Subgroups — #11743950

Order 896.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	#90401	C₂	1	1	yes	maximal, characteristic, complemented
3	#90400	C₂	1	1	yes	maximal, characteristic, complemented
4	#90397	C₂	1	1	yes	maximal, characteristic, complemented
5	#90396	C₂	1	1	yes	maximal, characteristic, complemented
6	#90384	C₂	1	1	yes	maximal, characteristic, complemented
7	#90383	C₂	1	1	yes	maximal, characteristic, complemented
8	#90355	C₂	1	1	yes	maximal, characteristic, complemented
9	#90348	C₂	1	1	yes	maximal, characteristic, complemented
10	#90346	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
12	#90308	C₂	1	1	yes	maximal, characteristic, complemented
13	#90306	C₂	1	1	yes	maximal, characteristic, complemented
14	#90301	C₂	1	1	yes	maximal, characteristic, complemented
15	#90301	C₂	1	1	yes	maximal, characteristic, complemented
16	#90301	C₂	1	1	yes	maximal, characteristic, complemented
17	#90300	C₂	1	1	yes	maximal, characteristic, complemented
18	#90297	C₂	1	1	yes	maximal, characteristic, complemented
19	#90293	C₂	1	1	yes	maximal, characteristic, complemented
20	#90247	C₂	1	1	yes	maximal, characteristic, complemented
21	#90247	C₂	1	1	yes	maximal, characteristic, complemented
22	#90241	C₂	1	1	yes	maximal, characteristic, complemented
23	#90238	C₂	1	1	yes	maximal, characteristic, complemented
24	#90237	C₂	1	1	yes	maximal, characteristic, complemented
25	#90236	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
27	#90231	C₂	1	1	yes	maximal, characteristic, complemented
28	#90219	C₂	1	1	yes	maximal, characteristic, complemented
29	#90218	C₂	1	1	yes	maximal, characteristic, complemented
30	#90202	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#6457	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#1159	C₂²	1	1	yes	characteristic
33	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
37	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₂₈	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
41	C₇×#126	C₂²	1	1	yes	characteristic, complemented
42	C₇×#126	C₂²	1	1	yes	characteristic, complemented
43	C₇×#125	C₂²	1	1	yes	characteristic, complemented
44	C₇×#123	C₂²	1	1	yes	characteristic, complemented
45	C₇×#123	C₂²	1	1	yes	characteristic, complemented
46	C₇×#121	C₂²	1	1	yes	characteristic
47	C₇×#121	C₂²	1	1	yes	characteristic, complemented
48	C₇×#121	C₂²	1	1	yes	characteristic, complemented
49	C₇×#121	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
53	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₇×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	#6503	C₂²	1	1	yes	characteristic
57	#6502	C₂²	1	1	yes	characteristic, complemented
58	#6502	C₂²	1	1	yes	characteristic, complemented
59	#6502	C₂²	1	1	yes	characteristic, complemented
60	#6502	C₂²	1	1	yes	characteristic, complemented
61	#6501	C₂²	1	1	yes	characteristic, complemented
62	#6500	C₂²	1	1	yes	characteristic
63	#6500	C₂²	1	1	yes	characteristic
64	#6500	C₂²	1	1	yes	characteristic, complemented
65	#6500	C₂²	1	1	yes	characteristic, complemented
66	#6500	C₂²	1	1	yes	characteristic, complemented
67	#6500	C₂²	1	1	yes	characteristic, complemented
68	#6498	C₂²	1	1	yes	characteristic, complemented
69	#6498	C₂²	1	1	yes	characteristic, complemented
70	#6498	C₂²	1	1	yes	characteristic, complemented
71	#6498	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
75	#6493	C₂²	1	1	yes	characteristic, complemented
76	#6492	C₂²	1	1	yes	characteristic, complemented
77	#6492	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
