Subgroups — #11743866

Order 896.

1124 conjugacy classes of subgroups.

The subgroup lattice has 996 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	#90401	C₂	1	1	yes	maximal, characteristic, complemented
3	#90399	C₂	1	1	yes	maximal, characteristic, complemented
4	#90398	C₂	1	1	yes	maximal, characteristic, complemented
5	#90393	C₂	1	1	yes	maximal, characteristic, complemented
6	#90368	C₂	1	1	yes	maximal, characteristic, complemented
7	#90360	C₂	1	1	yes	maximal, characteristic, complemented
8	#90356	C₂	1	1	yes	maximal, characteristic, complemented
9	#90351	C₂	1	1	yes	maximal, characteristic, complemented
10	#90349	C₂	1	1	yes	maximal, characteristic, complemented
11	#90346	C₂	1	1	yes	maximal, characteristic, complemented
12	#90346	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	#90327	C₂	1	1	yes	maximal, characteristic, complemented
16	#90323	C₂	1	1	yes	maximal, characteristic, complemented
17	D₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	#90282	C₂	1	1	yes	maximal, characteristic, complemented
19	#90277	C₂	1	1	yes	maximal, characteristic, complemented
20	#90243	C₂	1	1	yes	maximal, characteristic, complemented
21	#90238	C₂	1	1	yes	maximal, characteristic, complemented
22	#90237	C₂	1	1	yes	maximal, characteristic, complemented
23	#90230	C₂	1	1	yes	maximal, characteristic, complemented
24	#90222	C₂	1	1	yes	maximal, characteristic, complemented
25	#90218	C₂	1	1	yes	maximal, characteristic, complemented
26	#90214	C₂	1	1	yes	maximal, characteristic, complemented
27	#90208	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	C₂×(C₂²⋊D₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#6441	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×C₂²⋊D₇	C₂²	1	1	yes	characteristic
33	C₂³×Dic₇	C₂²	1	1	yes	characteristic
34	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#1159	C₂²	1	1	yes	characteristic
36	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
37	C₂×#1157	C₂²	1	1	yes	characteristic
38	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
40	C₂²×Dic₁₄	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×#124	C₂²	1	1	yes	characteristic, complemented
44	C₇×#123	C₂²	1	1	yes	characteristic
45	C₇×#123	C₂²	1	1	yes	characteristic, complemented
46	C₇×#123	C₂²	1	1	yes	characteristic, complemented
47	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₇×#120	C₂²	1	1	yes	characteristic
50	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
52	C₇×#117	C₂²	1	1	yes	characteristic
53	C₇×#117	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	#6516	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
58	#6509	C₂²	1	1	yes	characteristic, complemented
59	#6509	C₂²	1	1	yes	characteristic, complemented
60	#6507	C₂²	1	1	yes	characteristic, complemented
61	#6502	C₂²	1	1	yes	characteristic
62	#6502	C₂²	1	1	yes	characteristic
63	#6502	C₂²	1	1	yes	characteristic
64	#6502	C₂²	1	1	yes	characteristic, complemented
65	#6501	C₂²	1	1	yes	characteristic
66	#6500	C₂²	1	1	yes	characteristic
67	#6498	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₇	C₂²	1	1	yes	characteristic
69	D₄×Dic₇	C₂²	1	1	yes	characteristic
70	D₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
71	#6493	C₂²	1	1	yes	characteristic
72	#6492	C₂²	1	1	yes	characteristic
73	#6492	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, complemented
