Subgroups — #11744019

Order 896.

1038 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#90426	C₂	1	1	yes	maximal, characteristic, complemented
3	#90415	C₂	1	1	yes	maximal, characteristic, complemented
4	#90390	C₂	1	1	yes	maximal, characteristic, complemented
5	#90384	C₂	1	1	yes	maximal, characteristic, complemented
6	#90383	C₂	1	1	yes	maximal, characteristic, complemented
7	#90383	C₂	1	1	yes	maximal, characteristic, complemented
8	#90338	C₂	1	1	yes	maximal, characteristic, complemented
9	#90338	C₂	1	1	yes	maximal, characteristic, complemented
10	#90331	C₂	1	1	yes	maximal, characteristic, complemented
11	#90329	C₂	1	1	yes	maximal, characteristic, complemented
12	#90328	C₂	1	1	yes	maximal, characteristic, complemented
13	#90328	C₂	1	1	yes	maximal, characteristic, complemented
14	#90325	C₂	1	1	yes	maximal, characteristic, complemented
15	#90322	C₂	1	1	yes	maximal, characteristic, complemented
16	#90321	C₂	1	1	yes	maximal, characteristic, complemented
17	#90319	C₂	1	1	yes	maximal, characteristic, complemented
18	D₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
19	#90314	C₂	1	1	yes	maximal, characteristic, complemented
20	#90273	C₂	1	1	yes	maximal, characteristic, complemented
21	#90272	C₂	1	1	yes	maximal, characteristic, complemented
22	#90255	C₂	1	1	yes	maximal, characteristic, complemented
23	#90251	C₂	1	1	yes	maximal, characteristic, complemented
24	#90247	C₂	1	1	yes	maximal, characteristic, complemented
25	#90247	C₂	1	1	yes	maximal, characteristic, complemented
26	#90241	C₂	1	1	yes	maximal, characteristic, complemented
27	#90238	C₂	1	1	yes	maximal, characteristic, complemented
28	#90206	C₂	1	1	yes	maximal, characteristic, complemented
29	#90202	C₂	1	1	yes	maximal, characteristic, complemented
30	#90198	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#6457	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#1161	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#1157	C₂²	1	1	yes	characteristic
35	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₂₈	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
38	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₇×#125	C₂²	1	1	yes	characteristic, complemented
40	C₇×#125	C₂²	1	1	yes	characteristic, complemented
41	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
49	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
50	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
51	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	#6510	C₂²	1	1	yes	characteristic
54	#6510	C₂²	1	1	yes	characteristic, complemented
55	#6510	C₂²	1	1	yes	characteristic, complemented
56	#6509	C₂²	1	1	yes	characteristic, complemented
57	#6509	C₂²	1	1	yes	characteristic, complemented
58	#6509	C₂²	1	1	yes	characteristic, complemented
59	#6509	C₂²	1	1	yes	characteristic, complemented
60	#6509	C₂²	1	1	yes	characteristic, complemented
61	#6507	C₂²	1	1	yes	characteristic, complemented
62	#6507	C₂²	1	1	yes	characteristic, complemented
63	#6502	C₂²	1	1	yes	characteristic
64	#6500	C₂²	1	1	yes	characteristic
65	#6500	C₂²	1	1	yes	characteristic
66	#6498	C₂²	1	1	yes	characteristic
67	#6493	C₂²	1	1	yes	characteristic
68	#6493	C₂²	1	1	yes	characteristic, complemented
69	#6492	C₂²	1	1	yes	characteristic, complemented
70	#6492	C₂²	1	1	yes	characteristic, complemented
