Subgroups — #869

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆	C₂	1	2	yes	maximal
2	C₃×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₃	C₂	1	4	yes	maximal
4	C₄⋊Q₈	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄	C₂²	1	2	yes	—
7	C₂×Dic₃	C₂²	1	4	yes	—
8	Dic₆	—	2	4	no	—
9	C₂×Q₈	—	3	2	no	—
10	C₄⋊C₄	—	3	4	no	—
11	C₄²	D₃	1	1	yes	characteristic
12	C₂²×C₃	C₂³	1	1	yes	characteristic
13	C₃×C₄	D₄	1	2	yes	—
14	C₃×C₄	Q₈	1	4	yes	complemented
15	Dic₃	—	2	4	no	—
16	Q₈	—	6	4	no	—
17	C₂×C₄	—	3	4	no	—
18	C₂×C₄	C₂×D₃	1	2	yes	—
19	C₂×C₄	C₂×D₃	1	1	yes	characteristic
20	C₂×C₃	C₂×D₄	1	1	yes	characteristic
21	C₂×C₃	C₂×Q₈	1	2	yes	—
22	C₂²	C₂²×D₃	1	1	yes	characteristic
23	C₄	—	6	4	no	—
24	C₄	Dic₆	1	4	yes	complemented
25	C₄	D₁₂	1	2	yes	—
26	C₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
27	C₂	C₂×Dic₆	1	2	yes	—
28	C₂	C₂×D₁₂	1	1	yes	characteristic

	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	C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄²

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.