77	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
78	#6489	C₂²	1	1	yes	characteristic
79	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
80	#6487	C₂²	1	1	yes	characteristic
81	#6487	C₂²	1	1	yes	characteristic, complemented
82	C₂×Dic₇⋊C₄	C₂²	1	1	yes	characteristic
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
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	#6460	C₂²	1	1	yes	characteristic, complemented
92	#6460	C₂²	1	1	yes	characteristic, complemented
93	#6459	C₂²	1	1	yes	characteristic, complemented
94	#6459	C₂²	1	1	yes	characteristic, complemented
95	#6459	C₂²	1	1	yes	characteristic, complemented
96	#6459	C₂²	1	1	yes	characteristic, complemented
97	#6459	C₂²	1	1	yes	characteristic, complemented
98	#6459	C₂²	1	1	yes	characteristic, complemented
99	#6457	C₂²	1	1	yes	characteristic, complemented
100	#6457	C₂²	1	1	yes	characteristic, complemented
101	#6457	C₂²	1	1	yes	characteristic, complemented
102	#6455	C₂²	1	1	yes	characteristic, complemented
103	#6455	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	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	#6453	C₂²	1	1	yes	characteristic, complemented
109	#6453	C₂²	1	1	yes	characteristic, complemented
110	#6453	C₂²	1	1	yes	characteristic, complemented
111	#6452	C₂²	1	1	yes	characteristic, complemented
112	#6452	C₂²	1	1	yes	characteristic, complemented
113	#6452	C₂²	1	1	yes	characteristic, complemented
114	#6451	C₂²	1	1	yes	characteristic, complemented
115	#6451	C₂²	1	1	yes	characteristic, complemented
116	#6451	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	#6449	C₂²	1	1	yes	characteristic, complemented
122	#6449	C₂²	1	1	yes	characteristic, complemented
123	#6448	C₂²	1	1	yes	characteristic
124	#6448	C₂²	1	1	yes	characteristic
125	#6448	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	#6446	C₂²	1	1	yes	characteristic
132	#6446	C₂²	1	1	yes	characteristic
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
144	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
145	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
147	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
148	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
150	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
151	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
152	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
153	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
154	#6442	C₂²	1	1	yes	characteristic, complemented
155	#6442	C₂²	1	1	yes	characteristic, complemented
156	#6442	C₂²	1	1	yes	characteristic, complemented
157	#6441	C₂²	1	1	yes	characteristic
158	#6441	C₂²	1	1	yes	characteristic
159	#6441	C₂²	1	1	yes	characteristic
160	#6441	C₂²	1	1	yes	characteristic
161	#6441	C₂²	1	1	yes	characteristic
162	#6441	C₂²	1	1	yes	characteristic
163	#6441	C₂²	1	1	yes	characteristic
164	#6441	C₂²	1	1	yes	characteristic, complemented
165	#6441	C₂²	1	1	yes	characteristic, complemented
166	#6441	C₂²	1	1	yes	characteristic, complemented
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	#6441	C₂²	1	1	yes	characteristic, complemented
171	#6441	C₂²	1	1	yes	characteristic, complemented
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	#6438	C₂²	1	1	yes	characteristic, complemented
177	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
