Subgroups — #95⋊H(3,𝔽₃) #11720340

Order 864.

121 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#95	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#95⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₂×C₂²⋊H(3,𝔽₃)	—	4	1	no	maximal
4	C₂²×C₃²×C₄	—	3	1	no	—
5	C₂²⋊H(3,𝔽₃)	—	4	1	no	—
6	C₃×#95	—	3	1	no	—
7	C₃×#95	C₃²	1	1	yes	characteristic
8	#95⋊C₃	—	3	3	no	—
9	C₂³×C₃²	A₄	1	1	yes	characteristic
10	C₂×C₃×A₄	—	4	3	no	—
11	C₂×C₃²×C₄	—	3	2	no	—
12	C₂×C₃²×C₄	—	6	2	no	—
13	C₂×H(3,𝔽₃)	—	16	1	no	—
14	C₂²×C₃×C₄	—	3	3	no	—
15	C₂²×C₃×C₄	—	3	1	no	—
16	C₂²×C₃²	—	3	1	no	—
17	C₂²×C₃²	—	3	1	no	—
18	C₂²×C₃²	SL(2,𝔽₃)	1	1	yes	characteristic
19	C₃×A₄	—	4	3	no	—
20	C₃²×C₄	—	6	2	no	—
21	#95	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
22	H(3,𝔽₃)	—	16	1	no	Sylow
23	C₂³×C₃	—	3	1	no	—
24	C₂³×C₃	C₃×A₄	1	1	yes	characteristic
25	C₂×A₄	—	12	3	no	—
26	C₂×C₃×C₄	—	3	6	no	—
27	C₂×C₃×C₄	—	3	2	no	—
28	C₂×C₃×C₄	—	6	2	no	—
29	C₂×C₃×C₄	—	6	6	no	—
30	C₂×C₃²	—	3	1	no	—
31	C₂×C₃²	—	3	1	no	—
32	C₂×C₃²	—	16	3	no	—
33	C₂×C₃²	C₄²⋊C₃	1	1	yes	characteristic
34	C₂²×C₄	—	3	1	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	3	no	—
37	C₂²×C₃	—	3	3	no	—
38	C₂²×C₃	—	3	1	no	—
39	C₂²×C₃	—	3	1	no	—
40	C₂²×C₃	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
41	A₄	—	12	3	no	—
42	C₃×C₄	—	6	6	no	—
43	C₃×C₄	—	6	2	no	—
44	C₃²	—	16	3	no	—
45	C₃²	#95⋊C₃	1	1	yes	characteristic, complemented
46	C₂³	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
47	C₂×C₄	—	3	2	no	—
48	C₂×C₄	—	6	2	no	—
49	C₂×C₃	—	3	3	no	—
50	C₂×C₃	—	3	3	no	—
51	C₂×C₃	—	3	1	no	—
52	C₂×C₃	—	3	1	no	—
53	C₂×C₃	—	3	1	no	—
54	C₂×C₃	—	48	3	no	—
55	C₂×C₃	C₃×C₄²⋊C₃	1	1	yes	characteristic
56	C₂²	—	3	1	no	—
57	C₂²	—	3	1	no	—
58	C₂²	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
59	C₄	—	6	2	no	—
60	C₃	—	3	1	no	—
61	C₃	—	48	3	no	—
62	C₃	C₃×#95⋊C₃	1	1	yes	characteristic
63	C₂	—	3	1	no	—
64	C₂	—	3	1	no	—
65	C₂	C₃²⋊(C₄²⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₃×C₄²⋊C₃
commutator, cosocle	C₃×#95	C₃²
Frattini, socle	C₂³×C₃	C₃×A₄
Fitting	C₃²×#95	C₃
hypercenter	C₂×C₃²	C₄²⋊C₃
hypocenter	#95	H(3,𝔽₃)
LCS	G ▷ C₃×#95 ▷ #95
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×#95	C₃	semidirect
2. C₃×#95⋊C₃	C₃	semidirect
21. #95	H(3,𝔽₃)	semidirect
45. C₃²	#95⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#95	3
C₃×#95⋊C₃	3
C₂×C₂²⋊H(3,𝔽₃)	4

Subgroups — #95⋊H(3,𝔽3) #11720340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95⋊H(3,𝔽₃) #11720340