Subgroups — C₂²×Dic₃×C₂₃ #11764269

Order 1104.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₂₃	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₂₃	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₂₃	C₄	1	4	yes	complemented
5	C₂²×C₃×C₂₃	C₂²	1	3	yes	—
6	Dic₃×C₂₃	C₂²	1	4	yes	direct product factor
7	C₂³×C₂₃	D₃	1	1	yes	characteristic
8	C₂×C₄×C₂₃	—	3	6	no	—
9	C₂×C₃×C₂₃	C₂×C₄	1	6	yes	complemented
10	C₂×C₃×C₂₃	C₂³	1	1	yes	characteristic
11	C₂²×C₂₃	Dic₃	1	4	yes	direct product factor
12	C₂²×C₂₃	C₂×D₃	1	3	yes	—
13	C₄×C₂₃	—	3	4	no	—
14	C₃×C₂₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₂²×Dic₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₂₃	C₂×Dic₃	1	6	yes	direct product factor
17	C₂×C₂₃	C₂²×D₃	1	1	yes	characteristic
18	C₂³×C₃	C₂×C₂₃	1	1	yes	characteristic
19	C₂×Dic₃	C₂×C₂₃	1	6	yes	direct product factor
20	C₂₃	C₂²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₄	—	3	1	no	Sylow
22	C₂²×C₃	C₄×C₂₃	1	4	yes	complemented
23	C₂²×C₃	C₂²×C₂₃	1	3	yes	—
24	Dic₃	C₂²×C₂₃	1	4	yes	direct product factor
25	C₂³	D₃×C₂₃	1	1	yes	characteristic
26	C₂×C₄	—	3	6	no	—
27	C₂×C₃	C₂×C₄×C₂₃	1	6	yes	complemented
28	C₂×C₃	C₂³×C₂₃	1	1	yes	characteristic
29	C₂²	Dic₃×C₂₃	1	4	yes	direct product factor
30	C₂²	C₂×D₃×C₂₃	1	3	yes	—
31	C₄	—	3	4	no	—
32	C₃	C₂²×C₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₂×Dic₃×C₂₃	1	6	yes	direct product factor
34	C₂	C₂²×D₃×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₂₃	D₃
commutator, hypocenter	C₃	C₂²×C₄×C₂₃
Frattini	C₂	C₂²×D₃×C₂₃
Fitting, socle, prime radical	C₂³×C₃×C₂₃	C₂
cosocle	C₂×C₃	C₂³×C₂₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₂₃

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃×C₂₃	C₂	direct (N × H)
4. C₂²×C₃×C₂₃	C₄	semidirect
6. Dic₃×C₂₃	C₂²	direct (N × H)
9. C₂×C₃×C₂₃	C₂×C₄	semidirect
11. C₂²×C₂₃	Dic₃	direct (N × H)
14. C₃×C₂₃	C₂²×C₄	semidirect
15. C₂²×Dic₃	C₂₃	direct (N × H)
16. C₂×C₂₃	C₂×Dic₃	direct (N × H)
19. C₂×Dic₃	C₂×C₂₃	direct (N × H)
20. C₂₃	C₂²×Dic₃	direct (N × H)
22. C₂²×C₃	C₄×C₂₃	semidirect
24. Dic₃	C₂²×C₂₃	direct (N × H)
27. C₂×C₃	C₂×C₄×C₂₃	semidirect
29. C₂²	Dic₃×C₂₃	direct (N × H)
32. C₃	C₂²×C₄×C₂₃	semidirect
33. C₂	C₂×Dic₃×C₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₂₃	2
C₂×Dic₃×C₂₃	2
C₂²×C₄×C₂₃	3
C₂²×Dic₃	23

Subgroups — C22×Dic3×C23 #11764269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₃×C₂₃ #11764269