179	#6435	C₂²	1	1	yes	characteristic, complemented
180	#6435	C₂²	1	1	yes	characteristic, complemented
181	#6433	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₁₄	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	#3520	—	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	—	4	2	no	—
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	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	Q₈×D₇	—	4	2	no	—
223	#1159	—	2	4	no	—
224	#1159	—	4	2	no	—
225	#1157	—	2	4	no	—
226	#1157	—	4	2	no	—
227	C₂×D₂₈	C₂³	1	1	yes	characteristic
228	C₂×D₂₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₇	—	4	2	no	—
230	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₄	—	4	2	no	—
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
244	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
245	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
247	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₇×C₄⋊C₄	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
259	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
260	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
261	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
262	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
263	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
264	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
265	C₇×C₂²⋊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	C₄²×C₇	C₂³	1	1	yes	characteristic
273	C₄²×C₇	C₂³	1	1	yes	characteristic
274	C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₇	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	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
307	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
315	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
331	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
332	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
333	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
334	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
335	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
336	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
337	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
338	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
339	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
340	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
341	C₄×Dic₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	C₄×Dic₇	C₂³	1	1	yes	characteristic
350	C₄×Dic₇	C₂³	1	1	yes	characteristic
351	C₄×Dic₇	C₂³	1	1	yes	characteristic
352	#556	—	7	1	no	—
353	#554	—	7	1	no	—
354	#554	—	7	1	no	—
355	#552	—	7	1	no	—
356	#552	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	D₇	1	1	yes	characteristic, complemented
361	D₄×Q₈	—	7	1	no	—
362	#548	—	7	1	no	—
363	#548	—	7	1	no	—
364	#547	—	7	1	no	—
365	#547	—	7	1	no	—
366	#546	—	7	1	no	—
367	#546	—	7	1	no	—
368	#542	—	7	1	no	—
369	#542	—	7	1	no	—
370	#539	—	7	1	no	—
371	#539	—	7	1	no	—
372	#539	—	7	1	no	—
373	#539	—	7	1	no	—
374	#533	—	7	1	no	—
375	#529	—	7	1	no	—
376	#525	—	7	1	no	—
377	#525	—	7	1	no	—
378	C₂×C₂²⋊Q₈	—	7	1	no	—
379	C₂×C₂²⋊Q₈	—	7	1	no	—
380	#520	—	7	1	no	—
381	#520	—	7	1	no	—
382	C₂×C₄×D₄	—	7	1	no	—
383	C₂³×C₇	—	2	2	no	—
384	C₂³×C₇	—	2	2	no	—
385	C₂³×C₇	—	4	1	no	—
386	C₂³×C₇	C₂⁴	1	1	yes	characteristic
