Subgroups — C₂×Dic₂₃⋊C₈ #13092437

Order 1472.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	Dic₂₃⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₂₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₂₃	C₄	1	1	yes	characteristic
8	C₂×C₈×C₂₃	—	2	2	no	—
9	C₂×C₈×C₂₃	C₂²	1	2	yes	—
10	C₄×Dic₂₃	C₄	1	2	yes	—
11	C₄×Dic₂₃	C₂²	1	2	yes	—
12	C₂×C₂₃⋊C₈	—	2	2	no	—
13	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	D₄	1	2	yes	—
17	C₂×C₄×C₂₃	Q₈	1	2	yes	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₃	—	2	2	no	—
20	C₂×Dic₂₃	C₈	1	4	yes	complemented
21	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
22	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
23	C₈×C₂₃	—	2	2	no	—
24	C₂₃⋊C₈	—	2	2	no	—
25	C₂²×C₂₃	C₄⋊C₄	1	2	yes	—
26	C₂²×C₂₃	C₂×C₈	1	2	yes	—
27	C₂²×C₂₃	M₁₆	1	2	yes	—
28	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₃	C₄⋊C₄	1	2	yes	—
30	C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
32	Dic₂₃	—	2	2	no	—
33	Dic₂₃	C₂×C₈	1	4	yes	complemented
34	C₂×C₄⋊C₈	—	23	1	no	maximal, Sylow
35	C₂×C₂₃	C₄⋊C₈	1	4	yes	complemented
36	C₂×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₂₃	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₂₃	C₂×M₁₆	1	1	yes	characteristic
39	C₂²×C₈	—	23	1	no	—
40	C₂²×C₈	D₂₃	1	1	yes	characteristic
41	C₂×C₄²	—	23	1	no	—
42	C₄⋊C₈	—	23	4	no	—
43	C₂₃	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	23	1	no	—
45	C₂²×C₄	—	23	1	no	—
46	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
47	C₂×C₈	—	2	2	no	—
48	C₂×C₈	—	23	2	no	—
49	C₂×C₈	—	46	2	no	—
50	C₂×C₈	C₂×D₂₃	1	2	yes	—
51	C₄²	—	23	2	no	—
52	C₄²	—	23	2	no	—
53	C₂³	C₄×D₂₃	1	1	yes	characteristic
54	C₂×C₄	—	23	4	no	—
55	C₂×C₄	—	23	2	no	—
56	C₂×C₄	—	23	2	no	—
57	C₂×C₄	—	46	2	no	—
58	C₂×C₄	Dic₄₆	1	2	yes	—
59	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
61	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	46	2	no	—
64	C₂²	C₈×D₂₃	1	2	yes	—
65	C₂²	#67262	1	2	yes	—
66	C₂²	Dic₂₃⋊C₄	1	2	yes	—
67	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
68	C₄	—	23	4	no	—
69	C₄	—	46	2	no	—
70	C₄	Dic₂₃⋊C₄	1	2	yes	—
71	C₄	C₂×Dic₄₆	1	1	yes	characteristic
72	C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
73	C₂	Dic₂₃⋊C₈	1	4	yes	direct product factor
74	C₂	C₂×C₈×D₂₃	1	1	yes	characteristic
75	C₂	C₂×#67262	1	1	yes	characteristic
76	C₂	C₂×Dic₂₃⋊C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. Dic₂₃⋊C₈	C₂	direct (N × H)
20. C₂×Dic₂₃	C₈	semidirect
33. Dic₂₃	C₂×C₈	semidirect
35. C₂×C₂₃	C₄⋊C₈	semidirect
43. C₂₃	C₂×C₄⋊C₈	semidirect
73. C₂	Dic₂₃⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₃	2
C₂×C₄×Dic₂₃	2
C₂²×C₂₃⋊C₈	2
Dic₂₃⋊C₈	2
C₂×C₄⋊C₈	23

Subgroups — C2×Dic23⋊C8 #13092437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₃⋊C₈ #13092437