Group #49114896 — subgroups

Subgroups — C₃²×C₁₃×D₇×D₁₁ #49114896

Order 36036.

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

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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	C₃²×C₇×C₁₃×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₁₁×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×D₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×D₇×D₁₁	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×D₇₇	C₂×C₃	1	4	yes	complemented
7	C₃×C₁₁×C₁₃×D₇	C₂×C₃	1	4	yes	complemented
8	C₃×C₇×C₁₃×D₁₁	C₂×C₃	1	4	yes	complemented
9	C₂×C₃²×C₁₃×D₁₁	—	7	1	no	maximal, Hall
10	C₁₃×D₇×D₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃²×C₁₃×D₇	—	11	1	no	maximal, Hall
12	C₃×C₇×C₁₁×C₁₃	C₂²×C₃	1	4	yes	complemented
13	C₃²×D₇×D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃²×C₁₃×D₁₁	—	7	1	no	—
15	C₃²×C₁₃×D₁₁	D₇	1	1	yes	characteristic, direct product factor
16	C₂×C₃²×C₁₁×C₁₃	—	7	1	no	—
17	C₁₃×D₇₇	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₁₁×C₁₃×D₇	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₇×C₁₃×D₁₁	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₁₃×D₁₁	—	7	4	no	—
21	C₂×C₃²×C₇×C₁₃	—	11	1	no	—
22	C₃²×C₁₃×D₇	—	11	1	no	—
23	C₃²×C₁₃×D₇	D₁₁	1	1	yes	characteristic, direct product factor
24	C₃²×D₇₇	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃²×C₁₁×D₇	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₃²×C₇×D₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₃²×C₁₁×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃×D₇	—	11	4	no	—
29	C₇×C₁₁×C₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
30	C₃×D₇×D₁₁	C₃×C₁₃	1	4	yes	direct product factor
31	C₂×C₃×C₁₁×C₁₃	—	7	4	no	—
32	C₃×C₁₃×D₁₁	—	7	4	no	—
33	C₃×C₁₃×D₁₁	C₃×D₇	1	4	yes	direct product factor
34	C₃²×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
35	C₃²×C₇×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₁₃×D₁₁	—	7	1	no	Hall
37	C₂×C₃×C₇×C₁₃	—	11	4	no	—
38	C₃×C₁₃×D₇	—	11	4	no	—
39	C₃×C₁₃×D₇	C₃×D₁₁	1	4	yes	direct product factor
40	C₂²×C₃²×C₁₃	—	77	1	no	Hall
41	C₃×D₇₇	C₂×C₃×C₁₃	1	4	yes	complemented
42	C₃×C₁₁×D₇	C₂×C₃×C₁₃	1	4	yes	complemented
43	C₃×C₇×D₁₁	C₂×C₃×C₁₃	1	4	yes	complemented
44	C₃×C₁₁×C₁₃	C₂×C₃×D₇	1	4	yes	complemented
45	C₂×C₃²×D₁₁	—	7	1	no	Hall
46	C₂×C₁₃×D₇	—	11	1	no	Hall
47	D₇×D₁₁	C₃²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₁₁×C₁₃	—	7	1	no	—
49	C₁₃×D₁₁	—	7	1	no	—
50	C₁₃×D₁₁	C₃²×D₇	1	1	yes	characteristic, direct product factor
51	C₃×C₇×C₁₃	C₂×C₃×D₁₁	1	4	yes	complemented
52	C₂×C₃²×D₇	—	11	1	no	Hall
