Group #21432706 — subgroups

Subgroups — #21432706

Order 7552.

440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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	#16838168	C₂	1	2	yes	maximal
2	C₂×#14273735	C₂	1	1	yes	maximal, characteristic
3	#16837451	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837449	C₂	1	4	yes	maximal, complemented
5	C₂×#14273662	C₂	1	2	yes	maximal, complemented
6	#108×D₅₉	C₂	1	4	yes	maximal, complemented
7	C₅₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11745685	C₂²	1	1	yes	characteristic
9	#14273735	—	2	4	no	—
10	#14273735	C₄	1	8	yes	—
11	#14273733	—	2	4	no	—
12	C₂×#11745664	C₂²	1	2	yes	—
13	C₂×#11745659	C₂²	1	2	yes	—
14	M₁₆×D₅₉	C₂²	1	8	yes	—
15	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₅₉	C₂²	1	2	yes	—
17	#14273663	C₂²	1	4	yes	—
18	#14273662	C₂²	1	4	yes	—
19	#14273662	C₂²	1	4	yes	—
20	C₂×M₁₆×C₅₉	C₂²	1	2	yes	—
21	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
22	#108×C₅₉	C₂²	1	4	yes	—
23	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
24	C₂×C₂²⋊D₅₉	Q₈	1	2	yes	—
25	#11745685	C₂×C₄	1	4	yes	—
26	#11745685	D₄	1	4	yes	—
27	C₂×D₂₃₆	Q₈	1	1	yes	characteristic
28	C₂×C₄×D₅₉	C₂³	1	2	yes	—
29	C₂×Dic₁₁₈	Q₈	1	1	yes	characteristic
30	M₁₆×C₅₉	—	2	2	no	—
31	M₁₆×C₅₉	C₂×C₄	1	4	yes	—
32	M₁₆×C₅₉	C₂³	1	4	yes	—
33	C₂×C₈×C₅₉	—	2	2	no	—
34	C₂×C₈×C₅₉	C₂³	1	2	yes	—
35	#11745664	—	2	2	no	—
36	#11745664	C₂³	1	4	yes	—
37	C₂×C₅₉⋊C₈	—	2	2	no	—
38	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
39	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
40	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
41	#11745659	—	2	8	no	—
42	#11745659	C₂×C₄	1	8	yes	—
43	C₈×D₅₉	—	2	8	no	—
44	C₈×D₅₉	C₂×C₄	1	8	yes	—
45	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
46	C₂²×D₅₉	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
51	C₂²⋊D₅₉	C₄⋊C₄	1	8	yes	—
52	C₂×Dic₅₉	C₂×Q₈	1	2	yes	—
53	D₂₃₆	C₄⋊C₄	1	4	yes	—
54	C₄×D₅₉	C₂²×C₄	1	4	yes	—
55	C₄×D₅₉	C₂×D₄	1	4	yes	—
56	Dic₁₁₈	C₄⋊C₄	1	4	yes	—
57	C₈×C₅₉	—	2	4	no	—
58	C₈×C₅₉	C₂²×C₄	1	4	yes	—
59	C₅₉⋊C₈	—	2	4	no	—
60	C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
61	C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
62	C₂²×C₅₉	—	4	1	no	—
63	C₂²×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
64	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
65	C₂×D₅₉	—	4	2	no	—
66	C₂×D₅₉	C₂×C₄⋊C₄	1	4	yes	—
