Subgroups — #11743226

Order 896.

1152 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#90400	C₂	1	2	yes	maximal, complemented
3	#90396	C₂	1	2	yes	maximal, complemented
4	#90386	C₂	1	1	yes	maximal, characteristic, complemented
5	#90385	C₂	1	1	yes	maximal, characteristic, complemented
6	#90368	C₂	1	1	yes	maximal, characteristic, complemented
7	#90367	C₂	1	1	yes	maximal, characteristic, complemented
8	#90356	C₂	1	2	yes	maximal, complemented
9	#90344	C₂	1	2	yes	maximal, complemented
10	#90318	C₂	1	1	yes	maximal, characteristic, complemented
11	D₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#90297	C₂	1	1	yes	maximal, characteristic, complemented
13	D₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
14	#90272	C₂	1	1	yes	maximal, characteristic, complemented
15	#90267	C₂	1	1	yes	maximal, characteristic, complemented
16	#90251	C₂	1	2	yes	maximal, complemented
17	#90249	C₂	1	1	yes	maximal, characteristic, complemented
18	#90245	C₂	1	1	yes	maximal, characteristic, complemented
19	#90236	C₂	1	2	yes	maximal, complemented
20	#90221	C₂	1	2	yes	maximal, complemented
21	#90218	C₂	1	2	yes	maximal, complemented
22	#90170	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₄×D₇	C₂²	1	2	yes	—
28	C₂×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₂₈	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
32	C₇×#126	C₂²	1	2	yes	complemented
33	C₇×#125	C₂²	1	1	yes	characteristic, complemented
34	C₇×#124	C₂²	1	1	yes	characteristic, complemented
35	C₇×#123	C₂²	1	2	yes	complemented
36	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₇×#121	C₂²	1	1	yes	characteristic
38	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₇×D₄	C₂²	1	2	yes	complemented
40	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₇×#117	C₂²	1	2	yes	complemented
42	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
43	#6509	C₂²	1	1	yes	characteristic, complemented
44	#6509	C₂²	1	1	yes	characteristic, complemented
45	#6502	C₂²	1	2	yes	—
46	#6501	C₂²	1	1	yes	characteristic, complemented
47	#6501	C₂²	1	1	yes	characteristic, complemented
48	#6500	C₂²	1	2	yes	complemented
49	D₄×Dic₇	C₂²	1	2	yes	complemented
50	#6493	C₂²	1	1	yes	characteristic
51	#6493	C₂²	1	2	yes	complemented
52	#6492	C₂²	1	2	yes	complemented
53	#6492	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₇	C₂²	1	2	yes	complemented
56	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
59	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
60	#6487	C₂²	1	1	yes	characteristic, complemented
61	#6461	C₂²	1	2	yes	complemented
62	#6461	C₂²	1	2	yes	complemented
63	#6460	C₂²	1	1	yes	characteristic, complemented
64	#6460	C₂²	1	1	yes	characteristic, complemented
