Subgroups — #4858

Order 192.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#890	C₂	1	2	yes	maximal
2	C₃×#106	C₂	1	1	yes	maximal, characteristic
3	#817	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
5	#807	C₂	1	2	yes	maximal
6	#499	—	3	1	no	maximal, Sylow
7	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₄⋊Dic₃	—	2	2	no	—
10	C₄⋊Dic₃	C₂²	1	2	yes	—
11	Dic₃⋊C₄	—	2	2	no	—
12	C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	#125	—	3	2	no	—
15	#107	—	3	2	no	—
16	#106	—	3	1	no	—
17	#106	D₃	1	1	yes	characteristic
18	C₄×C₈	—	3	1	no	—
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₂×Dic₃	—	2	2	no	—
22	C₂×Dic₃	D₄	1	2	yes	—
23	C₃×C₈	Q₈	1	2	yes	—
24	C₃⋊C₈	Q₈	1	2	yes	—
25	C₂×C₈	—	3	1	no	—
26	C₂×C₈	C₂×D₃	1	1	yes	characteristic
27	C₄⋊C₄	—	3	2	no	—
28	C₄⋊C₄	—	6	2	no	—
29	C₄⋊C₄	—	6	2	no	—
30	C₄⋊C₄	C₂×D₃	1	2	yes	—
31	C₄²	—	3	1	no	—
32	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
33	C₃×C₄	—	4	2	no	—
34	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
35	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
36	Dic₃	—	2	2	no	—
37	Dic₃	—	4	2	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	—	3	2	no	—
40	C₂×C₄	—	6	2	no	—
41	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
42	C₈	—	3	2	no	—
43	C₈	Dic₆	1	2	yes	—
44	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
45	C₂×C₃	#135	1	2	yes	—
46	C₂²	D₃×D₄	1	1	yes	characteristic
47	C₄	—	4	2	no	—
48	C₄	—	6	2	no	—
49	C₄	—	12	2	no	—
50	C₄	C₂×Dic₆	1	1	yes	characteristic
51	C₄	D₃×Q₈	1	1	yes	characteristic
52	C₃	#499	1	1	yes	characteristic, complemented, Sylow
53	C₂	#888	1	1	yes	characteristic
54	C₂	#916	1	2	yes	—

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#106	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#106	D₃
hypocenter	C₃	#499
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
52. C₃	#499	semidirect

Maximal subgroups

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

subgroup	index
#890	2
C₃×#106	2
#817	2
C₈×Dic₃	2
#807	2
#499	3