Subgroups — #11743600

Order 896.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#90424	C₂	1	1	yes	maximal, characteristic, complemented
3	#90416	C₂	1	1	yes	maximal, characteristic, complemented
4	#90402	C₂	1	2	yes	maximal, complemented
5	#90400	C₂	1	2	yes	maximal, complemented
6	#90369	C₂	1	2	yes	maximal, complemented
7	#90365	C₂	1	1	yes	maximal, characteristic, complemented
8	#90365	C₂	1	2	yes	maximal, complemented
9	#90359	C₂	1	1	yes	maximal, characteristic, complemented
10	#90357	C₂	1	2	yes	maximal, complemented
11	#90345	C₂	1	2	yes	maximal, complemented
12	#90335	C₂	1	2	yes	maximal, complemented
13	#90322	C₂	1	1	yes	maximal, characteristic, complemented
14	#90321	C₂	1	1	yes	maximal, characteristic, complemented
15	#90320	C₂	1	2	yes	maximal, complemented
16	#90300	C₂	1	1	yes	maximal, characteristic, complemented
17	#90290	C₂	1	1	yes	maximal, characteristic, complemented
18	#90268	C₂	1	1	yes	maximal, characteristic, complemented
19	#90259	C₂	1	1	yes	maximal, characteristic, complemented
20	#90245	C₂	1	1	yes	maximal, characteristic, complemented
21	#90244	C₂	1	1	yes	maximal, characteristic, complemented
22	#90219	C₂	1	1	yes	maximal, characteristic, complemented
23	#90216	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#1161	C₂²	1	2	yes	complemented
25	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
26	C₂×#1161	C₂²	1	1	yes	characteristic, complemented
27	C₂×#1159	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₇	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₇	C₂²	1	2	yes	—
30	C₂×#1157	C₂²	1	1	yes	characteristic, complemented
31	C₂×#1157	C₂²	1	2	yes	complemented
32	C₂²×D₂₈	C₂²	1	1	yes	characteristic
33	C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₇×#126	C₂²	1	2	yes	complemented
35	C₇×#124	C₂²	1	2	yes	complemented
36	C₇×#124	C₂²	1	1	yes	characteristic, complemented
37	C₇×#123	C₂²	1	2	yes	complemented
38	C₇×C₂²⋊Q₈	C₂²	1	2	yes	complemented
39	C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₇×#121	C₂²	1	1	yes	characteristic
41	C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₇×#117	C₂²	1	1	yes	characteristic, complemented
44	#6510	C₂²	1	1	yes	characteristic
45	#6510	C₂²	1	2	yes	complemented
46	#6510	C₂²	1	2	yes	complemented
47	#6509	C₂²	1	2	yes	complemented
48	#6507	C₂²	1	1	yes	characteristic, complemented
49	#6503	C₂²	1	1	yes	characteristic
50	#6503	C₂²	1	1	yes	characteristic, complemented
51	#6503	C₂²	1	2	yes	complemented
52	#6502	C₂²	1	2	yes	complemented
53	#6500	C₂²	1	2	yes	—
54	#6493	C₂²	1	2	yes	complemented
55	#6493	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
59	#6461	C₂²	1	2	yes	complemented
