Subgroups — #21419372

Order 7533.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14578912	C₃	1	1	yes	maximal, characteristic
2	#14578892	C₃	1	1	yes	maximal, characteristic, complemented
3	#14578891	C₃	1	3	yes	maximal, complemented
4	#14578890	C₃	1	3	yes	maximal, complemented
5	C₃×C₃₁⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂₇×C₃₁⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₃²⋊(C₃₁⋊C₃)	C₉	1	1	yes	characteristic
10	#11719689	C₉	1	2	yes	—
11	#11719687	C₉	1	3	yes	—
12	#11719686	C₉	1	3	yes	—
13	C₉×C₃₁⋊C₃	C₃²	1	3	yes	—
14	C₂₇×C₃₁	C₃²	1	3	yes	—
15	C₃₁⋊C₂₇	C₃²	1	1	yes	characteristic
16	C₃₁⋊C₂₇	C₃²	1	3	yes	—
17	C₃₁⋊C₂₇	C₃²	1	1	yes	characteristic
18	C₃₁⋊C₂₇	C₃²	1	1	yes	characteristic
19	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
20	C₃×C₃₁⋊C₃	C₃×C₉	1	3	yes	—
21	C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
22	C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
23	C₉×C₃₁	C₃³	1	1	yes	characteristic
24	C₃₁⋊C₉	C₃×C₉	1	6	yes	—
25	#6903	—	31	1	no	maximal, Sylow
26	C₃×C₃₁	—	3	1	no	—
27	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
28	C₃₁⋊C₃	—	3	3	no	—
29	#737	—	31	1	no	—
30	C₂₇⋊C₃	—	31	1	no	—
31	C₂₇⋊C₃	—	31	3	no	—
32	C₂₇⋊C₃	—	31	3	no	—
33	C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
34	C₃×C₂₇	—	31	1	no	—
35	C₃×C₂₇	—	31	3	no	—
36	C₃₁	#6903	1	1	yes	characteristic, complemented, Sylow
37	3₋¹⁺²	—	31	2	no	—
38	3₋¹⁺²	—	31	3	no	—
39	3₋¹⁺²	—	31	3	no	—
40	H(3,𝔽₃)	—	31	1	no	—
41	C₃×C₉	—	31	3	no	—
42	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
43	C₂₇	—	31	1	no	—
44	C₂₇	—	31	3	no	—
45	C₂₇	—	31	1	no	—
46	C₂₇	—	31	1	no	—
47	C₂₇	C₃×C₃₁⋊C₃	1	3	yes	—
48	C₃²	—	31	3	no	—
49	C₃²	C₉×C₃₁⋊C₃	1	1	yes	characteristic
50	C₉	—	31	6	no	—
51	C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
52	C₉	C₉×C₃₁⋊C₃	1	1	yes	characteristic
53	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
54	C₃	—	3	1	no	—
55	C₃	—	93	3	no	—
56	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₃₁⋊C₃
commutator, socle	C₃×C₃₁	C₃²×C₉
Fitting	C₃₁×C₂₇⋊C₃	C₃
hypercenter	C₂₇⋊C₃	C₃₁⋊C₃
hypocenter	C₃₁	#6903
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #14578892	C₃	semidirect
3. #14578891	C₃	semidirect
4. #14578890	C₃	semidirect
5. C₃×C₃₁⋊C₂₇	C₃	semidirect
6. C₂₇×C₃₁⋊C₃	C₃	semidirect
7. C₃₁×C₂₇⋊C₃	C₃	semidirect
33. C₂₇⋊C₃	C₃₁⋊C₃	semidirect
36. C₃₁	#6903	semidirect