Subgroups — Dic₂₃⋊C₃₂ #15671592

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	1	yes	maximal, characteristic
2	C₁₆×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₈×Dic₂₃	C₄	1	1	yes	characteristic
6	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₂₃×C₃₂	—	2	1	no	—
8	C₂₃⋊C₃₂	—	2	1	no	—
9	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₂₃	C₈	1	1	yes	characteristic
11	C₂×C₂₃⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₂₃	D₄	1	1	yes	characteristic
13	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
14	C₂₃⋊C₁₆	—	2	1	no	—
15	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₂₃	C₁₆	1	1	yes	characteristic
17	C₂×Dic₂₃	C₁₆	1	1	yes	characteristic
18	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₂₃	M₁₆	1	1	yes	characteristic
20	C₂₃⋊C₈	—	2	1	no	—
21	C₄⋊C₃₂	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
23	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₃	M₃₂	1	1	yes	characteristic
25	Dic₂₃	—	2	1	no	—
26	Dic₂₃	C₃₂	1	2	yes	complemented
27	C₂×C₃₂	—	23	1	no	—
28	C₂×C₃₂	D₂₃	1	1	yes	characteristic
29	C₄×C₁₆	—	23	1	no	—
30	C₂×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₂₃	C₂×C₃₂	1	1	yes	characteristic
32	C₂×C₂₃	M₆₄	1	1	yes	characteristic
33	C₂×C₁₆	—	23	1	no	—
34	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
35	C₄×C₈	—	23	1	no	—
36	C₃₂	—	2	1	no	—
37	C₃₂	—	46	1	no	—
38	C₂₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₈	—	23	1	no	—
40	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
41	C₄²	—	23	1	no	—
42	C₁₆	—	46	1	no	—
43	C₁₆	Dic₄₆	1	1	yes	characteristic
44	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
45	C₂×C₄	—	23	1	no	—
46	C₂×C₄	—	23	1	no	—
47	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
48	C₈	—	46	1	no	—
49	C₈	#67262	1	1	yes	characteristic
50	C₈	Dic₂₃⋊C₄	1	1	yes	characteristic
51	C₂²	C₁₆×D₂₃	1	1	yes	characteristic
52	C₄	—	23	2	no	—
53	C₄	—	46	1	no	—
54	C₄	#10624980	1	1	yes	characteristic
55	C₄	Dic₂₃⋊C₈	1	1	yes	characteristic
56	C₂	Dic₂₃⋊C₁₆	1	1	yes	characteristic
57	C₂	C₃₂×D₂₃	1	1	yes	characteristic
58	C₂	#13092250	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
26. Dic₂₃	C₃₂	semidirect
38. C₂₃	C₄⋊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
C₁₆×Dic₂₃	2
C₂×C₂₃×C₃₂	2
C₄⋊C₃₂	23

Subgroups — Dic23⋊C32 #15671592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₃⋊C₃₂ #15671592