Subgroups — C₂×C₃²×C₁₃×D₇₇ #49115014

Order 36036.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×D₇₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₃×D₇₇	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×D₇₇	C₂×C₃	1	8	yes	direct product factor
6	C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	4	yes	complemented
7	C₂×C₃²×C₁₃×D₁₁	—	7	1	no	maximal, Hall
8	C₂×C₁₃×D₇₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²×C₁₃×D₇	—	11	1	no	maximal, Hall
10	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	4	yes	complemented
11	C₂×C₃²×D₇₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₁₃×D₁₁	—	7	2	no	—
13	C₂×C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic, complemented
14	C₁₃×D₇₇	C₂×C₃²	1	2	yes	direct product factor
15	C₂×C₇×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₃×D₁₁	—	7	4	no	—
17	C₂×C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented
18	C₃²×C₁₃×D₇	—	11	2	no	—
19	C₂×C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
20	C₃²×D₇₇	C₂×C₁₃	1	2	yes	direct product factor
21	C₃²×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₁₃×D₇	—	11	4	no	—
23	C₇×C₁₁×C₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₇₇	C₃×C₁₃	1	4	yes	direct product factor
25	C₂×C₃×C₁₁×C₁₃	C₃×D₇	1	4	yes	complemented
26	C₃×C₁₃×D₁₁	—	7	8	no	—
27	C₃²×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₇×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₃×D₁₁	—	7	1	no	Hall
30	C₂×C₃×C₇×C₁₃	C₃×D₁₁	1	4	yes	complemented
31	C₃×C₁₃×D₇	—	11	8	no	—
32	C₂²×C₃²×C₁₃	—	77	1	no	Hall
33	C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₃	1	4	yes	complemented
34	C₃×D₇₇	C₂×C₃×C₁₃	1	8	yes	direct product factor
35	C₃×C₁₁×C₁₃	C₂×C₃×D₇	1	4	yes	complemented
36	C₂×C₃²×D₁₁	—	7	1	no	Hall
37	C₂×C₁₃×D₇	—	11	1	no	Hall
38	C₂×D₇₇	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₁₁×C₁₃	C₃²×D₇	1	1	yes	characteristic, complemented
40	C₁₃×D₁₁	—	7	2	no	—
41	C₃×C₇×C₁₃	C₂×C₃×D₁₁	1	4	yes	complemented
42	C₂×C₃²×D₇	—	11	1	no	Hall
43	C₂×C₃²×C₁₃	—	77	2	no	—
44	C₂×C₃²×C₁₃	D₇₇	1	1	yes	characteristic, direct product factor
45	C₃×C₇×C₁₁	C₂²×C₃×C₁₃	1	4	yes	complemented
46	C₂×C₃²×C₁₁	C₁₃×D₇	1	1	yes	characteristic, complemented
47	C₃²×D₁₁	—	7	2	no	—
48	C₂×C₇×C₁₃	C₃²×D₁₁	1	1	yes	characteristic, complemented
49	C₁₃×D₇	—	11	2	no	—
50	C₂²×C₃×C₁₃	—	77	4	no	—
51	C₂×C₇×C₁₁	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
52	D₇₇	C₂×C₃²×C₁₃	1	2	yes	direct product factor
53	C₁₁×C₁₃	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×D₁₁	—	7	4	no	—
55	C₂×C₃²×C₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented
56	C₃²×D₇	—	11	2	no	—
57	C₃²×C₁₃	C₂×D₇₇	1	1	yes	characteristic, direct product factor, Hall
58	C₃²×C₁₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
59	C₇×C₁₃	C₂×C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₃×D₇	—	11	4	no	—
61	C₂×C₃×C₁₃	—	77	8	no	—
62	C₂×C₃×C₁₃	C₃×D₇₇	1	4	yes	direct product factor
63	C₇×C₁₁	C₂²×C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×C₁₁	C₃×C₁₃×D₇	1	4	yes	complemented
65	C₃×D₁₁	—	7	8	no	—
66	C₃²×C₇	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
67	C₂²×C₁₃	—	77	1	no	Hall
68	C₂×D₁₁	—	7	1	no	Hall
69	C₂×C₃×C₇	C₃×C₁₃×D₁₁	1	4	yes	complemented
70	C₃×D₇	—	11	8	no	—
71	C₃×C₁₃	C₂×C₃×D₇₇	1	4	yes	direct product factor
72	C₂²×C₃²	—	77	1	no	Hall
73	C₃×C₁₁	C₂×C₃×C₁₃×D₇	1	4	yes	complemented
