Subgroups — #393⋊C₃ #4636

Order 192.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	#393	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²×A₄	—	4	1	no	maximal
4	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂×C₂²⋊C₄	—	3	1	no	—
6	#95	—	3	1	no	—
7	C₂×A₄	—	4	2	no	—
8	C₂×A₄	—	4	1	no	—
9	SL(2,𝔽₃)	—	8	2	no	—
10	C₂⁴	A₄	1	1	yes	characteristic
11	C₂×Q₈	—	6	2	no	—
12	C₂²×C₄	—	3	1	no	—
13	C₂²×C₄	—	3	1	no	—
14	C₂²⋊C₄	—	6	2	no	—
15	C₂²×C₃	—	16	1	no	—
16	A₄	—	4	1	no	—
17	C₂³	—	6	1	no	—
18	C₂³	—	6	1	no	—
19	C₂³	SL(2,𝔽₃)	1	2	yes	complemented
20	C₂³	C₂×A₄	1	1	yes	characteristic
21	Q₈	—	2	2	no	—
22	Q₈	—	6	2	no	—
23	C₂×C₄	—	3	2	no	—
24	C₂×C₄	—	6	2	no	—
25	C₂×C₄	—	6	1	no	—
26	C₂×C₄	—	6	2	no	—
27	C₂×C₃	—	16	2	no	—
28	C₂×C₃	—	16	1	no	—
29	C₂²	—	3	1	no	—
30	C₂²	—	3	1	no	—
31	C₂²	—	4	1	no	—
32	C₂²	—	6	2	no	—
33	C₂²	—	12	1	no	—
34	C₂²	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
35	C₄	—	6	2	no	—
36	C₄	—	12	1	no	—
37	C₃	—	16	1	no	Sylow
38	C₂	—	3	1	no	—
39	C₂	—	3	1	no	—
40	C₂	—	4	2	no	—
41	C₂	#120⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#120⋊C₃
commutator, cosocle, hypocenter	C₂²×Q₈	C₂×C₃
Frattini, socle	C₂³	C₂×A₄
Fitting	#393	C₃
LCS	G ▷ C₂²×Q₈
UCS	C₁ ◁ C₂

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.