Subgroups — D₇×#376 #11730856

Order 896.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₇	C₂	1	3	yes	maximal
2	C₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	#89704	C₂	1	3	yes	maximal, complemented
4	D₇×#95	C₂	1	4	yes	maximal
5	#89420	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×D₇	C₂²	1	6	yes	—
7	C₂²×C₄×D₇	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₇	C₂²	1	3	yes	—
9	C₂×C₄×Dic₇	C₂²	1	6	yes	—
10	C₂×C₄×Dic₇	C₂²	1	3	yes	—
11	C₄²×D₇	C₄	1	24	yes	complemented
12	C₇×#95	C₂²	1	4	yes	—
13	C₇⋊#95	C₂²	1	12	yes	—
14	C₂×#376	—	7	1	no	maximal, Sylow
15	C₂³×D₇	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₇	C₂³	1	6	yes	—
17	C₂²×C₄×C₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₇	C₂³	1	6	yes	—
19	C₂²×Dic₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×D₇	—	2	24	no	—
21	C₂×C₄×D₇	C₂×C₄	1	24	yes	—
22	C₂×C₄×D₇	C₂×C₄	1	12	yes	—
23	C₄²×C₇	C₂×C₄	1	12	yes	complemented
24	C₄×Dic₇	C₂×C₄	1	12	yes	complemented
25	C₄×Dic₇	C₂×C₄	1	24	yes	complemented
26	C₂²×C₄²	—	7	3	no	—
27	#376	—	7	3	no	—
28	#376	—	7	4	no	—
29	#376	D₇	1	1	yes	characteristic, direct product factor
30	C₂×#95	—	7	4	no	—
31	C₂³×C₇	C₂⁴	1	1	yes	characteristic
32	C₂²×D₇	C₂²×C₄	1	6	yes	—
33	C₂²×D₇	#41	1	8	yes	—
34	C₂×C₄×C₇	—	2	12	no	—
35	C₂×C₄×C₇	C₂²×C₄	1	12	yes	—
36	C₂×C₄×C₇	C₂²×C₄	1	6	yes	—
37	C₂×Dic₇	—	2	12	no	—
38	C₂×Dic₇	C₂²×C₄	1	12	yes	—
39	C₂×Dic₇	C₂²×C₄	1	6	yes	—
40	C₄×D₇	—	2	48	no	—
41	C₄×D₇	C₄²	1	16	yes	—
42	C₂³×C₄	—	7	1	no	—
43	C₂³×C₄	—	7	6	no	—
44	C₂×C₄²	—	7	6	no	—
45	C₂×C₄²	—	7	3	no	—
46	C₂×C₄²	—	7	24	no	—
47	C₂×C₄²	C₂×D₇	1	3	yes	—
48	#95	—	7	12	no	—
49	#95	C₂×D₇	1	4	yes	—
50	C₂²×C₇	C₂³×C₄	1	3	yes	—
51	C₂²×C₇	C₂×#41	1	4	yes	—
52	C₂×D₇	C₂×C₄²	1	4	yes	—
53	C₂×D₇	#117	1	24	yes	—
54	C₄×C₇	—	2	12	no	—
55	C₄×C₇	C₂×C₄²	1	4	yes	—
56	Dic₇	—	2	12	no	—
57	Dic₇	C₂×C₄²	1	4	yes	—
58	C₂⁴	—	7	1	no	—
59	C₂²×C₄	—	7	1	no	—
60	C₂²×C₄	—	7	12	no	—
61	C₂²×C₄	—	7	6	no	—
62	C₂²×C₄	—	7	24	no	—
63	C₂²×C₄	—	14	24	no	—
64	C₂²×C₄	C₂²×D₇	1	6	yes	—
65	C₂²×C₄	C₂²×D₇	1	1	yes	characteristic
66	C₄²	—	7	24	no	—
67	C₄²	—	7	12	no	—
68	C₄²	C₄×D₇	1	12	yes	complemented
69	C₂×C₇	C₂²×C₄²	1	1	yes	characteristic
70	C₂×C₇	C₂×#117	1	6	yes	—
71	D₇	#376	1	8	yes	direct product factor
72	C₂³	—	7	6	no	—
73	C₂³	—	7	8	no	—
74	C₂³	C₂³×D₇	1	1	yes	characteristic
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	7	6	no	—
77	C₂×C₄	—	7	16	no	—
78	C₂×C₄	—	7	12	no	—
79	C₂×C₄	—	14	48	no	—
80	C₂×C₄	—	14	12	no	—
81	C₂×C₄	C₂×C₄×D₇	1	12	yes	—
82	C₂×C₄	C₂×C₄×D₇	1	6	yes	—
83	C₇	C₂×#376	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	7	4	no	—
85	C₂²	—	7	24	no	—
86	C₂²	C₂²×C₄×D₇	1	3	yes	—
87	C₂²	D₇×#41	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	—	7	4	no	—
90	C₄	—	14	12	no	—
91	C₄	C₄²×D₇	1	4	yes	—
92	C₂	—	7	8	no	—
93	C₂	C₂×C₄²×D₇	1	1	yes	characteristic
94	C₂	D₇×#117	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇
commutator	C₂×C₇	C₂²×C₄²
Frattini	C₂³	C₂³×D₇
Fitting	C₇×#376	C₂
socle, cosocle	C₂³×C₇	C₂⁴
prime radical	C₂³×D₇	C₂³
hypercenter	#376	D₇
hypocenter	C₇	C₂×#376
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
2. C₇×#376	C₂	semidirect
3. #89704	C₂	semidirect
5. #89420	C₂	semidirect
11. C₄²×D₇	C₄	semidirect
23. C₄²×C₇	C₂×C₄	semidirect
24. C₄×Dic₇	C₂×C₄	semidirect
25. C₄×Dic₇	C₂×C₄	semidirect
29. #376	D₇	direct (N × H)
68. C₄²	C₄×D₇	semidirect
71. D₇	#376	direct (N × H)
83. C₇	C₂×#376	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₇	2
C₇×#376	2
#89704	2
D₇×#95	2
#89420	2
C₂×#376	7

Subgroups — D7×#376 #11730856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#376 #11730856