Subgroups — C₂³×C₂²⋊D₂₃ #13093238

Order 1472.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊D₂₃	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₂₃	—	2	8	no	—
6	C₂⁴×C₂₃	C₂²	1	1	yes	characteristic
7	C₂⁴×C₂₃	C₂²	1	14	yes	complemented
8	C₂³×D₂₃	—	2	8	no	—
9	C₂³×D₂₃	C₂²	1	14	yes	complemented
10	C₂×C₂²⋊D₂₃	C₂²	1	112	yes	direct product factor
11	C₂²×Dic₂₃	C₂²	1	14	yes	complemented
12	C₂³×C₂₃	—	2	56	no	—
13	C₂³×C₂₃	D₄	1	8	yes	complemented
14	C₂³×C₂₃	C₂³	1	7	yes	—
15	C₂³×C₂₃	C₂³	1	28	yes	complemented
16	C₂²×D₂₃	—	2	56	no	—
17	C₂²×D₂₃	C₂³	1	28	yes	complemented
18	C₂²⋊D₂₃	C₂³	1	64	yes	direct product factor
19	C₂×Dic₂₃	C₂³	1	28	yes	complemented
20	C₂²×C₂₃	—	2	56	no	—
21	C₂²×C₂₃	C₂×D₄	1	28	yes	complemented
22	C₂²×C₂₃	C₂⁴	1	7	yes	—
23	C₂²×C₂₃	C₂⁴	1	8	yes	complemented
24	C₂×D₂₃	—	2	56	no	—
25	C₂×D₂₃	C₂⁴	1	8	yes	complemented
26	Dic₂₃	C₂⁴	1	8	yes	complemented
27	C₂³×D₄	—	23	1	no	maximal, Sylow
28	C₂×C₂₃	—	2	8	no	—
29	C₂×C₂₃	C₂²×D₄	1	14	yes	complemented
30	C₂×C₂₃	C₂⁵	1	1	yes	characteristic
31	D₂₃	—	2	8	no	—
32	C₂⁵	—	23	1	no	—
33	C₂⁵	D₂₃	1	1	yes	characteristic, complemented
34	C₂²×D₄	—	23	28	no	—
35	C₂³×C₄	—	23	1	no	—
36	C₂₃	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
37	C₂⁴	—	2	8	no	—
38	C₂⁴	—	23	14	no	—
39	C₂⁴	—	46	8	no	—
40	C₂⁴	C₂×D₂₃	1	1	yes	characteristic
41	C₂⁴	C₂×D₂₃	1	14	yes	complemented
42	C₂×D₄	—	23	112	no	—
43	C₂²×C₄	—	23	14	no	—
44	C₂³	—	2	56	no	—
45	C₂³	—	23	28	no	—
46	C₂³	—	46	56	no	—
47	C₂³	C₂²⋊D₂₃	1	8	yes	direct product factor
48	C₂³	C₂²×D₂₃	1	7	yes	—
49	C₂³	C₂²×D₂₃	1	28	yes	complemented
50	D₄	—	23	64	no	—
51	C₂×C₄	—	23	28	no	—
52	C₂²	—	2	56	no	—
53	C₂²	—	23	8	no	—
54	C₂²	—	46	56	no	—
55	C₂²	C₂×C₂²⋊D₂₃	1	28	yes	direct product factor
56	C₂²	C₂³×D₂₃	1	7	yes	—
57	C₂²	C₂³×D₂₃	1	8	yes	complemented
58	C₄	—	23	8	no	—
59	C₂	—	2	8	no	—
60	C₂	—	46	8	no	—
61	C₂	C₂²×C₂²⋊D₂₃	1	14	yes	direct product factor
62	C₂	C₂⁴×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₃
commutator, cosocle	C₂×C₂₃	C₂⁵
Frattini	C₂	C₂⁴×D₂₃
Fitting	C₂⁵×C₂₃	C₂
socle	C₂⁴×C₂₃	C₂²
hypercenter	C₂⁵	D₂₃
hypocenter	C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₂₃	C₂	semidirect
2. C₂⁴×D₂₃	C₂	semidirect
3. C₂²×C₂²⋊D₂₃	C₂	direct (N × H)
4. C₂³×Dic₂₃	C₂	semidirect
7. C₂⁴×C₂₃	C₂²	semidirect
9. C₂³×D₂₃	C₂²	semidirect
10. C₂×C₂²⋊D₂₃	C₂²	direct (N × H)
11. C₂²×Dic₂₃	C₂²	semidirect
13. C₂³×C₂₃	D₄	semidirect
15. C₂³×C₂₃	C₂³	semidirect
17. C₂²×D₂₃	C₂³	semidirect
18. C₂²⋊D₂₃	C₂³	direct (N × H)
19. C₂×Dic₂₃	C₂³	semidirect
21. C₂²×C₂₃	C₂×D₄	semidirect
23. C₂²×C₂₃	C₂⁴	semidirect
25. C₂×D₂₃	C₂⁴	semidirect
26. Dic₂₃	C₂⁴	semidirect
29. C₂×C₂₃	C₂²×D₄	semidirect
33. C₂⁵	D₂₃	semidirect
36. C₂₃	C₂³×D₄	semidirect
41. C₂⁴	C₂×D₂₃	semidirect
47. C₂³	C₂²⋊D₂₃	direct (N × H)
49. C₂³	C₂²×D₂₃	semidirect
55. C₂²	C₂×C₂²⋊D₂₃	direct (N × H)
57. C₂²	C₂³×D₂₃	semidirect
61. C₂	C₂²×C₂²⋊D₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₂₃	2
C₂⁴×D₂₃	2
C₂²×C₂²⋊D₂₃	2
C₂³×Dic₂₃	2
C₂³×D₄	23

Subgroups — C23×C22⋊D23 #13093238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂²⋊D₂₃ #13093238