60	#6461	C₂²	1	1	yes	characteristic, complemented
61	#6461	C₂²	1	2	yes	complemented
62	#6460	C₂²	1	1	yes	characteristic, complemented
63	#6459	C₂²	1	1	yes	characteristic, complemented
64	#6459	C₂²	1	2	yes	complemented
65	#6458	C₂²	1	1	yes	characteristic
66	#6458	C₂²	1	1	yes	characteristic
67	#6458	C₂²	1	2	yes	complemented
68	#6458	C₂²	1	2	yes	complemented
69	#6458	C₂²	1	2	yes	complemented
70	#6458	C₂²	1	1	yes	characteristic, complemented
71	#6458	C₂²	1	2	yes	complemented
72	#6458	C₂²	1	2	yes	complemented
73	#6458	C₂²	1	2	yes	complemented
74	#6457	C₂²	1	2	yes	complemented
75	#6457	C₂²	1	1	yes	characteristic, complemented
76	#6457	C₂²	1	2	yes	complemented
77	#6457	C₂²	1	2	yes	complemented
78	#6456	C₂²	1	1	yes	characteristic
79	#6456	C₂²	1	2	yes	complemented
80	#6456	C₂²	1	1	yes	characteristic, complemented
81	#6456	C₂²	1	1	yes	characteristic, complemented
82	D₇×C₄⋊C₄	C₂²	1	2	yes	complemented
83	#6452	C₂²	1	1	yes	characteristic, complemented
84	#6450	C₂²	1	1	yes	characteristic, complemented
85	#6449	C₂²	1	2	yes	complemented
86	#6448	C₂²	1	1	yes	characteristic
87	#6447	C₂²	1	2	yes	—
88	#6447	C₂²	1	1	yes	characteristic
89	#6447	C₂²	1	2	yes	—
90	#6447	C₂²	1	2	yes	complemented
91	#6447	C₂²	1	2	yes	complemented
92	#6447	C₂²	1	2	yes	complemented
93	#6447	C₂²	1	2	yes	complemented
94	#6447	C₂²	1	2	yes	complemented
95	#6447	C₂²	1	2	yes	complemented
96	#6447	C₂²	1	2	yes	complemented
97	#6446	C₂²	1	2	yes	complemented
98	#6446	C₂²	1	1	yes	characteristic, complemented
99	#6445	C₂²	1	2	yes	—
100	#6445	C₂²	1	2	yes	complemented
101	#6445	C₂²	1	2	yes	complemented
102	#6445	C₂²	1	2	yes	complemented
103	#6445	C₂²	1	2	yes	complemented
104	#6445	C₂²	1	2	yes	complemented
105	#6445	C₂²	1	2	yes	complemented
106	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
107	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
108	(C₂²⋊D₇)⋊C₄	C₂²	1	2	yes	complemented
109	D₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
110	#6442	C₂²	1	1	yes	characteristic, complemented
111	#6439	C₂²	1	2	yes	complemented
112	#6438	C₂²	1	1	yes	characteristic
113	#6438	C₂²	1	1	yes	characteristic, complemented
114	#6437	C₂²	1	1	yes	characteristic
115	#6437	C₂²	1	2	yes	complemented
116	#6437	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₂₈	C₂²	1	2	yes	complemented
118	C₄×D₂₈	C₂²	1	1	yes	characteristic, complemented
119	#6435	C₂²	1	2	yes	complemented
120	#6435	C₂²	1	1	yes	characteristic, complemented
121	C₄²×D₇	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
123	#3546	—	7	1	no	maximal, Sylow
124	C₂³×D₇	C₂³	1	2	yes	—
125	C₂³×D₇	C₂³	1	2	yes	—
126	C₂×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂×C₇×Q₈	C₂³	1	2	yes	—
