Group #21434411 — subgroups

Subgroups — C₂×#16837756 #21434411

Order 7552.

412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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, complemented
2	#16837756	C₂	1	8	yes	maximal, direct product factor
3	C₂×#14273651	C₂	1	2	yes	maximal, complemented
4	C₂×#14273648	C₂	1	2	yes	maximal
5	C₂×C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#124×C₅₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
8	#14273719	—	2	2	no	—
9	#14273719	C₂²	1	4	yes	complemented
10	C₂×C₄⋊Dic₅₉	C₂²	1	2	yes	—
11	C₂×Dic₅₉⋊C₄	—	2	2	no	—
12	#14273651	C₂²	1	8	yes	complemented
13	#14273648	C₂²	1	8	yes	—
14	C₄×C₅₉⋊C₈	C₂²	1	4	yes	complemented
15	C₂²×Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₅₉	C₂²	1	1	yes	characteristic
17	#124×C₅₉	—	2	2	no	—
18	#124×C₅₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
20	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
21	C₂⁴×C₅₉	—	2	1	no	—
22	C₂×Q₈×C₅₉	—	2	1	no	—
23	C₂×Q₈×C₅₉	—	2	4	no	—
24	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
25	C₂×D₄×C₅₉	—	2	1	no	—
26	C₂×D₄×C₅₉	—	2	4	no	—
27	C₂×D₄×C₅₉	C₂³	1	2	yes	—
28	C₂²×C₄×C₅₉	—	2	1	no	—
29	C₂²×C₄×C₅₉	D₄	1	2	yes	—
30	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₅₉	—	2	2	no	—
32	C₂²⋊C₄×C₅₉	—	2	8	no	—
33	C₄²×C₅₉	D₄	1	2	yes	—
34	C₄²×C₅₉	C₂³	1	2	yes	—
35	C₄⋊Dic₅₉	—	2	2	no	—
36	C₄⋊Dic₅₉	C₂³	1	4	yes	—
37	Dic₅₉⋊C₄	—	2	8	no	—
38	C₂×C₅₉⋊C₈	—	2	4	no	—
39	C₂×C₅₉⋊C₈	C₂³	1	4	yes	—
40	C₂³×C₅₉	—	2	2	no	—
41	C₂³×C₅₉	—	4	2	no	—
42	C₂³×C₅₉	—	4	4	no	—
43	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₅₉	—	2	4	no	—
45	Q₈×C₅₉	—	4	2	no	—
46	D₄×C₅₉	—	2	4	no	—
47	D₄×C₅₉	—	4	2	no	—
48	C₂×C₄×C₅₉	—	2	4	no	—
49	C₂×C₄×C₅₉	—	2	2	no	—
50	C₂×C₄×C₅₉	—	4	2	no	—
51	C₂×C₄×C₅₉	C₂×D₄	1	4	yes	—
52	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₅₉	#41	1	4	yes	—
54	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
55	C₂×Dic₅₉	—	2	4	no	—
56	C₂×Dic₅₉	—	4	4	no	—
57	C₅₉⋊C₈	—	2	4	no	—
58	C₂²×C₅₉	—	4	2	no	—
59	C₂²×C₅₉	—	4	4	no	—
60	C₂²×C₅₉	—	8	4	no	—
61	C₂²×C₅₉	#124	1	2	yes	—
62	C₂²×C₅₉	#135	1	4	yes	—
63	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
64	C₄×C₅₉	—	2	4	no	—
65	C₄×C₅₉	—	4	2	no	—
66	C₄×C₅₉	#124	1	2	yes	—
67	C₄×C₅₉	C₂×#41	1	2	yes	—
68	Dic₅₉	—	4	4	no	—
69	C₂×#488	—	59	1	no	maximal, Sylow
70	C₂×C₅₉	—	8	2	no	—
71	C₂×C₅₉	#488	1	4	yes	complemented
72	C₂×C₅₉	C₂×#124	1	1	yes	characteristic
73	C₂×C₅₉	C₂×#135	1	2	yes	—
74	C₂×#125	—	59	1	no	—
75	C₂×#124	D₅₉	1	1	yes	characteristic
76	#488	—	59	8	no	—
77	C₂×#103	—	59	2	no	—
78	C₂×#102	—	59	2	no	—
79	C₂×C₄×C₈	—	59	1	no	—
80	C₅₉	C₂×#488	1	1	yes	characteristic, complemented, Sylow
81	C₂²×Q₈	C₂×D₅₉	1	1	yes	characteristic
82	C₂²×D₄	C₂×D₅₉	1	1	yes	characteristic
83	C₂²×C₈	—	59	2	no	—
84	#125	—	59	4	no	—
85	#125	—	118	2	no	—
86	#124	—	2	2	no	—
87	#124	C₂×D₅₉	1	4	yes	—
88	C₂×C₄⋊C₄	—	59	2	no	—
89	C₂×C₄⋊C₄	—	118	2	no	—
90	C₂×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
92	#103	—	59	8	no	—
93	#102	—	59	8	no	—
94	C₄×C₈	—	59	4	no	—
95	C₂⁴	—	2	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	2	4	no	—
98	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
99	C₂×D₄	—	2	4	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	C₂²×D₅₉	1	2	yes	—
102	C₂²×C₄	—	2	1	no	—
103	C₂²×C₄	—	118	2	no	—
104	C₂²×C₄	C₂²⋊D₅₉	1	2	yes	—
105	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
106	C₂×C₈	—	59	4	no	—
107	C₂×C₈	—	118	4	no	—
108	C₄⋊C₄	—	59	4	no	—
109	C₄⋊C₄	—	118	2	no	—
110	C₄⋊C₄	—	118	8	no	—
111	C₂²⋊C₄	—	2	8	no	—
112	C₄²	C₂²⋊D₅₉	1	2	yes	—
113	C₄²	C₂²×D₅₉	1	2	yes	—
114	C₂³	—	2	2	no	—
115	C₂³	—	4	2	no	—
116	C₂³	—	4	4	no	—
117	C₂³	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
118	Q₈	—	2	4	no	—
119	Q₈	—	4	2	no	—
120	D₄	—	2	4	no	—
121	D₄	—	4	2	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	118	4	no	—
126	C₂×C₄	—	236	4	no	—
127	C₂×C₄	#11745687	1	4	yes	—
128	C₂×C₄	C₂×C₂²⋊D₅₉	1	4	yes	—
129	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
130	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
131	C₈	—	118	4	no	—
132	C₂²	—	4	2	no	—
133	C₂²	—	4	4	no	—
134	C₂²	—	8	4	no	—
135	C₂²	#14273714	1	2	yes	—
136	C₂²	#14273747	1	4	yes	—
137	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
138	C₄	—	2	4	no	—
139	C₄	—	4	2	no	—
140	C₄	—	236	4	no	—
141	C₄	#14273714	1	2	yes	—
142	C₄	C₂×#11745687	1	2	yes	—
143	C₂	—	8	2	no	—
144	C₂	#16837756	1	4	yes	direct product factor
145	C₂	C₂×#14273714	1	1	yes	characteristic
146	C₂	C₂×#14273747	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273719

