Subgroups — SD₃₂×D₂₃ #13092839

Order 1472.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10625010	C₂	1	1	yes	maximal, characteristic, complemented
5	#10625009	C₂	1	1	yes	maximal, characteristic, complemented
6	#10624982	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₂₃	—	2	1	no	—
9	D₄×D₂₃	—	2	1	no	—
10	Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₂₃	C₂²	1	1	yes	characteristic
12	#67275	—	2	1	no	—
13	#67272	—	2	1	no	—
14	Dic₉₂	C₂²	1	1	yes	characteristic, complemented
15	D₁₈₄	C₂²	1	1	yes	characteristic
16	C₈×D₂₃	C₂²	1	1	yes	characteristic
17	C₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
18	C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₂₃	—	4	1	no	—
20	Q₈×C₂₃	—	2	1	no	—
21	D₄×C₂₃	—	2	1	no	—
22	C₂²⋊D₂₃	—	4	1	no	—
23	D₉₂	—	2	1	no	—
24	C₄×D₂₃	—	4	1	no	—
25	C₄×D₂₃	D₄	1	1	yes	characteristic
26	Dic₄₆	—	2	1	no	—
27	Dic₄₆	—	4	1	no	—
28	C₈×C₂₃	C₂³	1	1	yes	characteristic
29	C₂₃⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₂₃	—	4	1	no	—
31	C₂×D₂₃	—	4	1	no	—
32	C₂×D₂₃	—	8	2	no	—
33	C₂×D₂₃	D₈	1	1	yes	characteristic
34	C₄×C₂₃	—	4	1	no	—
35	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
36	Dic₂₃	—	4	1	no	—
37	Dic₂₃	D₈	1	1	yes	characteristic
38	C₂×SD₃₂	—	23	1	no	maximal, Sylow
39	C₂×C₂₃	—	8	1	no	—
40	C₂×C₂₃	C₂×D₈	1	1	yes	characteristic
41	D₂₃	—	8	1	no	—
42	D₂₃	SD₃₂	1	2	yes	direct product factor
43	C₂×Q₁₆	—	23	1	no	—
44	C₂×D₈	—	23	1	no	—
45	SD₃₂	—	23	1	no	—
46	SD₃₂	—	23	1	no	—
47	SD₃₂	—	23	1	no	—
48	SD₃₂	D₂₃	1	1	yes	characteristic, direct product factor
49	C₂×C₁₆	—	23	1	no	—
50	C₂₃	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	46	1	no	—
52	C₂×D₄	—	46	1	no	—
53	Q₁₆	—	23	1	no	—
54	Q₁₆	—	46	1	no	—
55	Q₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
56	D₈	—	23	1	no	—
57	D₈	—	46	1	no	—
58	D₈	C₂×D₂₃	1	1	yes	characteristic
59	C₂×C₈	—	23	1	no	—
60	C₁₆	—	23	1	no	—
61	C₁₆	C₂×D₂₃	1	1	yes	characteristic, complemented
62	C₂³	—	92	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	46	1	no	—
65	Q₈	—	92	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	46	1	no	—
68	D₄	—	92	1	no	—
69	C₂×C₄	—	23	1	no	—
70	C₂×C₄	—	92	1	no	—
71	C₈	—	23	1	no	—
72	C₈	C₂²×D₂₃	1	1	yes	characteristic
73	C₂²	—	4	1	no	—
74	C₂²	—	23	1	no	—
75	C₂²	—	92	1	no	—
76	C₂²	—	184	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	23	1	no	—
79	C₄	—	92	1	no	—
80	C₄	D₄×D₂₃	1	1	yes	characteristic
81	C₂	—	8	1	no	—
82	C₂	—	23	2	no	—
83	C₂	—	184	1	no	—
84	C₂	D₈×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₃
commutator, cosocle	C₈×C₂₃	C₂³
Frattini	C₈	C₂²×D₂₃
Fitting	C₂₃×SD₃₂	C₂
socle	C₂×C₂₃	C₂×D₈
prime radical	D₈×D₂₃	C₂
hypercenter	SD₃₂	D₂₃
hypocenter	C₂₃	C₂×SD₃₂
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. Q₁₆×D₂₃	C₂	semidirect
3. C₂₃×SD₃₂	C₂	semidirect
4. #10625010	C₂	semidirect
5. #10625009	C₂	semidirect
6. #10624982	C₂	semidirect
7. C₁₆×D₂₃	C₂	semidirect
10. Q₁₆×C₂₃	C₂²	semidirect
14. Dic₉₂	C₂²	semidirect
17. C₁₆×C₂₃	C₂²	semidirect
18. C₂₃⋊C₁₆	C₂²	semidirect
42. D₂₃	SD₃₂	direct (N × H)
48. SD₃₂	D₂₃	direct (N × H)
50. C₂₃	C₂×SD₃₂	semidirect
55. Q₁₆	C₂×D₂₃	semidirect
61. C₁₆	C₂×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₂₃	2
D₈×D₂₃	2
C₂₃×SD₃₂	2
#10625010	2
#10625009	2
#10624982	2
C₁₆×D₂₃	2
C₂×SD₃₂	23

Subgroups — SD32×D23 #13092839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₃₂×D₂₃ #13092839