Subgroups — D₂₃×D₃₂ #15675693

Order 2944.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₂₃	C₂	1	2	yes	maximal, complemented
2	D₇₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092252	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₂₃	—	2	2	no	—
7	C₂₃×D₁₆	C₂²	1	2	yes	complemented
8	#10625008	—	2	2	no	—
9	D₃₆₈	C₂²	1	2	yes	complemented
10	C₁₆×D₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×C₃₂	C₂²	1	1	yes	characteristic, complemented
12	C₂₃⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₂₃	—	4	2	no	—
14	D₈×C₂₃	—	2	2	no	—
15	#67272	—	4	2	no	—
16	D₁₈₄	—	2	2	no	—
17	C₈×D₂₃	D₄	1	1	yes	characteristic
18	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₁₆	D₄	1	1	yes	characteristic
20	C₂²×D₂₃	—	8	2	no	—
21	D₄×C₂₃	—	4	2	no	—
22	C₂²⋊D₂₃	—	8	2	no	—
23	D₉₂	—	4	2	no	—
24	C₄×D₂₃	D₈	1	1	yes	characteristic
25	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₂₃⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₃₂	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	—	8	2	no	—
29	C₂×D₂₃	—	8	2	no	—
30	C₂×D₂₃	—	16	4	no	—
31	C₂×D₂₃	D₁₆	1	1	yes	characteristic
32	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
33	Dic₂₃	D₁₆	1	1	yes	characteristic
34	C₂×D₁₆	—	23	2	no	—
35	D₃₂	—	23	2	no	—
36	D₃₂	—	23	1	no	—
37	D₃₂	D₂₃	1	1	yes	characteristic, direct product factor
38	C₂×C₃₂	—	23	1	no	—
39	C₂×C₂₃	—	16	2	no	—
40	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
41	D₂₃	—	16	2	no	—
42	D₂₃	D₃₂	1	2	yes	direct product factor
43	C₂×D₈	—	46	2	no	—
44	D₁₆	—	23	2	no	—
45	D₁₆	—	46	2	no	—
46	D₁₆	C₂×D₂₃	1	2	yes	complemented
47	C₂×C₁₆	—	23	1	no	—
48	C₃₂	—	23	1	no	—
49	C₃₂	C₂×D₂₃	1	1	yes	characteristic, complemented
50	C₂₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	92	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	46	2	no	—
54	D₈	—	92	2	no	—
55	C₂×C₈	—	23	1	no	—
56	C₁₆	—	23	1	no	—
57	C₁₆	C₂²×D₂₃	1	1	yes	characteristic
58	C₂³	—	184	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	92	2	no	—
61	D₄	—	184	2	no	—
62	C₂×C₄	—	23	1	no	—
63	C₈	—	23	1	no	—
64	C₈	D₄×D₂₃	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	23	1	no	—
67	C₂²	—	368	4	no	—
68	C₂²	—	184	2	no	—
69	C₄	—	23	1	no	—
70	C₄	D₈×D₂₃	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	23	2	no	—
73	C₂	—	368	2	no	—
74	C₂	D₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₃
commutator, cosocle	C₁₆×C₂₃	C₂³
Frattini	C₁₆	C₂²×D₂₃
Fitting	C₂₃×D₃₂	C₂
socle	C₂×C₂₃	C₂×D₁₆
hypercenter	D₃₂	D₂₃
hypocenter	C₂₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₂₃	C₂	semidirect
2. D₇₃₆	C₂	semidirect
3. #13092252	C₂	semidirect
4. C₃₂×D₂₃	C₂	semidirect
5. C₂₃×D₃₂	C₂	semidirect
7. C₂₃×D₁₆	C₂²	semidirect
9. D₃₆₈	C₂²	semidirect
11. C₂₃×C₃₂	C₂²	semidirect
12. C₂₃⋊C₃₂	C₂²	semidirect
37. D₃₂	D₂₃	direct (N × H)
42. D₂₃	D₃₂	direct (N × H)
46. D₁₆	C₂×D₂₃	semidirect
49. C₃₂	C₂×D₂₃	semidirect
50. C₂₃	C₂×D₃₂	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₂₃	2
D₇₃₆	2
#13092252	2
C₃₂×D₂₃	2
C₂₃×D₃₂	2
C₂×D₃₂	23

Subgroups — D23×D32 #15675693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×D₃₂ #15675693