Group #44472985 — subgroups

Subgroups — C₇×D₇×C₁₇×C₃⋊D₃ #44472985

Order 29988.

312 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 88 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×D₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×C₁₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₇×C₃⋊D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₇×C₁₇	—	3	4	no	maximal
5	C₃²×C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×C₁₇×D₂₁	—	3	4	no	—
7	D₃×C₇²×C₁₇	—	3	4	no	—
8	C₃×C₇×D₇×C₁₇	D₃	1	4	yes	complemented
9	C₂×C₇×C₁₇×C₃⋊D₃	—	7	1	no	maximal
10	D₇×C₁₇×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₇×D₇×C₁₇	—	9	1	no	Hall
12	C₃×C₇²×C₁₇	C₂×D₃	1	4	yes	complemented
13	C₁₇×C₃⋊D₂₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×C₁₇×C₃⋊D₃	—	2	3	no	—
15	C₇×C₁₇×C₃⋊D₃	—	7	1	no	—
16	C₇×C₁₇×C₃⋊D₃	D₇	1	1	yes	characteristic, direct product factor
17	C₇×C₁₇×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic, complemented
18	C₃²×D₇×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₇×C₁₇	—	7	1	no	—
20	C₇×D₇×C₃⋊D₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₇²×C₁₇	—	9	1	no	—
22	C₇×D₇×C₁₇	—	9	1	no	—
23	C₇×D₇×C₁₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor
24	C₂×D₃×C₇×C₁₇	—	21	4	no	—
25	D₃×D₇×C₁₇	—	3	4	no	—
26	C₃²×C₇×C₁₇	—	2	3	no	—
27	C₃²×C₇×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented
28	C₃²×C₇×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented
29	C₇×C₃⋊D₂₁	C₂×C₁₇	1	1	yes	characteristic, complemented
30	C₇²×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic, complemented
31	C₃²×C₇×D₇	C₂×C₁₇	1	1	yes	characteristic, complemented
32	C₇²×C₁₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₇×C₁₇	—	7	4	no	—
34	C₁₇×D₂₁	—	3	4	no	—
35	D₃×C₇×C₁₇	—	3	4	no	—
36	D₃×C₇×C₁₇	—	3	4	no	—
37	D₃×C₇×C₁₇	—	6	12	no	—
38	D₃×C₇×C₁₇	—	21	4	no	—
39	C₃×D₇×C₁₇	D₃×C₇	1	4	yes	complemented
40	C₂×C₁₇×C₃⋊D₃	—	7	1	no	Hall
41	D₃×C₇×D₇	—	3	4	no	—
42	C₂²×C₇×C₁₇	—	63	1	no	—
43	C₂×D₇×C₁₇	—	9	1	no	—
44	C₃²×C₇²	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
45	C₃×C₇×C₁₇	—	2	12	no	—
46	C₃×C₇×C₁₇	D₃×D₇	1	4	yes	complemented
47	C₃×C₇×C₁₇	C₂×D₃×C₇	1	4	yes	complemented
48	C₂×C₃²×C₁₇	—	7	1	no	—
49	C₁₇×C₃⋊D₃	—	7	1	no	—
50	C₁₇×C₃⋊D₃	C₇×D₇	1	1	yes	characteristic, direct product factor
51	C₇×D₂₁	—	3	4	no	—
52	D₃×C₇²	—	3	4	no	—
53	C₃×C₇×D₇	D₃×C₁₇	1	4	yes	complemented
54	C₂×C₇×C₃⋊D₃	—	7	1	no	—
55	D₇×C₃⋊D₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor
56	C₂×C₇×C₁₇	—	7	1	no	—
57	C₂×C₇×C₁₇	—	9	1	no	—
58	C₂×C₇×C₁₇	—	9	1	no	—