128	C₂×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×D₄	C₂³	1	2	yes	—
130	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₇	C₂³	1	2	yes	—
141	C₂²×Dic₇	C₂³	1	2	yes	—
142	#1161	—	4	4	no	—
143	#1161	—	4	2	no	—
144	#1161	—	4	2	no	—
145	#1159	—	4	2	no	—
146	D₄×D₇	—	4	2	no	—
147	D₄×D₇	—	4	4	no	—
148	#1157	—	4	4	no	—
149	#1157	—	4	2	no	—
150	C₂×D₂₈	—	4	2	no	—
151	C₂×D₂₈	C₂³	1	1	yes	characteristic
152	C₂×D₂₈	C₂³	1	1	yes	characteristic
153	C₂×D₂₈	C₂³	1	1	yes	characteristic
154	C₂×D₂₈	C₂³	1	1	yes	characteristic
155	C₂×D₂₈	C₂³	1	2	yes	—
156	C₂×D₂₈	C₂³	1	2	yes	—
157	C₂×D₂₈	C₂³	1	2	yes	—
158	C₂×D₂₈	C₂³	1	2	yes	—
159	C₂×D₂₈	C₂³	1	2	yes	—
160	C₂×D₂₈	C₂³	1	2	yes	—
161	C₂×D₂₈	C₂³	1	2	yes	—
162	C₂×D₂₈	C₂³	1	2	yes	—
163	C₂×D₂₈	C₂³	1	2	yes	—
164	C₂×D₂₈	C₂³	1	2	yes	—
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	1	yes	characteristic
171	C₂×C₄×D₇	C₂³	1	2	yes	—
172	C₂×C₄×D₇	C₂³	1	2	yes	—
173	C₂×C₄×D₇	C₂³	1	2	yes	—
174	C₂×C₄×D₇	C₂³	1	2	yes	—
175	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
176	C₂×Dic₁₄	C₂³	1	1	yes	characteristic
177	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₇×C₄⋊C₄	C₂³	1	2	yes	—
180	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₇×C₄⋊C₄	C₂³	1	2	yes	—
184	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₄²×C₇	C₂³	1	2	yes	—
194	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
195	C₂²⋊Dic₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
200	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
211	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
213	(C₂×D₇)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₇)⋊C₄	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	2	yes	—
218	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
219	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
220	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
221	Dic₇⋊C₄	C₂³	1	2	yes	—
222	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
223	Dic₇⋊C₄	C₂³	1	2	yes	—
224	Dic₇⋊C₄	C₂³	1	2	yes	—
225	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
226	Dic₇⋊C₄	C₂³	1	1	yes	characteristic
227	C₄×Dic₇	C₂³	1	1	yes	characteristic
228	C₄×Dic₇	C₂³	1	1	yes	characteristic
229	C₄×Dic₇	C₂³	1	1	yes	characteristic
230	C₄×Dic₇	C₂³	1	1	yes	characteristic
231	C₄×Dic₇	C₂³	1	2	yes	—
232	#560	—	7	2	no	—
233	#560	—	7	2	no	—
234	#556	—	7	1	no	—
235	#553	—	7	2	no	—
236	#550	—	7	1	no	—
237	#550	—	7	1	no	—
238	#550	—	7	1	no	—
239	#547	—	7	1	no	—
240	#546	—	7	2	no	—
241	#546	—	7	1	no	—
242	#546	—	7	1	no	—
243	D₄²	—	7	1	no	—
244	#542	—	7	1	no	—
245	#542	D₇	1	1	yes	characteristic, complemented
246	#538	—	7	2	no	—
247	#538	—	7	2	no	—
248	#537	—	7	2	no	—