387	C₂³×C₇	C₂⁴	1	1	yes	characteristic
388	C₂³×C₇	C₂⁴	1	1	yes	characteristic
389	C₂³×C₇	C₂⁴	1	1	yes	characteristic
390	C₂²×D₇	—	2	2	no	—
391	C₂²×D₇	—	2	2	no	—
392	C₂²×D₇	—	4	1	no	—
393	C₂²×D₇	C₂⁴	1	1	yes	characteristic
394	C₂²×D₇	C₂⁴	1	1	yes	characteristic
395	C₂²×D₇	C₂⁴	1	1	yes	characteristic
396	C₇×Q₈	—	4	1	no	—
397	C₇×D₄	—	2	2	no	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	4	1	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	4	1	no	—
403	C₂×C₄×C₇	—	4	1	no	—
404	C₂×C₄×C₇	—	4	1	no	—
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	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
413	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
416	C₂²⋊D₇	—	2	2	no	—
417	C₂²⋊D₇	—	2	2	no	—
418	C₂²⋊D₇	—	2	2	no	—
419	C₂²⋊D₇	—	2	2	no	—
420	C₂²⋊D₇	—	2	2	no	—
421	C₂²⋊D₇	—	2	2	no	—
422	C₂²⋊D₇	—	2	2	no	—
423	C₂²⋊D₇	—	4	1	no	—
424	C₂²⋊D₇	—	4	1	no	—
425	C₂²⋊D₇	#41	1	4	yes	complemented
426	C₂×Dic₇	—	2	2	no	—
427	C₂×Dic₇	—	2	2	no	—
428	C₂×Dic₇	—	2	2	no	—
429	C₂×Dic₇	—	2	2	no	—
430	C₂×Dic₇	—	2	2	no	—
431	C₂×Dic₇	—	2	2	no	—
432	C₂×Dic₇	—	4	1	no	—
433	C₂×Dic₇	—	4	1	no	—
434	C₂×Dic₇	—	4	1	no	—
435	C₂×Dic₇	—	4	1	no	—
436	C₂×Dic₇	—	4	1	no	—
437	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
438	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
439	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
440	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
441	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
442	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
443	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
444	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
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	D₂₈	—	2	2	no	—
451	D₂₈	—	4	1	no	—
452	C₄×D₇	—	2	2	no	—
453	C₄×D₇	—	2	2	no	—
454	C₄×D₇	—	2	2	no	—
455	C₄×D₇	—	2	2	no	—
456	C₄×D₇	—	2	2	no	—
457	C₄×D₇	—	4	1	no	—
458	C₄×D₇	—	4	1	no	—
459	C₄×D₇	—	4	1	no	—
460	C₄×D₇	—	4	1	no	—
461	C₄×D₇	—	4	1	no	—
462	C₄×D₇	—	4	1	no	—
463	Dic₁₄	—	2	2	no	—
464	Dic₁₄	—	2	2	no	—
465	Dic₁₄	—	2	2	no	—
466	Dic₁₄	—	2	2	no	—
467	Dic₁₄	—	2	2	no	—
468	Dic₁₄	—	4	1	no	—
469	Dic₁₄	—	4	1	no	—
470	Dic₁₄	—	4	1	no	—
471	C₂×#41	—	7	1	no	—
472	C₂×#41	—	7	1	no	—
473	C₂×#41	—	7	1	no	—
474	C₂×#41	—	7	1	no	—
475	C₂²×Q₈	—	7	1	no	—
476	C₂²×Q₈	—	7	1	no	—
477	C₂²×D₄	—	7	1	no	—
478	C₂³×C₄	—	7	1	no	—
479	C₂³×C₄	—	7	1	no	—
480	C₄⋊Q₈	—	7	1	no	—
481	C₄⋊Q₈	—	7	1	no	—
482	C₄⋊Q₈	—	7	1	no	—
483	C₄⋊Q₈	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#126	—	7	1	no	—
489	#126	—	7	1	no	—
490	#126	—	7	1	no	—
491	#126	—	7	1	no	—
492	#126	C₂×D₇	1	1	yes	characteristic, complemented
493	#126	C₂×D₇	1	1	yes	characteristic, complemented
494	#125	—	7	1	no	—
495	#125	—	7	1	no	—
496	#125	—	7	1	no	—
497	#125	—	7	1	no	—
498	#125	—	7	1	no	—
499	#125	—	7	1	no	—
500	#125	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	7	1	no	—
506	#124	—	7	1	no	—
507	#124	C₂×D₇	1	1	yes	characteristic, complemented
508	#123	—	7	1	no	—
509	#123	—	7	1	no	—
510	#123	—	7	1	no	—
511	#123	—	7	1	no	—
512	#123	—	7	1	no	—
513	#123	—	7	1	no	—
514	#123	—	7	1	no	—
515	#123	—	7	1	no	—
516	#123	—	7	1	no	—
517	#123	—	7	1	no	—
518	#123	—	7	1	no	—
519	#123	—	7	1	no	—
520	#123	—	7	1	no	—
521	#123	—	7	1	no	—
522	#123	—	7	1	no	—
523	#123	C₂×D₇	1	1	yes	characteristic
524	#123	C₂×D₇	1	1	yes	characteristic, complemented
