Subgroups — C₂×C₂₃×D₃₂ #15669878

Order 2944.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₂₃×D₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₂₃	—	2	2	no	—
5	C₂₃×D₁₆	—	2	2	no	—
6	C₂₃×D₁₆	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₄×C₂₃	—	4	2	no	—
10	D₈×C₂₃	—	2	4	no	—
11	D₈×C₂₃	—	4	2	no	—
12	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
13	C₁₆×C₂₃	D₄	1	1	yes	characteristic
14	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
15	C₂³×C₂₃	—	8	2	no	—
16	D₄×C₂₃	—	4	4	no	—
17	D₄×C₂₃	—	8	2	no	—
18	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
19	C₈×C₂₃	D₈	1	1	yes	characteristic
20	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
21	C₂×D₃₂	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₂₃	—	8	4	no	—
23	C₂²×C₂₃	—	16	4	no	—
24	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
25	C₄×C₂₃	D₁₆	1	1	yes	characteristic
26	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
27	C₂×D₁₆	C₂×C₂₃	1	2	yes	complemented
28	D₃₂	C₂×C₂₃	1	4	yes	direct product factor
29	C₂×C₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
30	C₂×C₂₃	—	16	4	no	—
31	C₂×C₂₃	D₃₂	1	2	yes	direct product factor
32	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
33	C₂×D₈	—	2	2	no	—
34	D₁₆	—	2	2	no	—
35	D₁₆	C₂²×C₂₃	1	4	yes	complemented
36	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
37	C₃₂	C₂²×C₂₃	1	2	yes	complemented
38	C₂₃	C₂×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₄	—	4	2	no	—
40	D₈	—	2	4	no	—
41	D₈	—	4	2	no	—
42	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
43	C₁₆	D₄×C₂₃	1	1	yes	characteristic
44	C₁₆	C₂³×C₂₃	1	1	yes	characteristic
45	C₂³	—	8	2	no	—
46	D₄	—	4	4	no	—
47	D₄	—	8	2	no	—
48	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
49	C₈	D₈×C₂₃	1	1	yes	characteristic
50	C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
51	C₂²	—	8	4	no	—
52	C₂²	—	16	4	no	—
53	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
54	C₄	C₂₃×D₁₆	1	1	yes	characteristic
55	C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
56	C₂	—	16	4	no	—
57	C₂	C₂₃×D₃₂	1	2	yes	direct product factor
58	C₂	C₂×C₂₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₂₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×D₁₆	C₂	semidirect
2. C₂₃×D₃₂	C₂	direct (N × H)
3. C₂×C₂₃×C₃₂	C₂	semidirect
6. C₂₃×D₁₆	C₂²	semidirect
8. C₂₃×C₃₂	C₂²	semidirect
21. C₂×D₃₂	C₂₃	direct (N × H)
27. C₂×D₁₆	C₂×C₂₃	semidirect
28. D₃₂	C₂×C₂₃	direct (N × H)
29. C₂×C₃₂	C₂×C₂₃	semidirect
31. C₂×C₂₃	D₃₂	direct (N × H)
35. D₁₆	C₂²×C₂₃	semidirect
37. C₃₂	C₂²×C₂₃	semidirect
38. C₂₃	C₂×D₃₂	direct (N × H)
57. C₂	C₂₃×D₃₂	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×C₂₃×D₁₆	2
C₂₃×D₃₂	2
C₂×C₂₃×C₃₂	2
C₂×D₃₂	23

Subgroups — C2×C23×D32 #15669878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×D₃₂ #15669878