59	C₂×C₇×C₁₇	—	18	3	no	—
60	C₂×C₇×C₁₇	—	63	1	no	—
61	D₇×C₁₇	—	9	1	no	—
62	D₇×C₁₇	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
63	C₂×D₃×C₁₇	—	21	4	no	—
64	C₂×C₇×D₇	—	9	1	no	Hall
65	C₃²×C₁₇	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
66	C₃×C₇²	C₂×D₃×C₁₇	1	4	yes	complemented
67	C₂×C₃²×C₇	—	7	1	no	—
68	C₃⋊D₂₁	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
69	C₇×C₃⋊D₃	—	2	3	no	—
70	C₇×C₃⋊D₃	—	7	1	no	—
71	C₇×C₃⋊D₃	D₇×C₁₇	1	1	yes	characteristic, direct product factor
72	C₇×C₃⋊D₃	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
73	C₃²×D₇	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented
74	C₇×C₁₇	—	2	3	no	—
75	C₇×C₁₇	D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
76	C₇×C₁₇	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
77	C₂×C₃×C₁₇	—	7	4	no	—
78	D₃×C₁₇	—	3	4	no	—
79	D₃×C₁₇	—	21	4	no	—
80	C₂×C₇²	—	9	1	no	—
81	C₇×D₇	—	9	1	no	—
82	C₇×D₇	C₁₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
83	C₂×D₃×C₇	—	21	4	no	—
84	D₃×D₇	—	3	4	no	—
85	C₂²×C₁₇	—	63	1	no	Hall
86	C₃²×C₇	—	2	3	no	—
87	C₃²×C₇	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented
88	C₃²×C₇	C₂²×C₇×C₁₇	1	1	yes	characteristic, complemented
89	C₃×C₁₇	D₃×C₇×D₇	1	4	yes	complemented
90	C₇²	C₂×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
91	C₂×C₃×C₇	—	7	4	no	—
92	D₂₁	—	3	4	no	—
93	C₃×D₇	D₃×C₇×C₁₇	1	4	yes	complemented
94	D₃×C₇	—	3	4	no	—
95	D₃×C₇	—	3	4	no	—
96	D₃×C₇	—	6	12	no	—
97	D₃×C₇	—	21	4	no	—
98	C₂×C₃⋊D₃	—	7	1	no	Hall
99	C₂×C₁₇	—	7	1	no	—
100	C₂×C₁₇	—	9	1	no	—
101	C₂×C₁₇	—	63	1	no	—
102	C₂²×C₇	—	63	1	no	—
103	C₂×D₇	—	9	1	no	—
104	C₃×C₇	—	2	12	no	—
105	C₃×C₇	D₃×D₇×C₁₇	1	4	yes	complemented
106	C₃×C₇	C₂×D₃×C₇×C₁₇	1	4	yes	complemented
107	C₂×C₃²	—	7	1	no	—
108	C₃⋊D₃	—	7	1	no	—
109	C₃⋊D₃	C₇×D₇×C₁₇	1	1	yes	characteristic, direct product factor
110	C₁₇	C₇×D₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
111	C₂×C₇	—	7	1	no	—
112	C₂×C₇	—	9	1	no	—
113	C₂×C₇	—	9	1	no	—
114	C₂×C₇	—	18	3	no	—
115	C₂×C₇	—	63	1	no	—
116	D₇	—	9	1	no	—
117	D₇	C₇×C₁₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
118	C₂×D₃	—	21	4	no	—
119	C₃²	C₂×C₇×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
120	C₇	—	2	3	no	—
121	C₇	D₇×C₁₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
122	C₇	C₂×C₇×C₁₇×C₃⋊D₃	1	1	yes	characteristic, complemented
123	C₂×C₃	—	7	4	no	—
124	D₃	—	3	4	no	—
125	D₃	—	21	4	no	—
126	C₂²	—	63	1	no	Sylow
127	C₃	D₃×C₇×D₇×C₁₇	1	4	yes	complemented
128	C₂	—	7	1	no	—
129	C₂	—	9	1	no	—
130	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₇×D₇×C₁₇

