Subgroups — #11743867

Order 896.

1042 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#90396	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇×#126	C₂	1	1	yes	maximal, characteristic, complemented
4	#90393	C₂	1	1	yes	maximal, characteristic, complemented
5	#90392	C₂	1	1	yes	maximal, characteristic, complemented
6	#90371	C₂	1	1	yes	maximal, characteristic, complemented
7	#90370	C₂	1	1	yes	maximal, characteristic, complemented
8	#90353	C₂	1	1	yes	maximal, characteristic, complemented
9	#90352	C₂	1	1	yes	maximal, characteristic, complemented
10	#90348	C₂	1	1	yes	maximal, characteristic, complemented
11	#90346	C₂	1	1	yes	maximal, characteristic, complemented
12	#90341	C₂	1	1	yes	maximal, characteristic, complemented
13	#90340	C₂	1	1	yes	maximal, characteristic, complemented
14	#90336	C₂	1	1	yes	maximal, characteristic, complemented
15	#90332	C₂	1	1	yes	maximal, characteristic, complemented
16	#90329	C₂	1	1	yes	maximal, characteristic, complemented
17	#90326	C₂	1	1	yes	maximal, characteristic, complemented
18	#90284	C₂	1	1	yes	maximal, characteristic, complemented
19	#90282	C₂	1	1	yes	maximal, characteristic, complemented
20	#90256	C₂	1	1	yes	maximal, characteristic, complemented
21	#90248	C₂	1	1	yes	maximal, characteristic, complemented
22	#90237	C₂	1	1	yes	maximal, characteristic, complemented
23	#90231	C₂	1	1	yes	maximal, characteristic, complemented
24	#90222	C₂	1	1	yes	maximal, characteristic, complemented
25	#90220	C₂	1	1	yes	maximal, characteristic, complemented
26	#90219	C₂	1	1	yes	maximal, characteristic, complemented
27	#90213	C₂	1	1	yes	maximal, characteristic, complemented
28	#90186	C₂	1	1	yes	maximal, characteristic, complemented
29	#90181	C₂	1	1	yes	maximal, characteristic, complemented
30	#90177	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#6442	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic
33	C₂×#1159	C₂²	1	1	yes	characteristic
34	C₂×#1157	C₂²	1	1	yes	characteristic
35	C₇×#126	C₂²	1	1	yes	characteristic
36	C₇×#126	C₂²	1	1	yes	characteristic
37	C₇×#124	C₂²	1	1	yes	characteristic
38	C₇×#123	C₂²	1	1	yes	characteristic
39	C₇×#123	C₂²	1	1	yes	characteristic, complemented
40	C₇×#123	C₂²	1	1	yes	characteristic, complemented
41	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₇×#120	C₂²	1	1	yes	characteristic
44	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₇×#117	C₂²	1	1	yes	characteristic, complemented
47	C₇×#117	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	#6516	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
53	#6509	C₂²	1	1	yes	characteristic, complemented
54	#6509	C₂²	1	1	yes	characteristic, complemented
55	#6509	C₂²	1	1	yes	characteristic, complemented
56	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
57	#6502	C₂²	1	1	yes	characteristic
58	#6502	C₂²	1	1	yes	characteristic
59	#6502	C₂²	1	1	yes	characteristic, complemented
60	#6502	C₂²	1	1	yes	characteristic, complemented
61	#6501	C₂²	1	1	yes	characteristic
62	#6501	C₂²	1	1	yes	characteristic
63	#6500	C₂²	1	1	yes	characteristic
64	#6499	C₂²	1	1	yes	characteristic, complemented
65	#6498	C₂²	1	1	yes	characteristic
66	D₄×Dic₇	C₂²	1	1	yes	characteristic
67	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
68	#6493	C₂²	1	1	yes	characteristic
