Subgroups — #36379688

Order 22599.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁⋊C₈₁	C₃	1	2	yes	maximal
2	C₂₇×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₃₁×C₈₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₃₁⋊C₂₇	C₉	1	2	yes	—
5	C₉×C₃₁⋊C₉	C₉	1	1	yes	characteristic
6	C₃₁⋊C₈₁	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₃₁	C₃²	1	1	yes	characteristic
8	C₃₁×C₈₁	C₉	1	3	yes	complemented
9	C₃×C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
10	C₃×C₃₁⋊C₉	C₂₇	1	3	yes	—
11	C₂₇×C₃₁	C₃×C₉	1	2	yes	—
12	C₂₇×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₃₁⋊C₂₇	C₂₇	1	6	yes	—
14	#10624499	—	31	1	no	maximal, Sylow
15	C₃²×C₃₁	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₃₁	C₉²	1	1	yes	characteristic
17	C₉×C₃₁	C₃×C₂₇	1	2	yes	—
18	C₃₁⋊C₉	—	3	3	no	—
19	C₃×C₈₁	—	31	2	no	—
20	C₃×C₈₁	C₃₁⋊C₃	1	1	yes	characteristic
21	C₉×C₂₇	—	31	1	no	—
22	C₃×C₃₁	C₉×C₂₇	1	1	yes	characteristic
23	C₃×C₃₁	C₈₁⋊C₃	1	3	yes	—
24	C₃×C₂₇	—	31	2	no	—
25	C₃×C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
26	C₉²	—	31	1	no	—
27	C₈₁	—	31	6	no	—
28	C₈₁	C₃₁⋊C₉	1	3	yes	complemented
29	C₃₁	#10624499	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₉	—	31	3	no	—
31	C₃×C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
32	C₂₇	—	31	6	no	—
33	C₂₇	C₉×C₃₁⋊C₃	1	2	yes	—
34	C₂₇	C₃×C₃₁⋊C₉	1	1	yes	characteristic
35	C₃²	C₂₇×C₃₁⋊C₃	1	1	yes	characteristic
36	C₉	—	93	3	no	—
37	C₉	C₉×C₃₁⋊C₉	1	1	yes	characteristic
38	C₉	C₂₇×C₃₁⋊C₃	1	2	yes	—
39	C₃	C₂₇×C₃₁⋊C₉	1	1	yes	characteristic
40	C₃	#21419256	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₂₇	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₉×C₂₇
Fitting	C₃×C₃₁×C₈₁	C₃
socle, prime radical	C₃²×C₃₁	C₃×C₂₇
cosocle	C₃×C₂₇×C₃₁	C₃²
hypercenter	C₃×C₈₁	C₃₁⋊C₃
hypocenter	C₃₁	#10624499
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃×C₈₁

Complements

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

N	H ≅ G/N	type
6. C₃₁⋊C₈₁	C₉	semidirect
8. C₃₁×C₈₁	C₉	semidirect
28. C₈₁	C₃₁⋊C₉	semidirect
29. C₃₁	#10624499	semidirect

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
C₂₇×C₃₁⋊C₉	3
C₃×C₃₁×C₈₁	3
#10624499	31