65	#6460	C₂²	1	2	yes	complemented
66	#6459	C₂²	1	2	yes	complemented
67	#6458	C₂²	1	2	yes	complemented
68	#6458	C₂²	1	1	yes	characteristic, complemented
69	#6458	C₂²	1	1	yes	characteristic, complemented
70	#6458	C₂²	1	2	yes	complemented
71	#6457	C₂²	1	2	yes	—
72	#6457	C₂²	1	2	yes	—
73	#6457	C₂²	1	2	yes	complemented
74	#6457	C₂²	1	2	yes	complemented
75	#6456	C₂²	1	2	yes	complemented
76	#6456	C₂²	1	2	yes	complemented
77	#6455	C₂²	1	2	yes	complemented
78	#6455	C₂²	1	1	yes	characteristic, complemented
79	#6455	C₂²	1	1	yes	characteristic, complemented
80	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
81	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
83	#6453	C₂²	1	2	yes	complemented
84	#6452	C₂²	1	2	yes	complemented
85	#6449	C₂²	1	2	yes	complemented
86	#6448	C₂²	1	2	yes	complemented
87	#6447	C₂²	1	2	yes	complemented
88	#6447	C₂²	1	2	yes	complemented
89	#6447	C₂²	1	2	yes	complemented
90	#6447	C₂²	1	2	yes	complemented
91	#6446	C₂²	1	2	yes	complemented
92	#6446	C₂²	1	2	yes	complemented
93	#6445	C₂²	1	2	yes	—
94	#6445	C₂²	1	2	yes	—
95	#6445	C₂²	1	2	yes	complemented
96	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
99	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
101	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
102	#6442	C₂²	1	2	yes	complemented
103	#6441	C₂²	1	2	yes	complemented
104	#6441	C₂²	1	2	yes	complemented
105	#6439	C₂²	1	2	yes	complemented
106	#6439	C₂²	1	2	yes	complemented
107	#6438	C₂²	1	1	yes	characteristic, complemented
108	#6438	C₂²	1	2	yes	complemented
109	C₄×D₂₈	C₂²	1	1	yes	characteristic
110	C₄×D₂₈	C₂²	1	1	yes	characteristic
111	C₄×D₂₈	C₂²	1	1	yes	characteristic
112	C₄×D₂₈	C₂²	1	1	yes	characteristic
113	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₂₈	C₂²	1	2	yes	complemented
119	#6435	C₂²	1	2	yes	complemented
120	#6435	C₂²	1	2	yes	complemented
121	#6433	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3505	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂³×D₇	C₂³	1	1	yes	characteristic
126	C₂³×D₇	C₂³	1	1	yes	characteristic
127	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
128	C₂×C₇×D₄	C₂³	1	2	yes	—
129	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂²×Dic₇	C₂³	1	1	yes	characteristic
140	C₂²×Dic₇	C₂³	1	2	yes	—
141	C₂²×Dic₇	C₂³	1	1	yes	characteristic
142	#1161	—	4	2	no	—
143	Q₈×D₇	—	4	2	no	—
144	#1159	—	4	2	no	—
145	D₄×D₇	—	2	8	no	—
146	D₄×D₇	—	4	2	no	—
147	C₂×D₂₈	—	2	4	no	—
148	C₂×D₂₈	C₂³	1	1	yes	characteristic
149	C₂×D₂₈	C₂³	1	1	yes	characteristic
150	C₂×D₂₈	C₂³	1	1	yes	characteristic
151	C₂×D₂₈	C₂³	1	1	yes	characteristic
152	C₂×D₂₈	C₂³	1	1	yes	characteristic
153	C₂×D₂₈	C₂³	1	2	yes	—
154	C₂×D₂₈	C₂³	1	2	yes	—
155	C₂×D₂₈	C₂³	1	2	yes	—
156	C₂×C₄×D₇	—	4	2	no	—