249	#535	—	7	1	no	—
250	#535	—	7	2	no	—
251	#535	—	7	1	no	—
252	#532	—	7	1	no	—
253	#532	—	7	1	no	—
254	#529	—	7	1	no	—
255	C₂³×C₇	C₂⁴	1	1	yes	characteristic
256	C₂³×C₇	C₂⁴	1	2	yes	—
257	C₂²×D₇	—	4	2	no	—
258	C₂²×D₇	—	4	2	no	—
259	C₂²×D₇	—	4	2	no	—
260	C₂²×D₇	—	4	2	no	—
261	C₂²×D₇	—	4	2	no	—
262	C₂²×D₇	—	4	2	no	—
263	C₂²×D₇	C₂⁴	1	2	yes	—
264	C₂²×D₇	C₂⁴	1	1	yes	characteristic
265	C₂²×D₇	C₂⁴	1	2	yes	—
266	C₂²×D₇	C₂⁴	1	1	yes	characteristic
267	C₂²×D₇	C₂⁴	1	2	yes	—
268	C₇×Q₈	—	2	2	no	—
269	C₇×Q₈	—	4	2	no	—
270	C₇×D₄	—	2	2	no	—
271	C₇×D₄	—	4	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	4	2	no	—
274	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₇	C₂⁴	1	2	yes	—
282	C₂×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₂²⋊D₇	—	2	4	no	—
284	C₂²⋊D₇	—	2	2	no	—
285	C₂²⋊D₇	—	4	2	no	—
286	C₂²⋊D₇	—	4	2	no	—
287	C₂²⋊D₇	—	4	2	no	—
288	C₂²⋊D₇	—	4	2	no	—
289	C₂²⋊D₇	—	4	2	no	—
290	C₂²⋊D₇	—	4	1	no	—
291	C₂²⋊D₇	—	4	2	no	—
292	C₂×Dic₇	—	4	2	no	—
293	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
294	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
299	C₂×Dic₇	C₂⁴	1	1	yes	characteristic
300	D₂₈	—	2	2	no	—
301	D₂₈	—	2	2	no	—
302	D₂₈	—	2	2	no	—
303	D₂₈	—	4	2	no	—
304	D₂₈	—	4	2	no	—
305	D₂₈	—	4	1	no	—
306	D₂₈	—	4	2	no	—
307	D₂₈	—	4	2	no	—
308	D₂₈	—	4	2	no	—
309	D₂₈	—	4	2	no	—
310	D₂₈	—	4	2	no	—
311	D₂₈	—	4	2	no	—
312	D₂₈	—	4	2	no	—
313	D₂₈	—	4	2	no	—
314	C₄×D₇	—	2	2	no	—
315	C₄×D₇	—	2	2	no	—
316	C₄×D₇	—	2	4	no	—
317	C₄×D₇	—	2	4	no	—
318	C₄×D₇	—	2	2	no	—
319	C₄×D₇	—	4	1	no	—
320	C₄×D₇	—	4	2	no	—
321	C₄×D₇	—	4	2	no	—
322	C₄×D₇	—	4	2	no	—
323	C₄×D₇	—	4	2	no	—
324	Dic₁₄	—	2	2	no	—
325	Dic₁₄	—	2	2	no	—
326	C₂×#41	—	7	2	no	—
327	C₂×#41	—	7	1	no	—
328	C₂×#41	—	7	1	no	—
329	C₂×#41	—	7	1	no	—
330	C₂×#41	—	7	1	no	—
331	C₂×#41	—	7	2	no	—
332	C₂²×D₄	—	7	2	no	—
333	C₂²×D₄	—	7	1	no	—
334	C₂²×D₄	—	7	1	no	—
335	C₄⋊Q₈	—	7	1	no	—
336	C₄⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
337	#127	—	7	1	no	—
338	#127	—	7	1	no	—
339	#127	—	7	2	no	—
340	#127	—	7	1	no	—
341	#127	—	7	1	no	—
342	#127	—	7	2	no	—
343	#126	—	7	1	no	—
344	#126	—	7	2	no	—
345	#126	—	7	2	no	—
346	#126	—	7	1	no	—
347	#126	—	7	2	no	—
348	#126	C₂×D₇	1	2	yes	complemented
349	#125	—	7	1	no	—
350	#124	—	7	2	no	—
351	#124	—	7	2	no	—
352	#124	—	7	1	no	—
353	#124	—	7	1	no	—
354	#124	—	7	1	no	—
355	#124	—	7	1	no	—
356	#124	C₂×D₇	1	1	yes	characteristic, complemented
357	#124	C₂×D₇	1	2	yes	complemented
358	#123	—	7	1	no	—
359	#123	—	7	2	no	—
360	#123	—	7	2	no	—
361	#123	—	7	2	no	—
362	#123	—	7	1	no	—
363	#123	—	7	2	no	—
364	#123	—	7	2	no	—
365	#123	C₂×D₇	1	2	yes	complemented
366	C₂²⋊Q₈	—	7	2	no	—
367	C₂²⋊Q₈	—	7	1	no	—