C₂

yes

maximal, characteristic, complemented

C₇²×C₁₇×C₃⋊D₃

C₂

yes

maximal, characteristic, complemented

C₇×C₁₇×C₃⋊D₂₁

C₂

yes

maximal, characteristic, complemented

D₃×C₇×D₇×C₁₇

—

maximal

C₃²×C₇²×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₇×C₁₇×D₂₁

—

D₃×C₇²×C₁₇

—

C₃×C₇×D₇×C₁₇

D₃

yes

complemented

C₂×C₇×C₁₇×C₃⋊D₃

—

maximal

D₇×C₁₇×C₃⋊D₃

C₇

yes

maximal, characteristic, direct product factor

C₂×C₇×D₇×C₁₇

—

Hall

C₃×C₇²×C₁₇

C₂×D₃

yes

complemented

C₁₇×C₃⋊D₂₁

C₂×C₇

yes

characteristic, complemented

C₇×C₁₇×C₃⋊D₃

—

C₇×C₁₇×C₃⋊D₃

—

C₇×C₁₇×C₃⋊D₃

D₇

yes

characteristic, direct product factor

C₇×C₁₇×C₃⋊D₃

C₂×C₇

yes

characteristic, complemented

C₃²×D₇×C₁₇

C₂×C₇

yes

characteristic, complemented

C₂×C₃²×C₇×C₁₇

—

C₇×D₇×C₃⋊D₃

C₁₇

yes

maximal, characteristic, direct product factor, Hall

C₂×C₇²×C₁₇

—

C₇×D₇×C₁₇

—

C₇×D₇×C₁₇

C₃⋊D₃

yes

characteristic, direct product factor

C₂×D₃×C₇×C₁₇

—

D₃×D₇×C₁₇

—

C₃²×C₇×C₁₇

—

C₃²×C₇×C₁₇

C₂×D₇

yes

characteristic, complemented

C₃²×C₇×C₁₇

C₂²×C₇

yes

characteristic, complemented

C₇×C₃⋊D₂₁

C₂×C₁₇

yes

characteristic, complemented

C₇²×C₃⋊D₃

C₂×C₁₇

yes

characteristic, complemented

C₃²×C₇×D₇

C₂×C₁₇

yes

characteristic, complemented

C₇²×C₁₇

C₂×C₃⋊D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₇

—

C₁₇×D₂₁

—

D₃×C₇×C₁₇

—

D₃×C₇×C₁₇

—

D₃×C₇×C₁₇

—

D₃×C₇×C₁₇

—

C₃×D₇×C₁₇

D₃×C₇

yes

complemented

C₂×C₁₇×C₃⋊D₃

—

Hall

D₃×C₇×D₇

—

C₂²×C₇×C₁₇

—

C₂×D₇×C₁₇

—

C₃²×C₇²

C₂²×C₁₇

yes

characteristic, complemented, Hall

C₃×C₇×C₁₇

—

C₃×C₇×C₁₇

D₃×D₇

yes

complemented

C₃×C₇×C₁₇

C₂×D₃×C₇

yes

complemented

C₂×C₃²×C₁₇

—

C₁₇×C₃⋊D₃

—

C₁₇×C₃⋊D₃

C₇×D₇

yes

characteristic, direct product factor

C₇×D₂₁

—

D₃×C₇²

—

C₃×C₇×D₇

D₃×C₁₇

yes

complemented

C₂×C₇×C₃⋊D₃

—

D₇×C₃⋊D₃

C₇×C₁₇

yes

characteristic, direct product factor

C₂×C₇×C₁₇

—

C₂×C₇×C₁₇

—

C₂×C₇×C₁₇

—

C₂×C₇×C₁₇

—

C₂×C₇×C₁₇

—

D₇×C₁₇

—

D₇×C₁₇

C₇×C₃⋊D₃

yes

characteristic, direct product factor

