Group #49114485 — subgroups

Subgroups — C₁₃×D₇×D₉₉ #49114485

Order 36036.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₆₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₃×D₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×D₇×D₃₃	—	3	1	no	maximal
5	C₇×C₉×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×D₂₃₁	—	3	1	no	—
7	C₇×C₁₃×D₃₃	—	3	1	no	—
8	C₃×C₁₁×C₁₃×D₇	D₃	1	1	yes	characteristic
9	C₂×C₁₃×D₉₉	—	7	1	no	maximal, Hall
10	C₁₃×D₇×D₁₁	—	9	1	no	Hall
11	C₁₃×D₇×D₉	—	11	1	no	maximal, Hall
12	C₃×C₇×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic
13	D₇×D₉₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₁₃×D₉₉	—	7	1	no	—
15	C₁₃×D₉₉	D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₉×C₁₁×C₁₃	—	7	1	no	—
17	C₁₃×D₇₇	—	9	1	no	—
18	C₁₁×C₁₃×D₇	D₉	1	1	yes	characteristic, complemented
19	C₇×C₁₃×D₁₁	—	9	1	no	—
20	C₂×C₁₃×D₃₃	—	21	1	no	—
21	C₁₃×D₆₃	—	11	1	no	—
22	C₇×C₁₃×D₉	—	11	1	no	—
23	C₉×C₁₃×D₇	D₁₁	1	1	yes	characteristic, complemented
24	D₆₉₃	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₇×D₉₉	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₉×C₁₁×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₉×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	D₃×C₁₃×D₇	—	33	1	no	—
29	C₇×C₁₁×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
30	D₇×D₃₃	—	3	1	no	—
31	C₂×C₃×C₁₁×C₁₃	—	7	1	no	—
32	C₁₃×D₃₃	—	3	1	no	—
33	C₁₃×D₃₃	—	21	1	no	—
34	C₇×C₉×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
35	C₇×C₉×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₃×D₁₁	—	63	1	no	Hall
37	C₁₃×D₂₁	—	33	1	no	—
38	D₃×C₇×C₁₃	—	33	1	no	—
39	C₃×C₁₃×D₇	D₃₃	1	1	yes	characteristic
40	C₂×C₁₃×D₉	—	77	1	no	Hall
41	D₂₃₁	—	3	1	no	—
42	C₇×D₃₃	—	3	1	no	—
43	C₃×C₁₁×D₇	D₃×C₁₃	1	1	yes	characteristic
44	C₃×C₁₁×C₁₃	D₃×D₇	1	1	yes	characteristic
45	C₂×D₉₉	—	7	1	no	Hall
46	C₂×C₁₃×D₇	—	99	1	no	Hall
47	D₇×D₁₁	—	9	1	no	Hall
48	C₂×C₁₁×C₁₃	—	7	1	no	—
49	C₁₃×D₁₁	—	9	1	no	—
50	C₁₃×D₁₁	—	63	1	no	—
51	C₃×C₇×C₁₃	C₂×D₃₃	1	1	yes	characteristic
52	D₇×D₉	—	11	1	no	Hall
53	C₂×C₉×C₁₃	—	7	1	no	—
54	C₁₃×D₉	—	11	1	no	—
55	C₁₃×D₉	—	77	1	no	—
56	C₃×C₇×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic
