Subgroups — C₇×#22824 #13200040

Order 1792.

636 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2295	C₂	1	1	yes	maximal, characteristic
2	C₇×#1985	C₂	1	2	yes	maximal
3	C₇×#1917	C₂	1	2	yes	maximal
4	C₇×#1916	C₂	1	2	yes	maximal
5	C₇×#1842	C₂	1	1	yes	maximal, characteristic
6	C₇×#1832	C₂	1	2	yes	maximal
7	C₇×#1771	C₂	1	2	yes	maximal
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	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₇×#97	C₂²	1	2	yes	—
18	C₂×C₇×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
20	C₇×#391	C₄	1	1	yes	characteristic
21	C₇×#391	C₄	1	1	yes	characteristic
22	C₇×#389	C₄	1	1	yes	characteristic
23	C₇×#389	C₄	1	1	yes	characteristic
24	C₇×#387	C₄	1	2	yes	—
25	C₇×#387	C₄	1	2	yes	—
26	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
28	C₇×#376	C₂²	1	2	yes	—
29	C₄³×C₇	C₂²	1	1	yes	characteristic
30	C₇×#336	C₂²	1	2	yes	—
31	C₇×#336	C₂²	1	2	yes	—
32	C₇×#336	C₂²	1	2	yes	—
33	C₇×#336	C₂²	1	2	yes	—
34	C₇×#336	C₂²	1	2	yes	—
35	C₇×#336	C₂²	1	2	yes	—
36	C₇×#336	C₂²	1	2	yes	—
37	#22824	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₇×C₈	C₂³	1	2	yes	—
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	C₄×C₇×Q₈	—	2	2	no	—
44	C₄×C₇×Q₈	—	2	2	no	—
45	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇	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	C₂³	1	2	yes	—
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	1	yes	characteristic
60	C₇×C₄⋊C₈	—	2	4	no	—
61	C₇×C₄⋊C₈	—	2	2	no	—
62	C₇×C₄⋊C₈	—	2	4	no	—
63	C₇×C₄⋊C₈	—	4	1	no	—
64	C₇×C₄⋊C₈	—	4	1	no	—
65	C₇×C₄⋊C₈	Q₈	1	4	yes	complemented
66	C₇×#97	—	2	4	no	—
67	C₇×#97	—	4	2	no	—
68	C₄×C₇×C₈	—	4	2	no	—
69	C₇×#95	C₂×C₄	1	2	yes	—
70	C₇×#95	C₂×C₄	1	2	yes	—
71	C₇×#95	C₂×C₄	1	2	yes	—
72	C₇×#95	C₂×C₄	1	2	yes	—
73	C₇×#95	C₂×C₄	1	2	yes	—
74	C₇×#95	C₂×C₄	1	2	yes	—
75	C₇×#95	C₂×C₄	1	2	yes	—
76	#2295	C₂×C₇	1	1	yes	characteristic
77	#1985	C₂×C₇	1	2	yes	—
78	#1917	C₂×C₇	1	2	yes	—
79	#1916	C₂×C₇	1	2	yes	—
80	#1842	C₂×C₇	1	1	yes	characteristic
81	#1832	C₂×C₇	1	2	yes	—
82	#1771	C₂×C₇	1	2	yes	—
83	#1768	C₂×C₇	1	2	yes	—
84	#1767	C₂×C₇	1	1	yes	characteristic
85	C₂×C₇×Q₈	—	2	2	no	—
86	C₂×C₇×Q₈	—	4	1	no	—
87	C₂×C₇×Q₈	—	4	1	no	—
88	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
99	C₂×C₇×C₈	—	2	2	no	—
100	C₂×C₇×C₈	—	2	2	no	—
101	C₂×C₇×C₈	—	2	2	no	—
102	C₂×C₇×C₈	—	2	2	no	—
103	C₂×C₇×C₈	—	2	2	no	—
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	C₂×Q₈	1	4	yes	—
111	C₇×C₄⋊C₄	—	2	2	no	—
112	C₇×C₄⋊C₄	—	2	4	no	—
113	C₇×C₄⋊C₄	—	2	4	no	—
114	C₇×C₄⋊C₄	—	4	1	no	—
115	C₇×C₄⋊C₄	—	4	1	no	—
116	C₇×C₄⋊C₄	—	4	2	no	—
117	C₄²×C₇	—	2	2	no	—
118	C₄²×C₇	—	2	2	no	—
119	C₄²×C₇	—	2	2	no	—
120	C₄²×C₇	—	2	2	no	—
121	C₄²×C₇	—	2	1	no	—
122	C₄²×C₇	—	2	1	no	—
123	C₄²×C₇	—	2	2	no	—
124	C₄²×C₇	—	4	1	no	—
125	C₄²×C₇	—	4	1	no	—
126	C₄²×C₇	—	4	1	no	—
127	C₄²×C₇	C₂×Q₈	1	2	yes	—
128	C₄²×C₇	#41	1	2	yes	—
129	C₄²×C₇	#41	1	2	yes	—
130	C₄²×C₇	#41	1	2	yes	—
131	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
