Subgroups — C₇×#2845 #11742154

Order 896.

340 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#398	C₂	1	12	yes	maximal
2	C₇×#382	C₂	1	3	yes	maximal
3	C₂×C₇×C₄⋊C₄	C₂²	1	6	yes	—
4	C₂×C₇×C₄⋊C₄	C₂²	1	12	yes	—
5	C₂×C₄²×C₇	C₂²	1	1	yes	characteristic
6	C₇×#95	C₂²	1	12	yes	—
7	C₇×#95	C₂²	1	4	yes	—
8	#2845	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂²×C₄×C₇	C₂³	1	12	yes	—
10	C₂²×C₄×C₇	C₂³	1	3	yes	—
11	C₇×C₄⋊C₄	—	4	6	no	—
12	C₇×C₄⋊C₄	—	4	12	no	—
13	C₄²×C₇	Q₈	1	4	yes	—
14	#398	C₂×C₇	1	12	yes	—
15	#382	C₂×C₇	1	3	yes	—
16	C₂³×C₇	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₇	—	2	3	no	—
18	C₂×C₄×C₇	—	2	3	no	—
19	C₂×C₄×C₇	—	2	12	no	—
20	C₂×C₄×C₇	—	2	12	no	—
21	C₂×C₄×C₇	—	2	12	no	—
22	C₂×C₄×C₇	C₂×Q₈	1	6	yes	—
23	C₂×C₄⋊C₄	C₂²×C₇	1	6	yes	—
24	C₂×C₄⋊C₄	C₂²×C₇	1	12	yes	—
25	C₂×C₄²	C₂²×C₇	1	1	yes	characteristic
26	#95	C₂²×C₇	1	12	yes	—
27	#95	C₂²×C₇	1	4	yes	—
28	C₂²×C₇	C₂²×Q₈	1	1	yes	characteristic
29	C₂²×C₇	H(5,𝔽₂)	1	3	yes	—
30	C₂²×C₇	2₋¹⁺⁴	1	3	yes	—
31	C₄×C₇	—	2	6	no	—
32	C₄×C₇	—	4	12	no	—
33	C₂²×C₄	C₂³×C₇	1	12	yes	—
34	C₂²×C₄	C₂³×C₇	1	3	yes	—
35	C₄⋊C₄	—	4	6	no	—
36	C₄⋊C₄	—	4	12	no	—
37	C₄²	C₇×Q₈	1	4	yes	—
38	C₂×C₇	#544	1	3	yes	—
39	C₂×C₇	#562	1	3	yes	—
40	C₂×C₇	#564	1	1	yes	characteristic
41	C₂³	C₂⁴×C₇	1	1	yes	characteristic
42	C₂×C₄	—	2	3	no	—
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	12	no	—
45	C₂×C₄	—	2	12	no	—
46	C₂×C₄	—	2	12	no	—
47	C₂×C₄	C₂×C₇×Q₈	1	6	yes	—
48	C₇	#2845	1	1	yes	characteristic, direct product factor, Sylow
49	C₂²	C₂²×C₇×Q₈	1	1	yes	characteristic
50	C₂²	C₇×H(5,𝔽₂)	1	3	yes	—
51	C₂²	C₇×2₋¹⁺⁴	1	3	yes	—
52	C₄	—	2	6	no	—
53	C₄	—	4	12	no	—
54	C₂	C₇×#544	1	3	yes	—
55	C₂	C₇×#562	1	3	yes	—
56	C₂	C₇×#564	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
8. #2845	C₇	direct (N × H)
48. C₇	#2845	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×#398	2
C₇×#382	2
#2845	7

Subgroups — C7×#2845 #11742154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#2845 #11742154