69	#6493	C₂²	1	1	yes	characteristic, complemented
70	#6492	C₂²	1	1	yes	characteristic
71	#6492	C₂²	1	1	yes	characteristic, complemented
72	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
77	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
79	#6489	C₂²	1	1	yes	characteristic, complemented
80	#6489	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
82	#6487	C₂²	1	1	yes	characteristic, complemented
83	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
87	#6461	C₂²	1	1	yes	characteristic, complemented
88	#6461	C₂²	1	1	yes	characteristic, complemented
89	#6461	C₂²	1	1	yes	characteristic, complemented
90	#6461	C₂²	1	1	yes	characteristic, complemented
91	#6461	C₂²	1	1	yes	characteristic, complemented
92	#6461	C₂²	1	1	yes	characteristic, complemented
93	#6460	C₂²	1	1	yes	characteristic, complemented
94	#6460	C₂²	1	1	yes	characteristic, complemented
95	#6459	C₂²	1	1	yes	characteristic, complemented
96	#6459	C₂²	1	1	yes	characteristic, complemented
97	#6457	C₂²	1	1	yes	characteristic, complemented
98	#6457	C₂²	1	1	yes	characteristic, complemented
99	#6457	C₂²	1	1	yes	characteristic, complemented
100	#6456	C₂²	1	1	yes	characteristic, complemented
101	#6456	C₂²	1	1	yes	characteristic, complemented
102	#6455	C₂²	1	1	yes	characteristic, complemented
103	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	#6453	C₂²	1	1	yes	characteristic, complemented
107	#6453	C₂²	1	1	yes	characteristic, complemented
108	#6452	C₂²	1	1	yes	characteristic, complemented
109	#6452	C₂²	1	1	yes	characteristic, complemented
110	#6452	C₂²	1	1	yes	characteristic, complemented
111	#6452	C₂²	1	1	yes	characteristic, complemented
112	#6452	C₂²	1	1	yes	characteristic, complemented
113	#6451	C₂²	1	1	yes	characteristic, complemented
114	#6451	C₂²	1	1	yes	characteristic, complemented
115	#6450	C₂²	1	1	yes	characteristic, complemented
116	#6450	C₂²	1	1	yes	characteristic, complemented
117	#6450	C₂²	1	1	yes	characteristic, complemented
118	#6450	C₂²	1	1	yes	characteristic, complemented
119	#6449	C₂²	1	1	yes	characteristic
120	#6449	C₂²	1	1	yes	characteristic, complemented
121	#6448	C₂²	1	1	yes	characteristic
122	#6448	C₂²	1	1	yes	characteristic
123	#6448	C₂²	1	1	yes	characteristic
124	#6448	C₂²	1	1	yes	characteristic
125	#6448	C₂²	1	1	yes	characteristic, complemented
126	#6447	C₂²	1	1	yes	characteristic
127	#6447	C₂²	1	1	yes	characteristic
128	#6447	C₂²	1	1	yes	characteristic, complemented
129	#6446	C₂²	1	1	yes	characteristic
130	#6446	C₂²	1	1	yes	characteristic
131	#6446	C₂²	1	1	yes	characteristic
132	#6446	C₂²	1	1	yes	characteristic, complemented
133	#6446	C₂²	1	1	yes	characteristic, complemented
134	#6446	C₂²	1	1	yes	characteristic, complemented
135	#6446	C₂²	1	1	yes	characteristic, complemented
136	#6445	C₂²	1	1	yes	characteristic
137	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
138	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
139	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
140	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
141	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
142	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
143	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
144	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
145	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