53	C₂×C₃²×C₁₃	—	7	1	no	—
54	C₂×C₃²×C₁₃	—	11	1	no	—
55	C₂×C₃²×C₁₃	—	77	1	no	—
56	C₃×C₇×C₁₁	C₂²×C₃×C₁₃	1	4	yes	complemented
57	C₂×C₃²×C₁₁	—	7	1	no	—
58	C₃²×D₁₁	—	7	1	no	—
59	C₃²×D₁₁	C₁₃×D₇	1	1	yes	characteristic, direct product factor
60	C₂×C₇×C₁₃	—	11	1	no	—
61	C₁₃×D₇	—	11	1	no	—
62	C₁₃×D₇	C₃²×D₁₁	1	1	yes	characteristic, direct product factor
63	C₂²×C₃×C₁₃	—	77	4	no	—
64	D₇₇	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
65	C₇×D₁₁	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
66	C₁₁×D₇	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
67	C₁₁×C₁₃	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×D₁₁	—	7	4	no	—
69	C₂×C₃²×C₇	—	11	1	no	—
70	C₃²×D₇	—	11	1	no	—
71	C₃²×D₇	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
72	C₃²×C₁₃	D₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
73	C₃²×C₁₁	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
74	C₇×C₁₃	C₂×C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
75	C₂×C₃×D₇	—	11	4	no	—
76	C₂×C₃×C₁₃	—	7	4	no	—
77	C₂×C₃×C₁₃	—	11	4	no	—
78	C₂×C₃×C₁₃	—	77	4	no	—
79	C₇×C₁₁	C₂²×C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
80	C₂×C₃×C₁₁	—	7	4	no	—
81	C₃×D₁₁	—	7	4	no	—
82	C₃×D₁₁	C₃×C₁₃×D₇	1	4	yes	direct product factor
83	C₃²×C₇	C₂×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Hall
84	C₂²×C₁₃	—	77	1	no	Hall
85	C₂×D₁₁	—	7	1	no	Hall
86	C₂×C₃×C₇	—	11	4	no	—
87	C₃×D₇	—	11	4	no	—
88	C₃×D₇	C₃×C₁₃×D₁₁	1	4	yes	direct product factor
89	C₃×C₁₃	C₃×D₇×D₁₁	1	4	yes	direct product factor
90	C₂²×C₃²	—	77	1	no	Hall
91	C₃×C₁₁	C₂×C₃×C₁₃×D₇	1	4	yes	complemented
92	C₂×D₇	—	11	1	no	Hall
93	C₂×C₁₃	—	7	1	no	—
94	C₂×C₁₃	—	11	1	no	—
95	C₂×C₁₃	—	77	1	no	—
96	C₂×C₁₁	—	7	1	no	—
97	D₁₁	—	7	1	no	—
98	D₁₁	C₃²×C₁₃×D₇	1	1	yes	characteristic, direct product factor
99	C₃×C₇	C₂×C₃×C₁₃×D₁₁	1	4	yes	complemented
100	C₂×C₃²	—	7	1	no	—
101	C₂×C₃²	—	11	1	no	—
102	C₂×C₃²	—	77	1	no	—
103	C₂×C₇	—	11	1	no	—
104	D₇	—	11	1	no	—
105	D₇	C₃²×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
106	C₁₃	C₃²×D₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
107	C₂²×C₃	—	77	4	no	—
108	C₁₁	C₂×C₃²×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
109	C₃²	C₁₃×D₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
110	C₇	C₂×C₃²×C₁₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₃	—	7	4	no	—
112	C₂×C₃	—	11	4	no	—
113	C₂×C₃	—	77	4	no	—
114	C₂²	—	77	1	no	Sylow
115	C₃	C₃×C₁₃×D₇×D₁₁	1	4	yes	direct product factor
116	C₂	—	7	1	no	—
117	C₂	—	11	1	no	—
118	C₂	—	77	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₇×C₁₃×D₁₁

