Subgroups — C₁₃×C₃⋊D₃×C₇⋊D₇ #37525646

Order 22932.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×C₇⋊D₇	—	3	4	no	maximal
5	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₃⋊(C₇⋊D₇)	—	3	4	no	—
7	D₃×C₇²×C₁₃	—	3	4	no	—
8	C₃×C₁₃×C₇⋊D₇	D₃	1	4	yes	complemented
9	C₁₃×D₇×C₃⋊D₃	—	7	8	no	maximal
10	C₂×C₁₃×C₇⋊D₇	—	9	1	no	Hall
11	C₃×C₇²×C₁₃	C₂×D₃	1	4	yes	complemented
12	C₃⋊D₃×C₇⋊D₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₃×C₃⋊D₂₁	—	7	8	no	—
14	C₇×C₁₃×C₃⋊D₃	D₇	1	8	yes	complemented
15	C₃²×C₁₃×D₇	—	7	8	no	—
16	C₂×C₇²×C₁₃	—	9	1	no	—
17	C₁₃×C₇⋊D₇	—	9	1	no	—
18	C₁₃×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	D₃×C₁₃×D₇	—	21	32	no	—
20	C₃⋊(C₃⋊(C₇⋊D₇))	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₇²×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₃²×C₇⋊D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₃²×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
24	C₇²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
25	D₃×C₇⋊D₇	—	3	4	no	—
26	C₁₃×D₂₁	—	21	32	no	—
27	D₃×C₇×C₁₃	—	3	32	no	—
28	C₃×C₁₃×D₇	—	7	32	no	—
29	C₂×C₁₃×C₃⋊D₃	—	49	1	no	Hall
30	C₃²×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₁₃×D₇	—	63	8	no	—
32	C₃⋊(C₇⋊D₇)	—	3	4	no	—
33	D₃×C₇²	—	3	4	no	—
34	C₃×C₇⋊D₇	D₃×C₁₃	1	4	yes	complemented
35	C₃×C₇×C₁₃	D₃×D₇	1	32	yes	complemented
36	D₇×C₃⋊D₃	—	7	8	no	—
37	C₂×C₃²×C₁₃	—	49	1	no	—
38	C₁₃×C₃⋊D₃	—	49	1	no	—
39	C₁₃×C₃⋊D₃	C₇⋊D₇	1	1	yes	characteristic, direct product factor
40	C₂×C₇⋊D₇	—	9	1	no	Hall
41	C₂×C₇×C₁₃	—	9	8	no	—
42	C₁₃×D₇	—	7	8	no	—
43	C₁₃×D₇	—	63	8	no	—
44	C₂×D₃×C₁₃	—	147	4	no	—
45	C₃×C₇²	C₂×D₃×C₁₃	1	4	yes	complemented
46	C₃⋊D₂₁	—	7	8	no	—
47	C₇×C₃⋊D₃	C₁₃×D₇	1	8	yes	complemented
48	C₃²×D₇	—	7	8	no	—
49	C₃²×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
50	C₂×C₇²	—	9	1	no	—
51	C₇⋊D₇	—	9	1	no	—
52	C₇⋊D₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
53	C₇×C₁₃	D₇×C₃⋊D₃	1	8	yes	complemented
54	D₃×D₇	—	21	32	no	—
55	C₂×C₃×C₁₃	—	49	4	no	—
56	D₃×C₁₃	—	3	4	no	—
57	D₃×C₁₃	—	147	4	no	—
58	C₃²×C₇	C₂×C₁₃×D₇	1	8	yes	complemented
59	C₂²×C₁₃	—	441	1	no	Hall
60	C₇²	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
61	D₂₁	—	21	32	no	—
62	C₃×D₇	—	7	32	no	—
