Subgroups — #11743895

Order 896.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#90397	C₂	1	2	yes	maximal, complemented
3	#90396	C₂	1	2	yes	maximal, complemented
4	#90386	C₂	1	1	yes	maximal, characteristic, complemented
5	#90384	C₂	1	2	yes	maximal, complemented
6	#90382	C₂	1	2	yes	maximal, complemented
7	#90379	C₂	1	1	yes	maximal, characteristic, complemented
8	#90345	C₂	1	2	yes	maximal, complemented
9	#90340	C₂	1	2	yes	maximal, complemented
10	#90332	C₂	1	1	yes	maximal, characteristic, complemented
11	#90326	C₂	1	1	yes	maximal, characteristic, complemented
12	#90318	C₂	1	1	yes	maximal, characteristic, complemented
13	#90318	C₂	1	1	yes	maximal, characteristic, complemented
14	#90272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#1161	C₂	1	1	yes	maximal, characteristic, complemented
16	#90256	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#90223	C₂	1	1	yes	maximal, characteristic, complemented
19	#90218	C₂	1	2	yes	maximal, complemented
20	#90213	C₂	1	2	yes	maximal, complemented
21	D₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	#90198	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#6455	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#1161	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×#1157	C₂²	1	2	yes	—
27	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
29	C₇×#126	C₂²	1	2	yes	complemented
30	C₇×#125	C₂²	1	1	yes	characteristic, complemented
31	C₇×#125	C₂²	1	2	yes	complemented
32	C₇×#123	C₂²	1	2	yes	—
33	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₇×D₄	C₂²	1	1	yes	characteristic
37	C₇×#117	C₂²	1	1	yes	characteristic, complemented
38	C₇×#117	C₂²	1	2	yes	complemented
39	C₂×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	#6509	C₂²	1	1	yes	characteristic, complemented
41	#6509	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₇	C₂²	1	1	yes	characteristic, complemented
43	#6502	C₂²	1	2	yes	—
44	D₄×Dic₇	C₂²	1	1	yes	characteristic
45	#6493	C₂²	1	1	yes	characteristic, complemented
46	#6493	C₂²	1	1	yes	characteristic, complemented
47	#6492	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	—
51	#6489	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×Dic₇	C₂²	1	2	yes	complemented
54	#6461	C₂²	1	2	yes	complemented
55	#6461	C₂²	1	2	yes	complemented
56	#6461	C₂²	1	2	yes	complemented
57	#6460	C₂²	1	2	yes	complemented
58	#6459	C₂²	1	2	yes	—
59	#6459	C₂²	1	2	yes	—
60	#6459	C₂²	1	2	yes	complemented
61	#6458	C₂²	1	2	yes	—
62	#6458	C₂²	1	1	yes	characteristic, complemented
