Subgroups — D₆₁₁⋊(C₃⋊D₃) #36347274

Order 21996.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₆₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉⋊D₄₇	—	3	4	no	maximal
5	C₃²×C₁₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₄₇×D₃₉	—	3	4	no	—
7	C₁₃×D₁₄₁	—	3	4	no	—
8	C₃×D₆₁₁	D₃	1	4	yes	complemented
9	D₁₃×D₄₇	—	9	1	no	Hall
10	C₃×C₁₃×C₄₇	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₄₇	—	13	1	no	maximal, Hall
12	D₆₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
13	C₁₃×D₄₇	—	9	1	no	—
14	D₁₃×C₄₇	—	9	1	no	—
15	C₃⋊D₁₄₁	D₁₃	1	1	yes	characteristic, complemented
16	C₃⋊D₃×C₄₇	—	13	1	no	—
17	C₃²×D₄₇	—	13	1	no	—
18	C₁₃×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	D₃×D₄₇	—	39	4	no	—
20	C₃⋊D₃×D₁₃	—	47	1	no	maximal, Hall
21	C₃²×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
22	D₁₄₁	—	3	4	no	—
23	C₃×D₄₇	—	13	4	no	—
24	D₃×C₄₇	—	39	4	no	—
25	C₃⋊D₃₉	D₄₇	1	1	yes	characteristic, complemented
26	C₁₃×C₃⋊D₃	—	47	1	no	—
27	C₃²×D₁₃	—	47	1	no	—
28	C₂×D₄₇	—	117	1	no	Hall
29	D₃×D₁₃	—	141	4	no	—
30	C₃×C₄₇	D₃×D₁₃	1	4	yes	complemented
31	C₃²×C₁₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₄₇	—	117	1	no	—
33	D₄₇	—	9	1	no	—
34	D₄₇	—	13	1	no	—
35	D₃₉	—	3	4	no	—
36	C₃×D₁₃	—	47	4	no	—
37	D₃×C₁₃	—	141	4	no	—
38	C₂×D₁₃	—	423	1	no	Hall
39	C₄₇	C₃⋊D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₁₃	D₃×D₄₇	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	611	1	no	Hall
42	C₂×C₁₃	—	423	1	no	—
43	D₁₃	—	9	1	no	—
44	D₁₃	—	47	1	no	—
45	C₂×C₃²	—	611	1	no	—
46	C₃⋊D₃	—	13	1	no	—
47	C₃⋊D₃	—	47	1	no	—
48	C₁₃	C₃⋊D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	1833	4	no	—
50	C₃²	D₁₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	611	4	no	—
52	D₃	—	39	4	no	—
53	D₃	—	141	4	no	—
54	C₂²	—	5499	1	no	Sylow
55	C₃	D₃₉⋊D₄₇	1	4	yes	complemented
56	C₂	—	611	1	no	—
57	C₂	—	117	1	no	—
58	C₂	—	423	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃×C₄₇	C₂²
LCS	G ▷ C₃²×C₁₃×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×D₆₁₁	C₂	semidirect
2. C₁₃×C₃⋊D₁₄₁	C₂	semidirect
3. C₄₇×C₃⋊D₃₉	C₂	semidirect
5. C₃²×C₁₃×C₄₇	C₂²	semidirect
8. C₃×D₆₁₁	D₃	semidirect
10. C₃×C₁₃×C₄₇	C₂×D₃	semidirect
12. D₆₁₁	C₃⋊D₃	semidirect
15. C₃⋊D₁₄₁	D₁₃	semidirect
18. C₁₃×C₄₇	C₂×C₃⋊D₃	semidirect
21. C₃²×C₄₇	C₂×D₁₃	semidirect
25. C₃⋊D₃₉	D₄₇	semidirect
30. C₃×C₄₇	D₃×D₁₃	semidirect
31. C₃²×C₁₃	C₂×D₄₇	semidirect
39. C₄₇	C₃⋊D₃×D₁₃	semidirect
40. C₃×C₁₃	D₃×D₄₇	semidirect
48. C₁₃	C₃⋊D₃×D₄₇	semidirect
50. C₃²	D₁₃×D₄₇	semidirect
55. C₃	D₃₉⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₆₁₁	2
C₁₃×C₃⋊D₁₄₁	2
C₄₇×C₃⋊D₃₉	2
D₃₉⋊D₄₇	3
C₃⋊D₃×D₄₇	13
C₃⋊D₃×D₁₃	47

Subgroups — D611⋊(C3⋊D3) #36347274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁₁⋊(C₃⋊D₃) #36347274