Subgroups — #21419370

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

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

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. C₂₇×C₃₁⋊C₃	C₃	semidirect
6. C₃×C₂₇×C₃₁	C₃	semidirect
32. C₃×C₂₇	C₃₁⋊C₃	semidirect
33. C₃₁	#6903	semidirect