63	#6458	C₂²	1	1	yes	characteristic, complemented
64	#6457	C₂²	1	2	yes	—
65	#6457	C₂²	1	2	yes	—
66	#6457	C₂²	1	2	yes	—
67	#6457	C₂²	1	2	yes	complemented
68	#6457	C₂²	1	2	yes	complemented
69	#6456	C₂²	1	1	yes	characteristic
70	#6456	C₂²	1	2	yes	—
71	#6456	C₂²	1	2	yes	complemented
72	#6456	C₂²	1	2	yes	complemented
73	#6456	C₂²	1	2	yes	complemented
74	#6456	C₂²	1	1	yes	characteristic, complemented
75	#6455	C₂²	1	1	yes	characteristic
76	#6455	C₂²	1	1	yes	characteristic
77	#6455	C₂²	1	2	yes	—
78	#6455	C₂²	1	1	yes	characteristic
79	#6455	C₂²	1	2	yes	complemented
80	#6455	C₂²	1	2	yes	complemented
81	#6455	C₂²	1	1	yes	characteristic, complemented
82	#6455	C₂²	1	1	yes	characteristic, complemented
83	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
84	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
85	D₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	#6452	C₂²	1	2	yes	complemented
87	#6452	C₂²	1	2	yes	complemented
88	#6451	C₂²	1	1	yes	characteristic, complemented
89	#6451	C₂²	1	1	yes	characteristic, complemented
90	#6450	C₂²	1	2	yes	complemented
91	#6450	C₂²	1	2	yes	complemented
92	#6450	C₂²	1	2	yes	complemented
93	#6448	C₂²	1	2	yes	—
94	#6448	C₂²	1	2	yes	complemented
95	#6447	C₂²	1	2	yes	—
96	#6446	C₂²	1	2	yes	complemented
97	#6445	C₂²	1	2	yes	—
98	#6445	C₂²	1	2	yes	—
99	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
100	(C₂²⋊D₇)⋊C₄	C₂²	1	1	yes	characteristic
101	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	—
102	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
103	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
104	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
105	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	D₇×C₂²⋊C₄	C₂²	1	2	yes	—
107	D₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
108	#6442	C₂²	1	2	yes	complemented
109	#6441	C₂²	1	2	yes	complemented
110	#6440	C₂²	1	2	yes	complemented
111	#6439	C₂²	1	2	yes	complemented
112	#6438	C₂²	1	2	yes	complemented
113	C₄×D₂₈	C₂²	1	1	yes	characteristic
114	C₄×D₂₈	C₂²	1	2	yes	—
115	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
116	#6435	C₂²	1	2	yes	—
117	#6435	C₂²	1	2	yes	complemented
118	#6435	C₂²	1	2	yes	complemented
119	C₄²×D₇	C₂²	1	1	yes	characteristic
120	C₄²×D₇	C₂²	1	2	yes	complemented
121	C₄²×D₇	C₂²	1	2	yes	complemented
122	#6433	C₂²	1	1	yes	characteristic, complemented
123	#3475	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	1	yes	characteristic
125	C₂³×D₇	C₂³	1	1	yes	characteristic
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂³	1	2	yes	—