157	C₂×C₄×D₇	—	4	2	no	—
158	C₂×C₄×D₇	C₂³	1	2	yes	—
159	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₇	C₂³	1	2	yes	—
164	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
166	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₇	C₂³	1	2	yes	—
169	C₂×C₄×D₇	C₂³	1	2	yes	—
170	C₂×C₄×D₇	C₂³	1	2	yes	—
171	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
172	C₂×Dic₁₄	C₂³	1	2	yes	—
173	C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₇×C₄⋊C₄	C₂³	1	2	yes	—
175	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₄	C₂³	1	2	yes	—
178	C₇×C₄⋊C₄	C₂³	1	2	yes	—
179	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₄²×C₇	C₂³	1	1	yes	characteristic
185	C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₄²×C₇	C₂³	1	2	yes	—
188	C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₇	C₂³	1	2	yes	—
190	C₂²⋊Dic₇	C₂³	1	2	yes	—
191	C₂²⋊Dic₇	C₂³	1	2	yes	—
192	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
206	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
207	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
208	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
209	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
210	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
211	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
212	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
215	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
216	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
217	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
218	C₄⋊Dic₇	C₂³	1	2	yes	—
219	C₄⋊Dic₇	C₂³	1	2	yes	—
220	Dic₇⋊C₄	C₂³	1	2	yes	—
221	Dic₇⋊C₄	C₂³	1	2	yes	—
222	Dic₇⋊C₄	C₂³	1	2	yes	—
223	Dic₇⋊C₄	C₂³	1	2	yes	—
224	Dic₇⋊C₄	C₂³	1	2	yes	—
225	Dic₇⋊C₄	C₂³	1	2	yes	—
226	Dic₇⋊C₄	C₂³	1	2	yes	—
227	Dic₇⋊C₄	C₂³	1	2	yes	—
228	C₄×Dic₇	C₂³	1	2	yes	—
229	C₄×Dic₇	C₂³	1	2	yes	—
230	C₄×Dic₇	C₂³	1	2	yes	—
231	#553	—	7	2	no	—
232	#553	—	7	1	no	—
233	#553	—	7	1	no	—
234	#553	—	7	2	no	—
235	#552	—	7	1	no	—
236	#552	—	7	1	no	—
237	#551	—	7	2	no	—
238	#551	—	7	2	no	—
239	#548	—	7	1	no	—
240	#548	—	7	1	no	—
241	#546	—	7	1	no	—
242	#546	—	7	1	no	—
243	#539	—	7	2	no	—
244	#538	—	7	2	no	—
245	#534	—	7	2	no	—
246	#529	—	7	1	no	—
247	#529	D₇	1	1	yes	characteristic, complemented
248	#525	—	7	1	no	—
249	#525	—	7	1	no	—
250	C₂×C₂²⋊Q₈	—	7	1	no	—
251	C₂×#121	—	7	1	no	—
252	#518	—	7	2	no	—
253	C₂×C₄×D₄	—	7	1	no	—
254	C₂³×C₇	C₂⁴	1	2	yes	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂²×D₇	—	2	2	no	—
257	C₂²×D₇	—	2	4	no	—
258	C₂²×D₇	—	4	1	no	—
259	C₂²×D₇	—	4	1	no	—
260	C₂²×D₇	—	4	1	no	—
261	C₂²×D₇	—	4	1	no	—
262	C₂²×D₇	—	4	2	no	—
263	C₂²×D₇	—	4	2	no	—
264	C₂²×D₇	#41	1	4	yes	complemented
265	C₂²×D₇	C₂⁴	1	1	yes	characteristic
