Subgroups — C₄⋊GL(2,𝔽₃) #5393

Order 192.

91 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×GL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
2	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#460	—	3	1	no	maximal, Sylow
4	C₂×D₁₂	—	4	1	no	maximal
5	C₂×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
6	GL(2,𝔽₃)	—	2	2	no	—
7	C₂×SD₁₆	—	3	2	no	—
8	#127	—	3	1	no	—
9	C₄×Q₈	D₃	1	1	yes	characteristic, complemented
10	C₄⋊C₈	—	3	1	no	—
11	#102	—	3	2	no	—
12	C₂²×D₃	—	4	2	no	—
13	C₂×C₃×C₄	—	4	1	no	—
14	D₁₂	—	4	4	no	—
15	SL(2,𝔽₃)	D₄	1	1	yes	characteristic, complemented
16	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
17	C₂×D₄	—	3	2	no	—
18	C₂×D₄	—	6	1	no	—
19	C₂×D₄	—	6	1	no	—
20	SD₁₆	—	6	2	no	—
21	SD₁₆	—	6	2	no	—
22	C₂×C₈	—	3	2	no	—
23	C₄⋊C₄	—	3	1	no	—
24	C₄²	—	3	1	no	—
25	C₂²×C₃	—	4	1	no	—
26	C₂×D₃	—	4	4	no	—
27	C₂×D₃	—	8	2	no	—
28	C₂×D₃	—	8	2	no	—
29	C₃×C₄	—	4	2	no	—
30	C₂³	—	6	2	no	—
31	Q₈	—	3	1	no	—
32	Q₈	D₁₂	1	1	yes	characteristic, complemented
33	D₄	—	6	2	no	—
34	D₄	—	6	2	no	—
35	D₄	—	12	2	no	—
36	D₄	—	12	2	no	—
37	C₂×C₄	—	3	1	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	S₄	1	1	yes	characteristic
40	C₈	—	6	2	no	—
41	C₂×C₃	—	4	1	no	—
42	C₂×C₃	—	4	1	no	—
43	C₂×C₃	—	4	1	no	—
44	D₃	—	8	4	no	—
45	C₂²	—	12	2	no	—
46	C₂²	—	12	2	no	—
47	C₂²	—	12	2	no	—
48	C₂²	C₂×S₄	1	1	yes	characteristic
49	C₄	—	3	1	no	—
50	C₄	—	3	1	no	—
51	C₄	—	6	1	no	—
52	C₄	GL(2,𝔽₃)	1	2	yes	complemented
53	C₃	—	4	1	no	Sylow
54	C₂	—	24	2	no	—
55	C₂	C₄⋊S₄	1	1	yes	characteristic
56	C₂	C₂×GL(2,𝔽₃)	1	1	yes	characteristic
57	C₂	#986	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂²	C₂×S₄
commutator, cosocle	C₂×SL(2,𝔽₃)	C₂²
Fitting	C₄×Q₈	D₃
hypercenter	C₂×C₄	S₄
hypocenter	SL(2,𝔽₃)	D₄
LCS	G ▷ C₂×SL(2,𝔽₃) ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×GL(2,𝔽₃)	C₂	semidirect
2. C₄×SL(2,𝔽₃)	C₂	semidirect
9. C₄×Q₈	D₃	semidirect
15. SL(2,𝔽₃)	D₄	semidirect
32. Q₈	D₁₂	semidirect
52. C₄	GL(2,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂×GL(2,𝔽₃)	2
C₄×SL(2,𝔽₃)	2
#460	3
C₂×D₁₂	4

Subgroups — C4⋊GL(2,𝔽3) #5393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊GL(2,𝔽₃) #5393