129	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₇	C₂³	1	2	yes	—
138	#1161	—	2	4	no	—
139	D₄×D₇	—	2	4	no	—
140	#1157	—	2	8	no	—
141	C₂×D₂₈	C₂³	1	2	yes	—
142	C₂×D₂₈	C₂³	1	1	yes	characteristic
143	C₂×D₂₈	C₂³	1	1	yes	characteristic
144	C₂×D₂₈	C₂³	1	2	yes	—
145	C₂×D₂₈	C₂³	1	2	yes	—
146	C₂×C₄×D₇	—	2	4	no	—
147	C₂×C₄×D₇	—	2	4	no	—
148	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₇	C₂³	1	2	yes	—
151	C₂×C₄×D₇	C₂³	1	2	yes	—
152	C₂×C₄×D₇	C₂³	1	2	yes	—
153	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₇	C₂³	1	2	yes	—
160	C₂×C₄×D₇	C₂³	1	2	yes	—
161	C₂×C₄×D₇	C₂³	1	1	yes	characteristic
162	C₂×Dic₁₄	C₂³	1	2	yes	—
163	C₂×Dic₁₄	C₂³	1	2	yes	—
164	C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₇×C₄⋊C₄	C₂³	1	2	yes	—
167	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂³	1	2	yes	—
170	C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₇×C₄⋊C₄	C₂³	1	2	yes	—
174	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
179	C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₄²×C₇	C₂³	1	2	yes	—
181	C₄²×C₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
185	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₇)⋊C₄	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	1	yes	characteristic
195	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
202	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₇	C₂³	1	2	yes	—
205	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₇	C₂³	1	2	yes	—
208	Dic₇⋊C₄	C₂³	1	2	yes	—
209	Dic₇⋊C₄	C₂³	1	2	yes	—
210	Dic₇⋊C₄	C₂³	1	2	yes	—
211	Dic₇⋊C₄	C₂³	1	2	yes	—
212	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₇⋊C₄	C₂³	1	2	yes	—
214	Dic₇⋊C₄	C₂³	1	2	yes	—
215	Dic₇⋊C₄	C₂³	1	2	yes	—
216	Dic₇⋊C₄	C₂³	1	2	yes	—
217	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
218	C₄×Dic₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₇	C₂³	1	2	yes	—
222	C₄×Dic₇	C₂³	1	2	yes	—
223	C₄×Dic₇	C₂³	1	2	yes	—
224	C₄×Dic₇	C₂³	1	2	yes	—
225	C₄×Dic₇	C₂³	1	2	yes	—
226	C₄×Dic₇	C₂³	1	2	yes	—
227	C₄×Dic₇	C₂³	1	2	yes	—
228	#556	—	7	1	no	—
229	#555	—	7	1	no	—
230	#554	—	7	1	no	—
231	#553	—	7	1	no	—
232	#553	—	7	1	no	—
233	#552	—	7	2	no	—
234	#552	—	7	1	no	—
235	#552	D₇	1	1	yes	characteristic, complemented
236	#551	—	7	2	no	—
237	#551	—	7	2	no	—
238	#547	—	7	1	no	—
239	#546	—	7	2	no	—
240	#533	—	7	1	no	—
241	#529	—	7	2	no	—
242	#529	—	7	2	no	—
243	#529	—	7	2	no	—
244	#525	—	7	1	no	—
245	#525	—	7	1	no	—
246	C₄×#41	—	7	1	no	—
247	C₄×#41	—	7	2	no	—
248	C₂×C₄×D₄	—	7	1	no	—
249	C₂×#117	—	7	1	no	—