132	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
133	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
134	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
137	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
138	C₂×#97	C₂²×C₇	1	2	yes	—
139	C₂×#97	C₂²×C₇	1	2	yes	—
140	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
141	#391	C₄×C₇	1	1	yes	characteristic
142	#391	C₄×C₇	1	1	yes	characteristic
143	#389	C₄×C₇	1	1	yes	characteristic
144	#389	C₄×C₇	1	1	yes	characteristic
145	#387	C₄×C₇	1	2	yes	—
146	#387	C₄×C₇	1	2	yes	—
147	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
148	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
149	#376	C₂²×C₇	1	2	yes	—
150	C₄³	C₂²×C₇	1	1	yes	characteristic
151	#336	C₂²×C₇	1	2	yes	—
152	#336	C₂²×C₇	1	2	yes	—
153	#336	C₂²×C₇	1	2	yes	—
154	#336	C₂²×C₇	1	2	yes	—
155	#336	C₂²×C₇	1	2	yes	—
156	#336	C₂²×C₇	1	2	yes	—
157	#336	C₂²×C₇	1	2	yes	—
158	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
159	C₇×Q₈	—	4	4	no	—
160	C₂×C₄×C₇	—	2	1	no	—
161	C₂×C₄×C₇	—	2	1	no	—
162	C₂×C₄×C₇	—	2	1	no	—
163	C₂×C₄×C₇	—	2	1	no	—
164	C₂×C₄×C₇	—	2	1	no	—
165	C₂×C₄×C₇	—	2	1	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	1	no	—
170	C₂×C₄×C₇	—	2	2	no	—
171	C₂×C₄×C₇	—	2	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	2	no	—
174	C₂×C₄×C₇	—	2	1	no	—
175	C₂×C₄×C₇	—	2	2	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	1	no	—
178	C₂×C₄×C₇	—	2	1	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	2	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	#117	1	2	yes	—
186	C₂×C₄×C₇	#117	1	2	yes	—
187	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
188	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
189	C₂×C₄×C₇	#131	1	2	yes	—
190	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
196	C₇×C₈	—	2	4	no	—
197	C₇×C₈	—	4	2	no	—
198	C₇×C₈	—	4	2	no	—
199	C₇×C₈	—	4	2	no	—
200	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₇	1	2	yes	—
202	C₂²×C₈	C₂³×C₇	1	2	yes	—
203	C₂²×C₈	C₂³×C₇	1	2	yes	—
204	C₂²×C₈	C₂³×C₇	1	2	yes	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	—	2	2	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
208	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
213	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
214	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₇	1	2	yes	—
218	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₇	1	2	yes	—
220	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
222	C₄⋊C₈	—	2	4	no	—
223	C₄⋊C₈	—	2	2	no	—
224	C₄⋊C₈	—	2	4	no	—
225	C₄⋊C₈	—	4	1	no	—
226	C₄⋊C₈	—	4	1	no	—
227	C₄⋊C₈	C₇×Q₈	1	4	yes	complemented
228	#97	—	2	4	no	—
229	#97	—	4	2	no	—
230	C₄×C₈	—	4	2	no	—
231	#95	C₂×C₄×C₇	1	2	yes	—
232	#95	C₂×C₄×C₇	1	2	yes	—
233	#95	C₂×C₄×C₇	1	2	yes	—
234	#95	C₂×C₄×C₇	1	2	yes	—
235	#95	C₂×C₄×C₇	1	2	yes	—
236	#95	C₂×C₄×C₇	1	2	yes	—
237	#95	C₂×C₄×C₇	1	2	yes	—
238	C₂²×C₇	C₂×#117	1	1	yes	characteristic
239	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