57	C₂×C₉×C₁₁	—	7	1	no	—
58	D₉₉	—	7	1	no	—
59	D₉₉	C₁₃×D₇	1	1	yes	characteristic, direct product factor
60	C₂×C₇×C₁₃	—	99	1	no	—
61	C₁₃×D₇	—	99	1	no	—
62	C₁₃×D₇	D₉₉	1	1	yes	characteristic, direct product factor
63	C₂×D₃×C₁₃	—	231	1	no	—
64	D₇₇	—	9	1	no	—
65	C₇×D₁₁	—	9	1	no	—
66	C₁₁×D₇	C₁₃×D₉	1	1	yes	characteristic, complemented
67	C₁₁×C₁₃	D₇×D₉	1	1	yes	characteristic, complemented, Hall
68	C₂×D₃₃	—	21	1	no	—
69	D₆₃	—	11	1	no	—
70	C₉×D₇	C₁₃×D₁₁	1	1	yes	characteristic, complemented
71	C₇×D₉	—	11	1	no	—
72	C₉×C₁₃	D₇×D₁₁	1	1	yes	characteristic, complemented, Hall
73	C₉×C₁₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
74	C₇×C₁₃	C₂×D₉₉	1	1	yes	characteristic, complemented, Hall
75	D₃×D₇	—	33	1	no	—
76	C₂×C₃×C₁₃	—	7	1	no	—
77	D₃×C₁₃	—	33	1	no	—
78	D₃×C₁₃	—	231	1	no	—
79	C₇×C₁₁	C₂×C₁₃×D₉	1	1	yes	characteristic, complemented, Hall
80	C₂×C₃×C₁₁	—	7	1	no	—
81	D₃₃	—	3	1	no	—
82	D₃₃	—	21	1	no	—
83	C₇×C₉	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
84	C₂²×C₁₃	—	693	1	no	Hall
85	C₂×D₁₁	—	63	1	no	Hall
86	D₂₁	—	33	1	no	—
87	C₃×D₇	C₁₃×D₃₃	1	1	yes	characteristic
88	D₃×C₇	—	33	1	no	—
89	C₃×C₁₃	D₇×D₃₃	1	1	yes	characteristic
90	C₂×D₉	—	77	1	no	Hall
91	C₃×C₁₁	D₃×C₁₃×D₇	1	1	yes	characteristic
92	C₂×D₇	—	99	1	no	Hall
93	C₂×C₁₃	—	7	1	no	—
94	C₂×C₁₃	—	99	1	no	—
95	C₂×C₁₃	—	693	1	no	—
96	C₂×C₁₁	—	7	1	no	—
97	D₁₁	—	9	1	no	—
98	D₁₁	—	63	1	no	—
99	C₃×C₇	C₂×C₁₃×D₃₃	1	1	yes	characteristic
100	C₂×C₉	—	7	1	no	—
101	D₉	—	11	1	no	—
102	D₉	—	77	1	no	—
103	C₂×C₇	—	99	1	no	—
104	D₇	—	99	1	no	—
105	D₇	C₁₃×D₉₉	1	1	yes	characteristic, direct product factor
106	C₁₃	D₇×D₉₉	1	1	yes	characteristic, direct product factor, Sylow
107	C₂×D₃	—	231	1	no	—
108	C₁₁	C₁₃×D₇×D₉	1	1	yes	characteristic, complemented, Sylow
109	C₉	C₁₃×D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
110	C₇	C₂×C₁₃×D₉₉	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₃	—	7	1	no	—
112	D₃	—	33	1	no	—
113	D₃	—	231	1	no	—
114	C₂²	—	693	1	no	Sylow
115	C₃	C₁₃×D₇×D₃₃	1	1	yes	characteristic
116	C₂	—	7	1	no	—
117	C₂	—	99	1	no	—
118	C₂	—	693	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×D₆₉₃

