Subgroups — #4874

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×#107	C₂	1	1	yes	maximal, characteristic
3	#818	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
5	#807	C₂	1	2	yes	maximal
6	#500	—	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	#107	—	3	1	no	—
16	#107	—	3	2	no	—
17	#107	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	1	yes	characteristic
23	C₂×Dic₃	D₄	1	1	yes	characteristic
24	Dic₆	—	4	4	no	—
25	C₃×C₈	Q₈	1	2	yes	complemented
26	C₃⋊C₈	Q₈	1	2	yes	complemented
27	C₂×Q₈	—	6	2	no	—
28	C₂×C₈	—	3	1	no	—
29	C₂×C₈	C₂×D₃	1	1	yes	characteristic
30	C₄⋊C₄	—	3	2	no	—
31	C₄⋊C₄	—	6	2	no	—
32	C₄⋊C₄	C₂×D₃	1	2	yes	—
33	C₄²	—	3	1	no	—
34	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄	—	4	2	no	—
36	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
37	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
38	Dic₃	—	4	2	no	—
39	Dic₃	D₈	1	2	yes	—
40	Dic₃	Q₁₆	1	2	yes	—
41	Q₈	—	12	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	6	2	no	—
46	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
47	C₈	—	3	2	no	—
48	C₈	Dic₆	1	2	yes	complemented
49	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₃	C₂×D₈	1	1	yes	characteristic
51	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
52	C₂²	D₃×D₄	1	1	yes	characteristic
53	C₄	—	3	2	no	—
54	C₄	—	3	2	no	—
55	C₄	—	4	2	no	—
56	C₄	—	12	2	no	—
57	C₄	C₂×Dic₆	1	1	yes	characteristic
58	C₄	D₃×Q₈	1	1	yes	characteristic
59	C₃	#500	1	1	yes	characteristic, complemented, Sylow
60	C₂	#888	1	1	yes	characteristic
61	C₂	D₃×D₈	1	1	yes	characteristic
62	C₂	D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#107	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#107	D₃
hypocenter	C₃	#500
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
25. C₃×C₈	Q₈	semidirect
26. C₃⋊C₈	Q₈	semidirect
48. C₈	Dic₆	semidirect
59. C₃	#500	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×#107	2
#818	2
C₈×Dic₃	2
#807	2
#500	3