Subgroups — C₄×C₈×D₂₃ #13092361

Order 1472.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₄×C₈×C₂₃	C₂	semidirect
4. C₈×Dic₂₃	C₂	semidirect
5. C₄×C₂₃⋊C₈	C₂	semidirect
13. C₈×D₂₃	C₄	direct (N × H)
19. C₄×D₂₃	C₈	direct (N × H)
21. C₈×C₂₃	C₂×C₄	semidirect
22. C₂₃⋊C₈	C₂×C₄	semidirect
26. C₄×C₂₃	C₂×C₈	semidirect
29. Dic₂₃	C₂×C₈	semidirect
33. D₂₃	C₄×C₈	direct (N × H)
38. C₄×C₈	D₂₃	direct (N × H)
39. C₂₃	C₂×C₄×C₈	semidirect
56. C₈	C₄×D₂₃	direct (N × H)
62. C₄	C₈×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
C₂×C₈×D₂₃	2
C₄²×D₂₃	2
C₄×C₈×C₂₃	2
C₈×Dic₂₃	2
C₄×C₂₃⋊C₈	2
C₂×C₄×C₈	23

Subgroups — C4×C8×D23 #13092361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₈×D₂₃ #13092361