Subgroups — C₂³×A₄ #1021

Order 96.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×A₄	C₂	1	7	yes	maximal, direct product factor
2	C₂⁵	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂³×C₃	—	4	1	no	maximal
4	C₂×A₄	C₂²	1	7	yes	direct product factor
5	C₂⁴	—	3	7	no	—
6	C₂⁴	—	3	1	no	—
7	C₂⁴	C₂×C₃	1	7	yes	complemented
8	C₂²×C₃	—	4	7	no	—
9	A₄	C₂³	1	1	yes	characteristic, direct product factor
10	C₂³	—	3	21	no	—
11	C₂³	—	3	14	no	—
12	C₂³	—	3	7	no	—
13	C₂³	—	3	7	no	—
14	C₂³	A₄	1	1	yes	characteristic, direct product factor
15	C₂³	C₂²×C₃	1	7	yes	complemented
16	C₂×C₃	—	4	7	no	—
17	C₂²	—	3	7	no	—
18	C₂²	—	3	14	no	—
19	C₂²	—	3	21	no	—
20	C₂²	—	3	7	no	—
21	C₂²	C₂×A₄	1	7	yes	direct product factor
22	C₂²	C₂³×C₃	1	1	yes	characteristic, complemented
23	C₃	—	4	1	no	Sylow
24	C₂	—	3	7	no	—
25	C₂	—	3	1	no	—
26	C₂	C₂²×A₄	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	A₄
commutator, cosocle, hypocenter	C₂²	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂³

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.