Subgroups — C₄⋊(C₂₃⋊C₃₂) #15671593

Order 2944.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃⋊C₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃⋊C₃₂	—	2	2	no	—
7	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₃	C₈	1	1	yes	characteristic
10	C₁₆×C₂₃	—	2	1	no	—
11	C₁₆×C₂₃	D₄	1	1	yes	characteristic
12	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₃	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₂₃	C₁₆	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₂₃	—	2	1	no	—
17	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₃	M₁₆	1	1	yes	characteristic
19	C₄⋊C₃₂	—	23	1	no	maximal, Sylow
20	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₂₃	—	2	1	no	—
22	C₄×C₂₃	C₃₂	1	2	yes	complemented
23	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₃	M₃₂	1	1	yes	characteristic
25	C₂×C₃₂	—	23	2	no	—
26	C₄×C₁₆	D₂₃	1	1	yes	characteristic
27	C₂×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
28	C₂×C₂₃	C₂×C₃₂	1	1	yes	characteristic
29	C₂×C₂₃	M₆₄	1	1	yes	characteristic
30	C₂×C₁₆	Dic₂₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
32	C₄×C₈	Dic₂₃	1	1	yes	characteristic
33	C₃₂	—	46	2	no	—
34	C₂₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	C₂₃⋊C₈	1	1	yes	characteristic
36	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
37	C₄²	C₂₃⋊C₈	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	C₁₆	Dic₄₆	1	1	yes	characteristic
40	C₁₆	D₉₂	1	1	yes	characteristic
41	C₂×C₄	C₂₃⋊C₁₆	1	1	yes	characteristic
42	C₂×C₄	C₂₃⋊C₁₆	1	1	yes	characteristic
43	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	#67267	1	1	yes	characteristic
46	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
47	C₂²	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	C₂₃⋊C₃₂	1	2	yes	complemented
50	C₄	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
51	C₄	#10624994	1	1	yes	characteristic
52	C₂	C₄⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic
53	C₂	C₂×C₂₃⋊C₃₂	1	1	yes	characteristic
54	C₂	#13092251	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₂₃
commutator	C₂×C₂₃	C₂×C₃₂
Fitting	C₄×C₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	C₄×C₁₆	D₂₃
hypocenter	C₂₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₄×C₂₃	C₃₂	semidirect
34. C₂₃	C₄⋊C₃₂	semidirect
49. C₄	C₂₃⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃⋊C₃₂	2
C₄×C₁₆×C₂₃	2
C₄⋊C₃₂	23

Subgroups — C4⋊(C23⋊C32) #15671593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₂₃⋊C₃₂) #15671593