Group #21425629 — subgroups

Subgroups — #21425629

Order 7552.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14273658	C₂	1	2	yes	maximal, complemented
2	C₂×#14273648	C₂	1	2	yes	maximal
3	#16837272	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837157	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₅₉	—	2	2	no	—
8	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
9	#14273658	—	2	4	no	—
10	#14273648	—	2	4	no	—
11	C₂²×D₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
14	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₅₉	—	2	1	no	—
16	C₂×D₄×C₅₉	—	2	2	no	—
17	C₂×D₄×C₅₉	—	2	2	no	—
18	C₂×D₄×C₅₉	—	2	1	no	—
19	C₂×D₄×C₅₉	Q₈	1	2	yes	—
20	C₂²×C₄×C₅₉	—	2	1	no	—
21	C₂²×C₄×C₅₉	D₄	1	2	yes	—
22	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₅₉	—	2	2	no	—
24	C₄⋊C₄×C₅₉	—	2	2	no	—
25	C₂²⋊C₄×C₅₉	—	4	4	no	—
26	C₄²×C₅₉	—	2	2	no	—
27	C₄⋊Dic₅₉	—	2	2	no	—
28	C₄⋊Dic₅₉	—	2	2	no	—
29	C₄⋊Dic₅₉	—	4	4	no	—
30	C₂×C₅₉⋊C₈	—	2	2	no	—
31	C₂×C₅₉⋊C₈	—	2	2	no	—
32	C₂×C₅₉⋊C₈	D₄	1	4	yes	—
33	C₂³×C₅₉	—	2	2	no	—
34	C₂³×C₅₉	—	4	1	no	—
35	C₂³×C₅₉	—	4	1	no	—
36	C₂³×C₅₉	—	4	2	no	—
37	C₂³×C₅₉	—	4	2	no	—
38	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
39	D₄×C₅₉	—	2	4	no	—
40	D₄×C₅₉	—	4	2	no	—
41	C₂×C₄×C₅₉	—	2	2	no	—
42	C₂×C₄×C₅₉	—	2	2	no	—
43	C₂×C₄×C₅₉	—	4	1	no	—
44	C₂×C₄×C₅₉	—	4	2	no	—
45	C₂×C₄×C₅₉	SD₁₆	1	4	yes	—
46	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₅₉	#41	1	2	yes	—
50	C₂×Dic₅₉	—	4	2	no	—
51	C₂×Dic₅₉	—	4	4	no	—
52	C₅₉⋊C₈	—	2	4	no	—
53	C₂²×C₅₉	—	4	2	no	—
54	C₂²×C₅₉	—	4	4	no	—
55	C₂²×C₅₉	—	8	2	no	—
56	C₂²×C₅₉	—	8	1	no	—
57	C₂²×C₅₉	—	8	1	no	—
58	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂²×C₅₉	#123	1	1	yes	characteristic
60	C₂²×C₅₉	#127	1	1	yes	characteristic
61	C₂²×C₅₉	C₂×SD₁₆	1	2	yes	—
62	C₂²×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
63	C₄×C₅₉	—	2	4	no	—
64	C₄×C₅₉	—	8	1	no	—
65	C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
66	C₄×C₅₉	#123	1	2	yes	—
67	Dic₅₉	—	8	2	no	—
68	#2094	—	59	1	no	maximal, Sylow
69	C₂×C₅₉	—	8	2	no	—
70	C₂×C₅₉	#399	1	1	yes	characteristic
71	C₂×C₅₉	#476	1	2	yes	—
72	C₂×C₅₉	#481	1	2	yes	—
73	C₂×C₅₉	#492	1	1	yes	characteristic
74	C₂×C₅₉	#496	1	1	yes	characteristic
75	C₂×#106	—	59	2	no	—
76	C₂×#102	—	59	2	no	—
77	#390	D₅₉	1	1	yes	characteristic
78	#384	—	59	1	no	—
79	#336	—	59	1	no	—
80	C₅₉	#2094	1	1	yes	characteristic, complemented, Sylow
81	C₂²×D₄	C₂×D₅₉	1	1	yes	characteristic
82	C₂²×C₈	—	59	2	no	—
83	C₂×C₄⋊C₄	—	59	2	no	—
84	C₂×C₄⋊C₄	—	118	2	no	—
85	C₂×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
86	C₂×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
88	#106	—	118	4	no	—
89	#102	—	118	4	no	—
90	C₂⁴	—	2	1	no	—
91	C₂×D₄	—	2	1	no	—
92	C₂×D₄	—	2	2	no	—
93	C₂×D₄	—	2	2	no	—
94	C₂×D₄	Dic₁₁₈	1	2	yes	—
95	C₂²×C₄	—	2	1	no	—
96	C₂²×C₄	—	118	2	no	—
97	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
98	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
99	C₂×C₈	—	59	4	no	—
100	C₂×C₈	—	118	2	no	—
101	C₂×C₈	—	118	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	118	2	no	—
104	C₄⋊C₄	—	118	2	no	—
105	C₄⋊C₄	—	236	4	no	—
106	C₂²⋊C₄	—	4	4	no	—
107	C₄²	—	2	2	no	—
108	C₂³	—	2	2	no	—
109	C₂³	—	4	1	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	4	2	no	—
112	C₂³	—	4	2	no	—
113	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
114	D₄	—	2	4	no	—
115	D₄	—	4	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	236	2	no	—
121	C₂×C₄	—	236	4	no	—
122	C₂×C₄	#11745670	1	4	yes	—
123	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
124	C₂×C₄	#11745685	1	1	yes	characteristic
125	C₂×C₄	D₄×D₅₉	1	2	yes	—
126	C₂×C₄	#11745687	1	2	yes	—
127	C₈	—	118	4	no	—
128	C₂²	—	4	4	no	—
129	C₂²	—	4	2	no	—
130	C₂²	—	8	2	no	—
131	C₂²	—	8	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	#14273706	1	1	yes	characteristic
134	C₂²	#14273708	1	1	yes	characteristic
135	C₂²	#14273723	1	1	yes	characteristic
136	C₂²	C₂×#11745670	1	2	yes	—
137	C₂²	#14273752	1	2	yes	—
138	C₄	—	2	4	no	—
139	C₄	—	8	1	no	—
140	C₄	—	472	2	no	—
141	C₄	#14273704	1	2	yes	—
142	C₄	#14273709	1	2	yes	—
143	C₂	—	8	2	no	—
144	C₂	#16837338	1	1	yes	characteristic
145	C₂	#16837692	1	2	yes	—
146	C₂	#16837718	1	2	yes	—
147	C₂	#16837774	1	1	yes	characteristic
148	C₂	#16837792	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273658

