Subgroups — C₂²⋊(C₂₃⋊C₃₂) #15671535

Order 2944.

82 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, complemented
2	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₃	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃⋊C₃₂	—	2	2	no	—
8	C₂²×C₄×C₂₃	C₈	1	1	yes	characteristic
9	C₂×C₈×C₂₃	—	2	1	no	—
10	C₂×C₈×C₂₃	—	2	1	no	—
11	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₃	—	2	1	no	—
14	C₁₆×C₂₃	D₄	1	2	yes	—
15	C₂³×C₂₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₂₃	—	2	1	no	—
21	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₃	M₁₆	1	1	yes	characteristic
23	C₂²⋊C₃₂	—	23	1	no	maximal, Sylow
24	C₂²×C₂₃	—	2	1	no	—
25	C₂²×C₂₃	—	2	1	no	—
26	C₂²×C₂₃	C₃₂	1	2	yes	complemented
27	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
28	C₄×C₂₃	—	2	1	no	—
29	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₂₃	M₃₂	1	1	yes	characteristic
31	C₂²×C₁₆	D₂₃	1	1	yes	characteristic
32	C₂×C₃₂	—	23	2	no	—
33	C₂×C₂₃	—	2	2	no	—
34	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₂×C₂₃	C₂×C₃₂	1	1	yes	characteristic
36	C₂×C₂₃	M₆₄	1	1	yes	characteristic
37	C₂²×C₈	Dic₂₃	1	1	yes	characteristic
38	C₂×C₁₆	—	2	2	no	—
39	C₂×C₁₆	Dic₂₃	1	1	yes	characteristic
40	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
41	C₃₂	—	46	2	no	—
42	C₂₃	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	C₂₃⋊C₈	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	2	1	no	—
46	C₂×C₈	C₂₃⋊C₈	1	1	yes	characteristic
47	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	C₂²⋊D₂₃	1	2	yes	—
50	C₂³	C₂₃⋊C₁₆	1	1	yes	characteristic
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	C₂₃⋊C₁₆	1	1	yes	characteristic
54	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	#67267	1	1	yes	characteristic
57	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
58	C₂²	—	2	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	C₂₃⋊C₃₂	1	2	yes	complemented
61	C₂²	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
62	C₄	—	2	1	no	—
63	C₄	#10624994	1	1	yes	characteristic
64	C₄	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
65	C₂	—	2	2	no	—
66	C₂	C₂²⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic
67	C₂	C₂×C₂₃⋊C₃₂	1	1	yes	characteristic
68	C₂	#13092251	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃⋊C₃₂	C₂	semidirect
26. C₂²×C₂₃	C₃₂	semidirect
42. C₂₃	C₂²⋊C₃₂	semidirect
60. C₂²	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
C₂²×C₁₆×C₂₃	2
C₂²⋊C₃₂	23

Subgroups — C22⋊(C23⋊C32) #15671535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₂₃⋊C₃₂) #15671535