148	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
149	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
150	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
151	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
152	#6442	C₂²	1	1	yes	characteristic
153	#6442	C₂²	1	1	yes	characteristic
154	#6442	C₂²	1	1	yes	characteristic
155	#6442	C₂²	1	1	yes	characteristic
156	#6442	C₂²	1	1	yes	characteristic
157	#6442	C₂²	1	1	yes	characteristic
158	#6442	C₂²	1	1	yes	characteristic
159	#6442	C₂²	1	1	yes	characteristic, complemented
160	#6442	C₂²	1	1	yes	characteristic, complemented
161	#6442	C₂²	1	1	yes	characteristic, complemented
162	#6442	C₂²	1	1	yes	characteristic, complemented
163	#6442	C₂²	1	1	yes	characteristic, complemented
164	#6442	C₂²	1	1	yes	characteristic, complemented
165	#6441	C₂²	1	1	yes	characteristic
166	#6441	C₂²	1	1	yes	characteristic
167	#6441	C₂²	1	1	yes	characteristic, complemented
168	#6441	C₂²	1	1	yes	characteristic, complemented
169	#6441	C₂²	1	1	yes	characteristic, complemented
170	#6440	C₂²	1	1	yes	characteristic
171	#6440	C₂²	1	1	yes	characteristic
172	#6440	C₂²	1	1	yes	characteristic, complemented
173	#6440	C₂²	1	1	yes	characteristic, complemented
174	#6440	C₂²	1	1	yes	characteristic, complemented
175	#6439	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
177	#6435	C₂²	1	1	yes	characteristic, complemented
178	#6435	C₂²	1	1	yes	characteristic, complemented
179	#6435	C₂²	1	1	yes	characteristic, complemented
180	#6435	C₂²	1	1	yes	characteristic, complemented
181	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
182	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
183	#6433	C₂²	1	1	yes	characteristic, complemented
184	#6433	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3521	—	7	1	no	maximal, Sylow
188	C₂⁴×C₇	C₂³	1	1	yes	characteristic
189	C₂³×D₇	C₂³	1	1	yes	characteristic
190	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
192	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₇	—	2	4	no	—
200	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₇	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	C₂²×Dic₇	C₂³	1	1	yes	characteristic
211	C₂²×Dic₇	C₂³	1	1	yes	characteristic
212	C₂²×Dic₇	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	#1159	—	2	4	no	—
218	#1157	—	2	4	no	—
219	C₂×D₂₈	C₂³	1	1	yes	characteristic
220	C₂×D₂₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
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×Dic₁₄	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
236	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
242	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
243	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₂²⋊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	C₄²×C₇	C₂³	1	1	yes	characteristic
259	C₄²×C₇	C₂³	1	1	yes	characteristic
260	C₄²×C₇	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₇	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	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₇	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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
306	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
307	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