C₂×D₃×C₁₇

—

C₂×C₇×D₇

—

Hall

C₃²×C₁₇

C₂×C₇×D₇

yes

characteristic, complemented, Hall

C₃×C₇²

C₂×D₃×C₁₇

yes

complemented

C₂×C₃²×C₇

—

C₃⋊D₂₁

C₂×C₇×C₁₇

yes

characteristic, complemented

C₇×C₃⋊D₃

—

C₇×C₃⋊D₃

—

C₇×C₃⋊D₃

D₇×C₁₇

yes

characteristic, direct product factor

C₇×C₃⋊D₃

C₂×C₇×C₁₇

yes

characteristic, complemented

C₃²×D₇

C₂×C₇×C₁₇

yes

characteristic, complemented

C₇×C₁₇

—

C₇×C₁₇

D₇×C₃⋊D₃

yes

characteristic, direct product factor

C₇×C₁₇

C₂×C₇×C₃⋊D₃

yes

characteristic, complemented

C₂×C₃×C₁₇

—

D₃×C₁₇

—

D₃×C₁₇

—

C₂×C₇²

—

C₇×D₇

—

C₇×D₇

C₁₇×C₃⋊D₃

yes

characteristic, direct product factor

C₂×D₃×C₇

—

D₃×D₇

—

C₂²×C₁₇

—

Hall

C₃²×C₇

—

C₃²×C₇

C₂×D₇×C₁₇

yes

characteristic, complemented

C₃²×C₇

C₂²×C₇×C₁₇

yes

characteristic, complemented

C₃×C₁₇

D₃×C₇×D₇

yes

complemented

C₇²

C₂×C₁₇×C₃⋊D₃

yes

characteristic, complemented, Sylow

C₂×C₃×C₇

—

D₂₁

—

C₃×D₇

D₃×C₇×C₁₇

yes

complemented

D₃×C₇

—

D₃×C₇

—

D₃×C₇

—

D₃×C₇

—

C₂×C₃⋊D₃

—

Hall

C₂×C₁₇

—

100

C₂×C₁₇

—

101

C₂×C₁₇

—

102

C₂²×C₇

—

103

C₂×D₇

—

104

C₃×C₇

—

105

C₃×C₇

D₃×D₇×C₁₇

yes

complemented

106

C₃×C₇

C₂×D₃×C₇×C₁₇

yes

complemented

107

C₂×C₃²

—

108

C₃⋊D₃

—

109

C₃⋊D₃

C₇×D₇×C₁₇

yes

characteristic, direct product factor

110

C₁₇

C₇×D₇×C₃⋊D₃

yes

characteristic, direct product factor, Sylow

111

C₂×C₇

—

112

C₂×C₇

—

113

C₂×C₇

—

114

C₂×C₇

—

115

C₂×C₇

—

116

D₇

—

117

D₇

C₇×C₁₇×C₃⋊D₃

yes

characteristic, direct product factor

118

C₂×D₃

—

119

C₃²

C₂×C₇×D₇×C₁₇

yes

characteristic, complemented, Sylow

120

C₇

—

121

C₇

D₇×C₁₇×C₃⋊D₃

yes

characteristic, direct product factor

122

C₇

C₂×C₇×C₁₇×C₃⋊D₃

yes

characteristic, complemented

123

C₂×C₃

—

124

D₃

—

125

D₃

—

126

C₂²

—

Sylow

127

C₃

D₃×C₇×D₇×C₁₇

yes

complemented

128

C₂

—

129

C₂

—

130

C₂

—

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₇×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₇×C₁₇

