Group #21426275 — subgroups

Subgroups — #21426275

Order 7552.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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	#16837635	C₂	1	1	yes	maximal, characteristic
2	#107×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837228	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837227	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837203	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₅₉)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
9	#14273698	—	2	1	no	—
10	C₄⋊C₄×D₅₉	—	2	1	no	—
11	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	#14273661	C₂²	1	1	yes	characteristic
13	#14273661	C₂²	1	1	yes	characteristic
14	#14273660	—	2	1	no	—
15	#14273648	—	2	1	no	—
16	C₂×D₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	#107×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₅₉	—	2	1	no	—
20	C₂×C₂²⋊D₅₉	—	4	1	no	—
21	C₂×C₄×D₅₉	—	4	1	no	—
22	C₂×C₄×D₅₉	D₄	1	1	yes	characteristic
23	D₈×C₅₉	—	2	1	no	—
24	D₈×C₅₉	—	2	1	no	—
25	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₅₉	—	2	1	no	—
27	C₂²⋊Dic₅₉	—	4	1	no	—
28	C₄⋊Dic₅₉	—	2	1	no	—
29	C₄⋊Dic₅₉	—	2	1	no	—
30	Dic₅₉⋊C₄	—	4	1	no	—
31	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
32	C₈×D₅₉	—	2	1	no	—
33	C₈×D₅₉	—	2	1	no	—
34	C₁₆×C₅₉	—	2	1	no	—
35	C₅₉⋊C₁₆	—	2	1	no	—
36	C₂³×C₅₉	—	4	1	no	—
37	C₂²×D₅₉	D₈	1	1	yes	characteristic
38	D₄×C₅₉	—	4	1	no	—
39	D₄×C₅₉	—	4	1	no	—
40	C₂×C₄×C₅₉	—	4	1	no	—
41	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
42	C₂²⋊D₅₉	—	8	2	no	—
43	C₂×Dic₅₉	—	4	1	no	—
44	C₂×Dic₅₉	—	4	1	no	—
45	C₂×Dic₅₉	D₈	1	1	yes	characteristic
46	C₄×D₅₉	—	2	1	no	—
47	C₄×D₅₉	—	2	1	no	—
48	C₄×D₅₉	—	8	2	no	—
49	C₈×C₅₉	#41	1	1	yes	characteristic
50	C₈×C₅₉	#41	1	1	yes	characteristic
51	C₅₉⋊C₈	—	2	1	no	—
52	C₂²×C₅₉	—	8	1	no	—
53	C₂²×C₅₉	—	8	1	no	—
54	C₂²×C₅₉	—	8	1	no	—
55	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
56	C₂×D₅₉	—	2	1	no	—
57	C₂×D₅₉	—	2	1	no	—
58	C₂×D₅₉	D₁₆	1	2	yes	—
59	C₄×C₅₉	—	8	1	no	—
60	C₄×C₅₉	#123	1	1	yes	characteristic
61	C₄×C₅₉	#137	1	1	yes	characteristic
62	Dic₅₉	—	2	1	no	—
63	Dic₅₉	—	8	1	no	—
64	Dic₅₉	—	8	1	no	—
65	#2232	—	59	1	no	maximal, Sylow
66	C₂×C₅₉	—	16	1	no	—
67	C₂×C₅₉	#480	1	1	yes	characteristic
68	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
69	C₂×C₅₉	#510	1	1	yes	characteristic
70	D₅₉	—	2	2	no	—
71	#466	—	59	1	no	—
72	C₂×#107	—	59	1	no	—
73	#366	—	59	1	no	—
74	#366	—	59	1	no	—
75	#357	—	59	1	no	—
76	#357	D₅₉	1	1	yes	characteristic, complemented
77	C₂²⋊C₁₆	—	59	1	no	—
78	C₅₉	#2232	1	1	yes	characteristic, complemented, Sylow
79	C₂×D₈	C₂×D₅₉	1	1	yes	characteristic
80	C₂²×C₈	—	59	1	no	—
81	#121	—	118	1	no	—
82	C₂×C₄⋊C₄	—	118	1	no	—
83	C₂×C₁₆	—	59	1	no	—
84	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
85	#107	—	59	1	no	—
86	#107	—	59	1	no	—
87	#107	—	118	1	no	—
88	#107	C₂×D₅₉	1	1	yes	characteristic
89	#102	—	118	1	no	—
90	C₂×D₄	—	2	1	no	—
91	C₂×D₄	—	236	1	no	—
92	C₂²×C₄	—	59	1	no	—
93	C₂²×C₄	—	236	1	no	—
94	D₈	—	2	1	no	—
95	D₈	—	2	1	no	—
96	C₂×C₈	—	59	1	no	—
97	C₂×C₈	—	118	1	no	—
98	C₂×C₈	—	118	1	no	—
99	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	118	1	no	—
102	C₄⋊C₄	—	118	1	no	—
103	C₄⋊C₄	—	236	1	no	—
104	C₂²⋊C₄	—	236	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	118	1	no	—
107	C₂³	—	4	1	no	—
108	C₂³	—	59	1	no	—
109	D₄	—	4	1	no	—
110	D₄	—	4	1	no	—
111	D₄	—	472	2	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	59	1	no	—
114	C₂×C₄	—	118	1	no	—
115	C₂×C₄	—	118	1	no	—
116	C₂×C₄	—	472	2	no	—
117	C₂×C₄	—	236	1	no	—
118	C₂×C₄	—	236	1	no	—
119	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
120	C₈	—	118	1	no	—
121	C₈	#11745685	1	1	yes	characteristic
122	C₈	#11745687	1	1	yes	characteristic
123	C₂²	—	8	1	no	—
124	C₂²	—	8	1	no	—
125	C₂²	—	8	1	no	—
126	C₂²	—	59	2	no	—
127	C₂²	—	118	1	no	—
128	C₂²	—	118	1	no	—
129	C₂²	D₈×D₅₉	1	1	yes	characteristic
130	C₄	—	8	1	no	—
131	C₄	—	118	1	no	—
132	C₄	—	472	1	no	—
133	C₄	—	472	1	no	—
134	C₄	#14273709	1	1	yes	characteristic
135	C₄	#14273756	1	1	yes	characteristic
136	C₂	—	16	1	no	—
137	C₂	—	118	2	no	—
138	C₂	#16837714	1	1	yes	characteristic
139	C₂	D₁₆×D₅₉	1	1	yes	characteristic
140	C₂	#16837841	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837635