266	C₂²×D₇	C₂⁴	1	1	yes	characteristic
267	C₂²×D₇	C₂⁴	1	2	yes	—
268	C₂²×D₇	C₂⁴	1	1	yes	characteristic
269	C₂²×D₇	C₂⁴	1	1	yes	characteristic
270	C₇×Q₈	—	2	2	no	—
271	C₇×D₄	—	2	4	no	—
272	C₇×D₄	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	4	1	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₇	C₂⁴	1	2	yes	—
280	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂⁴	1	2	yes	—
285	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
286	C₂²⋊D₇	—	2	4	no	—
287	C₂²⋊D₇	—	2	4	no	—
288	C₂²⋊D₇	—	4	2	no	—
289	C₂²⋊D₇	—	4	2	no	—
290	C₂²⋊D₇	—	4	2	no	—
291	C₂×Dic₇	—	4	1	no	—
292	C₂×Dic₇	—	4	1	no	—
293	C₂×Dic₇	—	4	2	no	—
294	C₂×Dic₇	C₂⁴	1	2	yes	—
295	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
297	C₂×Dic₇	C₂⁴	1	2	yes	—
298	C₂×Dic₇	C₂⁴	1	2	yes	—
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
301	D₂₈	—	2	2	no	—
302	D₂₈	—	2	2	no	—
303	D₂₈	—	2	2	no	—
304	D₂₈	—	2	2	no	—
305	D₂₈	—	2	4	no	—
306	D₂₈	—	2	2	no	—
307	D₂₈	—	4	2	no	—
308	D₂₈	—	4	2	no	—
309	C₄×D₇	—	2	4	no	—
310	C₄×D₇	—	2	2	no	—
311	C₄×D₇	—	2	2	no	—
312	C₄×D₇	—	2	2	no	—
313	C₄×D₇	—	2	2	no	—
314	C₄×D₇	—	4	1	no	—
315	C₄×D₇	—	4	1	no	—
316	C₄×D₇	—	4	1	no	—
317	C₄×D₇	—	4	1	no	—
318	C₄×D₇	—	4	2	no	—
319	C₄×D₇	—	4	2	no	—
320	C₄×D₇	—	4	2	no	—
321	C₄×D₇	—	4	2	no	—
322	Dic₁₄	—	2	2	no	—
323	Dic₁₄	—	4	2	no	—
324	C₂×#41	—	7	1	no	—
325	C₂×#41	—	7	1	no	—
326	C₂²×Q₈	—	7	1	no	—
327	C₂²×D₄	—	7	2	no	—
328	C₂²×D₄	—	7	1	no	—
329	C₂²×D₄	—	7	1	no	—
330	C₂³×C₄	—	7	1	no	—
331	C₂³×C₄	—	7	1	no	—
332	#126	—	7	2	no	—
333	#126	—	7	2	no	—
334	#126	—	7	2	no	—
335	#126	—	7	2	no	—
336	#126	—	7	2	no	—
337	#126	C₂×D₇	1	2	yes	complemented
338	#125	—	7	2	no	—
339	#125	—	7	2	no	—
340	#125	—	7	1	no	—
341	#125	C₂×D₇	1	1	yes	characteristic, complemented
342	#124	—	7	2	no	—
343	#124	—	7	1	no	—
344	#124	—	7	2	no	—
345	#124	C₂×D₇	1	1	yes	characteristic, complemented
346	#123	—	7	2	no	—
347	#123	—	7	2	no	—
348	#123	—	7	2	no	—
349	#123	—	7	2	no	—
350	#123	—	7	2	no	—
351	#123	—	7	2	no	—
352	#123	—	7	2	no	—
353	#123	—	7	2	no	—
354	#123	—	7	2	no	—
355	#123	C₂×D₇	1	2	yes	complemented
356	C₂²⋊Q₈	—	7	1	no	—
357	C₂²⋊Q₈	—	7	1	no	—
358	C₂²⋊Q₈	—	7	1	no	—
359	C₂²⋊Q₈	—	7	1	no	—
360	C₂²⋊Q₈	—	7	2	no	—
361	C₂²⋊Q₈	—	7	1	no	—
362	C₂²⋊Q₈	—	7	2	no	—
363	C₂²⋊Q₈	—	7	2	no	—
364	C₂²⋊Q₈	—	7	2	no	—
365	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
366	#121	—	7	2	no	—
367	#121	—	7	1	no	—
368	#121	—	7	1	no	—
369	#121	—	7	1	no	—
370	#121	—	7	2	no	—
371	#121	—	7	1	no	—
372	#121	—	7	1	no	—
373	#121	—	7	2	no	—
374	#121	—	7	2	no	—
375	#121	—	7	2	no	—
376	#121	—	7	2	no	—
377	#121	—	7	2	no	—
378	#121	—	7	2	no	—
379	#121	C₂×D₇	1	1	yes	characteristic
380	#120	—	7	2	no	—
381	#120	—	7	2	no	—
382	#120	—	7	2	no	—
