Subgroups — #13097072

Order 1584.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₃₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₃₃	—	3	1	no	maximal
5	D₃₃⋊C₈	—	3	1	no	maximal
6	C₂×C₃⋊D₃₃	C₄	1	1	yes	characteristic
7	C₃²×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₃₃	C₄	1	1	yes	characteristic
9	C₄×D₃₃	—	3	1	no	—
10	C₄×D₃₃	—	3	1	no	—
11	C₄×D₃₃	—	6	1	no	—
12	C₃×C₈×C₁₁	—	3	1	no	—
13	C₃⋊(C₁₁⋊C₈)	D₃	1	1	yes	characteristic, complemented
14	C₃×C₁₁⋊C₈	—	3	1	no	—
15	C₁₁×C₃⋊C₈	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₃⋊D₃₃	C₈	1	2	yes	complemented
18	C₈×D₁₁	—	9	1	no	Hall
19	#3710	—	11	1	no	maximal, Hall
20	C₂×D₃₃	—	3	1	no	—
21	C₂×D₃₃	—	3	1	no	—
22	C₂×D₃₃	—	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	—	3	1	no	—
27	Dic₃₃	—	3	1	no	—
28	Dic₃₃	—	6	1	no	—
29	C₃²×C₁₁	C₂×C₈	1	1	yes	characteristic, complemented, Hall
30	C₄×D₁₁	—	9	1	no	—
31	C₈×C₁₁	—	3	1	no	—
32	C₁₁⋊C₈	—	3	1	no	—
33	C₄×C₃⋊D₃	—	11	1	no	—
34	C₃×C₃⋊C₈	—	11	1	no	—
35	C₃×C₃⋊C₈	D₁₁	1	1	yes	characteristic, complemented
36	C₂×C₃×C₁₁	—	2	1	no	—
37	C₂×C₃×C₁₁	C₄×D₃	1	1	yes	characteristic
38	C₂×C₃×C₁₁	C₄×D₃	1	1	yes	characteristic
39	D₃₃	—	3	2	no	—
40	D₃₃	—	3	2	no	—
41	D₃₃	—	6	2	no	—
42	D₃×C₈	—	33	1	no	—
43	D₃×C₈	—	33	1	no	—
44	C₂×D₁₁	—	9	1	no	—
45	C₄×C₁₁	D₃²	1	1	yes	characteristic
46	Dic₁₁	—	9	1	no	—
47	C₂×C₃⋊D₃	—	11	1	no	—
48	C₃²×C₄	C₂×D₁₁	1	1	yes	characteristic
49	C₃⋊Dic₃	—	11	1	no	—
50	C₃×C₁₁	—	2	1	no	—
51	C₃×C₁₁	D₃×C₈	1	1	yes	characteristic, complemented
52	C₃×C₁₁	D₃×C₈	1	1	yes	characteristic, complemented
53	C₄×D₃	—	33	1	no	—
54	C₄×D₃	—	33	1	no	—
55	C₄×D₃	—	66	1	no	—
56	C₃×C₈	—	3	1	no	—
57	C₃×C₈	—	33	1	no	—
58	C₃⋊C₈	—	11	1	no	—
59	C₃⋊C₈	D₃₃	1	1	yes	characteristic, complemented
60	C₂×C₁₁	#624	1	1	yes	characteristic
61	D₁₁	—	9	2	no	—
62	C₂×C₃²	C₄×D₁₁	1	1	yes	characteristic
63	C₃⋊D₃	—	11	2	no	—
64	C₂×C₈	—	99	1	no	Sylow
65	C₂×D₃	—	33	1	no	—
66	C₂×D₃	—	33	1	no	—
67	C₂×D₃	—	66	1	no	—
68	C₃×C₄	—	2	1	no	—
69	C₃×C₄	D₃×D₁₁	1	1	yes	characteristic
70	C₃×C₄	C₂×D₃₃	1	1	yes	characteristic
71	Dic₃	—	33	1	no	—
72	Dic₃	—	33	1	no	—
73	Dic₃	—	66	1	no	—
74	C₁₁	#3710	1	1	yes	characteristic, complemented, Sylow
75	C₃²	C₈×D₁₁	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₄	—	99	1	no	—
77	C₈	—	3	1	no	—
78	C₈	—	33	1	no	—
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	D₃₃⋊C₄	1	1	yes	characteristic
81	C₂×C₃	C₄×D₃₃	1	1	yes	characteristic
82	D₃	—	33	2	no	—
83	D₃	—	33	2	no	—
84	D₃	—	66	2	no	—
85	C₂²	—	99	1	no	—
86	C₄	—	99	1	no	—
87	C₄	D₃×D₃₃	1	1	yes	characteristic
88	C₃	—	2	1	no	—
89	C₃	D₃₃⋊C₈	1	1	yes	characteristic, complemented
90	C₃	C₈×D₃₃	1	1	yes	characteristic, complemented
91	C₂	—	99	2	no	—
92	C₂	#11716239	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃×D₃₃
commutator, hypocenter	C₃²×C₁₁	C₂×C₈
Fitting, cosocle	C₃²×C₄×C₁₁	C₂²
socle	C₂×C₃²×C₁₁	C₂×C₄
prime radical	C₂×C₃⋊D₃₃	C₄
LCS	G ▷ 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×C₁₁×C₃⋊C₈	C₂	semidirect
13. C₃⋊(C₁₁⋊C₈)	D₃	semidirect
15. C₁₁×C₃⋊C₈	D₃	semidirect
17. C₃⋊D₃₃	C₈	semidirect
29. C₃²×C₁₁	C₂×C₈	semidirect
35. C₃×C₃⋊C₈	D₁₁	semidirect
51. C₃×C₁₁	D₃×C₈	semidirect
52. C₃×C₁₁	D₃×C₈	semidirect
59. C₃⋊C₈	D₃₃	semidirect
74. C₁₁	#3710	semidirect
75. C₃²	C₈×D₁₁	semidirect
89. C₃	D₃₃⋊C₈	semidirect
90. C₃	C₈×D₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊D₃₃	2
C₃×C₃⋊(C₁₁⋊C₈)	2
C₃×C₁₁×C₃⋊C₈	2
C₈×D₃₃	3
D₃₃⋊C₈	3
#3710	11