Subgroups — #13097074

Order 1584.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587199	—	3	1	no	maximal
5	#10587139	—	3	1	no	maximal
6	C₂×C₃×D₃×C₁₁	C₄	1	1	yes	characteristic
7	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₃×C₁₁×Dic₃	C₄	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₁	—	3	1	no	—
10	C₄×D₃×C₁₁	D₃	1	1	yes	characteristic
11	C₃⋊(C₁₁⋊C₈)	—	3	1	no	—
12	C₃⋊(C₁₁⋊C₈)	—	3	1	no	—
13	C₃⋊(C₁₁⋊C₈)	—	6	1	no	—
14	C₃⋊(C₁₁⋊C₈)	D₃	1	1	yes	characteristic, complemented
15	C₃×C₁₁⋊C₈	—	3	1	no	—
16	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₃×D₃×C₁₁	—	2	1	no	—
18	#4318	—	9	1	no	Hall
19	#3711	—	11	1	no	maximal, Hall
20	C₂²×C₃×C₁₁	—	3	1	no	—
21	C₂×D₃×C₁₁	Dic₃	1	1	yes	characteristic
22	C₃×C₄×C₁₁	—	2	1	no	—
23	C₃×C₄×C₁₁	—	3	1	no	—
24	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
25	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
26	C₁₁×Dic₃	Dic₃	1	1	yes	characteristic
27	C₃²×C₁₁	M₁₆	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄×C₁₁	—	3	1	no	—
29	C₁₁⋊C₈	—	3	1	no	—
30	C₁₁⋊C₈	—	9	1	no	—
31	C₃×C₄×D₃	D₁₁	1	1	yes	characteristic
32	C₃⋊(C₃⋊C₈)	—	11	1	no	—
33	C₃×C₃⋊C₈	—	11	1	no	—
34	C₂×C₃×C₁₁	—	2	1	no	—
35	C₂×C₃×C₁₁	—	6	1	no	—
36	C₂×C₃×C₁₁	C₄×D₃	1	1	yes	characteristic
37	C₂×C₃×C₁₁	C₂×Dic₃	1	1	yes	characteristic
38	D₃×C₁₁	—	2	1	no	—
39	#208	—	33	1	no	—
40	ΓL(1,𝔽₂₅)	—	33	1	no	—
41	C₂²×C₁₁	—	3	1	no	—
42	C₄×C₁₁	—	3	1	no	—
43	C₄×C₁₁	D₃²	1	1	yes	characteristic
44	C₂×C₃×D₃	Dic₁₁	1	1	yes	characteristic
45	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
46	C₃×Dic₃	Dic₁₁	1	1	yes	characteristic
47	C₃×C₁₁	—	2	1	no	—
48	C₃×C₁₁	ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented
49	C₃×C₁₁	#208	1	1	yes	characteristic, complemented
50	C₂×C₃×C₄	—	3	1	no	—
51	C₄×D₃	D₃₃	1	1	yes	characteristic
52	C₃×C₈	—	33	1	no	—
53	C₃⋊C₈	—	11	1	no	—
54	C₃⋊C₈	—	33	1	no	—
55	C₃⋊C₈	—	33	1	no	—
56	C₃⋊C₈	—	66	1	no	—
57	C₂×C₁₁	—	6	1	no	—
58	C₂×C₁₁	D₃×Dic₃	1	1	yes	characteristic
59	C₂×C₃²	C₂×Dic₁₁	1	1	yes	characteristic
60	C₃×D₃	—	2	1	no	—
61	M₁₆	—	99	1	no	Sylow
62	C₂²×C₃	—	3	1	no	—
63	C₂×D₃	Dic₃₃	1	1	yes	characteristic
64	C₃×C₄	—	2	1	no	—
65	C₃×C₄	—	3	1	no	—
66	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
67	C₃×C₄	C₂×D₃₃	1	1	yes	characteristic
68	Dic₃	Dic₃₃	1	1	yes	characteristic
69	C₁₁	#3711	1	1	yes	characteristic, complemented, Sylow
70	C₃²	#4318	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₄	—	3	1	no	—
72	C₈	—	33	1	no	—
73	C₈	—	99	1	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	6	1	no	—
76	C₂×C₃	D₃×Dic₁₁	1	1	yes	characteristic
77	C₂×C₃	C₂×Dic₃₃	1	1	yes	characteristic
78	D₃	—	2	1	no	—
79	C₂²	—	3	1	no	—
80	C₄	—	3	1	no	—
81	C₄	D₃×D₃₃	1	1	yes	characteristic
82	C₃	—	2	1	no	—
83	C₃	#10587139	1	1	yes	characteristic, complemented
84	C₃	#10587199	1	1	yes	characteristic, complemented
85	C₂	—	6	1	no	—
86	C₂	D₃×Dic₃₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₃₃
commutator, socle	C₂×C₃²×C₁₁	C₂×C₄
Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
prime radical	C₂×C₃×D₃×C₁₁	C₄
hypocenter	C₃²×C₁₁	M₁₆
LCS	G ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃⋊(C₁₁⋊C₈))	C₂	semidirect
3. C₃×C₃⋊(C₁₁⋊C₈)	C₂	semidirect
14. C₃⋊(C₁₁⋊C₈)	D₃	semidirect
27. C₃²×C₁₁	M₁₆	semidirect
48. C₃×C₁₁	ΓL(1,𝔽₂₅)	semidirect
49. C₃×C₁₁	#208	semidirect
69. C₁₁	#3711	semidirect
70. C₃²	#4318	semidirect
83. C₃	#10587139	semidirect
84. C₃	#10587199	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×D₃×C₁₁	2
C₃⋊(C₃⋊(C₁₁⋊C₈))	2
C₃×C₃⋊(C₁₁⋊C₈)	2
#10587199	3
#10587139	3
#3711	11