Subgroups — C₇×#34385 #13211601

Order 1792.

2090 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₇×#2378	C₂	1	2	yes	maximal, complemented
3	C₇×#2377	C₂	1	2	yes	maximal
4	C₇×#2373	C₂	1	4	yes	maximal, complemented
5	C₇×#2355	C₂	1	2	yes	maximal, complemented
6	C₇×#2354	C₂	1	2	yes	maximal, complemented
7	C₇×#2352	C₂	1	2	yes	maximal, complemented
8	C₇×#2352	C₂	1	2	yes	maximal, complemented
9	C₇×#2337	C₂	1	2	yes	maximal, complemented
10	C₇×#2336	C₂	1	2	yes	maximal, complemented
11	C₇×#2335	C₂	1	4	yes	maximal, complemented
12	C₇×#2317	C₂	1	2	yes	maximal, complemented
13	C₇×#2314	C₂	1	2	yes	maximal, complemented
14	C₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#529	C₄	1	16	yes	complemented
17	C₂×C₇×#126	C₂²	1	2	yes	—
18	C₂×C₇×#125	C₂²	1	1	yes	characteristic
19	C₂×C₇×#124	C₂²	1	1	yes	characteristic
20	C₂×C₇×#123	C₂²	1	2	yes	—
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#121	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₇×#117	C₂²	1	1	yes	characteristic
27	C₂×C₇×#117	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	C₂²	1	2	yes	—
29	C₂×C₇×#117	C₂²	1	2	yes	—
30	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
32	C₇×#391	C₂²	1	4	yes	—
33	C₇×#390	C₂²	1	4	yes	—
34	C₇×#389	C₂²	1	4	yes	—
35	C₇×#389	C₂²	1	4	yes	—
36	C₇×#388	C₂²	1	4	yes	—
37	C₇×#388	C₂²	1	4	yes	—
38	C₇×#388	C₂²	1	4	yes	—
39	C₇×#388	C₂²	1	4	yes	—
40	C₇×#388	C₂²	1	4	yes	—
41	C₇×#388	C₂²	1	4	yes	—
42	C₇×#387	C₂²	1	4	yes	—
43	C₇×#387	C₂²	1	4	yes	—
44	C₇×#387	C₂²	1	4	yes	—
45	C₇×#387	C₂²	1	4	yes	—
46	C₇×#387	C₂²	1	4	yes	—
47	C₇×#387	C₂²	1	4	yes	—
48	C₇×#386	C₂²	1	4	yes	—
49	C₇×#386	C₂²	1	4	yes	—
50	C₇×#385	C₂²	1	4	yes	—
51	C₇×#385	C₂²	1	4	yes	—
52	C₇×#384	C₂²	1	2	yes	—
53	C₇×#384	C₂²	1	2	yes	—
54	C₇×#383	C₂²	1	2	yes	—
55	C₇×#382	C₂²	1	1	yes	characteristic
56	C₇×#382	C₂²	1	1	yes	characteristic
57	C₇×#382	C₂²	1	2	yes	—
58	C₇×#382	C₂²	1	2	yes	—
59	C₇×#381	C₂²	1	2	yes	—
60	C₇×#380	C₂²	1	2	yes	—
61	C₇×#380	C₂²	1	2	yes	—
62	C₇×#380	C₂²	1	2	yes	—
63	C₇×#380	C₂²	1	2	yes	—
64	C₇×#380	C₂²	1	2	yes	—
65	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
71	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
72	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₇×#376	C₂²	1	2	yes	—
76	#34385	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₇×D₄	C₂³	1	2	yes	—
80	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₇	C₂³	1	4	yes	—
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
85	C₇×#126	C₂×C₄	1	16	yes	complemented
86	C₇×#125	C₂×C₄	1	8	yes	complemented
87	C₇×#124	C₂×C₄	1	8	yes	—
88	C₇×#123	C₂×C₄	1	16	yes	complemented
89	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₇×#121	C₂×C₄	1	8	yes	—
91	C₄×C₇×Q₈	C₂×C₄	1	8	yes	complemented
92	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
93	C₄×C₇×D₄	C₂×C₄	1	16	yes	complemented
94	C₇×#117	—	4	2	no	—
95	C₇×#117	—	4	4	no	—