C₂

yes

maximal, characteristic, complemented

#16837756

C₂

yes

maximal, direct product factor

C₂×#14273651

C₂

yes

maximal, complemented

C₂×#14273648

C₂

yes

maximal

C₂×C₄×C₅₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#124×C₅₉

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

#14273719

—

#14273719

C₂²

yes

complemented

C₂×C₄⋊Dic₅₉

C₂²

yes

—

C₂×Dic₅₉⋊C₄

—

#14273651

C₂²

yes

complemented

#14273648

C₂²

yes

—

C₄×C₅₉⋊C₈

C₂²

yes

complemented

C₂²×Q₈×C₅₉

C₂²

yes

characteristic

C₂²×D₄×C₅₉

C₂²

yes

characteristic

#124×C₅₉

—

#124×C₅₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂⁴×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

C₂³

yes

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

C₂³

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

D₄

yes

—

C₄²×C₅₉

C₂³

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

Dic₅₉⋊C₄

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#124

yes

—

C₂²×C₅₉

#135

yes

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#124

yes

—

C₄×C₅₉

C₂×#41

yes

—

Dic₅₉

—

C₂×#488

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×#125

—

C₂×#124

D₅₉

yes

—

—

—

C₂×C₄×C₈

—

C₅₉

C₂×#488

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₅₉

yes

characteristic

C₂²×D₄

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

#125

—

#125

—

118

—

#124

—

#124

C₂×D₅₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

118

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#103

—

#102

—

C₄×C₈

—

C₂⁴

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₅₉

yes

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

C₂²×D₅₉

yes

—

102

C₂²×C₄

—

103

C₂²×C₄

—

118

—

104

C₂²×C₄

C₂²⋊D₅₉

yes

—

105

C₂²×C₄

C₂²×D₅₉

yes

characteristic

106

C₂×C₈

—

107

C₂×C₈

—

118

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

118

—

110

C₄⋊C₄

—

118

—

111

C₂²⋊C₄

—

112

C₄²

C₂²⋊D₅₉

yes

—

113

C₄²

C₂²×D₅₉

yes

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

C₂×C₂²⋊D₅₉

yes

characteristic

118

Q₈

—

119

Q₈

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

118

—

126

C₂×C₄

—

236

—

127

C₂×C₄

#11745687

yes

—

128

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

129

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

130

C₂×C₄

C₂³×D₅₉

yes

characteristic

131

C₈

—

118

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

#14273714

yes

—

136

C₂²

#14273747

yes

—

137

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

236

—

141

C₄

#14273714

yes

—

142

C₄

C₂×#11745687

yes

—

143

C₂

—

144

C₂

#16837756

yes

direct product factor

145

C₂

C₂×#14273714

yes

characteristic

146

C₂

C₂×#14273747

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₂×#124×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×#124	D₅₉
hypocenter	C₅₉	C₂×#488
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₂×#124×C₅₉

C₂

socle

C₂³×C₅₉

C₂×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#14273719	C₂	semidirect
2. #16837756	C₂	direct (N × H)
3. C₂×#14273651	C₂	semidirect
5. C₂×C₄×C₅₉⋊C₈	C₂	semidirect
9. #14273719	C₂²	semidirect
12. #14273651	C₂²	semidirect
14. C₄×C₅₉⋊C₈	C₂²	semidirect
71. C₂×C₅₉	#488	semidirect
80. C₅₉	C₂×#488	semidirect
144. C₂	#16837756	direct (N × H)

H ≅ G/N

type

1. C₂×#14273719

C₂

semidirect

2. #16837756

C₂

direct (N × H)

3. C₂×#14273651

C₂

semidirect

5. C₂×C₄×C₅₉⋊C₈

C₂

semidirect

9. #14273719

C₂²

semidirect

12. #14273651

C₂²

semidirect

14. C₄×C₅₉⋊C₈

C₂²

semidirect

71. C₂×C₅₉

#488

semidirect

80. C₅₉

C₂×#488

semidirect

144. C₂

#16837756

direct (N × H)

Subgroups — C₂×#16837756 #21434411

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16837756 #21434411

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16837756 #21434411