Subgroups — C₂×D₄×C₂₃ #67296

Order 368.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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