96	C₇×#117	—	4	2	no	—
97	C₇×#117	C₂×C₄	1	16	yes	complemented
98	C₂×C₇×C₄⋊C₄	—	4	4	no	—
99	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
115	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
118	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₄²×C₇	C₂×C₄	1	8	yes	complemented
126	C₂×C₄²×C₇	C₂³	1	4	yes	—
127	C₂×C₄²×C₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₇	C₂³	1	4	yes	—
129	C₂×C₄²×C₇	C₂³	1	4	yes	—
130	C₂×C₄²×C₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₇	C₂³	1	4	yes	—
132	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂³	1	2	yes	—
137	C₇×#95	C₂³	1	4	yes	—
138	C₇×#95	C₂³	1	2	yes	—
139	C₇×#95	C₂³	1	2	yes	—
140	C₇×#95	C₂³	1	4	yes	—
141	C₇×#95	C₂³	1	4	yes	—
142	C₇×#95	C₂³	1	2	yes	—
143	C₇×#95	C₂³	1	2	yes	—
144	C₇×#95	C₂³	1	4	yes	—
145	C₇×#95	C₂³	1	4	yes	—
146	C₇×#95	C₂³	1	4	yes	—
147	C₇×#95	C₂³	1	4	yes	—
148	C₇×#95	C₂³	1	4	yes	—
149	C₇×#95	C₂³	1	4	yes	—
150	C₇×#95	C₂³	1	4	yes	—
151	C₂×#529	C₂×C₇	1	1	yes	characteristic
152	#2378	C₂×C₇	1	2	yes	complemented
153	#2377	C₂×C₇	1	2	yes	—
154	#2373	C₂×C₇	1	4	yes	complemented
155	#2355	C₂×C₇	1	2	yes	complemented
156	#2354	C₂×C₇	1	2	yes	complemented
157	#2352	C₂×C₇	1	2	yes	complemented
158	#2352	C₂×C₇	1	2	yes	complemented
159	#2337	C₂×C₇	1	2	yes	complemented
160	#2336	C₂×C₇	1	2	yes	complemented
161	#2335	C₂×C₇	1	4	yes	complemented
162	#2317	C₂×C₇	1	2	yes	complemented
163	#2314	C₂×C₇	1	2	yes	complemented
164	#2285	C₂×C₇	1	1	yes	characteristic, complemented
165	#2283	C₂×C₇	1	1	yes	characteristic, complemented
166	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₇	C₂⁴	1	2	yes	—
168	C₂×C₇×Q₈	—	4	2	no	—
169	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
170	C₂×C₇×D₄	—	4	2	no	—
171	C₂×C₇×D₄	—	4	2	no	—
172	C₂×C₇×D₄	—	4	2	no	—
173	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
174	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	2	2	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	4	no	—
179	C₂²×C₄×C₇	—	4	2	no	—
180	C₂²×C₄×C₇	—	4	2	no	—
181	C₂²×C₄×C₇	—	4	4	no	—
182	C₂²×C₄×C₇	—	4	4	no	—
183	C₂²×C₄×C₇	—	4	4	no	—
184	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₇	C₂²×C₄	1	8	yes	—
186	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
188	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
201	C₇×C₄⋊C₄	—	2	4	no	—
202	C₇×C₄⋊C₄	—	2	4	no	—
203	C₇×C₄⋊C₄	—	2	4	no	—
204	C₇×C₄⋊C₄	—	2	4	no	—
205	C₇×C₄⋊C₄	—	4	4	no	—
206	C₇×C₄⋊C₄	—	4	4	no	—
207	C₇×C₄⋊C₄	—	4	4	no	—
208	C₇×C₄⋊C₄	—	4	4	no	—
209	C₇×C₄⋊C₄	—	4	4	no	—
210	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
211	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
212	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
213	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
214	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
215	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