368	C₂²⋊Q₈	—	7	2	no	—
369	C₂²⋊Q₈	—	7	1	no	—
370	C₂²⋊Q₈	C₂×D₇	1	2	yes	complemented
371	C₂²⋊Q₈	C₂×D₇	1	1	yes	characteristic, complemented
372	#121	—	7	2	no	—
373	#121	—	7	2	no	—
374	#121	—	7	2	no	—
375	#121	—	7	1	no	—
376	#121	—	7	1	no	—
377	#121	—	7	2	no	—
378	#121	—	7	2	no	—
379	#121	—	7	2	no	—
380	#121	—	7	2	no	—
381	#121	—	7	2	no	—
382	#121	—	7	2	no	—
383	#121	—	7	1	no	—
384	#121	—	7	1	no	—
385	#121	—	7	2	no	—
386	#121	—	7	2	no	—
387	#121	—	7	2	no	—
388	#121	—	7	2	no	—
389	#121	—	7	2	no	—
390	#121	—	7	2	no	—
391	#121	—	7	2	no	—
392	#121	—	7	2	no	—
393	#121	—	7	2	no	—
394	#121	C₂×D₇	1	1	yes	characteristic
395	#120	—	7	2	no	—
396	#120	—	7	2	no	—
397	#120	—	7	2	no	—
398	#120	—	7	2	no	—
399	#120	—	7	2	no	—
400	#120	—	7	2	no	—
401	#120	—	7	2	no	—
402	#120	—	7	2	no	—
403	C₄×Q₈	—	7	1	no	—
404	C₄×Q₈	—	7	1	no	—
405	C₄×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
406	C₄×D₄	—	7	1	no	—
407	C₄×D₄	—	7	1	no	—
408	C₄×D₄	—	7	1	no	—
409	C₄×D₄	—	7	2	no	—
410	C₄×D₄	—	7	1	no	—
411	C₄×D₄	—	7	1	no	—
412	C₄×D₄	—	7	2	no	—
413	C₄×D₄	—	7	2	no	—
414	C₄×D₄	—	7	2	no	—
415	C₄×D₄	—	7	1	no	—
416	C₄×D₄	—	7	2	no	—
417	C₄×D₄	C₂×D₇	1	1	yes	characteristic, complemented
418	#117	—	7	1	no	—
419	#117	—	7	2	no	—
420	#117	C₂×D₇	1	1	yes	characteristic, complemented
421	C₂×C₄⋊C₄	—	7	2	no	—
422	C₂×C₂²⋊C₄	—	7	2	no	—
423	C₂×C₂²⋊C₄	—	7	2	no	—
424	C₂×C₄²	—	7	1	no	—
425	C₂²×C₇	—	2	2	no	—
426	C₂²×C₇	—	2	2	no	—
427	C₂²×C₇	—	2	1	no	—
428	C₂²×C₇	—	2	1	no	—
429	C₂²×C₇	—	2	2	no	—
430	C₂²×C₇	—	2	1	no	—
431	C₂²×C₇	C₂⁵	1	1	yes	characteristic
432	C₂×D₇	—	2	1	no	—
433	C₂×D₇	—	2	2	no	—
434	C₂×D₇	—	2	1	no	—
435	C₂×D₇	—	2	1	no	—
436	C₂×D₇	—	2	2	no	—
437	C₂×D₇	—	2	2	no	—
438	C₂×D₇	—	2	2	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	—	2	2	no	—
444	C₂×D₇	—	2	2	no	—
445	C₂×D₇	—	2	2	no	—
446	C₂×D₇	—	2	1	no	—
447	C₂×D₇	—	8	4	no	—
448	C₂×D₇	—	8	4	no	—
449	C₄×C₇	—	2	1	no	—
450	C₄×C₇	—	2	2	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	—	2	1	no	—
457	C₄×C₇	H(5,𝔽₂)	1	2	yes	—
458	Dic₇	—	2	1	no	—
459	Dic₇	—	2	2	no	—
460	Dic₇	—	2	1	no	—
461	Dic₇	—	2	1	no	—
462	Dic₇	—	2	1	no	—
463	Dic₇	—	2	1	no	—
464	Dic₇	H(5,𝔽₂)	1	2	yes	—
465	C₂⁴	—	7	2	no	—
466	C₂⁴	—	7	2	no	—
467	#41	—	28	2	no	—
468	#41	—	28	4	no	—
469	#41	—	28	4	no	—
470	#41	—	28	2	no	—
471	#41	—	28	2	no	—
472	#41	—	28	2	no	—
473	C₂×Q₈	—	7	1	no	—
474	C₂×Q₈	—	7	1	no	—
475	C₂×Q₈	C₂²×D₇	1	1	yes	characteristic
476	C₂×Q₈	C₂²×D₇	1	2	yes	—
477	C₂×D₄	—	7	1	no	—
478	C₂×D₄	—	7	2	no	—
479	C₂×D₄	—	7	2	no	—
480	C₂×D₄	—	7	1	no	—
481	C₂×D₄	—	7	2	no	—
482	C₂×D₄	—	7	2	no	—
483	C₂×D₄	—	7	2	no	—
484	C₂×D₄	—	7	2	no	—
485	C₂×D₄	—	7	2	no	—
486	C₂×D₄	—	7	1	no	—
487	C₂×D₄	—	7	1	no	—
488	C₂×D₄	—	7	1	no	—
