Subgroups — C₄×C₂₃×C₃₁⋊C₉ #38787255

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×C₄×C₂₃×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₂₃×C₃₁⋊C₉	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₂₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₂₃×C₃₁	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	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₉×C₂₃	—	31	1	no	maximal, Hall
10	C₂₃×C₃₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₁⋊C₉	C₂×C₂₃	1	1	yes	characteristic
12	C₂×C₉×C₂₃	—	31	1	no	—
13	C₃×C₄×C₃₁	C₃×C₂₃	1	1	yes	characteristic
14	C₃₁⋊C₉	C₄×C₂₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₄×C₂₃	C₃₁⋊C₃	1	1	yes	characteristic
16	C₉×C₂₃	—	31	1	no	Hall
17	C₂×C₃×C₃₁	C₂×C₃×C₂₃	1	1	yes	characteristic
18	C₂×C₃×C₂₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic
19	C₄×C₃₁	C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₃₁	C₃×C₄×C₂₃	1	1	yes	characteristic
21	C₄×C₂₃	C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₂₃	C₄×C₃₁⋊C₃	1	1	yes	characteristic
23	C₂×C₃₁	C₂×C₉×C₂₃	1	1	yes	characteristic
24	C₂×C₂₃	C₂×C₃₁⋊C₉	1	1	yes	characteristic
25	C₄×C₉	—	31	1	no	Hall
26	C₃₁	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	C₄×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	—	31	1	no	—
29	C₃×C₄	C₂₃×C₃₁⋊C₃	1	1	yes	characteristic
30	C₉	—	31	1	no	Sylow
31	C₂×C₃	C₂×C₂₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₄	C₂₃×C₃₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×C₂₃×C₃₁⋊C₃	1	1	yes	characteristic
34	C₂	C₂×C₂₃×C₃₁⋊C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂₃×C₃₁⋊C₉	C₄	direct (N × H)
5. C₄×C₂₃×C₃₁	C₉	semidirect
8. C₄×C₃₁⋊C₉	C₂₃	direct (N × H)
10. C₂₃×C₃₁	C₄×C₉	semidirect
14. C₃₁⋊C₉	C₄×C₂₃	direct (N × H)
19. C₄×C₃₁	C₉×C₂₃	semidirect
21. C₄×C₂₃	C₃₁⋊C₉	direct (N × H)
26. C₃₁	C₄×C₉×C₂₃	semidirect
27. C₂₃	C₄×C₃₁⋊C₉	direct (N × H)
32. C₄	C₂₃×C₃₁⋊C₉	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×C₂₃×C₃₁⋊C₉	2
C₃×C₄×C₂₃×C₃₁	3
C₄×C₃₁⋊C₉	23
C₄×C₉×C₂₃	31

Subgroups — C4×C23×C31⋊C9 #38787255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×C₃₁⋊C₉ #38787255