Subgroups — #870

Order 96.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃	C₂	1	2	yes	maximal
3	Dic₃⋊C₄	C₂	1	4	yes	maximal
4	#125	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	2	yes	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂×Dic₃	C₂²	1	4	yes	—
8	C₄⋊C₄	—	3	4	no	—
9	C₄⋊C₄	—	3	2	no	—
10	C₄²	D₃	1	1	yes	characteristic
11	C₂²×C₃	C₂³	1	1	yes	characteristic
12	C₃×C₄	—	2	2	no	—
13	C₃×C₄	Q₈	1	2	yes	—
14	Dic₃	—	2	4	no	—
15	C₂×C₄	—	3	4	no	—
16	C₂×C₄	C₂×D₃	1	2	yes	—
17	C₂×C₄	C₂×D₃	1	1	yes	characteristic
18	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₃	#41	1	2	yes	—
20	C₂²	C₂²×D₃	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	—	6	4	no	—
23	C₄	Dic₆	1	2	yes	—
24	C₃	#125	1	1	yes	characteristic, complemented, Sylow
25	C₂	C₂×Dic₆	1	1	yes	characteristic
26	C₂	#235	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃
commutator, socle, prime radical, cosocle	C₂²×C₃	C₂³
Fitting	C₃×C₄²	C₂
hypercenter	C₄²	D₃
hypocenter	C₃	#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄²

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

N	H ≅ G/N	type
24. C₃	#125	semidirect

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