89	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	#6487	C₂²	1	1	yes	characteristic, complemented
91	#6487	C₂²	1	1	yes	characteristic, complemented
92	#6487	C₂²	1	1	yes	characteristic, complemented
93	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
94	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	#6461	C₂²	1	1	yes	characteristic, complemented
96	#6461	C₂²	1	1	yes	characteristic, complemented
97	#6461	C₂²	1	1	yes	characteristic, complemented
98	#6461	C₂²	1	1	yes	characteristic, complemented
99	#6460	C₂²	1	1	yes	characteristic, complemented
100	#6460	C₂²	1	1	yes	characteristic, complemented
101	#6459	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	#6459	C₂²	1	1	yes	characteristic, complemented
106	#6459	C₂²	1	1	yes	characteristic, complemented
107	#6458	C₂²	1	1	yes	characteristic
108	#6457	C₂²	1	1	yes	characteristic
109	#6457	C₂²	1	1	yes	characteristic
110	#6457	C₂²	1	1	yes	characteristic
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	#6457	C₂²	1	1	yes	characteristic, complemented
115	#6457	C₂²	1	1	yes	characteristic, complemented
116	#6457	C₂²	1	1	yes	characteristic, complemented
117	#6457	C₂²	1	1	yes	characteristic, complemented
118	#6457	C₂²	1	1	yes	characteristic, complemented
119	#6457	C₂²	1	1	yes	characteristic, complemented
120	#6456	C₂²	1	1	yes	characteristic
121	#6456	C₂²	1	1	yes	characteristic, complemented
122	#6456	C₂²	1	1	yes	characteristic, complemented
123	#6455	C₂²	1	1	yes	characteristic, complemented
124	#6455	C₂²	1	1	yes	characteristic, complemented
125	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
126	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
127	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
128	#6452	C₂²	1	1	yes	characteristic, complemented
129	#6452	C₂²	1	1	yes	characteristic, complemented
130	#6452	C₂²	1	1	yes	characteristic, complemented
131	#6452	C₂²	1	1	yes	characteristic, complemented
132	#6451	C₂²	1	1	yes	characteristic, complemented
133	#6450	C₂²	1	1	yes	characteristic, complemented
134	#6450	C₂²	1	1	yes	characteristic, complemented
135	#6449	C₂²	1	1	yes	characteristic, complemented
136	#6449	C₂²	1	1	yes	characteristic, complemented
137	#6448	C₂²	1	1	yes	characteristic, complemented
138	#6448	C₂²	1	1	yes	characteristic, complemented
139	#6448	C₂²	1	1	yes	characteristic, complemented
140	#6448	C₂²	1	1	yes	characteristic, complemented
141	#6448	C₂²	1	1	yes	characteristic, complemented
142	#6448	C₂²	1	1	yes	characteristic, complemented
143	#6447	C₂²	1	1	yes	characteristic
144	#6447	C₂²	1	1	yes	characteristic
145	#6447	C₂²	1	1	yes	characteristic
146	#6447	C₂²	1	1	yes	characteristic, complemented
147	#6447	C₂²	1	1	yes	characteristic, complemented
148	#6447	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	#6445	C₂²	1	1	yes	characteristic
154	#6445	C₂²	1	1	yes	characteristic
155	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
156	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	(C₂²⋊D₇)⋊C₄	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	D₇×C₂²⋊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	#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	#6440	C₂²	1	1	yes	characteristic, complemented
174	#6440	C₂²	1	1	yes	characteristic, complemented
175	#6439	C₂²	1	1	yes	characteristic, complemented
176	#6439	C₂²	1	1	yes	characteristic, complemented
177	#6438	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
181	#6435	C₂²	1	1	yes	characteristic, complemented
182	#6435	C₂²	1	1	yes	characteristic, complemented
183	#6435	C₂²	1	1	yes	characteristic, complemented
