Subgroups — #13097105

Order 1584.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Dic₆₆	C₂	1	2	yes	maximal
2	C₁₁×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#10587151	—	3	2	no	maximal
4	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₃×Dic₃₃	—	2	2	no	—
6	Dic₆₆	D₃	1	2	yes	—
7	C₃×Dic₂₂	—	3	2	no	—
8	C₁₁×C₃⋊C₈	—	3	2	no	—
9	C₁₁×C₃⋊C₈	—	6	1	no	—
10	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
11	Dic₄₄	—	9	1	no	Hall
12	#3718	—	11	1	no	maximal, Hall
13	C₃×C₄×C₁₁	—	2	1	no	—
14	C₃×C₄×C₁₁	C₂×D₃	1	2	yes	—
15	Dic₃₃	—	2	2	no	—
16	C₃×Dic₁₁	—	6	2	no	—
17	C₃²×C₁₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
18	Dic₂₂	—	3	2	no	—
19	C₈×C₁₁	—	9	1	no	—
20	C₃×Dic₆	—	11	2	no	—
21	C₃⋊(C₃⋊C₈)	D₁₁	1	1	yes	characteristic
22	C₂×C₃×C₁₁	—	2	1	no	—
23	C₂×C₃×C₁₁	#67	1	2	yes	—
24	#216	—	33	2	no	—
25	C₄×C₁₁	D₃²	1	1	yes	characteristic
26	Dic₁₁	—	6	2	no	—
27	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
28	C₃×Dic₃	—	22	2	no	—
29	C₃×C₁₁	—	2	1	no	—
30	C₃×C₁₁	#216	1	2	yes	complemented
31	C₃×Q₈	—	33	2	no	—
32	Dic₆	—	11	2	no	—
33	C₃⋊C₈	—	3	2	no	—
34	C₃⋊C₈	—	6	1	no	—
35	C₂×C₁₁	#625	1	1	yes	characteristic
36	C₂×C₃²	D₄₄	1	1	yes	characteristic
37	Q₁₆	—	99	1	no	Sylow
38	C₃×C₄	—	2	1	no	—
39	C₃×C₄	—	66	2	no	—
40	C₃×C₄	D₃×D₁₁	1	2	yes	—
41	Dic₃	—	22	2	no	—
42	C₁₁	#3718	1	1	yes	characteristic, complemented, Sylow
43	C₃²	Dic₄₄	1	1	yes	characteristic, complemented, Sylow
44	Q₈	—	33	2	no	—
45	C₈	—	9	1	no	—
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	#63141	1	2	yes	—
48	C₄	—	66	2	no	—
49	C₄	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic
50	C₃	—	2	1	no	—
51	C₃	#10587151	1	2	yes	complemented
52	C₂	#11716247	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716247
commutator, Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
Frattini, hypercenter	C₄	(C₃⋊D₃)⋊D₁₁
socle, prime radical	C₂×C₃²×C₁₁	D₄
hypocenter	C₃²×C₁₁	Q₁₆
LCS	G ▷ C₃²×C₄×C₁₁ ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
17. C₃²×C₁₁	Q₁₆	semidirect
30. C₃×C₁₁	#216	semidirect
42. C₁₁	#3718	semidirect
43. C₃²	Dic₄₄	semidirect
51. C₃	#10587151	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×Dic₆₆	2
C₁₁×C₃⋊(C₃⋊C₈)	2
#10587151	3
#3718	11