240	C₂²×C₇	#520	1	1	yes	characteristic
241	C₂²×C₇	C₂×#131	1	1	yes	characteristic
242	C₂²×C₇	#568	1	1	yes	characteristic
243	C₂²×C₇	#568	1	1	yes	characteristic
244	C₂²×C₇	#568	1	1	yes	characteristic
245	C₄×C₇	—	2	2	no	—
246	C₄×C₇	—	2	2	no	—
247	C₄×C₇	—	2	2	no	—
248	C₄×C₇	—	2	2	no	—
249	C₄×C₇	—	2	2	no	—
250	C₄×C₇	—	4	2	no	—
251	C₄×C₇	—	4	2	no	—
252	C₄×C₇	—	4	2	no	—
253	C₄×C₇	—	4	1	no	—
254	C₄×C₇	—	4	2	no	—
255	C₄×C₇	#554	1	1	yes	characteristic
256	C₄×C₇	#556	1	1	yes	characteristic
257	C₄×C₇	#557	1	1	yes	characteristic
258	C₄×C₇	#559	1	1	yes	characteristic
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	4	1	no	—
261	C₂×Q₈	—	4	1	no	—
262	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	C₂×C₇×Q₈	1	2	yes	—
302	C₄²	C₇×#41	1	2	yes	—
303	C₄²	C₇×#41	1	2	yes	—
304	C₄²	C₇×#41	1	2	yes	—
305	C₂×C₇	#2355	1	1	yes	characteristic
306	C₂×C₇	#2921	1	1	yes	characteristic
307	C₂×C₇	#2925	1	1	yes	characteristic
308	C₂×C₇	#2961	1	1	yes	characteristic
309	C₂×C₇	#2962	1	1	yes	characteristic
310	C₂×C₇	#2992	1	1	yes	characteristic
311	C₂×C₇	#2995	1	1	yes	characteristic
312	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
313	Q₈	—	4	4	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	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	C₇×#117	1	2	yes	—
340	C₂×C₄	C₇×#117	1	2	yes	—
341	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
342	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
343	C₂×C₄	C₇×#131	1	2	yes	—
344	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
346	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
347	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
348	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
350	C₈	—	2	4	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₇	#22824	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	C₂×C₇×#117	1	1	yes	characteristic
356	C₂²	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
357	C₂²	C₇×#520	1	1	yes	characteristic
358	C₂²	C₂×C₇×#131	1	1	yes	characteristic
359	C₂²	C₇×#568	1	1	yes	characteristic
360	C₂²	C₇×#568	1	1	yes	characteristic
361	C₂²	C₇×#568	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	C₇×#554	1	1	yes	characteristic
373	C₄	C₇×#556	1	1	yes	characteristic
374	C₄	C₇×#557	1	1	yes	characteristic
375	C₄	C₇×#559	1	1	yes	characteristic
376	C₂	C₇×#2355	1	1	yes	characteristic
377	C₂	C₇×#2921	1	1	yes	characteristic
378	C₂	C₇×#2925	1	1	yes	characteristic
379	C₂	C₇×#2961	1	1	yes	characteristic
380	C₂	C₇×#2962	1	1	yes	characteristic
381	C₂	C₇×#2992	1	1	yes	characteristic
382	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
37. #22824	C₇	direct (N × H)
65. C₇×C₄⋊C₈	Q₈	semidirect
227. C₄⋊C₈	C₇×Q₈	semidirect
354. C₇	#22824	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2295	2
C₇×#1985	2
C₇×#1917	2
C₇×#1916	2
C₇×#1842	2
C₇×#1832	2
C₇×#1771	2
C₇×#1768	2
C₇×#1767	2
#22824	7

Subgroups — C7×#22824 #13200040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22824 #13200040