Subgroups — D₁₃×C₃⋊D₁₄₁ #36347272

Order 21996.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₁₈₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₄₁	—	3	4	no	maximal
5	C₃²×C₁₃×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₈₃₃	—	3	4	no	—
7	C₁₃×D₁₄₁	—	3	4	no	—
8	C₃×D₁₃×C₄₇	D₃	1	4	yes	complemented
9	D₁₃×D₄₇	—	9	1	no	Hall
10	C₃×C₁₃×C₄₇	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₁₄₁	—	13	1	no	maximal, Hall
12	D₆₁₁	—	9	1	no	—
13	C₁₃×D₄₇	—	9	1	no	—
14	D₁₃×C₄₇	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₄₇	—	13	1	no	—
16	C₃⋊D₁₄₁	—	13	1	no	—
17	C₃⋊D₁₄₁	D₁₃	1	1	yes	characteristic, direct product factor
18	C₁₃×C₄₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₄₁	—	39	4	no	—
20	C₃⋊D₃×D₁₃	—	47	1	no	maximal, Hall
21	C₃²×C₄₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₄₇	—	13	4	no	—
23	D₁₄₁	—	3	4	no	—
24	D₁₄₁	—	39	4	no	—
25	C₃⋊D₃₉	—	47	1	no	—
26	C₁₃×C₃⋊D₃	—	47	1	no	—
27	C₃²×D₁₃	D₄₇	1	1	yes	characteristic, complemented
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	—	13	1	no	—
33	D₄₇	—	9	1	no	—
34	D₄₇	—	117	1	no	—
35	D₃₉	—	141	4	no	—
36	C₃×D₁₃	D₁₄₁	1	4	yes	complemented
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	C₂×D₁₄₁	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	611	1	no	Hall
42	C₂×C₁₃	—	423	1	no	—
43	D₁₃	—	423	1	no	—
44	D₁₃	C₃⋊D₁₄₁	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	13	1	no	—
46	C₃⋊D₃	—	47	1	no	—
47	C₃⋊D₃	—	611	1	no	—
48	C₁₃	C₂×C₃⋊D₁₄₁	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	—	13	4	no	—
52	D₃	—	1833	4	no	—
53	D₃	—	141	4	no	—
54	C₂²	—	5499	1	no	Sylow
55	C₃	D₁₃×D₁₄₁	1	4	yes	complemented
56	C₂	—	13	1	no	—
57	C₂	—	5499	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×D₁₃×C₄₇	C₂	semidirect
2. C₁₃×C₃⋊D₁₄₁	C₂	semidirect
3. C₃⋊D₁₈₃₃	C₂	semidirect
5. C₃²×C₁₃×C₄₇	C₂²	semidirect
8. C₃×D₁₃×C₄₇	D₃	semidirect
10. C₃×C₁₃×C₄₇	C₂×D₃	semidirect
14. D₁₃×C₄₇	C₃⋊D₃	semidirect
17. C₃⋊D₁₄₁	D₁₃	direct (N × H)
18. C₁₃×C₄₇	C₂×C₃⋊D₃	semidirect
21. C₃²×C₄₇	C₂×D₁₃	semidirect
27. C₃²×D₁₃	D₄₇	semidirect
30. C₃×C₄₇	D₃×D₁₃	semidirect
31. C₃²×C₁₃	C₂×D₄₇	semidirect
36. C₃×D₁₃	D₁₄₁	semidirect
39. C₄₇	C₃⋊D₃×D₁₃	semidirect
40. C₃×C₁₃	C₂×D₁₄₁	semidirect
44. D₁₃	C₃⋊D₁₄₁	direct (N × H)
48. C₁₃	C₂×C₃⋊D₁₄₁	semidirect
50. C₃²	D₁₃×D₄₇	semidirect
55. C₃	D₁₃×D₁₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₃×C₄₇	2
C₁₃×C₃⋊D₁₄₁	2
C₃⋊D₁₈₃₃	2
D₁₃×D₁₄₁	3
C₂×C₃⋊D₁₄₁	13
C₃⋊D₃×D₁₃	47

Subgroups — D13×C3⋊D141 #36347272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₃⋊D₁₄₁ #36347272