71	#6492	C₂²	1	1	yes	characteristic, complemented
72	#6492	C₂²	1	1	yes	characteristic, complemented
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, complemented
77	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
79	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
81	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
82	#6487	C₂²	1	1	yes	characteristic
83	#6487	C₂²	1	1	yes	characteristic
84	#6487	C₂²	1	1	yes	characteristic
85	#6487	C₂²	1	1	yes	characteristic, complemented
86	C₂×Dic₇⋊C₄	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	#6461	C₂²	1	1	yes	characteristic, complemented
92	#6461	C₂²	1	1	yes	characteristic, complemented
93	#6461	C₂²	1	1	yes	characteristic, complemented
94	#6460	C₂²	1	1	yes	characteristic, complemented
95	#6460	C₂²	1	1	yes	characteristic, complemented
96	#6460	C₂²	1	1	yes	characteristic, complemented
97	#6460	C₂²	1	1	yes	characteristic, complemented
98	#6459	C₂²	1	1	yes	characteristic, complemented
99	#6459	C₂²	1	1	yes	characteristic, complemented
100	#6459	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	#6459	C₂²	1	1	yes	characteristic, complemented
108	#6459	C₂²	1	1	yes	characteristic, complemented
109	#6459	C₂²	1	1	yes	characteristic, complemented
110	#6458	C₂²	1	1	yes	characteristic
111	#6458	C₂²	1	1	yes	characteristic
112	#6458	C₂²	1	1	yes	characteristic
113	#6457	C₂²	1	1	yes	characteristic
114	#6457	C₂²	1	1	yes	characteristic
115	#6457	C₂²	1	1	yes	characteristic
116	#6457	C₂²	1	1	yes	characteristic
117	#6457	C₂²	1	1	yes	characteristic
118	#6457	C₂²	1	1	yes	characteristic
119	#6457	C₂²	1	1	yes	characteristic
120	#6457	C₂²	1	1	yes	characteristic
121	#6457	C₂²	1	1	yes	characteristic
122	#6457	C₂²	1	1	yes	characteristic
123	#6457	C₂²	1	1	yes	characteristic
124	#6457	C₂²	1	1	yes	characteristic
125	#6457	C₂²	1	1	yes	characteristic, complemented
126	#6457	C₂²	1	1	yes	characteristic, complemented
127	#6457	C₂²	1	1	yes	characteristic, complemented
128	#6457	C₂²	1	1	yes	characteristic, complemented
129	#6457	C₂²	1	1	yes	characteristic, complemented
130	#6457	C₂²	1	1	yes	characteristic, complemented
131	#6456	C₂²	1	1	yes	characteristic
132	#6456	C₂²	1	1	yes	characteristic, complemented
133	#6456	C₂²	1	1	yes	characteristic, complemented
134	#6455	C₂²	1	1	yes	characteristic, complemented
135	#6455	C₂²	1	1	yes	characteristic, complemented
136	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
137	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
138	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
139	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
140	#6452	C₂²	1	1	yes	characteristic, complemented
141	#6452	C₂²	1	1	yes	characteristic, complemented
142	#6452	C₂²	1	1	yes	characteristic, complemented
143	#6452	C₂²	1	1	yes	characteristic, complemented
144	#6452	C₂²	1	1	yes	characteristic, complemented
145	#6452	C₂²	1	1	yes	characteristic, complemented
146	#6452	C₂²	1	1	yes	characteristic, complemented
147	#6451	C₂²	1	1	yes	characteristic, complemented
148	#6451	C₂²	1	1	yes	characteristic, complemented
149	#6451	C₂²	1	1	yes	characteristic, complemented
150	#6450	C₂²	1	1	yes	characteristic, complemented
151	#6449	C₂²	1	1	yes	characteristic
152	#6448	C₂²	1	1	yes	characteristic, complemented
153	#6448	C₂²	1	1	yes	characteristic, complemented
