Subgroups — #72243367

Order 2916.

334 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₉⋊D₉	C₂	1	3	yes	maximal, complemented
2	#11757745	—	3	3	no	maximal
3	C₉³	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₃×C₉⋊D₉	D₃	1	3	yes	—
5	C₉×C₃⋊D₉	—	3	6	no	—
6	C₉×C₃⋊D₉	—	6	3	no	—
7	#66431	—	9	3	no	—
8	D₉²	—	9	3	no	—
9	C₃×C₉²	—	2	3	no	—
10	C₃×C₉²	—	4	1	no	—
11	C₃×C₉²	C₂×D₃	1	3	yes	—
12	C₉×C₃⋊D₃	—	9	3	no	—
13	C₃×C₃⋊D₉	—	3	6	no	—
14	C₃×C₃⋊D₉	—	6	3	no	—
15	C₉⋊D₉	D₉	1	3	yes	complemented
16	C₉×D₉	—	9	6	no	—
17	C₉×D₉	—	18	6	no	—
18	C₉×D₉	—	18	9	no	—
19	#1113	—	27	1	no	—
20	D₃×D₉	—	27	6	no	—
21	C₃²×C₉	—	2	3	no	—
22	C₃²×C₉	—	4	1	no	—
23	C₃²×C₉	D₃²	1	3	yes	—
24	C₉²	—	2	9	no	—
25	C₉²	—	2	6	no	—
26	C₉²	—	4	3	no	—
27	C₉²	—	4	9	no	—
28	C₉²	—	4	9	no	—
29	C₉²	C₂×D₉	1	3	yes	complemented
30	C₃×C₃⋊D₃	—	9	3	no	—
31	C₃⋊D₉	—	3	6	no	—
32	C₃⋊D₉	—	6	3	no	—
33	D₃×C₉	—	27	6	no	—
34	D₃×C₉	—	54	3	no	—
35	C₃×D₉	—	9	6	no	—
36	C₃×D₉	—	18	6	no	—
37	C₃×D₉	—	18	9	no	—
38	D₃²	—	81	3	no	—
39	C₂×D₉	—	81	3	no	—
40	C₃³	#1113	1	1	yes	characteristic
41	C₃×C₉	—	2	3	no	—
42	C₃×C₉	—	2	9	no	—
43	C₃×C₉	—	2	6	no	—
44	C₃×C₉	—	2	3	no	—
45	C₃×C₉	—	4	3	no	—
46	C₃×C₉	—	4	9	no	—
47	C₃×C₉	—	4	9	no	—
48	C₃×C₉	—	4	3	no	—
49	C₃×C₉	—	4	3	no	—
50	C₃×C₉	D₃×D₉	1	6	yes	—
51	C₃⋊D₃	—	9	3	no	—
52	C₃×D₃	—	27	6	no	—
53	C₃×D₃	—	54	3	no	—
54	C₂×C₉	—	81	3	no	—
55	D₉	—	9	6	no	—
56	D₉	—	18	6	no	—
57	D₉	—	18	9	no	—
58	C₂×D₃	—	243	3	no	—
59	C₃²	—	2	3	no	—
60	C₃²	—	4	1	no	—
61	C₃²	#66431	1	3	yes	—
62	C₉	—	2	9	no	—
63	C₉	—	2	6	no	—
64	C₉	—	4	9	no	—
65	C₉	—	4	9	no	—
66	C₉	—	4	3	no	—
67	C₉	D₉²	1	3	yes	complemented
68	C₂×C₃	—	81	3	no	—
69	D₃	—	27	6	no	—
70	D₃	—	54	3	no	—
71	C₂²	—	729	1	no	Sylow
72	C₃	—	2	3	no	—
73	C₃	—	4	1	no	—
74	C₃	#11757745	1	3	yes	—
75	C₂	—	81	3	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉³	C₂²
Frattini, socle	C₃³	#1113
LCS	G ▷ C₉³
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₉⋊D₉	C₂	semidirect
3. C₉³	C₂²	semidirect
15. C₉⋊D₉	D₉	semidirect
29. C₉²	C₂×D₉	semidirect
67. C₉	D₉²	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₉⋊D₉	2
#11757745	3