Subgroups — #857

Order 96.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#104	—	3	1	no	maximal, Sylow
3	S₄	—	4	1	no	maximal
4	#41	—	3	1	no	—
5	M₁₆	—	3	1	no	—
6	C₄²	D₃	1	1	yes	characteristic, complemented
7	A₄	—	4	1	no	—
8	Q₈	—	3	1	no	—
9	D₄	—	3	1	no	—
10	D₄	—	6	1	no	—
11	C₂×C₄	—	3	1	no	—
12	C₂×C₄	—	6	1	no	—
13	C₈	—	6	1	no	—
14	D₃	—	16	1	no	—
15	C₂²	—	6	1	no	—
16	C₂²	S₄	1	1	yes	characteristic
17	C₄	—	3	1	no	—
18	C₄	—	3	1	no	—
19	C₄	—	6	1	no	—
20	C₃	—	16	1	no	Sylow
21	C₂	—	3	1	no	—
22	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄²⋊C₃	C₂
Frattini, socle	C₂²	S₄
Fitting	C₄²	D₃
LCS	G ▷ C₄²⋊C₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₄²⋊C₃	C₂	semidirect
6. C₄²	D₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.