Subgroups — C₃²×C₃₁⋊C₈₁ #36382061

Order 22599.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁⋊C₈₁	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃₁⋊C₈₁	C₃²	1	9	yes	direct product factor
4	C₃²×C₉×C₃₁	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₁	C₉	1	8	yes	—
6	C₃×C₂₇×C₃₁	C₃²	1	4	yes	—
7	C₃³×C₃₁	C₂₇	1	1	yes	characteristic
8	C₃×C₉×C₃₁	C₂₇	1	8	yes	—
9	C₃×C₉×C₃₁	C₃×C₉	1	4	yes	—
10	C₂₇×C₃₁	C₃×C₉	1	8	yes	—
11	C₂₇×C₃₁	C₃³	1	1	yes	characteristic
12	C₃²×C₈₁	—	31	1	no	maximal, Sylow
13	C₃²×C₃₁	C₈₁	1	9	yes	complemented
14	C₃²×C₃₁	C₃×C₂₇	1	4	yes	—
15	C₉×C₃₁	C₃×C₂₇	1	8	yes	—
16	C₉×C₃₁	C₃²×C₉	1	1	yes	characteristic
17	C₃²×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
18	C₃×C₈₁	—	31	12	no	—
19	C₃×C₃₁	C₃×C₈₁	1	12	yes	complemented
20	C₃×C₃₁	C₃²×C₂₇	1	1	yes	characteristic
21	C₃²×C₉	C₃₁⋊C₉	1	1	yes	characteristic
22	C₃×C₂₇	C₃₁⋊C₉	1	8	yes	—
23	C₃×C₂₇	C₃×C₃₁⋊C₃	1	4	yes	—
24	C₈₁	—	31	9	no	—
25	C₃₁	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
26	C₃³	C₃₁⋊C₂₇	1	1	yes	characteristic
27	C₃×C₉	C₃₁⋊C₂₇	1	8	yes	—
28	C₃×C₉	C₃×C₃₁⋊C₉	1	4	yes	—
29	C₂₇	C₃×C₃₁⋊C₉	1	8	yes	—
30	C₂₇	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
31	C₃²	C₃₁⋊C₈₁	1	9	yes	direct product factor
32	C₃²	C₃×C₃₁⋊C₂₇	1	4	yes	—
33	C₉	C₃×C₃₁⋊C₂₇	1	8	yes	—
34	C₉	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
35	C₃	C₃×C₃₁⋊C₈₁	1	12	yes	direct product factor
36	C₃	C₃²×C₃₁⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₂₇	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃²×C₈₁
Frattini	C₂₇	C₃²×C₃₁⋊C₃
Fitting	C₃²×C₂₇×C₃₁	C₃
socle, prime radical	C₃³×C₃₁	C₂₇
cosocle	C₂₇×C₃₁	C₃³
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁⋊C₈₁	C₃	direct (N × H)
3. C₃₁⋊C₈₁	C₃²	direct (N × H)
13. C₃²×C₃₁	C₈₁	semidirect
19. C₃×C₃₁	C₃×C₈₁	semidirect
25. C₃₁	C₃²×C₈₁	semidirect
31. C₃²	C₃₁⋊C₈₁	direct (N × H)
35. C₃	C₃×C₃₁⋊C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₁⋊C₈₁	3
C₃²×C₂₇×C₃₁	3
C₃²×C₈₁	31

Subgroups — C32×C31⋊C81 #36382061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃₁⋊C₈₁ #36382061