Subgroups — C₇×#22723 #13199939

Order 1792.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#446	C₂	1	2	yes	maximal
2	C₇×#2295	C₂	1	1	yes	maximal, characteristic
3	C₇×#1940	C₂	1	2	yes	maximal
4	C₇×#1940	C₂	1	2	yes	maximal
5	C₇×#1939	C₂	1	2	yes	maximal
6	C₇×#1843	C₂	1	2	yes	maximal
7	C₇×#1842	C₂	1	1	yes	maximal, characteristic
8	C₇×#1768	C₂	1	2	yes	maximal
9	C₇×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
11	C₇×#446	—	2	8	no	—
12	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#97	C₂²	1	2	yes	—
23	C₂×C₇×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
25	C₇×#391	C₄	1	1	yes	characteristic
26	C₇×#391	C₄	1	1	yes	characteristic
27	C₇×#389	C₄	1	1	yes	characteristic
28	C₇×#389	C₄	1	1	yes	characteristic
29	C₇×#387	C₄	1	2	yes	—
30	C₇×#387	C₄	1	2	yes	—
31	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₇×#376	C₂²	1	2	yes	—
34	C₄³×C₇	C₂²	1	1	yes	characteristic
35	C₇×#336	C₂²	1	2	yes	—
36	C₇×#336	C₂²	1	2	yes	—
37	C₇×#336	C₂²	1	2	yes	—
38	#22723	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₇×C₈	C₂³	1	2	yes	—
41	C₂²×C₇×C₈	C₂³	1	2	yes	—
42	C₂²×C₇×C₈	C₂³	1	2	yes	—
43	C₂²×C₇×C₈	C₂³	1	2	yes	—
44	C₄×C₇×Q₈	D₄	1	4	yes	—
45	C₄×C₇×Q₈	Q₈	1	4	yes	—
46	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂³	1	2	yes	—
58	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊C₈	—	2	4	no	—
62	C₇×C₄⋊C₈	—	2	4	no	—
63	C₇×C₄⋊C₈	—	2	4	no	—
64	C₇×C₄⋊C₈	—	2	2	no	—
65	C₇×C₄⋊C₈	—	2	4	no	—
66	C₇×C₄⋊C₈	—	4	1	no	—
67	C₇×C₄⋊C₈	—	4	1	no	—
68	C₇×C₄⋊C₈	—	4	2	no	—
69	C₇×C₄⋊C₈	—	4	2	no	—
70	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
71	C₇×#97	—	2	4	no	—
72	C₇×#97	—	2	4	no	—
73	C₄×C₇×C₈	—	2	4	no	—
74	C₇×#95	C₂×C₄	1	2	yes	—
75	C₇×#95	C₂×C₄	1	2	yes	—
76	C₇×#95	C₂×C₄	1	2	yes	—
77	C₇×#95	C₂×C₄	1	2	yes	—
78	C₇×#95	C₂×C₄	1	2	yes	—
79	C₇×#95	C₂×C₄	1	2	yes	—
80	C₇×#95	C₂×C₄	1	2	yes	—
81	C₂×#446	C₂×C₇	1	2	yes	—
82	#2295	C₂×C₇	1	1	yes	characteristic
83	#1940	C₂×C₇	1	2	yes	—
84	#1940	C₂×C₇	1	2	yes	—
85	#1939	C₂×C₇	1	2	yes	—
86	#1843	C₂×C₇	1	2	yes	—
87	#1842	C₂×C₇	1	1	yes	characteristic
88	#1768	C₂×C₇	1	2	yes	—
89	#1767	C₂×C₇	1	1	yes	characteristic
90	C₂×C₇×Q₈	—	4	1	no	—
91	C₂×C₇×Q₈	—	4	1	no	—
92	C₂×C₇×Q₈	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₇×C₈	—	2	2	no	—
105	C₂×C₇×C₈	—	2	2	no	—
106	C₂×C₇×C₈	—	2	2	no	—
107	C₂×C₇×C₈	—	2	2	no	—
108	C₂×C₇×C₈	—	2	2	no	—
109	C₂×C₇×C₈	—	2	2	no	—
110	C₂×C₇×C₈	—	2	2	no	—
111	C₂×C₇×C₈	—	2	2	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	2	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
116	C₇×C₄⋊C₄	—	2	4	no	—
117	C₇×C₄⋊C₄	—	4	1	no	—
118	C₇×C₄⋊C₄	—	4	1	no	—
119	C₇×C₄⋊C₄	—	4	2	no	—
120	C₇×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
121	C₇×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
122	C₄²×C₇	—	2	2	no	—
123	C₄²×C₇	—	2	1	no	—
124	C₄²×C₇	—	2	2	no	—
125	C₄²×C₇	—	2	1	no	—
126	C₄²×C₇	—	2	2	no	—
127	C₄²×C₇	—	4	1	no	—
128	C₄²×C₇	—	4	1	no	—
129	C₄²×C₇	—	4	1	no	—
130	C₄²×C₇	C₂×D₄	1	4	yes	—
131	C₄²×C₇	C₂×D₄	1	2	yes	—
132	C₄²×C₇	C₂×Q₈	1	2	yes	—
133	C₄²×C₇	C₂×Q₈	1	4	yes	—
134	C₄²×C₇	C₂×Q₈	1	2	yes	—
135	C₄²×C₇	#41	1	2	yes	—