subgroup

G/H

center, hypercenter

C₇×C₁₇

D₇×C₃⋊D₃

commutator, cosocle, hypocenter

C₃²×C₇

C₂²×C₇×C₁₇

Frattini

C₁

Fitting, socle

C₃²×C₇²×C₁₇

C₂²

LCS

G ▷ C₃²×C₇

UCS

C₁ ◁ C₇×C₁₇

N	H ≅ G/N	type
1. C₃²×C₇×D₇×C₁₇	C₂	semidirect
2. C₇²×C₁₇×C₃⋊D₃	C₂	semidirect
3. C₇×C₁₇×C₃⋊D₂₁	C₂	semidirect
5. C₃²×C₇²×C₁₇	C₂²	semidirect
8. C₃×C₇×D₇×C₁₇	D₃	semidirect
10. D₇×C₁₇×C₃⋊D₃	C₇	direct (N × H)
12. C₃×C₇²×C₁₇	C₂×D₃	semidirect
13. C₁₇×C₃⋊D₂₁	C₂×C₇	semidirect
16. C₇×C₁₇×C₃⋊D₃	D₇	direct (N × H)
17. C₇×C₁₇×C₃⋊D₃	C₂×C₇	semidirect
18. C₃²×D₇×C₁₇	C₂×C₇	semidirect
20. C₇×D₇×C₃⋊D₃	C₁₇	direct (N × H)
23. C₇×D₇×C₁₇	C₃⋊D₃	direct (N × H)
27. C₃²×C₇×C₁₇	C₂×D₇	semidirect
28. C₃²×C₇×C₁₇	C₂²×C₇	semidirect
29. C₇×C₃⋊D₂₁	C₂×C₁₇	semidirect
30. C₇²×C₃⋊D₃	C₂×C₁₇	semidirect
31. C₃²×C₇×D₇	C₂×C₁₇	semidirect
32. C₇²×C₁₇	C₂×C₃⋊D₃	semidirect
39. C₃×D₇×C₁₇	D₃×C₇	semidirect
44. C₃²×C₇²	C₂²×C₁₇	semidirect
46. C₃×C₇×C₁₇	D₃×D₇	semidirect
47. C₃×C₇×C₁₇	C₂×D₃×C₇	semidirect
50. C₁₇×C₃⋊D₃	C₇×D₇	direct (N × H)
53. C₃×C₇×D₇	D₃×C₁₇	semidirect
55. D₇×C₃⋊D₃	C₇×C₁₇	direct (N × H)
62. D₇×C₁₇	C₇×C₃⋊D₃	direct (N × H)
65. C₃²×C₁₇	C₂×C₇×D₇	semidirect
66. C₃×C₇²	C₂×D₃×C₁₇	semidirect
68. C₃⋊D₂₁	C₂×C₇×C₁₇	semidirect
71. C₇×C₃⋊D₃	D₇×C₁₇	direct (N × H)
72. C₇×C₃⋊D₃	C₂×C₇×C₁₇	semidirect
73. C₃²×D₇	C₂×C₇×C₁₇	semidirect
75. C₇×C₁₇	D₇×C₃⋊D₃	direct (N × H)
76. C₇×C₁₇	C₂×C₇×C₃⋊D₃	semidirect
82. C₇×D₇	C₁₇×C₃⋊D₃	direct (N × H)
87. C₃²×C₇	C₂×D₇×C₁₇	semidirect
88. C₃²×C₇	C₂²×C₇×C₁₇	semidirect
89. C₃×C₁₇	D₃×C₇×D₇	semidirect
90. C₇²	C₂×C₁₇×C₃⋊D₃	semidirect
93. C₃×D₇	D₃×C₇×C₁₇	semidirect
105. C₃×C₇	D₃×D₇×C₁₇	semidirect
106. C₃×C₇	C₂×D₃×C₇×C₁₇	semidirect
109. C₃⋊D₃	C₇×D₇×C₁₇	direct (N × H)
110. C₁₇	C₇×D₇×C₃⋊D₃	direct (N × H)
117. D₇	C₇×C₁₇×C₃⋊D₃	direct (N × H)
119. C₃²	C₂×C₇×D₇×C₁₇	semidirect
121. C₇	D₇×C₁₇×C₃⋊D₃	direct (N × H)
122. C₇	C₂×C₇×C₁₇×C₃⋊D₃	semidirect
127. C₃	D₃×C₇×D₇×C₁₇	semidirect

H ≅ G/N

type

1. C₃²×C₇×D₇×C₁₇

C₂

semidirect

2. C₇²×C₁₇×C₃⋊D₃

C₂

semidirect

3. C₇×C₁₇×C₃⋊D₂₁

C₂

semidirect

5. C₃²×C₇²×C₁₇

C₂²

semidirect

8. C₃×C₇×D₇×C₁₇

D₃

semidirect

10. D₇×C₁₇×C₃⋊D₃

C₇

direct (N × H)

12. C₃×C₇²×C₁₇

C₂×D₃

semidirect

13. C₁₇×C₃⋊D₂₁

C₂×C₇

semidirect

16. C₇×C₁₇×C₃⋊D₃

D₇

direct (N × H)

17. C₇×C₁₇×C₃⋊D₃

C₂×C₇

semidirect

18. C₃²×D₇×C₁₇

C₂×C₇

semidirect

20. C₇×D₇×C₃⋊D₃

C₁₇

direct (N × H)