250	C₂×#117	—	7	1	no	—
251	C₂³×C₇	C₂⁴	1	1	yes	characteristic
252	C₂³×C₇	C₂⁴	1	1	yes	characteristic
253	C₂²×D₇	—	2	2	no	—
254	C₂²×D₇	—	2	2	no	—
255	C₂²×D₇	—	2	2	no	—
256	C₂²×D₇	—	2	2	no	—
257	C₂²×D₇	—	4	1	no	—
258	C₂²×D₇	—	4	1	no	—
259	C₂²×D₇	C₂⁴	1	1	yes	characteristic
260	C₂²×D₇	C₂⁴	1	2	yes	—
261	C₂²×D₇	C₂⁴	1	1	yes	characteristic
262	C₂²×D₇	C₂⁴	1	1	yes	characteristic
263	C₇×Q₈	—	2	2	no	—
264	C₇×D₄	—	2	2	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	2	2	no	—
267	C₂×C₄×C₇	—	2	2	no	—
268	C₂×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²⋊D₇	—	2	4	no	—
278	C₂²⋊D₇	—	2	2	no	—
279	C₂²⋊D₇	—	4	2	no	—
280	C₂²⋊D₇	#41	1	4	yes	complemented
281	C₂×Dic₇	—	2	2	no	—
282	C₂×Dic₇	—	2	2	no	—
283	C₂×Dic₇	—	4	2	no	—
284	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₇	C₂⁴	1	2	yes	—
286	C₂×Dic₇	C₂⁴	1	2	yes	—
287	C₂×Dic₇	C₂⁴	1	2	yes	—
288	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
292	D₂₈	—	2	4	no	—
293	D₂₈	—	2	2	no	—
294	D₂₈	—	2	4	no	—
295	D₂₈	—	2	2	no	—
296	D₂₈	—	4	2	no	—
297	C₄×D₇	—	2	2	no	—
298	C₄×D₇	—	2	2	no	—
299	C₄×D₇	—	2	4	no	—
300	C₄×D₇	—	2	2	no	—
301	C₄×D₇	—	2	2	no	—
302	C₄×D₇	—	2	2	no	—
303	C₄×D₇	—	2	2	no	—
304	C₄×D₇	—	2	4	no	—
305	C₄×D₇	—	2	2	no	—
306	C₄×D₇	—	2	4	no	—
307	C₄×D₇	—	4	1	no	—
308	C₄×D₇	—	4	2	no	—
309	C₄×D₇	—	4	2	no	—
310	C₄×D₇	#41	1	4	yes	complemented
311	Dic₁₄	—	2	4	no	—
312	Dic₁₄	—	4	2	no	—
313	C₂×#41	—	7	1	no	—
314	C₂×#41	—	7	2	no	—
315	C₂²×D₄	—	7	1	no	—
316	C₂³×C₄	—	7	1	no	—
317	C₂³×C₄	—	7	1	no	—
318	C₄⋊Q₈	—	7	1	no	—
319	C₄⋊Q₈	—	7	1	no	—
320	#126	—	7	2	no	—
321	#126	—	7	2	no	—
322	#126	—	7	2	no	—
323	#126	—	7	2	no	—
324	#126	—	7	2	no	—
325	#126	C₂×D₇	1	2	yes	complemented
326	#125	—	7	2	no	—
327	#125	—	7	2	no	—
328	#125	—	7	1	no	—
329	#125	C₂×D₇	1	2	yes	complemented
330	#125	C₂×D₇	1	1	yes	characteristic, complemented
331	#124	—	7	2	no	—
332	#124	—	7	2	no	—
333	#124	—	7	2	no	—
334	#123	—	7	2	no	—
335	#123	—	7	2	no	—
336	#123	—	7	2	no	—
337	#123	—	7	2	no	—
338	#123	—	7	2	no	—
339	#123	—	7	2	no	—
340	#123	—	7	2	no	—
341	#123	C₂×D₇	1	2	yes	—
342	C₂²⋊Q₈	—	7	1	no	—
343	C₂²⋊Q₈	—	7	1	no	—
344	C₂²⋊Q₈	—	7	2	no	—
345	C₂²⋊Q₈	—	7	2	no	—
346	C₂²⋊Q₈	—	7	2	no	—
347	C₂²⋊Q₈	—	7	2	no	—
348	C₂²⋊Q₈	—	7	2	no	—
349	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
350	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
351	#121	—	7	2	no	—
352	#121	—	7	1	no	—
353	#121	—	7	1	no	—
354	#121	—	7	1	no	—
355	#121	—	7	1	no	—
356	#121	—	7	2	no	—
357	#121	—	7	2	no	—
358	#120	—	7	2	no	—
359	#120	—	7	2	no	—
360	C₄×Q₈	—	7	1	no	—