136	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
137	#446	—	2	8	no	—
138	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
139	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
140	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
141	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
142	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
143	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
144	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
146	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
148	C₂×#97	C₂²×C₇	1	2	yes	—
149	C₂×#97	C₂²×C₇	1	2	yes	—
150	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
151	#391	C₄×C₇	1	1	yes	characteristic
152	#391	C₄×C₇	1	1	yes	characteristic
153	#389	C₄×C₇	1	1	yes	characteristic
154	#389	C₄×C₇	1	1	yes	characteristic
155	#387	C₄×C₇	1	2	yes	—
156	#387	C₄×C₇	1	2	yes	—
157	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
158	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
159	#376	C₂²×C₇	1	2	yes	—
160	C₄³	C₂²×C₇	1	1	yes	characteristic
161	#336	C₂²×C₇	1	2	yes	—
162	#336	C₂²×C₇	1	2	yes	—
163	#336	C₂²×C₇	1	2	yes	—
164	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
165	C₇×Q₈	—	4	4	no	—
166	C₂×C₄×C₇	—	2	1	no	—
167	C₂×C₄×C₇	—	2	1	no	—
168	C₂×C₄×C₇	—	2	1	no	—
169	C₂×C₄×C₇	—	2	2	no	—
170	C₂×C₄×C₇	—	2	1	no	—
171	C₂×C₄×C₇	—	2	1	no	—
172	C₂×C₄×C₇	—	2	1	no	—
173	C₂×C₄×C₇	—	2	1	no	—
174	C₂×C₄×C₇	—	2	1	no	—
175	C₂×C₄×C₇	—	2	1	no	—
176	C₂×C₄×C₇	—	2	1	no	—
177	C₂×C₄×C₇	—	2	2	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	1	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	1	no	—
185	C₂×C₄×C₇	—	2	1	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
190	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×C₄×C₇	C₂×C₄⋊C₄	1	4	yes	—
192	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
193	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
194	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
195	C₂×C₄×C₇	#131	1	2	yes	—
196	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
202	C₇×C₈	—	2	4	no	—
203	C₇×C₈	—	4	2	no	—
204	C₇×C₈	—	4	2	no	—
205	C₇×C₈	—	4	2	no	—
206	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₇	1	2	yes	—
208	C₂²×C₈	C₂³×C₇	1	2	yes	—
209	C₂²×C₈	C₂³×C₇	1	2	yes	—
210	C₂²×C₈	C₂³×C₇	1	2	yes	—
211	C₄×Q₈	C₇×D₄	1	4	yes	—
212	C₄×Q₈	C₇×Q₈	1	4	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₇	1	2	yes	—
225	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₇	1	2	yes	—
227	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
228	C₄⋊C₈	—	2	4	no	—
229	C₄⋊C₈	—	2	4	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	—	4	1	no	—
234	C₄⋊C₈	—	4	1	no	—
235	C₄⋊C₈	—	4	2	no	—
236	C₄⋊C₈	—	4	2	no	—
237	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
238	#97	—	2	4	no	—
239	#97	—	2	4	no	—
240	C₄×C₈	—	2	4	no	—
241	#95	C₂×C₄×C₇	1	2	yes	—
242	#95	C₂×C₄×C₇	1	2	yes	—
243	#95	C₂×C₄×C₇	1	2	yes	—
244	#95	C₂×C₄×C₇	1	2	yes	—
245	#95	C₂×C₄×C₇	1	2	yes	—
246	#95	C₂×C₄×C₇	1	2	yes	—
247	#95	C₂×C₄×C₇	1	2	yes	—
248	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
250	C₂²×C₇	#520	1	1	yes	characteristic