154	#6448	C₂²	1	1	yes	characteristic, complemented
155	#6447	C₂²	1	1	yes	characteristic
156	#6447	C₂²	1	1	yes	characteristic
157	#6447	C₂²	1	1	yes	characteristic, complemented
158	#6447	C₂²	1	1	yes	characteristic, complemented
159	#6446	C₂²	1	1	yes	characteristic, complemented
160	#6446	C₂²	1	1	yes	characteristic, complemented
161	#6446	C₂²	1	1	yes	characteristic, complemented
162	#6446	C₂²	1	1	yes	characteristic, complemented
163	#6445	C₂²	1	1	yes	characteristic
164	#6445	C₂²	1	1	yes	characteristic
165	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
166	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
167	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
168	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
169	#6442	C₂²	1	1	yes	characteristic, complemented
170	#6441	C₂²	1	1	yes	characteristic
171	#6441	C₂²	1	1	yes	characteristic
172	#6441	C₂²	1	1	yes	characteristic
173	#6440	C₂²	1	1	yes	characteristic
174	#6440	C₂²	1	1	yes	characteristic
175	#6439	C₂²	1	1	yes	characteristic, complemented
176	#6439	C₂²	1	1	yes	characteristic, complemented
177	#6439	C₂²	1	1	yes	characteristic, complemented
178	#6439	C₂²	1	1	yes	characteristic, complemented
179	#6438	C₂²	1	1	yes	characteristic
180	#6438	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₂₈	C₂²	1	1	yes	characteristic
182	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
183	#6435	C₂²	1	1	yes	characteristic, complemented
184	#6435	C₂²	1	1	yes	characteristic, complemented
185	#6435	C₂²	1	1	yes	characteristic, complemented
186	#6433	C₂²	1	1	yes	characteristic, complemented
187	#3535	—	7	1	no	maximal, Sylow
188	C₂³×D₇	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×Q₈	C₂³	1	1	yes	characteristic
192	C₂×C₇×Q₈	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	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
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	C₂²×Dic₇	C₂³	1	1	yes	characteristic
207	C₂²×Dic₇	C₂³	1	1	yes	characteristic
208	#1161	—	4	2	no	—
209	Q₈×D₇	—	4	2	no	—
210	#1157	—	4	2	no	—
211	#1157	—	4	2	no	—
212	C₂×D₂₈	—	4	2	no	—
213	C₂×D₂₈	C₂³	1	1	yes	characteristic
214	C₂×D₂₈	C₂³	1	1	yes	characteristic
215	C₂×D₂₈	C₂³	1	1	yes	characteristic
216	C₂×D₂₈	C₂³	1	1	yes	characteristic
217	C₂×D₂₈	C₂³	1	1	yes	characteristic
218	C₂×D₂₈	C₂³	1	1	yes	characteristic
219	C₂×D₂₈	C₂³	1	1	yes	characteristic
220	C₂×D₂₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₇	—	4	2	no	—
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×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×Dic₁₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
242	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
243	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₇×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×C₄⋊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	C₄²×C₇	C₂³	1	1	yes	characteristic
266	C₄²×C₇	C₂³	1	1	yes	characteristic
267	C₄²×C₇	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	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(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	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	C₄⋊Dic₇	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	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
