Group #21424240 — subgroups

Subgroups — #21424240

Order 7552.

196 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 85 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	#16837248	C₂	1	1	yes	maximal, characteristic
2	#16837157	C₂	1	1	yes	maximal, characteristic
3	#16837156	C₂	1	2	yes	maximal
4	#16837156	C₂	1	2	yes	maximal
5	C₅₉×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
9	C₅₉⋊#95	C₄	1	2	yes	—
10	C₅₉⋊#95	C₄	1	2	yes	—
11	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₅₉	—	2	2	no	—
19	C₂×C₈×C₅₉	—	2	2	no	—
20	C₂×C₈×C₅₉	—	2	2	no	—
21	C₄²×C₅₉	—	2	2	no	—
22	C₄×Dic₅₉	—	2	2	no	—
23	C₄×Dic₅₉	—	2	1	no	—
24	C₄×Dic₅₉	—	2	1	no	—
25	C₂×C₅₉⋊C₈	—	2	2	no	—
26	C₂×C₅₉⋊C₈	—	2	2	no	—
27	C₂×C₅₉⋊C₈	—	2	2	no	—
28	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₅₉	—	2	2	no	—
30	C₂×C₄×C₅₉	—	2	2	no	—
31	C₂×C₄×C₅₉	—	2	2	no	—
32	C₂×C₄×C₅₉	#41	1	2	yes	—
33	C₂×C₄×C₅₉	#41	1	2	yes	—
34	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
35	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
36	C₂×Dic₅₉	—	2	1	no	—
37	C₂×Dic₅₉	—	2	1	no	—
38	C₂×Dic₅₉	—	2	2	no	—
39	C₂×Dic₅₉	—	2	2	no	—
40	C₂×Dic₅₉	—	2	2	no	—
41	C₂×Dic₅₉	—	2	2	no	—
42	C₂×Dic₅₉	—	2	2	no	—
43	C₈×C₅₉	—	4	2	no	—
44	C₅₉⋊C₈	—	4	2	no	—
45	C₂²×C₅₉	#117	1	1	yes	characteristic
46	C₂²×C₅₉	#117	1	1	yes	characteristic
47	C₂²×C₅₉	#117	1	1	yes	characteristic
48	C₂²×C₅₉	#131	1	2	yes	—
49	C₂²×C₅₉	#131	1	2	yes	—
50	C₄×C₅₉	—	4	2	no	—
51	C₄×C₅₉	#126	1	2	yes	—
52	C₄×C₅₉	#126	1	2	yes	—
53	Dic₅₉	—	4	1	no	—
54	Dic₅₉	—	4	2	no	—
55	Dic₅₉	—	4	1	no	—
56	#1840	—	59	1	no	maximal, Sylow
57	C₂×C₅₉	#383	1	1	yes	characteristic
58	C₂×C₅₉	#433	1	2	yes	—
59	C₂×C₅₉	#433	1	1	yes	characteristic
60	C₂×C₅₉	#433	1	2	yes	—
61	C₂×C₅₉	#433	1	1	yes	characteristic
62	#376	—	59	1	no	—
63	#336	—	59	2	no	—
64	#336	—	59	2	no	—
65	#336	—	59	1	no	—
66	#336	D₅₉	1	1	yes	characteristic
67	C₅₉	#1840	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₈	—	59	2	no	—
69	C₂²×C₈	C₂×D₅₉	1	2	yes	—
70	C₂×C₄²	—	59	1	no	—
71	C₂×C₄²	—	59	1	no	—
72	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
73	#95	—	59	2	no	—
74	#95	—	59	2	no	—
75	C₂²×C₄	—	59	1	no	—
76	C₂²×C₄	—	59	1	no	—
77	C₂²×C₄	—	59	2	no	—
78	C₂²×C₄	C₄×D₅₉	1	2	yes	—
79	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	118	2	no	—
84	C₂×C₈	—	118	2	no	—
85	C₂×C₈	—	118	2	no	—
86	C₄²	—	2	2	no	—
87	C₄²	—	118	2	no	—
88	C₄²	—	118	1	no	—
89	C₄²	—	118	1	no	—
90	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	118	1	no	—
95	C₂×C₄	—	118	1	no	—
96	C₂×C₄	—	118	2	no	—
97	C₂×C₄	—	118	2	no	—
98	C₂×C₄	—	118	2	no	—
99	C₂×C₄	—	118	2	no	—
100	C₂×C₄	—	118	2	no	—
101	C₂×C₄	#11745685	1	2	yes	—
102	C₂×C₄	#11745687	1	1	yes	characteristic
103	C₂×C₄	#11745687	1	2	yes	—
104	C₂×C₄	#11745689	1	1	yes	characteristic
105	C₈	—	4	2	no	—
106	C₈	—	236	2	no	—
107	C₂²	#14273683	1	1	yes	characteristic
108	C₂²	#14273684	1	1	yes	characteristic
109	C₂²	#14273685	1	1	yes	characteristic
110	C₂²	#14273733	1	2	yes	—
111	C₂²	#14273735	1	2	yes	—
112	C₄	—	4	2	no	—
113	C₄	—	236	1	no	—
114	C₄	—	236	2	no	—
115	C₄	—	236	1	no	—
116	C₄	#14273720	1	2	yes	—
117	C₄	#14273722	1	2	yes	—
118	C₂	#16837269	1	1	yes	characteristic
119	C₂	#16837460	1	2	yes	—
120	C₂	#16837461	1	1	yes	characteristic
121	C₂	#16837462	1	2	yes	—
122	C₂	#16837464	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837248

