Group #21422387 — subgroups

Subgroups — #21422387

Order 7552.

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

normal subgroups only

This group has 196 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	#16837453	C₂	1	1	yes	maximal, characteristic
2	#16837453	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#16837124	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837124	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837123	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₅₉	C₄	1	2	yes	—
9	C₄²×D₅₉	C₂²	1	1	yes	characteristic
10	Dic₅₉⋊C₈	C₄	1	2	yes	—
11	Dic₅₉⋊C₈	C₄	1	2	yes	—
12	(C₂×D₅₉)⋊C₈	C₄	1	2	yes	—
13	(C₂×D₅₉)⋊C₈	C₄	1	2	yes	—
14	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₈×Dic₅₉	C₄	1	2	yes	—
18	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
27	C₄²×C₅₉	C₂³	1	1	yes	characteristic
28	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
34	C₈×D₅₉	—	2	4	no	—
35	C₂²×D₅₉	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₅₉	C₄²	1	1	yes	characteristic
40	C₂×Dic₅₉	C₄²	1	1	yes	characteristic
41	C₂×Dic₅₉	C₄²	1	1	yes	characteristic
42	C₄×D₅₉	—	2	2	no	—
43	C₄×D₅₉	—	2	2	no	—
44	C₄×D₅₉	M₁₆	1	4	yes	—
45	C₈×C₅₉	—	2	2	no	—
46	C₈×C₅₉	—	2	2	no	—
47	C₈×C₅₉	—	2	2	no	—
48	C₅₉⋊C₈	—	2	2	no	—
49	C₅₉⋊C₈	—	2	2	no	—
50	C₅₉⋊C₈	—	2	2	no	—
51	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
52	C₂×D₅₉	—	2	1	no	—
53	C₂×D₅₉	—	2	1	no	—
54	C₂×D₅₉	#97	1	2	yes	—
55	C₄×C₅₉	C₂×M₁₆	1	2	yes	—
56	C₄×C₅₉	#131	1	2	yes	—
57	C₄×C₅₉	#131	1	2	yes	—
58	Dic₅₉	—	2	1	no	—
59	Dic₅₉	—	2	1	no	—
60	Dic₅₉	#97	1	2	yes	—
61	#1452	—	59	1	no	maximal, Sylow
62	C₂×C₅₉	C₂×#97	1	1	yes	characteristic
63	C₂×C₅₉	#405	1	1	yes	characteristic
64	C₂×C₅₉	#405	1	1	yes	characteristic
65	D₅₉	—	2	2	no	—
66	#431	—	59	1	no	—
67	#431	—	59	1	no	—
68	C₂×C₄×C₈	—	59	1	no	—
69	#322	—	59	1	no	—
70	#322	—	59	1	no	—
71	#322	—	59	1	no	—
72	#322	D₅₉	1	1	yes	characteristic, complemented
73	C₅₉	#1452	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₈	—	59	2	no	—
75	C₂×C₄²	—	59	1	no	—
76	C₄⋊C₈	—	59	2	no	—
77	C₄⋊C₈	—	59	2	no	—
78	C₂²⋊C₈	—	59	2	no	—
79	C₂²⋊C₈	—	59	2	no	—
80	C₄×C₈	—	59	2	no	—
81	C₄×C₈	—	59	1	no	—
82	C₄×C₈	—	59	1	no	—
83	C₄×C₈	—	59	1	no	—
84	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
85	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
86	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
87	C₂²×C₄	—	59	1	no	—
88	C₂²×C₄	—	59	1	no	—
89	C₂²×C₄	—	59	1	no	—
90	C₂×C₈	—	59	2	no	—
91	C₂×C₈	—	59	2	no	—
92	C₂×C₈	—	59	2	no	—
93	C₂×C₈	—	118	4	no	—
94	C₂×C₈	C₄×D₅₉	1	2	yes	—
95	C₂×C₈	C₄×D₅₉	1	2	yes	—
96	C₂×C₈	C₄×D₅₉	1	2	yes	—
97	C₄²	—	59	1	no	—
98	C₄²	—	59	1	no	—
99	C₄²	—	59	1	no	—
100	C₄²	C₂²×D₅₉	1	1	yes	characteristic
101	C₂³	—	59	1	no	—
102	C₂×C₄	—	59	1	no	—
103	C₂×C₄	—	59	4	no	—
104	C₂×C₄	—	59	1	no	—
105	C₂×C₄	—	59	1	no	—
106	C₂×C₄	—	118	2	no	—
107	C₂×C₄	—	118	2	no	—
108	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
109	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
110	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	2	2	no	—
113	C₈	—	2	2	no	—
114	C₈	—	118	2	no	—
115	C₈	—	118	2	no	—
116	C₈	—	118	2	no	—
117	C₂²	—	59	2	no	—
118	C₂²	—	118	1	no	—
119	C₂²	—	118	1	no	—
120	C₂²	C₄²×D₅₉	1	1	yes	characteristic
121	C₄	—	59	2	no	—
122	C₄	—	118	1	no	—
123	C₄	—	118	1	no	—
124	C₄	M₁₆×D₅₉	1	2	yes	—
125	C₄	#14273733	1	2	yes	—
126	C₄	#14273735	1	2	yes	—
127	C₂	—	118	2	no	—
128	C₂	#97×D₅₉	1	1	yes	characteristic
129	C₂	#16837356	1	1	yes	characteristic
130	C₂	#16837359	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837453