184	#6435	C₂²	1	1	yes	characteristic, complemented
185	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
187	#3513	—	7	1	no	maximal, Sylow
188	C₂³×D₇	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	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
193	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
194	C₂×C₇×D₄	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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₇	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	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	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	C₂²×Dic₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₇	C₂³	1	1	yes	characteristic
222	#1159	—	2	4	no	—
223	#1159	—	4	2	no	—
224	D₄×D₇	—	2	4	no	—
225	D₄×D₇	—	2	4	no	—
226	D₄×D₇	—	4	2	no	—
227	#1157	—	4	2	no	—
228	C₂×D₂₈	—	4	2	no	—
229	C₂×D₂₈	C₂³	1	1	yes	characteristic
230	C₂×D₂₈	C₂³	1	1	yes	characteristic
231	C₂×D₂₈	C₂³	1	1	yes	characteristic
232	C₂×D₂₈	C₂³	1	1	yes	characteristic
233	C₂×D₂₈	C₂³	1	1	yes	characteristic
234	C₂×D₂₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	—	4	2	no	—
236	C₂×C₄×D₇	—	4	2	no	—
237	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
252	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
253	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
254	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
255	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
256	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
267	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
272	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
273	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
274	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
275	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₄²×C₇	C₂³	1	1	yes	characteristic
277	C₄²×C₇	C₂³	1	1	yes	characteristic
278	C₄²×C₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
288	C₂²⋊Dic₇	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	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇)⋊C₄	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	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
342	Dic₇⋊C₄	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	C₄×Dic₇	C₂³	1	1	yes	characteristic
350	C₄×Dic₇	C₂³	1	1	yes	characteristic
351	C₄×Dic₇	C₂³	1	1	yes	characteristic
352	#559	—	7	1	no	—
353	#554	—	7	1	no	—
354	#553	—	7	1	no	—
355	#553	—	7	1	no	—
356	#553	D₇	1	1	yes	characteristic, complemented
357	#552	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#551	—	7	1	no	—
362	#547	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#546	—	7	1	no	—
366	#546	—	7	1	no	—
367	D₄²	—	7	1	no	—
368	#542	—	7	1	no	—
369	#540	—	7	1	no	—
370	#539	—	7	1	no	—
371	#539	—	7	1	no	—
372	#538	—	7	1	no	—
373	#538	—	7	1	no	—
374	#529	—	7	1	no	—
375	#529	—	7	1	no	—
376	#525	—	7	1	no	—
377	#525	—	7	1	no	—
378	C₂×#123	—	7	1	no	—
379	C₂×#123	—	7	1	no	—
380	#520	—	7	1	no	—
381	#518	—	7	1	no	—
382	C₂×C₄×D₄	—	7	1	no	—
383	C₂³×C₇	C₂⁴	1	1	yes	characteristic
384	C₂³×C₇	C₂⁴	1	1	yes	characteristic
385	C₂³×C₇	C₂⁴	1	1	yes	characteristic
386	C₂³×C₇	C₂⁴	1	1	yes	characteristic
387	C₂²×D₇	—	2	2	no	—
388	C₂²×D₇	—	2	2	no	—
389	C₂²×D₇	—	2	2	no	—
390	C₂²×D₇	—	2	2	no	—
391	C₂²×D₇	—	2	2	no	—
392	C₂²×D₇	—	2	2	no	—
393	C₂²×D₇	—	4	1	no	—
394	C₂²×D₇	—	4	1	no	—
395	C₂²×D₇	—	4	1	no	—
396	C₂²×D₇	—	4	1	no	—
397	C₂²×D₇	—	4	1	no	—
398	C₂²×D₇	—	4	1	no	—
399	C₂²×D₇	C₂⁴	1	1	yes	characteristic
400	C₂²×D₇	C₂⁴	1	1	yes	characteristic
401	C₂²×D₇	C₂⁴	1	1	yes	characteristic
402	C₂²×D₇	C₂⁴	1	1	yes	characteristic
