Subgroups — #888

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×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Q₈	—	3	1	no	maximal, Sylow
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	1	yes	characteristic
11	C₂×Dic₃	C₂²	1	1	yes	characteristic
12	Dic₆	—	2	4	no	—
13	C₂×Q₈	—	3	2	no	—
14	C₄⋊C₄	—	3	2	no	—
15	C₄⋊C₄	—	3	1	no	—
16	C₄⋊C₄	D₃	1	1	yes	characteristic
17	C₄²	—	3	1	no	—
18	C₂²×C₃	C₂³	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	Q₈	1	2	yes	complemented
21	Dic₃	—	2	2	no	—
22	Dic₃	D₄	1	2	yes	—
23	Dic₃	Q₈	1	2	yes	complemented
24	Q₈	—	6	4	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₄	—	3	1	no	—
27	C₂×C₄	—	3	2	no	—
28	C₂×C₄	C₂×D₃	1	2	yes	—
29	C₂×C₄	C₂×D₃	1	1	yes	characteristic
30	C₂×C₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²	C₂²×D₃	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	3	2	no	—
36	C₄	—	3	2	no	—
37	C₄	—	6	2	no	—
38	C₄	Dic₆	1	2	yes	complemented
39	C₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
40	C₂	C₂×Dic₆	1	1	yes	characteristic
41	C₂	D₃×D₄	1	1	yes	characteristic
42	C₂	D₃×Q₈	1	1	yes	characteristic

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

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.