Subgroups — C₂×#818 #5105

Order 192.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	#818	C₂	1	4	yes	maximal, direct product factor
4	C₂×#107	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂²×Dic₃	—	2	2	no	—
7	C₂×C₃×C₈	C₄	1	4	yes	complemented
8	C₂×C₃×C₈	C₂²	1	2	yes	—
9	C₄⋊Dic₃	—	2	2	no	—
10	C₄⋊Dic₃	C₂²	1	4	yes	—
11	C₂²×C₈	D₃	1	1	yes	characteristic
12	C₂×C₄⋊C₄	—	3	2	no	—
13	#107	—	3	4	no	—
14	C₂³×C₃	D₄	1	1	yes	characteristic
15	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₂×C₃×C₄	Q₈	1	2	yes	—
18	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
19	C₂×Dic₃	—	2	4	no	—
20	C₂×Dic₃	—	4	4	no	—
21	C₃×C₈	C₂×C₄	1	4	yes	complemented
22	C₂²×C₄	—	6	2	no	—
23	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
24	C₂×C₈	Dic₃	1	4	yes	complemented
25	C₂×C₈	C₂×D₃	1	2	yes	—
26	C₄⋊C₄	—	3	4	no	—
27	C₄⋊C₄	—	6	2	no	—
28	C₂²×C₃	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃	D₈	1	2	yes	—
30	C₂²×C₃	Q₁₆	1	2	yes	—
31	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
32	C₃×C₄	C₄⋊C₄	1	2	yes	—
33	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
35	Dic₃	—	4	4	no	—
36	C₂³	D₁₂	1	1	yes	characteristic
37	C₂×C₄	—	6	4	no	—
38	C₂×C₄	—	12	4	no	—
39	C₂×C₄	Dic₆	1	2	yes	—
40	C₂×C₄	D₁₂	1	1	yes	characteristic
41	C₂×C₄	C₂×Dic₃	1	2	yes	—
42	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
43	C₈	C₂×Dic₃	1	4	yes	complemented
44	C₂×C₃	#107	1	4	yes	complemented
45	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₃	C₂×D₈	1	1	yes	characteristic
47	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₂²	D₂₄	1	2	yes	—
49	C₂²	Dic₁₂	1	2	yes	—
50	C₂²	C₄⋊Dic₃	1	2	yes	—
51	C₂²	C₂×D₁₂	1	1	yes	characteristic
52	C₄	—	12	4	no	—
53	C₄	C₄⋊Dic₃	1	2	yes	—
54	C₄	C₂×Dic₆	1	1	yes	characteristic
55	C₄	C₂²×Dic₃	1	1	yes	characteristic
56	C₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
57	C₂	#818	1	4	yes	direct product factor
58	C₂	C₂×D₂₄	1	1	yes	characteristic
59	C₂	C₂×Dic₁₂	1	1	yes	characteristic
60	C₂	C₂×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂²×C₃×C₈	C₂
socle, prime radical	C₂³×C₃	D₄
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂×#107
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #818	C₂	direct (N × H)
7. C₂×C₃×C₈	C₄	semidirect
21. C₃×C₈	C₂×C₄	semidirect
24. C₂×C₈	Dic₃	semidirect
43. C₈	C₂×Dic₃	semidirect
44. C₂×C₃	#107	semidirect
56. C₃	C₂×#107	semidirect
57. C₂	#818	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈	2
C₂×C₄⋊Dic₃	2
#818	2
C₂×#107	3

Subgroups — C2×#818 #5105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#818 #5105