	—
846	C₂²⋊C₄	—	7	1	no	—
847	C₂²⋊C₄	—	7	1	no	—
848	C₂²⋊C₄	—	7	1	no	—
849	C₂²⋊C₄	—	7	1	no	—
850	C₂²⋊C₄	—	7	1	no	—
851	C₂²⋊C₄	—	7	1	no	—
852	C₂²⋊C₄	—	7	1	no	—
853	C₂²⋊C₄	—	7	1	no	—
854	C₂²⋊C₄	—	7	1	no	—
855	C₂²⋊C₄	—	7	1	no	—
856	C₂²⋊C₄	—	7	1	no	—
857	C₂²⋊C₄	—	7	1	no	—
858	C₂²⋊C₄	—	7	1	no	—
859	C₂²⋊C₄	—	7	1	no	—
860	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
861	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
862	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
863	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
864	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
865	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
866	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
867	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
868	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
869	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
870	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
871	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
872	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
873	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
874	C₄²	—	7	1	no	—
875	C₄²	—	7	1	no	—
876	C₄²	—	7	1	no	—
877	C₄²	—	7	1	no	—
878	C₄²	C₂²×D₇	1	1	yes	characteristic
879	C₄²	C₂²×D₇	1	1	yes	characteristic
880	C₂×C₇	—	4	1	no	—
881	C₂×C₇	—	4	1	no	—
882	C₂×C₇	—	4	1	no	—
883	C₂×C₇	—	4	1	no	—
884	C₂×C₇	—	4	1	no	—
885	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
886	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
887	C₂×C₇	#585	1	1	yes	characteristic
888	D₇	—	2	2	no	—
889	D₇	—	2	2	no	—
890	D₇	—	4	1	no	—
891	D₇	—	4	1	no	—
892	D₇	—	4	1	no	—
893	D₇	—	4	1	no	—
894	C₂³	—	4	1	no	—
895	C₂³	—	4	1	no	—
896	C₂³	—	4	1	no	—
897	C₂³	—	7	1	no	—
898	C₂³	—	7	1	no	—
899	C₂³	—	7	1	no	—
900	C₂³	—	7	1	no	—
901	C₂³	—	7	1	no	—
902	C₂³	—	7	1	no	—
903	C₂³	—	14	2	no	—
904	C₂³	—	14	2	no	—
905	C₂³	—	14	2	no	—
906	C₂³	—	14	2	no	—
907	C₂³	—	14	2	no	—
908	C₂³	—	28	1	no	—
909	C₂³	—	28	1	no	—
910	C₂³	—	28	1	no	—
911	C₂³	—	28	1	no	—
912	C₂³	—	28	1	no	—
913	C₂³	—	28	1	no	—
914	C₂³	—	28	1	no	—
915	C₂³	—	28	1	no	—
916	C₂³	—	28	1	no	—
917	C₂³	—	28	1	no	—
918	C₂³	C₂³×D₇	1	1	yes	characteristic
919	C₂³	C₂³×D₇	1	1	yes	characteristic
920	C₂³	C₂³×D₇	1	1	yes	characteristic
921	C₂³	C₂³×D₇	1	1	yes	characteristic
922	C₂³	C₂³×D₇	1	1	yes	characteristic
923	Q₈	—	4	1	no	—
924	Q₈	—	28	1	no	—
925	Q₈	—	28	1	no	—
926	D₄	—	4	1	no	—
927	D₄	—	4	1	no	—
928	D₄	—	4	1	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	1	no	—
931	D₄	—	4	1	no	—
932	D₄	—	4	1	no	—
933	D₄	—	14	2	no	—
934	D₄	—	14	2	no	—
935	D₄	—	14	2	no	—
936	D₄	—	14	2	no	—
937	D₄	—	14	2	no	—
938	D₄	—	14	2	no	—
939	D₄	—	14	2	no	—
940	D₄	—	14	2	no	—
941	D₄	—	14	2	no	—
942	D₄	—	14	2	no	—
943	D₄	—	28	1	no	—
944	D₄	—	28	1	no	—
945	D₄	—	28	1	no	—
946	D₄	—	28	1	no	—
947	D₄	—	28	1	no	—
948	D₄	—	28	1	no	—
949	D₄	—	28	1	no	—
950	D₄	—	28	1	no	—
951	D₄	—	28	1	no	—
952	D₄	—	28	1	no	—
