Subgroups — #13097044

Order 1584.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#634	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₂₂	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	1	1	yes	maximal, characteristic
4	#10587150	—	3	4	no	maximal
5	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×C₃⋊Dic₃	—	2	1	no	—
7	C₃²×Dic₁₁	—	2	1	no	—
8	C₁₁×Dic₆	—	3	4	no	—
9	C₃×Dic₂₂	D₃	1	4	yes	—
10	C₃⋊(C₁₁⋊C₈)	—	3	4	no	—
11	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
12	#4326	—	9	1	no	Hall
13	#3756	—	11	1	no	maximal, Hall
14	C₃×C₄×C₁₁	C₂×D₃	1	4	yes	—
15	C₃×Dic₁₁	—	2	4	no	—
16	C₁₁×Dic₃	—	6	4	no	—
17	C₃²×C₁₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
18	Q₈×C₁₁	—	9	1	no	—
19	Dic₂₂	C₃⋊D₃	1	1	yes	characteristic
20	C₁₁⋊C₈	—	9	1	no	—
21	C₃²×Q₈	—	11	1	no	—
22	#634	D₁₁	1	1	yes	characteristic
23	C₃⋊(C₃⋊C₈)	—	11	1	no	—
24	C₂×C₃×C₁₁	#67	1	4	yes	—
25	#216	—	33	4	no	—
26	C₄×C₁₁	—	18	1	no	—
27	C₄×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic
28	Dic₁₁	—	2	1	no	—
29	C₃²×C₄	—	22	1	no	—
30	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
31	C₃⋊Dic₃	—	2	1	no	—
32	C₃×C₁₁	#216	1	4	yes	complemented
33	C₃×Q₈	—	11	4	no	—
34	Dic₆	—	3	4	no	—
35	C₃⋊C₈	—	33	4	no	—
36	C₂×C₁₁	#638	1	1	yes	characteristic
37	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
38	Q₁₆	—	99	1	no	Sylow
39	C₃×C₄	—	22	4	no	—
40	C₃×C₄	D₃×D₁₁	1	4	yes	—
41	Dic₃	—	6	4	no	—
42	C₁₁	#3756	1	1	yes	characteristic, complemented, Sylow
43	C₃²	#4326	1	1	yes	characteristic, complemented, Sylow
44	Q₈	—	9	1	no	—
45	Q₈	—	11	1	no	—
46	C₈	—	99	1	no	—
47	C₂×C₃	#63140	1	4	yes	—
48	C₄	—	18	1	no	—
49	C₄	—	22	1	no	—
50	C₄	C₃⋊D₃×D₁₁	1	1	yes	characteristic
51	C₃	#10587150	1	4	yes	complemented
52	C₂	#11716228	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716228
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
32. C₃×C₁₁	#216	semidirect
42. C₁₁	#3756	semidirect
43. C₃²	#4326	semidirect
51. C₃	#10587150	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#634	2
C₃²×Dic₂₂	2
C₃⋊(C₃⋊(C₁₁⋊C₈))	2
#10587150	3
#3756	11