361	C₄×Q₈	—	7	2	no	—
362	C₄×Q₈	—	7	2	no	—
363	C₄×Q₈	—	7	2	no	—
364	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
365	C₄×D₄	—	7	1	no	—
366	C₄×D₄	—	7	1	no	—
367	C₄×D₄	—	7	1	no	—
368	C₄×D₄	—	7	1	no	—
369	C₄×D₄	—	7	2	no	—
370	C₄×D₄	—	7	2	no	—
371	C₄×D₄	—	7	1	no	—
372	C₄×D₄	—	7	2	no	—
373	C₄×D₄	—	7	2	no	—
374	C₄×D₄	—	7	1	no	—
375	C₄×D₄	—	7	1	no	—
376	C₄×D₄	—	7	2	no	—
377	C₄×D₄	—	7	2	no	—
378	C₄×D₄	—	7	2	no	—
379	C₄×D₄	—	7	2	no	—
380	C₄×D₄	—	7	1	no	—
381	C₄×D₄	—	7	2	no	—
382	C₄×D₄	—	7	1	no	—
383	C₄×D₄	C₂×D₇	1	1	yes	characteristic
384	#117	—	7	1	no	—
385	#117	—	7	1	no	—
386	#117	—	7	1	no	—
387	#117	—	7	1	no	—
388	#117	—	7	2	no	—
389	#117	—	7	2	no	—
390	#117	—	7	1	no	—
391	#117	—	7	1	no	—
392	#117	—	7	2	no	—
393	#117	—	7	2	no	—
394	#117	—	7	2	no	—
395	#117	—	7	2	no	—
396	#117	—	7	2	no	—
397	#117	C₂×D₇	1	1	yes	characteristic, complemented
398	#117	C₂×D₇	1	2	yes	complemented
399	C₂×C₄⋊C₄	—	7	1	no	—
400	C₂×C₄⋊C₄	—	7	1	no	—
401	C₂×C₄⋊C₄	—	7	1	no	—
402	C₂×C₄⋊C₄	—	7	1	no	—
403	C₂×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
404	C₂×C₂²⋊C₄	—	7	2	no	—
405	C₂×C₂²⋊C₄	—	7	2	no	—
406	C₂×C₂²⋊C₄	—	7	1	no	—
407	C₂×C₂²⋊C₄	—	7	1	no	—
408	C₂×C₄²	—	7	2	no	—
409	C₂×C₄²	—	7	2	no	—
410	C₂×C₄²	—	7	1	no	—
411	C₂×C₄²	—	7	2	no	—
412	C₂²×C₇	—	2	1	no	—
413	C₂²×C₇	—	2	1	no	—
414	C₂²×C₇	—	2	1	no	—
415	C₂²×C₇	—	2	1	no	—
416	C₂²×C₇	—	2	1	no	—
417	C₂²×C₇	C₂×#41	1	2	yes	—
418	C₂²×C₇	C₂⁵	1	1	yes	characteristic
419	C₂×D₇	—	2	1	no	—
420	C₂×D₇	—	2	1	no	—
421	C₂×D₇	—	2	1	no	—
422	C₂×D₇	—	2	1	no	—
423	C₂×D₇	—	2	1	no	—
424	C₂×D₇	—	2	2	no	—
425	C₂×D₇	—	2	2	no	—
426	C₂×D₇	—	2	1	no	—
427	C₂×D₇	—	2	2	no	—
428	C₂×D₇	—	2	1	no	—
429	C₂×D₇	—	4	4	no	—
430	C₂×D₇	—	4	4	no	—
431	C₂×D₇	C₂×#41	1	2	yes	—
432	C₂×D₇	C₂×#41	1	2	yes	—
433	C₄×C₇	—	2	2	no	—
434	C₄×C₇	—	2	2	no	—
435	C₄×C₇	—	2	1	no	—
436	C₄×C₇	—	2	1	no	—
437	C₄×C₇	—	2	1	no	—
438	C₄×C₇	—	2	2	no	—
439	C₄×C₇	—	2	2	no	—
440	C₄×C₇	—	2	1	no	—
441	C₄×C₇	C₂×#41	1	2	yes	—
442	Dic₇	—	2	2	no	—
443	Dic₇	—	2	1	no	—
444	Dic₇	—	2	1	no	—
445	Dic₇	—	2	1	no	—
446	Dic₇	—	2	2	no	—
447	Dic₇	—	2	2	no	—
448	Dic₇	C₂×#41	1	2	yes	—
449	Dic₇	C₂×#41	1	2	yes	—
450	C₂⁴	—	7	1	no	—
451	C₂⁴	—	7	1	no	—
452	#41	—	14	8	no	—
453	#41	—	14	4	no	—
454	C₂×Q₈	—	7	2	no	—
455	C₂×Q₈	—	7	2	no	—
456	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
457	C₂×D₄	—	7	1	no	—
458	C₂×D₄	—	7	2	no	—
459	C₂×D₄	—	7	1	no	—
460	C₂×D₄	—	7	2	no	—
461	C₂×D₄	—	7	2	no	—
462	C₂×D₄	—	7	2	no	—
463	C₂×D₄	—	7	1	no	—
464	C₂×D₄	—	7	1	no	—
465	C₂×D₄	—	7	2	no	—
466	C₂×D₄	—	14	4	no	—