67	C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
68	C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
69	C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
70	Dic₅₉	C₂×C₄⋊C₄	1	4	yes	—
71	#2916	—	59	1	no	maximal, Sylow
72	C₂×C₅₉	—	2	1	no	—
73	C₂×C₅₉	—	2	2	no	—
74	C₂×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
75	D₅₉	—	2	4	no	—
76	#568	—	59	2	no	—
77	C₂×#131	—	59	1	no	—
78	#430	—	59	1	no	—
79	#430	—	59	4	no	—
80	#430	D₅₉	1	1	yes	characteristic, complemented
81	C₂×#108	—	59	2	no	—
82	C₂×#108	—	59	4	no	—
83	C₅₉	#2916	1	1	yes	characteristic, complemented, Sylow
84	C₂×#41	—	59	1	no	—
85	#131	—	59	8	no	—
86	#131	—	118	4	no	—
87	#131	—	118	4	no	—
88	C₂×M₁₆	—	59	2	no	—
89	C₂×M₁₆	—	59	2	no	—
90	C₂×M₁₆	—	59	8	no	—
91	C₂×M₁₆	C₂×D₅₉	1	2	yes	—
92	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
93	C₂²×C₈	—	59	1	no	—
94	C₂²×C₈	—	59	2	no	—
95	#108	—	59	4	no	—
96	#108	—	59	4	no	—
97	#108	—	59	4	no	—
98	#108	C₂×D₅₉	1	4	yes	—
99	#41	—	59	4	no	—
100	#41	—	59	4	no	—
101	C₂×Q₈	—	59	1	no	—
102	C₂×D₄	—	59	2	no	—
103	C₂×D₄	—	59	1	no	—
104	C₂²×C₄	—	59	2	no	—
105	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
106	M₁₆	—	2	2	no	—
107	M₁₆	—	59	8	no	—
108	M₁₆	—	59	4	no	—
109	M₁₆	—	118	8	no	—
110	M₁₆	—	118	2	no	—
111	M₁₆	C₄×D₅₉	1	4	yes	—
112	M₁₆	C₂²×D₅₉	1	4	yes	—
113	C₂×C₈	—	2	2	no	—
114	C₂×C₈	—	59	4	no	—
115	C₂×C₈	—	59	1	no	—
116	C₂×C₈	—	59	1	no	—
117	C₂×C₈	—	59	8	no	—
118	C₂×C₈	—	118	8	no	—
119	C₂×C₈	—	118	2	no	—
120	C₂×C₈	C₂²×D₅₉	1	2	yes	—
121	C₂³	—	59	2	no	—
122	C₂³	Q₈×D₅₉	1	1	yes	characteristic
123	Q₈	—	59	4	no	—
124	D₄	—	59	8	no	—
125	D₄	—	59	4	no	—
126	C₂×C₄	—	59	2	no	—
127	C₂×C₄	—	59	4	no	—
128	C₂×C₄	—	59	4	no	—
129	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
130	C₂×C₄	D₄×D₅₉	1	2	yes	—
131	C₂×C₄	Q₈×D₅₉	1	1	yes	characteristic
132	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
133	C₈	—	2	4	no	—
134	C₈	—	59	2	no	—
135	C₈	—	59	2	no	—
136	C₈	—	118	4	no	—
137	C₈	C₂×C₄×D₅₉	1	4	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	—	59	4	no	—
140	C₂²	—	236	2	no	—
141	C₂²	C₄⋊C₄×D₅₉	1	2	yes	—
142	C₂²	C₂×Q₈×D₅₉	1	1	yes	characteristic
143	C₄	—	59	4	no	—
144	C₄	C₄⋊C₄×D₅₉	1	2	yes	—
145	C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
146	C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	2	no	—
149	C₂	—	118	4	no	—
150	C₂	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838168

