Group #21421939 — subgroups

Subgroups — #21421939

Order 7552.

264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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×C₂²⋊(C₅₉⋊C₈)	C₂	1	2	yes	maximal
2	C₂×#95×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅₉⋊C₈	—	2	2	no	—
4	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
5	C₂²⋊(C₅₉⋊C₈)	C₄	1	4	yes	complemented
6	C₂³×C₄×C₅₉	C₄	1	2	yes	—
7	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
8	#95×C₅₉	—	2	2	no	—
9	C₂⁴×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₅₉	—	2	2	no	—
11	C₂²×C₄×C₅₉	—	2	2	no	—
12	C₂²×C₄×C₅₉	—	4	2	no	—
13	C₂²×C₄×C₅₉	—	4	2	no	—
14	C₂²×C₄×C₅₉	—	4	2	no	—
15	C₂²×C₄×C₅₉	C₈	1	4	yes	complemented
16	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₅₉	D₄	1	2	yes	—
18	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₅₉	Q₈	1	1	yes	characteristic
20	C₂×C₅₉⋊C₈	—	2	4	no	—
21	C₂×C₅₉⋊C₈	—	4	4	no	—
22	C₂³×C₅₉	—	2	2	no	—
23	C₂³×C₅₉	—	2	1	no	—
24	C₂³×C₅₉	—	2	1	no	—
25	C₂³×C₅₉	C₄²	1	1	yes	characteristic
26	C₂³×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂³×C₅₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂³×C₅₉	C₂×C₈	1	2	yes	—
29	C₂³×C₅₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₅₉	—	2	4	no	—
31	C₂×C₄×C₅₉	—	2	4	no	—
32	C₂×C₄×C₅₉	—	4	2	no	—
33	C₂×C₄×C₅₉	—	4	1	no	—
34	C₂×C₄×C₅₉	—	4	1	no	—
35	C₂×C₄×C₅₉	—	4	4	no	—
36	C₂×C₄×C₅₉	—	4	2	no	—
37	C₂×C₄×C₅₉	—	4	2	no	—
38	C₂×C₄×C₅₉	—	4	4	no	—
39	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
41	C₅₉⋊C₈	—	4	4	no	—
42	C₂²×C₅₉	—	2	2	no	—
43	C₂²×C₅₉	—	2	2	no	—
44	C₂²×C₅₉	—	2	2	no	—
45	C₂²×C₅₉	—	2	2	no	—
46	C₂²×C₅₉	—	2	1	no	—
47	C₂²×C₅₉	—	2	1	no	—
48	C₂²×C₅₉	—	2	1	no	—
49	C₂²×C₅₉	—	2	1	no	—
50	C₂²×C₅₉	#95	1	1	yes	characteristic
51	C₂²×C₅₉	C₄×C₈	1	1	yes	characteristic
52	C₂²×C₅₉	#97	1	1	yes	characteristic
53	C₂²×C₅₉	C₂²⋊C₈	1	2	yes	—
54	C₂²×C₅₉	#99	1	2	yes	—
55	C₂²×C₅₉	#100	1	1	yes	characteristic
56	C₂²×C₅₉	#101	1	1	yes	characteristic
57	C₂²×C₅₉	C₄⋊C₈	1	2	yes	—
58	C₄×C₅₉	—	2	2	no	—
59	C₄×C₅₉	—	2	2	no	—
60	C₄×C₅₉	—	4	4	no	—
61	#1280	—	59	1	no	maximal, Sylow
62	C₂×C₅₉	—	2	1	no	—
63	C₂×C₅₉	—	2	1	no	—
64	C₂×C₅₉	—	2	2	no	—
65	C₂×C₅₉	#323	1	2	yes	—
66	C₂×C₅₉	#324	1	2	yes	—
67	C₂×C₅₉	#336	1	1	yes	characteristic
68	C₂×C₅₉	#342	1	1	yes	characteristic
69	C₂×C₅₉	#343	1	1	yes	characteristic
70	C₂×C₂²⋊C₈	—	59	2	no	—
71	C₂×#95	D₅₉	1	1	yes	characteristic
72	C₅₉	#1280	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	Dic₅₉	1	2	yes	—
74	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
75	C₂²×C₈	—	118	2	no	—
76	C₂²⋊C₈	—	59	4	no	—
77	C₂²⋊C₈	—	118	2	no	—
78	#95	—	2	2	no	—
79	C₂⁴	C₂×Dic₅₉	1	1	yes	characteristic
80	C₂²×C₄	—	2	2	no	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	—	4	2	no	—
83	C₂²×C₄	—	4	2	no	—
84	C₂²×C₄	—	4	2	no	—
85	C₂²×C₄	C₅₉⋊C₈	1	4	yes	complemented
86	C₂²×C₄	Dic₁₁₈	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₅₉	1	2	yes	—
88	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
89	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
90	C₂×C₈	—	118	4	no	—
91	C₂×C₈	—	236	4	no	—
92	C₂³	—	2	2	no	—
93	C₂³	—	2	1	no	—
94	C₂³	—	2	1	no	—
95	C₂³	C₂×C₅₉⋊C₈	1	2	yes	—
96	C₂³	#11745664	1	2	yes	—
97	C₂³	C₄×Dic₅₉	1	1	yes	characteristic
98	C₂³	C₄⋊Dic₅₉	1	1	yes	characteristic
99	C₂³	C₂²⋊Dic₅₉	1	1	yes	characteristic
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	Dic₅₉⋊C₄	1	2	yes	—
110	C₂×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
111	C₈	—	236	4	no	—
112	C₂²	—	2	2	no	—
113	C₂²	—	2	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	2	1	no	—
120	C₂²	C₅₉⋊#95	1	1	yes	characteristic
121	C₂²	C₄×C₅₉⋊C₈	1	1	yes	characteristic
122	C₂²	#14273638	1	1	yes	characteristic
123	C₂²	C₂²⋊(C₅₉⋊C₈)	1	2	yes	—
124	C₂²	#14273642	1	2	yes	—
125	C₂²	#14273644	1	1	yes	characteristic
126	C₂²	#14273646	1	1	yes	characteristic
127	C₂²	C₄⋊(C₅₉⋊C₈)	1	2	yes	—
128	C₄	—	2	2	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	4	no	—
131	C₂	—	2	1	no	—
132	C₂	—	2	1	no	—
133	C₂	—	2	2	no	—
134	C₂	#16837126	1	2	yes	—
135	C₂	#16837128	1	2	yes	—
136	C₂	#16837157	1	1	yes	characteristic
137	C₂	#16837169	1	1	yes	characteristic
138	C₂	#16837171	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂²⋊(C₅₉⋊C₈)

