Subgroups — C₂²⋊(C₄²⋊C₃) #5461

Order 192.

103 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂²⋊A₄	—	4	1	no	maximal
3	C₄²⋊C₃	—	4	4	no	maximal
4	C₂³×C₄	—	3	1	no	—
5	C₂×C₄²	—	3	4	no	—
6	C₂⁴	A₄	1	1	yes	characteristic
7	C₂²×C₄	—	3	6	no	—
8	C₂²×C₄	—	3	8	no	—
9	C₄²	—	3	4	no	—
10	C₄²	A₄	1	4	yes	complemented
11	A₄	—	16	4	no	—
12	A₄	—	16	1	no	—
13	C₂³	—	3	4	no	—
14	C₂³	—	3	1	no	—
15	C₂×C₄	—	3	24	no	—
16	C₂×C₄	—	3	4	no	—
17	C₂²	—	3	6	no	—
18	C₂²	—	3	4	no	—
19	C₂²	C₄²⋊C₃	1	4	yes	complemented
20	C₂²	C₂²⋊A₄	1	1	yes	characteristic
21	C₄	—	3	8	no	—
22	C₃	—	64	1	no	Sylow
23	C₂	—	3	1	no	—
24	C₂	—	3	4	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂²×C₄²	C₃
Frattini	C₂²	C₂²⋊A₄
socle	C₂⁴	A₄
LCS	G ▷ C₂²×C₄²
UCS	C₁

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.