Group #21433201 — subgroups

Subgroups — #21433201

Order 7552.

314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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	#16837959	C₂	1	1	yes	maximal, characteristic
2	#16837531	C₂	1	4	yes	maximal, complemented
3	#16837530	C₂	1	4	yes	maximal, complemented
4	#16837460	C₂	1	4	yes	maximal
5	#16837459	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#432	C₂	1	1	yes	maximal, characteristic
7	#14273727	C₄	1	1	yes	characteristic
8	#14273727	C₄	1	1	yes	characteristic
9	#14273719	C₄	1	2	yes	—
10	#14273706	C₄	1	2	yes	—
11	#14273706	C₄	1	2	yes	—
12	C₄×Dic₁₁₈	C₂²	1	2	yes	—
13	C₄×Dic₁₁₈	C₂²	1	2	yes	—
14	#14273686	C₂²	1	2	yes	—
15	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
16	Dic₅₉⋊C₈	C₂²	1	8	yes	—
17	C₂²⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
18	#14273638	C₂²	1	2	yes	—
19	#14273637	C₂²	1	4	yes	—
20	C₈×Dic₅₉	C₂²	1	4	yes	—
21	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
23	C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
24	#97×C₅₉	C₂²	1	2	yes	—
25	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₁₁₈	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₁₈	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₅₉	C₂³	1	4	yes	—
31	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
33	C₄²×C₅₉	C₂³	1	1	yes	characteristic
34	C₄²×C₅₉	C₂³	1	1	yes	characteristic
35	C₂²⋊Dic₅₉	C₂×C₄	1	4	yes	—
36	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
37	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
38	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
39	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
40	Dic₅₉⋊C₄	C₂×C₄	1	4	yes	—
41	Dic₅₉⋊C₄	C₂×C₄	1	4	yes	—
42	C₄×Dic₅₉	C₂³	1	4	yes	—
43	C₂×C₅₉⋊C₈	C₂³	1	4	yes	—
44	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅₉	—	2	2	no	—
46	C₂×C₄×C₅₉	—	4	1	no	—
47	C₂×C₄×C₅₉	—	4	1	no	—
48	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₅₉	C₂²×C₄	1	4	yes	—
55	C₂×Dic₅₉	C₂²×C₄	1	4	yes	—
56	Dic₁₁₈	—	4	2	no	—
57	Dic₁₁₈	—	4	2	no	—
58	C₈×C₅₉	—	2	4	no	—
59	C₅₉⋊C₈	—	2	4	no	—
60	C₂²×C₅₉	—	2	1	no	—
61	C₂²×C₅₉	—	2	1	no	—
62	C₂²×C₅₉	—	2	1	no	—
63	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
64	C₄×C₅₉	—	2	1	no	—
65	C₄×C₅₉	—	2	1	no	—
66	C₄×C₅₉	—	2	1	no	—
67	C₄×C₅₉	—	2	1	no	—
68	C₄×C₅₉	—	2	1	no	—
69	C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
70	Dic₅₉	—	2	4	no	—
71	Dic₅₉	—	2	4	no	—
72	#2987	—	59	1	no	maximal, Sylow
73	C₂×C₅₉	—	4	1	no	—
74	C₂×C₅₉	#519	1	1	yes	characteristic
75	C₂×C₅₉	#568	1	1	yes	characteristic
76	C₂×C₅₉	#568	1	1	yes	characteristic
77	#533	—	59	1	no	—
78	#446	—	59	4	no	—
79	#446	—	59	4	no	—
80	#433	—	59	4	no	—
81	#432	—	59	1	no	—
82	#432	D₅₉	1	1	yes	characteristic
83	C₅₉	#2987	1	1	yes	characteristic, complemented, Sylow
84	C₄⋊Q₈	—	59	1	no	—
85	C₄⋊Q₈	—	59	1	no	—
86	#125	—	59	2	no	—
87	C₂²⋊Q₈	—	59	2	no	—
88	C₂²⋊Q₈	—	59	2	no	—
89	C₄×Q₈	—	59	2	no	—
90	C₄×Q₈	—	59	2	no	—
91	#117	—	59	2	no	—
92	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
93	C₄⋊C₈	—	59	8	no	—
94	C₄⋊C₈	—	59	2	no	—
95	C₄⋊C₈	C₂×D₅₉	1	2	yes	—
96	C₂²⋊C₈	—	59	2	no	—
97	C₂²⋊C₈	C₂×D₅₉	1	2	yes	—
98	#97	—	59	4	no	—
99	#97	—	59	2	no	—
100	#97	C₂×D₅₉	1	2	yes	—
101	C₄×C₈	—	59	4	no	—
102	C₂×Q₈	—	59	2	no	—
103	C₂×Q₈	—	59	2	no	—
104	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
105	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
106	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
107	C₂×C₈	—	59	4	no	—
108	C₂×C₈	C₂²×D₅₉	1	4	yes	—
109	C₄⋊C₄	—	59	2	no	—
110	C₄⋊C₄	—	59	2	no	—
111	C₄⋊C₄	—	59	4	no	—
112	C₄⋊C₄	—	59	4	no	—
113	C₄⋊C₄	—	59	2	no	—
114	C₄⋊C₄	—	59	2	no	—
115	C₂²⋊C₄	—	59	4	no	—
116	C₄²	—	59	4	no	—
117	C₄²	C₄×D₅₉	1	1	yes	characteristic
118	C₄²	C₄×D₅₉	1	1	yes	characteristic
119	C₄²	C₂²×D₅₉	1	1	yes	characteristic
120	C₄²	C₂²×D₅₉	1	1	yes	characteristic
121	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
122	Q₈	—	236	2	no	—
123	Q₈	—	236	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	59	4	no	—
128	C₂×C₄	—	59	4	no	—
129	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
131	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
133	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
135	C₈	—	2	4	no	—
136	C₈	—	118	4	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	2	1	no	—
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	118	4	no	—
147	C₄	—	118	4	no	—
148	C₄	#14273774	1	2	yes	—
149	C₂	—	4	1	no	—
150	C₂	#16837879	1	1	yes	characteristic
151	C₂	#16838168	1	1	yes	characteristic
152	C₂	#16838168	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837959