216	C₇×C₂²⋊C₄	—	4	4	no	—
217	C₇×C₂²⋊C₄	—	4	4	no	—
218	C₇×C₂²⋊C₄	—	4	4	no	—
219	C₇×C₂²⋊C₄	—	4	2	no	—
220	C₇×C₂²⋊C₄	—	4	4	no	—
221	C₇×C₂²⋊C₄	—	4	2	no	—
222	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
223	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
224	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
225	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
226	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
227	C₄²×C₇	—	4	4	no	—
228	C₄²×C₇	—	4	4	no	—
229	C₄²×C₇	—	4	4	no	—
230	C₄²×C₇	—	4	2	no	—
231	C₄²×C₇	—	4	2	no	—
232	C₄²×C₇	—	4	4	no	—
233	C₄²×C₇	C₂²×C₄	1	4	yes	—
234	C₄²×C₇	C₂²×C₄	1	4	yes	—
235	C₄²×C₇	C₂²×C₄	1	4	yes	—
236	C₄²×C₇	C₂²×C₄	1	4	yes	—
237	C₄²×C₇	C₂²×C₄	1	8	yes	—
238	#529	C₄×C₇	1	16	yes	complemented
239	C₂×#126	C₂²×C₇	1	2	yes	—
240	C₂×#125	C₂²×C₇	1	1	yes	characteristic
241	C₂×#124	C₂²×C₇	1	1	yes	characteristic
242	C₂×#123	C₂²×C₇	1	2	yes	—
243	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×#121	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
248	C₂×#117	C₂²×C₇	1	2	yes	—
249	C₂×#117	C₂²×C₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₇	1	1	yes	characteristic
251	C₂×#117	C₂²×C₇	1	2	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
253	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
254	#391	C₂²×C₇	1	4	yes	—
255	#390	C₂²×C₇	1	4	yes	—
256	#389	C₂²×C₇	1	4	yes	—
257	#389	C₂²×C₇	1	4	yes	—
258	#388	C₂²×C₇	1	4	yes	—
259	#388	C₂²×C₇	1	4	yes	—
260	#388	C₂²×C₇	1	4	yes	—
261	#388	C₂²×C₇	1	4	yes	—
262	#388	C₂²×C₇	1	4	yes	—
263	#388	C₂²×C₇	1	4	yes	—
264	#387	C₂²×C₇	1	4	yes	—
265	#387	C₂²×C₇	1	4	yes	—
266	#387	C₂²×C₇	1	4	yes	—
267	#387	C₂²×C₇	1	4	yes	—
268	#387	C₂²×C₇	1	4	yes	—
269	#387	C₂²×C₇	1	4	yes	—
270	#386	C₂²×C₇	1	4	yes	—
271	#386	C₂²×C₇	1	4	yes	—
272	#385	C₂²×C₇	1	4	yes	—
273	#385	C₂²×C₇	1	4	yes	—
274	#384	C₂²×C₇	1	2	yes	—
275	#384	C₂²×C₇	1	2	yes	—
276	#383	C₂²×C₇	1	2	yes	—
277	#382	C₂²×C₇	1	1	yes	characteristic
278	#382	C₂²×C₇	1	1	yes	characteristic
279	#382	C₂²×C₇	1	2	yes	—
280	#382	C₂²×C₇	1	2	yes	—
281	#381	C₂²×C₇	1	2	yes	—
282	#380	C₂²×C₇	1	2	yes	—
283	#380	C₂²×C₇	1	2	yes	—
284	#380	C₂²×C₇	1	2	yes	—
285	#380	C₂²×C₇	1	2	yes	—
286	#380	C₂²×C₇	1	2	yes	—
287	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
288	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
290	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
291	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
292	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
293	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
294	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
295	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
296	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
297	#376	C₂²×C₇	1	2	yes	—
298	C₂³×C₇	—	2	1	no	—
299	C₂³×C₇	—	2	2	no	—
300	C₂³×C₇	—	2	1	no	—
301	C₂³×C₇	—	2	2	no	—
302	C₂³×C₇	—	2	2	no	—
303	C₂³×C₇	—	2	2	no	—
