Subgroups — C₇×#500 #90146

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₇×#107	C₂	1	4	yes	maximal
3	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×Q₈	—	2	2	no	—
5	C₂×C₇×C₈	C₂²	1	2	yes	—
6	C₇×C₄⋊C₄	—	2	2	no	—
7	C₇×C₄⋊C₄	C₂²	1	4	yes	—
8	C₄²×C₇	C₂²	1	1	yes	characteristic
9	#500	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₇×Q₈	—	4	4	no	—
11	C₂×C₄×C₇	—	2	4	no	—
12	C₂×C₄×C₇	D₄	1	1	yes	characteristic
13	C₂×C₄×C₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
15	C₇×C₈	Q₈	1	4	yes	complemented
16	C₄⋊Q₈	C₂×C₇	1	2	yes	—
17	#107	C₂×C₇	1	4	yes	—
18	C₄×C₈	C₂×C₇	1	1	yes	characteristic
19	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
20	C₄×C₇	—	4	4	no	—
21	C₄×C₇	D₈	1	2	yes	—
22	C₄×C₇	Q₁₆	1	2	yes	—
23	C₄×C₇	C₂×Q₈	1	2	yes	—
24	C₂×Q₈	—	2	2	no	—
25	C₂×C₈	C₂²×C₇	1	2	yes	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄⋊C₄	C₂²×C₇	1	4	yes	—
28	C₄²	C₂²×C₇	1	1	yes	characteristic
29	C₂×C₇	C₄⋊Q₈	1	1	yes	characteristic
30	C₂×C₇	C₂×D₈	1	1	yes	characteristic
31	C₂×C₇	C₂×Q₁₆	1	1	yes	characteristic
32	Q₈	—	4	4	no	—
33	C₂×C₄	—	2	4	no	—
34	C₂×C₄	C₇×D₄	1	1	yes	characteristic
35	C₂×C₄	C₇×D₄	1	1	yes	characteristic
36	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
37	C₈	C₇×Q₈	1	4	yes	complemented
38	C₇	#500	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
40	C₄	—	4	4	no	—
41	C₄	C₇×D₈	1	2	yes	—
42	C₄	C₇×Q₁₆	1	2	yes	—
43	C₄	C₂×C₇×Q₈	1	2	yes	—
44	C₂	C₇×C₄⋊Q₈	1	1	yes	characteristic
45	C₂	C₂×C₇×D₈	1	1	yes	characteristic
46	C₂	C₂×C₇×Q₁₆	1	1	yes	characteristic

	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
9. #500	C₇	direct (N × H)
15. C₇×C₈	Q₈	semidirect
37. C₈	C₇×Q₈	semidirect
38. C₇	#500	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×#107	2
C₄×C₇×C₈	2
#500	7

Subgroups — C7×#500 #90146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#500 #90146