Subgroups — C₃⋊D₃×D₃₆₁ #27188697

Order 12996.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₀₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₃₆₁	—	3	4	no	maximal
5	C₃²×C₃₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₀₈₃	—	3	4	no	—
7	C₃×D₃₆₁	D₃	1	4	yes	complemented
8	D₃×C₃₆₁	—	3	4	no	—
9	C₂×D₃₆₁	—	9	1	no	Hall
10	C₃×C₃₆₁	C₂×D₃	1	4	yes	complemented
11	C₂×C₃₆₁	—	9	1	no	—
12	D₃₆₁	—	9	1	no	—
13	D₃₆₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₃⋊D₃×D₁₉	—	19	1	no	maximal
15	C₃₆₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
16	C₃⋊D₅₇	—	19	1	no	—
17	C₃⋊D₃×C₁₉	D₁₉	1	1	yes	characteristic
18	C₃²×D₁₉	—	19	1	no	—
19	D₃×D₁₉	—	57	4	no	—
20	C₃²×C₁₉	C₂×D₁₉	1	1	yes	characteristic
21	D₅₇	—	57	4	no	—
22	C₃×D₁₉	—	19	4	no	—
23	D₃×C₁₉	—	3	4	no	—
24	C₂×D₁₉	—	171	1	no	—
25	C₃×C₁₉	D₃×D₁₉	1	4	yes	—
26	C₂×C₁₉	—	9	1	no	—
27	D₁₉	—	19	1	no	—
28	D₁₉	—	171	1	no	—
29	C₂×C₃⋊D₃	—	361	1	no	Hall
30	C₁₉	C₃⋊D₃×D₁₉	1	1	yes	characteristic
31	C₂×C₃²	—	361	1	no	—
32	C₃⋊D₃	—	361	1	no	—
33	C₃⋊D₃	D₃₆₁	1	1	yes	characteristic, direct product factor
34	C₂×D₃	—	1083	4	no	—
35	C₃²	C₂×D₃₆₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	361	4	no	—
37	D₃	—	3	4	no	—
38	D₃	—	1083	4	no	—
39	C₂²	—	3249	1	no	Sylow
40	C₃	D₃×D₃₆₁	1	4	yes	complemented
41	C₂	—	9	1	no	—
42	C₂	—	361	1	no	—
43	C₂	—	3249	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₃₆₁	C₂²
Frattini	C₁₉	C₃⋊D₃×D₁₉
socle	C₃²×C₁₉	C₂×D₁₉
LCS	G ▷ C₃²×C₃₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₀₈₃	C₂	semidirect
2. C₃⋊D₃×C₃₆₁	C₂	semidirect
3. C₃²×D₃₆₁	C₂	semidirect
5. C₃²×C₃₆₁	C₂²	semidirect
7. C₃×D₃₆₁	D₃	semidirect
10. C₃×C₃₆₁	C₂×D₃	semidirect
13. D₃₆₁	C₃⋊D₃	direct (N × H)
15. C₃₆₁	C₂×C₃⋊D₃	semidirect
33. C₃⋊D₃	D₃₆₁	direct (N × H)
35. C₃²	C₂×D₃₆₁	semidirect
40. C₃	D₃×D₃₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₁₀₈₃	2
C₃⋊D₃×C₃₆₁	2
C₃²×D₃₆₁	2
D₃×D₃₆₁	3
C₃⋊D₃×D₁₉	19

Subgroups — C3⋊D3×D361 #27188697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₃₆₁ #27188697