251	C₂²×C₇	C₂×#131	1	1	yes	characteristic
252	C₂²×C₇	#568	1	1	yes	characteristic
253	C₂²×C₇	#568	1	1	yes	characteristic
254	C₂²×C₇	#568	1	1	yes	characteristic
255	C₄×C₇	—	2	2	no	—
256	C₄×C₇	—	2	4	no	—
257	C₄×C₇	—	2	2	no	—
258	C₄×C₇	—	2	4	no	—
259	C₄×C₇	—	2	2	no	—
260	C₄×C₇	—	2	2	no	—
261	C₄×C₇	—	2	2	no	—
262	C₄×C₇	—	4	2	no	—
263	C₄×C₇	—	4	1	no	—
264	C₄×C₇	—	4	2	no	—
265	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
266	C₄×C₇	#550	1	1	yes	characteristic
267	C₄×C₇	#557	1	1	yes	characteristic
268	C₄×C₇	Q₈²	1	1	yes	characteristic
269	C₂×Q₈	—	4	1	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×Q₈	C₇×C₄⋊C₄	1	4	yes	—
272	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄⋊C₄	C₇×C₄⋊C₄	1	8	yes	—
300	C₄⋊C₄	C₇×C₄⋊C₄	1	4	yes	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	C₂×C₇×D₄	1	4	yes	—
310	C₄²	C₂×C₇×D₄	1	2	yes	—
311	C₄²	C₂×C₇×Q₈	1	2	yes	—
312	C₄²	C₂×C₇×Q₈	1	4	yes	—
313	C₄²	C₂×C₇×Q₈	1	2	yes	—
314	C₄²	C₇×#41	1	2	yes	—
315	C₂×C₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₇	#2905	1	1	yes	characteristic
317	C₂×C₇	#2906	1	1	yes	characteristic
318	C₂×C₇	#2961	1	1	yes	characteristic
319	C₂×C₇	#2962	1	1	yes	characteristic
320	C₂×C₇	#2992	1	1	yes	characteristic
321	C₂×C₇	#2995	1	1	yes	characteristic
322	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
323	Q₈	—	4	4	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
348	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
349	C₂×C₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
350	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
351	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
352	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
353	C₂×C₄	C₇×#131	1	2	yes	—
354	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
357	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
358	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
360	C₈	—	2	4	no	—
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₇	#22723	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
366	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
367	C₂²	C₇×#520	1	1	yes	characteristic
368	C₂²	C₂×C₇×#131	1	1	yes	characteristic
369	C₂²	C₇×#568	1	1	yes	characteristic
370	C₂²	C₇×#568	1	1	yes	characteristic
371	C₂²	C₇×#568	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
383	C₄	C₇×#550	1	1	yes	characteristic
384	C₄	C₇×#557	1	1	yes	characteristic
385	C₄	C₇×Q₈²	1	1	yes	characteristic
386	C₂	C₇×Q₈×C₄⋊C₄	1	1	yes	characteristic
387	C₂	C₇×#2905	1	1	yes	characteristic
388	C₂	C₇×#2906	1	1	yes	characteristic
389	C₂	C₇×#2961	1	1	yes	characteristic
390	C₂	C₇×#2962	1	1	yes	characteristic
391	C₂	C₇×#2992	1	1	yes	characteristic
392	C₂	C₇×#2995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
38. #22723	C₇	direct (N × H)
70. C₇×C₄⋊C₈	Q₈	semidirect
237. C₄⋊C₈	C₇×Q₈	semidirect
364. C₇	#22723	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×#446	2
C₇×#2295	2
C₇×#1940	2
C₇×#1939	2
C₇×#1843	2
C₇×#1842	2
C₇×#1768	2
C₇×#1767	2
#22723	7

Subgroups — C7×#22723 #13199939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22723 #13199939