Subgroups — C₂×C₄×C₇⋊C₈ #89692

Order 448.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇⋊C₈	C₂	1	2	yes	maximal
3	C₄×C₇⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₇	C₄	1	2	yes	—
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₄²×C₇	C₄	1	2	yes	—
7	C₄²×C₇	C₂²	1	2	yes	—
8	C₂×C₇⋊C₈	C₄	1	8	yes	direct product factor
9	C₂×C₇⋊C₈	C₂²	1	4	yes	—
10	C₂×C₄×C₈	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₇	C₈	1	8	yes	complemented
13	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₇⋊C₈	C₂×C₄	1	8	yes	direct product factor
18	C₂²×C₈	—	7	2	no	—
19	C₂×C₄²	D₇	1	1	yes	characteristic
20	C₄×C₈	—	7	4	no	—
21	C₂²×C₇	C₄²	1	2	yes	—
22	C₂²×C₇	C₂×C₈	1	4	yes	—
23	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₇	C₄²	1	2	yes	—
25	C₄×C₇	C₂×C₈	1	8	yes	complemented
26	C₄×C₇	C₂²×C₄	1	2	yes	—
27	C₂²×C₄	Dic₇	1	2	yes	—
28	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
29	C₂×C₈	—	7	8	no	—
30	C₂×C₈	—	7	4	no	—
31	C₄²	Dic₇	1	2	yes	—
32	C₄²	C₂×D₇	1	2	yes	—
33	C₂×C₇	C₄×C₈	1	4	yes	complemented
34	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
35	C₂×C₇	C₂²×C₈	1	2	yes	—
36	C₂³	C₂×Dic₇	1	1	yes	characteristic
37	C₂×C₄	C₇⋊C₈	1	8	yes	direct product factor
38	C₂×C₄	C₄×D₇	1	4	yes	—
39	C₂×C₄	C₂×Dic₇	1	4	yes	—
40	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
41	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
42	C₈	—	7	8	no	—
43	C₇	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
44	C₂²	C₂×C₇⋊C₈	1	4	yes	—
45	C₂²	C₄×Dic₇	1	2	yes	—
46	C₂²	C₂²×Dic₇	1	1	yes	characteristic
47	C₄	C₂×C₇⋊C₈	1	8	yes	direct product factor
48	C₄	C₄×Dic₇	1	2	yes	—
49	C₄	C₂×C₄×D₇	1	2	yes	—
50	C₂	C₄×C₇⋊C₈	1	4	yes	direct product factor
51	C₂	C₂²×C₇⋊C₈	1	2	yes	—
52	C₂	C₂×C₄×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₇
commutator, hypocenter	C₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂×C₄²×C₇	C₂
socle, prime radical	C₂³×C₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂³
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×C₇⋊C₈	C₂	direct (N × H)
8. C₂×C₇⋊C₈	C₄	direct (N × H)
12. C₂×C₄×C₇	C₈	semidirect
17. C₇⋊C₈	C₂×C₄	direct (N × H)
25. C₄×C₇	C₂×C₈	semidirect
33. C₂×C₇	C₄×C₈	semidirect
37. C₂×C₄	C₇⋊C₈	direct (N × H)
43. C₇	C₂×C₄×C₈	semidirect
47. C₄	C₂×C₇⋊C₈	direct (N × H)
50. C₂	C₄×C₇⋊C₈	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×C₄²×C₇	2
C₂²×C₇⋊C₈	2
C₄×C₇⋊C₈	2
C₂×C₄×C₈	7

Subgroups — C2×C4×C7⋊C8 #89692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇⋊C₈ #89692