467	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
468	C₂²×C₄	—	7	1	no	—
469	C₂²×C₄	—	7	1	no	—
470	C₂²×C₄	—	7	1	no	—
471	C₂²×C₄	—	7	2	no	—
472	C₂²×C₄	—	7	1	no	—
473	C₂²×C₄	—	7	2	no	—
474	C₂²×C₄	—	7	1	no	—
475	C₂²×C₄	—	7	2	no	—
476	C₂²×C₄	—	7	2	no	—
477	C₂²×C₄	—	7	1	no	—
478	C₂²×C₄	—	7	1	no	—
479	C₂²×C₄	—	7	1	no	—
480	C₂²×C₄	—	7	1	no	—
481	C₂²×C₄	—	7	1	no	—
482	C₂²×C₄	—	7	1	no	—
483	C₂²×C₄	—	7	2	no	—
484	C₂²×C₄	—	7	2	no	—
485	C₂²×C₄	—	14	4	no	—
486	C₂²×C₄	—	14	4	no	—
487	C₂²×C₄	C₂²×D₇	1	2	yes	—
488	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
490	C₄⋊C₄	—	7	1	no	—
491	C₄⋊C₄	—	7	2	no	—
492	C₄⋊C₄	—	7	2	no	—
493	C₄⋊C₄	—	7	1	no	—
494	C₄⋊C₄	—	7	2	no	—
495	C₄⋊C₄	—	7	2	no	—
496	C₄⋊C₄	—	7	2	no	—
497	C₄⋊C₄	—	7	2	no	—
498	C₄⋊C₄	—	7	2	no	—
499	C₄⋊C₄	—	7	2	no	—
500	C₄⋊C₄	—	7	1	no	—
501	C₄⋊C₄	—	7	1	no	—
502	C₄⋊C₄	—	7	1	no	—
503	C₄⋊C₄	—	7	2	no	—
504	C₄⋊C₄	—	7	1	no	—
505	C₄⋊C₄	—	7	2	no	—
506	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₇	1	2	yes	—
511	C₄⋊C₄	C₂²×D₇	1	2	yes	—
512	C₄⋊C₄	C₂²×D₇	1	2	yes	—
513	C₄⋊C₄	C₂²×D₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₇	1	2	yes	—
516	C₂²⋊C₄	—	7	2	no	—
517	C₂²⋊C₄	—	7	1	no	—
518	C₂²⋊C₄	—	7	1	no	—
519	C₂²⋊C₄	—	7	2	no	—
520	C₂²⋊C₄	—	7	1	no	—
521	C₂²⋊C₄	—	7	2	no	—
522	C₂²⋊C₄	—	7	2	no	—
523	C₂²⋊C₄	—	7	2	no	—
524	C₂²⋊C₄	—	7	2	no	—
525	C₂²⋊C₄	—	7	1	no	—
526	C₂²⋊C₄	—	7	1	no	—
527	C₂²⋊C₄	—	7	1	no	—
528	C₂²⋊C₄	—	7	2	no	—
529	C₂²⋊C₄	—	7	2	no	—
530	C₂²⋊C₄	—	7	2	no	—
531	C₂²⋊C₄	—	7	2	no	—
532	C₂²⋊C₄	—	7	2	no	—
533	C₂²⋊C₄	—	7	2	no	—
534	C₂²⋊C₄	—	7	2	no	—
535	C₂²⋊C₄	—	7	2	no	—
536	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
538	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
539	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
541	C₄²	—	7	2	no	—
542	C₄²	—	7	1	no	—
543	C₄²	—	7	2	no	—
544	C₄²	—	7	1	no	—
545	C₄²	—	7	2	no	—
546	C₄²	—	7	2	no	—
547	C₄²	—	7	2	no	—
548	C₄²	—	7	2	no	—
549	C₄²	—	7	1	no	—
550	C₄²	—	7	2	no	—
551	C₄²	C₂²×D₇	1	2	yes	—
552	C₄²	C₂²×D₇	1	2	yes	—
553	C₄²	C₂²×D₇	1	1	yes	characteristic
554	C₂×C₇	—	2	2	no	—
555	C₂×C₇	—	4	1	no	—
556	C₂×C₇	C₂²×#41	1	1	yes	characteristic
557	C₂×C₇	C₂²×#41	1	1	yes	characteristic
558	C₂×C₇	#585	1	1	yes	characteristic
559	D₇	—	2	2	no	—
560	D₇	—	2	2	no	—
561	D₇	—	4	2	no	—
562	D₇	—	4	1	no	—
563	C₂³	—	7	1	no	—
564	C₂³	—	7	1	no	—
565	C₂³	—	7	1	no	—
566	C₂³	—	7	2	no	—
567	C₂³	—	14	2	no	—
568	C₂³	—	14	2	no	—
569	C₂³	—	14	2	no	—
570	C₂³	—	14	2	no	—
571	C₂³	—	28	1	no	—
572	C₂³	—	28	1	no	—
573	C₂³	C₂³×D₇	1	1	yes	characteristic
574	C₂³	C₂³×D₇	1	1	yes	characteristic
