Subgroups — C₃×#10587148 #13097017

Order 1584.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₃	#63142
commutator, cosocle	C₃×C₄×C₁₁	C₂²×C₃
Frattini	C₄	C₃×D₃×D₁₁
Fitting	C₃²×C₄×C₁₁	C₂²
socle	C₂×C₃²×C₁₁	D₄
prime radical	C₃×C₁₁×D₁₂	C₂
hypercenter	C₃×C₄	D₃×D₁₁
hypocenter	C₃×C₁₁	C₃×SD₁₆
LCS	G ▷ C₃×C₄×C₁₁ ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₃×Dic₆₆	C₂	semidirect
3. C₃²×C₁₁⋊C₈	C₂	semidirect
5. #10587148	C₃	direct (N × H)
10. Dic₆₆	C₂×C₃	semidirect
14. C₃×C₁₁⋊C₈	D₃	semidirect
15. C₃×C₁₁⋊C₈	C₂×C₃	semidirect
27. C₃²×C₁₁	SD₁₆	semidirect
30. C₁₁⋊C₈	C₃×D₃	semidirect
48. C₃×C₁₁	#204	semidirect
49. C₃×C₁₁	C₃×SD₁₆	semidirect
69. C₁₁	C₃×#204	semidirect
70. C₃²	#4324	semidirect
83. C₃	#10587148	direct (N × H)
84. C₃	C₃×#4324	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
C₃×C₁₁×D₁₂	2
C₃²×C₁₁⋊C₈	2
C₃×#4324	3
#10587148	3
C₃×#204	11

Subgroups — C3×#10587148 #13097017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10587148 #13097017