Group #21432457 — subgroups

Subgroups — #21432457

Order 7552.

472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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	C₂×#14273718	C₂	1	2	yes	maximal
2	#16837301	C₂	1	4	yes	maximal
3	#16837298	C₂	1	4	yes	maximal
4	#16837272	C₂	1	1	yes	maximal, characteristic
5	#16837267	C₂	1	2	yes	maximal
6	C₄²×Dic₅₉	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#384	C₂	1	1	yes	maximal, characteristic
8	#14273718	—	2	8	no	—
9	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
12	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₅₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
17	C₅₉⋊#95	C₂²	1	8	yes	—
18	C₂×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
19	C₂×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
20	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅₉	C₂³	1	4	yes	—
22	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
24	C₂²×Dic₅₉	C₂³	1	4	yes	—
25	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₅₉	C₂³	1	2	yes	—
28	C₄⋊C₄×C₅₉	—	2	4	no	—
29	C₄⋊C₄×C₅₉	—	2	8	no	—
30	C₄²×C₅₉	Q₈	1	4	yes	—
31	C₄⋊Dic₅₉	—	2	4	no	—
32	C₄⋊Dic₅₉	—	2	8	no	—
33	C₄⋊Dic₅₉	—	2	8	no	—
34	Dic₅₉⋊C₄	—	2	8	no	—
35	C₄×Dic₅₉	—	2	4	no	—
36	C₄×Dic₅₉	—	2	4	no	—
37	C₄×Dic₅₉	D₄	1	4	yes	—
38	C₄×Dic₅₉	Q₈	1	4	yes	—
39	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₅₉	—	2	4	no	—
41	C₂×C₄×C₅₉	—	2	8	no	—
42	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₅₉	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
46	C₂×C₄×C₅₉	#41	1	4	yes	—
47	C₂×C₄×C₅₉	#41	1	4	yes	—
48	C₂×Dic₅₉	—	2	2	no	—
49	C₂×Dic₅₉	—	2	2	no	—
50	C₂×Dic₅₉	—	2	2	no	—
51	C₂×Dic₅₉	—	2	2	no	—
52	C₂×Dic₅₉	—	2	4	no	—
53	C₂×Dic₅₉	—	2	8	no	—
54	C₂×Dic₅₉	C₂×D₄	1	2	yes	—
55	C₂×Dic₅₉	C₂×D₄	1	2	yes	—
56	C₂×Dic₅₉	C₂×Q₈	1	4	yes	—
57	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
58	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
59	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
60	C₂²×C₅₉	C₂×#41	1	2	yes	—
61	C₂²×C₅₉	C₂×#41	1	2	yes	—
62	C₄×C₅₉	—	4	4	no	—
63	C₄×C₅₉	#125	1	8	yes	complemented
64	C₄×C₅₉	C₄⋊Q₈	1	4	yes	—
65	Dic₅₉	—	2	2	no	—
66	Dic₅₉	—	2	2	no	—
67	Dic₅₉	—	2	4	no	—
68	Dic₅₉	—	4	4	no	—
69	#2859	—	59	1	no	maximal, Sylow
70	C₂×C₅₉	C₂×#125	1	2	yes	—
71	C₂×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₅₉	#532	1	1	yes	characteristic
73	C₂×C₅₉	#532	1	1	yes	characteristic
74	C₂×C₅₉	#533	1	2	yes	—
75	C₂×#125	—	59	2	no	—
76	#389	—	59	4	no	—
77	#389	—	59	4	no	—
78	#384	—	59	1	no	—
79	#384	D₅₉	1	1	yes	characteristic
80	#382	—	59	2	no	—
81	C₄³	—	59	1	no	—
82	C₅₉	#2859	1	1	yes	characteristic, complemented, Sylow
83	#125	—	118	8	no	—
84	C₂×C₄⋊C₄	—	59	2	no	—
85	C₂×C₄⋊C₄	—	59	4	no	—
86	C₂×C₄⋊C₄	—	59	4	no	—
87	C₂×C₄⋊C₄	—	59	4	no	—
88	C₂×C₄⋊C₄	C₂×D₅₉	1	2	yes	—
89	C₂×C₄⋊C₄	C₂×D₅₉	1	4	yes	—
90	C₂×C₄²	—	59	1	no	—
91	C₂×C₄²	—	59	1	no	—
92	C₂×C₄²	—	59	2	no	—
93	C₂×C₄²	—	59	2	no	—
94	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
95	#95	—	59	8	no	—
96	C₂²×C₄	—	59	2	no	—
97	C₂²×C₄	—	59	1	no	—
98	C₂²×C₄	—	59	1	no	—
99	C₂²×C₄	—	59	4	no	—
100	C₂²×C₄	C₂²×D₅₉	1	4	yes	—
101	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	2	8	no	—
105	C₄⋊C₄	—	118	8	no	—
106	C₄⋊C₄	—	118	8	no	—
107	C₄⋊C₄	—	118	4	no	—
108	C₄⋊C₄	—	118	8	no	—
109	C₄²	—	59	4	no	—
110	C₄²	—	59	4	no	—
111	C₄²	—	118	4	no	—
112	C₄²	—	118	4	no	—
113	C₄²	Dic₁₁₈	1	4	yes	—
114	C₂³	C₂³×D₅₉	1	1	yes	characteristic
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	8	no	—
117	C₂×C₄	—	59	2	no	—
118	C₂×C₄	—	59	2	no	—
119	C₂×C₄	—	59	4	no	—
120	C₂×C₄	—	118	2	no	—
121	C₂×C₄	—	118	2	no	—
122	C₂×C₄	—	118	2	no	—
123	C₂×C₄	—	118	2	no	—
124	C₂×C₄	—	118	4	no	—
125	C₂×C₄	—	118	8	no	—
126	C₂×C₄	C₂×Dic₁₁₈	1	4	yes	—
127	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
128	C₂×C₄	D₄×D₅₉	1	2	yes	—
129	C₂×C₄	#11745687	1	4	yes	—
130	C₂×C₄	Q₈×D₅₉	1	2	yes	—
131	C₂×C₄	#11745689	1	4	yes	—
132	C₂²	C₂×D₄×D₅₉	1	1	yes	characteristic
133	C₂²	C₂×Q₈×D₅₉	1	1	yes	characteristic
134	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
135	C₂²	C₂×#11745687	1	2	yes	—
136	C₂²	C₂×#11745689	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	118	2	no	—
139	C₄	—	118	2	no	—
140	C₄	—	118	4	no	—
141	C₄	—	236	4	no	—
142	C₄	#14273718	1	8	yes	complemented
143	C₄	#14273726	1	4	yes	—
144	C₂	C₂×#14273718	1	2	yes	—
145	C₂	C₂×#14273726	1	1	yes	characteristic
146	C₂	#16837950	1	1	yes	characteristic
147	C₂	#16837953	1	1	yes	characteristic
148	C₂	#16837957	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273718

