Subgroups — #13091376

Order 1458.

443 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#737	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊#4208	—	3	1	no	maximal
3	C₉⋊#272	C₃	1	1	yes	maximal, characteristic
4	#92295	—	3	8	no	maximal
5	C₉×C₃⋊D₉	—	3	4	no	maximal
6	C₃×#737	D₃	1	1	yes	characteristic
7	C₉×3₋¹⁺²	—	2	4	no	—
8	C₉×3₋¹⁺²	—	2	8	no	—
9	C₉×H(3,𝔽₃)	—	2	1	no	—
10	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
11	#6887	D₃	1	8	yes	complemented
12	C₃×C₉²	D₃	1	4	yes	complemented
13	C₃⋊#272	—	3	1	no	—
14	#4208	—	9	9	no	—
15	C₉×C₃⋊D₃	—	9	4	no	—
16	C₃×C₃⋊D₉	—	3	4	no	—
17	#4181	—	3	8	no	—
18	C₉×D₉	—	9	1	no	—
19	C₉×D₉	—	9	8	no	—
20	#737	—	2	9	no	—
21	#737	D₉	1	9	yes	complemented
22	C₃×3₋¹⁺²	—	2	4	no	—
23	C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
24	C₃²×C₉	—	2	4	no	—
25	C₃²×C₉	C₃×D₃	1	4	yes	—
26	C₃²×C₉	C₃⋊D₃	1	4	yes	—
27	C₉⋊C₉	—	2	24	no	—
28	C₃²⋊C₉	—	2	8	no	—
29	C₃²⋊C₉	C₃×D₃	1	8	yes	—
30	C₉²	—	2	8	no	—
31	C₉²	—	2	4	no	—
32	C₉²	C₃⋊D₃	1	1	yes	characteristic
33	C₉²	C₃⋊D₃	1	8	yes	—
34	C₃×C₃⋊D₃	—	9	4	no	—
35	#272	—	9	9	no	—
36	C₃⋊D₉	—	3	4	no	—
37	D₃×C₉	—	27	12	no	—
38	D₃×C₉	—	27	1	no	—
39	C₃×D₉	—	9	8	no	—
40	C₃×D₉	—	9	1	no	—
41	C₃³	C₃×C₃⋊D₃	1	4	yes	—
42	3₋¹⁺²	—	2	36	no	—
43	H(3,𝔽₃)	C₃×D₉	1	9	yes	—
44	C₃×C₉	—	2	12	no	—
45	C₃×C₉	—	2	1	no	—
46	C₃×C₉	—	2	4	no	—
47	C₃×C₉	—	2	8	no	—
48	C₃×C₉	—	3	4	no	—
49	C₃×C₉	—	6	4	no	—
50	C₃×C₉	—	6	12	no	—
51	C₃×C₉	C₃⋊D₉	1	12	yes	complemented
52	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₃⋊D₃	1	8	yes	—
54	C₃×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
55	C₃⋊D₃	—	9	4	no	—
56	C₃×D₃	—	27	12	no	—
57	C₃×D₃	—	27	1	no	—
58	C₂×C₉	—	81	1	no	—
59	D₉	—	9	8	no	—
60	D₉	—	9	1	no	—
61	C₃²	—	3	4	no	—
62	C₃²	—	6	4	no	—
63	C₃²	C₃×C₃⋊D₉	1	12	yes	—
64	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
65	C₉	—	2	3	no	—
66	C₉	—	2	1	no	—
67	C₉	—	2	12	no	—
68	C₉	—	2	1	no	—
69	C₉	—	3	8	no	—
70	C₉	—	6	8	no	—
71	C₉	#4208	1	1	yes	characteristic, complemented
72	C₉	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
73	C₂×C₃	—	81	1	no	—
74	D₃	—	27	12	no	—
75	D₃	—	27	1	no	—
76	C₃	—	2	1	no	—
77	C₃	—	3	12	no	—
78	C₃	C₃×C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
79	C₃	C₃⋊#4208	1	1	yes	characteristic
80	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	C₃⋊(C₃⋊D₉)
commutator, cosocle, hypocenter	C₉×H(3,𝔽₃)	C₂×C₃
Frattini, socle	C₃²	C₃×C₃⋊(C₃⋊D₃)
Fitting	C₉×#737	C₂
prime radical	C₉⋊#272	C₃
LCS	G ▷ C₉×H(3,𝔽₃)
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×#737	C₂	semidirect
11. #6887	D₃	semidirect
12. C₃×C₉²	D₃	semidirect
21. #737	D₉	semidirect
51. C₃×C₉	C₃⋊D₉	semidirect
71. C₉	#4208	semidirect

Maximal subgroups

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

subgroup	index
C₉×#737	2
C₃⋊#4208	3
C₉⋊#272	3
#92295	3
C₉×C₃⋊D₉	3