308	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₇⋊C₄	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	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	C₄×Dic₇	C₂³	1	1	yes	characteristic
336	C₄×Dic₇	C₂³	1	1	yes	characteristic
337	C₄×Dic₇	C₂³	1	1	yes	characteristic
338	C₄×Dic₇	C₂³	1	1	yes	characteristic
339	C₄×Dic₇	C₂³	1	1	yes	characteristic
340	C₄×Dic₇	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	#556	—	7	1	no	—
347	#556	—	7	1	no	—
348	#554	—	7	1	no	—
349	#553	—	7	1	no	—
350	#553	—	7	1	no	—
351	#553	—	7	1	no	—
352	#552	—	7	1	no	—
353	#552	—	7	1	no	—
354	#552	—	7	1	no	—
355	#551	—	7	1	no	—
356	#551	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	D₇	1	1	yes	characteristic, complemented
359	#547	—	7	1	no	—
360	#546	—	7	1	no	—
361	#546	—	7	1	no	—
362	#542	—	7	1	no	—
363	#541	—	7	1	no	—
364	#539	—	7	1	no	—
365	#539	—	7	1	no	—
366	#538	—	7	1	no	—
367	#538	—	7	1	no	—
368	#529	—	7	1	no	—
369	#529	—	7	1	no	—
370	#529	—	7	1	no	—
371	#529	—	7	1	no	—
372	C₂×#126	—	7	1	no	—
373	C₂×#126	—	7	1	no	—
374	#520	—	7	1	no	—
375	#518	—	7	1	no	—
376	C₄×#41	—	7	1	no	—
377	C₂³×C₇	—	2	2	no	—
378	C₂³×C₇	—	4	1	no	—
379	C₂³×C₇	—	4	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	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂²×D₇	—	2	2	no	—
385	C₂²×D₇	—	4	1	no	—
386	C₂²×D₇	—	4	1	no	—
387	C₂²×D₇	C₂⁴	1	1	yes	characteristic
388	C₂²×D₇	C₂⁴	1	1	yes	characteristic
389	C₂²×D₇	C₂⁴	1	1	yes	characteristic
390	C₇×Q₈	—	4	1	no	—
391	C₇×D₄	—	2	2	no	—
392	C₇×D₄	—	4	1	no	—
393	C₇×D₄	—	4	1	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	4	1	no	—
396	C₂×C₄×C₇	—	4	1	no	—
397	C₂×C₄×C₇	—	4	1	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
402	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
404	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
405	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₇	—	2	2	no	—
411	C₂²⋊D₇	—	2	2	no	—
412	C₂²⋊D₇	—	2	2	no	—
413	C₂²⋊D₇	—	2	2	no	—
414	C₂²⋊D₇	—	2	2	no	—
415	C₂²⋊D₇	—	4	1	no	—
416	C₂²⋊D₇	—	4	1	no	—
417	C₂²⋊D₇	—	4	1	no	—
418	C₂²⋊D₇	—	4	1	no	—
419	C₂²⋊D₇	#41	1	4	yes	—
420	C₂×Dic₇	—	2	2	no	—
421	C₂×Dic₇	—	2	2	no	—
422	C₂×Dic₇	—	2	2	no	—
423	C₂×Dic₇	—	4	1	no	—
424	C₂×Dic₇	—	4	1	no	—
425	C₂×Dic₇	—	4	1	no	—
426	C₂×Dic₇	—	4	1	no	—
427	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
428	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
429	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
431	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
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	D₂₈	—	2	2	no	—
441	D₂₈	—	4	1	no	—
442	C₄×D₇	—	2	2	no	—
443	C₄×D₇	—	2	2	no	—
444	C₄×D₇	—	2	2	no	—
445	C₄×D₇	—	4	1	no	—
446	C₄×D₇	—	4	1	no	—
447	C₄×D₇	—	4	1	no	—
448	C₄×D₇	—	4	1	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	Dic₁₄	—	2	2	no	—
454	Dic₁₄	—	2	2	no	—
455	Dic₁₄	—	4	1	no	—
456	Dic₁₄	—	4	1	no	—
457	C₂×#41	—	7	1	no	—
458	C₂×#41	—	7	1	no	—
459	C₂²×D₄	—	7	1	no	—
460	C₄⋊Q₈	—	7	1	no	—
461	C₄⋊Q₈	—	7	1	no	—
462	#126	—	7	1	no	—
463	#126	—	7	1	no	—
464	#126	—	7	1	no	—
465	#126	—	7	1	no	—
466	#126	—	7	1	no	—
467	#126	—	7	1	no	—
468	#126	—	7	1	no	—
469	#126	—	7	1	no	—
470	#126	—	7	1	no	—
471	#126	—	7	1	no	—
472	#126	—	7	1	no	—
473	#126	—	7	1	no	—
474	#126	—	7	1	no	—
475	#126	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
