Subgroups — Dic₂₃×C₃₁⋊C₉ #38787264

Order 25668.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₃₁⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁×Dic₂₃	C₃	1	1	yes	maximal, characteristic
3	C₂₃×C₃₁⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₃₁×Dic₂₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₂₃×C₃₁	C₃×C₄	1	1	yes	characteristic
7	C₂×C₂₃×C₃₁	C₂×C₉	1	1	yes	characteristic
8	C₄×C₃₁⋊C₉	—	23	1	no	maximal, Hall
9	C₉×Dic₂₃	—	31	1	no	maximal, Hall
10	C₂₃×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₁⋊C₉	D₂₃	1	1	yes	characteristic
12	C₂×C₉×C₂₃	—	31	1	no	—
13	C₃×C₄×C₃₁	—	23	1	no	—
14	C₃₁⋊C₉	Dic₂₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×Dic₂₃	C₃₁⋊C₃	1	1	yes	characteristic
16	C₉×C₂₃	—	31	1	no	Hall
17	C₂×C₃×C₃₁	C₃×D₂₃	1	1	yes	characteristic
18	C₂×C₃×C₂₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic
19	C₄×C₃₁	—	23	1	no	Hall
20	C₃×C₃₁	C₃×Dic₂₃	1	1	yes	characteristic
21	Dic₂₃	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₂₃	C₄×C₃₁⋊C₃	1	1	yes	characteristic
23	C₂×C₃₁	C₉×D₂₃	1	1	yes	characteristic
24	C₂×C₂₃	C₂×C₃₁⋊C₉	1	1	yes	characteristic
25	C₄×C₉	—	713	1	no	Hall
26	C₃₁	C₉×Dic₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	C₄×C₃₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₉	—	31	1	no	—
29	C₃×C₄	—	23	1	no	—
30	C₉	—	31	1	no	Sylow
31	C₂×C₃	D₂₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₄	—	23	1	no	Sylow
33	C₃	Dic₂₃×C₃₁⋊C₃	1	1	yes	characteristic
34	C₂	D₂₃×C₃₁⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₂₃×C₃₁⋊C₃
commutator, hypocenter	C₂₃×C₃₁	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₃×C₃₁	C₂×C₃
LCS	G ▷ C₂₃×C₃₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₂₃×C₃₁⋊C₉	C₄	semidirect
5. C₃₁×Dic₂₃	C₉	semidirect
10. C₂₃×C₃₁	C₄×C₉	semidirect
14. C₃₁⋊C₉	Dic₂₃	direct (N × H)
21. Dic₂₃	C₃₁⋊C₉	direct (N × H)
26. C₃₁	C₉×Dic₂₃	semidirect
27. C₂₃	C₄×C₃₁⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×C₃₁⋊C₉	2
C₃×C₃₁×Dic₂₃	3
C₄×C₃₁⋊C₉	23
C₉×Dic₂₃	31

Subgroups — Dic23×C31⋊C9 #38787264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₃×C₃₁⋊C₉ #38787264