403	C₂²×D₇	C₂⁴	1	1	yes	characteristic
404	C₇×D₄	—	2	2	no	—
405	C₇×D₄	—	2	2	no	—
406	C₇×D₄	—	2	2	no	—
407	C₇×D₄	—	4	1	no	—
408	C₇×D₄	—	4	1	no	—
409	C₇×D₄	—	4	1	no	—
410	C₂×C₄×C₇	—	4	1	no	—
411	C₂×C₄×C₇	—	4	1	no	—
412	C₂×C₄×C₇	—	4	1	no	—
413	C₂×C₄×C₇	—	4	1	no	—
414	C₂×C₄×C₇	—	4	1	no	—
415	C₂×C₄×C₇	—	4	1	no	—
416	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
424	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
427	C₂²⋊D₇	—	2	2	no	—
428	C₂²⋊D₇	—	2	2	no	—
429	C₂²⋊D₇	—	2	2	no	—
430	C₂²⋊D₇	—	2	2	no	—
431	C₂²⋊D₇	—	2	2	no	—
432	C₂²⋊D₇	—	4	1	no	—
433	C₂²⋊D₇	—	4	1	no	—
434	C₂²⋊D₇	—	4	1	no	—
435	C₂²⋊D₇	—	4	1	no	—
436	C₂²⋊D₇	—	4	1	no	—
437	C₂²⋊D₇	—	4	1	no	—
438	C₂²⋊D₇	#41	1	4	yes	complemented
439	C₂×Dic₇	—	2	2	no	—
440	C₂×Dic₇	—	2	2	no	—
441	C₂×Dic₇	—	4	1	no	—
442	C₂×Dic₇	—	4	1	no	—
443	C₂×Dic₇	—	4	1	no	—
444	C₂×Dic₇	—	4	1	no	—
445	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
446	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
447	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
448	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
449	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
450	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
451	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
452	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
453	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
454	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
455	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
456	D₂₈	—	2	2	no	—
457	D₂₈	—	2	2	no	—
458	D₂₈	—	2	2	no	—
459	D₂₈	—	2	2	no	—
460	D₂₈	—	4	1	no	—
461	D₂₈	—	4	1	no	—
462	C₄×D₇	—	2	2	no	—
463	C₄×D₇	—	2	2	no	—
464	C₄×D₇	—	2	2	no	—
465	C₄×D₇	—	2	2	no	—
466	C₄×D₇	—	2	2	no	—
467	C₄×D₇	—	2	2	no	—
468	C₄×D₇	—	4	1	no	—
469	C₄×D₇	—	4	1	no	—
470	C₄×D₇	—	4	1	no	—
471	C₄×D₇	—	4	1	no	—
472	C₄×D₇	—	4	1	no	—
473	C₄×D₇	—	4	1	no	—
474	C₄×D₇	—	4	1	no	—
475	C₄×D₇	—	4	1	no	—
476	C₄×D₇	—	4	1	no	—
477	Dic₁₄	—	2	2	no	—
478	Dic₁₄	—	4	1	no	—
479	Dic₁₄	—	4	1	no	—
480	Dic₁₄	—	4	1	no	—
481	C₂×#41	—	7	1	no	—
482	C₂×#41	—	7	1	no	—
483	C₂×#41	—	7	1	no	—
484	C₂²×D₄	—	7	1	no	—
485	C₂²×D₄	—	7	1	no	—
486	C₂²×D₄	—	7	1	no	—
487	C₂²×D₄	—	7	1	no	—
488	C₂³×C₄	—	7	1	no	—
489	C₂³×C₄	—	7	1	no	—
490	C₄⋊Q₈	—	7	1	no	—
491	#127	—	7	1	no	—
492	#126	—	7	1	no	—
493	#126	—	7	1	no	—
494	#126	—	7	1	no	—
495	#126	—	7	1	no	—
496	#126	—	7	1	no	—
497	#126	—	7	1	no	—
498	#126	—	7	1	no	—
499	#126	—	7	1	no	—
500	#126	C₂×D₇	1	1	yes	characteristic, complemented
501	#126	C₂×D₇	1	1	yes	characteristic, complemented
502	#125	—	7	1	no	—
503	#125	—	7	1	no	—
504	#125	—	7	1	no	—
505	#125	—	7	1	no	—
506	#125	C₂×D₇	1	1	yes	characteristic, complemented
507	#124	—	7	1	no	—
508	#124	—	7	1	no	—
509	#124	—	7	1	no	—
510	#124	—	7	1	no	—
511	#124	—	7	1	no	—
512	#124	—	7	1	no	—
513	#124	—	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	—	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	C₂×D₇	1	1	yes	characteristic, complemented
539	#123	C₂×D₇	1	1	yes	characteristic, complemented
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	#121	—	7	1	no	—
554	#121	—	7	1	no	—
555	#121	—	7	1	no	—
556	#121	—	7	1	no	—
557	#121	—	7	1	no	—
558	#121	—	7	1	no	—
559	#121	—	7	1	no	—
560	#121	—	7	1	no	—
561	#121	—	7	1	no	—
562	#121	—	7	1	no	—
563	#121	—	7	1	no	—
564	#121	—	7	1	no	—
565	#121	—	7	1	no	—
566	#121	C₂×D₇	1	1	yes	characteristic
567	#121	C₂×D₇	1	1	yes	characteristic, complemented
568	#121	C₂×D₇	1	1	yes	characteristic, complemented
569	#121	C₂×D₇	1	1	yes	characteristic, complemented
570	#120	—	7	1	no	—
571	#120	—	7	1	no	—