483	#126	C₂×D₇	1	1	yes	characteristic
484	#125	—	7	1	no	—
485	#125	—	7	1	no	—
486	#125	—	7	1	no	—
487	#125	—	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	#124	—	7	1	no	—
494	#124	—	7	1	no	—
495	#124	—	7	1	no	—
496	#124	—	7	1	no	—
497	#124	—	7	1	no	—
498	#124	—	7	1	no	—
499	#124	C₂×D₇	1	1	yes	characteristic
500	#123	—	7	1	no	—
501	#123	—	7	1	no	—
502	#123	—	7	1	no	—
503	#123	—	7	1	no	—
504	#123	—	7	1	no	—
505	#123	—	7	1	no	—
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	C₂×D₇	1	1	yes	characteristic
516	#123	C₂×D₇	1	1	yes	characteristic, complemented
517	#123	C₂×D₇	1	1	yes	characteristic, complemented
518	C₂²⋊Q₈	—	7	1	no	—
519	C₂²⋊Q₈	—	7	1	no	—
520	C₂²⋊Q₈	—	7	1	no	—
521	C₂²⋊Q₈	—	7	1	no	—
522	C₂²⋊Q₈	—	7	1	no	—
523	C₂²⋊Q₈	—	7	1	no	—
524	C₂²⋊Q₈	—	7	1	no	—
525	C₂²⋊Q₈	—	7	1	no	—
526	C₂²⋊Q₈	—	7	1	no	—
527	C₂²⋊Q₈	—	7	1	no	—
528	C₂²⋊Q₈	—	7	1	no	—
529	C₂²⋊Q₈	—	7	1	no	—
530	C₂²⋊Q₈	—	7	1	no	—
531	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
532	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
533	#121	—	7	1	no	—
534	#121	—	7	1	no	—
535	#121	—	7	1	no	—
536	#121	—	7	1	no	—
537	#121	—	7	1	no	—
538	#121	—	7	1	no	—
539	#121	—	7	1	no	—
540	#121	—	7	1	no	—
541	#121	—	7	1	no	—
542	#121	—	7	1	no	—
543	#121	—	7	1	no	—
544	#120	—	7	1	no	—
545	#120	—	7	1	no	—
546	#120	—	7	1	no	—
547	#120	C₂×D₇	1	1	yes	characteristic
548	C₄×Q₈	—	7	1	no	—
549	C₄×Q₈	—	7	1	no	—
550	C₄×Q₈	—	7	1	no	—
551	C₄×Q₈	—	7	1	no	—
552	C₄×Q₈	—	7	1	no	—
553	C₄×Q₈	—	7	1	no	—
554	C₄×Q₈	—	7	1	no	—
555	C₄×D₄	—	7	1	no	—
556	C₄×D₄	—	7	1	no	—
557	C₄×D₄	—	7	1	no	—
558	C₄×D₄	—	7	1	no	—
559	C₄×D₄	—	7	1	no	—
560	C₄×D₄	—	7	1	no	—
561	C₄×D₄	—	7	1	no	—
562	C₄×D₄	—	7	1	no	—
563	C₄×D₄	—	7	1	no	—
564	C₄×D₄	—	7	1	no	—
565	C₄×D₄	—	7	1	no	—
566	C₄×D₄	—	7	1	no	—
567	C₄×D₄	—	7	1	no	—
568	C₄×D₄	—	7	1	no	—
569	C₄×D₄	—	7	1	no	—
570	C₄×D₄	—	7	1	no	—
571	C₄×D₄	—	7	1	no	—
572	C₄×D₄	—	7	1	no	—
573	C₄×D₄	—	7	1	no	—
574	C₄×D₄	—	7	1	no	—
575	C₄×D₄	—	7	1	no	—
576	C₄×D₄	—	7	1	no	—
577	C₄×D₄	—	7	1	no	—
578	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
579	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
580	#117	—	7	1	no	—
581	#117	—	7	1	no	—
582	#117	—	7	1	no	—
583	#117	—	7	1	no	—
584	#117	—	7	1	no	—
585	#117	—	7	1	no	—
586	#117	—	7	1	no	—
587	#117	—	7	1	no	—
588	#117	—	7	1	no	—
589	#117	—	7	1	no	—
590	#117	—	7	1	no	—
591	#117	—	7	1	no	—
592	#117	C₂×D₇	1	1	yes	characteristic, complemented
593	#117	C₂×D₇	1	1	yes	characteristic, complemented
594	C₂×C₄⋊C₄	—	7	1	no	—
595	C₂×C₄⋊C₄	—	7	1	no	—
596	C₂×C₄⋊C₄	—	7	1	no	—
597	C₂×C₄⋊C₄	—	7	1	no	—
598	C₂×C₄⋊C₄	—	7	1	no	—
599	C₂×C₄⋊C₄	—	7	1	no	—
600	C₂×C₄⋊C₄	—	7	1	no	—
601	C₂×C₂²⋊C₄	—	7	1	no	—
602	C₂×C₂²⋊C₄	—	7	1	no	—
603	C₂×C₂²⋊C₄	—	7	1	no	—
604	C₂×C₂²⋊C₄	—	7	1	no	—
605	C₂×C₂²⋊C₄	—	7	1	no	—
606	C₂×C₂²⋊C₄	—	7	1	no	—
607	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
609	C₂×C₄²	—	7	1	no	—
610	C₂×C₄²	—	7	1	no	—
611	C₂×C₄²	—	7	1	no	—
612	C₂²×C₇	—	2	1	no	—
613	C₂²×C₇	—	2	1	no	—
614	C₂²×C₇	—	2	1	no	—
615	C₂²×C₇	—	2	1	no	—
616	C₂²×C₇	—	2	1	no	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	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	—	8	2	no	—
624	C₂²×C₇	C₂×#41	1	2	yes	—
625	C₂²×C₇	C₂⁵	1	1	yes	characteristic
626	C₂×D₇	—	2	1	no	—
627	C₂×D₇	—	2	1	no	—
628	C₂×D₇	—	2	1	no	—
