Group #21424846 — subgroups

Subgroups — #21424846

Order 7552.

200 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14273662	C₂	1	1	yes	maximal, characteristic
2	#16837438	C₂	1	1	yes	maximal, characteristic
3	#16837428	C₂	1	1	yes	maximal, characteristic
4	C₂×#14273637	C₂	1	1	yes	maximal, characteristic
5	#16837163	C₂	1	1	yes	maximal, characteristic
6	#16837161	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#424	C₂	1	1	yes	maximal, characteristic
8	C₂×#11745664	C₂²	1	1	yes	characteristic
9	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
10	#14273686	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
12	#14273662	—	2	2	no	—
13	#14273660	C₄	1	2	yes	complemented
14	#14273658	C₄	1	2	yes	complemented
15	Dic₅₉⋊C₈	—	2	2	no	—
16	#14273637	—	2	2	no	—
17	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	#117×C₅₉	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₅₉	—	2	2	no	—
21	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₅₉	—	2	1	no	—
23	M₁₆×C₅₉	—	2	1	no	—
24	M₁₆×C₅₉	—	2	1	no	—
25	C₂×C₈×C₅₉	—	2	1	no	—
26	C₂×C₈×C₅₉	—	2	1	no	—
27	C₂×C₈×C₅₉	—	2	1	no	—
28	C₂×C₈×C₅₉	D₄	1	2	yes	—
29	C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
30	C₂²⋊C₄×C₅₉	—	2	1	no	—
31	C₄²×C₅₉	—	2	1	no	—
32	C₂²⋊Dic₅₉	—	2	1	no	—
33	C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
34	C₄×Dic₅₉	—	2	1	no	—
35	C₄×Dic₅₉	—	2	1	no	—
36	C₄×Dic₅₉	Q₈	1	2	yes	—
37	#11745664	—	2	1	no	—
38	#11745664	—	2	1	no	—
39	C₂×C₅₉⋊C₈	—	2	1	no	—
40	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₅₉⋊C₈	D₄	1	2	yes	—
43	C₂×C₅₉⋊C₈	Q₈	1	2	yes	—
44	C₂³×C₅₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₅₉	—	2	2	no	—
46	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
52	C₂×Dic₅₉	—	2	2	no	—
53	C₂×Dic₅₉	—	2	2	no	—
54	C₂×Dic₅₉	—	4	2	no	—
55	C₈×C₅₉	—	2	2	no	—
56	C₈×C₅₉	—	4	1	no	—
57	C₅₉⋊C₈	—	4	1	no	—
58	C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
59	C₅₉⋊C₈	C₄⋊C₄	1	2	yes	—
60	C₂²×C₅₉	—	2	2	no	—
61	C₂²×C₅₉	C₄×D₄	1	1	yes	characteristic
62	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₅₉	#125	1	1	yes	characteristic
64	C₄×C₅₉	—	4	2	no	—
65	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
67	C₄×C₅₉	#121	1	1	yes	characteristic
68	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
69	Dic₅₉	—	4	2	no	—
70	Dic₅₉	—	4	2	no	—
71	#1946	—	59	1	no	maximal, Sylow
72	C₂×C₅₉	—	2	1	no	—
73	C₂×C₅₉	—	2	1	no	—
74	C₂×C₅₉	#389	1	1	yes	characteristic
75	C₂×C₅₉	#444	1	2	yes	—
76	C₂×#108	—	59	1	no	—
77	#427	—	59	1	no	—
78	#424	—	59	1	no	—
79	#424	D₅₉	1	1	yes	characteristic
80	C₂×#97	—	59	1	no	—
81	#339	—	59	1	no	—
82	#339	—	59	1	no	—
83	C₅₉	#1946	1	1	yes	characteristic, complemented, Sylow
84	C₂×M₁₆	—	59	1	no	—
85	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
86	C₂²×C₈	—	59	1	no	—
87	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
88	#117	—	59	1	no	—
89	#117	C₂×D₅₉	1	1	yes	characteristic
90	C₂×C₄²	—	59	1	no	—
91	#108	—	118	2	no	—
92	#107	—	59	2	no	—
93	#106	—	59	2	no	—
94	C₄⋊C₈	—	2	2	no	—
95	C₄⋊C₈	—	118	2	no	—
96	#97	—	118	2	no	—
97	C₂²×C₄	—	118	1	no	—
98	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
99	M₁₆	—	2	1	no	—
100	M₁₆	—	2	1	no	—
101	M₁₆	—	118	1	no	—
102	M₁₆	—	118	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	59	1	no	—
107	C₂×C₈	—	59	1	no	—
108	C₂×C₈	—	59	2	no	—
109	C₂×C₈	—	59	2	no	—
110	C₂×C₈	—	118	1	no	—
111	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
112	C₄⋊C₄	—	59	2	no	—
113	C₄⋊C₄	C₄×D₅₉	1	2	yes	—
114	C₂²⋊C₄	—	2	1	no	—
115	C₂²⋊C₄	—	118	1	no	—
116	C₄²	—	2	1	no	—
117	C₄²	—	59	2	no	—
118	C₄²	—	118	1	no	—
119	C₄²	—	118	1	no	—
120	C₂³	#11745685	1	1	yes	characteristic
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	118	2	no	—
123	C₂×C₄	—	118	2	no	—
124	C₂×C₄	—	236	2	no	—
125	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
126	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
127	C₂×C₄	#11745687	1	1	yes	characteristic
128	C₂×C₄	Q₈×D₅₉	1	1	yes	characteristic
129	C₂×C₄	Q₈×D₅₉	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
131	C₈	—	2	2	no	—
132	C₈	—	4	1	no	—
133	C₈	—	59	2	no	—
134	C₈	—	59	2	no	—
135	C₈	—	236	1	no	—
136	C₂²	—	2	2	no	—
137	C₂²	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
138	C₂²	#14273705	1	1	yes	characteristic
139	C₂²	#14273717	1	1	yes	characteristic
140	C₄	—	4	2	no	—
141	C₄	—	236	2	no	—
142	C₄	—	236	2	no	—
143	C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
144	C₄	#14273692	1	1	yes	characteristic
145	C₄	#14273699	1	1	yes	characteristic
146	C₄	#14273725	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#16837297	1	1	yes	characteristic
150	C₂	#16837522	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273662

