Subgroups — C₃²×C₄×D₂₃ #13110243

Order 1656.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₂₃	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×C₂₃	C₂²	1	1	yes	characteristic
6	C₃²×D₂₃	C₄	1	2	yes	direct product factor
7	C₂×C₃×D₂₃	C₂×C₃	1	4	yes	—
8	C₃×C₄×C₂₃	C₂×C₃	1	4	yes	complemented
9	C₃×Dic₂₃	C₂×C₃	1	4	yes	complemented
10	C₃²×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₄×D₂₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₂₃	C₂²×C₃	1	4	yes	—
13	C₃×D₂₃	C₃×C₄	1	8	yes	direct product factor
14	C₂×D₂₃	C₂×C₃²	1	1	yes	characteristic
15	C₄×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
16	Dic₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₂×C₃²×C₄	—	23	1	no	maximal, Hall
18	C₃×C₂₃	C₂×C₃×C₄	1	4	yes	complemented
19	C₂×C₂₃	C₂²×C₃²	1	1	yes	characteristic
20	D₂₃	C₃²×C₄	1	2	yes	direct product factor
21	C₂²×C₃²	—	23	1	no	—
22	C₃²×C₄	—	23	1	no	—
23	C₃²×C₄	D₂₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃×C₄	—	23	4	no	—
25	C₂₃	C₂×C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃²	—	23	2	no	—
27	C₂×C₃²	C₂×D₂₃	1	1	yes	characteristic
28	C₂²×C₃	—	23	4	no	—
29	C₃×C₄	—	23	4	no	—
30	C₃×C₄	C₃×D₂₃	1	4	yes	direct product factor
31	C₃²	C₄×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₄	—	23	1	no	Sylow
33	C₂×C₃	—	23	8	no	—
34	C₂×C₃	C₂×C₃×D₂₃	1	4	yes	—
35	C₂²	—	23	1	no	—
36	C₄	—	23	1	no	—
37	C₄	C₃²×D₂₃	1	1	yes	characteristic, direct product factor
38	C₃	C₃×C₄×D₂₃	1	4	yes	direct product factor
39	C₂	—	23	2	no	—
40	C₂	C₂×C₃²×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	D₂₃
commutator, hypocenter	C₂₃	C₂×C₃²×C₄
Frattini	C₂	C₂×C₃²×D₂₃
Fitting	C₃²×C₄×C₂₃	C₂
socle	C₂×C₃²×C₂₃	C₂²
prime radical	C₂×C₃²×D₂₃	C₂
cosocle	C₂×C₂₃	C₂²×C₃²
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×C₂₃	C₂	semidirect
3. C₃²×Dic₂₃	C₂	semidirect
4. C₃×C₄×D₂₃	C₃	direct (N × H)
6. C₃²×D₂₃	C₄	direct (N × H)
8. C₃×C₄×C₂₃	C₂×C₃	semidirect
9. C₃×Dic₂₃	C₂×C₃	semidirect
10. C₃²×C₂₃	C₂×C₄	semidirect
11. C₄×D₂₃	C₃²	direct (N × H)
13. C₃×D₂₃	C₃×C₄	direct (N × H)
15. C₄×C₂₃	C₂×C₃²	semidirect
16. Dic₂₃	C₂×C₃²	semidirect
18. C₃×C₂₃	C₂×C₃×C₄	semidirect
20. D₂₃	C₃²×C₄	direct (N × H)
23. C₃²×C₄	D₂₃	direct (N × H)
25. C₂₃	C₂×C₃²×C₄	semidirect
30. C₃×C₄	C₃×D₂₃	direct (N × H)
31. C₃²	C₄×D₂₃	direct (N × H)
37. C₄	C₃²×D₂₃	direct (N × H)
38. C₃	C₃×C₄×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×C₃²×D₂₃	2
C₃²×C₄×C₂₃	2
C₃²×Dic₂₃	2
C₃×C₄×D₂₃	3
C₂×C₃²×C₄	23

Subgroups — C32×C4×D23 #13110243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×D₂₃ #13110243