572	#120	—	7	1	no	—
573	#120	—	7	1	no	—
574	#120	—	7	1	no	—
575	#120	—	7	1	no	—
576	#120	—	7	1	no	—
577	#120	—	7	1	no	—
578	C₄×Q₈	—	7	1	no	—
579	C₄×Q₈	—	7	1	no	—
580	C₄×Q₈	—	7	1	no	—
581	C₄×D₄	—	7	1	no	—
582	C₄×D₄	—	7	1	no	—
583	C₄×D₄	—	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	C₄×D₄	—	7	1	no	—
599	C₄×D₄	—	7	1	no	—
600	C₄×D₄	—	7	1	no	—
601	C₄×D₄	—	7	1	no	—
602	C₄×D₄	—	7	1	no	—
603	C₄×D₄	—	7	1	no	—
604	C₄×D₄	—	7	1	no	—
605	C₄×D₄	—	7	1	no	—
606	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
607	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
608	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
609	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
610	#117	—	7	1	no	—
611	#117	—	7	1	no	—
612	#117	—	7	1	no	—
613	#117	—	7	1	no	—
614	#117	—	7	1	no	—
615	#117	—	7	1	no	—
616	#117	—	7	1	no	—
617	#117	—	7	1	no	—
618	#117	C₂×D₇	1	1	yes	characteristic, complemented
619	C₂×C₄⋊C₄	—	7	1	no	—
620	C₂×C₄⋊C₄	—	7	1	no	—
621	C₂×C₄⋊C₄	—	7	1	no	—
622	C₂×C₄⋊C₄	—	7	1	no	—
623	C₂×C₄⋊C₄	—	7	1	no	—
624	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
625	C₂×C₂²⋊C₄	—	7	1	no	—
626	C₂×C₂²⋊C₄	—	7	1	no	—
627	C₂×C₂²⋊C₄	—	7	1	no	—
628	C₂×C₂²⋊C₄	—	7	1	no	—
629	C₂×C₂²⋊C₄	—	7	1	no	—
630	C₂×C₂²⋊C₄	—	7	1	no	—
631	C₂×C₂²⋊C₄	—	7	1	no	—
632	C₂×C₂²⋊C₄	—	7	1	no	—
633	C₂×C₂²⋊C₄	—	7	1	no	—
634	C₂×C₂²⋊C₄	—	7	1	no	—
635	C₂×C₄²	—	7	1	no	—
636	C₂²×C₇	—	2	1	no	—
637	C₂²×C₇	—	2	1	no	—
638	C₂²×C₇	—	2	1	no	—
639	C₂²×C₇	—	2	1	no	—
640	C₂²×C₇	—	2	1	no	—
641	C₂²×C₇	—	2	1	no	—
642	C₂²×C₇	—	2	1	no	—
643	C₂²×C₇	—	2	1	no	—
644	C₂²×C₇	—	2	1	no	—
645	C₂²×C₇	—	2	1	no	—
646	C₂²×C₇	—	2	1	no	—
647	C₂²×C₇	C₂×#41	1	2	yes	—
648	C₂²×C₇	C₂⁵	1	1	yes	characteristic
649	C₂×D₇	—	2	1	no	—
650	C₂×D₇	—	2	1	no	—
651	C₂×D₇	—	2	1	no	—
652	C₂×D₇	—	2	1	no	—
653	C₂×D₇	—	2	1	no	—
654	C₂×D₇	—	2	1	no	—
655	C₂×D₇	—	2	1	no	—
656	C₂×D₇	—	2	1	no	—
657	C₂×D₇	—	2	1	no	—
658	C₂×D₇	—	2	1	no	—
659	C₂×D₇	—	2	1	no	—
660	C₂×D₇	—	2	1	no	—
661	C₂×D₇	—	2	1	no	—
662	C₂×D₇	—	4	4	no	—
663	C₂×D₇	—	4	4	no	—
664	C₂×D₇	—	8	2	no	—
665	C₂×D₇	—	8	2	no	—
666	C₂×D₇	C₂×#41	1	2	yes	—
667	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
668	C₄×C₇	—	2	1	no	—
669	C₄×C₇	—	2	1	no	—
670	C₄×C₇	—	2	1	no	—
671	C₄×C₇	—	2	1	no	—
672	C₄×C₇	—	2	1	no	—
673	C₄×C₇	—	2	1	no	—
674	C₄×C₇	—	2	1	no	—
675	C₄×C₇	—	2	1	no	—
676	C₄×C₇	—	2	1	no	—
677	C₄×C₇	—	2	1	no	—
678	C₄×C₇	—	2	1	no	—
679	Dic₇	—	2	1	no	—
680	Dic₇	—	2	1	no	—
681	Dic₇	—	2	1	no	—
682	Dic₇	—	2	1	no	—
683	Dic₇	—	2	1	no	—
684	Dic₇	—	2	1	no	—
685	Dic₇	—	2	1	no	—
686	Dic₇	—	2	1	no	—
687	Dic₇	—	2	1	no	—
688	Dic₇	—	2	1	no	—
689	Dic₇	C₂×#41	1	2	yes	—
690	C₂⁴	—	7	1	no	—
691	C₂⁴	—	7	1	no	—
692	C₂⁴	—	7	1	no	—
693	C₂⁴	—	7	1	no	—
694	#41	—	14	4	no	—
695	#41	—	28	2	no	—
696	#41	—	28	2	no	—
697	C₂×Q₈	—	7	1	no	—
698	C₂×Q₈	—	7	1	no	—
699	C₂×Q₈	—	7	1	no	—
700	C₂×Q₈	—	7	1	no	—
701	C₂×D₄	—	7	1	no	—
702	C₂×D₄	—	7	1	no	—
703	C₂×D₄	—	7	1	no	—
704	C₂×D₄	—	7	1	no	—
705	C₂×D₄	—	7	1	no	—
706	C₂×D₄	—	7	1	no	—
707	C₂×D₄	—	7	1	no	—
708	C₂×D₄	—	7	1	no	—
709	C₂×D₄	—	7	1	no	—
710	C₂×D₄	—	7	1	no	—
711	C₂×D₄	—	7	1	no	—
712	C₂×D₄	—	7	1	no	—
713	C₂×D₄	—	7	1	no	—
714	C₂×D₄	—	7	1	no	—
715	C₂×D₄	—	7	1	no	—
716	C₂×D₄	—	7	1	no	—
717	C₂×D₄	—	7	1	no	—
718	C₂×D₄	—	7	1	no	—
719	C₂×D₄	—	14	4	no	—
720	C₂×D₄	—	14	4	no	—
721	C₂×D₄	—	28	2	no	—
722	C₂×D₄	—	28	2	no	—
723	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
724	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
725	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
726	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