C₂

yes

maximal, characteristic

#16837438

C₂

yes

maximal, characteristic

#16837428

C₂

yes

maximal, characteristic

C₂×#14273637

C₂

yes

maximal, characteristic

#16837163

C₂

yes

maximal, characteristic

#16837161

C₂

yes

maximal, characteristic

C₅₉×#424

C₂

yes

maximal, characteristic

C₂×#11745664

C₂²

yes

characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

characteristic

#14273686

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

#14273662

—

#14273660

C₄

yes

complemented

#14273658

C₄

yes

complemented

Dic₅₉⋊C₈

—

#14273637

—

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

#117×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

—

C₄⋊C₄×C₅₉

C₂×C₄

yes

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

Q₈

yes

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

D₄

yes

—

C₂×C₅₉⋊C₈

Q₈

yes

—

C₂³×C₅₉

#41

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

#41

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

C₄⋊C₄

yes

—

C₅₉⋊C₈

C₄⋊C₄

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

C₄×D₄

yes

characteristic

C₂²×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₅₉

#125

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₄×Q₈

yes

characteristic

C₄×C₅₉

#121

yes

characteristic

C₄×C₅₉

C₄⋊Q₈

yes

characteristic

Dic₅₉

—

Dic₅₉

—

#1946

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#389

yes

characteristic

C₂×C₅₉

#444

yes

—

—

—

—

D₅₉

yes

characteristic

C₂×#97

—

#339

—

#339

—

C₅₉

#1946

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

characteristic

#117

—

#117

C₂×D₅₉

yes

characteristic

C₂×C₄²

—

#108

—

118

—

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

118

—

#97

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

M₁₆

—

100

M₁₆

—

101

M₁₆

—

118

—

102

M₁₆

—

118

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

118

—

111

C₂×C₈

C₂²⋊D₅₉

yes

—

112

C₄⋊C₄

—

113

C₄⋊C₄

C₄×D₅₉

yes

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

118

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

118

—

119

C₄²

—

118

—

120

C₂³

#11745685

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

118

—

123

C₂×C₄

—

118

—

124

C₂×C₄

—

236

—

125

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

126

C₂×C₄

D₄×D₅₉

yes

characteristic

127

C₂×C₄

#11745687

yes

characteristic

128

C₂×C₄

Q₈×D₅₉

yes

characteristic

129

C₂×C₄

Q₈×D₅₉

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

236

—

136

C₂²

—

137

C₂²

C₄×C₂²⋊D₅₉

yes

characteristic

138

C₂²

#14273705

yes

characteristic

139

C₂²

#14273717

yes

characteristic

140

C₄

—

141

C₄

—

236

—

142

C₄

—

236

—

143

C₄

C₄⋊C₄×D₅₉

yes

characteristic

144

C₄

#14273692

yes

characteristic

145

C₄

#14273699

yes

characteristic

146

C₄

#14273725

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#16837297

yes

characteristic

150

C₂

#16837522

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#424	C₂
socle	C₂²×C₅₉	C₄×D₄
hypercenter	#424	D₅₉
hypocenter	C₅₉	#1946
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #424

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#424

C₂

socle

C₂²×C₅₉

C₄×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #424

N	H ≅ G/N	type
13. #14273660	C₄	semidirect
14. #14273658	C₄	semidirect
83. C₅₉	#1946	semidirect

H ≅ G/N

type

13. #14273660

C₄

semidirect

14. #14273658

C₄

semidirect

83. C₅₉

#1946

semidirect

Subgroups — #21424846

Conjugacy classes of subgroups

Complements