23. C₇×D₇×C₁₇

C₃⋊D₃

direct (N × H)

27. C₃²×C₇×C₁₇

C₂×D₇

semidirect

28. C₃²×C₇×C₁₇

C₂²×C₇

semidirect

29. C₇×C₃⋊D₂₁

C₂×C₁₇

semidirect

30. C₇²×C₃⋊D₃

C₂×C₁₇

semidirect

31. C₃²×C₇×D₇

C₂×C₁₇

semidirect

32. C₇²×C₁₇

C₂×C₃⋊D₃

semidirect

39. C₃×D₇×C₁₇

D₃×C₇

semidirect

44. C₃²×C₇²

C₂²×C₁₇

semidirect

46. C₃×C₇×C₁₇

D₃×D₇

semidirect

47. C₃×C₇×C₁₇

C₂×D₃×C₇

semidirect

50. C₁₇×C₃⋊D₃

C₇×D₇

direct (N × H)

53. C₃×C₇×D₇

D₃×C₁₇

semidirect

55. D₇×C₃⋊D₃

C₇×C₁₇

direct (N × H)

62. D₇×C₁₇

C₇×C₃⋊D₃

direct (N × H)

65. C₃²×C₁₇

C₂×C₇×D₇

semidirect

66. C₃×C₇²

C₂×D₃×C₁₇

semidirect

68. C₃⋊D₂₁

C₂×C₇×C₁₇

semidirect

71. C₇×C₃⋊D₃

D₇×C₁₇

direct (N × H)

72. C₇×C₃⋊D₃

C₂×C₇×C₁₇

semidirect

73. C₃²×D₇

C₂×C₇×C₁₇

semidirect

75. C₇×C₁₇

D₇×C₃⋊D₃

direct (N × H)

76. C₇×C₁₇

C₂×C₇×C₃⋊D₃

semidirect

82. C₇×D₇

C₁₇×C₃⋊D₃

direct (N × H)

87. C₃²×C₇

C₂×D₇×C₁₇

semidirect

88. C₃²×C₇

C₂²×C₇×C₁₇

semidirect

89. C₃×C₁₇

D₃×C₇×D₇

semidirect

90. C₇²

C₂×C₁₇×C₃⋊D₃

semidirect

93. C₃×D₇

D₃×C₇×C₁₇

semidirect

105. C₃×C₇

D₃×D₇×C₁₇

semidirect

106. C₃×C₇

C₂×D₃×C₇×C₁₇

semidirect

109. C₃⋊D₃

C₇×D₇×C₁₇

direct (N × H)

110. C₁₇

C₇×D₇×C₃⋊D₃

direct (N × H)

117. D₇

C₇×C₁₇×C₃⋊D₃

direct (N × H)

119. C₃²

C₂×C₇×D₇×C₁₇

semidirect

121. C₇

D₇×C₁₇×C₃⋊D₃

direct (N × H)

122. C₇

C₂×C₇×C₁₇×C₃⋊D₃

semidirect

127. C₃

D₃×C₇×D₇×C₁₇

semidirect

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

subgroup	index
C₃²×C₇×D₇×C₁₇	2
C₇²×C₁₇×C₃⋊D₃	2
C₇×C₁₇×C₃⋊D₂₁	2
D₃×C₇×D₇×C₁₇	3
C₂×C₇×C₁₇×C₃⋊D₃	7
D₇×C₁₇×C₃⋊D₃	7
C₇×D₇×C₃⋊D₃	17

subgroup

index

C₃²×C₇×D₇×C₁₇

C₇²×C₁₇×C₃⋊D₃

C₇×C₁₇×C₃⋊D₂₁

D₃×C₇×D₇×C₁₇

C₂×C₇×C₁₇×C₃⋊D₃

D₇×C₁₇×C₃⋊D₃

C₇×D₇×C₃⋊D₃

Subgroups — C₇×D₇×C₁₇×C₃⋊D₃ #44472985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×D7×C17×C3⋊D3 #44472985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×C₁₇×C₃⋊D₃ #44472985