342	C₄×Dic₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₇	C₂³	1	1	yes	characteristic
348	C₄×Dic₇	C₂³	1	1	yes	characteristic
349	#563	—	7	1	no	—
350	#563	—	7	1	no	—
351	#562	—	7	1	no	—
352	#562	—	7	1	no	—
353	#554	—	7	1	no	—
354	#554	D₇	1	1	yes	characteristic, complemented
355	#552	—	7	1	no	—
356	#552	—	7	1	no	—
357	#551	—	7	1	no	—
358	#551	—	7	1	no	—
359	#551	—	7	1	no	—
360	#551	—	7	1	no	—
361	#547	—	7	1	no	—
362	#547	—	7	1	no	—
363	#546	—	7	1	no	—
364	#546	—	7	1	no	—
365	#544	—	7	1	no	—
366	#543	—	7	1	no	—
367	#542	—	7	1	no	—
368	#542	—	7	1	no	—
369	#539	—	7	1	no	—
370	#539	—	7	1	no	—
371	#539	—	7	1	no	—
372	#539	—	7	1	no	—
373	#539	—	7	1	no	—
374	#538	—	7	1	no	—
375	#536	—	7	1	no	—
376	#536	—	7	1	no	—
377	#525	—	7	1	no	—
378	C₂×#123	—	7	1	no	—
379	C₂×C₂²⋊Q₈	—	7	1	no	—
380	C₂³×C₇	C₂⁴	1	1	yes	characteristic
381	C₂³×C₇	C₂⁴	1	1	yes	characteristic
382	C₂²×D₇	—	2	2	no	—
383	C₂²×D₇	—	2	2	no	—
384	C₂²×D₇	—	2	2	no	—
385	C₂²×D₇	—	4	1	no	—
386	C₂²×D₇	—	4	1	no	—
387	C₂²×D₇	—	4	1	no	—
388	C₂²×D₇	C₂⁴	1	1	yes	characteristic
389	C₂²×D₇	C₂⁴	1	1	yes	characteristic
390	C₂²×D₇	C₂⁴	1	1	yes	characteristic
391	C₂²×D₇	C₂⁴	1	1	yes	characteristic
392	C₂²×D₇	C₂⁴	1	1	yes	characteristic
393	C₇×Q₈	—	4	1	no	—
394	C₇×Q₈	—	4	1	no	—
395	C₇×Q₈	—	4	1	no	—
396	C₇×D₄	—	2	2	no	—
397	C₂×C₄×C₇	—	4	1	no	—
398	C₂×C₄×C₇	—	4	1	no	—
399	C₂×C₄×C₇	—	4	1	no	—
400	C₂×C₄×C₇	—	4	1	no	—
401	C₂×C₄×C₇	—	4	1	no	—
402	C₂×C₄×C₇	—	4	1	no	—
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	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	—	4	1	no	—
419	C₂²⋊D₇	—	4	1	no	—
420	C₂²⋊D₇	—	4	1	no	—
421	C₂²⋊D₇	—	4	1	no	—
422	C₂×Dic₇	—	2	2	no	—
423	C₂×Dic₇	—	4	1	no	—
424	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
425	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
426	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
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	D₂₈	—	2	2	no	—
436	D₂₈	—	2	2	no	—
437	D₂₈	—	2	2	no	—
438	D₂₈	—	4	1	no	—
439	D₂₈	—	4	1	no	—
440	D₂₈	—	4	1	no	—
441	D₂₈	—	4	1	no	—
442	D₂₈	—	4	1	no	—
443	C₄×D₇	—	2	2	no	—
444	C₄×D₇	—	2	2	no	—
445	C₄×D₇	—	2	2	no	—
446	C₄×D₇	—	2	2	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	C₄×D₇	—	4	1	no	—
454	C₄×D₇	—	4	1	no	—
455	C₄×D₇	—	4	1	no	—
456	C₄×D₇	—	4	1	no	—
457	C₄×D₇	—	4	1	no	—
458	Dic₁₄	—	4	1	no	—
459	Dic₁₄	—	4	1	no	—
460	Dic₁₄	—	4	1	no	—
461	Dic₁₄	—	4	1	no	—
462	Dic₁₄	—	4	1	no	—
463	Dic₁₄	—	4	1	no	—
464	C₂×#41	—	7	1	no	—
465	C₂×#41	—	7	1	no	—
466	C₂×#41	—	7	1	no	—
467	C₂²×Q₈	—	7	1	no	—
468	C₂²×D₄	—	7	1	no	—
469	C₂³×C₄	—	7	1	no	—
470	C₄⋊Q₈	—	7	1	no	—
471	C₄⋊Q₈	—	7	1	no	—
472	C₄⋊Q₈	—	7	1	no	—
473	C₄⋊Q₈	—	7	1	no	—
474	C₄⋊Q₈	—	7	1	no	—
475	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
476	#126	—	7	1	no	—
477	#126	—	7	1	no	—
478	#126	—	7	1	no	—
479	#126	—	7	1	no	—
480	#126	—	7	1	no	—
481	#126	—	7	1	no	—
482	#126	—	7	1	no	—
483	#126	—	7	1	no	—
484	#126	—	7	1	no	—
485	#126	—	7	1	no	—
486	#126	—	7	1	no	—
487	#126	—	7	1	no	—
488	#125	—	7	1	no	—
489	#125	—	7	1	no	—
490	#125	—	7	1	no	—
491	#125	—	7	1	no	—
492	#125	—	7	1	no	—
493	#125	—	7	1	no	—
494	#125	—	7	1	no	—
495	#125	—	7	1	no	—
496	#125	C₂×D₇	1	1	yes	characteristic, complemented
497	#125	C₂×D₇	1	1	yes	characteristic, complemented
498	#124	—	7	1	no	—
499	#124	—	7	1	no	—
500	#124	—	7	1	no	—
501	#124	—	7	1	no	—
502	#124	—	7	1	no	—
503	#124	—	7	1	no	—
