Subgroups — C₈²×D₂₃ #15671669

Order 2944.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×D₂₃	C₂	1	3	yes	maximal
2	C₈×C₂₃⋊C₈	C₂	1	3	yes	maximal, complemented
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₃	C₄	1	6	yes	—
5	C₄²×D₂₃	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₃	C₂²	1	3	yes	—
7	C₈×Dic₂₃	C₄	1	6	yes	—
8	C₄×C₂₃⋊C₈	C₂²	1	3	yes	—
9	C₂×C₄×D₂₃	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₂₃	C₂×C₄	1	6	yes	—
11	C₄²×C₂₃	C₂³	1	1	yes	characteristic
12	C₄×Dic₂₃	C₂×C₄	1	3	yes	—
13	C₂×C₂₃⋊C₈	C₂×C₄	1	6	yes	—
14	C₈×D₂₃	C₈	1	24	yes	direct product factor
15	C₂²×D₂₃	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂²×C₄	1	3	yes	—
17	C₂×Dic₂₃	C₄²	1	3	yes	—
18	C₄×D₂₃	C₂×C₈	1	12	yes	—
19	C₈×C₂₃	C₂×C₈	1	12	yes	complemented
20	C₂₃⋊C₈	C₂×C₈	1	12	yes	complemented
21	C₂×C₈²	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	C₂×C₄²	1	1	yes	characteristic
23	C₂×D₂₃	C₄×C₈	1	6	yes	—
24	C₄×C₂₃	C₂²×C₈	1	6	yes	—
25	Dic₂₃	C₄×C₈	1	6	yes	—
26	C₂×C₄×C₈	—	23	3	no	—
27	C₈²	—	23	3	no	—
28	C₈²	D₂₃	1	1	yes	characteristic, direct product factor
29	C₂×C₂₃	C₂×C₄×C₈	1	3	yes	—
30	D₂₃	C₈²	1	4	yes	direct product factor
31	C₂²×C₈	—	23	6	no	—
32	C₂×C₄²	—	23	1	no	—
33	C₄×C₈	—	23	6	no	—
34	C₄×C₈	—	23	3	no	—
35	C₄×C₈	C₂×D₂₃	1	3	yes	—
36	C₂₃	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₄	—	23	3	no	—
38	C₂×C₈	—	23	6	no	—
39	C₂×C₈	—	23	24	no	—
40	C₂×C₈	C₄×D₂₃	1	6	yes	—
41	C₄²	—	23	3	no	—
42	C₄²	C₂²×D₂₃	1	1	yes	characteristic
43	C₂³	—	23	1	no	—
44	C₂×C₄	—	23	3	no	—
45	C₂×C₄	—	23	12	no	—
46	C₂×C₄	C₂×C₄×D₂₃	1	3	yes	—
47	C₈	—	23	12	no	—
48	C₈	C₈×D₂₃	1	12	yes	direct product factor
49	C₂²	—	23	6	no	—
50	C₂²	C₄²×D₂₃	1	1	yes	characteristic
51	C₄	—	23	6	no	—
52	C₄	C₂×C₈×D₂₃	1	6	yes	—
53	C₂	—	23	4	no	—
54	C₂	C₄×C₈×D₂₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₂₃
commutator, hypocenter	C₂₃	C₂×C₈²
Frattini	C₄²	C₂²×D₂₃
Fitting	C₈²×C₂₃	C₂
socle	C₂²×C₂₃	C₂×C₄²
prime radical	C₂²×D₂₃	C₄²
cosocle	C₄²×C₂₃	C₂³
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₈×C₂₃⋊C₈	C₂	semidirect
3. C₈²×C₂₃	C₂	semidirect
14. C₈×D₂₃	C₈	direct (N × H)
19. C₈×C₂₃	C₂×C₈	semidirect
20. C₂₃⋊C₈	C₂×C₈	semidirect
28. C₈²	D₂₃	direct (N × H)
30. D₂₃	C₈²	direct (N × H)
36. C₂₃	C₂×C₈²	semidirect
48. C₈	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
C₄×C₈×D₂₃	2
C₈×C₂₃⋊C₈	2
C₈²×C₂₃	2
C₂×C₈²	23

Subgroups — C82×D23 #15671669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈²×D₂₃ #15671669