304	C₂³×C₇	—	2	2	no	—
305	C₂³×C₇	—	2	2	no	—
306	C₂³×C₇	—	2	2	no	—
307	C₂³×C₇	—	2	2	no	—
308	C₂³×C₇	C₂³×C₄	1	4	yes	—
309	C₂³×C₇	C₂³×C₄	1	2	yes	—
310	C₂³×C₇	C₂⁵	1	1	yes	characteristic
311	C₇×Q₈	—	4	4	no	—
312	C₇×D₄	—	4	4	no	—
313	C₇×D₄	—	4	8	no	—
314	C₂×C₄×C₇	—	2	1	no	—
315	C₂×C₄×C₇	—	2	2	no	—
316	C₂×C₄×C₇	—	2	1	no	—
317	C₂×C₄×C₇	—	2	2	no	—
318	C₂×C₄×C₇	—	2	2	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	2	no	—
321	C₂×C₄×C₇	—	2	2	no	—
322	C₂×C₄×C₇	—	2	2	no	—
323	C₂×C₄×C₇	—	2	2	no	—
324	C₂×C₄×C₇	—	2	2	no	—
325	C₂×C₄×C₇	—	2	2	no	—
326	C₂×C₄×C₇	—	2	16	no	—
327	C₂×C₄×C₇	—	2	8	no	—
328	C₂×C₄×C₇	—	2	4	no	—
329	C₂×C₄×C₇	—	2	4	no	—
330	C₂×C₄×C₇	—	2	4	no	—
331	C₂×C₄×C₇	—	2	4	no	—
332	C₂×C₄×C₇	—	2	4	no	—
333	C₂×C₄×C₇	—	2	4	no	—
334	C₂×C₄×C₇	—	2	4	no	—
335	C₂×C₄×C₇	—	2	4	no	—
336	C₂×C₄×C₇	—	2	4	no	—
337	C₂×C₄×C₇	—	2	4	no	—
338	C₂×C₄×C₇	—	2	4	no	—
339	C₂×C₄×C₇	—	2	4	no	—
340	C₂×C₄×C₇	—	4	4	no	—
341	C₂×C₄×C₇	—	4	4	no	—
342	C₂×C₄×C₇	—	8	8	no	—
343	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
344	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
345	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
346	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
347	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
348	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
349	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
350	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
351	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
352	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
353	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
354	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₇	1	2	yes	—
356	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₇	1	2	yes	—
358	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₇	1	4	yes	—
360	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
362	#126	C₂×C₄×C₇	1	16	yes	complemented
363	#125	C₂×C₄×C₇	1	8	yes	complemented
364	#124	C₂×C₄×C₇	1	8	yes	—
365	#123	C₂×C₄×C₇	1	16	yes	complemented
366	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	complemented
367	#121	C₂×C₄×C₇	1	8	yes	—
368	C₄×Q₈	C₂×C₄×C₇	1	8	yes	complemented
369	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
370	C₄×D₄	C₂×C₄×C₇	1	16	yes	complemented
371	#117	—	4	2	no	—
372	#117	—	4	4	no	—
373	#117	—	4	2	no	—
374	#117	C₂×C₄×C₇	1	16	yes	complemented
375	C₂×C₄⋊C₄	—	4	4	no	—
376	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
402	C₂×C₄²	C₂×C₄×C₇	1	8	yes	complemented
403	C₂×C₄²	C₂³×C₇	1	2	yes	—
404	C₂×C₄²	C₂³×C₇	1	4	yes	—
405	C₂×C₄²	C₂³×C₇	1	2	yes	—
406	C₂×C₄²	C₂³×C₇	1	4	yes	—
407	C₂×C₄²	C₂³×C₇	1	4	yes	—
408	C₂×C₄²	C₂³×C₇	1	4	yes	—
409	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₇	1	2	yes	—
411	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
414	#95	C₂³×C₇	1	4	yes	—
415	#95	C₂³×C₇	1	2	yes	—