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	—	8	2	no	—
635	C₂×D₇	C₂×#41	1	2	yes	—
636	C₄×C₇	—	2	1	no	—
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	1	no	—
642	C₄×C₇	—	2	1	no	—
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	Dic₇	—	2	1	no	—
648	Dic₇	—	2	1	no	—
649	Dic₇	—	2	1	no	—
650	Dic₇	—	2	1	no	—
651	Dic₇	—	2	1	no	—
652	Dic₇	—	2	1	no	—
653	Dic₇	—	2	1	no	—
654	Dic₇	—	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	C₂×#41	1	2	yes	—
660	C₂⁴	—	7	1	no	—
661	C₂⁴	C₂²×D₇	1	1	yes	characteristic
662	#41	—	14	4	no	—
663	#41	—	14	4	no	—
664	C₂×Q₈	—	7	1	no	—
665	C₂×Q₈	—	7	1	no	—
666	C₂×Q₈	—	7	1	no	—
667	C₂×Q₈	—	7	1	no	—
668	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
669	C₂×D₄	—	7	1	no	—
670	C₂×D₄	—	7	1	no	—
671	C₂×D₄	—	7	1	no	—
672	C₂×D₄	—	7	1	no	—
673	C₂×D₄	—	7	1	no	—
674	C₂×D₄	—	7	1	no	—
675	C₂×D₄	—	7	1	no	—
676	C₂×D₄	—	7	1	no	—
677	C₂×D₄	—	7	1	no	—
678	C₂×D₄	—	7	1	no	—
679	C₂×D₄	—	7	1	no	—
680	C₂×D₄	—	7	1	no	—
681	C₂×D₄	—	14	4	no	—
682	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
683	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
685	C₂²×C₄	—	7	1	no	—
686	C₂²×C₄	—	7	1	no	—
687	C₂²×C₄	—	7	1	no	—
688	C₂²×C₄	—	7	1	no	—
689	C₂²×C₄	—	7	1	no	—
690	C₂²×C₄	—	7	1	no	—
691	C₂²×C₄	—	7	1	no	—
692	C₂²×C₄	—	7	1	no	—
693	C₂²×C₄	—	7	1	no	—
694	C₂²×C₄	—	7	1	no	—
695	C₂²×C₄	—	7	1	no	—
696	C₂²×C₄	—	7	1	no	—
697	C₂²×C₄	—	7	1	no	—
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	C₂²×D₇	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
706	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
707	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
708	C₄⋊C₄	—	7	1	no	—
709	C₄⋊C₄	—	7	1	no	—
710	C₄⋊C₄	—	7	1	no	—
711	C₄⋊C₄	—	7	1	no	—
712	C₄⋊C₄	—	7	1	no	—
713	C₄⋊C₄	—	7	1	no	—
714	C₄⋊C₄	—	7	1	no	—
715	C₄⋊C₄	—	7	1	no	—
716	C₄⋊C₄	—	7	1	no	—
717	C₄⋊C₄	—	7	1	no	—
718	C₄⋊C₄	—	7	1	no	—
719	C₄⋊C₄	—	7	1	no	—
720	C₄⋊C₄	—	7	1	no	—
721	C₄⋊C₄	—	7	1	no	—
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	C₂²×D₇	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
752	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
754	C₂²⋊C₄	—	7	1	no	—
755	C₂²⋊C₄	—	7	1	no	—
756	C₂²⋊C₄	—	7	1	no	—
757	C₂²⋊C₄	—	7	1	no	—
758	C₂²⋊C₄	—	7	1	no	—
759	C₂²⋊C₄	—	7	1	no	—
760	C₂²⋊C₄	—	7	1	no	—
761	C₂²⋊C₄	—	7	1	no	—
762	C₂²⋊C₄	—	7	1	no	—
763	C₂²⋊C₄	—	7	1	no	—
764	C₂²⋊C₄	—	7	1	no	—
765	C₂²⋊C₄	—	7	1	no	—
766	C₂²⋊C₄	—	7	1	no	—
767	C₂²⋊C₄	—	7	1	no	—
768	C₂²⋊C₄	—	7	1	no	—
769	C₂²⋊C₄	—	7	1	no	—
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	C₂²×D₇	1	1	yes	characteristic
787	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
800	C₄²	—	7	1	no	—
801	C₄²	—	7	1	no	—
802	C₄²	—	7	1	no	—
803	C₄²	—	7	1	no	—
804	C₄²	—	7	1	no	—
805	C₄²	—	7	1	no	—
806	C₄²	—	7	1	no	—
807	C₄²	—	7	1	no	—
808	C₄²	—	7	1	no	—
809	C₄²	—	7	1	no	—
810	C₄²	—	7	1	no	—
811	C₄²	—	7	1	no	—
812	C₄²	—	7	1	no	—
813	C₄²	—	7	1	no	—
814	C₄²	—	7	1	no	—
815	C₄²	C₂²×D₇	1	1	yes	characteristic
816	C₄²	C₂²×D₇	1	1	yes	characteristic
817	C₄²	C₂²×D₇	1	1	yes	characteristic
818	C₂×C₇	—	2	2	no	—
819	C₂×C₇	—	4	1	no	—
820	C₂×C₇	—	4	1	no	—
821	C₂×C₇	—	4	1	no	—
822	C₂×C₇	C₂²×#41	1	1	yes	characteristic
823	C₂×C₇	#585	1	1	yes	characteristic
824	C₂×C₇	#585	1	1	yes	characteristic
825	D₇	—	2	2	no	—
826	D₇	—	4	1	no	—
827	D₇	—	4	1	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	7	1	no	—