C₂

yes

maximal, characteristic

#107×D₅₉

C₂

yes

maximal, characteristic, complemented

#16837228

C₂

yes

maximal, characteristic, complemented

#16837227

C₂

yes

maximal, characteristic, complemented

#16837203

C₂

yes

maximal, characteristic, complemented

(C₂×D₅₉)⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₅₉×#357

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₅₉

C₂²

yes

characteristic

#14273698

—

C₄⋊C₄×D₅₉

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

#14273661

C₂²

yes

characteristic

#14273661

C₂²

yes

characteristic

#14273660

—

#14273648

—

C₂×D₈×C₅₉

C₂²

yes

characteristic

C₂×C₁₆×C₅₉

C₂²

yes

characteristic

#107×C₅₉

C₂²

yes

characteristic

C₂×D₄×C₅₉

—

C₂×C₂²⋊D₅₉

—

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

D₄

yes

characteristic

D₈×C₅₉

—

D₈×C₅₉

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

C₂×C₅₉⋊C₈

D₄

yes

characteristic

C₈×D₅₉

—

C₈×D₅₉

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂²×D₅₉

D₈

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²⋊D₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

D₈

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₈×C₅₉

yes

C₈×C₅₉

yes

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂×D₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

D₁₆

yes

—

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

#2232

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

#480

yes

characteristic

C₂×C₅₉

C₂×D₁₆

yes

characteristic

C₂×C₅₉

#510

yes

characteristic

D₅₉

—

—

—

—

—

—

D₅₉

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₅₉

#2232

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

#121

—

118

—

C₂×C₄⋊C₄

—

118

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₉

yes

—

—

—

118

—

#107

C₂×D₅₉

yes

characteristic

#102

—

118

—

C₂×D₄

—

C₂×D₄

—

236

—

C₂²×C₄

—

C₂²×C₄

—

236

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

—

118

—

102

C₄⋊C₄

—

118

—

103

C₄⋊C₄

—

236

—

104

C₂²⋊C₄

—

236

—

105

C₁₆

—

106

C₁₆

—

118

—

107

C₂³

—

108

C₂³

—

109

D₄

—

110

D₄

—

111

D₄

—

472

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

118

—

115

C₂×C₄

—

118

—

116

C₂×C₄

—

472

—

117

C₂×C₄

—

236

—

118

C₂×C₄

—

236

—

119

C₂×C₄

D₄×D₅₉

yes

characteristic

120

C₈

—

118

—

121

C₈

#11745685

yes

characteristic

122

C₈

#11745687

yes

characteristic

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

118

—

128

C₂²

—

118

—

129

C₂²

D₈×D₅₉

yes

characteristic

130

C₄

—

131

C₄

—

118

—

132

C₄

—

472

—

133

C₄

—

472

—

134

C₄

#14273709

yes

characteristic

135

C₄

#14273756

yes

characteristic

136

C₂

—

137

C₂

—

118

—

138

C₂

#16837714

yes

characteristic

139

C₂

D₁₆×D₅₉

yes

characteristic

140

C₂

#16837841

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#357	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#357	D₅₉
hypocenter	C₅₉	#2232
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₅₉

commutator

C₂×C₈×C₅₉

C₂³

Frattini

C₂×C₈

C₂²×D₅₉

Fitting

C₅₉×#357

C₂

socle

C₂²×C₅₉

C₂×D₈

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
2. #107×D₅₉	C₂	semidirect
3. #16837228	C₂	semidirect
4. #16837227	C₂	semidirect
5. #16837203	C₂	semidirect
6. (C₂×D₅₉)⋊C₁₆	C₂	semidirect
7. C₅₉×#357	C₂	semidirect
76. #357	D₅₉	semidirect
78. C₅₉	#2232	semidirect

H ≅ G/N

type

2. #107×D₅₉

C₂

semidirect

3. #16837228

C₂

semidirect

4. #16837227

C₂

semidirect

5. #16837203

C₂

semidirect

6. (C₂×D₅₉)⋊C₁₆

C₂

semidirect

7. C₅₉×#357

C₂

semidirect

76. #357

D₅₉

semidirect

78. C₅₉

#2232

semidirect

Subgroups — #21426275

Conjugacy classes of subgroups

Complements