Subgroups — C₁₃×C₃⋊Dic₁₄₇ #37524178

Order 22932.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₁₄₇	—	3	4	no	maximal
3	C₃²×C₁₃×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₄₉	D₃	1	4	yes	—
5	C₁₃×C₃⋊Dic₂₁	—	7	1	no	maximal
6	C₁₃×Dic₄₉	—	9	1	no	Hall
7	C₃×C₁₃×C₄₉	Dic₃	1	4	yes	complemented
8	C₃⋊Dic₁₄₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃²×C₇×C₁₃	D₇	1	1	yes	characteristic
10	C₂×C₁₃×C₄₉	C₃⋊D₃	1	1	yes	characteristic
11	C₁₃×Dic₂₁	—	21	4	no	—
12	C₂×C₃²×C₄₉	C₂×C₁₃	1	1	yes	characteristic
13	C₃²×C₇×C₁₃	Dic₇	1	1	yes	characteristic
14	C₁₃×C₄₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
15	Dic₁₄₇	—	3	4	no	—
16	C₂×C₃×C₇×C₁₃	D₂₁	1	4	yes	—
17	C₁₃×C₃⋊Dic₃	—	49	1	no	Hall
18	C₃²×C₄₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₁₃×Dic₇	—	63	1	no	—
20	C₂×C₃×C₄₉	D₃×C₁₃	1	4	yes	—
21	C₃×C₇×C₁₃	Dic₂₁	1	4	yes	—
22	C₃⋊Dic₂₁	—	7	1	no	—
23	C₂×C₃²×C₁₃	D₄₉	1	1	yes	characteristic
24	Dic₄₉	—	9	1	no	Hall
25	C₂×C₇×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic
26	Dic₃×C₁₃	—	147	4	no	—
27	C₃×C₄₉	Dic₃×C₁₃	1	4	yes	complemented
28	C₂×C₃²×C₇	C₁₃×D₇	1	1	yes	characteristic
29	C₃²×C₁₃	Dic₄₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₄₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic
31	C₇×C₁₃	C₃⋊Dic₂₁	1	1	yes	characteristic
32	Dic₂₁	—	21	4	no	—
33	C₂×C₃×C₁₃	D₁₄₇	1	4	yes	—
34	C₃²×C₇	C₁₃×Dic₇	1	1	yes	characteristic
35	C₄×C₁₃	—	441	1	no	Hall
36	C₄₉	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	C₁₃×D₂₁	1	4	yes	—
38	C₃×C₁₃	Dic₁₄₇	1	4	yes	complemented
39	C₃⋊Dic₃	—	49	1	no	Hall
40	Dic₇	—	63	1	no	—
41	C₂×C₁₃	C₃⋊D₁₄₇	1	1	yes	characteristic
42	C₃×C₇	C₁₃×Dic₂₁	1	4	yes	—
43	C₂×C₃²	C₁₃×D₄₉	1	1	yes	characteristic
44	C₂×C₇	C₁₃×C₃⋊D₂₁	1	1	yes	characteristic
45	C₁₃	C₃⋊Dic₁₄₇	1	1	yes	characteristic, direct product factor, Sylow
46	Dic₃	—	147	4	no	—
47	C₃²	C₁₃×Dic₄₉	1	1	yes	characteristic, complemented, Sylow
48	C₇	C₁₃×C₃⋊Dic₂₁	1	1	yes	characteristic
49	C₂×C₃	C₁₃×D₁₄₇	1	4	yes	—
50	C₄	—	441	1	no	Sylow
51	C₃	C₁₃×Dic₁₄₇	1	4	yes	complemented
52	C₂	C₁₃×C₃⋊D₁₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₁₄₇
commutator, hypocenter	C₃²×C₄₉	C₄×C₁₃
Frattini	C₂×C₇	C₁₃×C₃⋊D₂₁
Fitting	C₂×C₃²×C₁₃×C₄₉	C₂
socle, prime radical	C₂×C₃²×C₇×C₁₃	D₇
cosocle	C₂×C₃²×C₄₉	C₂×C₁₃
LCS	G ▷ C₃²×C₄₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃²×C₁₃×C₄₉	C₄	semidirect
7. C₃×C₁₃×C₄₉	Dic₃	semidirect
8. C₃⋊Dic₁₄₇	C₁₃	direct (N × H)
14. C₁₃×C₄₉	C₃⋊Dic₃	semidirect
18. C₃²×C₄₉	C₄×C₁₃	semidirect
27. C₃×C₄₉	Dic₃×C₁₃	semidirect
29. C₃²×C₁₃	Dic₄₉	semidirect
36. C₄₉	C₁₃×C₃⋊Dic₃	semidirect
38. C₃×C₁₃	Dic₁₄₇	semidirect
45. C₁₃	C₃⋊Dic₁₄₇	direct (N × H)
47. C₃²	C₁₃×Dic₄₉	semidirect
51. C₃	C₁₃×Dic₁₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₃×C₄₉	2
C₁₃×Dic₁₄₇	3
C₁₃×C₃⋊Dic₂₁	7
C₃⋊Dic₁₄₇	13

Subgroups — C13×C3⋊Dic147 #37524178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊Dic₁₄₇ #37524178