C₂

yes

maximal, characteristic, complemented

C₃²×C₁₁×C₁₃×D₇

C₂

yes

maximal, characteristic, complemented

C₃²×C₁₃×D₇₇

C₂

yes

maximal, characteristic, complemented

C₃×C₁₃×D₇×D₁₁

C₃

yes

maximal, direct product factor

C₃²×C₇×C₁₁×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₃×C₁₃×D₇₇

C₂×C₃

yes

complemented

C₃×C₁₁×C₁₃×D₇

C₂×C₃

yes

complemented

C₃×C₇×C₁₃×D₁₁

C₂×C₃

yes

complemented

C₂×C₃²×C₁₃×D₁₁

—

maximal, Hall

C₁₃×D₇×D₁₁

C₃²

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₁₃×D₇

—

maximal, Hall

C₃×C₇×C₁₁×C₁₃

C₂²×C₃

yes

complemented

C₃²×D₇×D₁₁

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₁₃×D₁₁

—

C₃²×C₁₃×D₁₁

D₇

yes

characteristic, direct product factor

C₂×C₃²×C₁₁×C₁₃

—

C₁₃×D₇₇

C₂×C₃²

yes

characteristic, complemented

C₁₁×C₁₃×D₇

C₂×C₃²

yes

characteristic, complemented

C₇×C₁₃×D₁₁

C₂×C₃²

yes

characteristic, complemented

C₂×C₃×C₁₃×D₁₁

—

C₂×C₃²×C₇×C₁₃

—

C₃²×C₁₃×D₇

—

C₃²×C₁₃×D₇

D₁₁

yes

characteristic, direct product factor

C₃²×D₇₇

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₁₁×D₇

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₇×D₁₁

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₁₁×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₁₃×D₇

