Group #21426656 — subgroups

Subgroups — C₄×#14273719 #21426656

Order 7552.

484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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×#14273719	C₂	1	1	yes	maximal, characteristic
2	#16837300	C₂	1	2	yes	maximal
3	#16837286	C₂	1	4	yes	maximal
4	#16837268	C₂	1	1	yes	maximal, characteristic
5	C₄×Dic₅₉⋊C₄	C₂	1	4	yes	maximal
6	C₄×C₄⋊Dic₅₉	C₂	1	2	yes	maximal
7	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic
8	#14273719	C₄	1	8	yes	direct product factor
9	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
11	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₅₉⋊C₄	C₂²	1	4	yes	—
13	C₂×C₄×Dic₅₉	C₂²	1	4	yes	—
14	C₅₉⋊#95	C₂²	1	4	yes	—
15	C₅₉⋊#95	C₂²	1	4	yes	—
16	C₅₉⋊#95	C₂²	1	4	yes	—
17	C₂×C₄²×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄²×C₅₉	C₂²	1	2	yes	—
19	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
23	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₅₉	C₂³	1	4	yes	—
28	C₂²×Dic₅₉	C₂³	1	4	yes	—
29	C₄²×C₅₉	—	2	4	no	—
30	C₄²×C₅₉	—	2	2	no	—
31	C₄²×C₅₉	—	2	4	no	—
32	C₄²×C₅₉	C₂×C₄	1	4	yes	—
33	C₄²×C₅₉	Q₈	1	4	yes	—
34	C₄⋊Dic₅₉	—	2	4	no	—
35	C₄⋊Dic₅₉	C₂×C₄	1	8	yes	—
36	Dic₅₉⋊C₄	—	2	8	no	—
37	Dic₅₉⋊C₄	C₂×C₄	1	16	yes	—
38	C₄×Dic₅₉	—	2	8	no	—
39	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
40	C₂×C₄×C₅₉	—	2	2	no	—
41	C₂×C₄×C₅₉	—	2	2	no	—
42	C₂×C₄×C₅₉	—	2	2	no	—
43	C₂×C₄×C₅₉	—	2	2	no	—
44	C₂×C₄×C₅₉	—	2	2	no	—
45	C₂×C₄×C₅₉	C₂²×C₄	1	4	yes	—
46	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₅₉	#41	1	4	yes	—
51	C₂×C₄×C₅₉	#41	1	2	yes	—
52	C₂×C₄×C₅₉	#41	1	4	yes	—
53	C₂×Dic₅₉	—	2	4	no	—
54	C₂×Dic₅₉	—	2	4	no	—
55	C₂×Dic₅₉	—	2	4	no	—
56	C₂×Dic₅₉	—	2	4	no	—
57	C₂×Dic₅₉	—	2	4	no	—
58	C₂×Dic₅₉	C₂²×C₄	1	8	yes	—
59	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
60	C₂²×C₅₉	C₂²×Q₈	1	1	yes	characteristic
61	C₂²×C₅₉	C₂×#41	1	1	yes	characteristic
62	C₂²×C₅₉	C₂×#41	1	2	yes	—
63	C₂²×C₅₉	C₂×#41	1	2	yes	—
64	C₄×C₅₉	—	2	4	no	—
65	C₄×C₅₉	—	2	4	no	—
66	C₄×C₅₉	—	2	2	no	—
67	C₄×C₅₉	C₄×Q₈	1	4	yes	—
68	C₄×C₅₉	#125	1	4	yes	complemented
69	Dic₅₉	—	2	8	no	—
70	Dic₅₉	—	4	4	no	—
71	C₄×#125	—	59	1	no	maximal, Sylow
72	C₂×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
73	C₂×C₅₉	C₄×#41	1	2	yes	—
74	C₂×C₅₉	C₂×#125	1	1	yes	characteristic
75	C₂×C₅₉	#529	1	2	yes	—
76	C₂×C₅₉	#533	1	1	yes	characteristic
