Subgroups — C₂×C₃⋊S₄ #3846

Order 144.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊S₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×S₄	—	3	3	no	maximal
4	C₂×#67	—	3	1	no	maximal
5	C₂×C₃⋊D₃	—	4	1	no	maximal
6	C₃×A₄	C₂²	1	1	yes	characteristic, complemented
7	C₂³×C₃	D₃	1	1	yes	characteristic, complemented
8	C₂²×D₃	—	3	1	no	—
9	C₂×A₄	D₃	1	3	yes	complemented
10	S₄	—	3	6	no	—
11	#67	—	3	2	no	—
12	#67	—	3	2	no	—
13	C₂×Dic₃	—	3	1	no	—
14	C₂×C₃²	—	4	1	no	—
15	C₃⋊D₃	—	4	2	no	—
16	C₂×D₄	—	9	1	no	Sylow
17	C₂²×C₃	—	3	1	no	—
18	C₂²×C₃	—	3	1	no	—
19	C₂²×C₃	C₂×D₃	1	1	yes	characteristic, complemented
20	C₂×D₃	—	3	2	no	—
21	C₂×D₃	—	6	1	no	—
22	C₂×D₃	—	6	1	no	—
23	C₂×D₃	—	12	3	no	—
24	A₄	C₂×D₃	1	3	yes	complemented
25	Dic₃	—	3	2	no	—
26	C₃²	—	4	1	no	Sylow
27	C₂³	—	9	1	no	—
28	C₂³	C₃⋊D₃	1	1	yes	characteristic, complemented
29	D₄	—	9	2	no	—
30	D₄	—	9	2	no	—
31	C₂×C₄	—	9	1	no	—
32	C₂×C₃	—	3	1	no	—
33	C₂×C₃	—	3	1	no	—
34	C₂×C₃	—	4	3	no	—
35	C₂×C₃	S₄	1	1	yes	characteristic, complemented
36	D₃	—	6	2	no	—
37	D₃	—	12	6	no	—
38	C₂²	—	3	1	no	—
39	C₂²	—	3	1	no	—
40	C₂²	—	9	2	no	—
41	C₂²	—	18	1	no	—
42	C₂²	—	18	1	no	—
43	C₂²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
44	C₄	—	9	2	no	—
45	C₃	—	4	3	no	—
46	C₃	C₂×S₄	1	1	yes	characteristic, complemented
47	C₂	—	3	1	no	—
48	C₂	—	3	1	no	—
49	C₂	—	18	2	no	—
50	C₂	C₃⋊S₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×A₄	C₂²
Frattini	C₁	G
Fitting, socle	C₂³×C₃	D₃
LCS	G ▷ C₃×A₄
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.