953	D₄	—	28	1	no	—
954	D₄	—	28	1	no	—
955	D₄	—	28	1	no	—
956	D₄	—	28	1	no	—
957	D₄	—	28	1	no	—
958	D₄	—	28	1	no	—
959	D₄	—	28	1	no	—
960	D₄	—	28	1	no	—
961	D₄	—	28	1	no	—
962	D₄	—	28	1	no	—
963	C₂×C₄	—	4	1	no	—
964	C₂×C₄	—	4	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	7	1	no	—
968	C₂×C₄	—	7	1	no	—
969	C₂×C₄	—	7	1	no	—
970	C₂×C₄	—	7	1	no	—
971	C₂×C₄	—	7	1	no	—
972	C₂×C₄	—	7	1	no	—
973	C₂×C₄	—	7	1	no	—
974	C₂×C₄	—	7	1	no	—
975	C₂×C₄	—	7	1	no	—
976	C₂×C₄	—	7	1	no	—
977	C₂×C₄	—	14	2	no	—
978	C₂×C₄	—	14	2	no	—
979	C₂×C₄	—	14	2	no	—
980	C₂×C₄	—	28	1	no	—
981	C₂×C₄	—	28	1	no	—
982	C₂×C₄	—	28	1	no	—
983	C₂×C₄	—	28	1	no	—
984	C₂×C₄	—	28	1	no	—
985	C₂×C₄	—	28	1	no	—
986	C₂×C₄	—	28	1	no	—
987	C₂×C₄	—	28	1	no	—
988	C₂×C₄	—	28	1	no	—
989	C₂×C₄	—	28	1	no	—
990	C₂×C₄	—	28	1	no	—
991	C₂×C₄	—	28	1	no	—
992	C₂×C₄	—	28	1	no	—
993	C₂×C₄	—	28	1	no	—
994	C₂×C₄	—	28	1	no	—
995	C₂×C₄	—	28	1	no	—
996	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
997	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
998	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
999	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1000	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1001	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1002	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1003	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1004	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1005	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
1006	C₇	#3534	1	1	yes	characteristic, complemented, Sylow
1007	C₂²	—	2	1	no	—
1008	C₂²	—	2	1	no	—
1009	C₂²	—	2	1	no	—
1010	C₂²	—	2	1	no	—
1011	C₂²	—	2	1	no	—
1012	C₂²	—	2	1	no	—
1013	C₂²	—	2	1	no	—
1014	C₂²	—	2	1	no	—
1015	C₂²	—	2	1	no	—
1016	C₂²	—	2	1	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	1	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	7	2	no	—
1023	C₂²	—	7	2	no	—
1024	C₂²	—	8	2	no	—
1025	C₂²	—	14	1	no	—
1026	C₂²	—	14	1	no	—
1027	C₂²	—	14	1	no	—
1028	C₂²	—	14	1	no	—
1029	C₂²	—	14	1	no	—
1030	C₂²	—	14	1	no	—
1031	C₂²	—	14	1	no	—
1032	C₂²	—	14	1	no	—
1033	C₂²	—	14	1	no	—
1034	C₂²	—	14	1	no	—
1035	C₂²	—	14	1	no	—
1036	C₂²	—	14	1	no	—
1037	C₂²	—	14	1	no	—
1038	C₂²	—	14	1	no	—
1039	C₂²	—	14	1	no	—
1040	C₂²	—	14	1	no	—
1041	C₂²	—	28	4	no	—
1042	C₂²	—	56	2	no	—
1043	C₂²	—	56	2	no	—
1044	C₂²	—	56	2	no	—
1045	C₂²	—	56	2	no	—
1046	C₂²	C₂⁴×D₇	1	1	yes	characteristic
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	14	1	no	—
1058	C₄	—	14	1	no	—
1059	C₄	—	14	1	no	—
1060	C₄	—	14	1	no	—
1061	C₄	—	14	1	no	—
1062	C₄	—	14	1	no	—
1063	C₄	—	14	1	no	—
1064	C₄	—	14	1	no	—
1065	C₄	—	14	1	no	—
1066	C₄	—	14	1	no	—
1067	C₂	—	4	1	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	14	2	no	—
1073	C₂	—	14	2	no	—
1074	C₂	—	28	1	no	—
1075	C₂	—	28	1	no	—
1076	C₂	—	28	1	no	—
1077	C₂	—	28	1	no	—
1078	C₂	#90616	1	1	yes	characteristic
1079	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#538	C₂
