Subgroups — C₇×#491 #90137

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#125	C₂	1	1	yes	maximal, characteristic
3	C₇×#103	C₂	1	4	yes	maximal
4	C₇×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×Q₈	C₂²	1	2	yes	—
6	C₂×C₇×C₈	C₂²	1	2	yes	—
7	C₇×C₄⋊C₄	—	2	2	no	—
8	C₇×C₄⋊C₄	—	2	2	no	—
9	C₇×C₄⋊C₄	C₂²	1	2	yes	—
10	C₄²×C₇	C₂²	1	1	yes	characteristic
11	#491	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₇×Q₈	—	2	4	no	—
13	C₂×C₄×C₇	—	2	2	no	—
14	C₂×C₄×C₇	—	2	2	no	—
15	C₂×C₄×C₇	D₄	1	2	yes	—
16	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₇×C₈	—	2	2	no	—
18	C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
19	#125	C₂×C₇	1	1	yes	characteristic
20	#103	C₂×C₇	1	4	yes	—
21	#97	C₂×C₇	1	1	yes	characteristic
22	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
23	C₄×C₇	—	2	2	no	—
24	C₄×C₇	—	4	2	no	—
25	C₄×C₇	—	4	2	no	—
26	C₄×C₇	#41	1	2	yes	—
27	C₂×Q₈	C₂²×C₇	1	2	yes	—
28	C₂×C₈	C₂²×C₇	1	2	yes	—
29	C₄⋊C₄	—	2	2	no	—
30	C₄⋊C₄	—	2	2	no	—
31	C₄⋊C₄	C₂²×C₇	1	2	yes	—
32	C₄²	C₂²×C₇	1	1	yes	characteristic
33	C₂×C₇	#124	1	1	yes	characteristic
34	C₂×C₇	#137	1	2	yes	—
35	Q₈	—	2	4	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	C₇×D₄	1	2	yes	—
39	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₇	#491	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	4	2	no	—
46	C₄	C₇×#41	1	2	yes	—
47	C₂	C₇×#124	1	1	yes	characteristic
48	C₂	C₇×#137	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
11. #491	C₇	direct (N × H)
41. C₇	#491	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×C₄⋊Q₈	2
C₇×#125	2
C₇×#103	2
C₇×#97	2
#491	7

Subgroups — C7×#491 #90137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#491 #90137