—

C₇×C₁₁×C₁₃

C₂²×C₃²

yes

characteristic, complemented, Hall

C₃×D₇×D₁₁

C₃×C₁₃

yes

direct product factor

C₂×C₃×C₁₁×C₁₃

—

C₃×C₁₃×D₁₁

—

C₃×C₁₃×D₁₁

C₃×D₇

yes

direct product factor

C₃²×C₇×C₁₃

C₂×D₁₁

yes

characteristic, complemented, Hall

C₃²×C₇×C₁₁

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₂×C₁₃×D₁₁

—

Hall

C₂×C₃×C₇×C₁₃

—

C₃×C₁₃×D₇

—

C₃×C₁₃×D₇

C₃×D₁₁

yes

direct product factor

C₂²×C₃²×C₁₃

—

Hall

C₃×D₇₇

C₂×C₃×C₁₃

yes

complemented

C₃×C₁₁×D₇

C₂×C₃×C₁₃

yes

complemented

C₃×C₇×D₁₁

C₂×C₃×C₁₃

yes

complemented

C₃×C₁₁×C₁₃

C₂×C₃×D₇

yes

complemented

C₂×C₃²×D₁₁

—

Hall

C₂×C₁₃×D₇

—

Hall

D₇×D₁₁

C₃²×C₁₃

yes

characteristic, direct product factor, Hall

C₂×C₁₁×C₁₃

—

C₁₃×D₁₁

—

C₁₃×D₁₁

C₃²×D₇

yes

characteristic, direct product factor

C₃×C₇×C₁₃

C₂×C₃×D₁₁

yes

complemented

C₂×C₃²×D₇

—

Hall

C₂×C₃²×C₁₃

—

C₂×C₃²×C₁₃

—

C₂×C₃²×C₁₃

—

C₃×C₇×C₁₁

C₂²×C₃×C₁₃

yes

complemented

C₂×C₃²×C₁₁

—

C₃²×D₁₁

—

C₃²×D₁₁

C₁₃×D₇

yes

characteristic, direct product factor

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

C₃²×D₁₁

yes

characteristic, direct product factor

C₂²×C₃×C₁₃

—

D₇₇

C₂×C₃²×C₁₃

yes

characteristic, complemented

C₇×D₁₁

C₂×C₃²×C₁₃

yes

characteristic, complemented

C₁₁×D₇

C₂×C₃²×C₁₃

yes

characteristic, complemented

C₁₁×C₁₃

C₂×C₃²×D₇

yes

characteristic, complemented, Hall

C₂×C₃×D₁₁

—

C₂×C₃²×C₇

—

C₃²×D₇

—

C₃²×D₇

C₁₃×D₁₁

yes

characteristic, direct product factor

C₃²×C₁₃

D₇×D₁₁

yes

characteristic, direct product factor, Hall

C₃²×C₁₁

C₂×C₁₃×D₇

yes

characteristic, complemented, Hall

C₇×C₁₃

C₂×C₃²×D₁₁

yes

characteristic, complemented, Hall

C₂×C₃×D₇

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

C₇×C₁₁

C₂²×C₃²×C₁₃

yes

characteristic, complemented, Hall

C₂×C₃×C₁₁

—

C₃×D₁₁

—

C₃×D₁₁

C₃×C₁₃×D₇

yes

direct product factor

C₃²×C₇

C₂×C₁₃×D₁₁

yes

characteristic, complemented, Hall

C₂²×C₁₃

—

Hall

C₂×D₁₁

—

Hall

C₂×C₃×C₇

—

C₃×D₇

—

C₃×D₇

C₃×C₁₃×D₁₁

yes

direct product factor

C₃×C₁₃

C₃×D₇×D₁₁

yes

direct product factor

C₂²×C₃²

—

Hall

C₃×C₁₁

C₂×C₃×C₁₃×D₇

yes

complemented

C₂×D₇

—

Hall

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₁

—

D₁₁

—

D₁₁

C₃²×C₁₃×D₇

yes

characteristic, direct product factor

C₃×C₇

C₂×C₃×C₁₃×D₁₁

yes

complemented

100

C₂×C₃²

—

101

C₂×C₃²

—

102

C₂×C₃²

—

103

C₂×C₇

—

104

D₇

—

105

D₇

C₃²×C₁₃×D₁₁

yes

characteristic, direct product factor

106

C₁₃

C₃²×D₇×D₁₁

yes

characteristic, direct product factor, Sylow

107

C₂²×C₃

—

108

C₁₁

C₂×C₃²×C₁₃×D₇

yes

characteristic, complemented, Sylow

109

C₃²

C₁₃×D₇×D₁₁

yes

characteristic, direct product factor, Sylow

110

C₇

C₂×C₃²×C₁₃×D₁₁

yes

characteristic, complemented, Sylow

111

C₂×C₃

—

112

C₂×C₃

—

113

C₂×C₃

—

114

C₂²

—

Sylow

115

C₃

C₃×C₁₃×D₇×D₁₁

yes

direct product factor

116

C₂

—

117

C₂

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₃²×C₁₃	D₇×D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂²
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₃²×C₁₃

