Subgroups — Dic₉×#10597244 #36344797

Order 21780.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#10597244	C₂	1	1	yes	maximal, characteristic
2	Dic₃×#10597244	—	3	1	no	maximal
3	C₉×#10597244	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁²×Dic₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×#10597244	D₃	1	1	yes	characteristic
6	C₄×#10597244	—	9	1	no	Hall
7	C₂×C₉×C₁₁²	C₂×C₅	1	1	yes	characteristic
8	Dic₉×C₁₁⋊C₅	—	11	2	no	maximal
9	C₃×#10597244	Dic₃	1	1	yes	characteristic
10	C₁₁²×Dic₃	—	3	1	no	—
11	C₂×#10597244	D₉	1	1	yes	characteristic
12	C₉×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₁₁⋊C₅	—	11	2	no	—
14	C₂×C₃×C₁₁²	C₅×D₃	1	1	yes	characteristic
15	Dic₃×C₁₁⋊C₅	—	33	2	no	—
16	#10597244	Dic₉	1	1	yes	characteristic, direct product factor, Hall
17	C₉×C₁₁⋊C₅	—	11	2	no	—
18	C₄×C₁₁²	—	9	1	no	Hall
19	C₁₁×Dic₉	—	5	2	no	—
20	C₁₁×Dic₉	C₁₁⋊C₅	1	2	yes	complemented
21	C₃×C₁₁²	C₅×Dic₃	1	1	yes	characteristic
22	C₂×C₃×C₁₁⋊C₅	—	11	2	no	—
23	C₂×C₁₁²	C₅×D₉	1	1	yes	characteristic
24	C₄×C₁₁⋊C₅	—	99	2	no	—
25	C₂×C₉×C₁₁	—	5	2	no	—
26	C₂×C₉×C₁₁	C₂×C₁₁⋊C₅	1	2	yes	—
27	C₅×Dic₉	—	121	1	no	Hall
28	C₃×C₁₁⋊C₅	—	11	2	no	—
29	C₁₁×Dic₃	—	3	2	no	—
30	C₁₁×Dic₃	—	15	2	no	—
31	C₁₁²	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₁₁⋊C₅	—	11	2	no	—
33	C₉×C₁₁	—	5	2	no	—
34	C₉×C₁₁	C₄×C₁₁⋊C₅	1	2	yes	complemented
35	C₂×C₅×C₉	—	121	1	no	—
36	C₂×C₃×C₁₁	—	5	2	no	—
37	C₂×C₃×C₁₁	D₃×C₁₁⋊C₅	1	2	yes	—
38	C₅×Dic₃	—	363	1	no	—
39	C₁₁⋊C₅	—	11	2	no	—
40	C₅×C₉	—	121	1	no	Hall
41	C₄×C₁₁	—	9	2	no	—
42	C₄×C₁₁	—	45	2	no	—
43	Dic₉	#10597244	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₁₁	—	5	2	no	—
45	C₃×C₁₁	Dic₃×C₁₁⋊C₅	1	2	yes	—
46	C₂×C₃×C₅	—	121	1	no	—
47	C₂×C₁₁	—	5	2	no	—
48	C₂×C₁₁	D₉×C₁₁⋊C₅	1	2	yes	—
49	C₄×C₅	—	1089	1	no	Hall
50	C₂×C₉	C₂×#10597244	1	1	yes	characteristic
51	C₃×C₅	—	121	1	no	—
52	Dic₃	—	3	1	no	—
53	C₁₁	—	5	2	no	—
54	C₁₁	Dic₉×C₁₁⋊C₅	1	2	yes	complemented
55	C₂×C₅	—	121	1	no	—
56	C₉	C₄×#10597244	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	D₃×#10597244	1	1	yes	characteristic
58	C₅	—	121	1	no	Sylow
59	C₄	—	9	1	no	Sylow
60	C₃	Dic₃×#10597244	1	1	yes	characteristic
61	C₂	D₉×#10597244	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉×#10597244
commutator, hypocenter	C₉×C₁₁²	C₄×C₅
Frattini	C₂×C₃	D₃×#10597244
Fitting, cosocle	C₂×C₉×C₁₁²	C₂×C₅
socle	C₂×C₃×C₁₁²	C₅×D₃
prime radical	C₂×C₃×#10597244	D₃
LCS	G ▷ C₉×C₁₁²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₉×#10597244	C₄	semidirect
4. C₁₁²×Dic₉	C₅	semidirect
12. C₉×C₁₁²	C₄×C₅	semidirect
16. #10597244	Dic₉	direct (N × H)
20. C₁₁×Dic₉	C₁₁⋊C₅	semidirect
31. C₁₁²	C₅×Dic₉	semidirect
34. C₉×C₁₁	C₄×C₁₁⋊C₅	semidirect
43. Dic₉	#10597244	direct (N × H)
54. C₁₁	Dic₉×C₁₁⋊C₅	semidirect
56. C₉	C₄×#10597244	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#10597244	2
Dic₃×#10597244	3
C₁₁²×Dic₉	5
Dic₉×C₁₁⋊C₅	11

Subgroups — Dic9×#10597244 #36344797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉×#10597244 #36344797