Subgroups — #543⋊C₃ #5462

Order 192.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#543	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂²×A₄	—	4	1	no	maximal
3	C₂×SL(2,𝔽₃)	—	4	4	no	maximal
4	C₂²⋊Q₈	—	3	4	no	—
5	C₂×C₂²⋊C₄	—	3	1	no	—
6	C₂×A₄	—	4	2	no	—
7	C₂×A₄	—	4	1	no	—
8	SL(2,𝔽₃)	—	4	4	no	—
9	C₂⁴	A₄	1	1	yes	characteristic
10	C₂×Q₈	A₄	1	4	yes	complemented
11	C₂²×C₄	—	3	2	no	—
12	C₄⋊C₄	—	3	4	no	—
13	C₂²⋊C₄	—	3	4	no	—
14	C₂²×C₃	—	16	1	no	—
15	A₄	—	4	1	no	—
16	C₂³	—	3	1	no	—
17	C₂³	—	3	1	no	—
18	C₂³	—	4	2	no	—
19	C₂³	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
20	Q₈	—	4	4	no	—
21	C₂×C₄	—	3	4	no	—
22	C₂×C₄	—	12	2	no	—
23	C₂×C₃	—	16	1	no	—
24	C₂×C₃	—	16	2	no	—
25	C₂²	—	3	1	no	—
26	C₂²	—	3	1	no	—
27	C₂²	—	4	1	no	—
28	C₂²	—	6	2	no	—
29	C₂²	—	12	1	no	—
30	C₂²	C₂²⋊A₄	1	1	yes	characteristic
31	C₄	—	6	4	no	—
32	C₃	—	16	1	no	Sylow
33	C₂	—	6	1	no	—
34	C₂	—	6	1	no	—
35	C₂	C₂²⋊SL(2,𝔽₃)	1	1	yes	characteristic
36	C₂	#997	1	2	yes	—

	subgroup	G/H
center, Frattini, socle, hypercenter	C₂²	C₂²⋊A₄
commutator, Fitting, cosocle, hypocenter	#543	C₃
LCS	G ▷ #543
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.