Subgroups — C₇×#499 #90145

Order 448.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#125	C₂	1	2	yes	maximal
2	C₇×#107	C₂	1	2	yes	maximal
3	C₇×#106	C₂	1	2	yes	maximal
4	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
7	C₇×C₄⋊C₄	—	2	4	no	—
8	C₇×C₄⋊C₄	C₂²	1	4	yes	—
9	C₄²×C₇	C₂²	1	1	yes	characteristic
10	#499	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₄×C₇	—	2	4	no	—
12	C₂×C₄×C₇	D₄	1	2	yes	—
13	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
14	C₇×C₈	Q₈	1	2	yes	—
15	C₇×C₈	Q₈	1	2	yes	—
16	#125	C₂×C₇	1	2	yes	—
17	#107	C₂×C₇	1	2	yes	—
18	#106	C₂×C₇	1	2	yes	—
19	C₄×C₈	C₂×C₇	1	1	yes	characteristic
20	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₇	—	2	2	no	—
22	C₄×C₇	—	4	4	no	—
23	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₇	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
26	C₂×C₈	C₂²×C₇	1	1	yes	characteristic
27	C₄⋊C₄	—	2	4	no	—
28	C₄⋊C₄	C₂²×C₇	1	4	yes	—
29	C₄²	C₂²×C₇	1	1	yes	characteristic
30	C₂×C₇	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₇	#135	1	2	yes	—
32	C₂×C₄	—	2	4	no	—
33	C₂×C₄	C₇×D₄	1	2	yes	—
34	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
35	C₈	C₇×Q₈	1	2	yes	—
36	C₈	C₇×Q₈	1	2	yes	—
37	C₇	#499	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	4	4	no	—
41	C₄	C₂×C₇×Q₈	1	1	yes	characteristic
42	C₄	C₂×C₇×Q₈	1	1	yes	characteristic
43	C₂	C₇×C₄⋊Q₈	1	1	yes	characteristic
44	C₂	C₇×#135	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
10. #499	C₇	direct (N × H)
37. C₇	#499	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×#125	2
C₇×#107	2
C₇×#106	2
C₄×C₇×C₈	2
#499	7

Subgroups — C7×#499 #90145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#499 #90145