383	#120	—	7	2	no	—
384	C₄×Q₈	—	7	1	no	—
385	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
386	C₄×D₄	—	7	2	no	—
387	C₄×D₄	—	7	2	no	—
388	C₄×D₄	—	7	2	no	—
389	C₄×D₄	—	7	2	no	—
390	C₄×D₄	—	7	2	no	—
391	C₄×D₄	—	7	2	no	—
392	C₄×D₄	—	7	2	no	—
393	C₄×D₄	—	7	2	no	—
394	C₄×D₄	—	7	1	no	—
395	C₄×D₄	—	7	1	no	—
396	C₄×D₄	—	7	1	no	—
397	C₄×D₄	—	7	1	no	—
398	C₄×D₄	—	7	1	no	—
399	C₄×D₄	—	7	1	no	—
400	C₄×D₄	—	7	1	no	—
401	C₄×D₄	—	7	1	no	—
402	C₄×D₄	—	7	2	no	—
403	C₄×D₄	—	7	1	no	—
404	C₄×D₄	C₂×D₇	1	2	yes	complemented
405	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
406	#117	—	7	2	no	—
407	#117	—	7	1	no	—
408	#117	—	7	1	no	—
409	#117	—	7	2	no	—
410	#117	—	7	2	no	—
411	#117	C₂×D₇	1	2	yes	complemented
412	C₂×C₄⋊C₄	—	7	1	no	—
413	C₂×C₄⋊C₄	—	7	1	no	—
414	C₂×C₄⋊C₄	—	7	2	no	—
415	C₂×C₄⋊C₄	—	7	1	no	—
416	C₂×C₂²⋊C₄	—	7	1	no	—
417	C₂×C₂²⋊C₄	—	7	1	no	—
418	C₂×C₂²⋊C₄	—	7	2	no	—
419	C₂×C₂²⋊C₄	—	7	2	no	—
420	C₂×C₂²⋊C₄	—	7	2	no	—
421	C₂×C₂²⋊C₄	—	7	2	no	—
422	C₂×C₄²	C₂×D₇	1	1	yes	characteristic, complemented
423	C₂²×C₇	—	2	1	no	—
424	C₂²×C₇	—	2	1	no	—
425	C₂²×C₇	—	2	2	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	2	no	—
428	C₂²×C₇	C₂×#41	1	2	yes	—
429	C₂²×C₇	C₂⁵	1	1	yes	characteristic
430	C₂×D₇	—	2	1	no	—
431	C₂×D₇	—	2	1	no	—
432	C₂×D₇	—	2	1	no	—
433	C₂×D₇	—	2	1	no	—
434	C₂×D₇	—	2	1	no	—
435	C₂×D₇	—	2	1	no	—
436	C₂×D₇	—	2	2	no	—
437	C₂×D₇	—	2	1	no	—
438	C₂×D₇	—	2	1	no	—
439	C₂×D₇	—	2	2	no	—
440	C₂×D₇	—	2	2	no	—
441	C₂×D₇	—	2	1	no	—
442	C₂×D₇	—	2	1	no	—
443	C₂×D₇	—	4	4	no	—
444	C₂×D₇	—	4	4	no	—
445	C₂×D₇	—	8	4	no	—
446	C₂×D₇	C₂×#41	1	2	yes	—
447	C₂×D₇	C₂×#41	1	2	yes	—
448	C₄×C₇	—	2	2	no	—
449	C₄×C₇	—	2	1	no	—
450	C₄×C₇	—	2	1	no	—
451	C₄×C₇	—	2	2	no	—
452	C₄×C₇	—	2	1	no	—
453	C₄×C₇	—	2	1	no	—
454	C₄×C₇	—	2	2	no	—
455	C₄×C₇	—	2	1	no	—
456	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
457	Dic₇	—	2	2	no	—
458	Dic₇	—	2	2	no	—
459	Dic₇	—	2	1	no	—
460	Dic₇	—	2	1	no	—
461	Dic₇	—	2	1	no	—
462	Dic₇	—	2	1	no	—
463	Dic₇	—	2	2	no	—
464	C₂⁴	—	7	1	no	—
465	C₂⁴	—	7	2	no	—
466	C₂⁴	—	7	1	no	—
467	#41	—	28	2	no	—
468	#41	—	28	2	no	—
469	C₂×Q₈	—	7	1	no	—
470	C₂×Q₈	—	7	2	no	—
471	C₂×Q₈	—	28	2	no	—
472	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
473	C₂×D₄	—	7	2	no	—
474	C₂×D₄	—	7	2	no	—
475	C₂×D₄	—	7	2	no	—
476	C₂×D₄	—	7	2	no	—
477	C₂×D₄	—	7	2	no	—
478	C₂×D₄	—	7	1	no	—
479	C₂×D₄	—	7	1	no	—
480	C₂×D₄	—	7	2	no	—
481	C₂×D₄	—	7	1	no	—
482	C₂×D₄	—	7	1	no	—
483	C₂×D₄	—	7	1	no	—
484	C₂×D₄	—	7	2	no	—
485	C₂×D₄	—	7	2	no	—
486	C₂×D₄	—	14	4	no	—
487	C₂×D₄	—	14	8	no	—
488	C₂×D₄	—	28	2	no	—
489	C₂×D₄	C₂²×D₇	1	2	yes	—
490	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
491	C₂²×C₄	—	7	1	no	—
492	C₂²×C₄	—	7	1	no	—
493	C₂²×C₄	—	7	2	no	—
