Subgroups — #944

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic
3	Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Q₈	—	3	1	no	maximal, Sylow
6	C₃×Q₈	—	2	2	no	—
7	C₂×C₃×C₄	C₂²	1	2	yes	—
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₃	C₂²	1	2	yes	—
10	C₂×Dic₃	C₂²	1	2	yes	—
11	Dic₆	—	2	2	no	—
12	C₂×Q₈	—	3	1	no	—
13	C₂×Q₈	D₃	1	1	yes	characteristic
14	C₄⋊C₄	—	3	4	no	—
15	C₄²	—	3	1	no	—
16	C₂²×C₃	C₂³	1	1	yes	characteristic
17	C₃×C₄	—	2	2	no	—
18	C₃×C₄	D₄	1	2	yes	—
19	Dic₃	—	2	2	no	—
20	Dic₃	Q₈	1	4	yes	complemented
21	Q₈	—	2	2	no	—
22	Q₈	—	6	2	no	—
23	C₂×C₄	—	3	2	no	—
24	C₂×C₄	—	3	2	no	—
25	C₂×C₄	C₂×D₃	1	2	yes	—
26	C₂×C₄	C₂×D₃	1	1	yes	characteristic
27	C₂×C₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃	C₂×Q₈	1	2	yes	—
29	C₂²	C₂²×D₃	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	3	4	no	—
32	C₄	—	6	2	no	—
33	C₄	#67	1	2	yes	—
34	C₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₂	D₃×Q₈	1	2	yes	—
36	C₂	C₂×#67	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃
commutator, socle, prime radical, cosocle	C₂²×C₃	C₂³
Fitting	C₂×C₃×Q₈	C₂
hypercenter	C₂×Q₈	D₃
hypocenter	C₃	C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

N	H ≅ G/N	type
20. Dic₃	Q₈	semidirect
34. C₃	C₄⋊Q₈	semidirect

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