Subgroups — #4880

Order 192.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	#892	C₂	1	2	yes	maximal
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#818	C₂	1	1	yes	maximal, characteristic, complemented
5	#808	C₂	1	2	yes	maximal, complemented
6	#427	—	3	1	no	maximal, Sylow
7	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊C₄	C₂²	1	2	yes	—
10	(C₂×D₃)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₄×Dic₃	—	2	2	no	—
13	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	D₃×C₈	C₄	1	4	yes	complemented
15	C₂²×C₈	—	3	1	no	—
16	#117	—	3	2	no	—
17	#107	—	3	1	no	—
18	#107	D₃	1	1	yes	characteristic, complemented
19	#106	—	3	2	no	—
20	C₂²×D₃	D₄	1	1	yes	characteristic
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
23	C₂×Dic₃	—	2	2	no	—
24	C₂×Dic₃	D₄	1	1	yes	characteristic
25	C₄×D₃	C₂×C₄	1	2	yes	—
26	C₄×D₃	Q₈	1	2	yes	—
27	C₃×C₈	C₂×C₄	1	2	yes	—
28	C₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₄	—	3	1	no	—
30	C₂×C₈	—	3	1	no	—
31	C₂×C₈	—	3	4	no	—
32	C₂×C₈	C₂×D₃	1	1	yes	characteristic
33	C₄⋊C₄	—	3	2	no	—
34	C₄⋊C₄	C₂×D₃	1	2	yes	—
35	C₂²⋊C₄	—	6	2	no	—
36	C₄²	—	6	2	no	—
37	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
38	C₂×D₃	—	2	1	no	—
39	C₂×D₃	—	2	1	no	—
40	C₂×D₃	C₄⋊C₄	1	2	yes	—
41	C₃×C₄	—	4	2	no	—
42	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
44	Dic₃	—	4	2	no	—
45	Dic₃	C₄⋊C₄	1	2	yes	—
46	C₂³	—	3	1	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	3	1	no	—
49	C₂×C₄	—	3	2	no	—
50	C₂×C₄	—	3	2	no	—
51	C₂×C₄	—	6	2	no	—
52	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
53	C₈	—	3	2	no	—
54	C₈	C₄×D₃	1	2	yes	—
55	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₃	#135	1	1	yes	characteristic
57	C₂×C₃	#135	1	1	yes	characteristic
58	D₃	—	2	2	no	—
59	C₂²	—	3	2	no	—
60	C₂²	—	6	1	no	—
61	C₂²	—	6	1	no	—
62	C₂²	D₃×D₄	1	1	yes	characteristic
63	C₄	—	3	2	no	—
64	C₄	—	4	2	no	—
65	C₄	—	12	2	no	—
66	C₄	C₂×C₄×D₃	1	1	yes	characteristic
67	C₄	D₃×Q₈	1	1	yes	characteristic
68	C₃	#427	1	1	yes	characteristic, complemented, Sylow
69	C₂	—	6	2	no	—
70	C₂	D₃×C₄⋊C₄	1	1	yes	characteristic
71	C₂	#912	1	1	yes	characteristic
72	C₂	#919	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	C₂²×C₃	C₂×D₄
prime radical	C₂²×D₃	D₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	#107	D₃
hypocenter	C₃	#427
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
3. C₃×#107	C₂	semidirect
4. #818	C₂	semidirect
5. #808	C₂	semidirect
14. D₃×C₈	C₄	semidirect
18. #107	D₃	semidirect
68. C₃	#427	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×C₈	2
#892	2
C₃×#107	2
#818	2
#808	2
#427	3