77	C₂×#125	—	59	1	no	—
78	#389	—	59	2	no	—
79	#387	—	59	4	no	—
80	#382	—	59	1	no	—
81	C₄×C₄⋊C₄	—	59	2	no	—
82	C₄×C₄⋊C₄	—	59	4	no	—
83	C₄³	D₅₉	1	1	yes	characteristic
84	C₅₉	C₄×#125	1	1	yes	characteristic, complemented, Sylow
85	#125	—	59	8	no	—
86	C₂×C₄⋊C₄	—	59	4	no	—
87	C₂×C₄⋊C₄	—	59	2	no	—
88	C₂×C₄⋊C₄	—	59	2	no	—
89	C₂×C₄⋊C₄	—	59	4	no	—
90	C₂×C₄²	—	59	4	no	—
91	C₂×C₄²	C₂×D₅₉	1	2	yes	—
92	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
93	C₂×C₄²	C₂×D₅₉	1	2	yes	—
94	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
95	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
96	#95	—	59	4	no	—
97	#95	—	59	4	no	—
98	#95	—	59	4	no	—
99	C₂²×C₄	—	59	4	no	—
100	C₂²×C₄	—	59	4	no	—
101	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
103	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
105	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
106	C₄⋊C₄	—	59	16	no	—
107	C₄⋊C₄	—	59	8	no	—
108	C₄⋊C₄	—	118	8	no	—
109	C₄⋊C₄	—	118	4	no	—
110	C₄²	—	2	4	no	—
111	C₄²	—	2	2	no	—
112	C₄²	—	2	4	no	—
113	C₄²	—	118	8	no	—
114	C₄²	Dic₁₁₈	1	4	yes	—
115	C₄²	C₄×D₅₉	1	4	yes	—
116	C₂³	C₂³×D₅₉	1	1	yes	characteristic
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	59	8	no	—
123	C₂×C₄	—	118	4	no	—
124	C₂×C₄	—	118	4	no	—
125	C₂×C₄	—	118	4	no	—
126	C₂×C₄	—	118	4	no	—
127	C₂×C₄	—	118	4	no	—
128	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
129	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
130	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
131	C₂×C₄	C₂×C₄×D₅₉	1	4	yes	—
132	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
133	C₂×C₄	#11745685	1	4	yes	—
134	C₂×C₄	#11745685	1	2	yes	—
135	C₂×C₄	#11745685	1	4	yes	—
136	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
137	C₂²	C₂²×Dic₁₁₈	1	1	yes	characteristic
138	C₂²	C₂×#11745685	1	2	yes	—
139	C₂²	C₂×#11745685	1	1	yes	characteristic
140	C₂²	C₂×#11745685	1	2	yes	—
141	C₄	—	2	4	no	—
142	C₄	—	2	2	no	—
143	C₄	—	2	4	no	—
144	C₄	—	118	8	no	—
145	C₄	—	236	4	no	—
146	C₄	C₄×Dic₁₁₈	1	4	yes	—
147	C₄	#14273719	1	4	yes	direct product factor
148	C₂	C₂×C₄×Dic₁₁₈	1	1	yes	characteristic
149	C₂	C₄×#11745685	1	2	yes	—
150	C₂	C₂×#14273719	1	1	yes	characteristic
151	C₂	#16837936	1	2	yes	—
152	C₂	#16837959	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal, characteristic