C₂

yes

maximal

C₂×#14273735

C₂

yes

maximal, characteristic

#16837451

C₂

yes

maximal, characteristic, complemented

#16837449

C₂

yes

maximal, complemented

C₂×#14273662

C₂

yes

maximal, complemented

#108×D₅₉

C₂

yes

maximal, complemented

C₅₉×#430

C₂

yes

maximal, characteristic, complemented

C₂×#11745685

C₂²

yes

characteristic

#14273735

—

#14273735

C₄

yes

—

#14273733

—

C₂×#11745664

C₂²

yes

—

C₂×#11745659

C₂²

yes

—

M₁₆×D₅₉

C₂²

yes

—

C₂²×C₅₉⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₅₉

C₂²

yes

—

#14273663

C₂²

yes

—

#14273662

C₂²

yes

—

#14273662

C₂²

yes

—

C₂×M₁₆×C₅₉

C₂²

yes

—

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

#108×C₅₉

C₂²

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂×C₂²⋊D₅₉

Q₈

yes

—

#11745685

C₂×C₄

yes

—

#11745685

D₄

yes

—

C₂×D₂₃₆

Q₈

yes

characteristic

C₂×C₄×D₅₉

C₂³

yes

—

C₂×Dic₁₁₈

Q₈

yes

characteristic

M₁₆×C₅₉

—

M₁₆×C₅₉

C₂×C₄

yes

—

M₁₆×C₅₉

C₂³

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

—

#11745664

—

#11745664

C₂³

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

#11745659

—

#11745659

C₂×C₄

yes

—

C₈×D₅₉

—

C₈×D₅₉

C₂×C₄

yes

—

C₂³×C₅₉

C₂×Q₈

yes

characteristic

C₂²×D₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂²⋊D₅₉

C₄⋊C₄

yes

—

C₂×Dic₅₉

C₂×Q₈

yes

—

D₂₃₆

C₄⋊C₄

yes

—

C₄×D₅₉

C₂²×C₄

yes

—

C₄×D₅₉

C₂×D₄

yes

—

Dic₁₁₈

C₄⋊C₄

yes

—

C₈×C₅₉

—

C₈×C₅₉

C₂²×C₄

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂²×C₄

yes

—

C₅₉⋊C₈

C₂²×C₄

yes

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×C₄⋊C₄

yes

—

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

C₂×C₄⋊C₄

yes

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

—

C₄×C₅₉

C₂³×C₄

yes

characteristic

C₄×C₅₉

C₂²×D₄

yes

characteristic

Dic₅₉

C₂×C₄⋊C₄

yes

—

#2916

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

C₂²×C₄⋊C₄

yes

characteristic

D₅₉

—

—

—

—

—

D₅₉

yes

characteristic, complemented

C₂×#108

—

C₂×#108

—

C₅₉

#2916

yes

characteristic, complemented, Sylow

C₂×#41

—

#131

—

#131

—

118

—

#131

—

118

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

—

—

—

C₂×D₅₉

yes

—

#41

—

100

#41

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₂²×D₅₉

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

118

—

110

M₁₆

—

118

—

111

M₁₆

C₄×D₅₉

yes

—

112

M₁₆

C₂²×D₅₉

yes

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

118

—

119

C₂×C₈

—

118

—

120

C₂×C₈

C₂²×D₅₉

yes

—

121

C₂³

—

122

C₂³

Q₈×D₅₉

yes

characteristic

123

Q₈

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₅₉

yes

—

130

C₂×C₄

D₄×D₅₉

yes

—

131

C₂×C₄

Q₈×D₅₉

yes

characteristic

132

C₂×C₄

C₂³×D₅₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

118

—

137

C₈

C₂×C₄×D₅₉

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

236

—

141

C₂²

C₄⋊C₄×D₅₉

yes

—

142

C₂²

C₂×Q₈×D₅₉

yes

characteristic

143

C₄

—

144

C₄

C₄⋊C₄×D₅₉

yes

—

145

C₄

C₂²×C₄×D₅₉

yes

characteristic

146

C₄

C₂×D₄×D₅₉

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

—

118

—

150

C₂

C₂×C₄⋊C₄×D₅₉

yes

characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#430	C₂
socle	C₂×C₅₉	C₂²×C₄⋊C₄
hypercenter	#430	D₅₉
hypocenter	C₅₉	#2916
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

C₂×D₄×D₅₉

commutator

C₄×C₅₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#430

C₂

socle

C₂×C₅₉

C₂²×C₄⋊C₄

D₅₉

C₅₉

G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
3. #16837451	C₂	semidirect
4. #16837449	C₂	semidirect
5. C₂×#14273662	C₂	semidirect
6. #108×D₅₉	C₂	semidirect
7. C₅₉×#430	C₂	semidirect
80. #430	D₅₉	semidirect
83. C₅₉	#2916	semidirect

H ≅ G/N

type

3. #16837451

C₂

semidirect

4. #16837449

C₂

semidirect

5. C₂×#14273662

C₂

semidirect

6. #108×D₅₉

C₂

semidirect

7. C₅₉×#430

C₂

semidirect

80. #430

D₅₉

semidirect

83. C₅₉

#2916

semidirect

Subgroups — #21432706

Conjugacy classes of subgroups

Complements