489	C₂×D₄	—	7	2	no	—
490	C₂×D₄	—	7	1	no	—
491	C₂×D₄	—	7	2	no	—
492	C₂×D₄	—	7	2	no	—
493	C₂×D₄	—	7	2	no	—
494	C₂×D₄	—	7	2	no	—
495	C₂×D₄	—	7	2	no	—
496	C₂×D₄	—	7	2	no	—
497	C₂×D₄	—	7	2	no	—
498	C₂×D₄	—	7	2	no	—
499	C₂×D₄	—	7	2	no	—
500	C₂×D₄	—	28	2	no	—
501	C₂×D₄	—	28	2	no	—
502	C₂×D₄	—	28	4	no	—
503	C₂×D₄	C₂²×D₇	1	1	yes	characteristic
504	C₂×D₄	C₂²×D₇	1	2	yes	—
505	C₂²×C₄	—	7	2	no	—
506	C₂²×C₄	—	7	1	no	—
507	C₂²×C₄	—	7	1	no	—
508	C₂²×C₄	—	7	2	no	—
509	C₂²×C₄	—	7	2	no	—
510	C₂²×C₄	—	7	1	no	—
511	C₂²×C₄	—	7	1	no	—
512	C₂²×C₄	—	7	2	no	—
513	C₂²×C₄	—	7	2	no	—
514	C₂²×C₄	—	7	2	no	—
515	C₂²×C₄	—	7	2	no	—
516	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
517	C₂²×C₄	C₂²×D₇	1	2	yes	—
518	C₄⋊C₄	—	7	1	no	—
519	C₄⋊C₄	—	7	2	no	—
520	C₄⋊C₄	—	7	1	no	—
521	C₄⋊C₄	—	7	1	no	—
522	C₄⋊C₄	—	7	1	no	—
523	C₄⋊C₄	—	7	1	no	—
524	C₄⋊C₄	—	7	2	no	—
525	C₄⋊C₄	—	7	2	no	—
526	C₄⋊C₄	—	7	1	no	—
527	C₄⋊C₄	—	7	2	no	—
528	C₄⋊C₄	—	7	1	no	—
529	C₄⋊C₄	—	7	1	no	—
530	C₄⋊C₄	C₂²×D₇	1	2	yes	—
531	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₇	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₇	1	2	yes	—
536	C₄⋊C₄	C₂²×D₇	1	2	yes	—
537	C₂²⋊C₄	—	7	1	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	2	no	—
544	C₂²⋊C₄	—	7	2	no	—
545	C₂²⋊C₄	—	7	2	no	—
546	C₂²⋊C₄	—	7	1	no	—
547	C₂²⋊C₄	—	7	1	no	—
548	C₂²⋊C₄	—	7	2	no	—
549	C₂²⋊C₄	—	7	2	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	1	no	—
556	C₂²⋊C₄	—	7	1	no	—
557	C₂²⋊C₄	—	7	2	no	—
558	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₇	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₇	1	2	yes	—
565	C₄²	—	7	1	no	—
566	C₄²	—	7	1	no	—
567	C₄²	—	7	1	no	—
568	C₄²	—	7	1	no	—
569	C₄²	—	7	2	no	—
570	C₄²	C₂²×D₇	1	1	yes	characteristic
571	C₄²	C₂²×D₇	1	2	yes	—
572	C₄²	C₂²×D₇	1	1	yes	characteristic
573	C₂×C₇	—	4	1	no	—
574	C₂×C₇	—	4	2	no	—
575	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₇	#585	1	1	yes	characteristic
578	D₇	—	4	1	no	—
579	D₇	—	4	2	no	—
580	D₇	—	4	2	no	—
581	D₇	—	4	2	no	—
582	D₇	—	4	1	no	—
583	C₂³	—	7	1	no	—
584	C₂³	—	7	2	no	—
585	C₂³	—	7	2	no	—
586	C₂³	—	7	1	no	—
587	C₂³	—	7	2	no	—
588	C₂³	—	28	2	no	—
589	C₂³	—	28	2	no	—
590	C₂³	—	28	2	no	—
591	C₂³	—	28	2	no	—
592	C₂³	—	28	2	no	—
593	C₂³	—	28	2	no	—
594	C₂³	C₂³×D₇	1	1	yes	characteristic
595	C₂³	C₂³×D₇	1	2	yes	—
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	14	2	no	—
599	Q₈	—	14	2	no	—
600	D₄	—	2	2	no	—
601	D₄	—	4	2	no	—
602	D₄	—	14	2	no	—
603	D₄	—	14	4	no	—
604	D₄	—	14	2	no	—
605	D₄	—	14	2	no	—
606	D₄	—	14	2	no	—
607	D₄	—	28	2	no	—
608	D₄	—	28	1	no	—
609	D₄	—	28	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	D₄	—	28	2	no	—
616	D₄	—	28	2	no	—
