Subgroups — #11765626

Order 1134.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₇⋊C₉)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₃⋊D₂₁	C₃	1	1	yes	maximal, characteristic
3	C₃⋊(D₇⋊C₉)	—	3	1	no	maximal
4	C₃³×C₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₇⋊C₉	—	2	1	no	—
6	C₃×C₇⋊C₉	D₃	1	1	yes	characteristic, complemented
7	(C₃⋊D₃)⋊C₉	—	7	1	no	maximal, Hall
8	C₃⋊D₂₁	C₉	1	1	yes	characteristic, complemented
9	C₃×D₂₁	—	3	1	no	—
10	C₃×D₂₁	—	9	1	no	—
11	D₇⋊C₉	—	9	1	no	—
12	C₃²⋊C₉	—	7	1	no	Sylow
13	C₃²×C₇	—	2	1	no	—
14	C₃²×C₇	—	3	1	no	—
15	C₃²×C₇	—	6	1	no	—
16	C₃²×C₇	C₂×C₉	1	1	yes	characteristic, complemented
17	C₃²×C₇	C₃×D₃	1	1	yes	characteristic
18	C₇⋊C₉	—	3	1	no	—
19	C₇⋊C₉	—	6	1	no	—
20	C₃×C₃⋊D₃	—	7	1	no	—
21	D₃×C₉	—	21	1	no	—
22	D₂₁	—	3	1	no	—
23	D₂₁	—	9	1	no	—
24	C₃×D₇	—	9	1	no	—
25	C₃³	AGL(1,𝔽₇)	1	1	yes	characteristic
26	C₃×C₉	—	7	1	no	—
27	C₃×C₉	—	14	1	no	—
28	C₃×C₇	—	2	1	no	—
29	C₃×C₇	—	3	1	no	—
30	C₃×C₇	—	6	1	no	—
31	C₃×C₇	D₃×C₉	1	1	yes	characteristic
32	C₃×C₇	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
33	C₃⋊D₃	—	7	1	no	—
34	C₃×D₃	—	21	1	no	—
35	C₃×D₃	—	63	1	no	—
36	C₂×C₉	—	63	1	no	—
37	D₇	—	9	1	no	Hall
38	C₃²	—	2	1	no	—
39	C₃²	—	3	1	no	—
40	C₃²	—	6	1	no	—
41	C₃²	D₇⋊C₉	1	1	yes	characteristic, complemented
42	C₃²	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
43	C₉	—	21	1	no	—
44	C₉	—	42	1	no	—
45	C₇	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	63	1	no	—
47	D₃	—	21	1	no	—
48	D₃	—	63	1	no	—
49	C₃	—	2	1	no	—
50	C₃	—	3	1	no	—
51	C₃	—	6	1	no	—
52	C₃	C₃⋊(D₇⋊C₉)	1	1	yes	characteristic
53	C₃	#67369	1	1	yes	characteristic
54	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#67369
commutator, hypocenter	C₃²×C₇	C₂×C₉
Frattini	C₃²	C₃⋊AGL(1,𝔽₇)
Fitting, cosocle	C₃³×C₇	C₂×C₃
socle	C₃²×C₇	C₃×D₃
prime radical	C₃×C₃⋊D₂₁	C₃
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²⋊(C₇⋊C₉)	C₂	semidirect
6. C₃×C₇⋊C₉	D₃	semidirect
8. C₃⋊D₂₁	C₉	semidirect
16. C₃²×C₇	C₂×C₉	semidirect
41. C₃²	D₇⋊C₉	semidirect
45. C₇	(C₃⋊D₃)⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊(C₇⋊C₉)	2
C₃×C₃⋊D₂₁	3
C₃⋊(D₇⋊C₉)	3
(C₃⋊D₃)⋊C₉	7