Subgroups — C₇×#1385 #11725751

Order 896.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#108	C₂	1	2	yes	maximal
3	C₂×C₇×M₁₆	—	2	2	no	—
4	C₂²×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₇×M₃₂	—	2	2	no	—
6	C₂×C₇×C₁₆	C₄	1	2	yes	—
7	C₇×#108	—	2	2	no	—
8	C₇×#108	C₄	1	4	yes	—
9	#1385	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂²×C₄×C₇	D₄	1	1	yes	characteristic
11	C₇×M₁₆	—	2	4	no	—
12	C₇×M₁₆	—	4	2	no	—
13	C₂×C₇×C₈	—	4	2	no	—
14	C₂×C₇×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂×C₇×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₇×C₈	D₄	1	2	yes	—
17	C₂×C₇×C₈	Q₈	1	1	yes	characteristic
18	C₇×C₁₆	—	2	2	no	—
19	C₂×M₃₂	C₂×C₇	1	1	yes	characteristic
20	C₂×#108	C₂×C₇	1	2	yes	—
21	C₂³×C₇	Q₁₆	1	1	yes	characteristic
22	C₂×C₄×C₇	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₇	D₈	1	1	yes	characteristic
25	C₂×C₄×C₇	SD₁₆	1	2	yes	—
26	C₇×C₈	—	4	4	no	—
27	C₇×C₈	C₄²	1	1	yes	characteristic
28	C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
29	C₇×C₈	C₄⋊C₄	1	2	yes	—
30	C₂×M₁₆	—	2	2	no	—
31	C₂²×C₈	C₂²×C₇	1	1	yes	characteristic
32	M₃₂	—	2	2	no	—
33	C₂×C₁₆	C₄×C₇	1	2	yes	—
34	#108	—	2	2	no	—
35	#108	C₄×C₇	1	4	yes	—
36	C₂²×C₇	—	4	1	no	—
37	C₂²×C₇	#103	1	2	yes	—
38	C₂²×C₇	#107	1	1	yes	characteristic
39	C₄×C₇	#95	1	1	yes	characteristic
40	C₄×C₇	#102	1	2	yes	—
41	C₄×C₇	#106	1	1	yes	characteristic
42	C₂²×C₄	C₇×D₄	1	1	yes	characteristic
43	M₁₆	—	2	4	no	—
44	M₁₆	—	4	2	no	—
45	C₂×C₈	—	4	2	no	—
46	C₂×C₈	C₂×C₄×C₇	1	1	yes	characteristic
47	C₂×C₈	C₂×C₄×C₇	1	2	yes	—
48	C₂×C₈	C₇×D₄	1	2	yes	—
49	C₂×C₈	C₇×Q₈	1	1	yes	characteristic
50	C₁₆	—	2	2	no	—
51	C₂×C₇	—	2	2	no	—
52	C₂×C₇	—	2	1	no	—
53	C₂×C₇	#340	1	1	yes	characteristic
54	C₂³	C₇×Q₁₆	1	1	yes	characteristic
55	C₂×C₄	C₇×C₂²⋊C₄	1	2	yes	—
56	C₂×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄	C₇×D₈	1	1	yes	characteristic
58	C₂×C₄	C₇×SD₁₆	1	2	yes	—
59	C₈	—	4	4	no	—
60	C₈	C₄²×C₇	1	1	yes	characteristic
61	C₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
62	C₈	C₇×C₄⋊C₄	1	2	yes	—
63	C₇	#1385	1	1	yes	characteristic, direct product factor, Sylow
64	C₂²	—	4	1	no	—
65	C₂²	C₇×#103	1	2	yes	—
66	C₂²	C₇×#107	1	1	yes	characteristic
67	C₄	C₇×#95	1	1	yes	characteristic
68	C₄	C₇×#102	1	2	yes	—
69	C₄	C₇×#106	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	C₇×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	#106
commutator	C₈	C₄²×C₇
Frattini, cosocle	C₂²×C₈	C₂²×C₇
socle	C₂×C₇	#340
prime radical	C₂³×C₇	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇ ◁ C₂²×C₄×C₇ ◁ C₂²×C₇×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
9. #1385	C₇	direct (N × H)
63. C₇	#1385	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×M₃₂	2
C₂×C₇×#108	2
#1385	7

Subgroups — C7×#1385 #11725751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#1385 #11725751