Subgroups — C₂×C₁₃×C₃⋊D₁₄₇ #37524313

Order 22932.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₁₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₄₇	—	3	4	no	maximal
4	C₃²×C₁₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₁₄₇	—	3	8	no	—
6	C₂×C₃×C₁₃×C₄₉	D₃	1	4	yes	complemented
7	C₂×C₁₃×C₃⋊D₂₁	—	7	1	no	maximal
8	C₂×C₁₃×D₄₉	—	9	1	no	Hall
9	C₃×C₁₃×C₄₉	C₂×D₃	1	4	yes	complemented
10	C₂×C₃⋊D₁₄₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃²×C₇×C₁₃	D₇	1	1	yes	characteristic
12	C₁₃×C₃⋊D₂₁	—	7	2	no	—
13	C₂×C₁₃×C₄₉	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₁₃×D₄₉	—	9	2	no	—
15	C₂×C₁₃×D₂₁	—	21	4	no	—
16	C₂×C₃²×C₄₉	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃⋊D₁₄₇	C₂×C₁₃	1	2	yes	direct product factor
18	C₃²×C₇×C₁₃	C₂×D₇	1	1	yes	characteristic
19	C₁₃×C₄₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₁₄₇	—	3	4	no	—
21	C₂×C₃×C₇×C₁₃	D₂₁	1	4	yes	—
22	C₁₃×D₂₁	—	21	8	no	—
23	C₂×C₁₃×C₃⋊D₃	—	49	1	no	Hall
24	C₃²×C₄₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₃×D₇	—	63	1	no	—
26	C₂×C₃×C₄₉	D₃×C₁₃	1	4	yes	complemented
27	D₁₄₇	—	3	8	no	—
28	C₃×C₇×C₁₃	C₂×D₂₁	1	4	yes	—
29	C₂×C₃⋊D₂₁	—	7	1	no	—
30	C₂×C₃²×C₁₃	D₄₉	1	1	yes	characteristic, complemented
31	C₁₃×C₃⋊D₃	—	49	2	no	—
32	C₂×D₄₉	—	9	1	no	Hall
33	C₂×C₇×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic
34	C₁₃×D₇	—	63	2	no	—
35	C₂×D₃×C₁₃	—	147	4	no	—
36	C₃×C₄₉	C₂×D₃×C₁₃	1	4	yes	complemented
37	C₂×C₃²×C₇	C₁₃×D₇	1	1	yes	characteristic
38	C₃⋊D₂₁	—	7	2	no	—
39	C₃²×C₁₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
40	C₂×C₄₉	C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
41	D₄₉	—	9	2	no	—
42	C₇×C₁₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic
43	C₂×D₂₁	—	21	4	no	—
44	C₂×C₃×C₁₃	D₁₄₇	1	4	yes	complemented
45	D₃×C₁₃	—	147	8	no	—
46	C₃²×C₇	C₂×C₁₃×D₇	1	1	yes	characteristic
47	C₂²×C₁₃	—	441	1	no	Hall
48	C₄₉	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	C₁₃×D₂₁	1	4	yes	—
50	D₂₁	—	21	8	no	—
51	C₃×C₁₃	C₂×D₁₄₇	1	4	yes	complemented
52	C₂×C₃⋊D₃	—	49	1	no	Hall
53	C₂×D₇	—	63	1	no	—
54	C₂×C₁₃	—	441	2	no	—
55	C₂×C₁₃	C₃⋊D₁₄₇	1	1	yes	characteristic, direct product factor
56	C₃×C₇	C₂×C₁₃×D₂₁	1	4	yes	—
57	C₂×C₃²	C₁₃×D₄₉	1	1	yes	characteristic, complemented
58	C₃⋊D₃	—	49	2	no	—
59	C₂×C₇	C₁₃×C₃⋊D₂₁	1	1	yes	characteristic
60	D₇	—	63	2	no	—
61	C₁₃	C₂×C₃⋊D₁₄₇	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×D₃	—	147	4	no	—
63	C₃²	C₂×C₁₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
64	C₇	C₂×C₁₃×C₃⋊D₂₁	1	1	yes	characteristic
65	C₂×C₃	C₁₃×D₁₄₇	1	4	yes	complemented
66	D₃	—	147	8	no	—
67	C₂²	—	441	1	no	Sylow
68	C₃	C₂×C₁₃×D₁₄₇	1	4	yes	complemented
69	C₂	—	441	2	no	—
70	C₂	C₁₃×C₃⋊D₁₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊D₁₄₇
commutator, cosocle, hypocenter	C₃²×C₄₉	C₂²×C₁₃
Frattini	C₇	C₂×C₁₃×C₃⋊D₂₁
Fitting	C₂×C₃²×C₁₃×C₄₉	C₂
socle	C₂×C₃²×C₇×C₁₃	D₇
LCS	G ▷ C₃²×C₄₉
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₁₄₇	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₄₉	C₂	semidirect
4. C₃²×C₁₃×C₄₉	C₂²	semidirect
6. C₂×C₃×C₁₃×C₄₉	D₃	semidirect
9. C₃×C₁₃×C₄₉	C₂×D₃	semidirect
10. C₂×C₃⋊D₁₄₇	C₁₃	direct (N × H)
13. C₂×C₁₃×C₄₉	C₃⋊D₃	semidirect
16. C₂×C₃²×C₄₉	C₂×C₁₃	semidirect
17. C₃⋊D₁₄₇	C₂×C₁₃	direct (N × H)
19. C₁₃×C₄₉	C₂×C₃⋊D₃	semidirect
24. C₃²×C₄₉	C₂²×C₁₃	semidirect
26. C₂×C₃×C₄₉	D₃×C₁₃	semidirect
30. C₂×C₃²×C₁₃	D₄₉	semidirect
36. C₃×C₄₉	C₂×D₃×C₁₃	semidirect
39. C₃²×C₁₃	C₂×D₄₉	semidirect
40. C₂×C₄₉	C₁₃×C₃⋊D₃	semidirect
44. C₂×C₃×C₁₃	D₁₄₇	semidirect
48. C₄₉	C₂×C₁₃×C₃⋊D₃	semidirect
51. C₃×C₁₃	C₂×D₁₄₇	semidirect
55. C₂×C₁₃	C₃⋊D₁₄₇	direct (N × H)
57. C₂×C₃²	C₁₃×D₄₉	semidirect
61. C₁₃	C₂×C₃⋊D₁₄₇	direct (N × H)
63. C₃²	C₂×C₁₃×D₄₉	semidirect
65. C₂×C₃	C₁₃×D₁₄₇	semidirect
68. C₃	C₂×C₁₃×D₁₄₇	semidirect
70. C₂	C₁₃×C₃⋊D₁₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊D₁₄₇	2
C₂×C₃²×C₁₃×C₄₉	2
C₂×C₁₃×D₁₄₇	3
C₂×C₁₃×C₃⋊D₂₁	7
C₂×C₃⋊D₁₄₇	13

Subgroups — C2×C13×C3⋊D147 #37524313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₃⋊D₁₄₇ #37524313