525	#123	C₂×D₇	1	1	yes	characteristic, complemented
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	—	7	1	no	—
532	C₂²⋊Q₈	—	7	1	no	—
533	C₂²⋊Q₈	—	7	1	no	—
534	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	—	7	1	no	—
539	C₂²⋊Q₈	—	7	1	no	—
540	C₂²⋊Q₈	—	7	1	no	—
541	C₂²⋊Q₈	—	7	1	no	—
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
554	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
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	#120	—	7	1	no	—
565	#120	—	7	1	no	—
566	#120	—	7	1	no	—
567	#120	C₂×D₇	1	1	yes	characteristic
568	C₄×Q₈	—	7	1	no	—
569	C₄×Q₈	—	7	1	no	—
570	C₄×Q₈	—	7	1	no	—
571	C₄×Q₈	—	7	1	no	—
572	C₄×Q₈	—	7	1	no	—
573	C₄×Q₈	—	7	1	no	—
574	C₄×Q₈	—	7	1	no	—
575	C₄×D₄	—	7	1	no	—
576	C₄×D₄	—	7	1	no	—
577	C₄×D₄	—	7	1	no	—
578	C₄×D₄	—	7	1	no	—
579	C₄×D₄	—	7	1	no	—
580	C₄×D₄	—	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	C₂×D₇	1	1	yes	characteristic
599	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
600	#117	—	7	1	no	—
601	#117	—	7	1	no	—
602	#117	—	7	1	no	—
603	#117	—	7	1	no	—
604	#117	—	7	1	no	—
605	#117	—	7	1	no	—
606	#117	—	7	1	no	—
607	#117	—	7	1	no	—
608	#117	C₂×D₇	1	1	yes	characteristic
609	#117	C₂×D₇	1	1	yes	characteristic, complemented
610	C₂×C₄⋊C₄	—	7	1	no	—
611	C₂×C₄⋊C₄	—	7	1	no	—
612	C₂×C₄⋊C₄	—	7	1	no	—
613	C₂×C₄⋊C₄	—	7	1	no	—
614	C₂×C₄⋊C₄	—	7	1	no	—
615	C₂×C₄⋊C₄	—	7	1	no	—
616	C₂×C₄⋊C₄	—	7	1	no	—
617	C₂×C₄⋊C₄	—	7	1	no	—
618	C₂×C₄⋊C₄	—	7	1	no	—
619	C₂×C₂²⋊C₄	—	7	1	no	—
620	C₂×C₂²⋊C₄	—	7	1	no	—
621	C₂×C₂²⋊C₄	—	7	1	no	—
622	C₂×C₂²⋊C₄	—	7	1	no	—
623	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
625	C₂×C₄²	—	7	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	1	no	—
628	C₂²×C₇	—	2	1	no	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	1	no	—
631	C₂²×C₇	—	2	1	no	—
632	C₂²×C₇	—	2	1	no	—
633	C₂²×C₇	—	2	1	no	—
634	C₂²×C₇	—	2	1	no	—
635	C₂²×C₇	—	2	1	no	—
636	C₂²×C₇	—	4	4	no	—
637	C₂²×C₇	C₂×#41	1	2	yes	—
638	C₂²×C₇	2₋¹⁺⁴	1	2	yes	—
639	C₂²×C₇	C₂⁵	1	1	yes	characteristic
640	C₂×D₇	—	2	1	no	—
641	C₂×D₇	—	2	1	no	—
642	C₂×D₇	—	2	1	no	—
643	C₂×D₇	—	2	1	no	—
644	C₂×D₇	—	2	1	no	—
645	C₂×D₇	—	2	1	no	—
646	C₂×D₇	—	2	1	no	—
647	C₂×D₇	—	2	1	no	—
648	C₂×D₇	—	4	4	no	—
649	C₂×D₇	C₂×#41	1	2	yes	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	1	no	—
652	C₄×C₇	—	2	1	no	—
653	C₄×C₇	—	2	1	no	—
654	C₄×C₇	—	2	1	no	—
655	C₄×C₇	—	2	1	no	—
656	C₄×C₇	—	2	1	no	—
657	C₄×C₇	—	2	1	no	—
658	C₄×C₇	—	2	1	no	—
659	C₄×C₇	—	2	1	no	—
660	C₄×C₇	—	2	1	no	—
661	Dic₇	—	2	1	no	—
662	Dic₇	—	2	1	no	—
663	Dic₇	—	2	1	no	—
664	Dic₇	—	2	1	no	—
665	Dic₇	—	2	1	no	—
666	Dic₇	—	2	1	no	—
667	Dic₇	—	2	1	no	—
668	Dic₇	—	2	1	no	—
669	Dic₇	—	2	1	no	—
670	Dic₇	—	2	1	no	—
671	Dic₇	—	2	1	no	—
672	Dic₇	C₂×#41	1	2	yes	—
673	Dic₇	H(5,𝔽₂)	1	2	yes	—
674	C₂⁴	—	7	1	no	—
675	C₂⁴	C₂²×D₇	1	1	yes	characteristic
676	#41	—	14	4	no	—
677	#41	—	14	4	no	—
678	#41	—	28	2	no	—
679	#41	—	28	2	no	—
680	C₂×Q₈	—	7	1	no	—
681	C₂×Q₈	—	7	1	no	—
682	C₂×Q₈	—	7	1	no	—
683	C₂×Q₈	—	7	1	no	—
684	C₂×Q₈	—	7	1	no	—
685	C₂×Q₈	—	7	1	no	—
686	C₂×Q₈	—	7	1	no	—
687	C₂×Q₈	—	7	1	no	—
688	C₂×Q₈	—	28	2	no	—
689	C₂×Q₈	—	28	2	no	—
690	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
691	C₂×D₄	—	7	1	no	—
692	C₂×D₄	—	7	1	no	—
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	7	1	no	—
695	C₂×D₄	—	7	1	no	—
696	C₂×D₄	—	7	1	no	—