727	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
728	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
729	C₂²×C₄	—	7	1	no	—
730	C₂²×C₄	—	7	1	no	—
731	C₂²×C₄	—	7	1	no	—
732	C₂²×C₄	—	7	1	no	—
733	C₂²×C₄	—	7	1	no	—
734	C₂²×C₄	—	7	1	no	—
735	C₂²×C₄	—	7	1	no	—
736	C₂²×C₄	—	7	1	no	—
737	C₂²×C₄	—	7	1	no	—
738	C₂²×C₄	—	7	1	no	—
739	C₂²×C₄	—	7	1	no	—
740	C₂²×C₄	—	7	1	no	—
741	C₂²×C₄	—	7	1	no	—
742	C₂²×C₄	—	7	1	no	—
743	C₂²×C₄	—	7	1	no	—
744	C₂²×C₄	—	7	1	no	—
745	C₂²×C₄	—	7	1	no	—
746	C₂²×C₄	—	7	1	no	—
747	C₂²×C₄	—	7	1	no	—
748	C₂²×C₄	—	7	1	no	—
749	C₂²×C₄	—	7	1	no	—
750	C₂²×C₄	—	28	2	no	—
751	C₂²×C₄	—	28	2	no	—
752	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
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	—	7	1	no	—
763	C₄⋊C₄	—	7	1	no	—
764	C₄⋊C₄	—	7	1	no	—
765	C₄⋊C₄	—	7	1	no	—
766	C₄⋊C₄	—	7	1	no	—
767	C₄⋊C₄	—	7	1	no	—
768	C₄⋊C₄	—	7	1	no	—
769	C₄⋊C₄	—	7	1	no	—
770	C₄⋊C₄	—	7	1	no	—
771	C₄⋊C₄	—	7	1	no	—
772	C₄⋊C₄	—	7	1	no	—
773	C₄⋊C₄	—	7	1	no	—
774	C₄⋊C₄	—	7	1	no	—
775	C₄⋊C₄	—	7	1	no	—
776	C₄⋊C₄	—	7	1	no	—
777	C₄⋊C₄	—	7	1	no	—
778	C₄⋊C₄	—	7	1	no	—
779	C₄⋊C₄	—	7	1	no	—
780	C₄⋊C₄	—	7	1	no	—
781	C₄⋊C₄	—	7	1	no	—
782	C₄⋊C₄	—	7	1	no	—
783	C₄⋊C₄	—	7	1	no	—
784	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
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	—	7	1	no	—
809	C₂²⋊C₄	—	7	1	no	—
810	C₂²⋊C₄	—	7	1	no	—
811	C₂²⋊C₄	—	7	1	no	—
812	C₂²⋊C₄	—	7	1	no	—
813	C₂²⋊C₄	—	7	1	no	—
814	C₂²⋊C₄	—	7	1	no	—
815	C₂²⋊C₄	—	7	1	no	—
816	C₂²⋊C₄	—	7	1	no	—
817	C₂²⋊C₄	—	7	1	no	—
818	C₂²⋊C₄	—	7	1	no	—
819	C₂²⋊C₄	—	7	1	no	—
820	C₂²⋊C₄	—	7	1	no	—
821	C₂²⋊C₄	—	7	1	no	—
822	C₂²⋊C₄	—	7	1	no	—
823	C₂²⋊C₄	—	7	1	no	—
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	C₂²×D₇	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
842	C₄²	—	7	1	no	—
843	C₄²	—	7	1	no	—
844	C₄²	—	7	1	no	—
845	C₄²	—	7	1	no	—
846	C₄²	—	7	1	no	—
847	C₄²	—	7	1	no	—
848	C₄²	—	7	1	no	—
849	C₄²	—	7	1	no	—
850	C₄²	—	7	1	no	—
851	C₄²	C₂²×D₇	1	1	yes	characteristic
852	C₄²	C₂²×D₇	1	1	yes	characteristic
853	C₄²	C₂²×D₇	1	1	yes	characteristic
854	C₂×C₇	—	2	2	no	—
855	C₂×C₇	—	4	1	no	—
856	C₂×C₇	—	4	1	no	—
857	C₂×C₇	—	4	1	no	—
858	C₂×C₇	C₂²×#41	1	1	yes	characteristic
859	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
860	C₂×C₇	#585	1	1	yes	characteristic
861	D₇	—	2	2	no	—
862	D₇	—	2	2	no	—
863	D₇	—	4	1	no	—
864	D₇	—	4	1	no	—
865	D₇	—	4	1	no	—
866	C₂³	—	7	1	no	—
867	C₂³	—	7	1	no	—
868	C₂³	—	7	1	no	—
869	C₂³	—	7	1	no	—
870	C₂³	—	7	1	no	—
871	C₂³	—	14	2	no	—
872	C₂³	—	14	2	no	—
873	C₂³	—	14	2	no	—
874	C₂³	—	14	2	no	—
875	C₂³	—	14	2	no	—
876	C₂³	—	14	2	no	—
877	C₂³	—	28	1	no	—
878	C₂³	—	28	1	no	—
879	C₂³	—	28	1	no	—
880	C₂³	—	28	1	no	—
881	C₂³	—	28	1	no	—
882	C₂³	—	28	1	no	—
883	C₂³	C₂³×D₇	1	1	yes	characteristic
884	C₂³	C₂³×D₇	1	1	yes	characteristic
885	C₂³	C₂³×D₇	1	1	yes	characteristic
886	C₂³	C₂³×D₇	1	1	yes	characteristic
887	Q₈	—	14	2	no	—
888	Q₈	—	28	1	no	—
889	Q₈	—	28	1	no	—
890	Q₈	—	28	1	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	7	4	no	—
898	D₄	—	14	2	no	—
899	D₄	—	14	2	no	—
900	D₄	—	14	2	no	—
901	D₄	—	14	2	no	—
902	D₄	—	14	2	no	—
903	D₄	—	14	2	no	—
904	D₄	—	14	2	no	—
905	D₄	—	14	2	no	—
906	D₄	—	14	2	no	—
907	D₄	—	28	1	no	—
908	D₄	—	28	1	no	—
909	D₄	—	28	1	no	—
910	D₄	—	28	1	no	—
911	D₄	—	28	1	no	—
912	D₄	—	28	1	no	—
913	D₄	—	28	1	no	—
914	D₄	—	28	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	7	1	no	—
922	C₂×C₄	—	7	1	no	—
923	C₂×C₄	—	7	1	no	—
924	C₂×C₄	—	7	1	no	—
925	C₂×C₄	—	7	1	no	—
926	C₂×C₄	—	7	1	no	—
927	C₂×C₄	—	7	1	no	—
928	C₂×C₄	—	7	1	no	—
929	C₂×C₄	—	7	1	no	—