832	C₂³	—	7	1	no	—
833	C₂³	—	7	1	no	—
834	C₂³	—	14	2	no	—
835	C₂³	—	28	1	no	—
836	C₂³	—	28	1	no	—
837	C₂³	C₂³×D₇	1	1	yes	characteristic
838	C₂³	C₂³×D₇	1	1	yes	characteristic
839	C₂³	C₂³×D₇	1	1	yes	characteristic
840	C₂³	C₂³×D₇	1	1	yes	characteristic
841	Q₈	—	4	1	no	—
842	Q₈	—	14	2	no	—
843	Q₈	—	14	2	no	—
844	Q₈	—	28	1	no	—
845	Q₈	—	28	1	no	—
846	D₄	—	2	2	no	—
847	D₄	—	4	1	no	—
848	D₄	—	4	1	no	—
849	D₄	—	7	4	no	—
850	D₄	—	14	2	no	—
851	D₄	—	14	2	no	—
852	D₄	—	14	2	no	—
853	D₄	—	14	2	no	—
854	D₄	—	14	2	no	—
855	D₄	—	14	2	no	—
856	D₄	—	28	1	no	—
857	D₄	—	28	1	no	—
858	D₄	—	28	1	no	—
859	D₄	—	28	1	no	—
860	D₄	—	28	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	7	1	no	—
867	C₂×C₄	—	7	1	no	—
868	C₂×C₄	—	7	1	no	—
869	C₂×C₄	—	7	1	no	—
870	C₂×C₄	—	7	1	no	—
871	C₂×C₄	—	7	1	no	—
872	C₂×C₄	—	7	1	no	—
873	C₂×C₄	—	7	1	no	—
874	C₂×C₄	—	7	1	no	—
875	C₂×C₄	—	7	1	no	—
876	C₂×C₄	—	7	1	no	—
877	C₂×C₄	—	7	1	no	—
878	C₂×C₄	—	7	1	no	—
879	C₂×C₄	—	14	2	no	—
880	C₂×C₄	—	14	2	no	—
881	C₂×C₄	—	14	2	no	—
882	C₂×C₄	—	14	2	no	—
883	C₂×C₄	—	14	2	no	—
884	C₂×C₄	—	14	2	no	—
885	C₂×C₄	—	28	1	no	—
886	C₂×C₄	—	28	1	no	—
887	C₂×C₄	—	28	1	no	—
888	C₂×C₄	—	28	1	no	—
889	C₂×C₄	—	28	1	no	—
890	C₂×C₄	—	28	1	no	—
891	C₂×C₄	—	28	1	no	—
892	C₂×C₄	—	28	1	no	—
893	C₂×C₄	—	28	1	no	—
894	C₂×C₄	—	28	1	no	—
895	C₂×C₄	—	28	1	no	—
896	C₂×C₄	—	28	1	no	—
897	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
908	C₇	#3521	1	1	yes	characteristic, complemented, Sylow
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	7	2	no	—
921	C₂²	—	8	2	no	—
922	C₂²	—	14	1	no	—
923	C₂²	—	14	1	no	—
924	C₂²	—	14	1	no	—
925	C₂²	—	14	1	no	—
926	C₂²	—	14	1	no	—
927	C₂²	—	14	1	no	—
928	C₂²	—	14	1	no	—
929	C₂²	—	14	1	no	—
930	C₂²	—	56	2	no	—
931	C₂²	D₇×#41	1	2	yes	—
932	C₂²	C₂⁴×D₇	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	7	2	no	—
945	C₄	—	14	1	no	—
946	C₄	—	14	1	no	—
947	C₄	—	14	1	no	—
948	C₄	—	14	1	no	—
949	C₄	—	14	1	no	—
950	C₄	—	14	1	no	—
951	C₄	—	14	1	no	—
952	C₄	—	14	1	no	—
953	C₄	—	14	1	no	—
954	C₄	—	14	1	no	—
955	C₄	—	14	1	no	—
956	C₄	—	14	1	no	—
957	C₂	—	2	2	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	14	2	no	—
962	C₂	—	28	1	no	—
963	C₂	—	28	1	no	—
964	C₂	C₂×D₇×#41	1	1	yes	characteristic
965	C₂	#90616	1	1	yes	characteristic
966	C₂	#90618	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#551	C₂
hypercenter	#551	D₇
hypocenter	C₇	#3521
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₇×#551	C₂	semidirect
2. #90396	C₂	semidirect
3. D₇×#126	C₂	semidirect
4. #90393	C₂	semidirect
5. #90392	C₂	semidirect
6. #90371	C₂	semidirect
7. #90370	C₂	semidirect
8. #90353	C₂	semidirect
9. #90352	C₂	semidirect
10. #90348	C₂	semidirect
11. #90346	C₂	semidirect
12. #90341	C₂	semidirect
13. #90340	C₂	semidirect
14. #90336	C₂	semidirect
15. #90332	C₂	semidirect
16. #90329	C₂	semidirect
17. #90326	C₂	semidirect
18. #90284	C₂	semidirect
19. #90282	C₂	semidirect
20. #90256	C₂	semidirect
21. #90248	C₂	semidirect
22. #90237	C₂	semidirect
23. #90231	C₂	semidirect
24. #90222	C₂	semidirect
25. #90220	C₂	semidirect
26. #90219	C₂	semidirect
27. #90213	C₂	semidirect
28. #90186	C₂	semidirect
29. #90181	C₂	semidirect
30. #90177	C₂	semidirect
31. C₂×#6442	C₂	semidirect
39. C₇×#123	C₂²	semidirect
40. C₇×#123	C₂²	semidirect