63	D₃×C₇	—	3	32	no	—
64	C₃×C₁₃	D₃×C₇⋊D₇	1	4	yes	complemented
65	C₂×C₃⋊D₃	—	49	1	no	Hall
66	C₂×D₇	—	63	8	no	—
67	C₂×C₁₃	—	9	1	no	—
68	C₂×C₁₃	—	49	1	no	—
69	C₂×C₁₃	—	441	1	no	—
70	C₃×C₇	D₃×C₁₃×D₇	1	32	yes	complemented
71	C₂×C₃²	—	49	1	no	—
72	C₃⋊D₃	—	49	1	no	—
73	C₃⋊D₃	C₁₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor
74	C₂×C₇	—	9	8	no	—
75	D₇	—	7	8	no	—
76	D₇	—	63	8	no	—
77	C₁₃	C₃⋊D₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×D₃	—	147	4	no	—
79	C₃²	C₂×C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
80	C₇	C₁₃×D₇×C₃⋊D₃	1	8	yes	complemented
81	C₂×C₃	—	49	4	no	—
82	D₃	—	3	4	no	—
83	D₃	—	147	4	no	—
84	C₂²	—	441	1	no	Sylow
85	C₃	D₃×C₁₃×C₇⋊D₇	1	4	yes	complemented
86	C₂	—	9	1	no	—
87	C₂	—	49	1	no	—
88	C₂	—	441	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊D₃×C₇⋊D₇
commutator, cosocle, hypocenter	C₃²×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₇²×C₁₃×C₃⋊D₃	C₂	semidirect
3. C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	semidirect
5. C₃²×C₇²×C₁₃	C₂²	semidirect
8. C₃×C₁₃×C₇⋊D₇	D₃	semidirect
11. C₃×C₇²×C₁₃	C₂×D₃	semidirect
12. C₃⋊D₃×C₇⋊D₇	C₁₃	direct (N × H)
14. C₇×C₁₃×C₃⋊D₃	D₇	semidirect
18. C₁₃×C₇⋊D₇	C₃⋊D₃	direct (N × H)
20. C₃⋊(C₃⋊(C₇⋊D₇))	C₂×C₁₃	semidirect
21. C₇²×C₃⋊D₃	C₂×C₁₃	semidirect
22. C₃²×C₇⋊D₇	C₂×C₁₃	semidirect
23. C₃²×C₇×C₁₃	C₂×D₇	semidirect
24. C₇²×C₁₃	C₂×C₃⋊D₃	semidirect
30. C₃²×C₇²	C₂²×C₁₃	semidirect
34. C₃×C₇⋊D₇	D₃×C₁₃	semidirect
35. C₃×C₇×C₁₃	D₃×D₇	semidirect
39. C₁₃×C₃⋊D₃	C₇⋊D₇	direct (N × H)
45. C₃×C₇²	C₂×D₃×C₁₃	semidirect
47. C₇×C₃⋊D₃	C₁₃×D₇	semidirect
49. C₃²×C₁₃	C₂×C₇⋊D₇	semidirect
52. C₇⋊D₇	C₁₃×C₃⋊D₃	direct (N × H)
53. C₇×C₁₃	D₇×C₃⋊D₃	semidirect
58. C₃²×C₇	C₂×C₁₃×D₇	semidirect
60. C₇²	C₂×C₁₃×C₃⋊D₃	semidirect
64. C₃×C₁₃	D₃×C₇⋊D₇	semidirect
70. C₃×C₇	D₃×C₁₃×D₇	semidirect
73. C₃⋊D₃	C₁₃×C₇⋊D₇	direct (N × H)
77. C₁₃	C₃⋊D₃×C₇⋊D₇	direct (N × H)
79. C₃²	C₂×C₁₃×C₇⋊D₇	semidirect
80. C₇	C₁₃×D₇×C₃⋊D₃	semidirect
85. C₃	D₃×C₁₃×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇⋊D₇	2
C₇²×C₁₃×C₃⋊D₃	2
C₁₃×C₃⋊(C₃⋊(C₇⋊D₇))	2
D₃×C₁₃×C₇⋊D₇	3
C₁₃×D₇×C₃⋊D₃	7
C₃⋊D₃×C₇⋊D₇	13

Subgroups — C13×C3⋊D3×C7⋊D7 #37525646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₃⋊D₃×C₇⋊D₇ #37525646