Subgroups — #36345170

Order 21780.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊#11925896)	C₂	1	2	yes	maximal, complemented
2	C₃²×#11925893	C₂	1	1	yes	maximal, characteristic, complemented
3	#20300010	—	3	4	no	maximal
4	C₃²×#10597245	C₂²	1	1	yes	characteristic, complemented, Hall
5	#17983775	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃⋊#11925896	—	3	8	no	—
7	C₃×#11925893	D₃	1	4	yes	complemented
8	#11925896⋊C₂	—	9	1	no	Hall
9	C₁₁×C₃⋊D₃₃	C₂×C₅	1	2	yes	complemented
10	C₃²×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃⋊D₃×AGL(1,𝔽₁₁)	—	11	2	no	maximal
12	C₃×#10597245	C₂×D₃	1	4	yes	complemented
13	D₃₃⋊D₁₁	—	3	4	no	—
14	#11925896	—	9	2	no	—
15	#11925893	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₃²×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	—	11	2	no	—
18	C₃⋊D₃×C₁₁⋊C₅	—	11	2	no	—
19	C₃²×AGL(1,𝔽₁₁)	—	11	2	no	—
20	C₁₁×D₃₃	—	3	8	no	—
21	C₃×C₁₁⋊D₁₁	C₅×D₃	1	4	yes	complemented
22	D₃×AGL(1,𝔽₁₁)	—	33	8	no	—
23	#10597245	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₁₁⋊C₅	—	11	2	no	—
25	D₁₁²	—	9	1	no	Hall
26	C₃⋊D₃×D₁₁	—	11	2	no	—
27	C₃×C₁₁²	C₂×C₅×D₃	1	4	yes	complemented
28	C₃⋊AGL(1,𝔽₁₁)	—	33	8	no	—
29	D₃×C₁₁⋊C₅	—	33	8	no	—
30	C₃×AGL(1,𝔽₁₁)	—	11	8	no	—
31	C₁₁⋊D₁₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
32	C₁₁×D₁₁	—	9	2	no	—
33	C₂×AGL(1,𝔽₁₁)	—	99	2	no	—
34	C₃⋊D₃₃	AGL(1,𝔽₁₁)	1	2	yes	complemented
35	C₁₁×C₃⋊D₃	—	11	2	no	—
36	C₃²×D₁₁	—	11	2	no	—
37	C₃²×D₁₁	—	110	1	no	—
38	C₂×C₅×C₃⋊D₃	—	121	1	no	Hall
39	C₃×C₁₁⋊C₅	—	11	8	no	—
40	D₃×D₁₁	—	33	8	no	—
41	C₁₁²	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁⋊C₅	—	99	2	no	—
43	AGL(1,𝔽₁₁)	—	11	2	no	—
44	AGL(1,𝔽₁₁)	—	99	2	no	—
45	C₃²×C₁₁	—	10	1	no	—
46	C₃²×C₁₁	C₂×AGL(1,𝔽₁₁)	1	2	yes	complemented
47	C₂×C₃²×C₅	—	121	1	no	—
48	C₅×C₃⋊D₃	—	121	2	no	—
49	D₃₃	—	3	8	no	—
50	C₃×D₁₁	—	11	8	no	—
51	C₃×D₁₁	—	110	4	no	—
52	D₃×C₁₁	—	33	8	no	—
53	C₂×C₅×D₃	—	363	4	no	—
54	C₁₁⋊C₅	—	11	2	no	—
55	C₃²×C₅	—	121	1	no	Hall
56	C₂×D₁₁	—	99	2	no	—
57	C₂×C₃⋊D₃	—	121	1	no	Hall
58	C₃×C₁₁	—	10	4	no	—
59	C₃×C₁₁	D₃×AGL(1,𝔽₁₁)	1	8	yes	complemented
60	C₂×C₃×C₅	—	121	4	no	—
61	C₅×D₃	—	363	8	no	—
62	C₂×C₁₁	—	99	2	no	—
63	D₁₁	—	9	2	no	—
64	D₁₁	—	11	2	no	—
65	D₁₁	—	110	1	no	—
66	C₂²×C₅	—	1089	1	no	Hall
67	C₂×C₃²	—	121	1	no	—
68	C₃⋊D₃	—	11	2	no	—
69	C₃×C₅	—	121	4	no	—
70	C₂×D₃	—	363	4	no	—
71	C₁₁	—	10	1	no	—
72	C₁₁	C₃⋊D₃×AGL(1,𝔽₁₁)	1	2	yes	complemented
73	C₂×C₅	—	1089	2	no	—
74	C₂×C₅	—	121	1	no	—
75	C₃²	#11925896⋊C₂	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	121	4	no	—
77	D₃	—	33	8	no	—
78	C₅	—	121	1	no	Sylow
79	C₂²	—	1089	1	no	Sylow
80	C₃	#20300010	1	4	yes	complemented
81	C₂	—	99	2	no	—
82	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁²	C₂²×C₅
LCS	G ▷ C₃²×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊#11925896)	C₂	semidirect
2. C₃²×#11925893	C₂	semidirect
4. C₃²×#10597245	C₂²	semidirect
5. #17983775	C₅	semidirect
7. C₃×#11925893	D₃	semidirect
9. C₁₁×C₃⋊D₃₃	C₂×C₅	semidirect
10. C₃²×C₁₁⋊D₁₁	C₂×C₅	semidirect
12. C₃×#10597245	C₂×D₃	semidirect
15. #11925893	C₃⋊D₃	semidirect
16. C₃²×C₁₁²	C₂²×C₅	semidirect
21. C₃×C₁₁⋊D₁₁	C₅×D₃	semidirect
23. #10597245	C₂×C₃⋊D₃	semidirect
27. C₃×C₁₁²	C₂×C₅×D₃	semidirect
31. C₁₁⋊D₁₁	C₅×C₃⋊D₃	semidirect
34. C₃⋊D₃₃	AGL(1,𝔽₁₁)	semidirect
41. C₁₁²	C₂×C₅×C₃⋊D₃	semidirect
46. C₃²×C₁₁	C₂×AGL(1,𝔽₁₁)	semidirect
59. C₃×C₁₁	D₃×AGL(1,𝔽₁₁)	semidirect
72. C₁₁	C₃⋊D₃×AGL(1,𝔽₁₁)	semidirect
75. C₃²	#11925896⋊C₂	semidirect
80. C₃	#20300010	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊#11925896)	2
C₃²×#11925893	2
#20300010	3
#17983775	5
C₃⋊D₃×AGL(1,𝔽₁₁)	11