C₂

yes

maximal, characteristic, complemented

C₇×C₁₃×D₉₉

C₂

yes

maximal, characteristic, complemented

C₉×C₁₁×C₁₃×D₇

C₂

yes

maximal, characteristic, complemented

C₁₃×D₇×D₃₃

—

maximal

C₇×C₉×C₁₁×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₁₃×D₂₃₁

—

C₇×C₁₃×D₃₃

—

C₃×C₁₁×C₁₃×D₇

D₃

yes

characteristic

C₂×C₁₃×D₉₉

—

maximal, Hall

C₁₃×D₇×D₁₁

—

Hall

C₁₃×D₇×D₉

—

maximal, Hall

C₃×C₇×C₁₁×C₁₃

C₂×D₃

yes

characteristic

D₇×D₉₉

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₁₃×D₉₉

—

C₁₃×D₉₉

D₇

yes

characteristic, direct product factor

C₂×C₉×C₁₁×C₁₃

—

C₁₃×D₇₇

—

C₁₁×C₁₃×D₇

D₉

yes

characteristic, complemented

C₇×C₁₃×D₁₁

—

C₂×C₁₃×D₃₃

—

C₁₃×D₆₃

—

C₇×C₁₃×D₉

—

C₉×C₁₃×D₇

D₁₁

yes

characteristic, complemented

D₆₉₃

C₂×C₁₃

yes

characteristic, complemented

C₇×D₉₉

C₂×C₁₃

yes

characteristic, complemented

C₉×C₁₁×D₇

C₂×C₁₃

yes

characteristic, complemented

C₉×C₁₁×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

D₃×C₁₃×D₇

—

C₇×C₁₁×C₁₃

C₂×D₉

yes

characteristic, complemented, Hall

D₇×D₃₃

—

C₂×C₃×C₁₁×C₁₃

—

C₁₃×D₃₃

—

C₁₃×D₃₃

—

C₇×C₉×C₁₃

C₂×D₁₁

yes

characteristic, complemented, Hall

C₇×C₉×C₁₁

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₂×C₁₃×D₁₁

—

Hall

C₁₃×D₂₁

—

D₃×C₇×C₁₃

—

C₃×C₁₃×D₇

D₃₃

yes

characteristic

C₂×C₁₃×D₉

—

Hall

D₂₃₁

—

C₇×D₃₃

—

C₃×C₁₁×D₇

D₃×C₁₃

yes

characteristic

C₃×C₁₁×C₁₃

D₃×D₇

yes

characteristic

C₂×D₉₉

—

Hall

C₂×C₁₃×D₇

—

Hall

D₇×D₁₁

—

Hall

C₂×C₁₁×C₁₃

—

C₁₃×D₁₁

—

C₁₃×D₁₁

—

C₃×C₇×C₁₃

C₂×D₃₃

yes

characteristic

D₇×D₉

—

Hall

C₂×C₉×C₁₃

—

C₁₃×D₉

—

C₁₃×D₉

—

C₃×C₇×C₁₁

C₂×D₃×C₁₃

yes

characteristic

C₂×C₉×C₁₁

—

D₉₉

—

D₉₉

C₁₃×D₇

yes

characteristic, direct product factor

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

D₉₉

yes

characteristic, direct product factor

C₂×D₃×C₁₃

—

231

—

D₇₇

—

C₇×D₁₁

—

C₁₁×D₇

C₁₃×D₉

yes

characteristic, complemented

C₁₁×C₁₃

D₇×D₉

yes

characteristic, complemented, Hall

C₂×D₃₃

—

D₆₃

—

C₉×D₇

C₁₃×D₁₁

yes

characteristic, complemented

C₇×D₉

—

C₉×C₁₃

D₇×D₁₁

yes

characteristic, complemented, Hall

C₉×C₁₁

C₂×C₁₃×D₇

yes

characteristic, complemented, Hall

C₇×C₁₃

C₂×D₉₉

yes

characteristic, complemented, Hall

D₃×D₇

—

C₂×C₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

—

231

—

C₇×C₁₁

C₂×C₁₃×D₉

yes

characteristic, complemented, Hall

C₂×C₃×C₁₁

—

D₃₃

—

D₃₃

—

C₇×C₉

C₂×C₁₃×D₁₁

yes

characteristic, complemented, Hall

C₂²×C₁₃

—

693

Hall

C₂×D₁₁

—

Hall

D₂₁

—

C₃×D₇

C₁₃×D₃₃

yes

characteristic

D₃×C₇

—

C₃×C₁₃

D₇×D₃₃

yes

characteristic

C₂×D₉

—

Hall

C₃×C₁₁

D₃×C₁₃×D₇

yes

characteristic

C₂×D₇

—

Hall

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

693

—

C₂×C₁₁

—

D₁₁

—

D₁₁

—

C₃×C₇

C₂×C₁₃×D₃₃

yes

characteristic

100

C₂×C₉

—

101

D₉

—

102

D₉

—

103

C₂×C₇

—

104

D₇

—

105

D₇

C₁₃×D₉₉

yes

characteristic, direct product factor

106

C₁₃

D₇×D₉₉

yes

characteristic, direct product factor, Sylow

107

C₂×D₃

—

231

—

108

C₁₁

C₁₃×D₇×D₉

yes

characteristic, complemented, Sylow

109

C₉

C₁₃×D₇×D₁₁

yes

characteristic, complemented, Sylow

110

C₇

C₂×C₁₃×D₉₉

yes

characteristic, complemented, Sylow

111

C₂×C₃

—

112

D₃

—

113

D₃

—

231

—

114

C₂²

—

693

Sylow

115

C₃

C₁₃×D₇×D₃₃

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

—

693

—

	subgroup	G/H
center, hypercenter	C₁₃	D₇×D₉₉
commutator, cosocle, hypocenter	C₇×C₉×C₁₁	C₂²×C₁₃
Frattini	C₃	C₁₃×D₇×D₃₃
Fitting	C₇×C₉×C₁₁×C₁₃	C₂²
socle	C₃×C₇×C₁₁×C₁₃	C₂×D₃
LCS	G ▷ C₇×C₉×C₁₁
UCS	C₁ ◁ C₁₃

