Subgroups — C₂×C₃×D₈ #972

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×D₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃	—	2	2	no	—
6	C₃×D₄	—	2	2	no	—
7	C₃×D₄	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₃×C₈	C₂²	1	2	yes	complemented
10	C₂×D₄	C₂×C₃	1	2	yes	complemented
11	D₈	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₈	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃	—	2	4	no	—
14	C₂²×C₃	—	4	4	no	—
15	C₂²×C₃	D₄	1	1	yes	characteristic
16	C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×C₄	C₂³	1	1	yes	characteristic
18	C₂³	—	2	2	no	—
19	D₄	—	2	2	no	—
20	D₄	C₂²×C₃	1	4	yes	complemented
21	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₈	C₂²×C₃	1	2	yes	complemented
23	C₂×C₃	—	4	4	no	—
24	C₂×C₃	D₈	1	2	yes	direct product factor
25	C₂×C₃	C₂×D₄	1	1	yes	characteristic
26	C₂²	—	2	4	no	—
27	C₂²	—	4	4	no	—
28	C₂²	C₃×D₄	1	1	yes	characteristic
29	C₄	C₃×D₄	1	1	yes	characteristic
30	C₄	C₂³×C₃	1	1	yes	characteristic
31	C₃	C₂×D₈	1	1	yes	characteristic, direct product factor, Sylow
32	C₂	—	4	4	no	—
33	C₂	C₃×D₈	1	2	yes	direct product factor
34	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ 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.