930	C₂×C₄	—	7	1	no	—
931	C₂×C₄	—	7	1	no	—
932	C₂×C₄	—	14	2	no	—
933	C₂×C₄	—	14	2	no	—
934	C₂×C₄	—	14	2	no	—
935	C₂×C₄	—	14	2	no	—
936	C₂×C₄	—	14	2	no	—
937	C₂×C₄	—	14	2	no	—
938	C₂×C₄	—	14	2	no	—
939	C₂×C₄	—	14	2	no	—
940	C₂×C₄	—	28	1	no	—
941	C₂×C₄	—	28	1	no	—
942	C₂×C₄	—	28	1	no	—
943	C₂×C₄	—	28	1	no	—
944	C₂×C₄	—	28	1	no	—
945	C₂×C₄	—	28	1	no	—
946	C₂×C₄	—	28	1	no	—
947	C₂×C₄	—	28	1	no	—
948	C₂×C₄	—	28	1	no	—
949	C₂×C₄	—	28	1	no	—
950	C₂×C₄	—	28	1	no	—
951	C₂×C₄	—	28	1	no	—
952	C₂×C₄	—	28	1	no	—
953	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
954	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
964	C₇	#3513	1	1	yes	characteristic, complemented, Sylow
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	7	2	no	—
977	C₂²	—	7	2	no	—
978	C₂²	—	14	1	no	—
979	C₂²	—	14	1	no	—
980	C₂²	—	14	1	no	—
981	C₂²	—	14	1	no	—
982	C₂²	—	14	1	no	—
983	C₂²	—	14	1	no	—
984	C₂²	—	14	1	no	—
985	C₂²	—	14	1	no	—
986	C₂²	—	14	1	no	—
987	C₂²	—	14	1	no	—
988	C₂²	—	14	1	no	—
989	C₂²	—	14	1	no	—
990	C₂²	—	14	1	no	—
991	C₂²	—	28	4	no	—
992	C₂²	—	28	4	no	—
993	C₂²	—	56	2	no	—
994	C₂²	—	56	2	no	—
995	C₂²	D₇×#41	1	2	yes	—
996	C₂²	C₂⁴×D₇	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	7	2	no	—
1009	C₄	—	14	1	no	—
1010	C₄	—	14	1	no	—
1011	C₄	—	14	1	no	—
1012	C₄	—	14	1	no	—
1013	C₄	—	14	1	no	—
1014	C₄	—	14	1	no	—
1015	C₄	—	14	1	no	—
1016	C₄	—	14	1	no	—
1017	C₄	—	14	1	no	—
1018	C₄	—	14	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	14	2	no	—
1024	C₂	—	14	2	no	—
1025	C₂	—	28	1	no	—
1026	C₂	—	28	1	no	—
1027	C₂	—	28	1	no	—
1028	C₂	C₂×D₇×#41	1	1	yes	characteristic
1029	C₂	#90616	1	1	yes	characteristic
1030	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×#553	C₂
hypercenter	#553	D₇
hypocenter	C₇	#3513
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. C₇×#553	C₂	semidirect
2. #90401	C₂	semidirect
3. #90400	C₂	semidirect
4. #90397	C₂	semidirect
5. #90396	C₂	semidirect
6. #90384	C₂	semidirect
7. #90383	C₂	semidirect
8. #90355	C₂	semidirect
9. #90348	C₂	semidirect
10. #90346	C₂	semidirect
11. D₇×#123	C₂	semidirect
12. #90308	C₂	semidirect
13. #90306	C₂	semidirect
14. #90301	C₂	semidirect
15. #90301	C₂	semidirect
16. #90301	C₂	semidirect
17. #90300	C₂	semidirect
18. #90297	C₂	semidirect
19. #90293	C₂	semidirect
20. #90247	C₂	semidirect
21. #90247	C₂	semidirect
22. #90241	C₂	semidirect
23. #90238	C₂	semidirect
24. #90237	C₂	semidirect
25. #90236	C₂	semidirect
26. C₄×D₄×D₇	C₂	semidirect
27. #90231	C₂	semidirect
28. #90219	C₂	semidirect
29. #90218	C₂	semidirect
30. #90202	C₂	semidirect
31. C₂×#6457	C₂	semidirect
33. C₂×#1159	C₂²	semidirect
37. C₂×#1157	C₂²	semidirect
39. C₂²×C₄×D₇	C₂²	semidirect
40. C₂²×C₄×D₇	C₂²	semidirect
41. C₇×#126	C₂²	semidirect
42. C₇×#126	C₂²	semidirect
43. C₇×#125	C₂²	semidirect
44. C₇×#123	C₂²	semidirect
45. C₇×#123	C₂²	semidirect
47. C₇×#121	C₂²	semidirect
48. C₇×#121	C₂²	semidirect
49. C₇×#121	C₂²	semidirect
50. C₄×C₇×D₄	C₂²	semidirect
51. C₄×C₇×D₄	C₂²	semidirect
52. C₄×C₇×D₄	C₂²	semidirect
53. C₄×C₇×D₄	C₂²	semidirect
54. C₇×#117	C₂²	semidirect
55. C₂×C₇×C₄⋊C₄	C₂²	semidirect
57. #6502	C₂²	semidirect
58. #6502	C₂²	semidirect
59. #6502	C₂²	semidirect
60. #6502	C₂²	semidirect
61. #6501	C₂²	semidirect
64. #6500	C₂²	semidirect
65. #6500	C₂²	semidirect
66. #6500	C₂²	semidirect
67. #6500	C₂²	semidirect
68. #6498	C₂²	semidirect
69. #6498	C₂²	semidirect
70. #6498	C₂²	semidirect
71. #6498	C₂²	semidirect
72. D₄×Dic₇	C₂²	semidirect
73. D₄×Dic₇	C₂²	semidirect
74. D₄×Dic₇	C₂²	semidirect
75. #6493	C₂²	semidirect
76. #6492	C₂²	semidirect