504	#124	—	7	1	no	—
505	#124	—	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	—	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	C₂²⋊Q₈	—	7	1	no	—
535	C₂²⋊Q₈	—	7	1	no	—
536	C₂²⋊Q₈	—	7	1	no	—
537	C₂²⋊Q₈	—	7	1	no	—
538	C₂²⋊Q₈	—	7	1	no	—
539	C₂²⋊Q₈	—	7	1	no	—
540	C₂²⋊Q₈	—	7	1	no	—
541	C₂²⋊Q₈	—	7	1	no	—
542	C₂²⋊Q₈	—	7	1	no	—
543	C₂²⋊Q₈	—	7	1	no	—
544	C₂²⋊Q₈	—	7	1	no	—
545	C₂²⋊Q₈	—	7	1	no	—
546	C₂²⋊Q₈	—	7	1	no	—
547	C₂²⋊Q₈	—	7	1	no	—
548	C₂²⋊Q₈	—	7	1	no	—
549	C₂²⋊Q₈	—	7	1	no	—
550	C₂²⋊Q₈	—	7	1	no	—
551	C₂²⋊Q₈	—	7	1	no	—
552	C₂²⋊Q₈	—	7	1	no	—
553	C₂²⋊Q₈	—	7	1	no	—
554	C₂²⋊Q₈	—	7	1	no	—
555	C₂²⋊Q₈	—	7	1	no	—
556	C₂²⋊Q₈	—	7	1	no	—
557	C₂²⋊Q₈	—	7	1	no	—
558	C₂²⋊Q₈	—	7	1	no	—
559	C₂²⋊Q₈	—	7	1	no	—
560	C₂²⋊Q₈	—	7	1	no	—
561	C₂²⋊Q₈	—	7	1	no	—
562	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
563	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
564	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic
565	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
566	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
567	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
568	#121	—	7	1	no	—
569	#121	—	7	1	no	—
570	#121	—	7	1	no	—
571	#121	—	7	1	no	—
572	#121	—	7	1	no	—
573	#121	—	7	1	no	—
574	#121	—	7	1	no	—
575	#121	—	7	1	no	—
576	#121	—	7	1	no	—
577	#121	—	7	1	no	—
578	#120	—	7	1	no	—
579	#120	—	7	1	no	—
580	#120	—	7	1	no	—
581	#120	—	7	1	no	—
582	C₄×Q₈	—	7	1	no	—
583	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
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	C₂×D₇	1	1	yes	characteristic
596	C₄×D₄	C₂×D₇	1	1	yes	characteristic
597	C₄×D₄	C₂×D₇	1	1	yes	characteristic
598	#117	—	7	1	no	—
599	#117	—	7	1	no	—
600	#117	—	7	1	no	—
601	#117	—	7	1	no	—
602	#117	—	7	1	no	—
603	#117	—	7	1	no	—
604	#117	—	7	1	no	—
605	C₂×C₄⋊C₄	—	7	1	no	—
606	C₂×C₄⋊C₄	—	7	1	no	—
607	C₂×C₄⋊C₄	—	7	1	no	—
608	C₂×C₄⋊C₄	—	7	1	no	—
609	C₂×C₄⋊C₄	—	7	1	no	—
610	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
612	C₂×C₂²⋊C₄	—	7	1	no	—
613	C₂×C₂²⋊C₄	—	7	1	no	—
614	C₂×C₂²⋊C₄	—	7	1	no	—
615	C₂×C₂²⋊C₄	—	7	1	no	—
616	C₂×C₂²⋊C₄	—	7	1	no	—
617	C₂×C₂²⋊C₄	—	7	1	no	—
618	C₂×C₂²⋊C₄	—	7	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	2	1	no	—
621	C₂²×C₇	—	2	1	no	—
622	C₂²×C₇	—	2	1	no	—
623	C₂²×C₇	—	2	1	no	—
624	C₂²×C₇	2₋¹⁺⁴	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	—	2	1	no	—
635	C₂×D₇	—	2	1	no	—
636	C₂×D₇	—	2	1	no	—
637	C₂×D₇	—	2	1	no	—
638	C₂×D₇	—	2	1	no	—
639	C₂×D₇	—	2	1	no	—
640	C₂×D₇	—	4	4	no	—
641	C₂×D₇	—	8	2	no	—
642	C₂×D₇	H(5,𝔽₂)	1	2	yes	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	1	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	1	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	1	no	—
650	C₄×C₇	—	2	1	no	—
651	C₄×C₇	—	2	1	no	—
652	C₄×C₇	—	2	1	no	—
653	C₄×C₇	—	2	1	no	—
654	C₄×C₇	—	2	1	no	—
655	C₄×C₇	—	2	1	no	—
656	Dic₇	—	2	1	no	—
657	Dic₇	—	2	1	no	—
658	Dic₇	—	2	1	no	—
659	Dic₇	—	2	1	no	—
660	Dic₇	—	2	1	no	—
661	Dic₇	—	2	1	no	—
662	Dic₇	—	2	1	no	—
663	Dic₇	—	2	1	no	—
664	Dic₇	—	2	1	no	—
665	Dic₇	—	2	1	no	—
666	Dic₇	—	2	1	no	—
667	C₂⁴	—	7	1	no	—
668	C₂⁴	—	7	1	no	—
669	#41	—	28	2	no	—
670	#41	—	28	2	no	—
671	#41	—	28	2	no	—
672	C₂×Q₈	—	7	1	no	—
673	C₂×Q₈	—	7	1	no	—
674	C₂×Q₈	—	7	1	no	—
675	C₂×Q₈	—	7	1	no	—
676	C₂×Q₈	—	7	1	no	—
677	C₂×Q₈	—	7	1	no	—
