Subgroups — #21419293

Order 7533.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
2	(C₃₁⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
3	C₃²⋊(C₃₁⋊C₉)	C₃	1	2	yes	maximal
4	C₉×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
5	C₃₁×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃³×C₃₁	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₃₁	C₃²	1	3	yes	—
8	C₃×C₃₁⋊C₉	C₉	1	9	yes	complemented
9	C₃×C₃₁⋊C₉	C₃²	1	6	yes	—
10	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
11	C₃×C₃₁⋊C₉	C₃²	1	2	yes	—
12	C₃²×C₃₁	—	3	1	no	—
13	C₃²×C₃₁	—	3	2	no	—
14	C₃²×C₃₁	C₃×C₉	1	3	yes	—
15	C₃²×C₃₁	C₃³	1	1	yes	characteristic
16	C₉×C₃₁	—	3	3	no	—
17	C₃₁⋊C₉	—	3	6	no	—
18	C₃₁⋊C₉	C₃×C₉	1	3	yes	—
19	C₃₁⋊C₉	C₃×C₉	1	6	yes	—
20	#6887	—	31	1	no	maximal, Sylow
21	C₃×C₃₁	—	3	3	no	—
22	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
23	C₃×C₃₁	#737	1	1	yes	characteristic
24	C₃×C₃₁	#737	1	2	yes	—
25	C₃²×C₉	—	31	1	no	—
26	C₉⋊C₉	—	31	6	no	—
27	C₃²⋊C₉	—	31	2	no	—
28	C₃²⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic
29	C₉²	—	31	3	no	—
30	C₃₁	#6887	1	1	yes	characteristic, complemented, Sylow
31	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₃×C₉	—	31	9	no	—
33	C₃×C₉	—	31	1	no	—
34	C₃×C₉	—	31	2	no	—
35	C₃×C₉	—	31	6	no	—
36	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
37	C₃²	—	3	1	no	—
38	C₃²	—	3	2	no	—
39	C₃²	C₉×C₃₁⋊C₃	1	3	yes	—
40	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	31	3	no	—
43	C₉	—	31	6	no	—
44	C₉	—	93	6	no	—
45	C₃	—	3	3	no	—
46	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
47	C₃	#14578911	1	1	yes	characteristic
48	C₃	#14578913	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃²×C₉
Fitting	C₃₁×C₃²⋊C₉	C₃
socle	C₃²×C₃₁	C₃³
hypercenter	C₃²⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	#6887
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
2. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
4. C₉×C₃₁⋊C₉	C₃	semidirect
8. C₃×C₃₁⋊C₉	C₉	semidirect
30. C₃₁	#6887	semidirect