41. C₇×C₂²⋊Q₈	C₂²	semidirect
42. C₇×C₂²⋊Q₈	C₂²	semidirect
44. C₄×C₇×D₄	C₂²	semidirect
45. C₄×C₇×D₄	C₂²	semidirect
46. C₇×#117	C₂²	semidirect
47. C₇×#117	C₂²	semidirect
53. #6509	C₂²	semidirect
54. #6509	C₂²	semidirect
55. #6509	C₂²	semidirect
56. Q₈×Dic₇	C₂²	semidirect
59. #6502	C₂²	semidirect
60. #6502	C₂²	semidirect
64. #6499	C₂²	semidirect
67. D₄×Dic₇	C₂²	semidirect
69. #6493	C₂²	semidirect
71. #6492	C₂²	semidirect
77. C₄×C₂²⋊D₇	C₂²	semidirect
78. C₄×C₂²⋊D₇	C₂²	semidirect
79. #6489	C₂²	semidirect
80. #6489	C₂²	semidirect
81. C₂×C₄⋊Dic₇	C₂²	semidirect
82. #6487	C₂²	semidirect
83. C₂×Dic₇⋊C₄	C₂²	semidirect
84. C₂×Dic₇⋊C₄	C₂²	semidirect
85. C₂×Dic₇⋊C₄	C₂²	semidirect
86. C₂×C₄×Dic₇	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6461	C₂²	semidirect
90. #6461	C₂²	semidirect
91. #6461	C₂²	semidirect
92. #6461	C₂²	semidirect
93. #6460	C₂²	semidirect
94. #6460	C₂²	semidirect
95. #6459	C₂²	semidirect
96. #6459	C₂²	semidirect
97. #6457	C₂²	semidirect
98. #6457	C₂²	semidirect
99. #6457	C₂²	semidirect
100. #6456	C₂²	semidirect
101. #6456	C₂²	semidirect
102. #6455	C₂²	semidirect
103. D₇×C₄⋊C₄	C₂²	semidirect
104. D₇×C₄⋊C₄	C₂²	semidirect
105. D₇×C₄⋊C₄	C₂²	semidirect
106. #6453	C₂²	semidirect
107. #6453	C₂²	semidirect
108. #6452	C₂²	semidirect
109. #6452	C₂²	semidirect
110. #6452	C₂²	semidirect
111. #6452	C₂²	semidirect
112. #6452	C₂²	semidirect
113. #6451	C₂²	semidirect
114. #6451	C₂²	semidirect
115. #6450	C₂²	semidirect
116. #6450	C₂²	semidirect
117. #6450	C₂²	semidirect
118. #6450	C₂²	semidirect
120. #6449	C₂²	semidirect
125. #6448	C₂²	semidirect
128. #6447	C₂²	semidirect
132. #6446	C₂²	semidirect
133. #6446	C₂²	semidirect
134. #6446	C₂²	semidirect
135. #6446	C₂²	semidirect
143. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
144. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
145. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
146. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
147. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
159. #6442	C₂²	semidirect
160. #6442	C₂²	semidirect
161. #6442	C₂²	semidirect
162. #6442	C₂²	semidirect
163. #6442	C₂²	semidirect
164. #6442	C₂²	semidirect
167. #6441	C₂²	semidirect
168. #6441	C₂²	semidirect
169. #6441	C₂²	semidirect
172. #6440	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. C₄×D₂₈	C₂²	semidirect
177. #6435	C₂²	semidirect
178. #6435	C₂²	semidirect
179. #6435	C₂²	semidirect
180. #6435	C₂²	semidirect
181. C₄²×D₇	C₂²	semidirect
182. C₄²×D₇	C₂²	semidirect
183. #6433	C₂²	semidirect
184. #6433	C₂²	semidirect
185. C₄×Dic₁₄	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
358. #551	D₇	semidirect
516. #123	C₂×D₇	semidirect
517. #123	C₂×D₇	semidirect
531. C₂²⋊Q₈	C₂×D₇	semidirect
532. C₂²⋊Q₈	C₂×D₇	semidirect
578. C₄×D₄	C₂×D₇	semidirect
579. C₄×D₄	C₂×D₇	semidirect
592. #117	C₂×D₇	semidirect
593. #117	C₂×D₇	semidirect
908. C₇	#3521	semidirect

Maximal subgroups

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

subgroup	index
C₇×#551	2
#90396	2
D₇×#126	2
#90393	2
#90392	2
#90371	2
#90370	2
#90353	2
#90352	2
#90348	2
#90346	2
#90341	2
#90340	2
#90336	2
#90332	2
#90329	2
#90326	2
#90284	2
#90282	2
#90256	2
#90248	2
#90237	2
#90231	2
#90222	2
#90220	2
#90219	2
#90213	2
#90186	2
#90181	2
#90177	2
C₂×#6442	2
#3521	7