Subgroups — #13097102

Order 1584.

96 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	C₃×Dic₆₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587148	—	3	1	no	maximal
5	#10587145	—	3	1	no	maximal
6	C₂×C₁₁×C₃⋊D₃	—	2	1	no	—
7	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₃×Dic₃₃	—	2	1	no	—
9	Dic₆₆	D₃	1	1	yes	characteristic, complemented
10	C₁₁×D₁₂	—	3	1	no	—
11	C₁₁×D₁₂	—	3	1	no	—
12	C₁₁×D₁₂	—	6	1	no	—
13	C₃×Dic₂₂	—	3	1	no	—
14	C₃⋊(C₁₁⋊C₈)	D₃	1	1	yes	characteristic, complemented
15	C₃×C₁₁⋊C₈	—	3	1	no	—
16	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
17	C₁₁×C₃⋊D₃	—	4	1	no	—
18	#4324	—	9	1	no	Hall
19	#3717	—	11	1	no	maximal, Hall
20	C₂×D₃×C₁₁	—	6	2	no	—
21	C₂×D₃×C₁₁	—	6	1	no	—
22	C₂×D₃×C₁₁	—	6	1	no	—
23	C₃×C₄×C₁₁	—	2	1	no	—
24	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
25	C₃×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
26	Dic₃₃	—	2	1	no	—
27	C₃×Dic₁₁	—	6	1	no	—
28	C₃²×C₁₁	SD₁₆	1	1	yes	characteristic, complemented, Hall
29	D₄×C₁₁	—	9	1	no	—
30	Dic₂₂	—	3	1	no	—
31	C₁₁⋊C₈	—	3	1	no	—
32	C₄⋊(C₃⋊D₃)	D₁₁	1	1	yes	characteristic
33	C₃×Dic₆	—	11	1	no	—
34	C₃×C₃⋊C₈	—	11	1	no	—
35	C₂×C₃×C₁₁	—	2	1	no	—
36	C₂×C₃×C₁₁	D₁₂	1	1	yes	characteristic
37	C₂×C₃×C₁₁	#67	1	1	yes	characteristic
38	D₃×C₁₁	—	12	2	no	—
39	D₃×C₁₁	—	12	1	no	—
40	D₃×C₁₁	—	12	1	no	—
41	#215	—	33	1	no	—
42	#204	—	33	1	no	—
43	C₂²×C₁₁	—	18	1	no	—
44	C₄×C₁₁	D₃²	1	1	yes	characteristic
45	Dic₁₁	—	6	1	no	—
46	C₂×C₃⋊D₃	—	2	1	no	—
47	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
48	C₃×Dic₃	—	22	1	no	—
49	C₃×C₁₁	—	2	1	no	—
50	C₃×C₁₁	#204	1	1	yes	characteristic, complemented
51	C₃×C₁₁	#215	1	1	yes	characteristic, complemented
52	C₃×Q₈	—	33	1	no	—
53	D₁₂	—	3	1	no	—
54	D₁₂	—	3	1	no	—
55	D₁₂	—	6	1	no	—
56	Dic₆	—	11	1	no	—
57	C₃×C₈	—	33	1	no	—
58	C₃⋊C₈	—	11	1	no	—
59	C₂×C₁₁	—	36	1	no	—
60	C₂×C₁₁	#626	1	1	yes	characteristic
61	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
62	C₃⋊D₃	—	4	1	no	—
63	SD₁₆	—	99	1	no	Sylow
64	C₂×D₃	—	6	2	no	—
65	C₂×D₃	—	6	1	no	—
66	C₂×D₃	—	6	1	no	—
67	C₃×C₄	—	2	1	no	—
68	C₃×C₄	—	66	1	no	—
69	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
70	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
71	Dic₃	—	22	1	no	—
72	C₁₁	#3717	1	1	yes	characteristic, complemented, Sylow
73	C₃²	#4324	1	1	yes	characteristic, complemented, Sylow
74	Q₈	—	33	1	no	—
75	D₄	—	9	1	no	—
76	C₈	—	33	1	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	#63140	1	1	yes	characteristic
79	C₂×C₃	#63142	1	1	yes	characteristic
80	D₃	—	12	2	no	—
81	D₃	—	12	1	no	—
82	D₃	—	12	1	no	—
83	C₂²	—	18	1	no	—
84	C₄	—	66	1	no	—
85	C₄	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic
86	C₃	—	2	1	no	—
87	C₃	#10587145	1	1	yes	characteristic, complemented
88	C₃	#10587148	1	1	yes	characteristic, complemented
89	C₂	—	36	1	no	—
90	C₂	#11716246	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11716246
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. C₃×Dic₆₆	C₂	semidirect
3. C₃×C₃⋊(C₁₁⋊C₈)	C₂	semidirect
9. Dic₆₆	D₃	semidirect
14. C₃⋊(C₁₁⋊C₈)	D₃	semidirect
28. C₃²×C₁₁	SD₁₆	semidirect
50. C₃×C₁₁	#204	semidirect
51. C₃×C₁₁	#215	semidirect
72. C₁₁	#3717	semidirect
73. C₃²	#4324	semidirect
87. C₃	#10587145	semidirect
88. C₃	#10587148	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
C₃×Dic₆₆	2
C₃×C₃⋊(C₁₁⋊C₈)	2
#10587148	3
#10587145	3
#3717	11