subgroup

G/H

center, hypercenter

C₁₃

D₇×D₉₉

commutator, cosocle, hypocenter

C₇×C₉×C₁₁

C₂²×C₁₃

Frattini

C₃

C₁₃×D₇×D₃₃

Fitting

C₇×C₉×C₁₁×C₁₃

C₂²

socle

C₃×C₇×C₁₁×C₁₃

C₂×D₃

LCS

G ▷ C₇×C₉×C₁₁

UCS

C₁ ◁ C₁₃

N	H ≅ G/N	type
1. C₁₃×D₆₉₃	C₂	semidirect
2. C₇×C₁₃×D₉₉	C₂	semidirect
3. C₉×C₁₁×C₁₃×D₇	C₂	semidirect
5. C₇×C₉×C₁₁×C₁₃	C₂²	semidirect
13. D₇×D₉₉	C₁₃	direct (N × H)
15. C₁₃×D₉₉	D₇	direct (N × H)
18. C₁₁×C₁₃×D₇	D₉	semidirect
23. C₉×C₁₃×D₇	D₁₁	semidirect
24. D₆₉₃	C₂×C₁₃	semidirect
25. C₇×D₉₉	C₂×C₁₃	semidirect
26. C₉×C₁₁×D₇	C₂×C₁₃	semidirect
27. C₉×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₇×C₁₁×C₁₃	C₂×D₉	semidirect
34. C₇×C₉×C₁₃	C₂×D₁₁	semidirect
35. C₇×C₉×C₁₁	C₂²×C₁₃	semidirect
59. D₉₉	C₁₃×D₇	direct (N × H)
62. C₁₃×D₇	D₉₉	direct (N × H)
66. C₁₁×D₇	C₁₃×D₉	semidirect
67. C₁₁×C₁₃	D₇×D₉	semidirect
70. C₉×D₇	C₁₃×D₁₁	semidirect
72. C₉×C₁₃	D₇×D₁₁	semidirect
73. C₉×C₁₁	C₂×C₁₃×D₇	semidirect
74. C₇×C₁₃	C₂×D₉₉	semidirect
79. C₇×C₁₁	C₂×C₁₃×D₉	semidirect
83. C₇×C₉	C₂×C₁₃×D₁₁	semidirect
105. D₇	C₁₃×D₉₉	direct (N × H)
106. C₁₃	D₇×D₉₉	direct (N × H)
108. C₁₁	C₁₃×D₇×D₉	semidirect
109. C₉	C₁₃×D₇×D₁₁	semidirect
110. C₇	C₂×C₁₃×D₉₉	semidirect

H ≅ G/N

type

1. C₁₃×D₆₉₃

C₂

semidirect

2. C₇×C₁₃×D₉₉

C₂

semidirect

3. C₉×C₁₁×C₁₃×D₇

C₂

semidirect

5. C₇×C₉×C₁₁×C₁₃

C₂²

semidirect

13. D₇×D₉₉

C₁₃

direct (N × H)

15. C₁₃×D₉₉

D₇

direct (N × H)

18. C₁₁×C₁₃×D₇

D₉

semidirect

23. C₉×C₁₃×D₇

D₁₁

semidirect

24. D₆₉₃

C₂×C₁₃

semidirect

25. C₇×D₉₉

C₂×C₁₃

semidirect

26. C₉×C₁₁×D₇

C₂×C₁₃

semidirect

27. C₉×C₁₁×C₁₃

C₂×D₇

semidirect

29. C₇×C₁₁×C₁₃

C₂×D₉

semidirect

34. C₇×C₉×C₁₃

C₂×D₁₁

semidirect

35. C₇×C₉×C₁₁

C₂²×C₁₃

semidirect

59. D₉₉

C₁₃×D₇

direct (N × H)

62. C₁₃×D₇

D₉₉

direct (N × H)

66. C₁₁×D₇

C₁₃×D₉

semidirect

67. C₁₁×C₁₃

D₇×D₉

semidirect

70. C₉×D₇

C₁₃×D₁₁

semidirect

72. C₉×C₁₃

D₇×D₁₁

semidirect

73. C₉×C₁₁

C₂×C₁₃×D₇

semidirect

74. C₇×C₁₃

C₂×D₉₉

semidirect

79. C₇×C₁₁

C₂×C₁₃×D₉

semidirect

83. C₇×C₉

C₂×C₁₃×D₁₁

semidirect

105. D₇

C₁₃×D₉₉

direct (N × H)

106. C₁₃

D₇×D₉₉

direct (N × H)

108. C₁₁

C₁₃×D₇×D₉

semidirect

109. C₉

C₁₃×D₇×D₁₁

semidirect

110. C₇

C₂×C₁₃×D₉₉

semidirect

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

subgroup	index
C₁₃×D₆₉₃	2
C₇×C₁₃×D₉₉	2
C₉×C₁₁×C₁₃×D₇	2
C₁₃×D₇×D₃₃	3
C₂×C₁₃×D₉₉	7
C₁₃×D₇×D₉	11
D₇×D₉₉	13

subgroup

index

C₁₃×D₆₉₃

C₇×C₁₃×D₉₉

C₉×C₁₁×C₁₃×D₇

C₁₃×D₇×D₃₃

C₂×C₁₃×D₉₉

C₁₃×D₇×D₉

D₇×D₉₉

Subgroups — C₁₃×D₇×D₉₉ #49114485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×D7×D99 #49114485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×D₇×D₉₉ #49114485