Subgroups — C₂³×C₄⋊Dic₂₃ #15686558

Order 2944.

2488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₂₃	C₂	1	2	yes	maximal
2	C₂²×C₄⋊Dic₂₃	C₂	1	28	yes	maximal, direct product factor
3	C₂⁴×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×C₂₃	C₂²	1	1	yes	characteristic
5	C₂³×C₄×C₂₃	C₄	1	16	yes	complemented
6	C₂³×C₄×C₂₃	C₂²	1	14	yes	—
7	C₂³×Dic₂₃	—	2	16	no	—
8	C₂³×Dic₂₃	C₂²	1	28	yes	—
9	C₂×C₄⋊Dic₂₃	C₂²	1	112	yes	direct product factor
10	C₂⁴×C₂₃	C₂×C₄	1	8	yes	—
11	C₂⁴×C₂₃	D₄	1	8	yes	—
12	C₂⁴×C₂₃	Q₈	1	8	yes	—
13	C₂⁴×C₂₃	C₂³	1	7	yes	—
14	C₂²×C₄×C₂₃	C₂×C₄	1	112	yes	complemented
15	C₂²×C₄×C₂₃	C₂³	1	28	yes	—
16	C₂²×Dic₂₃	—	2	112	no	—
17	C₂²×Dic₂₃	C₂³	1	56	yes	—
18	C₄⋊Dic₂₃	C₂³	1	64	yes	direct product factor
19	C₂³×C₂₃	C₄⋊C₄	1	64	yes	complemented
20	C₂³×C₂₃	C₂²×C₄	1	28	yes	—
21	C₂³×C₂₃	C₂×D₄	1	28	yes	—
22	C₂³×C₂₃	C₂×Q₈	1	28	yes	—
23	C₂³×C₂₃	C₂⁴	1	7	yes	—
24	C₂×C₄×C₂₃	C₂²×C₄	1	112	yes	complemented
25	C₂×C₄×C₂₃	C₂⁴	1	8	yes	—
26	C₂×Dic₂₃	—	2	112	no	—
27	C₂×Dic₂₃	C₂⁴	1	16	yes	—
28	C₂³×C₄⋊C₄	—	23	1	no	maximal, Sylow
29	C₂²×C₂₃	C₂×C₄⋊C₄	1	112	yes	complemented
30	C₂²×C₂₃	C₂³×C₄	1	14	yes	—
31	C₂²×C₂₃	C₂²×D₄	1	14	yes	—
32	C₂²×C₂₃	C₂²×Q₈	1	14	yes	—
33	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
34	C₄×C₂₃	C₂³×C₄	1	16	yes	complemented
35	Dic₂₃	—	2	16	no	—
36	C₂⁴×C₄	—	23	2	no	—
37	C₂⁴×C₄	D₂₃	1	1	yes	characteristic
38	C₂²×C₄⋊C₄	—	23	28	no	—
39	C₂×C₂₃	C₂²×C₄⋊C₄	1	28	yes	complemented
40	C₂×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
41	C₂×C₂₃	C₂³×D₄	1	1	yes	characteristic
42	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
43	C₂⁵	C₂×D₂₃	1	1	yes	characteristic
44	C₂³×C₄	—	23	28	no	—
45	C₂³×C₄	—	46	16	no	—
46	C₂³×C₄	Dic₂₃	1	16	yes	complemented
47	C₂³×C₄	C₂×D₂₃	1	14	yes	—
48	C₂×C₄⋊C₄	—	23	112	no	—
49	C₂₃	C₂³×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
50	C₂⁴	Dic₄₆	1	8	yes	—
51	C₂⁴	D₉₂	1	8	yes	—
52	C₂⁴	C₂×Dic₂₃	1	8	yes	—
53	C₂⁴	C₂²×D₂₃	1	7	yes	—
54	C₂²×C₄	—	23	56	no	—
55	C₂²×C₄	—	46	112	no	—
56	C₂²×C₄	C₂×Dic₂₃	1	112	yes	complemented
57	C₂²×C₄	C₂²×D₂₃	1	28	yes	—
58	C₄⋊C₄	—	23	64	no	—
59	C₂³	C₄⋊Dic₂₃	1	64	yes	direct product factor
60	C₂³	C₂×Dic₄₆	1	28	yes	—
61	C₂³	C₂×D₉₂	1	28	yes	—
62	C₂³	C₂²×Dic₂₃	1	28	yes	—
63	C₂³	C₂³×D₂₃	1	7	yes	—
64	C₂×C₄	—	23	16	no	—
65	C₂×C₄	—	46	112	no	—
66	C₂×C₄	C₂²×Dic₂₃	1	112	yes	complemented
67	C₂×C₄	C₂³×D₂₃	1	8	yes	—
68	C₂²	C₂×C₄⋊Dic₂₃	1	112	yes	direct product factor
69	C₂²	C₂²×Dic₄₆	1	14	yes	—
70	C₂²	C₂²×D₉₂	1	14	yes	—
71	C₂²	C₂³×Dic₂₃	1	14	yes	—
72	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
73	C₄	—	46	16	no	—
74	C₄	C₂³×Dic₂₃	1	16	yes	complemented
75	C₂	C₂²×C₄⋊Dic₂₃	1	28	yes	direct product factor
76	C₂	C₂⁴×Dic₂₃	1	1	yes	characteristic
77	C₂	C₂³×D₉₂	1	1	yes	characteristic
78	C₂	C₂³×Dic₄₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₂₃
commutator	C₂×C₂₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂⁴×C₄×C₂₃	C₂
socle, prime radical	C₂⁵×C₂₃	C₂²
cosocle	C₂²×C₂₃	C₂⁵
hypercenter	C₂⁴×C₄	D₂₃
hypocenter	C₂₃	C₂³×C₄⋊C₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Dic₂₃	C₂	direct (N × H)
5. C₂³×C₄×C₂₃	C₄	semidirect
9. C₂×C₄⋊Dic₂₃	C₂²	direct (N × H)
14. C₂²×C₄×C₂₃	C₂×C₄	semidirect
18. C₄⋊Dic₂₃	C₂³	direct (N × H)
19. C₂³×C₂₃	C₄⋊C₄	semidirect
24. C₂×C₄×C₂₃	C₂²×C₄	semidirect
29. C₂²×C₂₃	C₂×C₄⋊C₄	semidirect
34. C₄×C₂₃	C₂³×C₄	semidirect
39. C₂×C₂₃	C₂²×C₄⋊C₄	semidirect
46. C₂³×C₄	Dic₂₃	semidirect
49. C₂₃	C₂³×C₄⋊C₄	semidirect
56. C₂²×C₄	C₂×Dic₂₃	semidirect
59. C₂³	C₄⋊Dic₂₃	direct (N × H)
66. C₂×C₄	C₂²×Dic₂₃	semidirect
68. C₂²	C₂×C₄⋊Dic₂₃	direct (N × H)
74. C₄	C₂³×Dic₂₃	semidirect
75. C₂	C₂²×C₄⋊Dic₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₂₃	2
C₂²×C₄⋊Dic₂₃	2
C₂⁴×C₄×C₂₃	2
C₂³×C₄⋊C₄	23

Subgroups — C23×C4⋊Dic23 #15686558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄⋊Dic₂₃ #15686558