494	C₂²×C₄	—	7	2	no	—
495	C₂²×C₄	—	7	1	no	—
496	C₂²×C₄	—	7	1	no	—
497	C₂²×C₄	—	7	1	no	—
498	C₂²×C₄	—	7	1	no	—
499	C₂²×C₄	—	7	1	no	—
500	C₂²×C₄	—	7	2	no	—
501	C₂²×C₄	—	7	2	no	—
502	C₂²×C₄	—	7	2	no	—
503	C₂²×C₄	—	7	2	no	—
504	C₂²×C₄	—	7	1	no	—
505	C₂²×C₄	—	7	1	no	—
506	C₂²×C₄	—	7	1	no	—
507	C₂²×C₄	—	28	2	no	—
508	C₂²×C₄	—	28	2	no	—
509	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₇	1	2	yes	—
513	C₄⋊C₄	—	7	2	no	—
514	C₄⋊C₄	—	7	2	no	—
515	C₄⋊C₄	—	7	2	no	—
516	C₄⋊C₄	—	7	2	no	—
517	C₄⋊C₄	—	7	2	no	—
518	C₄⋊C₄	—	7	2	no	—
519	C₄⋊C₄	—	7	2	no	—
520	C₄⋊C₄	—	7	2	no	—
521	C₄⋊C₄	—	7	1	no	—
522	C₄⋊C₄	—	7	1	no	—
523	C₄⋊C₄	—	7	1	no	—
524	C₄⋊C₄	—	7	1	no	—
525	C₄⋊C₄	—	7	1	no	—
526	C₄⋊C₄	—	7	1	no	—
527	C₄⋊C₄	—	7	2	no	—
528	C₄⋊C₄	—	7	2	no	—
529	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₇	1	2	yes	—
532	C₄⋊C₄	C₂²×D₇	1	2	yes	—
533	C₄⋊C₄	C₂²×D₇	1	2	yes	—
534	C₄⋊C₄	C₂²×D₇	1	2	yes	—
535	C₂²⋊C₄	—	7	2	no	—
536	C₂²⋊C₄	—	7	2	no	—
537	C₂²⋊C₄	—	7	2	no	—
538	C₂²⋊C₄	—	7	1	no	—
539	C₂²⋊C₄	—	7	1	no	—
540	C₂²⋊C₄	—	7	2	no	—
541	C₂²⋊C₄	—	7	2	no	—
542	C₂²⋊C₄	—	7	2	no	—
543	C₂²⋊C₄	—	7	1	no	—
544	C₂²⋊C₄	—	7	1	no	—
545	C₂²⋊C₄	—	7	1	no	—
546	C₂²⋊C₄	—	7	1	no	—
547	C₂²⋊C₄	—	7	2	no	—
548	C₂²⋊C₄	—	7	2	no	—
549	C₂²⋊C₄	—	7	1	no	—
550	C₂²⋊C₄	—	7	1	no	—
551	C₂²⋊C₄	—	7	2	no	—
552	C₂²⋊C₄	—	7	2	no	—
553	C₂²⋊C₄	—	7	2	no	—
554	C₂²⋊C₄	—	7	2	no	—
555	C₂²⋊C₄	—	7	2	no	—
556	C₂²⋊C₄	—	7	2	no	—
557	C₂²⋊C₄	—	7	2	no	—
558	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
563	C₄²	—	7	2	no	—
564	C₄²	—	7	2	no	—
565	C₄²	—	7	2	no	—
566	C₄²	C₂²×D₇	1	1	yes	characteristic
567	C₄²	C₂²×D₇	1	1	yes	characteristic
568	C₄²	C₂²×D₇	1	1	yes	characteristic
569	C₄²	C₂²×D₇	1	1	yes	characteristic
570	C₄²	C₂²×D₇	1	2	yes	—
571	C₂×C₇	—	2	2	no	—
572	C₂×C₇	—	4	2	no	—
573	C₂×C₇	C₂²×#41	1	1	yes	characteristic
574	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×C₇	#585	1	1	yes	characteristic
576	D₇	—	2	2	no	—
577	D₇	—	2	2	no	—
578	D₇	—	4	1	no	—
579	D₇	—	4	1	no	—
580	D₇	—	4	2	no	—
581	C₂³	—	7	1	no	—
582	C₂³	—	7	1	no	—
583	C₂³	—	7	4	no	—
584	C₂³	—	7	1	no	—
585	C₂³	—	7	1	no	—
586	C₂³	—	7	2	no	—
587	C₂³	—	14	4	no	—
588	C₂³	—	14	2	no	—
589	C₂³	—	28	1	no	—
590	C₂³	—	28	1	no	—
591	C₂³	—	28	1	no	—
592	C₂³	—	28	1	no	—
593	C₂³	—	28	2	no	—
594	C₂³	—	28	2	no	—
595	C₂³	C₂³×D₇	1	2	yes	—
596	C₂³	C₂³×D₇	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	14	2	no	—
599	Q₈	—	28	2	no	—
600	D₄	—	2	4	no	—
601	D₄	—	2	2	no	—
602	D₄	—	14	2	no	—
603	D₄	—	14	2	no	—
604	D₄	—	14	2	no	—
605	D₄	—	14	2	no	—
606	D₄	—	14	4	no	—
607	D₄	—	14	4	no	—
608	D₄	—	14	4	no	—
609	D₄	—	14	2	no	—
610	D₄	—	28	2	no	—
611	D₄	—	28	2	no	—
612	D₄	—	28	2	no	—
613	D₄	—	28	2	no	—
614	D₄	—	28	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	7	2	no	—
