Subgroups — C₂²×C₃×D₄ #1014

Order 96.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂³×C₃	—	2	8	no	—
6	C₂³×C₃	C₂²	1	1	yes	characteristic
7	C₂³×C₃	C₂²	1	12	yes	complemented
8	C₃×D₄	C₂²	1	16	yes	direct product factor
9	C₂×C₃×C₄	C₂²	1	6	yes	complemented
10	C₂⁴	C₂×C₃	1	2	yes	complemented
11	C₂×D₄	C₂×C₃	1	12	yes	direct product factor
12	C₂²×C₄	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃	—	2	24	no	—
14	C₂²×C₃	D₄	1	4	yes	direct product factor
15	C₂²×C₃	C₂³	1	3	yes	—
16	C₂²×C₃	C₂³	1	8	yes	complemented
17	C₃×C₄	C₂³	1	4	yes	complemented
18	C₂³	—	2	8	no	—
19	C₂³	C₂²×C₃	1	1	yes	characteristic
20	C₂³	C₂²×C₃	1	12	yes	complemented
21	D₄	C₂²×C₃	1	16	yes	direct product factor
22	C₂×C₄	C₂²×C₃	1	6	yes	complemented
23	C₂×C₃	—	2	8	no	—
24	C₂×C₃	C₂×D₄	1	6	yes	direct product factor
25	C₂×C₃	C₂⁴	1	1	yes	characteristic
26	C₂²	—	2	24	no	—
27	C₂²	C₃×D₄	1	4	yes	direct product factor
28	C₂²	C₂³×C₃	1	3	yes	—
29	C₂²	C₂³×C₃	1	8	yes	complemented
30	C₄	C₂³×C₃	1	4	yes	complemented
31	C₃	C₂²×D₄	1	1	yes	characteristic, direct product factor, Sylow
32	C₂	—	2	8	no	—
33	C₂	C₂×C₃×D₄	1	6	yes	direct product factor
34	C₂	C₂⁴×C₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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.