Subgroups — #21419357

Order 7533.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719686	C₃	1	1	yes	maximal, characteristic
2	#14578887	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578886	C₃	1	3	yes	maximal, complemented
4	(C₃₁⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
5	(C₃×C₃₁⋊C₃)⋊C₉	C₃	1	3	yes	maximal
6	C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃₁×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₃₁	C₃²	1	3	yes	—
10	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
11	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
12	C₃×C₃₁⋊C₉	C₃²	1	3	yes	—
13	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
15	#11719686	—	3	3	no	—
16	C₃²×C₃₁	C₃³	1	1	yes	characteristic
17	C₃×C₃₁⋊C₃	—	3	1	no	—
18	C₃×C₃₁⋊C₃	—	3	3	no	—
19	C₉×C₃₁	—	3	3	no	—
20	C₉×C₃₁	3₋¹⁺²	1	3	yes	—
21	C₃₁⋊C₉	—	3	1	no	—
22	C₃₁⋊C₉	—	3	1	no	—
23	C₃₁⋊C₉	—	3	3	no	—
24	C₃₁⋊C₉	—	3	3	no	—
25	#6899	—	31	1	no	maximal, Sylow
26	C₃×C₃₁	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₃₁	#737	1	3	yes	—
28	C₃₁⋊C₃	—	9	1	no	—
29	C₃×3₋¹⁺²	—	31	1	no	—
30	C₉⋊C₉	—	31	3	no	—
31	C₉⋊C₉	—	31	3	no	—
32	C₉⋊C₉	—	31	1	no	—
33	C₉⋊C₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₃²⋊C₉	—	31	3	no	—
35	C₉²	—	31	1	no	—
36	C₃₁	#6899	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	31	1	no	—
38	3₋¹⁺²	—	93	3	no	—
39	C₃×C₉	—	31	3	no	—
40	C₃×C₉	—	31	3	no	—
41	C₃×C₉	—	31	1	no	—
42	C₃×C₉	—	31	1	no	—
43	C₃×C₉	C₃×C₃₁⋊C₃	1	3	yes	—
44	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
45	C₃²	—	93	1	no	—
46	C₃²	—	93	3	no	—
47	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	93	1	no	—
50	C₉	—	93	1	no	—
51	C₉	—	93	3	no	—
52	C₉	—	93	3	no	—
53	C₉	#11719686	1	3	yes	—
54	C₃	—	279	1	no	—
55	C₃	C₃×#11719686	1	1	yes	characteristic
56	C₃	#14578913	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₃₁×C₉⋊C₉	C₃
hypercenter	C₉⋊C₉	C₃₁⋊C₃
hypocenter	C₃₁	#6899
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
2. #14578887	C₃	semidirect
3. #14578886	C₃	semidirect
4. (C₃₁⋊C₉)⋊C₉	C₃	semidirect
6. C₉×C₃₁⋊C₉	C₃	semidirect
7. C₃₁×C₉⋊C₉	C₃	semidirect
33. C₉⋊C₉	C₃₁⋊C₃	semidirect
36. C₃₁	#6899	semidirect