Subgroups — #890

Order 96.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃	C₂	1	2	yes	maximal
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	#125	—	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	1	yes	characteristic
10	C₂×Dic₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₃	C₂²	1	2	yes	—
12	C₄⋊C₄	—	3	2	no	—
13	C₄⋊C₄	—	3	2	no	—
14	C₄⋊C₄	—	3	1	no	—
15	C₄⋊C₄	D₃	1	1	yes	characteristic
16	C₄²	—	3	1	no	—
17	C₂²×C₃	C₂³	1	1	yes	characteristic
18	C₃×C₄	—	2	2	no	—
19	C₃×C₄	Q₈	1	2	yes	—
20	Dic₃	—	2	1	no	—
21	Dic₃	—	2	1	no	—
22	Dic₃	—	2	2	no	—
23	C₂×C₄	—	3	1	no	—
24	C₂×C₄	—	3	1	no	—
25	C₂×C₄	—	3	2	no	—
26	C₂×C₄	C₂×D₃	1	2	yes	—
27	C₂×C₄	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₃	#41	1	1	yes	characteristic
30	C₂×C₃	#41	1	1	yes	characteristic
31	C₂²	C₂²×D₃	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	—	6	1	no	—
34	C₄	—	6	1	no	—
35	C₄	—	6	2	no	—
36	C₄	Dic₆	1	2	yes	—
37	C₃	#125	1	1	yes	characteristic, complemented, Sylow
38	C₂	C₂×Dic₆	1	1	yes	characteristic
39	C₂	#237	1	1	yes	characteristic
40	C₂	#239	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	#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

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

N	H ≅ G/N	type
37. C₃	#125	semidirect

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