Subgroups — C₂₃×#638 #13110261

Order 1656.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#67	—	3	4	no	maximal
5	C₂×C₃²×C₂₃	—	2	1	no	—
6	C₂×C₃²×C₂₃	C₂²	1	1	yes	characteristic
7	C₃⋊D₃×C₂₃	—	2	1	no	—
8	C₂²×C₃×C₂₃	D₃	1	4	yes	complemented
9	C₂×D₃×C₂₃	—	3	4	no	—
10	Dic₃×C₂₃	—	3	4	no	—
11	C₃²×C₂₃	D₄	1	1	yes	characteristic, complemented, Hall
12	D₄×C₂₃	—	9	1	no	Hall
13	C₂×C₃×C₂₃	—	2	4	no	—
14	C₂×C₃×C₂₃	C₂×D₃	1	4	yes	—
15	D₃×C₂₃	—	6	4	no	—
16	C₂²×C₂₃	—	9	1	no	—
17	C₂²×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₄×C₂₃	—	9	1	no	—
19	#638	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₃×C₂₃	#67	1	4	yes	complemented
21	C₂×C₂₃	—	2	1	no	—
22	C₂×C₂₃	—	18	1	no	—
23	C₂×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic
24	C₂²×C₃²	C₂×C₂₃	1	1	yes	characteristic, complemented
25	C₂×C₃⋊D₃	C₂×C₂₃	1	1	yes	characteristic, complemented
26	C₃⋊Dic₃	C₂×C₂₃	1	1	yes	characteristic, complemented
27	#67	—	3	4	no	—
28	C₂₃	#638	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃²	—	2	1	no	—
30	C₂×C₃²	C₂²×C₂₃	1	1	yes	characteristic
31	C₃⋊D₃	—	2	1	no	—
32	C₂²×C₃	D₃×C₂₃	1	4	yes	complemented
33	C₂×D₃	—	3	4	no	—
34	Dic₃	—	3	4	no	—
35	C₃²	D₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
36	D₄	—	9	1	no	Sylow
37	C₂×C₃	—	2	4	no	—
38	C₂×C₃	C₂×D₃×C₂₃	1	4	yes	—
39	D₃	—	6	4	no	—
40	C₂²	—	9	1	no	—
41	C₂²	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented
42	C₄	—	9	1	no	—
43	C₃	C₂₃×#67	1	4	yes	complemented
44	C₂	—	2	1	no	—
45	C₂	—	18	1	no	—
46	C₂	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₂₃	C₂×C₃⋊D₃
commutator, cosocle	C₂×C₃²	C₂²×C₂₃
Frattini	C₂	C₂×C₃⋊D₃×C₂₃
Fitting	C₂²×C₃²×C₂₃	C₂
socle	C₂×C₃²×C₂₃	C₂²
hypercenter	C₂²×C₂₃	C₃⋊D₃
hypocenter	C₃²	D₄×C₂₃
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₂₃	C₂	semidirect
2. C₂×C₃⋊D₃×C₂₃	C₂	semidirect
3. C₂₃×C₃⋊Dic₃	C₂	semidirect
8. C₂²×C₃×C₂₃	D₃	semidirect
11. C₃²×C₂₃	D₄	semidirect
17. C₂²×C₂₃	C₃⋊D₃	semidirect
19. #638	C₂₃	direct (N × H)
20. C₃×C₂₃	#67	semidirect
24. C₂²×C₃²	C₂×C₂₃	semidirect
25. C₂×C₃⋊D₃	C₂×C₂₃	semidirect
26. C₃⋊Dic₃	C₂×C₂₃	semidirect
28. C₂₃	#638	direct (N × H)
32. C₂²×C₃	D₃×C₂₃	semidirect
35. C₃²	D₄×C₂₃	semidirect
41. C₂²	C₃⋊D₃×C₂₃	semidirect
43. C₃	C₂₃×#67	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₂₃	2
C₂×C₃⋊D₃×C₂₃	2
C₂₃×C₃⋊Dic₃	2
C₂₃×#67	3
#638	23

Subgroups — C23×#638 #13110261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#638 #13110261