678	C₂×Q₈	—	28	2	no	—
679	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
680	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
681	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
682	C₂×D₄	—	7	1	no	—
683	C₂×D₄	—	7	1	no	—
684	C₂×D₄	—	7	1	no	—
685	C₂×D₄	—	7	1	no	—
686	C₂×D₄	—	7	1	no	—
687	C₂×D₄	—	7	1	no	—
688	C₂×D₄	—	7	1	no	—
689	C₂×D₄	—	7	1	no	—
690	C₂×D₄	—	7	1	no	—
691	C₂×D₄	—	7	1	no	—
692	C₂×D₄	—	7	1	no	—
693	C₂×D₄	—	7	1	no	—
694	C₂×D₄	—	7	1	no	—
695	C₂×D₄	—	7	1	no	—
696	C₂×D₄	—	28	2	no	—
697	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
698	C₂²×C₄	—	7	1	no	—
699	C₂²×C₄	—	7	1	no	—
700	C₂²×C₄	—	7	1	no	—
701	C₂²×C₄	—	7	1	no	—
702	C₂²×C₄	—	7	1	no	—
703	C₂²×C₄	—	7	1	no	—
704	C₂²×C₄	—	7	1	no	—
705	C₂²×C₄	—	7	1	no	—
706	C₂²×C₄	—	7	1	no	—
707	C₂²×C₄	—	7	1	no	—
708	C₂²×C₄	—	7	1	no	—
709	C₂²×C₄	—	7	1	no	—
710	C₂²×C₄	—	7	1	no	—
711	C₂²×C₄	—	7	1	no	—
712	C₂²×C₄	—	7	1	no	—
713	C₂²×C₄	—	7	1	no	—
714	C₂²×C₄	—	7	1	no	—
715	C₂²×C₄	—	28	2	no	—
716	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
720	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
721	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
722	C₄⋊C₄	—	7	1	no	—
723	C₄⋊C₄	—	7	1	no	—
724	C₄⋊C₄	—	7	1	no	—
725	C₄⋊C₄	—	7	1	no	—
726	C₄⋊C₄	—	7	1	no	—
727	C₄⋊C₄	—	7	1	no	—
728	C₄⋊C₄	—	7	1	no	—
729	C₄⋊C₄	—	7	1	no	—
730	C₄⋊C₄	—	7	1	no	—
731	C₄⋊C₄	—	7	1	no	—
732	C₄⋊C₄	—	7	1	no	—
733	C₄⋊C₄	—	7	1	no	—
734	C₄⋊C₄	—	7	1	no	—
735	C₄⋊C₄	—	7	1	no	—
736	C₄⋊C₄	—	7	1	no	—
737	C₄⋊C₄	—	7	1	no	—
738	C₄⋊C₄	—	7	1	no	—
739	C₄⋊C₄	—	7	1	no	—
740	C₄⋊C₄	—	7	1	no	—
741	C₄⋊C₄	—	7	1	no	—
742	C₄⋊C₄	—	7	1	no	—
743	C₄⋊C₄	—	7	1	no	—
744	C₄⋊C₄	—	7	1	no	—
745	C₄⋊C₄	—	7	1	no	—
746	C₄⋊C₄	—	7	1	no	—
747	C₄⋊C₄	—	7	1	no	—
748	C₄⋊C₄	—	7	1	no	—
749	C₄⋊C₄	—	7	1	no	—
750	C₄⋊C₄	—	7	1	no	—
751	C₄⋊C₄	—	7	1	no	—
752	C₄⋊C₄	—	7	1	no	—
753	C₄⋊C₄	—	7	1	no	—
754	C₄⋊C₄	—	7	1	no	—
755	C₄⋊C₄	—	7	1	no	—
756	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
765	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
772	C₂²⋊C₄	—	7	1	no	—
773	C₂²⋊C₄	—	7	1	no	—
774	C₂²⋊C₄	—	7	1	no	—
775	C₂²⋊C₄	—	7	1	no	—
776	C₂²⋊C₄	—	7	1	no	—
777	C₂²⋊C₄	—	7	1	no	—
778	C₂²⋊C₄	—	7	1	no	—
779	C₂²⋊C₄	—	7	1	no	—
780	C₂²⋊C₄	—	7	1	no	—
781	C₂²⋊C₄	—	7	1	no	—
782	C₂²⋊C₄	—	7	1	no	—
783	C₂²⋊C₄	—	7	1	no	—
784	C₂²⋊C₄	—	7	1	no	—
785	C₂²⋊C₄	—	7	1	no	—
786	C₂²⋊C₄	—	7	1	no	—
787	C₂²⋊C₄	—	7	1	no	—
788	C₂²⋊C₄	—	7	1	no	—
789	C₂²⋊C₄	—	7	1	no	—
790	C₂²⋊C₄	—	7	1	no	—
791	C₂²⋊C₄	—	7	1	no	—
792	C₂²⋊C₄	—	7	1	no	—
793	C₂²⋊C₄	—	7	1	no	—
794	C₂²⋊C₄	—	7	1	no	—
795	C₂²⋊C₄	—	7	1	no	—
796	C₂²⋊C₄	—	7	1	no	—
797	C₂²⋊C₄	—	7	1	no	—
798	C₂²⋊C₄	—	7	1	no	—
799	C₂²⋊C₄	—	7	1	no	—
800	C₂²⋊C₄	—	7	1	no	—
801	C₂²⋊C₄	—	7	1	no	—
802	C₂²⋊C₄	—	7	1	no	—
803	C₂²⋊C₄	—	7	1	no	—
804	C₂²⋊C₄	—	7	1	no	—
805	C₂²⋊C₄	—	7	1	no	—
806	C₂²⋊C₄	—	7	1	no	—
807	C₂²⋊C₄	—	7	1	no	—
808	C₂²⋊C₄	—	7	1	no	—
809	C₂²⋊C₄	—	7	1	no	—
810	C₂²⋊C₄	—	7	1	no	—
811	C₂²⋊C₄	—	7	1	no	—
812	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
813	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
814	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
815	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
818	C₄²	—	7	1	no	—
819	C₄²	—	7	1	no	—
820	C₄²	—	7	1	no	—
821	C₄²	—	7	1	no	—
822	C₄²	—	7	1	no	—
823	C₄²	—	7	1	no	—
824	C₄²	—	7	1	no	—
825	C₄²	C₂²×D₇	1	1	yes	characteristic
