Subgroups — #13097039

Order 1584.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₂₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587145	—	3	4	no	maximal
5	C₂×C₁₁×C₃⋊D₃	—	2	1	no	—
6	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₃²×Dic₁₁	—	2	1	no	—
8	C₁₁×D₁₂	—	3	4	no	—
9	C₃×Dic₂₂	D₃	1	4	yes	complemented
10	C₃⋊(C₁₁⋊C₈)	—	3	4	no	—
11	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
12	C₁₁×C₃⋊D₃	—	4	1	no	—
13	#4324	—	9	1	no	Hall
14	#3755	—	11	1	no	maximal, Hall
15	C₂×D₃×C₁₁	—	6	4	no	—
16	C₃×C₄×C₁₁	C₂×D₃	1	4	yes	—
17	C₃×Dic₁₁	—	2	4	no	—
18	C₃²×C₁₁	SD₁₆	1	1	yes	characteristic, complemented, Hall
19	D₄×C₁₁	—	9	1	no	—
20	Dic₂₂	C₃⋊D₃	1	1	yes	characteristic, complemented
21	C₁₁⋊C₈	—	9	1	no	—
22	C₃²×Q₈	—	11	1	no	—
23	C₄⋊(C₃⋊D₃)	D₁₁	1	1	yes	characteristic
24	C₃⋊(C₃⋊C₈)	—	11	1	no	—
25	C₂×C₃×C₁₁	#67	1	4	yes	—
26	D₃×C₁₁	—	12	4	no	—
27	#215	—	33	4	no	—
28	C₂²×C₁₁	—	18	1	no	—
29	C₄×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic
30	Dic₁₁	—	2	1	no	—
31	C₂×C₃⋊D₃	—	2	1	no	—
32	C₃²×C₄	—	22	1	no	—
33	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
34	C₃×C₁₁	#215	1	4	yes	complemented
35	C₃×Q₈	—	11	4	no	—
36	D₁₂	—	3	4	no	—
37	C₃⋊C₈	—	33	4	no	—
38	C₂×C₁₁	—	36	1	no	—
39	C₂×C₁₁	#638	1	1	yes	characteristic
40	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
41	C₃⋊D₃	—	4	1	no	—
42	SD₁₆	—	99	1	no	Sylow
43	C₂×D₃	—	6	4	no	—
44	C₃×C₄	—	22	4	no	—
45	C₃×C₄	D₃×D₁₁	1	4	yes	—
46	C₁₁	#3755	1	1	yes	characteristic, complemented, Sylow
47	C₃²	#4324	1	1	yes	characteristic, complemented, Sylow
48	Q₈	—	11	1	no	—
49	D₄	—	9	1	no	—
50	C₈	—	99	1	no	—
51	C₂×C₃	#63140	1	4	yes	—
52	D₃	—	12	4	no	—
53	C₂²	—	18	1	no	—
54	C₄	—	22	1	no	—
55	C₄	C₃⋊D₃×D₁₁	1	1	yes	characteristic
56	C₃	#10587145	1	4	yes	complemented
57	C₂	—	36	1	no	—
58	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	C₂×C₃²×C₁₁	D₄
prime radical	C₁₁×C₄⋊(C₃⋊D₃)	C₂
hypocenter	C₃²×C₁₁	SD₁₆
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
2. C₃²×Dic₂₂	C₂	semidirect
3. C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	semidirect
9. C₃×Dic₂₂	D₃	semidirect
18. C₃²×C₁₁	SD₁₆	semidirect
20. Dic₂₂	C₃⋊D₃	semidirect
34. C₃×C₁₁	#215	semidirect
46. C₁₁	#3755	semidirect
47. C₃²	#4324	semidirect
56. C₃	#10587145	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₄⋊(C₃⋊D₃)	2
C₃²×Dic₂₂	2
C₃⋊(C₃⋊(C₁₁⋊C₈))	2
#10587145	3
#3755	11