Subgroups — D₄₅⋊(C₁₁⋊D₁₁) #36344945

Order 21780.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₉⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₅⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊(C₁₁⋊D₁₁)	—	3	1	no	maximal
5	C₅×C₉×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×C₁₁⋊D₁₁	—	5	1	no	maximal, Hall
7	C₁₁²×D₁₅	—	3	1	no	—
8	C₅×C₃⋊(C₁₁⋊D₁₁)	—	3	1	no	—
9	C₃×C₅⋊(C₁₁⋊D₁₁)	D₃	1	1	yes	characteristic
10	D₅×C₁₁⋊D₁₁	—	9	1	no	Hall
11	C₉⋊(C₁₁⋊D₁₁)	D₅	1	1	yes	characteristic, complemented
12	C₁₁²×D₉	—	5	1	no	—
13	C₉×C₁₁⋊D₁₁	—	5	1	no	—
14	D₄₅⋊D₁₁	—	11	12	no	maximal
15	C₃×C₅×C₁₁²	C₂×D₃	1	1	yes	characteristic
16	D₃×C₁₁⋊D₁₁	—	15	1	no	—
17	C₅⋊(C₁₁⋊D₁₁)	D₉	1	1	yes	characteristic, complemented
18	D₅×C₁₁²	—	9	1	no	—
19	C₅×C₁₁⋊D₁₁	—	9	1	no	—
20	C₉×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
21	C₁₁×D₄₅	D₁₁	1	12	yes	complemented
22	C₅×D₉₉	—	11	12	no	—
23	C₉×D₅₅	—	11	12	no	—
24	C₃⋊(C₁₁⋊D₁₁)	—	3	1	no	—
25	D₃×C₁₁²	—	15	1	no	—
26	C₃×C₁₁⋊D₁₁	—	5	1	no	—
27	D₁₅⋊D₁₁	—	33	12	no	—
28	C₅×C₁₁²	C₂×D₉	1	1	yes	characteristic, complemented, Hall
29	C₅×C₉×C₁₁	C₂×D₁₁	1	12	yes	complemented
30	C₂×C₁₁⋊D₁₁	—	45	1	no	Hall
31	D₉×D₁₁	—	55	12	no	—
32	C₃×C₁₁²	D₃×D₅	1	1	yes	characteristic
33	C₁₁×D₁₅	—	3	12	no	—
34	C₅×D₃₃	—	33	12	no	—
35	C₃×D₅₅	—	11	12	no	—
36	C₂×C₁₁²	—	45	1	no	—
37	C₁₁⋊D₁₁	—	5	1	no	—
38	C₁₁⋊D₁₁	—	9	1	no	—
39	D₅×D₁₁	—	99	12	no	—
40	D₉₉	—	11	12	no	—
41	C₉×D₁₁	—	55	12	no	—
42	C₁₁×D₉	—	5	12	no	—
43	D₅×D₉	—	121	1	no	Hall
44	C₃×C₅×C₁₁	D₃×D₁₁	1	12	yes	—
45	D₃×D₁₁	—	165	12	no	—
46	C₁₁²	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
47	D₅₅	—	11	12	no	—
48	C₅×D₁₁	—	99	12	no	—
49	D₅×C₁₁	—	9	12	no	—
50	C₉×C₁₁	D₅×D₁₁	1	12	yes	complemented
51	D₄₅	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
52	C₉×D₅	—	121	1	no	—
53	C₅×D₉	—	121	1	no	—
54	D₃₃	—	33	12	no	—
55	C₃×D₁₁	—	55	12	no	—
56	D₃×C₁₁	—	15	12	no	—
57	D₃×D₅	—	363	1	no	—
58	C₅×C₁₁	D₉×D₁₁	1	12	yes	complemented
59	C₅×C₉	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×D₁₁	—	495	12	no	—
61	C₂×D₉	—	605	1	no	Hall
62	C₃×C₁₁	D₁₅⋊D₁₁	1	12	yes	—
63	D₁₅	—	3	1	no	—
64	C₃×D₅	—	121	1	no	—
65	C₅×D₃	—	363	1	no	—
66	C₂×C₁₁	—	45	12	no	—
67	D₁₁	—	55	12	no	—
68	D₁₁	—	99	12	no	—
69	C₂×D₅	—	1089	1	no	Hall
70	C₂×C₉	—	605	1	no	—
71	D₉	—	5	1	no	—
72	D₉	—	121	1	no	—
73	C₃×C₅	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic
74	C₂×D₃	—	1815	1	no	—
75	C₁₁	D₄₅⋊D₁₁	1	12	yes	complemented
76	C₂×C₅	—	1089	1	no	—
77	D₅	—	9	1	no	—
78	D₅	—	121	1	no	—
79	C₉	D₅×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	605	1	no	—
81	D₃	—	15	1	no	—
82	D₃	—	363	1	no	—
83	C₅	D₉×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	5445	1	no	Sylow
85	C₃	D₁₅⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic
86	C₂	—	45	1	no	—
87	C₂	—	1089	1	no	—
88	C₂	—	605	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₁²	C₂²
Frattini	C₃	D₁₅⋊(C₁₁⋊D₁₁)
socle	C₃×C₅×C₁₁²	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×D₄₅	C₂	semidirect
2. C₅×C₉⋊(C₁₁⋊D₁₁)	C₂	semidirect
3. C₉×C₅⋊(C₁₁⋊D₁₁)	C₂	semidirect
5. C₅×C₉×C₁₁²	C₂²	semidirect
11. C₉⋊(C₁₁⋊D₁₁)	D₅	semidirect
17. C₅⋊(C₁₁⋊D₁₁)	D₉	semidirect
20. C₉×C₁₁²	C₂×D₅	semidirect
21. C₁₁×D₄₅	D₁₁	semidirect
28. C₅×C₁₁²	C₂×D₉	semidirect
29. C₅×C₉×C₁₁	C₂×D₁₁	semidirect
46. C₁₁²	D₅×D₉	semidirect
50. C₉×C₁₁	D₅×D₁₁	semidirect
51. D₄₅	C₁₁⋊D₁₁	semidirect
58. C₅×C₁₁	D₉×D₁₁	semidirect
59. C₅×C₉	C₂×C₁₁⋊D₁₁	semidirect
75. C₁₁	D₄₅⋊D₁₁	semidirect
79. C₉	D₅×C₁₁⋊D₁₁	semidirect
83. C₅	D₉×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×D₄₅	2
C₅×C₉⋊(C₁₁⋊D₁₁)	2
C₉×C₅⋊(C₁₁⋊D₁₁)	2
D₁₅⋊(C₁₁⋊D₁₁)	3
D₉×C₁₁⋊D₁₁	5
D₄₅⋊D₁₁	11

Subgroups — D45⋊(C11⋊D11) #36344945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₅⋊(C₁₁⋊D₁₁) #36344945