C₂

yes

maximal, complemented

C₂×#14273648

C₂

yes

maximal

#16837272

C₂

yes

maximal, characteristic, complemented

#16837157

C₂

yes

maximal, characteristic, complemented

C₅₉×#390

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

#14273658

—

#14273648

—

C₂²×D₄×C₅₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂⁴×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

Q₈

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

D₄

yes

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

SD₁₆

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²⋊Q₈

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

C₂×SD₁₆

yes

—

C₂²×C₅₉

AGL(1,ℤ/8)

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₂²⋊Q₈

yes

—

C₄×C₅₉

#123

yes

—

Dic₅₉

—

#2094

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#399

yes

characteristic

C₂×C₅₉

#476

yes

—

C₂×C₅₉

#481

yes

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

D₅₉

yes

characteristic

#384

—

#336

—

C₅₉

#2094

yes

characteristic, complemented, Sylow

C₂²×D₄

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

118

—

C₂×C₄⋊C₄

C₂×D₅₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#106

—

118

—

#102

—

118

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

Dic₁₁₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂²⋊D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

118

—

101

C₂×C₈

—

118

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

118

—

104

C₄⋊C₄

—

118

—

105

C₄⋊C₄

—

236

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

236

—

121

C₂×C₄

—

236

—

122

C₂×C₄

#11745670

yes

—

123

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

124

C₂×C₄

#11745685

yes

characteristic

125

C₂×C₄

D₄×D₅₉

yes

—

126

C₂×C₄

#11745687

yes

—

127

C₈

—

118

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#14273706

yes

characteristic

134

C₂²

#14273708

yes

characteristic

135

C₂²

#14273723

yes

characteristic

136

C₂²

C₂×#11745670

yes

—

137

C₂²

#14273752

yes

—

138

C₄

—

139

C₄

—

140

C₄

—

472

—

141

C₄

#14273704

yes

—

142

C₄

#14273709

yes

—

143

C₂

—

144

C₂

#16837338

yes

characteristic

145

C₂

#16837692

yes

—

146

C₂

#16837718

yes

—

147

C₂

#16837774

yes

characteristic

148

C₂

#16837792

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅₉
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#390	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	#390	D₅₉
hypocenter	C₅₉	#2094
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅₉

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#390

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
1. C₂×#14273658	C₂	semidirect
3. #16837272	C₂	semidirect
4. #16837157	C₂	semidirect
80. C₅₉	#2094	semidirect

H ≅ G/N

type

1. C₂×#14273658

C₂

semidirect

3. #16837272

C₂

semidirect

4. #16837157

C₂

semidirect

80. C₅₉

#2094

semidirect

Subgroups — #21425629

Conjugacy classes of subgroups

Complements