Subgroups — #985

Order 96.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	GL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#226	C₂	1	1	yes	maximal, characteristic, complemented
4	#135	—	3	1	no	maximal, Sylow
5	C₄×D₃	—	4	1	no	maximal
6	SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	#41	—	3	1	no	—
8	#41	D₃	1	1	yes	characteristic, complemented
9	Q₁₆	—	3	1	no	—
10	SD₁₆	—	3	1	no	—
11	SD₁₆	—	3	1	no	—
12	D₈	—	3	1	no	—
13	C₂×C₈	—	3	1	no	—
14	C₂×D₃	—	4	1	no	—
15	C₃×C₄	—	4	1	no	—
16	Dic₃	—	4	1	no	—
17	Q₈	—	3	1	no	—
18	Q₈	C₂×D₃	1	1	yes	characteristic
19	D₄	—	3	1	no	—
20	D₄	—	3	1	no	—
21	D₄	—	6	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	—	6	1	no	—
24	C₈	—	3	1	no	—
25	C₈	—	3	1	no	—
26	C₂×C₃	—	4	1	no	—
27	D₃	—	4	2	no	—
28	C₂²	—	3	1	no	—
29	C₂²	—	6	1	no	—
30	C₄	—	3	1	no	—
31	C₄	—	6	1	no	—
32	C₄	S₄	1	1	yes	characteristic
33	C₃	—	4	1	no	Sylow
34	C₂	—	6	1	no	—
35	C₂	—	12	1	no	—
36	C₂	C₂×S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²
Frattini, socle	C₂	C₂×S₄
Fitting	#41	D₃
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₄

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.