Subgroups — C₂×GL(2,𝔽₃) #982

Order 96.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	GL(2,𝔽₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×SD₁₆	—	3	1	no	maximal, Sylow
4	C₂²×D₃	—	4	1	no	maximal
5	SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
6	C₂×Q₈	D₃	1	1	yes	characteristic, complemented
7	C₂×D₄	—	3	1	no	—
8	SD₁₆	—	3	2	no	—
9	SD₁₆	—	3	2	no	—
10	C₂×C₈	—	3	1	no	—
11	C₂²×C₃	—	4	1	no	—
12	C₂×D₃	—	4	2	no	—
13	C₂×D₃	—	4	4	no	—
14	C₂³	—	6	1	no	—
15	Q₈	—	3	1	no	—
16	Q₈	C₂×D₃	1	1	yes	characteristic, complemented
17	D₄	—	3	2	no	—
18	D₄	—	6	1	no	—
19	C₂×C₄	—	3	1	no	—
20	C₈	—	3	2	no	—
21	C₂×C₃	—	4	2	no	—
22	C₂×C₃	—	4	1	no	—
23	D₃	—	4	4	no	—
24	C₂²	—	6	2	no	—
25	C₂²	—	12	2	no	—
26	C₂²	S₄	1	1	yes	characteristic
27	C₄	—	3	1	no	—
28	C₄	—	3	1	no	—
29	C₃	—	4	1	no	Sylow
30	C₂	—	12	2	no	—
31	C₂	GL(2,𝔽₃)	1	2	yes	direct product factor
32	C₂	C₂×S₄	1	1	yes	characteristic

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

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

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