77. #6492	C₂²	semidirect
81. C₄×C₂²⋊D₇	C₂²	semidirect
82. C₄×C₂²⋊D₇	C₂²	semidirect
83. C₄×C₂²⋊D₇	C₂²	semidirect
84. C₄×C₂²⋊D₇	C₂²	semidirect
85. C₄×C₂²⋊D₇	C₂²	semidirect
86. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
87. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
88. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
89. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
90. #6487	C₂²	semidirect
91. #6487	C₂²	semidirect
92. #6487	C₂²	semidirect
93. C₂×Dic₇⋊C₄	C₂²	semidirect
94. C₂×Dic₇⋊C₄	C₂²	semidirect
95. #6461	C₂²	semidirect
96. #6461	C₂²	semidirect
97. #6461	C₂²	semidirect
98. #6461	C₂²	semidirect
99. #6460	C₂²	semidirect
100. #6460	C₂²	semidirect
101. #6459	C₂²	semidirect
102. #6459	C₂²	semidirect
103. #6459	C₂²	semidirect
104. #6459	C₂²	semidirect
105. #6459	C₂²	semidirect
106. #6459	C₂²	semidirect
111. #6457	C₂²	semidirect
112. #6457	C₂²	semidirect
113. #6457	C₂²	semidirect
114. #6457	C₂²	semidirect
115. #6457	C₂²	semidirect
116. #6457	C₂²	semidirect
117. #6457	C₂²	semidirect
118. #6457	C₂²	semidirect
119. #6457	C₂²	semidirect
121. #6456	C₂²	semidirect
122. #6456	C₂²	semidirect
123. #6455	C₂²	semidirect
124. #6455	C₂²	semidirect
125. D₇×C₄⋊C₄	C₂²	semidirect
126. D₇×C₄⋊C₄	C₂²	semidirect
127. D₇×C₄⋊C₄	C₂²	semidirect
128. #6452	C₂²	semidirect
129. #6452	C₂²	semidirect
130. #6452	C₂²	semidirect
131. #6452	C₂²	semidirect
132. #6451	C₂²	semidirect
133. #6450	C₂²	semidirect
134. #6450	C₂²	semidirect
135. #6449	C₂²	semidirect
136. #6449	C₂²	semidirect
137. #6448	C₂²	semidirect
138. #6448	C₂²	semidirect
139. #6448	C₂²	semidirect
140. #6448	C₂²	semidirect
141. #6448	C₂²	semidirect
142. #6448	C₂²	semidirect
146. #6447	C₂²	semidirect
147. #6447	C₂²	semidirect
148. #6447	C₂²	semidirect
149. #6446	C₂²	semidirect
150. #6446	C₂²	semidirect
151. #6446	C₂²	semidirect
152. #6446	C₂²	semidirect
156. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
157. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
159. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
160. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
161. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
162. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
163. D₇×C₂²⋊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. #6442	C₂²	semidirect
170. #6442	C₂²	semidirect
171. #6441	C₂²	semidirect
172. #6441	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6439	C₂²	semidirect
177. #6438	C₂²	semidirect
178. C₄×D₂₈	C₂²	semidirect
179. C₄×D₂₈	C₂²	semidirect
180. C₄×D₂₈	C₂²	semidirect
181. #6435	C₂²	semidirect
182. #6435	C₂²	semidirect
183. #6435	C₂²	semidirect
184. #6435	C₂²	semidirect
185. C₄²×D₇	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
356. #553	D₇	semidirect
438. C₂²⋊D₇	#41	semidirect
500. #126	C₂×D₇	semidirect
501. #126	C₂×D₇	semidirect
506. #125	C₂×D₇	semidirect
538. #123	C₂×D₇	semidirect
539. #123	C₂×D₇	semidirect
567. #121	C₂×D₇	semidirect
568. #121	C₂×D₇	semidirect
569. #121	C₂×D₇	semidirect
606. C₄×D₄	C₂×D₇	semidirect
607. C₄×D₄	C₂×D₇	semidirect
608. C₄×D₄	C₂×D₇	semidirect
609. C₄×D₄	C₂×D₇	semidirect
618. #117	C₂×D₇	semidirect
624. C₂×C₄⋊C₄	C₂×D₇	semidirect
964. C₇	#3513	semidirect

Maximal subgroups

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

subgroup	index
C₇×#553	2
#90401	2
#90400	2
#90397	2
#90396	2
#90384	2
#90383	2
#90355	2
#90348	2
#90346	2
D₇×#123	2
#90308	2
#90306	2
#90301	2
#90300	2
#90297	2
#90293	2
#90247	2
#90241	2
#90238	2
#90237	2
#90236	2
C₄×D₄×D₇	2
#90231	2
#90219	2
#90218	2
#90202	2
C₂×#6457	2
#3513	7