74	C₂×D₇	—	11	1	no	Hall
75	C₂×C₁₃	—	77	2	no	—
76	C₂×C₁₃	C₃²×D₇₇	1	1	yes	characteristic, direct product factor
77	C₂×C₁₁	C₃²×C₁₃×D₇	1	1	yes	characteristic, complemented
78	D₁₁	—	7	2	no	—
79	C₃×C₇	C₂×C₃×C₁₃×D₁₁	1	4	yes	complemented
80	C₂×C₃²	—	77	2	no	—
81	C₂×C₃²	C₁₃×D₇₇	1	1	yes	characteristic, direct product factor
82	C₂×C₇	C₃²×C₁₃×D₁₁	1	1	yes	characteristic, complemented
83	D₇	—	11	2	no	—
84	C₁₃	C₂×C₃²×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₃	—	77	4	no	—
86	C₁₁	C₂×C₃²×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
87	C₃²	C₂×C₁₃×D₇₇	1	1	yes	characteristic, direct product factor, Sylow
88	C₇	C₂×C₃²×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
89	C₂×C₃	—	77	8	no	—
90	C₂×C₃	C₃×C₁₃×D₇₇	1	4	yes	direct product factor
91	C₂²	—	77	1	no	Sylow
92	C₃	C₂×C₃×C₁₃×D₇₇	1	4	yes	direct product factor
93	C₂	—	77	2	no	—
94	C₂	C₃²×C₁₃×D₇₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₃	D₇₇
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₃²×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×D₇₇	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₂×C₃×C₁₃×D₇₇	C₃	direct (N × H)
4. C₃²×C₇×C₁₁×C₁₃	C₂²	semidirect
5. C₃×C₁₃×D₇₇	C₂×C₃	direct (N × H)
6. C₂×C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
8. C₂×C₁₃×D₇₇	C₃²	direct (N × H)
10. C₃×C₇×C₁₁×C₁₃	C₂²×C₃	semidirect
11. C₂×C₃²×D₇₇	C₁₃	direct (N × H)
13. C₂×C₃²×C₁₁×C₁₃	D₇	semidirect
14. C₁₃×D₇₇	C₂×C₃²	direct (N × H)
15. C₂×C₇×C₁₁×C₁₃	C₂×C₃²	semidirect
17. C₂×C₃²×C₇×C₁₃	D₁₁	semidirect
19. C₂×C₃²×C₇×C₁₁	C₂×C₁₃	semidirect
20. C₃²×D₇₇	C₂×C₁₃	direct (N × H)
21. C₃²×C₁₁×C₁₃	C₂×D₇	semidirect
23. C₇×C₁₁×C₁₃	C₂²×C₃²	semidirect
24. C₂×C₃×D₇₇	C₃×C₁₃	direct (N × H)
25. C₂×C₃×C₁₁×C₁₃	C₃×D₇	semidirect
27. C₃²×C₇×C₁₃	C₂×D₁₁	semidirect
28. C₃²×C₇×C₁₁	C₂²×C₁₃	semidirect
30. C₂×C₃×C₇×C₁₃	C₃×D₁₁	semidirect
33. C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₃	semidirect
34. C₃×D₇₇	C₂×C₃×C₁₃	direct (N × H)
35. C₃×C₁₁×C₁₃	C₂×C₃×D₇	semidirect
38. C₂×D₇₇	C₃²×C₁₃	direct (N × H)
39. C₂×C₁₁×C₁₃	C₃²×D₇	semidirect
41. C₃×C₇×C₁₃	C₂×C₃×D₁₁	semidirect
44. C₂×C₃²×C₁₃	D₇₇	direct (N × H)
45. C₃×C₇×C₁₁	C₂²×C₃×C₁₃	semidirect
46. C₂×C₃²×C₁₁	C₁₃×D₇	semidirect
48. C₂×C₇×C₁₃	C₃²×D₁₁	semidirect
51. C₂×C₇×C₁₁	C₂×C₃²×C₁₃	semidirect
52. D₇₇	C₂×C₃²×C₁₃	direct (N × H)
53. C₁₁×C₁₃	C₂×C₃²×D₇	semidirect
55. C₂×C₃²×C₇	C₁₃×D₁₁	semidirect
57. C₃²×C₁₃	C₂×D₇₇	direct (N × H)
58. C₃²×C₁₁	C₂×C₁₃×D₇	semidirect
59. C₇×C₁₃	C₂×C₃²×D₁₁	semidirect
62. C₂×C₃×C₁₃	C₃×D₇₇	direct (N × H)
63. C₇×C₁₁	C₂²×C₃²×C₁₃	semidirect
64. C₂×C₃×C₁₁	C₃×C₁₃×D₇	semidirect
66. C₃²×C₇	C₂×C₁₃×D₁₁	semidirect
69. C₂×C₃×C₇	C₃×C₁₃×D₁₁	semidirect
71. C₃×C₁₃	C₂×C₃×D₇₇	direct (N × H)
73. C₃×C₁₁	C₂×C₃×C₁₃×D₇	semidirect
76. C₂×C₁₃	C₃²×D₇₇	direct (N × H)
77. C₂×C₁₁	C₃²×C₁₃×D₇	semidirect
79. C₃×C₇	C₂×C₃×C₁₃×D₁₁	semidirect
81. C₂×C₃²	C₁₃×D₇₇	direct (N × H)
82. C₂×C₇	C₃²×C₁₃×D₁₁	semidirect
84. C₁₃	C₂×C₃²×D₇₇	direct (N × H)
86. C₁₁	C₂×C₃²×C₁₃×D₇	semidirect
87. C₃²	C₂×C₁₃×D₇₇	direct (N × H)
88. C₇	C₂×C₃²×C₁₃×D₁₁	semidirect
90. C₂×C₃	C₃×C₁₃×D₇₇	direct (N × H)
92. C₃	C₂×C₃×C₁₃×D₇₇	direct (N × H)
94. C₂	C₃²×C₁₃×D₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×D₇₇	2
C₂×C₃²×C₇×C₁₁×C₁₃	2
C₂×C₃×C₁₃×D₇₇	3
C₂×C₃²×C₁₃×D₁₁	7
C₂×C₃²×C₁₃×D₇	11
C₂×C₃²×D₇₇	13

Subgroups — C2×C32×C13×D77 #49115014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₃×D₇₇ #49115014