C₂

yes

maximal, characteristic

#16837453

C₂

yes

maximal, characteristic

C₄×C₈×D₅₉

C₂

yes

maximal, characteristic

#16837124

C₂

yes

maximal, characteristic, complemented

#16837124

C₂

yes

maximal, characteristic, complemented

#16837123

C₂

yes

maximal, characteristic, complemented

C₅₉×#322

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₅₉

C₄

yes

—

C₄²×D₅₉

C₂²

yes

characteristic

Dic₅₉⋊C₈

C₄

yes

—

Dic₅₉⋊C₈

C₄

yes

—

(C₂×D₅₉)⋊C₈

C₄

yes

—

(C₂×D₅₉)⋊C₈

C₄

yes

—

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₅₉

C₄

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₄×D₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₄×Dic₅₉

C₂×C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₈×D₅₉

—

C₂²×D₅₉

C₄²

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×Dic₅₉

C₄²

yes

characteristic

C₂×Dic₅₉

C₄²

yes

characteristic

C₂×Dic₅₉

C₄²

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

M₁₆

yes

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₄²

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

#97

yes

—

C₄×C₅₉

C₂×M₁₆

yes

—

C₄×C₅₉

#131

yes

—

C₄×C₅₉

#131

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

#97

yes

—

#1452

—

maximal, Sylow

C₂×C₅₉

C₂×#97

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

D₅₉

—

#431

—

#431

—

C₂×C₄×C₈

—

—

—

—

D₅₉

yes

characteristic, complemented

C₅₉

#1452

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₄×C₈

C₂×D₅₉

yes

characteristic

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₄×D₅₉

yes

—

C₂×C₈

C₄×D₅₉

yes

—

C₂×C₈

C₄×D₅₉

yes

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

C₂²×D₅₉

yes

characteristic

101

C₂³

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

118

—

107

C₂×C₄

—

118

—

108

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

109

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

110

C₂×C₄

C₂×C₄×D₅₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

114

C₈

—

118

—

115

C₈

—

118

—

116

C₈

—

118

—

117

C₂²

—

118

C₂²

—

118

—

119

C₂²

—

118

—

120

C₂²

C₄²×D₅₉

yes

characteristic

121

C₄

—

122

C₄

—

118

—

123

C₄

—

118

—

124

C₄

M₁₆×D₅₉

yes

—

125

C₄

#14273733

yes

—

126

C₄

#14273735

yes

—

127

C₂

—

118

—

128

C₂

#97×D₅₉

yes

characteristic

129

C₂

#16837356

yes

characteristic

130

C₂

#16837359

yes

characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₅₉
commutator, socle	C₂²×C₅₉	C₂×C₄²
Fitting	C₅₉×#322	C₂
hypercenter	#322	D₅₉
hypocenter	C₅₉	#1452
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄² ◁ #322

subgroup

G/H

center, Frattini

C₄²

C₂²×D₅₉

commutator, socle

C₂²×C₅₉

C₂×C₄²

Fitting

C₅₉×#322

C₂

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₄² ◁ #322

N	H ≅ G/N	type
4. #16837124	C₂	semidirect
5. #16837124	C₂	semidirect
6. #16837123	C₂	semidirect
7. C₅₉×#322	C₂	semidirect
72. #322	D₅₉	semidirect
73. C₅₉	#1452	semidirect

H ≅ G/N

type

4. #16837124

C₂

semidirect

5. #16837124

C₂

semidirect

6. #16837123

C₂

semidirect

7. C₅₉×#322

C₂

semidirect

72. #322

D₅₉

semidirect

73. C₅₉

#1452

semidirect

Subgroups — #21422387

Conjugacy classes of subgroups

Complements