620	C₂×C₄	—	7	1	no	—
621	C₂×C₄	—	7	1	no	—
622	C₂×C₄	—	7	2	no	—
623	C₂×C₄	—	7	2	no	—
624	C₂×C₄	—	7	1	no	—
625	C₂×C₄	—	7	1	no	—
626	C₂×C₄	—	14	4	no	—
627	C₂×C₄	—	14	2	no	—
628	C₂×C₄	—	14	2	no	—
629	C₂×C₄	—	14	2	no	—
630	C₂×C₄	—	14	2	no	—
631	C₂×C₄	—	28	2	no	—
632	C₂×C₄	—	28	2	no	—
633	C₂×C₄	—	28	1	no	—
634	C₂×C₄	—	28	1	no	—
635	C₂×C₄	—	28	1	no	—
636	C₂×C₄	—	28	1	no	—
637	C₂×C₄	—	28	2	no	—
638	C₂×C₄	—	28	2	no	—
639	C₂×C₄	—	28	1	no	—
640	C₂×C₄	—	28	1	no	—
641	C₂×C₄	—	28	2	no	—
642	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
643	C₂×C₄	C₂³×D₇	1	2	yes	—
644	C₂×C₄	C₂³×D₇	1	2	yes	—
645	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₇	1	2	yes	—
650	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
651	C₇	#3505	1	1	yes	characteristic, complemented, Sylow
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	7	2	no	—
658	C₂²	—	7	2	no	—
659	C₂²	—	14	1	no	—
660	C₂²	—	14	1	no	—
661	C₂²	—	14	1	no	—
662	C₂²	—	14	1	no	—
663	C₂²	—	14	1	no	—
664	C₂²	—	14	1	no	—
665	C₂²	—	14	2	no	—
666	C₂²	—	14	1	no	—
667	C₂²	—	14	1	no	—
668	C₂²	—	14	2	no	—
669	C₂²	—	14	2	no	—
670	C₂²	—	14	1	no	—
671	C₂²	—	14	1	no	—
672	C₂²	—	28	4	no	—
673	C₂²	—	28	4	no	—
674	C₂²	—	56	4	no	—
675	C₂²	D₇×#41	1	2	yes	—
676	C₂²	C₂⁴×D₇	1	1	yes	characteristic
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	14	2	no	—
686	C₄	—	14	1	no	—
687	C₄	—	14	1	no	—
688	C₄	—	14	1	no	—
689	C₄	—	14	1	no	—
690	C₄	—	14	2	no	—
691	C₄	—	14	2	no	—
692	C₄	#6553	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	14	2	no	—
696	C₂	—	14	2	no	—
697	C₂	—	28	1	no	—
698	C₂	—	28	1	no	—
699	C₂	—	28	2	no	—
700	C₂	C₂×D₇×#41	1	1	yes	characteristic
701	C₂	C₂×#6553	1	1	yes	characteristic
702	C₂	#90616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#529	C₂
hypercenter	#529	D₇
hypocenter	C₇	#3505
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₇×#529	C₂	semidirect
2. #90400	C₂	semidirect
3. #90396	C₂	semidirect
4. #90386	C₂	semidirect
5. #90385	C₂	semidirect
6. #90368	C₂	semidirect
7. #90367	C₂	semidirect
8. #90356	C₂	semidirect
9. #90344	C₂	semidirect
10. #90318	C₂	semidirect
11. D₇×C₂²⋊Q₈	C₂	semidirect
12. #90297	C₂	semidirect
13. D₇×#121	C₂	semidirect
14. #90272	C₂	semidirect
15. #90267	C₂	semidirect
16. #90251	C₂	semidirect
17. #90249	C₂	semidirect
18. #90245	C₂	semidirect
19. #90236	C₂	semidirect
20. #90221	C₂	semidirect
21. #90218	C₂	semidirect
22. #90170	C₂	semidirect
23. C₂×C₄×D₂₈	C₂	semidirect
24. C₂×#1161	C₂²	semidirect
25. C₂×Q₈×D₇	C₂²	semidirect
26. C₂×#1159	C₂²	semidirect
28. C₂×D₄×D₇	C₂²	semidirect
31. C₂²×C₄×D₇	C₂²	semidirect
32. C₇×#126	C₂²	semidirect
33. C₇×#125	C₂²	semidirect
34. C₇×#124	C₂²	semidirect
35. C₇×#123	C₂²	semidirect
