Subgroups — #4873

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂	C₂	1	1	yes	maximal, characteristic
2	#887	C₂	1	2	yes	maximal
3	C₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
5	#810	C₂	1	2	yes	maximal
6	C₄×Q₁₆	—	3	1	no	maximal, Sylow
7	C₂×Dic₆	C₂²	1	2	yes	—
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊C₄	C₂²	1	2	yes	—
10	Dic₃⋊C₄	—	2	2	no	—
11	C₄×Dic₃	—	2	2	no	—
12	C₄×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	Dic₁₂	C₄	1	4	yes	complemented
15	C₂×Q₁₆	—	3	1	no	—
16	C₄×Q₈	—	3	2	no	—
17	#107	D₃	1	1	yes	characteristic
18	#103	—	3	2	no	—
19	C₄×C₈	—	3	1	no	—
20	C₂×C₃×C₄	—	2	2	no	—
21	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
22	C₂×Dic₃	—	2	2	no	—
23	C₂×Dic₃	D₄	1	1	yes	characteristic
24	C₂×Dic₃	D₄	1	1	yes	characteristic
25	Dic₆	—	2	2	no	—
26	Dic₆	C₂×C₄	1	4	yes	—
27	C₃×C₈	C₂×C₄	1	2	yes	—
28	C₃⋊C₈	—	2	1	no	—
29	C₂×Q₈	—	3	2	no	—
30	Q₁₆	—	3	4	no	—
31	C₂×C₈	—	3	1	no	—
32	C₂×C₈	C₂×D₃	1	1	yes	characteristic
33	C₄⋊C₄	—	6	2	no	—
34	C₄⋊C₄	C₂×D₃	1	2	yes	—
35	C₄²	—	3	1	no	—
36	C₄²	—	6	2	no	—
37	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
38	C₃×C₄	—	4	2	no	—
39	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
40	C₃×C₄	#41	1	1	yes	characteristic
41	Dic₃	—	2	4	no	—
42	Dic₃	—	2	1	no	—
43	Dic₃	Q₁₆	1	2	yes	complemented
44	Q₈	—	3	4	no	—
45	Q₈	—	6	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	3	1	no	—
48	C₂×C₄	—	3	1	no	—
49	C₂×C₄	—	6	2	no	—
50	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
51	C₈	—	6	1	no	—
52	C₈	C₄×D₃	1	2	yes	—
53	C₂×C₃	C₄×D₄	1	1	yes	characteristic
54	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
55	C₂×C₃	#135	1	1	yes	characteristic
56	C₂²	D₃×D₄	1	1	yes	characteristic
57	C₄	—	3	2	no	—
58	C₄	—	4	2	no	—
59	C₄	—	6	4	no	—
60	C₄	—	6	1	no	—
61	C₄	C₂×C₄×D₃	1	1	yes	characteristic
62	C₄	#239	1	1	yes	characteristic
63	C₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂	#893	1	1	yes	characteristic
65	C₂	#912	1	1	yes	characteristic
66	C₂	D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#107	C₂
socle, prime radical	C₂²×C₃	C₂×D₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	#107	D₃
hypocenter	C₃	C₄×Q₁₆
LCS	G ▷ 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
14. Dic₁₂	C₄	semidirect
43. Dic₃	Q₁₆	semidirect
63. C₃	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₂	2
#887	2
C₃×#107	2
C₈×Dic₃	2
#810	2
C₄×Q₁₆	3