C₂

yes

maximal

#16837301

C₂

yes

maximal

#16837298

C₂

yes

maximal

#16837272

C₂

yes

maximal, characteristic

#16837267

C₂

yes

maximal

C₄²×Dic₅₉

C₂

yes

maximal, characteristic

C₅₉×#384

C₂

yes

maximal, characteristic

#14273718

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₅₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

D₄

yes

—

C₄×Dic₅₉

Q₈

yes

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₂×D₄

yes

—

C₂×Dic₅₉

C₂×D₄

yes

—

C₂×Dic₅₉

C₂×Q₈

yes

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

C₂×#41

yes

—

C₄×C₅₉

—

C₄×C₅₉

#125

yes

complemented

C₄×C₅₉

C₄⋊Q₈

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

#2859

—

maximal, Sylow

C₂×C₅₉

C₂×#125

yes

—

C₂×C₅₉

C₂×C₄⋊Q₈

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

—

—

—

D₅₉

yes

characteristic

#382

—

C₄³

—

C₅₉

#2859

yes

characteristic, complemented, Sylow

#125

—

118

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×D₅₉

yes

—

101

C₂²×C₄

C₂²×D₅₉

yes

characteristic

102

C₂²×C₄

C₂²×D₅₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

118

—

106

C₄⋊C₄

—

118

—

107

C₄⋊C₄

—

118

—

108

C₄⋊C₄

—

118

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

118

—

112

C₄²

—

118

—

113

C₄²

Dic₁₁₈

yes

—

114

C₂³

C₂³×D₅₉

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

118

—

121

C₂×C₄

—

118

—

122

C₂×C₄

—

118

—

123

C₂×C₄

—

118

—

124

C₂×C₄

—

118

—

125

C₂×C₄

—

118

—

126

C₂×C₄

C₂×Dic₁₁₈

yes

—

127

C₂×C₄

C₂×Dic₁₁₈

yes

—

128

C₂×C₄

D₄×D₅₉

yes

—

129

C₂×C₄

#11745687

yes

—

130

C₂×C₄

Q₈×D₅₉

yes

—

131

C₂×C₄

#11745689

yes

—

132

C₂²

C₂×D₄×D₅₉

yes

characteristic

133

C₂²

C₂×Q₈×D₅₉

yes

characteristic

134

C₂²

C₂²×Dic₁₁₈

yes

characteristic

135

C₂²

C₂×#11745687

yes

—

136

C₂²

C₂×#11745689

yes

—

137

C₄

—

138

C₄

—

118

—

139

C₄

—

118

—

140

C₄

—

118

—

141

C₄

—

236

—

142

C₄

#14273718

yes

complemented

143

C₄

#14273726

yes

—

144

C₂

C₂×#14273718

yes

—

145

C₂

C₂×#14273726

yes

characteristic

146

C₂

#16837950

yes

characteristic

147

C₂

#16837953

yes

characteristic

148

C₂

#16837957

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₅₉×#384	C₂
hypercenter	#384	D₅₉
hypocenter	C₅₉	#2859
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #384

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂⁴

Fitting

C₅₉×#384

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂³ ◁ #384

N	H ≅ G/N	type
63. C₄×C₅₉	#125	semidirect
82. C₅₉	#2859	semidirect
142. C₄	#14273718	semidirect

H ≅ G/N

type

63. C₄×C₅₉

#125

semidirect

82. C₅₉

#2859

semidirect

142. C₄

#14273718

semidirect

Subgroups — #21432457

Conjugacy classes of subgroups

Complements