#16837300

C₂

yes

maximal

#16837286

C₂

yes

maximal

#16837268

C₂

yes

maximal, characteristic

C₄×Dic₅₉⋊C₄

C₂

yes

maximal

C₄×C₄⋊Dic₅₉

C₂

yes

maximal

C₄³×C₅₉

C₂

yes

maximal, characteristic

#14273719

C₄

yes

direct product factor

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×Dic₅₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₅₉⋊#95

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂³

yes

—

C₂²×Dic₅₉

C₂³

yes

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂×C₄

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₅₉

—

C₂³×C₅₉

C₂⁴

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

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×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₂²×C₄

yes

—

C₂²×C₅₉

C₂³×C₄

yes

characteristic

C₂²×C₅₉

C₂²×Q₈

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

characteristic

C₂²×C₅₉

C₂×#41

yes

—

C₂²×C₅₉

C₂×#41

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₄×Q₈

yes

—

C₄×C₅₉

#125

yes

complemented

Dic₅₉

—

Dic₅₉

—

C₄×#125

—

maximal, Sylow

C₂×C₅₉

C₂×C₄×Q₈

yes

characteristic

C₂×C₅₉

C₄×#41

yes

—

C₂×C₅₉

C₂×#125

yes

characteristic

C₂×C₅₉

#529

yes

—

C₂×C₅₉

yes

—

—

—

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

D₅₉

yes

characteristic

C₅₉

C₄×#125

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₂×C₄²

C₂×D₅₉

yes

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₂×C₄²

C₂×D₅₉

yes

—

—

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₅₉

yes

characteristic

102

C₂²×C₄

C₂²×D₅₉

yes

—

103

C₂²×C₄

C₂²×D₅₉

yes

—

104

C₂²×C₄

C₂²×D₅₉

yes

characteristic

105

C₂²×C₄

C₂²×D₅₉

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

118

—

109

C₄⋊C₄

—

118

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

118

—

114

C₄²

Dic₁₁₈

yes

—

115

C₄²

C₄×D₅₉

yes

—

116

C₂³

C₂³×D₅₉

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

118

—

124

C₂×C₄

—

118

—

125

C₂×C₄

—

118

—

126

C₂×C₄

—

118

—

127

C₂×C₄

—

118

—

128

C₂×C₄

C₂×Dic₁₁₈

yes

—

129

C₂×C₄

C₂×Dic₁₁₈

yes

—

130

C₂×C₄

C₂×Dic₁₁₈

yes

—

131

C₂×C₄

C₂×C₄×D₅₉

yes

—

132

C₂×C₄

C₂×C₄×D₅₉

yes

—

133

C₂×C₄

#11745685

yes

—

134

C₂×C₄

#11745685

yes

—

135

C₂×C₄

#11745685

yes

—

136

C₂²

C₂²×C₄×D₅₉

yes

characteristic

137

C₂²

C₂²×Dic₁₁₈

yes

characteristic

138

C₂²

C₂×#11745685

yes

—

139

C₂²

C₂×#11745685

yes

characteristic

140

C₂²

C₂×#11745685

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

118

—

145

C₄

—

236

—

146

C₄

C₄×Dic₁₁₈

yes

—

147

C₄

#14273719

yes

direct product factor

148

C₂

C₂×C₄×Dic₁₁₈

yes

characteristic

149

C₂

C₄×#11745685

yes

—

150

C₂

C₂×#14273719

yes

characteristic

151

C₂

#16837936

yes

—

152

C₂

#16837959

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂³×C₄
Frattini	C₂³	C₂³×D₅₉
Fitting	C₄³×C₅₉	C₂
socle	C₂³×C₅₉	C₂⁴
hypercenter	C₄³	D₅₉
hypocenter	C₅₉	C₄×#125
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

subgroup

G/H

center

C₂²×C₄

C₂²×D₅₉

commutator

C₂²×C₅₉

C₂³×C₄

Frattini

C₂³

C₂³×D₅₉

Fitting

C₄³×C₅₉

C₂

socle

C₂³×C₅₉

C₂⁴

hypercenter

C₄³

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ C₄³

N	H ≅ G/N	type
8. #14273719	C₄	direct (N × H)
68. C₄×C₅₉	#125	semidirect
84. C₅₉	C₄×#125	semidirect
147. C₄	#14273719	direct (N × H)

H ≅ G/N

type

8. #14273719

C₄

direct (N × H)

68. C₄×C₅₉

#125

semidirect

84. C₅₉

C₄×#125

semidirect

147. C₄

#14273719

direct (N × H)

Subgroups — C₄×#14273719 #21426656

Conjugacy classes of subgroups

Complements

Subgroups — C4×#14273719 #21426656

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14273719 #21426656