Subgroups — (C₃×C₃₁⋊C₃)⋊H(3,𝔽₃) #21419307

Order 7533.

378 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	9	yes	maximal, complemented
3	C₃×C₃²⋊(C₃₁⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₃₁	C₃²	1	1	yes	characteristic
6	C₃³×C₃₁	C₃²	1	3	yes	complemented
7	C₃²×C₃₁⋊C₃	—	3	3	no	—
8	C₃²×C₃₁⋊C₃	—	3	9	no	—
9	C₃²×C₃₁⋊C₃	C₃²	1	3	yes	—
10	C₃²×C₃₁⋊C₃	C₃²	1	6	yes	complemented
11	H(3,𝔽₃)×C₃₁	—	3	3	no	—
12	C₃²⋊(C₃₁⋊C₃)	—	3	6	no	—
13	C₃²⋊(C₃₁⋊C₃)	—	3	27	no	—
14	C₃²×C₃₁	—	3	3	no	—
15	C₃²×C₃₁	—	3	9	no	—
16	C₃²×C₃₁	—	3	3	no	—
17	C₃²×C₃₁	H(3,𝔽₃)	1	3	yes	complemented
18	C₃²×C₃₁	C₃³	1	1	yes	characteristic
19	C₃×C₃₁⋊C₃	—	3	27	no	—
20	C₃×C₃₁⋊C₃	—	3	6	no	—
21	C₃×C₃₁⋊C₃	—	3	3	no	—
22	C₃×C₃₁⋊C₃	—	3	18	no	—
23	C₃×C₃₁⋊C₃	—	3	6	no	—
24	C₃×C₃₁⋊C₃	H(3,𝔽₃)	1	9	yes	complemented
25	C₃²⋊H(3,𝔽₃)	—	31	1	no	maximal, Sylow
26	C₃×C₃₁	—	3	3	no	—
27	C₃×C₃₁	—	9	3	no	—
28	C₃×C₃₁	C₃×H(3,𝔽₃)	1	3	yes	—
29	C₃×C₃₁	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₃₁⋊C₃	—	3	9	no	—
31	C₃₁⋊C₃	—	9	6	no	—
32	C₃⁴	—	31	1	no	—
33	C₃×H(3,𝔽₃)	—	31	2	no	—
34	C₃×H(3,𝔽₃)	—	31	9	no	—
35	C₃×H(3,𝔽₃)	C₃₁⋊C₃	1	1	yes	characteristic, complemented
36	C₃₁	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	31	3	no	—
38	C₃³	—	31	6	no	—
39	C₃³	—	93	9	no	—
40	C₃³	—	93	3	no	—
41	C₃³	C₃×C₃₁⋊C₃	1	1	yes	characteristic
42	C₃³	C₃×C₃₁⋊C₃	1	3	yes	complemented
43	H(3,𝔽₃)	—	3	3	no	—
44	H(3,𝔽₃)	—	93	27	no	—
45	H(3,𝔽₃)	—	93	6	no	—
46	C₃²	—	3	3	no	—
47	C₃²	—	3	9	no	—
48	C₃²	—	3	3	no	—
49	C₃²	—	31	9	no	—
50	C₃²	—	93	27	no	—
51	C₃²	—	93	18	no	—
52	C₃²	—	93	6	no	—
53	C₃²	—	93	6	no	—
54	C₃²	—	93	3	no	—
55	C₃²	C₃²⋊(C₃₁⋊C₃)	1	3	yes	complemented
56	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
57	C₃	—	3	3	no	—
58	C₃	—	9	3	no	—
59	C₃	—	279	6	no	—
60	C₃	—	93	9	no	—
61	C₃	H(3,𝔽₃)×C₃₁⋊C₃	1	3	yes	—
62	C₃	C₃×C₃²⋊(C₃₁⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₃₁⋊C₃
commutator, socle	C₃²×C₃₁	C₃³
Fitting	C₃×H(3,𝔽₃)×C₃₁	C₃
hypercenter	C₃×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	C₃²⋊H(3,𝔽₃)
LCS	G ▷ C₃²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃³×C₃₁⋊C₃	C₃	semidirect
2. C₃×C₃²⋊(C₃₁⋊C₃)	C₃	semidirect
3. C₃×C₃²⋊(C₃₁⋊C₃)	C₃	semidirect
4. C₃×H(3,𝔽₃)×C₃₁	C₃	semidirect
6. C₃³×C₃₁	C₃²	semidirect
10. C₃²×C₃₁⋊C₃	C₃²	semidirect
17. C₃²×C₃₁	H(3,𝔽₃)	semidirect
24. C₃×C₃₁⋊C₃	H(3,𝔽₃)	semidirect
35. C₃×H(3,𝔽₃)	C₃₁⋊C₃	semidirect
36. C₃₁	C₃²⋊H(3,𝔽₃)	semidirect
42. C₃³	C₃×C₃₁⋊C₃	semidirect
55. C₃²	C₃²⋊(C₃₁⋊C₃)	semidirect

Subgroups — (C3×C31⋊C3)⋊H(3,𝔽3) #21419307

Conjugacy classes of subgroups

Complements

Subgroups — (C₃×C₃₁⋊C₃)⋊H(3,𝔽₃) #21419307