Subgroups — C₃³×C₃₁⋊C₂₇ #36382864

Order 22599.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₂₇	C₃	1	39	yes	maximal, direct product factor
2	C₃³×C₉×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₁⋊C₂₇	C₃²	1	117	yes	direct product factor
4	C₃⁴×C₃₁	C₉	1	1	yes	characteristic
5	C₃²×C₉×C₃₁	C₉	1	26	yes	—
6	C₃²×C₉×C₃₁	C₃²	1	13	yes	—
7	C₃³×C₃₁	C₂₇	1	27	yes	complemented
8	C₃³×C₃₁	C₃×C₉	1	13	yes	—
9	C₃×C₉×C₃₁	C₃×C₉	1	104	yes	—
10	C₃×C₉×C₃₁	C₃³	1	13	yes	—
11	C₃₁⋊C₂₇	C₃³	1	27	yes	direct product factor
12	C₃³×C₂₇	—	31	1	no	maximal, Sylow
13	C₃²×C₃₁	C₃×C₂₇	1	117	yes	complemented
14	C₃²×C₃₁	C₃²×C₉	1	13	yes	—
15	C₉×C₃₁	C₃²×C₉	1	26	yes	—
16	C₉×C₃₁	C₃⁴	1	1	yes	characteristic
17	C₃³×C₉	C₃₁⋊C₃	1	1	yes	characteristic
18	C₃²×C₂₇	—	31	39	no	—
19	C₃×C₃₁	C₃²×C₂₇	1	39	yes	complemented
20	C₃×C₃₁	C₃³×C₉	1	1	yes	characteristic
21	C₃⁴	C₃₁⋊C₉	1	1	yes	characteristic
22	C₃²×C₉	C₃₁⋊C₉	1	26	yes	—
23	C₃²×C₉	C₃×C₃₁⋊C₃	1	13	yes	—
24	C₃×C₂₇	—	31	117	no	—
25	C₃₁	C₃³×C₂₇	1	1	yes	characteristic, complemented, Sylow
26	C₃³	C₃₁⋊C₂₇	1	27	yes	direct product factor
27	C₃³	C₃×C₃₁⋊C₉	1	13	yes	—
28	C₃×C₉	C₃×C₃₁⋊C₉	1	104	yes	—
29	C₃×C₉	C₃²×C₃₁⋊C₃	1	13	yes	—
30	C₂₇	—	31	27	no	—
31	C₃²	C₃×C₃₁⋊C₂₇	1	117	yes	direct product factor
32	C₃²	C₃²×C₃₁⋊C₉	1	13	yes	—
33	C₉	C₃²×C₃₁⋊C₉	1	26	yes	—
34	C₉	C₃³×C₃₁⋊C₃	1	1	yes	characteristic
35	C₃	C₃²×C₃₁⋊C₂₇	1	39	yes	direct product factor
36	C₃	C₃³×C₃₁⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃³×C₉	C₃₁⋊C₃
commutator, hypocenter	C₃₁	C₃³×C₂₇
Frattini	C₉	C₃³×C₃₁⋊C₃
Fitting	C₃³×C₉×C₃₁	C₃
socle, prime radical	C₃⁴×C₃₁	C₉
cosocle	C₉×C₃₁	C₃⁴
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₁⋊C₂₇	C₃	direct (N × H)
3. C₃×C₃₁⋊C₂₇	C₃²	direct (N × H)
7. C₃³×C₃₁	C₂₇	semidirect
11. C₃₁⋊C₂₇	C₃³	direct (N × H)
13. C₃²×C₃₁	C₃×C₂₇	semidirect
19. C₃×C₃₁	C₃²×C₂₇	semidirect
25. C₃₁	C₃³×C₂₇	semidirect
26. C₃³	C₃₁⋊C₂₇	direct (N × H)
31. C₃²	C₃×C₃₁⋊C₂₇	direct (N × H)
35. C₃	C₃²×C₃₁⋊C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₁⋊C₂₇	3
C₃³×C₉×C₃₁	3
C₃³×C₂₇	31

Subgroups — C33×C31⋊C27 #36382864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₃₁⋊C₂₇ #36382864