Subgroups — C₂×#3746 #64114

Order 288.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#634	C₂	1	2	yes	maximal
2	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
3	#3746	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₂	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊Dic₃	—	2	2	no	—
7	#634	—	2	2	no	—
8	#634	C₂²	1	4	yes	—
9	C₃²×C₈	C₂²	1	2	yes	—
10	C₂×Dic₆	—	3	8	no	—
11	C₂×C₃×C₈	D₃	1	4	yes	—
12	Dic₁₂	—	3	16	no	—
13	C₂²×C₃²	D₄	1	1	yes	characteristic
14	C₃²×C₄	D₄	1	1	yes	characteristic
15	C₃²×C₄	C₂³	1	1	yes	characteristic
16	C₃⋊Dic₃	—	2	4	no	—
17	C₂×Q₁₆	—	9	1	no	Sylow
18	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
19	C₂×Dic₃	—	6	8	no	—
20	Dic₆	—	3	16	no	—
21	Dic₆	—	6	8	no	—
22	C₃×C₈	C₂×D₃	1	8	yes	—
23	C₂×C₃²	Q₁₆	1	2	yes	complemented
24	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
25	C₂×Q₈	—	9	2	no	—
26	Q₁₆	—	9	4	no	—
27	C₂×C₈	C₃⋊D₃	1	1	yes	characteristic
28	C₂²×C₃	D₁₂	1	4	yes	—
29	C₃×C₄	D₁₂	1	4	yes	—
30	C₃×C₄	C₂²×D₃	1	4	yes	—
31	Dic₃	—	6	16	no	—
32	C₃²	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
33	Q₈	—	9	4	no	—
34	Q₈	—	18	2	no	—
35	C₂×C₄	—	18	2	no	—
36	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₈	C₂×C₃⋊D₃	1	2	yes	—
38	C₂×C₃	Dic₁₂	1	8	yes	complemented
39	C₂×C₃	C₂×D₁₂	1	4	yes	—
40	C₂²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
41	C₄	—	18	4	no	—
42	C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
43	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
44	C₃	C₂×Dic₁₂	1	4	yes	complemented
45	C₂	#3746	1	2	yes	direct product factor
46	C₂	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊(C₃⋊D₃)
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×C₈	C₂
socle, prime radical	C₂²×C₃²	D₄
hypercenter	C₂×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×Q₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #3746	C₂	direct (N × H)
23. C₂×C₃²	Q₁₆	semidirect
32. C₃²	C₂×Q₁₆	semidirect
38. C₂×C₃	Dic₁₂	semidirect
44. C₃	C₂×Dic₁₂	semidirect
45. C₂	#3746	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#634	2
C₂×C₃²×C₈	2
#3746	2
C₂×Dic₁₂	3

Subgroups — C2×#3746 #64114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3746 #64114