575	Q₈	—	2	2	no	—
576	Q₈	—	14	4	no	—
577	Q₈	—	28	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	7	4	no	—
580	D₄	—	14	2	no	—
581	D₄	—	14	4	no	—
582	D₄	—	14	4	no	—
583	D₄	—	14	2	no	—
584	D₄	—	14	4	no	—
585	D₄	—	14	2	no	—
586	D₄	—	28	2	no	—
587	D₄	—	28	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	7	1	no	—
592	C₂×C₄	—	7	1	no	—
593	C₂×C₄	—	7	4	no	—
594	C₂×C₄	—	7	1	no	—
595	C₂×C₄	—	7	2	no	—
596	C₂×C₄	—	7	1	no	—
597	C₂×C₄	—	7	2	no	—
598	C₂×C₄	—	7	2	no	—
599	C₂×C₄	—	7	1	no	—
600	C₂×C₄	—	14	2	no	—
601	C₂×C₄	—	14	2	no	—
602	C₂×C₄	—	14	2	no	—
603	C₂×C₄	—	14	4	no	—
604	C₂×C₄	—	14	4	no	—
605	C₂×C₄	—	14	2	no	—
606	C₂×C₄	—	14	2	no	—
607	C₂×C₄	—	14	4	no	—
608	C₂×C₄	—	14	2	no	—
609	C₂×C₄	—	14	2	no	—
610	C₂×C₄	—	14	2	no	—
611	C₂×C₄	—	14	2	no	—
612	C₂×C₄	—	28	2	no	—
613	C₂×C₄	—	28	1	no	—
614	C₂×C₄	—	28	2	no	—
615	C₂×C₄	—	28	2	no	—
616	C₂×C₄	C₂³×D₇	1	2	yes	—
617	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₇	1	2	yes	—
619	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₇	1	2	yes	—
621	C₂×C₄	C₂³×D₇	1	2	yes	—
622	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
625	C₇	#3475	1	1	yes	characteristic, complemented, Sylow
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	7	2	no	—
632	C₂²	—	7	2	no	—
633	C₂²	—	14	1	no	—
634	C₂²	—	14	1	no	—
635	C₂²	—	14	1	no	—
636	C₂²	—	14	1	no	—
637	C₂²	—	14	1	no	—
638	C₂²	—	14	2	no	—
639	C₂²	—	14	2	no	—
640	C₂²	—	14	1	no	—
641	C₂²	—	14	2	no	—
642	C₂²	—	14	1	no	—
643	C₂²	—	28	4	no	—
644	C₂²	—	28	4	no	—
645	C₂²	D₇×#41	1	2	yes	—
646	C₂²	C₂⁴×D₇	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	7	2	no	—
656	C₄	—	7	2	no	—
657	C₄	—	14	1	no	—
658	C₄	—	14	1	no	—
659	C₄	—	14	2	no	—
660	C₄	—	14	2	no	—
661	C₄	—	14	2	no	—
662	C₄	—	14	1	no	—
663	C₄	D₇×#41	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	14	2	no	—
667	C₂	—	14	2	no	—
668	C₂	—	28	1	no	—
669	C₂	—	28	2	no	—
670	C₂	C₂×D₇×#41	1	1	yes	characteristic
671	C₂	C₂×D₇×#41	1	1	yes	characteristic
672	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#552	C₂
hypercenter	#552	D₇
hypocenter	C₇	#3475
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₇×#552	C₂	semidirect
2. #90397	C₂	semidirect
3. #90396	C₂	semidirect
4. #90386	C₂	semidirect
5. #90384	C₂	semidirect
6. #90382	C₂	semidirect
7. #90379	C₂	semidirect
8. #90345	C₂	semidirect
9. #90340	C₂	semidirect
10. #90332	C₂	semidirect
11. #90326	C₂	semidirect
12. #90318	C₂	semidirect
13. #90318	C₂	semidirect
14. #90272	C₂	semidirect
15. C₄×#1161	C₂	semidirect
16. #90256	C₂	semidirect