C₂

yes

maximal

C₂×#95×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

—

C₂²⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

C₄

yes

complemented

C₂³×C₄×C₅₉

C₄

yes

—

C₂³×C₄×C₅₉

C₂²

yes

characteristic

#95×C₅₉

—

C₂⁴×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₈

yes

complemented

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

Q₈

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₄²

yes

characteristic

C₂³×C₅₉

C₂²⋊C₄

yes

characteristic

C₂³×C₅₉

C₄⋊C₄

yes

characteristic

C₂³×C₅₉

C₂×C₈

yes

—

C₂³×C₅₉

M₁₆

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#95

yes

characteristic

C₂²×C₅₉

C₄×C₈

yes

characteristic

C₂²×C₅₉

#97

yes

characteristic

C₂²×C₅₉

C₂²⋊C₈

yes

—

C₂²×C₅₉

#99

yes

—

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

C₄⋊C₈

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

#1280

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

#323

yes

—

C₂×C₅₉

#324

yes

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₂²⋊C₈

—

C₂×#95

D₅₉

yes

characteristic

C₅₉

#1280

yes

characteristic, complemented, Sylow

C₂³×C₄

Dic₅₉

yes

—

C₂³×C₄

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

118

—

C₂²⋊C₈

—

C₂²⋊C₈

—

118

—

#95

—

C₂⁴

C₂×Dic₅₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₅₉⋊C₈

yes

complemented

C₂²×C₄

Dic₁₁₈

yes

characteristic

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

D₂₃₆

yes

characteristic

C₂²×C₄

C₂²⋊D₅₉

yes

—

C₂×C₈

—

118

—

C₂×C₈

—

236

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂×C₅₉⋊C₈

yes

—

C₂³

#11745664

yes

—

C₂³

C₄×Dic₅₉

yes

characteristic

C₂³

C₄⋊Dic₅₉

yes

characteristic

C₂³

C₂²⋊Dic₅₉

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

Dic₅₉⋊C₄

yes

—

110

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

—

111

C₈

—

236

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₅₉⋊#95

yes

characteristic

121

C₂²

C₄×C₅₉⋊C₈

yes

characteristic

122

C₂²

#14273638

yes

characteristic

123

C₂²

C₂²⋊(C₅₉⋊C₈)

yes

—

124

C₂²

#14273642

yes

—

125

C₂²

#14273644

yes

characteristic

126

C₂²

#14273646

yes

characteristic

127

C₂²

C₄⋊(C₅₉⋊C₈)

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#16837126

yes

—

135

C₂

#16837128

yes

—

136

C₂

#16837157

yes

characteristic

137

C₂

#16837169

yes

characteristic

138

C₂

#16837171

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊Dic₅₉
commutator	C₂²×C₅₉	C₄×C₈
Frattini	C₂³×C₄	C₂×D₅₉
Fitting	C₂×#95×C₅₉	C₂
socle	C₂³×C₅₉	C₂²⋊C₄
hypercenter	C₂×#95	D₅₉
hypocenter	C₅₉	#1280
LCS	G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#95

subgroup

G/H

center

C₂³

C₂²⋊Dic₅₉

commutator

C₂²×C₅₉

C₄×C₈

Frattini

C₂³×C₄

C₂×D₅₉

Fitting

C₂×#95×C₅₉

C₂

socle

C₂³×C₅₉

C₂²⋊C₄

hypercenter

C₂×#95

D₅₉

hypocenter

C₅₉

#1280

LCS

G ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#95

N	H ≅ G/N	type
5. C₂²⋊(C₅₉⋊C₈)	C₄	semidirect
15. C₂²×C₄×C₅₉	C₈	semidirect
72. C₅₉	#1280	semidirect
85. C₂²×C₄	C₅₉⋊C₈	semidirect

H ≅ G/N

type

5. C₂²⋊(C₅₉⋊C₈)

C₄

semidirect

15. C₂²×C₄×C₅₉

C₈

semidirect

72. C₅₉

#1280

semidirect

85. C₂²×C₄

C₅₉⋊C₈

semidirect

Subgroups — #21421939

Conjugacy classes of subgroups

Complements