C₂

yes

maximal, characteristic

#16837531

C₂

yes

maximal, complemented

#16837530

C₂

yes

maximal, complemented

#16837460

C₂

yes

maximal

#16837459

C₂

yes

maximal, characteristic

C₅₉×#432

C₂

yes

maximal, characteristic

#14273727

C₄

yes

characteristic

#14273727

C₄

yes

characteristic

#14273719

C₄

yes

—

#14273706

C₄

yes

—

#14273706

C₄

yes

—

C₄×Dic₁₁₈

C₂²

yes

—

C₄×Dic₁₁₈

C₂²

yes

—

#14273686

C₂²

yes

—

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

Dic₅₉⋊C₈

C₂²

yes

—

C₂²⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273638

C₂²

yes

—

#14273637

C₂²

yes

—

C₈×Dic₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

—

C₂²⋊C₈×C₅₉

C₂²

yes

—

#97×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂×Dic₁₁₈

C₂×C₄

yes

—

C₂×Dic₁₁₈

C₂×C₄

yes

—

C₂×C₈×C₅₉

C₂³

yes

—

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

characteristic

C₂²⋊Dic₅₉

C₂×C₄

yes

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

Dic₅₉⋊C₄

C₂×C₄

yes

—

Dic₅₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₅₉

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

C₂²×C₄

yes

—

C₂×Dic₅₉

C₂²×C₄

yes

—

Dic₁₁₈

—

Dic₁₁₈

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂³×C₄

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

2₋¹⁺⁴

yes

—

Dic₅₉

—

Dic₅₉

—

#2987

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#2987

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₅₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₅₉

yes

—

#97

—

#97

—

100

#97

C₂×D₅₉

yes

—

101

C₄×C₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂²×C₄

C₄×D₅₉

yes

characteristic

105

C₂²×C₄

C₄×D₅₉

yes

characteristic

106

C₂²×C₄

C₂²×D₅₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₅₉

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

C₄×D₅₉

yes

characteristic

118

C₄²

C₄×D₅₉

yes

characteristic

119

C₄²

C₂²×D₅₉

yes

characteristic

120

C₄²

C₂²×D₅₉

yes

characteristic

121

C₂³

C₂×C₄×D₅₉

yes

characteristic

122

Q₈

—

236

—

123

Q₈

—

236

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

130

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

131

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

132

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

133

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

134

C₂×C₄

C₂³×D₅₉

yes

characteristic

135

C₈

—

136

C₈

—

118

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂²×C₄×D₅₉

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

118

—

147

C₄

—

118

—

148

C₄

#14273774

yes

—

149

C₂

—

150

C₂

#16837879

yes

characteristic

151

C₂

#16838168

yes

characteristic

152

C₂

#16838168

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂³×C₄
Fitting	C₅₉×#432	C₂
hypercenter	#432	D₅₉
hypocenter	C₅₉	#2987
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #432

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₅₉

commutator, socle

C₂²×C₅₉

C₂³×C₄

Fitting

C₅₉×#432

C₂

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₄ ◁ #432

N	H ≅ G/N	type
2. #16837531	C₂	semidirect
3. #16837530	C₂	semidirect
83. C₅₉	#2987	semidirect

H ≅ G/N

type

2. #16837531

C₂

semidirect

3. #16837530

C₂

semidirect

83. C₅₉

#2987

semidirect

Subgroups — #21433201

Conjugacy classes of subgroups

Complements