17. C₄×D₄×D₇	C₂	semidirect
18. #90223	C₂	semidirect
19. #90218	C₂	semidirect
20. #90213	C₂	semidirect
21. D₇×#117	C₂	semidirect
22. #90198	C₂	semidirect
23. C₂×#6455	C₂	semidirect
29. C₇×#126	C₂²	semidirect
30. C₇×#125	C₂²	semidirect
31. C₇×#125	C₂²	semidirect
33. C₇×C₂²⋊Q₈	C₂²	semidirect
34. C₇×C₂²⋊Q₈	C₂²	semidirect
35. C₄×C₇×Q₈	C₂²	semidirect
37. C₇×#117	C₂²	semidirect
38. C₇×#117	C₂²	semidirect
39. C₂×C₇×C₄⋊C₄	C₂²	semidirect
40. #6509	C₂²	semidirect
41. #6509	C₂²	semidirect
42. Q₈×Dic₇	C₂²	semidirect
45. #6493	C₂²	semidirect
46. #6493	C₂²	semidirect
47. #6492	C₂²	semidirect
51. #6489	C₂²	semidirect
52. C₂×C₄⋊Dic₇	C₂²	semidirect
53. C₂×C₄×Dic₇	C₂²	semidirect
54. #6461	C₂²	semidirect
55. #6461	C₂²	semidirect
56. #6461	C₂²	semidirect
57. #6460	C₂²	semidirect
60. #6459	C₂²	semidirect
62. #6458	C₂²	semidirect
63. #6458	C₂²	semidirect
67. #6457	C₂²	semidirect
68. #6457	C₂²	semidirect
71. #6456	C₂²	semidirect
72. #6456	C₂²	semidirect
73. #6456	C₂²	semidirect
74. #6456	C₂²	semidirect
79. #6455	C₂²	semidirect
80. #6455	C₂²	semidirect
81. #6455	C₂²	semidirect
82. #6455	C₂²	semidirect
84. D₇×C₄⋊C₄	C₂²	semidirect
85. D₇×C₄⋊C₄	C₂²	semidirect
86. #6452	C₂²	semidirect
87. #6452	C₂²	semidirect
88. #6451	C₂²	semidirect
89. #6451	C₂²	semidirect
90. #6450	C₂²	semidirect
91. #6450	C₂²	semidirect
92. #6450	C₂²	semidirect
94. #6448	C₂²	semidirect
96. #6446	C₂²	semidirect
102. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
103. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
104. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
108. #6442	C₂²	semidirect
109. #6441	C₂²	semidirect
110. #6440	C₂²	semidirect
111. #6439	C₂²	semidirect
112. #6438	C₂²	semidirect
115. C₄×D₂₈	C₂²	semidirect
117. #6435	C₂²	semidirect
118. #6435	C₂²	semidirect
120. C₄²×D₇	C₂²	semidirect
121. C₄²×D₇	C₂²	semidirect
122. #6433	C₂²	semidirect
235. #552	D₇	semidirect
280. C₂²⋊D₇	#41	semidirect
310. C₄×D₇	#41	semidirect
325. #126	C₂×D₇	semidirect
329. #125	C₂×D₇	semidirect
330. #125	C₂×D₇	semidirect
349. C₂²⋊Q₈	C₂×D₇	semidirect
350. C₂²⋊Q₈	C₂×D₇	semidirect
364. C₄×Q₈	C₂×D₇	semidirect
397. #117	C₂×D₇	semidirect
398. #117	C₂×D₇	semidirect
403. C₂×C₄⋊C₄	C₂×D₇	semidirect
625. C₇	#3475	semidirect

Maximal subgroups

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

subgroup	index
C₇×#552	2
#90397	2
#90396	2
#90386	2
#90384	2
#90382	2
#90379	2
#90345	2
#90340	2
#90332	2
#90326	2
#90318	2
#90272	2
C₄×#1161	2
#90256	2
C₄×D₄×D₇	2
#90223	2
#90218	2
#90213	2
D₇×#117	2
#90198	2
C₂×#6455	2
#3475	7