697	C₂×D₄	—	7	1	no	—
698	C₂×D₄	—	7	1	no	—
699	C₂×D₄	—	7	1	no	—
700	C₂×D₄	—	7	1	no	—
701	C₂×D₄	—	7	1	no	—
702	C₂×D₄	—	7	1	no	—
703	C₂×D₄	—	14	4	no	—
704	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
705	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
706	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
707	C₂²×C₄	—	7	1	no	—
708	C₂²×C₄	—	7	1	no	—
709	C₂²×C₄	—	7	1	no	—
710	C₂²×C₄	—	7	1	no	—
711	C₂²×C₄	—	7	1	no	—
712	C₂²×C₄	—	7	1	no	—
713	C₂²×C₄	—	7	1	no	—
714	C₂²×C₄	—	7	1	no	—
715	C₂²×C₄	—	7	1	no	—
716	C₂²×C₄	—	7	1	no	—
717	C₂²×C₄	—	7	1	no	—
718	C₂²×C₄	—	7	1	no	—
719	C₂²×C₄	—	7	1	no	—
720	C₂²×C₄	—	7	1	no	—
721	C₂²×C₄	—	7	1	no	—
722	C₂²×C₄	—	7	1	no	—
723	C₂²×C₄	—	7	1	no	—
724	C₂²×C₄	—	7	1	no	—
725	C₂²×C₄	—	7	1	no	—
726	C₂²×C₄	—	7	1	no	—
727	C₂²×C₄	—	7	1	no	—
728	C₂²×C₄	—	7	1	no	—
729	C₂²×C₄	—	28	2	no	—
730	C₂²×C₄	—	28	2	no	—
731	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
733	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
734	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
735	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	—	7	1	no	—
739	C₄⋊C₄	—	7	1	no	—
740	C₄⋊C₄	—	7	1	no	—
741	C₄⋊C₄	—	7	1	no	—
742	C₄⋊C₄	—	7	1	no	—
743	C₄⋊C₄	—	7	1	no	—
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	—	7	1	no	—
757	C₄⋊C₄	—	7	1	no	—
758	C₄⋊C₄	—	7	1	no	—
759	C₄⋊C₄	—	7	1	no	—
760	C₄⋊C₄	—	7	1	no	—
761	C₄⋊C₄	—	7	1	no	—
762	C₄⋊C₄	—	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	C₂²×D₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
782	C₂²⋊C₄	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	—	7	1	no	—
801	C₂²⋊C₄	—	7	1	no	—
802	C₂²⋊C₄	—	7	1	no	—
803	C₂²⋊C₄	—	7	1	no	—
804	C₂²⋊C₄	—	7	1	no	—
805	C₂²⋊C₄	—	7	1	no	—
806	C₂²⋊C₄	—	7	1	no	—
807	C₂²⋊C₄	—	7	1	no	—
808	C₂²⋊C₄	—	7	1	no	—
809	C₂²⋊C₄	—	7	1	no	—
810	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
811	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
812	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
824	C₄²	—	7	1	no	—
825	C₄²	—	7	1	no	—
826	C₄²	—	7	1	no	—
827	C₄²	—	7	1	no	—
828	C₄²	—	7	1	no	—
829	C₄²	—	7	1	no	—
830	C₄²	—	7	1	no	—
831	C₄²	—	7	1	no	—
832	C₄²	—	7	1	no	—
833	C₄²	—	7	1	no	—
834	C₄²	—	7	1	no	—
835	C₄²	C₂²×D₇	1	1	yes	characteristic
836	C₄²	C₂²×D₇	1	1	yes	characteristic
837	C₄²	C₂²×D₇	1	1	yes	characteristic
838	C₂×C₇	—	2	2	no	—
839	C₂×C₇	—	2	2	no	—
840	C₂×C₇	—	4	1	no	—
841	C₂×C₇	—	4	1	no	—
842	C₂×C₇	C₂²×#41	1	1	yes	characteristic
843	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
845	D₇	—	2	2	no	—
846	D₇	—	4	1	no	—
847	D₇	—	4	1	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	4	1	no	—
851	C₂³	—	7	1	no	—
852	C₂³	—	7	1	no	—
853	C₂³	—	7	1	no	—
854	C₂³	—	14	2	no	—
855	C₂³	—	14	2	no	—
856	C₂³	—	28	1	no	—
857	C₂³	C₂³×D₇	1	1	yes	characteristic
858	C₂³	C₂³×D₇	1	1	yes	characteristic
859	C₂³	C₂³×D₇	1	1	yes	characteristic
860	C₂³	C₂³×D₇	1	1	yes	characteristic
861	Q₈	—	4	1	no	—
862	Q₈	—	14	2	no	—
863	Q₈	—	14	2	no	—
864	Q₈	—	14	2	no	—
865	Q₈	—	14	2	no	—
866	Q₈	—	14	2	no	—
867	Q₈	—	28	1	no	—
868	Q₈	—	28	1	no	—
869	Q₈	—	28	1	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	1	no	—
873	D₄	—	7	4	no	—
874	D₄	—	14	2	no	—
875	D₄	—	14	2	no	—
876	D₄	—	14	2	no	—
877	D₄	—	14	2	no	—
878	D₄	—	14	2	no	—
879	D₄	—	14	2	no	—
880	D₄	—	14	2	no	—
881	D₄	—	14	2	no	—
882	D₄	—	28	1	no	—
883	D₄	—	28	1	no	—
