Subgroups — #36344839

Order 21780.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊#11925895	C₂	1	2	yes	maximal, complemented
2	C₉×#11925892	C₂	1	1	yes	maximal, characteristic, complemented
3	#20300008	—	3	1	no	maximal
4	C₉×#10597243	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₉₉⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃⋊#11925895	—	3	2	no	—
7	C₃×#11925892	D₃	1	1	yes	characteristic
8	#11925892⋊C₂	—	9	1	no	Hall
9	C₁₁×D₉₉	C₂×C₅	1	2	yes	complemented
10	C₉×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
11	D₉×AGL(1,𝔽₁₁)	—	11	2	no	maximal
12	C₃×#10597243	C₂×D₃	1	1	yes	characteristic
13	D₃₃⋊D₁₁	—	3	1	no	—
14	#11925895	—	9	2	no	—
15	#11925892	D₉	1	1	yes	characteristic, complemented
16	C₉×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₉⋊AGL(1,𝔽₁₁)	—	11	2	no	—
18	D₉×C₁₁⋊C₅	—	11	2	no	—
19	C₉×AGL(1,𝔽₁₁)	—	11	2	no	—
20	C₉×AGL(1,𝔽₁₁)	—	22	5	no	—
21	C₁₁×D₃₃	—	3	2	no	—
22	C₃×C₁₁⋊D₁₁	C₅×D₃	1	1	yes	characteristic
23	D₃×AGL(1,𝔽₁₁)	—	33	2	no	—
24	#10597243	C₂×D₉	1	1	yes	characteristic, complemented, Hall
25	C₉×C₁₁⋊C₅	—	11	2	no	—
26	C₉×C₁₁⋊C₅	—	22	5	no	—
27	D₁₁²	—	9	1	no	Hall
28	D₉×D₁₁	—	11	2	no	—
29	C₃×C₁₁²	C₂×C₅×D₃	1	1	yes	characteristic
30	C₃⋊AGL(1,𝔽₁₁)	—	33	2	no	—
31	D₃×C₁₁⋊C₅	—	33	2	no	—
32	C₃×AGL(1,𝔽₁₁)	—	11	2	no	—
33	C₃×AGL(1,𝔽₁₁)	—	22	5	no	—
34	C₁₁⋊D₁₁	C₅×D₉	1	1	yes	characteristic, complemented
35	C₁₁×D₁₁	—	9	2	no	—
36	C₂×AGL(1,𝔽₁₁)	—	99	2	no	—
37	D₉₉	AGL(1,𝔽₁₁)	1	2	yes	complemented
38	C₉×D₁₁	—	11	2	no	—
39	C₉×D₁₁	—	22	5	no	—
40	C₁₁×D₉	—	11	2	no	—
41	C₂×C₅×D₉	—	121	1	no	Hall
42	C₃×C₁₁⋊C₅	—	11	2	no	—
43	C₃×C₁₁⋊C₅	—	22	5	no	—
44	D₃×D₁₁	—	33	2	no	—
45	C₁₁²	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁⋊C₅	—	99	2	no	—
47	AGL(1,𝔽₁₁)	—	11	2	no	—
48	AGL(1,𝔽₁₁)	—	22	5	no	—
49	AGL(1,𝔽₁₁)	—	99	2	no	—
50	C₉×C₁₁	—	2	5	no	—
51	C₉×C₁₁	C₂×AGL(1,𝔽₁₁)	1	2	yes	complemented
52	C₂×C₅×C₉	—	121	1	no	—
53	C₅×D₉	—	121	2	no	—
54	D₃₃	—	3	2	no	—
55	C₃×D₁₁	—	11	2	no	—
56	C₃×D₁₁	—	22	5	no	—
57	D₃×C₁₁	—	33	2	no	—
58	C₂×C₅×D₃	—	363	1	no	—
59	C₁₁⋊C₅	—	11	2	no	—
60	C₁₁⋊C₅	—	22	5	no	—
61	C₅×C₉	—	121	1	no	Hall
62	C₂×D₁₁	—	99	2	no	—
63	C₂×D₉	—	121	1	no	Hall
64	C₃×C₁₁	—	2	5	no	—
65	C₃×C₁₁	D₃×AGL(1,𝔽₁₁)	1	2	yes	—
66	C₂×C₃×C₅	—	121	1	no	—
67	C₅×D₃	—	363	2	no	—
68	C₂×C₁₁	—	99	2	no	—
69	D₁₁	—	9	2	no	—
70	D₁₁	—	11	2	no	—
71	D₁₁	—	22	5	no	—
72	C₂²×C₅	—	1089	1	no	Hall
73	C₂×C₉	—	121	1	no	—
74	D₉	—	11	2	no	—
75	C₃×C₅	—	121	1	no	—
76	C₂×D₃	—	363	1	no	—
77	C₁₁	—	2	5	no	—
78	C₁₁	D₉×AGL(1,𝔽₁₁)	1	2	yes	complemented
79	C₂×C₅	—	1089	2	no	—
80	C₂×C₅	—	121	1	no	—
81	C₉	#11925892⋊C₂	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₃	—	121	1	no	—
83	D₃	—	33	2	no	—
84	C₅	—	121	1	no	Sylow
85	C₂²	—	1089	1	no	Sylow
86	C₃	#20300008	1	1	yes	characteristic
87	C₂	—	99	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁²	C₂²×C₅
Frattini	C₃	#20300008
socle	C₃×C₁₁²	C₂×C₅×D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉⋊#11925895	C₂	semidirect
2. C₉×#11925892	C₂	semidirect
4. C₉×#10597243	C₂²	semidirect
5. D₉₉⋊D₁₁	C₅	semidirect
9. C₁₁×D₉₉	C₂×C₅	semidirect
10. C₉×C₁₁⋊D₁₁	C₂×C₅	semidirect
15. #11925892	D₉	semidirect
16. C₉×C₁₁²	C₂²×C₅	semidirect
24. #10597243	C₂×D₉	semidirect
34. C₁₁⋊D₁₁	C₅×D₉	semidirect
37. D₉₉	AGL(1,𝔽₁₁)	semidirect
45. C₁₁²	C₂×C₅×D₉	semidirect
51. C₉×C₁₁	C₂×AGL(1,𝔽₁₁)	semidirect
78. C₁₁	D₉×AGL(1,𝔽₁₁)	semidirect
81. C₉	#11925892⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₉⋊#11925895	2
C₉×#11925892	2
#20300008	3
D₉₉⋊D₁₁	5
D₉×AGL(1,𝔽₁₁)	11