617	D₄	—	28	2	no	—
618	D₄	—	28	2	no	—
619	D₄	—	28	2	no	—
620	D₄	—	28	1	no	—
621	D₄	—	28	2	no	—
622	D₄	—	28	2	no	—
623	D₄	—	28	2	no	—
624	D₄	—	28	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	7	1	no	—
628	C₂×C₄	—	7	1	no	—
629	C₂×C₄	—	7	1	no	—
630	C₂×C₄	—	7	1	no	—
631	C₂×C₄	—	7	2	no	—
632	C₂×C₄	—	7	1	no	—
633	C₂×C₄	—	7	1	no	—
634	C₂×C₄	—	14	4	no	—
635	C₂×C₄	—	14	4	no	—
636	C₂×C₄	—	14	2	no	—
637	C₂×C₄	—	14	2	no	—
638	C₂×C₄	—	14	2	no	—
639	C₂×C₄	—	28	1	no	—
640	C₂×C₄	—	28	2	no	—
641	C₂×C₄	—	28	2	no	—
642	C₂×C₄	—	28	2	no	—
643	C₂×C₄	—	28	2	no	—
644	C₂×C₄	—	28	2	no	—
645	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₇	1	2	yes	—
648	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₇	1	2	yes	—
651	C₂×C₄	C₂³×D₇	1	2	yes	—
652	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₇	1	1	yes	characteristic
654	C₇	#3546	1	1	yes	characteristic, complemented, Sylow
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	14	1	no	—
662	C₂²	—	14	1	no	—
663	C₂²	—	14	2	no	—
664	C₂²	—	14	2	no	—
665	C₂²	—	14	2	no	—
666	C₂²	—	14	1	no	—
667	C₂²	—	14	2	no	—
668	C₂²	—	14	2	no	—
669	C₂²	—	14	2	no	—
670	C₂²	—	14	1	no	—
671	C₂²	—	14	1	no	—
672	C₂²	—	14	2	no	—
673	C₂²	—	14	2	no	—
674	C₂²	—	14	1	no	—
675	C₂²	—	14	2	no	—
676	C₂²	—	56	4	no	—
677	C₂²	—	56	4	no	—
678	C₂²	C₂⁴×D₇	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	7	2	no	—
688	C₄	—	14	1	no	—
689	C₄	—	14	1	no	—
690	C₄	—	14	2	no	—
691	C₄	—	14	1	no	—
692	C₄	—	14	1	no	—
693	C₄	—	14	1	no	—
694	C₄	#6553	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	28	1	no	—
698	C₂	—	28	2	no	—
699	C₂	—	28	2	no	—
700	C₂	—	28	1	no	—
701	C₂	—	28	2	no	—
702	C₂	C₂×#6553	1	1	yes	characteristic
703	C₂	D₇×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂	#90620	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇
commutator, socle, cosocle	C₂²×C₇	C₂⁵
Fitting	C₇×#542	C₂
hypercenter	#542	D₇
hypocenter	C₇	#3546
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₇×#542	C₂	semidirect
2. #90424	C₂	semidirect
3. #90416	C₂	semidirect
4. #90402	C₂	semidirect
5. #90400	C₂	semidirect
6. #90369	C₂	semidirect
7. #90365	C₂	semidirect
8. #90365	C₂	semidirect
9. #90359	C₂	semidirect
10. #90357	C₂	semidirect
11. #90345	C₂	semidirect
12. #90335	C₂	semidirect
13. #90322	C₂	semidirect
14. #90321	C₂	semidirect
15. #90320	C₂	semidirect
16. #90300	C₂	semidirect
17. #90290	C₂	semidirect
18. #90268	C₂	semidirect
19. #90259	C₂	semidirect
20. #90245	C₂	semidirect
21. #90244	C₂	semidirect
22. #90219	C₂	semidirect
23. #90216	C₂	semidirect
24. C₂×#1161	C₂²	semidirect
25. C₂×#1161	C₂²	semidirect
26. C₂×#1161	C₂²	semidirect
27. C₂×#1159	C₂²	semidirect
30. C₂×#1157	C₂²	semidirect