subgroup

G/H

center, hypercenter

C₃²×C₁₃

D₇×D₁₁

commutator, cosocle, hypocenter

C₇×C₁₁

C₂²×C₃²×C₁₃

Frattini

C₁

Fitting, socle

C₃²×C₇×C₁₁×C₁₃

C₂²

LCS

G ▷ C₇×C₁₁

UCS

C₁ ◁ C₃²×C₁₃

N	H ≅ G/N	type
1. C₃²×C₇×C₁₃×D₁₁	C₂	semidirect
2. C₃²×C₁₁×C₁₃×D₇	C₂	semidirect
3. C₃²×C₁₃×D₇₇	C₂	semidirect
4. C₃×C₁₃×D₇×D₁₁	C₃	direct (N × H)
5. C₃²×C₇×C₁₁×C₁₃	C₂²	semidirect
6. C₃×C₁₃×D₇₇	C₂×C₃	semidirect
7. C₃×C₁₁×C₁₃×D₇	C₂×C₃	semidirect
8. C₃×C₇×C₁₃×D₁₁	C₂×C₃	semidirect
10. C₁₃×D₇×D₁₁	C₃²	direct (N × H)
12. C₃×C₇×C₁₁×C₁₃	C₂²×C₃	semidirect
13. C₃²×D₇×D₁₁	C₁₃	direct (N × H)
15. C₃²×C₁₃×D₁₁	D₇	direct (N × H)
17. C₁₃×D₇₇	C₂×C₃²	semidirect
18. C₁₁×C₁₃×D₇	C₂×C₃²	semidirect
19. C₇×C₁₃×D₁₁	C₂×C₃²	semidirect
23. C₃²×C₁₃×D₇	D₁₁	direct (N × H)
24. C₃²×D₇₇	C₂×C₁₃	semidirect
25. C₃²×C₁₁×D₇	C₂×C₁₃	semidirect
26. C₃²×C₇×D₁₁	C₂×C₁₃	semidirect
27. C₃²×C₁₁×C₁₃	C₂×D₇	semidirect
29. C₇×C₁₁×C₁₃	C₂²×C₃²	semidirect
30. C₃×D₇×D₁₁	C₃×C₁₃	direct (N × H)
33. C₃×C₁₃×D₁₁	C₃×D₇	direct (N × H)
34. C₃²×C₇×C₁₃	C₂×D₁₁	semidirect
35. C₃²×C₇×C₁₁	C₂²×C₁₃	semidirect
39. C₃×C₁₃×D₇	C₃×D₁₁	direct (N × H)
41. C₃×D₇₇	C₂×C₃×C₁₃	semidirect
42. C₃×C₁₁×D₇	C₂×C₃×C₁₃	semidirect
43. C₃×C₇×D₁₁	C₂×C₃×C₁₃	semidirect
44. C₃×C₁₁×C₁₃	C₂×C₃×D₇	semidirect
47. D₇×D₁₁	C₃²×C₁₃	direct (N × H)
50. C₁₃×D₁₁	C₃²×D₇	direct (N × H)
51. C₃×C₇×C₁₃	C₂×C₃×D₁₁	semidirect
56. C₃×C₇×C₁₁	C₂²×C₃×C₁₃	semidirect
59. C₃²×D₁₁	C₁₃×D₇	direct (N × H)
62. C₁₃×D₇	C₃²×D₁₁	direct (N × H)
64. D₇₇	C₂×C₃²×C₁₃	semidirect
65. C₇×D₁₁	C₂×C₃²×C₁₃	semidirect
66. C₁₁×D₇	C₂×C₃²×C₁₃	semidirect
67. C₁₁×C₁₃	C₂×C₃²×D₇	semidirect
71. C₃²×D₇	C₁₃×D₁₁	direct (N × H)
72. C₃²×C₁₃	D₇×D₁₁	direct (N × H)
73. C₃²×C₁₁	C₂×C₁₃×D₇	semidirect
74. C₇×C₁₃	C₂×C₃²×D₁₁	semidirect
79. C₇×C₁₁	C₂²×C₃²×C₁₃	semidirect
82. C₃×D₁₁	C₃×C₁₃×D₇	direct (N × H)
83. C₃²×C₇	C₂×C₁₃×D₁₁	semidirect
88. C₃×D₇	C₃×C₁₃×D₁₁	direct (N × H)
89. C₃×C₁₃	C₃×D₇×D₁₁	direct (N × H)
91. C₃×C₁₁	C₂×C₃×C₁₃×D₇	semidirect
98. D₁₁	C₃²×C₁₃×D₇	direct (N × H)
99. C₃×C₇	C₂×C₃×C₁₃×D₁₁	semidirect
105. D₇	C₃²×C₁₃×D₁₁	direct (N × H)
106. C₁₃	C₃²×D₇×D₁₁	direct (N × H)
108. C₁₁	C₂×C₃²×C₁₃×D₇	semidirect
109. C₃²	C₁₃×D₇×D₁₁	direct (N × H)
110. C₇	C₂×C₃²×C₁₃×D₁₁	semidirect
115. C₃	C₃×C₁₃×D₇×D₁₁	direct (N × H)

H ≅ G/N

type

1. C₃²×C₇×C₁₃×D₁₁

C₂

semidirect

2. C₃²×C₁₁×C₁₃×D₇

C₂

semidirect

3. C₃²×C₁₃×D₇₇

C₂

semidirect

4. C₃×C₁₃×D₇×D₁₁

C₃

direct (N × H)

5. C₃²×C₇×C₁₁×C₁₃

C₂²

semidirect

6. C₃×C₁₃×D₇₇

C₂×C₃

semidirect

7. C₃×C₁₁×C₁₃×D₇

C₂×C₃

semidirect

8. C₃×C₇×C₁₃×D₁₁

C₂×C₃

semidirect

10. C₁₃×D₇×D₁₁

C₃²

direct (N × H)

12. C₃×C₇×C₁₁×C₁₃

C₂²×C₃

semidirect

13. C₃²×D₇×D₁₁

C₁₃

direct (N × H)

15. C₃²×C₁₃×D₁₁

D₇

direct (N × H)