C₂

yes

maximal, characteristic

#16837157

C₂

yes

maximal, characteristic

#16837156

C₂

yes

maximal

#16837156

C₂

yes

maximal

C₅₉×#336

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₅₉⋊#95

C₄

yes

—

C₅₉⋊#95

C₄

yes

—

C₂²×C₈×C₅₉

C₂²

yes

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

characteristic

C₂²×Dic₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₂²×C₅₉

#131

yes

—

C₄×C₅₉

—

C₄×C₅₉

#126

yes

—

C₄×C₅₉

#126

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#433

yes

characteristic

C₂×C₅₉

#433

yes

—

C₂×C₅₉

yes

—

—

—

—

D₅₉

yes

characteristic

C₅₉

#1840

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅₉

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₄²

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

—

118

—

C₂³

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

100

C₂×C₄

—

118

—

101

C₂×C₄

#11745685

yes

—

102

C₂×C₄

#11745687

yes

characteristic

103

C₂×C₄

#11745687

yes

—

104

C₂×C₄

#11745689

yes

characteristic

105

C₈

—

106

C₈

—

236

—

107

C₂²

#14273683

yes

characteristic

108

C₂²

#14273684

yes

characteristic

109

C₂²

#14273685

yes

characteristic

110

C₂²

#14273733

yes

—

111

C₂²

#14273735

yes

—

112

C₄

—

113

C₄

—

236

—

114

C₄

—

236

—

115

C₄

—

236

—

116

C₄

#14273720

yes

—

117

C₄

#14273722

yes

—

118

C₂

#16837269

yes

characteristic

119

C₂

#16837460

yes

—

120

C₂

#16837461

yes

characteristic

121

C₂

#16837462

yes

—

122

C₂

#16837464

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator, socle	C₂³×C₅₉	C₂²×C₄
Fitting	C₅₉×#336	C₂
hypercenter	#336	D₅₉
hypocenter	C₅₉	#1840
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅₉

commutator, socle

C₂³×C₅₉

C₂²×C₄

Fitting

C₅₉×#336

C₂

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
67. C₅₉	#1840	semidirect

H ≅ G/N

type

67. C₅₉

#1840

semidirect

Subgroups — #21424240

Conjugacy classes of subgroups

Complements