826	C₄²	C₂²×D₇	1	1	yes	characteristic
827	C₄²	C₂²×D₇	1	1	yes	characteristic
828	C₂×C₇	—	2	2	no	—
829	C₂×C₇	—	4	1	no	—
830	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
832	C₂×C₇	#585	1	1	yes	characteristic
833	D₇	—	2	2	no	—
834	D₇	—	4	1	no	—
835	D₇	—	4	1	no	—
836	D₇	—	4	1	no	—
837	D₇	—	4	1	no	—
838	C₂³	—	7	1	no	—
839	C₂³	—	7	1	no	—
840	C₂³	—	7	1	no	—
841	C₂³	—	7	1	no	—
842	C₂³	—	7	1	no	—
843	C₂³	—	14	2	no	—
844	C₂³	—	14	2	no	—
845	C₂³	—	14	2	no	—
846	C₂³	—	28	1	no	—
847	C₂³	—	28	1	no	—
848	C₂³	—	28	1	no	—
849	C₂³	C₂³×D₇	1	1	yes	characteristic
850	C₂³	C₂³×D₇	1	1	yes	characteristic
851	Q₈	—	4	1	no	—
852	Q₈	—	4	1	no	—
853	Q₈	—	4	1	no	—
854	Q₈	—	28	1	no	—
855	Q₈	—	28	1	no	—
856	Q₈	—	28	1	no	—
857	Q₈	—	28	1	no	—
858	Q₈	—	28	1	no	—
859	Q₈	—	28	1	no	—
860	D₄	—	2	2	no	—
861	D₄	—	14	2	no	—
862	D₄	—	14	2	no	—
863	D₄	—	14	2	no	—
864	D₄	—	14	2	no	—
865	D₄	—	14	2	no	—
866	D₄	—	28	1	no	—
867	D₄	—	28	1	no	—
868	D₄	—	28	1	no	—
869	D₄	—	28	1	no	—
870	D₄	—	28	1	no	—
871	D₄	—	28	1	no	—
872	D₄	—	28	1	no	—
873	D₄	—	28	1	no	—
874	D₄	—	28	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	7	1	no	—
882	C₂×C₄	—	7	1	no	—
883	C₂×C₄	—	7	1	no	—
884	C₂×C₄	—	7	1	no	—
885	C₂×C₄	—	7	1	no	—
886	C₂×C₄	—	7	1	no	—
887	C₂×C₄	—	7	1	no	—
888	C₂×C₄	—	7	1	no	—
889	C₂×C₄	—	7	1	no	—
890	C₂×C₄	—	7	1	no	—
891	C₂×C₄	—	7	1	no	—
892	C₂×C₄	—	14	2	no	—
893	C₂×C₄	—	14	2	no	—
894	C₂×C₄	—	14	2	no	—
895	C₂×C₄	—	14	2	no	—
896	C₂×C₄	—	14	2	no	—
897	C₂×C₄	—	28	1	no	—
898	C₂×C₄	—	28	1	no	—
899	C₂×C₄	—	28	1	no	—
900	C₂×C₄	—	28	1	no	—
901	C₂×C₄	—	28	1	no	—
902	C₂×C₄	—	28	1	no	—
903	C₂×C₄	—	28	1	no	—
904	C₂×C₄	—	28	1	no	—
905	C₂×C₄	—	28	1	no	—
906	C₂×C₄	—	28	1	no	—
907	C₂×C₄	—	28	1	no	—
908	C₂×C₄	—	28	1	no	—
909	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
922	C₇	#3535	1	1	yes	characteristic, complemented, Sylow
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	7	2	no	—
929	C₂²	—	14	1	no	—
930	C₂²	—	14	1	no	—
931	C₂²	—	14	1	no	—
932	C₂²	—	14	1	no	—
933	C₂²	—	14	1	no	—
934	C₂²	—	14	1	no	—
935	C₂²	—	14	1	no	—
936	C₂²	—	14	1	no	—
937	C₂²	—	14	1	no	—
938	C₂²	—	14	1	no	—
939	C₂²	—	14	1	no	—
940	C₂²	—	14	1	no	—
941	C₂²	—	14	1	no	—
942	C₂²	—	14	1	no	—
943	C₂²	—	28	4	no	—
944	C₂²	—	56	2	no	—
945	C₂²	#6551	1	2	yes	—
946	C₂²	C₂⁴×D₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	14	1	no	—
961	C₄	—	14	1	no	—
962	C₄	—	14	1	no	—
963	C₄	—	14	1	no	—
964	C₄	—	14	1	no	—
965	C₄	—	14	1	no	—
966	C₄	—	14	1	no	—
967	C₄	—	14	1	no	—
968	C₄	—	14	1	no	—
969	C₄	—	14	1	no	—
970	C₄	—	14	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	14	2	no	—
974	C₂	—	28	1	no	—
975	C₂	—	28	1	no	—
976	C₂	—	28	1	no	—
977	C₂	—	28	1	no	—
978	C₂	C₂×#6551	1	1	yes	characteristic
979	C₂	#90616	1	1	yes	characteristic
980	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×#554	C₂
hypercenter	#554	D₇
hypocenter	C₇	#3535
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₇×#554	C₂	semidirect
2. #90426	C₂	semidirect
3. #90415	C₂	semidirect
4. #90390	C₂	semidirect
5. #90384	C₂	semidirect
6. #90383	C₂	semidirect
7. #90383	C₂	semidirect
8. #90338	C₂	semidirect
9. #90338	C₂	semidirect
10. #90331	C₂	semidirect
11. #90329	C₂	semidirect
12. #90328	C₂	semidirect
13. #90328	C₂	semidirect
14. #90325	C₂	semidirect
15. #90322	C₂	semidirect
16. #90321	C₂	semidirect
17. #90319	C₂	semidirect