884	D₄	—	28	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	7	1	no	—
891	C₂×C₄	—	7	1	no	—
892	C₂×C₄	—	7	1	no	—
893	C₂×C₄	—	7	1	no	—
894	C₂×C₄	—	7	1	no	—
895	C₂×C₄	—	7	1	no	—
896	C₂×C₄	—	7	1	no	—
897	C₂×C₄	—	7	1	no	—
898	C₂×C₄	—	7	1	no	—
899	C₂×C₄	—	7	1	no	—
900	C₂×C₄	—	7	1	no	—
901	C₂×C₄	—	7	1	no	—
902	C₂×C₄	—	7	1	no	—
903	C₂×C₄	—	14	2	no	—
904	C₂×C₄	—	14	2	no	—
905	C₂×C₄	—	14	2	no	—
906	C₂×C₄	—	14	2	no	—
907	C₂×C₄	—	14	2	no	—
908	C₂×C₄	—	14	2	no	—
909	C₂×C₄	—	14	2	no	—
910	C₂×C₄	—	14	2	no	—
911	C₂×C₄	—	14	2	no	—
912	C₂×C₄	—	14	2	no	—
913	C₂×C₄	—	14	2	no	—
914	C₂×C₄	—	28	1	no	—
915	C₂×C₄	—	28	1	no	—
916	C₂×C₄	—	28	1	no	—
917	C₂×C₄	—	28	1	no	—
918	C₂×C₄	—	28	1	no	—
919	C₂×C₄	—	28	1	no	—
920	C₂×C₄	—	28	1	no	—
921	C₂×C₄	—	28	1	no	—
922	C₂×C₄	—	28	1	no	—
923	C₂×C₄	—	28	1	no	—
924	C₂×C₄	—	28	1	no	—
925	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
926	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
927	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
928	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
929	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
930	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
931	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
932	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
933	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
934	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
935	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
936	C₇	#3520	1	1	yes	characteristic, complemented, Sylow
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	7	2	no	—
949	C₂²	—	14	1	no	—
950	C₂²	—	14	1	no	—
951	C₂²	—	14	1	no	—
952	C₂²	—	14	1	no	—
953	C₂²	—	14	1	no	—
954	C₂²	—	14	1	no	—
955	C₂²	—	14	1	no	—
956	C₂²	—	14	1	no	—
957	C₂²	—	28	4	no	—
958	C₂²	D₇×#41	1	2	yes	—
959	C₂²	#6554	1	2	yes	—
960	C₂²	C₂⁴×D₇	1	1	yes	characteristic
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	7	2	no	—
973	C₄	—	7	2	no	—
974	C₄	—	14	1	no	—
975	C₄	—	14	1	no	—
976	C₄	—	14	1	no	—
977	C₄	—	14	1	no	—
978	C₄	—	14	1	no	—
979	C₄	—	14	1	no	—
980	C₄	—	14	1	no	—
981	C₄	—	14	1	no	—
982	C₄	—	14	1	no	—
983	C₄	—	14	1	no	—
984	C₄	—	14	1	no	—
985	C₂	—	2	2	no	—
986	C₂	—	2	2	no	—
987	C₂	—	4	1	no	—
988	C₂	—	4	1	no	—
989	C₂	—	14	2	no	—
990	C₂	—	28	1	no	—
991	C₂	—	28	1	no	—
992	C₂	C₂×D₇×#41	1	1	yes	characteristic
993	C₂	C₂×#6554	1	1	yes	characteristic
994	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×#551	C₂
hypercenter	#551	D₇
hypocenter	C₇	#3520
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. #90401	C₂	semidirect
3. #90399	C₂	semidirect
4. #90398	C₂	semidirect
5. #90393	C₂	semidirect
6. #90368	C₂	semidirect
7. #90360	C₂	semidirect
8. #90356	C₂	semidirect
9. #90351	C₂	semidirect
10. #90349	C₂	semidirect
11. #90346	C₂	semidirect
12. #90346	C₂	semidirect
13. #90340	C₂	semidirect
14. #90336	C₂	semidirect
15. #90327	C₂	semidirect
16. #90323	C₂	semidirect
17. D₇×C₂²⋊Q₈	C₂	semidirect
18. #90282	C₂	semidirect
19. #90277	C₂	semidirect
20. #90243	C₂	semidirect
21. #90238	C₂	semidirect
22. #90237	C₂	semidirect
23. #90230	C₂	semidirect
24. #90222	C₂	semidirect
25. #90218	C₂	semidirect
26. #90214	C₂	semidirect
27. #90208	C₂	semidirect
28. #90186	C₂	semidirect
29. #90181	C₂	semidirect
30. C₂×(C₂²⋊D₇)⋊C₄	C₂	semidirect
31. C₂×#6441	C₂	semidirect
34. C₂×Q₈×D₇	C₂²	semidirect
