Subgroups — (C₂×D₂₃)⋊C₃₂ #15671534

Order 2944.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₆×D₂₃	—	2	1	no	—
8	C₁₆×D₂₃	—	2	1	no	—
9	C₂₃×C₃₂	—	2	1	no	—
10	C₂₃⋊C₃₂	—	2	1	no	—
11	C₂×C₄×D₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₂₃⋊C₈	C₈	1	1	yes	characteristic
14	C₈×D₂₃	—	2	1	no	—
15	C₈×D₂₃	—	2	1	no	—
16	C₁₆×C₂₃	D₄	1	1	yes	characteristic
17	C₁₆×C₂₃	D₄	1	1	yes	characteristic
18	C₂₃⋊C₁₆	—	2	1	no	—
19	C₂²×D₂₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₂₃	C₁₆	1	1	yes	characteristic
22	C₄×D₂₃	—	2	1	no	—
23	C₄×D₂₃	—	2	1	no	—
24	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₂₃	M₁₆	1	1	yes	characteristic
26	C₂₃⋊C₈	—	2	1	no	—
27	C₂²⋊C₃₂	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₂₃	—	2	1	no	—
30	C₂×D₂₃	—	2	1	no	—
31	C₂×D₂₃	C₃₂	1	2	yes	complemented
32	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₂₃	M₃₂	1	1	yes	characteristic
34	Dic₂₃	—	2	1	no	—
35	C₂²×C₁₆	—	23	1	no	—
36	C₂×C₃₂	—	23	1	no	—
37	C₂×C₃₂	D₂₃	1	1	yes	characteristic, complemented
38	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₂×C₂₃	C₂×C₃₂	1	1	yes	characteristic
40	C₂×C₂₃	M₆₄	1	1	yes	characteristic
41	D₂₃	—	2	2	no	—
42	C₂²×C₈	—	23	1	no	—
43	C₂×C₁₆	—	23	1	no	—
44	C₂×C₁₆	—	46	1	no	—
45	C₂×C₁₆	—	46	1	no	—
46	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
47	C₃₂	—	2	1	no	—
48	C₃₂	—	46	1	no	—
49	C₂₃	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	23	1	no	—
51	C₂×C₈	—	23	1	no	—
52	C₂×C₈	—	46	1	no	—
53	C₂×C₈	—	46	1	no	—
54	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
55	C₁₆	—	46	1	no	—
56	C₁₆	D₉₂	1	1	yes	characteristic
57	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
58	C₂³	—	23	1	no	—
59	C₂×C₄	—	23	1	no	—
60	C₂×C₄	—	46	1	no	—
61	C₂×C₄	—	46	1	no	—
62	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
63	C₈	—	46	1	no	—
64	C₈	#67262	1	1	yes	characteristic
65	C₈	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
66	C₂²	—	23	2	no	—
67	C₂²	—	46	1	no	—
68	C₂²	—	46	1	no	—
69	C₂²	C₁₆×D₂₃	1	1	yes	characteristic
70	C₄	—	46	1	no	—
71	C₄	#10624980	1	1	yes	characteristic
72	C₄	(C₂×D₂₃)⋊C₈	1	1	yes	characteristic
73	C₂	—	46	2	no	—
74	C₂	(C₂×D₂₃)⋊C₁₆	1	1	yes	characteristic
75	C₂	C₃₂×D₂₃	1	1	yes	characteristic
76	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	C₂²×C₂₃	C₂×C₁₆
prime radical	C₂²×D₂₃	C₁₆
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	C₂×C₃₂	D₂₃
hypocenter	C₂₃	C₂²⋊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
2. C₂×C₂₃⋊C₃₂	C₂	semidirect
3. C₂×C₂₃×C₃₂	C₂	semidirect
31. C₂×D₂₃	C₃₂	semidirect
37. C₂×C₃₂	D₂₃	semidirect
49. C₂₃	C₂²⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₂₃	2
C₂×C₂₃⋊C₃₂	2
C₂×C₂₃×C₃₂	2
C₂²⋊C₃₂	23

Subgroups — (C2×D23)⋊C32 #15671534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₂₃)⋊C₃₂ #15671534