18. D₇×C₂²⋊Q₈	C₂	semidirect
19. #90314	C₂	semidirect
20. #90273	C₂	semidirect
21. #90272	C₂	semidirect
22. #90255	C₂	semidirect
23. #90251	C₂	semidirect
24. #90247	C₂	semidirect
25. #90247	C₂	semidirect
26. #90241	C₂	semidirect
27. #90238	C₂	semidirect
28. #90206	C₂	semidirect
29. #90202	C₂	semidirect
30. #90198	C₂	semidirect
31. C₂×#6457	C₂	semidirect
33. C₂×Q₈×D₇	C₂²	semidirect
35. C₂×#1157	C₂²	semidirect
38. C₇×C₄⋊Q₈	C₂²	semidirect
39. C₇×#125	C₂²	semidirect
40. C₇×#125	C₂²	semidirect
44. C₇×C₂²⋊Q₈	C₂²	semidirect
45. C₇×C₂²⋊Q₈	C₂²	semidirect
46. C₇×C₂²⋊Q₈	C₂²	semidirect
47. C₄×C₇×Q₈	C₂²	semidirect
52. C₂×C₇×C₄⋊C₄	C₂²	semidirect
54. #6510	C₂²	semidirect
55. #6510	C₂²	semidirect
56. #6509	C₂²	semidirect
57. #6509	C₂²	semidirect
58. #6509	C₂²	semidirect
59. #6509	C₂²	semidirect
60. #6509	C₂²	semidirect
61. #6507	C₂²	semidirect
62. #6507	C₂²	semidirect
68. #6493	C₂²	semidirect
69. #6492	C₂²	semidirect
70. #6492	C₂²	semidirect
71. #6492	C₂²	semidirect
72. #6492	C₂²	semidirect
76. C₄×C₂²⋊D₇	C₂²	semidirect
77. C₄×C₂²⋊D₇	C₂²	semidirect
78. C₄×C₂²⋊D₇	C₂²	semidirect
85. #6487	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. #6461	C₂²	semidirect
94. #6460	C₂²	semidirect
95. #6460	C₂²	semidirect
96. #6460	C₂²	semidirect
97. #6460	C₂²	semidirect
98. #6459	C₂²	semidirect
99. #6459	C₂²	semidirect
100. #6459	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
107. #6459	C₂²	semidirect
108. #6459	C₂²	semidirect
109. #6459	C₂²	semidirect
125. #6457	C₂²	semidirect
126. #6457	C₂²	semidirect
127. #6457	C₂²	semidirect
128. #6457	C₂²	semidirect
129. #6457	C₂²	semidirect
130. #6457	C₂²	semidirect
132. #6456	C₂²	semidirect
133. #6456	C₂²	semidirect
134. #6455	C₂²	semidirect
135. #6455	C₂²	semidirect
136. D₇×C₄⋊C₄	C₂²	semidirect
137. D₇×C₄⋊C₄	C₂²	semidirect
138. D₇×C₄⋊C₄	C₂²	semidirect
139. D₇×C₄⋊C₄	C₂²	semidirect
140. #6452	C₂²	semidirect
141. #6452	C₂²	semidirect
142. #6452	C₂²	semidirect
143. #6452	C₂²	semidirect
144. #6452	C₂²	semidirect
145. #6452	C₂²	semidirect
146. #6452	C₂²	semidirect
147. #6451	C₂²	semidirect
148. #6451	C₂²	semidirect
149. #6451	C₂²	semidirect
150. #6450	C₂²	semidirect
152. #6448	C₂²	semidirect
153. #6448	C₂²	semidirect
154. #6448	C₂²	semidirect
157. #6447	C₂²	semidirect
158. #6447	C₂²	semidirect
159. #6446	C₂²	semidirect
160. #6446	C₂²	semidirect
161. #6446	C₂²	semidirect
162. #6446	C₂²	semidirect
169. #6442	C₂²	semidirect
175. #6439	C₂²	semidirect
176. #6439	C₂²	semidirect
177. #6439	C₂²	semidirect
178. #6439	C₂²	semidirect
180. #6438	C₂²	semidirect
182. C₄×D₂₈	C₂²	semidirect
183. #6435	C₂²	semidirect
184. #6435	C₂²	semidirect
185. #6435	C₂²	semidirect
186. #6433	C₂²	semidirect
354. #554	D₇	semidirect
475. C₄⋊Q₈	C₂×D₇	semidirect
496. #125	C₂×D₇	semidirect
497. #125	C₂×D₇	semidirect
565. C₂²⋊Q₈	C₂×D₇	semidirect
566. C₂²⋊Q₈	C₂×D₇	semidirect
567. C₂²⋊Q₈	C₂×D₇	semidirect
583. C₄×Q₈	C₂×D₇	semidirect
611. C₂×C₄⋊C₄	C₂×D₇	semidirect
922. C₇	#3535	semidirect

Maximal subgroups

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

subgroup	index
C₇×#554	2
#90426	2
#90415	2
#90390	2
#90384	2
#90383	2
#90338	2
#90331	2
#90329	2
#90328	2
#90325	2
#90322	2
#90321	2
#90319	2
D₇×C₂²⋊Q₈	2
#90314	2
#90273	2
#90272	2
#90255	2
#90251	2
#90247	2
#90241	2
#90238	2
#90206	2
#90202	2
#90198	2
C₂×#6457	2
#3535	7