Subgroups — #4855

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#888	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	#808	C₂	1	2	yes	maximal
6	#498	—	3	1	no	maximal, Sylow
7	C₂×Dic₆	—	2	2	no	—
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊C₄	C₂²	1	2	yes	—
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	C₄⋊Q₈	—	3	2	no	—
15	#106	—	3	1	no	—
16	#106	—	3	2	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	Dic₆	—	4	4	no	—
24	C₃×C₈	Q₈	1	2	yes	complemented
25	C₃⋊C₈	Q₈	1	2	yes	complemented
26	C₂×Q₈	—	6	2	no	—
27	C₂×C₈	—	3	1	no	—
28	C₂×C₈	C₂×D₃	1	1	yes	characteristic
29	C₄⋊C₄	—	3	2	no	—
30	C₄⋊C₄	—	6	2	no	—
31	C₄⋊C₄	C₂×D₃	1	2	yes	—
32	C₄²	—	3	1	no	—
33	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
34	C₃×C₄	—	4	2	no	—
35	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
36	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
37	Dic₃	—	4	2	no	—
38	Dic₃	SD₁₆	1	4	yes	—
39	Q₈	—	12	4	no	—
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	3	2	no	—
42	C₂×C₄	—	6	2	no	—
43	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
44	C₈	—	3	2	no	—
45	C₈	Dic₆	1	2	yes	complemented
46	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
47	C₂×C₃	C₂×SD₁₆	1	2	yes	—
48	C₂²	D₃×D₄	1	1	yes	characteristic
49	C₄	—	3	4	no	—
50	C₄	—	4	2	no	—
51	C₄	—	12	2	no	—
52	C₄	C₂×Dic₆	1	1	yes	characteristic
53	C₄	D₃×Q₈	1	1	yes	characteristic
54	C₃	#498	1	1	yes	characteristic, complemented, Sylow
55	C₂	#888	1	1	yes	characteristic
56	C₂	D₃×SD₁₆	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	#498
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
24. C₃×C₈	Q₈	semidirect
25. C₃⋊C₈	Q₈	semidirect
45. C₈	Dic₆	semidirect
54. C₃	#498	semidirect

Maximal subgroups

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

subgroup	index
#888	2
C₃×#106	2
#817	2
C₈×Dic₃	2
#808	2
#498	3