31. C₂×#1157	C₂²	semidirect
33. C₇×C₄⋊Q₈	C₂²	semidirect
34. C₇×#126	C₂²	semidirect
35. C₇×#124	C₂²	semidirect
36. C₇×#124	C₂²	semidirect
37. C₇×#123	C₂²	semidirect
38. C₇×C₂²⋊Q₈	C₂²	semidirect
39. C₇×C₂²⋊Q₈	C₂²	semidirect
41. C₄×C₇×Q₈	C₂²	semidirect
42. C₄×C₇×D₄	C₂²	semidirect
43. C₇×#117	C₂²	semidirect
45. #6510	C₂²	semidirect
46. #6510	C₂²	semidirect
47. #6509	C₂²	semidirect
48. #6507	C₂²	semidirect
50. #6503	C₂²	semidirect
51. #6503	C₂²	semidirect
52. #6502	C₂²	semidirect
54. #6493	C₂²	semidirect
55. #6493	C₂²	semidirect
57. C₄×C₂²⋊D₇	C₂²	semidirect
58. C₂×(C₂×D₇)⋊C₄	C₂²	semidirect
59. #6461	C₂²	semidirect
60. #6461	C₂²	semidirect
61. #6461	C₂²	semidirect
62. #6460	C₂²	semidirect
63. #6459	C₂²	semidirect
64. #6459	C₂²	semidirect
67. #6458	C₂²	semidirect
68. #6458	C₂²	semidirect
69. #6458	C₂²	semidirect
70. #6458	C₂²	semidirect
71. #6458	C₂²	semidirect
72. #6458	C₂²	semidirect
73. #6458	C₂²	semidirect
74. #6457	C₂²	semidirect
75. #6457	C₂²	semidirect
76. #6457	C₂²	semidirect
77. #6457	C₂²	semidirect
79. #6456	C₂²	semidirect
80. #6456	C₂²	semidirect
81. #6456	C₂²	semidirect
82. D₇×C₄⋊C₄	C₂²	semidirect
83. #6452	C₂²	semidirect
84. #6450	C₂²	semidirect
85. #6449	C₂²	semidirect
90. #6447	C₂²	semidirect
91. #6447	C₂²	semidirect
92. #6447	C₂²	semidirect
93. #6447	C₂²	semidirect
94. #6447	C₂²	semidirect
95. #6447	C₂²	semidirect
96. #6447	C₂²	semidirect
97. #6446	C₂²	semidirect
98. #6446	C₂²	semidirect
100. #6445	C₂²	semidirect
101. #6445	C₂²	semidirect
102. #6445	C₂²	semidirect
103. #6445	C₂²	semidirect
104. #6445	C₂²	semidirect
105. #6445	C₂²	semidirect
106. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
108. (C₂²⋊D₇)⋊C₄	C₂²	semidirect
109. D₇×C₂²⋊C₄	C₂²	semidirect
110. #6442	C₂²	semidirect
111. #6439	C₂²	semidirect
113. #6438	C₂²	semidirect
115. #6437	C₂²	semidirect
116. #6437	C₂²	semidirect
117. C₄×D₂₈	C₂²	semidirect
118. C₄×D₂₈	C₂²	semidirect
119. #6435	C₂²	semidirect
120. #6435	C₂²	semidirect
121. C₄²×D₇	C₂²	semidirect
122. C₄×Dic₁₄	C₂²	semidirect
245. #542	D₇	semidirect
336. C₄⋊Q₈	C₂×D₇	semidirect
348. #126	C₂×D₇	semidirect
356. #124	C₂×D₇	semidirect
357. #124	C₂×D₇	semidirect
365. #123	C₂×D₇	semidirect
370. C₂²⋊Q₈	C₂×D₇	semidirect
371. C₂²⋊Q₈	C₂×D₇	semidirect
405. C₄×Q₈	C₂×D₇	semidirect
417. C₄×D₄	C₂×D₇	semidirect
420. #117	C₂×D₇	semidirect
654. C₇	#3546	semidirect

Maximal subgroups

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

subgroup	index
C₇×#542	2
#90424	2
#90416	2
#90402	2
#90400	2
#90369	2
#90365	2
#90359	2
#90357	2
#90345	2
#90335	2
#90322	2
#90321	2
#90320	2
#90300	2
#90290	2
#90268	2
#90259	2
#90245	2
#90244	2
#90219	2
#90216	2
#3546	7