hypercenter	#538	D₇
hypocenter	C₇	#3534
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. C₇×#538	C₂	semidirect
2. #90400	C₂	semidirect
3. #90398	C₂	semidirect
4. #90396	C₂	semidirect
5. #90395	C₂	semidirect
6. #90375	C₂	semidirect
7. #90370	C₂	semidirect
8. #90367	C₂	semidirect
9. #90367	C₂	semidirect
10. #90354	C₂	semidirect
11. #90351	C₂	semidirect
12. #90344	C₂	semidirect
13. D₇×#123	C₂	semidirect
14. #90329	C₂	semidirect
15. #90320	C₂	semidirect
16. #90312	C₂	semidirect
17. #90311	C₂	semidirect
18. #90304	C₂	semidirect
19. #90303	C₂	semidirect
20. #90300	C₂	semidirect
21. D₇×#121	C₂	semidirect
22. #90286	C₂	semidirect
23. #90281	C₂	semidirect
24. #90280	C₂	semidirect
25. #90280	C₂	semidirect
26. #90253	C₂	semidirect
27. #90249	C₂	semidirect
28. #90241	C₂	semidirect
29. #90238	C₂	semidirect
30. #90181	C₂	semidirect
31. #90181	C₂	semidirect
32. C₂²×C₂²⋊D₇	C₂²	semidirect
33. C₂²×C₂²⋊D₇	C₂²	semidirect
34. C₂×#1161	C₂²	semidirect
36. C₂×D₄×D₇	C₂²	semidirect
37. C₂×D₄×D₇	C₂²	semidirect
38. C₂×D₄×D₇	C₂²	semidirect
39. C₂×D₄×D₇	C₂²	semidirect
40. C₂×#1157	C₂²	semidirect
41. C₂×#1157	C₂²	semidirect
42. C₂²×D₂₈	C₂²	semidirect
43. C₂²×C₄×D₇	C₂²	semidirect
44. C₇×#126	C₂²	semidirect
45. C₇×#126	C₂²	semidirect
46. C₇×#124	C₂²	semidirect
47. C₇×#124	C₂²	semidirect
48. C₇×#123	C₂²	semidirect
49. C₇×#123	C₂²	semidirect
50. C₇×C₂²⋊Q₈	C₂²	semidirect
51. C₇×#121	C₂²	semidirect
52. C₇×#121	C₂²	semidirect
53. C₇×#121	C₂²	semidirect
54. C₇×#120	C₂²	semidirect
55. C₇×#120	C₂²	semidirect
56. C₄×C₇×D₄	C₂²	semidirect
57. C₄×C₇×D₄	C₂²	semidirect
58. C₂×C₇×C₂²⋊C₄	C₂²	semidirect
59. #6516	C₂²	semidirect
60. #6516	C₂²	semidirect
61. #6509	C₂²	semidirect
62. #6509	C₂²	semidirect
63. #6509	C₂²	semidirect
64. #6503	C₂²	semidirect
65. #6503	C₂²	semidirect
66. #6502	C₂²	semidirect
67. #6502	C₂²	semidirect
68. #6502	C₂²	semidirect
69. #6502	C₂²	semidirect
70. #6502	C₂²	semidirect
72. #6501	C₂²	semidirect
73. #6501	C₂²	semidirect
74. #6501	C₂²	semidirect
75. #6501	C₂²	semidirect
76. #6501	C₂²	semidirect
78. #6500	C₂²	semidirect
79. #6500	C₂²	semidirect
80. #6500	C₂²	semidirect
81. #6500	C₂²	semidirect
82. #6500	C₂²	semidirect
83. #6499	C₂²	semidirect
84. #6498	C₂²	semidirect
85. #6498	C₂²	semidirect
86. #6498	C₂²	semidirect
87. #6493	C₂²	semidirect
88. #6493	C₂²	semidirect
89. #6493	C₂²	semidirect
90. #6492	C₂²	semidirect
91. #6492	C₂²	semidirect
92. #6492	C₂²	semidirect
93. #6492	C₂²	semidirect
94. C₄×C₂²⋊D₇	C₂²	semidirect
95. C₄×C₂²⋊D₇	C₂²	semidirect
96. C₄×C₂²⋊D₇	C₂²	semidirect
97. C₄×C₂²⋊D₇	C₂²	semidirect
98. #6487	C₂²	semidirect
99. #6461	C₂²	semidirect
100. #6461	C₂²	semidirect
101. #6460	C₂²	semidirect
102. #6459	C₂²	semidirect
103. #6459	C₂²	semidirect
104. #6459	C₂²	semidirect
105. #6458	C₂²	semidirect
106. #6458	C₂²	semidirect
107. #6458	C₂²	semidirect
108. #6458	C₂²	semidirect
109. #6457	C₂²	semidirect
110. #6457	C₂²	semidirect
