Subgroups — #4681

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#869	C₂	1	1	yes	maximal, characteristic
2	#869	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	#816	C₂	1	4	yes	maximal
5	#487	—	3	1	no	maximal, Sylow
6	C₂×Dic₆	—	2	1	no	—
7	C₂×Dic₆	C₂²	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃	—	2	1	no	—
11	C₄⋊Dic₃	—	2	1	no	—
12	C₄⋊Dic₃	—	2	1	no	—
13	C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₄⋊Q₈	—	3	1	no	—
15	C₄⋊Q₈	—	3	1	no	—
16	#103	—	3	4	no	—
17	C₄×C₈	D₃	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×C₃×C₄	D₄	1	1	yes	characteristic
20	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₂×Dic₃	—	2	2	no	—
22	C₂×Dic₃	—	2	2	no	—
23	Dic₆	—	2	4	no	—
24	Dic₆	—	4	2	no	—
25	C₃×C₈	—	2	2	no	—
26	C₂×Q₈	—	3	2	no	—
27	C₂×Q₈	—	6	1	no	—
28	C₂×C₈	C₂×D₃	1	2	yes	—
29	C₄⋊C₄	—	3	2	no	—
30	C₄⋊C₄	—	6	1	no	—
31	C₄⋊C₄	—	6	1	no	—
32	C₄⋊C₄	—	6	1	no	—
33	C₄²	C₂×D₃	1	1	yes	characteristic
34	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
35	C₃×C₄	SD₁₆	1	2	yes	—
36	C₃×C₄	Q₁₆	1	2	yes	—
37	C₃×C₄	#41	1	2	yes	—
38	Dic₃	—	4	2	no	—
39	Dic₃	—	4	2	no	—
40	Q₈	—	6	4	no	—
41	Q₈	—	12	2	no	—
42	C₂×C₄	—	6	2	no	—
43	C₂×C₄	—	6	2	no	—
44	C₂×C₄	D₁₂	1	1	yes	characteristic
45	C₂×C₄	D₁₂	1	1	yes	characteristic
46	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₂×C₃	#124	1	1	yes	characteristic
49	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
51	C₂²	C₂×D₁₂	1	1	yes	characteristic
52	C₄	—	12	2	no	—
53	C₄	—	12	2	no	—
54	C₄	#204	1	2	yes	—
55	C₄	Dic₁₂	1	2	yes	—
56	C₄	#235	1	2	yes	—
57	C₃	#487	1	1	yes	characteristic, complemented, Sylow
58	C₂	#875	1	1	yes	characteristic
59	C₂	C₂×#204	1	1	yes	characteristic
60	C₂	C₂×Dic₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×C₄×C₈	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
hypercenter	C₄×C₈	D₃
hypocenter	C₃	#487
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
57. C₃	#487	semidirect

Maximal subgroups

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

subgroup	index
#869	2
C₃×C₄×C₈	2
#816	2
#487	3