416	#95	C₂³×C₇	1	2	yes	—
417	#95	C₂³×C₇	1	4	yes	—
418	#95	C₂³×C₇	1	4	yes	—
419	#95	C₂³×C₇	1	2	yes	—
420	#95	C₂³×C₇	1	2	yes	—
421	#95	C₂³×C₇	1	4	yes	—
422	#95	C₂³×C₇	1	4	yes	—
423	#95	C₂³×C₇	1	4	yes	—
424	#95	C₂³×C₇	1	4	yes	—
425	#95	C₂³×C₇	1	4	yes	—
426	#95	C₂³×C₇	1	4	yes	—
427	#95	C₂³×C₇	1	4	yes	—
428	C₂²×C₇	—	2	2	no	—
429	C₂²×C₇	—	2	4	no	—
430	C₂²×C₇	—	2	2	no	—
431	C₂²×C₇	—	2	2	no	—
432	C₂²×C₇	—	2	4	no	—
433	C₂²×C₇	—	2	4	no	—
434	C₂²×C₇	—	4	2	no	—
435	C₂²×C₇	—	4	2	no	—
436	C₂²×C₇	—	4	2	no	—
437	C₂²×C₇	—	4	2	no	—
438	C₂²×C₇	—	4	2	no	—
439	C₂²×C₇	—	4	2	no	—
440	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
441	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
443	C₂²×C₇	#585	1	2	yes	—
444	C₂²×C₇	#585	1	2	yes	—
445	C₄×C₇	—	2	2	no	—
446	C₄×C₇	—	2	4	no	—
447	C₄×C₇	—	2	2	no	—
448	C₄×C₇	—	2	2	no	—
449	C₄×C₇	—	2	2	no	—
450	C₄×C₇	—	2	2	no	—
451	C₄×C₇	—	2	4	no	—
452	C₄×C₇	—	2	4	no	—
453	C₄×C₇	—	4	4	no	—
454	C₄×C₇	—	4	4	no	—
455	C₄×C₇	—	4	4	no	—
456	C₄×C₇	—	4	4	no	—
457	C₄×C₇	#520	1	4	yes	—
458	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
459	C₂⁴	C₂⁴×C₇	1	2	yes	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
466	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
477	C₂²×C₄	C₂²×C₄×C₇	1	8	yes	—
478	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
479	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	4	4	no	—
498	C₄⋊C₄	—	4	4	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
503	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
504	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
505	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
506	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
507	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
515	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
516	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
517	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
518	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	4	4	no	—
522	C₄²	—	4	4	no	—
523	C₄²	—	4	4	no	—
524	C₄²	—	4	4	no	—
525	C₄²	C₂²×C₄×C₇	1	4	yes	—
526	C₄²	C₂²×C₄×C₇	1	4	yes	—
527	C₄²	C₂²×C₄×C₇	1	4	yes	—
528	C₄²	C₂²×C₄×C₇	1	4	yes	—
529	C₄²	C₂²×C₄×C₇	1	8	yes	—
530	C₂×C₇	—	4	2	no	—
531	C₂×C₇	—	4	4	no	—
532	C₂×C₇	C₂×#520	1	1	yes	characteristic
533	C₂×C₇	#3428	1	1	yes	characteristic
534	C₂×C₇	#3428	1	1	yes	characteristic
535	C₂×C₇	#3562	1	2	yes	—
536	C₂×C₇	#3565	1	2	yes	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	C₂³×C₄×C₇	1	4	yes	—
548	C₂³	C₂³×C₄×C₇	1	2	yes	—
549	C₂³	C₂⁵×C₇	1	1	yes	characteristic
550	Q₈	—	4	4	no	—
551	D₄	—	4	4	no	—
552	D₄	—	4	8	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	16	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	8	8	no	—
582	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
583	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
