Subgroups — C₂×#626 #3808

Order 144.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#626	C₂	1	4	yes	maximal, direct product factor
5	C₂×#67	—	3	1	no	maximal
6	C₂×D₁₂	—	3	1	no	maximal
7	C₂²×C₃²	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊D₃	—	2	2	no	—
9	C₂×C₃⋊D₃	C₂²	1	2	yes	complemented
10	C₂×C₃×D₃	—	2	2	no	—
11	C₂×C₃×D₃	C₂²	1	2	yes	complemented
12	C₃×Dic₃	C₂²	1	2	yes	complemented
13	C₂³×C₃	—	3	1	no	—
14	C₂²×D₃	—	3	1	no	—
15	C₂²×D₃	—	3	1	no	—
16	C₂²×D₃	—	6	1	no	—
17	C₂²×D₃	D₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄	—	3	1	no	—
19	#67	—	3	4	no	—
20	C₂×Dic₃	D₃	1	1	yes	characteristic, complemented
21	D₁₂	—	3	4	no	—
22	C₂×C₃²	D₄	1	2	yes	complemented
23	C₂×C₃²	C₂³	1	1	yes	characteristic
24	C₃⋊D₃	—	2	2	no	—
25	C₃×D₃	—	2	2	no	—
26	C₂×D₄	—	9	1	no	Sylow
27	C₂²×C₃	—	2	1	no	—
28	C₂²×C₃	—	3	2	no	—
29	C₂²×C₃	—	6	2	no	—
30	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
31	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
32	C₂×D₃	—	2	2	no	—
33	C₂×D₃	—	3	2	no	—
34	C₂×D₃	—	3	2	no	—
35	C₂×D₃	—	6	2	no	—
36	C₂×D₃	—	6	4	no	—
37	C₂×D₃	—	6	2	no	—
38	C₂×D₃	—	6	2	no	—
39	C₂×D₃	C₂×D₃	1	2	yes	complemented
40	C₃×C₄	—	3	2	no	—
41	Dic₃	C₂×D₃	1	2	yes	complemented
42	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
43	C₂³	—	3	1	no	—
44	C₂³	—	9	1	no	—
45	D₄	—	9	4	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	6	2	no	—
50	C₂×C₃	D₁₂	1	2	yes	complemented
51	C₂×C₃	#67	1	2	yes	complemented
52	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
53	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
54	D₃	—	2	2	no	—
55	D₃	—	6	4	no	—
56	D₃	—	6	2	no	—
57	D₃	—	6	2	no	—
58	C₂²	—	3	2	no	—
59	C₂²	—	6	2	no	—
60	C₂²	—	9	2	no	—
61	C₂²	—	18	2	no	—
62	C₂²	D₃²	1	1	yes	characteristic
63	C₄	—	3	2	no	—
64	C₃	—	2	1	no	—
65	C₃	C₂×D₁₂	1	1	yes	characteristic, complemented
66	C₃	C₂×#67	1	1	yes	characteristic, complemented
67	C₂	—	6	2	no	—
68	C₂	—	18	2	no	—
69	C₂	#626	1	2	yes	direct product factor
70	C₂	C₂×D₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃²
commutator, cosocle	C₂×C₃²	C₂³
Frattini	C₂	C₂×D₃²
Fitting, socle	C₂²×C₃²	C₂²
hypocenter	C₃²	C₂×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃×D₃	C₂	semidirect
3. C₂×C₃×Dic₃	C₂	semidirect
4. #626	C₂	direct (N × H)
9. C₂×C₃⋊D₃	C₂²	semidirect
11. C₂×C₃×D₃	C₂²	semidirect
12. C₃×Dic₃	C₂²	semidirect
17. C₂²×D₃	D₃	semidirect
20. C₂×Dic₃	D₃	semidirect
22. C₂×C₃²	D₄	semidirect
39. C₂×D₃	C₂×D₃	semidirect
41. Dic₃	C₂×D₃	semidirect
42. C₃²	C₂×D₄	semidirect
50. C₂×C₃	D₁₂	semidirect
51. C₂×C₃	#67	semidirect
65. C₃	C₂×D₁₂	semidirect
66. C₃	C₂×#67	semidirect
69. C₂	#626	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⋊D₃	2
C₂²×C₃×D₃	2
C₂×C₃×Dic₃	2
#626	2
C₂×#67	3
C₂×D₁₂	3

Subgroups — C2×#626 #3808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#626 #3808