111. #6457	C₂²	semidirect
112. #6457	C₂²	semidirect
113. #6457	C₂²	semidirect
114. #6456	C₂²	semidirect
115. #6456	C₂²	semidirect
116. #6455	C₂²	semidirect
117. D₇×C₄⋊C₄	C₂²	semidirect
118. D₇×C₄⋊C₄	C₂²	semidirect
119. D₇×C₄⋊C₄	C₂²	semidirect
120. #6453	C₂²	semidirect
121. #6452	C₂²	semidirect
122. #6452	C₂²	semidirect
123. #6449	C₂²	semidirect
124. #6449	C₂²	semidirect
125. #6449	C₂²	semidirect
126. #6448	C₂²	semidirect
127. #6448	C₂²	semidirect
130. #6447	C₂²	semidirect
131. #6447	C₂²	semidirect
132. #6447	C₂²	semidirect
133. #6447	C₂²	semidirect
134. #6447	C₂²	semidirect
135. #6447	C₂²	semidirect
136. #6447	C₂²	semidirect
137. #6447	C₂²	semidirect
138. #6447	C₂²	semidirect
139. #6447	C₂²	semidirect
140. #6447	C₂²	semidirect
141. #6447	C₂²	semidirect
142. #6447	C₂²	semidirect
143. #6446	C₂²	semidirect
144. #6446	C₂²	semidirect
145. #6446	C₂²	semidirect
146. #6446	C₂²	semidirect
147. #6446	C₂²	semidirect
148. #6446	C₂²	semidirect
149. #6446	C₂²	semidirect
150. #6446	C₂²	semidirect
151. #6446	C₂²	semidirect
152. #6446	C₂²	semidirect
153. #6446	C₂²	semidirect
155. #6445	C₂²	semidirect
156. #6445	C₂²	semidirect
157. #6445	C₂²	semidirect
158. #6445	C₂²	semidirect
159. #6445	C₂²	semidirect
160. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
161. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
162. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
163. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
164. D₇×C₂²⋊C₄	C₂²	semidirect
165. D₇×C₂²⋊C₄	C₂²	semidirect
166. D₇×C₂²⋊C₄	C₂²	semidirect
167. D₇×C₂²⋊C₄	C₂²	semidirect
168. D₇×C₂²⋊C₄	C₂²	semidirect
169. D₇×C₂²⋊C₄	C₂²	semidirect
170. D₇×C₂²⋊C₄	C₂²	semidirect
171. D₇×C₂²⋊C₄	C₂²	semidirect
172. #6442	C₂²	semidirect
173. #6442	C₂²	semidirect
174. #6442	C₂²	semidirect
175. #6442	C₂²	semidirect
176. #6441	C₂²	semidirect
177. #6441	C₂²	semidirect
178. #6441	C₂²	semidirect
179. #6438	C₂²	semidirect
180. C₄×D₂₈	C₂²	semidirect
181. C₄×D₂₈	C₂²	semidirect
182. C₄×D₂₈	C₂²	semidirect
183. C₄×D₂₈	C₂²	semidirect
184. #6435	C₂²	semidirect
185. #6435	C₂²	semidirect
186. #6433	C₂²	semidirect
378. #538	D₇	semidirect
518. #126	C₂×D₇	semidirect
519. #126	C₂×D₇	semidirect
528. #124	C₂×D₇	semidirect
529. #124	C₂×D₇	semidirect
556. #123	C₂×D₇	semidirect
557. #123	C₂×D₇	semidirect
569. C₂²⋊Q₈	C₂×D₇	semidirect
603. #121	C₂×D₇	semidirect
604. #121	C₂×D₇	semidirect
605. #121	C₂×D₇	semidirect
620. #120	C₂×D₇	semidirect
621. #120	C₂×D₇	semidirect
636. C₄×D₄	C₂×D₇	semidirect
637. C₄×D₄	C₂×D₇	semidirect
652. C₂×C₂²⋊C₄	C₂×D₇	semidirect
1006. C₇	#3534	semidirect

Maximal subgroups

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

subgroup	index
C₇×#538	2
#90400	2
#90398	2
#90396	2
#90395	2
#90375	2
#90370	2
#90367	2
#90354	2
#90351	2
#90344	2
D₇×#123	2
#90329	2
#90320	2
#90312	2
#90311	2
#90304	2
#90303	2
#90300	2
D₇×#121	2
#90286	2
#90281	2
#90280	2
#90253	2
#90249	2
#90241	2
#90238	2
#90181	2
#3534	7