584	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
585	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
586	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
587	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
588	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
589	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
590	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
591	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
592	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
593	C₇	#34385	1	1	yes	characteristic, direct product factor, Sylow
594	C₂²	—	2	2	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
607	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
609	C₂²	C₇×#585	1	2	yes	—
610	C₂²	C₇×#585	1	2	yes	—
611	C₄	—	2	2	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	4	no	—
618	C₄	—	2	4	no	—
619	C₄	—	4	4	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	4	no	—
623	C₄	C₇×#520	1	4	yes	—
624	C₂	—	4	2	no	—
625	C₂	—	4	4	no	—
626	C₂	C₂×C₇×#520	1	1	yes	characteristic
627	C₂	C₇×#3428	1	1	yes	characteristic
628	C₂	C₇×#3428	1	1	yes	characteristic
629	C₂	C₇×#3562	1	2	yes	—
630	C₂	C₇×#3565	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2378	C₂	semidirect
4. C₇×#2373	C₂	semidirect
5. C₇×#2355	C₂	semidirect
6. C₇×#2354	C₂	semidirect
7. C₇×#2352	C₂	semidirect
8. C₇×#2352	C₂	semidirect
9. C₇×#2337	C₂	semidirect
10. C₇×#2336	C₂	semidirect
11. C₇×#2335	C₂	semidirect
12. C₇×#2317	C₂	semidirect
13. C₇×#2314	C₂	semidirect
14. C₇×#2285	C₂	semidirect
15. C₇×#2283	C₂	semidirect
16. C₇×#529	C₄	semidirect
76. #34385	C₇	direct (N × H)
85. C₇×#126	C₂×C₄	semidirect
86. C₇×#125	C₂×C₄	semidirect
88. C₇×#123	C₂×C₄	semidirect
89. C₇×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₄×C₇×Q₈	C₂×C₄	semidirect
93. C₄×C₇×D₄	C₂×C₄	semidirect
97. C₇×#117	C₂×C₄	semidirect
125. C₂×C₄²×C₇	C₂×C₄	semidirect
152. #2378	C₂×C₇	semidirect
154. #2373	C₂×C₇	semidirect
155. #2355	C₂×C₇	semidirect
156. #2354	C₂×C₇	semidirect
157. #2352	C₂×C₇	semidirect
158. #2352	C₂×C₇	semidirect
159. #2337	C₂×C₇	semidirect
160. #2336	C₂×C₇	semidirect
161. #2335	C₂×C₇	semidirect
162. #2317	C₂×C₇	semidirect
163. #2314	C₂×C₇	semidirect
164. #2285	C₂×C₇	semidirect
165. #2283	C₂×C₇	semidirect
238. #529	C₄×C₇	semidirect
362. #126	C₂×C₄×C₇	semidirect
363. #125	C₂×C₄×C₇	semidirect
365. #123	C₂×C₄×C₇	semidirect
366. C₂²⋊Q₈	C₂×C₄×C₇	semidirect
368. C₄×Q₈	C₂×C₄×C₇	semidirect
370. C₄×D₄	C₂×C₄×C₇	semidirect
374. #117	C₂×C₄×C₇	semidirect
402. C₂×C₄²	C₂×C₄×C₇	semidirect
593. C₇	#34385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#529	2
C₇×#2378	2
C₇×#2377	2
C₇×#2373	2
C₇×#2355	2
C₇×#2354	2
C₇×#2352	2
C₇×#2337	2
C₇×#2336	2
C₇×#2335	2
C₇×#2317	2
C₇×#2314	2
C₇×#2285	2
C₇×#2283	2
#34385	7

Subgroups — C7×#34385 #13211601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34385 #13211601