17. C₁₃×D₇₇

C₂×C₃²

semidirect

18. C₁₁×C₁₃×D₇

C₂×C₃²

semidirect

19. C₇×C₁₃×D₁₁

C₂×C₃²

semidirect

23. C₃²×C₁₃×D₇

D₁₁

direct (N × H)

24. C₃²×D₇₇

C₂×C₁₃

semidirect

25. C₃²×C₁₁×D₇

C₂×C₁₃

semidirect

26. C₃²×C₇×D₁₁

C₂×C₁₃

semidirect

27. C₃²×C₁₁×C₁₃

C₂×D₇

semidirect

29. C₇×C₁₁×C₁₃

C₂²×C₃²

semidirect

30. C₃×D₇×D₁₁

C₃×C₁₃

direct (N × H)

33. C₃×C₁₃×D₁₁

C₃×D₇

direct (N × H)

34. C₃²×C₇×C₁₃

C₂×D₁₁

semidirect

35. C₃²×C₇×C₁₁

C₂²×C₁₃

semidirect

39. C₃×C₁₃×D₇

C₃×D₁₁

direct (N × H)

41. C₃×D₇₇

C₂×C₃×C₁₃

semidirect

42. C₃×C₁₁×D₇

C₂×C₃×C₁₃

semidirect

43. C₃×C₇×D₁₁

C₂×C₃×C₁₃

semidirect

44. C₃×C₁₁×C₁₃

C₂×C₃×D₇

semidirect

47. D₇×D₁₁

C₃²×C₁₃

direct (N × H)

50. C₁₃×D₁₁

C₃²×D₇

direct (N × H)

51. C₃×C₇×C₁₃

C₂×C₃×D₁₁

semidirect

56. C₃×C₇×C₁₁

C₂²×C₃×C₁₃

semidirect

59. C₃²×D₁₁

C₁₃×D₇

direct (N × H)

62. C₁₃×D₇

C₃²×D₁₁

direct (N × H)

64. D₇₇

C₂×C₃²×C₁₃

semidirect

65. C₇×D₁₁

C₂×C₃²×C₁₃

semidirect

66. C₁₁×D₇

C₂×C₃²×C₁₃

semidirect

67. C₁₁×C₁₃

C₂×C₃²×D₇

semidirect

71. C₃²×D₇

C₁₃×D₁₁

direct (N × H)

72. C₃²×C₁₃

D₇×D₁₁

direct (N × H)

73. C₃²×C₁₁

C₂×C₁₃×D₇

semidirect

74. C₇×C₁₃

C₂×C₃²×D₁₁

semidirect

79. C₇×C₁₁

C₂²×C₃²×C₁₃

semidirect

82. C₃×D₁₁

C₃×C₁₃×D₇

direct (N × H)

83. C₃²×C₇

C₂×C₁₃×D₁₁

semidirect

88. C₃×D₇

C₃×C₁₃×D₁₁

direct (N × H)

89. C₃×C₁₃

C₃×D₇×D₁₁

direct (N × H)

91. C₃×C₁₁

C₂×C₃×C₁₃×D₇

semidirect

98. D₁₁

C₃²×C₁₃×D₇

direct (N × H)

99. C₃×C₇

C₂×C₃×C₁₃×D₁₁

semidirect

105. D₇

C₃²×C₁₃×D₁₁

direct (N × H)

106. C₁₃

C₃²×D₇×D₁₁

direct (N × H)

108. C₁₁

C₂×C₃²×C₁₃×D₇

semidirect

109. C₃²

C₁₃×D₇×D₁₁

direct (N × H)

110. C₇

C₂×C₃²×C₁₃×D₁₁

semidirect

115. C₃

C₃×C₁₃×D₇×D₁₁

direct (N × H)

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

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

subgroup

index

C₃²×C₇×C₁₃×D₁₁

C₃²×C₁₁×C₁₃×D₇

C₃²×C₁₃×D₇₇

C₃×C₁₃×D₇×D₁₁

C₂×C₃²×C₁₃×D₁₁

C₂×C₃²×C₁₃×D₇

C₃²×D₇×D₁₁

Subgroups — C₃²×C₁₃×D₇×D₁₁ #49114896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×C13×D7×D11 #49114896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₁₃×D₇×D₁₁ #49114896