Subgroups — C₂×C₃×D₄ #243

Order 48.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃	C₂	1	2	yes	maximal, complemented
2	C₃×D₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃	—	2	4	no	—
6	C₂²×C₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃	C₂²	1	4	yes	complemented
8	C₃×C₄	C₂²	1	2	yes	complemented
9	C₂³	C₂×C₃	1	2	yes	complemented
10	D₄	C₂×C₃	1	4	yes	direct product factor
11	C₂×C₄	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃	—	2	4	no	—
13	C₂×C₃	D₄	1	2	yes	direct product factor
14	C₂×C₃	C₂³	1	1	yes	characteristic
15	C₂²	—	2	4	no	—
16	C₂²	C₂²×C₃	1	1	yes	characteristic
17	C₂²	C₂²×C₃	1	4	yes	complemented
18	C₄	C₂²×C₃	1	2	yes	complemented
19	C₃	C₂×D₄	1	1	yes	characteristic, direct product factor, Sylow
20	C₂	—	2	4	no	—
21	C₂	C₃×D₄	1	2	yes	direct product factor
22	C₂	C₂³×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

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.