36. C₇×C₂²⋊Q₈	C₂²	semidirect
38. C₄×C₇×Q₈	C₂²	semidirect
39. C₄×C₇×D₄	C₂²	semidirect
40. C₄×C₇×D₄	C₂²	semidirect
41. C₇×#117	C₂²	semidirect
42. C₂×C₄²×C₇	C₂²	semidirect
43. #6509	C₂²	semidirect
44. #6509	C₂²	semidirect
46. #6501	C₂²	semidirect
47. #6501	C₂²	semidirect
48. #6500	C₂²	semidirect
49. D₄×Dic₇	C₂²	semidirect
51. #6493	C₂²	semidirect
52. #6492	C₂²	semidirect
53. #6492	C₂²	semidirect
54. C₄×C₂²⋊D₇	C₂²	semidirect
55. C₄×C₂²⋊D₇	C₂²	semidirect
57. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
58. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
59. C₂×C₄⋊Dic₇	C₂²	semidirect
60. #6487	C₂²	semidirect
61. #6461	C₂²	semidirect
62. #6461	C₂²	semidirect
63. #6460	C₂²	semidirect
64. #6460	C₂²	semidirect
65. #6460	C₂²	semidirect
66. #6459	C₂²	semidirect
67. #6458	C₂²	semidirect
68. #6458	C₂²	semidirect
69. #6458	C₂²	semidirect
70. #6458	C₂²	semidirect
73. #6457	C₂²	semidirect
74. #6457	C₂²	semidirect
75. #6456	C₂²	semidirect
76. #6456	C₂²	semidirect
77. #6455	C₂²	semidirect
78. #6455	C₂²	semidirect
79. #6455	C₂²	semidirect
80. D₇×C₄⋊C₄	C₂²	semidirect
81. D₇×C₄⋊C₄	C₂²	semidirect
82. D₇×C₄⋊C₄	C₂²	semidirect
83. #6453	C₂²	semidirect
84. #6452	C₂²	semidirect
85. #6449	C₂²	semidirect
86. #6448	C₂²	semidirect
87. #6447	C₂²	semidirect
88. #6447	C₂²	semidirect
89. #6447	C₂²	semidirect
90. #6447	C₂²	semidirect
91. #6446	C₂²	semidirect
92. #6446	C₂²	semidirect
95. #6445	C₂²	semidirect
96. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
100. D₇×C₂²⋊C₄	C₂²	semidirect
101. D₇×C₂²⋊C₄	C₂²	semidirect
102. #6442	C₂²	semidirect
103. #6441	C₂²	semidirect
104. #6441	C₂²	semidirect
105. #6439	C₂²	semidirect
106. #6439	C₂²	semidirect
107. #6438	C₂²	semidirect
108. #6438	C₂²	semidirect
113. C₄×D₂₈	C₂²	semidirect
114. C₄×D₂₈	C₂²	semidirect
115. C₄×D₂₈	C₂²	semidirect
116. C₄×D₂₈	C₂²	semidirect
117. C₄×D₂₈	C₂²	semidirect
118. C₄×D₂₈	C₂²	semidirect
119. #6435	C₂²	semidirect
120. #6435	C₂²	semidirect
121. #6433	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
247. #529	D₇	semidirect
264. C₂²×D₇	#41	semidirect
337. #126	C₂×D₇	semidirect
341. #125	C₂×D₇	semidirect
345. #124	C₂×D₇	semidirect
355. #123	C₂×D₇	semidirect
365. C₂²⋊Q₈	C₂×D₇	semidirect
385. C₄×Q₈	C₂×D₇	semidirect
404. C₄×D₄	C₂×D₇	semidirect
405. C₄×D₄	C₂×D₇	semidirect
411. #117	C₂×D₇	semidirect
422. C₂×C₄²	C₂×D₇	semidirect
651. C₇	#3505	semidirect

Maximal subgroups

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

subgroup	index
C₇×#529	2
#90400	2
#90396	2
#90386	2
#90385	2
#90368	2
#90367	2
#90356	2
#90344	2
#90318	2
D₇×C₂²⋊Q₈	2
#90297	2
D₇×#121	2
#90272	2
#90267	2
#90251	2
#90249	2
#90245	2
#90236	2
#90221	2
#90218	2
#90170	2
C₂×C₄×D₂₈	2
#3505	7