Subgroups — C₄⋊(C₇⋊C₁₆) #89257

Order 448.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇⋊C₁₆	C₂	1	2	yes	maximal
3	C₂×C₇×C₈	C₄	1	1	yes	characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₄²×C₇	C₄	1	1	yes	characteristic
6	C₇⋊C₁₆	—	2	2	no	—
7	C₄⋊C₁₆	—	7	1	no	maximal, Sylow
8	C₂×C₄×C₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₇	C₈	1	1	yes	characteristic
10	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
11	C₇×C₈	—	2	1	no	—
12	C₇×C₈	D₄	1	1	yes	characteristic
13	C₇×C₈	Q₈	1	1	yes	characteristic
14	C₂×C₁₆	—	7	2	no	—
15	C₄×C₈	D₇	1	1	yes	characteristic
16	C₂²×C₇	C₂×C₈	1	1	yes	characteristic
17	C₄×C₇	—	2	1	no	—
18	C₄×C₇	C₁₆	1	2	yes	complemented
19	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₇	M₁₆	1	1	yes	characteristic
21	C₂×C₈	Dic₇	1	1	yes	characteristic
22	C₂×C₈	C₂×D₇	1	1	yes	characteristic
23	C₄²	Dic₇	1	1	yes	characteristic
24	C₁₆	—	14	2	no	—
25	C₂×C₇	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₇	C₂×C₁₆	1	1	yes	characteristic
27	C₂×C₇	M₃₂	1	1	yes	characteristic
28	C₂×C₄	C₇⋊C₈	1	1	yes	characteristic
29	C₂×C₄	C₇⋊C₈	1	1	yes	characteristic
30	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	Dic₁₄	1	1	yes	characteristic
33	C₈	D₂₈	1	1	yes	characteristic
34	C₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂²	C₂×C₇⋊C₈	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₇⋊C₁₆	1	2	yes	complemented
38	C₄	#1136	1	1	yes	characteristic
39	C₄	C₄⋊Dic₇	1	1	yes	characteristic
40	C₂	C₄⋊(C₇⋊C₈)	1	1	yes	characteristic
41	C₂	C₂×C₇⋊C₁₆	1	1	yes	characteristic
42	C₂	#6386	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₇
commutator	C₂×C₇	C₂×C₁₆
Fitting	C₄×C₇×C₈	C₂
socle, prime radical	C₂²×C₇	C₂×C₈
cosocle	C₂×C₇×C₈	C₂²
hypercenter	C₄×C₈	D₇
hypocenter	C₇	C₄⋊C₁₆
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
18. C₄×C₇	C₁₆	semidirect
34. C₇	C₄⋊C₁₆	semidirect
37. C₄	C₇⋊C₁₆	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₇×C₈	2
C₂×C₇⋊C₁₆	2
C₄⋊C₁₆	7

Subgroups — C4⋊(C7⋊C16) #89257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₇⋊C₁₆) #89257