36. C₂×#1159	C₂²	semidirect
38. C₂×#1157	C₂²	semidirect
40. C₂²×Dic₁₄	C₂²	semidirect
41. C₇×#126	C₂²	semidirect
42. C₇×#126	C₂²	semidirect
43. C₇×#124	C₂²	semidirect
45. C₇×#123	C₂²	semidirect
46. C₇×#123	C₂²	semidirect
48. C₇×C₂²⋊Q₈	C₂²	semidirect
51. C₄×C₇×D₄	C₂²	semidirect
53. C₇×#117	C₂²	semidirect
58. #6509	C₂²	semidirect
59. #6509	C₂²	semidirect
60. #6507	C₂²	semidirect
64. #6502	C₂²	semidirect
67. #6498	C₂²	semidirect
70. D₄×Dic₇	C₂²	semidirect
76. C₄×C₂²⋊D₇	C₂²	semidirect
79. C₂×C₄⋊Dic₇	C₂²	semidirect
81. #6487	C₂²	semidirect
83. C₂×Dic₇⋊C₄	C₂²	semidirect
84. C₂×Dic₇⋊C₄	C₂²	semidirect
85. C₂×Dic₇⋊C₄	C₂²	semidirect
87. #6461	C₂²	semidirect
88. #6461	C₂²	semidirect
89. #6461	C₂²	semidirect
90. #6461	C₂²	semidirect
91. #6460	C₂²	semidirect
92. #6460	C₂²	semidirect
93. #6459	C₂²	semidirect
94. #6459	C₂²	semidirect
95. #6459	C₂²	semidirect
96. #6459	C₂²	semidirect
97. #6459	C₂²	semidirect
98. #6459	C₂²	semidirect
99. #6457	C₂²	semidirect
100. #6457	C₂²	semidirect
101. #6457	C₂²	semidirect
102. #6455	C₂²	semidirect
103. #6455	C₂²	semidirect
104. D₇×C₄⋊C₄	C₂²	semidirect
105. D₇×C₄⋊C₄	C₂²	semidirect
106. D₇×C₄⋊C₄	C₂²	semidirect
107. D₇×C₄⋊C₄	C₂²	semidirect
108. #6453	C₂²	semidirect
109. #6453	C₂²	semidirect
110. #6453	C₂²	semidirect
111. #6452	C₂²	semidirect
112. #6452	C₂²	semidirect
113. #6452	C₂²	semidirect
114. #6451	C₂²	semidirect
115. #6451	C₂²	semidirect
116. #6451	C₂²	semidirect
117. #6450	C₂²	semidirect
118. #6450	C₂²	semidirect
120. #6449	C₂²	semidirect
121. #6449	C₂²	semidirect
122. #6449	C₂²	semidirect
125. #6448	C₂²	semidirect
126. #6448	C₂²	semidirect
127. #6448	C₂²	semidirect
130. #6447	C₂²	semidirect
133. #6446	C₂²	semidirect
134. #6446	C₂²	semidirect
135. #6446	C₂²	semidirect
148. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
149. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
150. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
151. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
154. #6442	C₂²	semidirect
155. #6442	C₂²	semidirect
156. #6442	C₂²	semidirect
164. #6441	C₂²	semidirect
165. #6441	C₂²	semidirect
166. #6441	C₂²	semidirect
167. #6441	C₂²	semidirect
168. #6441	C₂²	semidirect
169. #6441	C₂²	semidirect
170. #6441	C₂²	semidirect
171. #6441	C₂²	semidirect
172. #6440	C₂²	semidirect
173. #6440	C₂²	semidirect
174. #6440	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6438	C₂²	semidirect
177. C₄×D₂₈	C₂²	semidirect
178. C₄×D₂₈	C₂²	semidirect
179. #6435	C₂²	semidirect
180. #6435	C₂²	semidirect
181. #6433	C₂²	semidirect
182. C₄×Dic₁₄	C₂²	semidirect
183. C₄×Dic₁₄	C₂²	semidirect
184. C₄×Dic₁₄	C₂²	semidirect
185. C₄×Dic₁₄	C₂²	semidirect
186. C₄×Dic₁₄	C₂²	semidirect
360. #551	D₇	semidirect
425. C₂²⋊D₇	#41	semidirect
492. #126	C₂×D₇	semidirect
493. #126	C₂×D₇	semidirect
507. #124	C₂×D₇	semidirect
524. #123	C₂×D₇	semidirect
525. #123	C₂×D₇	semidirect
554. C₂²⋊Q₈	C₂×D₇	semidirect
599. C₄×D₄	C₂×D₇	semidirect
609. #117	C₂×D₇	semidirect
936. C₇	#3520	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
#90401	2
#90399	2
#90398	2
#90393	2
#90368	2
#90360	2
#90356	2
#90351	2
#90349	2
#90346	2
#90340	2
#90336	2
#90327	2
#90323	2
D₇×C₂²⋊Q₈	2
#90282	2
#90277	2
#90243	2
#90238	2
#90237	2
#90230	2
#90222	2
#90218	2
#90214	2
#90208	2
#90186	2
#90181	2
C₂×(C₂²⋊D₇)⋊C₄	2
C₂×#6441	2
#3520	7