Subgroups — #13097106

Order 1584.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃₃	C₂	1	2	yes	maximal
3	Dic₃×Dic₁₁	—	3	2	no	maximal
4	C₂²×C₃²×C₁₁	C₂²	1	1	yes	characteristic
5	C₁₁×C₃⋊Dic₃	C₄	1	2	yes	complemented
6	C₃×Dic₃₃	C₄	1	4	yes	complemented
7	C₂×Dic₃₃	D₃	1	2	yes	—
8	C₂×C₁₁×Dic₃	—	3	2	no	—
9	C₂×C₁₁×Dic₃	—	6	1	no	—
10	C₂×C₃×Dic₁₁	—	3	2	no	—
11	C₂×C₃²×C₁₁	C₂×C₄	1	2	yes	—
12	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₄×Dic₁₁	—	9	1	no	Hall
14	Dic₃²	—	11	1	no	maximal, Hall
15	C₂²×C₃×C₁₁	—	2	1	no	—
16	C₂²×C₃×C₁₁	C₂×D₃	1	2	yes	—
17	Dic₃₃	Dic₃	1	4	yes	complemented
18	C₃×Dic₁₁	—	3	4	no	—
19	C₁₁×Dic₃	—	3	4	no	—
20	C₁₁×Dic₃	—	6	2	no	—
21	C₃²×C₁₁	C₄²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₄×C₁₁	—	9	1	no	—
23	C₂×Dic₁₁	—	3	2	no	—
24	C₂×C₃⋊Dic₃	D₁₁	1	1	yes	characteristic
25	C₂×C₃×Dic₃	—	11	2	no	—
26	C₂×C₃×C₁₁	—	2	2	no	—
27	C₂×C₃×C₁₁	—	2	1	no	—
28	C₂×C₃×C₁₁	C₄×D₃	1	2	yes	—
29	C₂×C₃×C₁₁	C₄×D₃	1	2	yes	—
30	C₂×C₃×C₁₁	C₂×Dic₃	1	2	yes	—
31	C₄×Dic₃	—	33	2	no	—
32	C₂²×C₁₁	D₃²	1	1	yes	characteristic
33	C₄×C₁₁	—	9	2	no	—
34	Dic₁₁	—	3	4	no	—
35	C₂²×C₃²	C₂×D₁₁	1	1	yes	characteristic
36	C₃⋊Dic₃	Dic₁₁	1	2	yes	complemented
37	C₃×Dic₃	—	11	4	no	—
38	C₃×C₁₁	—	2	1	no	—
39	C₃×C₁₁	C₄×Dic₃	1	2	yes	complemented
40	C₂×C₃×C₄	—	33	2	no	—
41	C₂×Dic₃	—	3	2	no	—
42	C₂×Dic₃	—	6	1	no	—
43	C₂×Dic₃	—	11	2	no	—
44	C₂×C₁₁	D₃×Dic₃	1	2	yes	—
45	C₂×C₁₁	#624	1	1	yes	characteristic
46	C₂×C₃²	C₄×D₁₁	1	2	yes	—
47	C₂×C₃²	C₂×Dic₁₁	1	1	yes	characteristic
48	C₄²	—	99	1	no	Sylow
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	D₃×D₁₁	1	2	yes	—
51	C₃×C₄	—	33	4	no	—
52	Dic₃	—	3	4	no	—
53	Dic₃	—	6	2	no	—
54	Dic₃	—	11	4	no	—
55	C₁₁	Dic₃²	1	1	yes	characteristic, complemented, Sylow
56	C₃²	C₄×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	9	1	no	—
58	C₂×C₄	—	33	2	no	—
59	C₂×C₃	—	2	2	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	Dic₃×D₁₁	1	2	yes	—
62	C₂×C₃	D₃×Dic₁₁	1	2	yes	—
63	C₂×C₃	D₃₃⋊C₄	1	2	yes	—
64	C₂²	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic
65	C₄	—	9	2	no	—
66	C₄	—	33	4	no	—
67	C₃	—	2	1	no	—
68	C₃	Dic₃×Dic₁₁	1	2	yes	complemented
69	C₂	D₃₃⋊Dic₃	1	2	yes	—
70	C₂	#11716245	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	(C₃⋊D₃)⋊D₁₁
commutator, hypocenter	C₃²×C₁₁	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₃²×C₁₁	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
5. C₁₁×C₃⋊Dic₃	C₄	semidirect
6. C₃×Dic₃₃	C₄	semidirect
17. Dic₃₃	Dic₃	semidirect
21. C₃²×C₁₁	C₄²	semidirect
36. C₃⋊Dic₃	Dic₁₁	semidirect
39. C₃×C₁₁	C₄×Dic₃	semidirect
55. C₁₁	Dic₃²	semidirect
56. C₃²	C₄×Dic₁₁	semidirect
68. C₃	Dic₃×Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₃⋊Dic₃	2
C₂×C₃×Dic₃₃	2
Dic₃×Dic₁₁	3
Dic₃²	11