Group #21423843 — subgroups

Subgroups — #21423843

Order 7552.

272 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14273637	C₂	1	2	yes	maximal
2	C₄²×Dic₅₉	C₂	1	1	yes	maximal, characteristic
3	#16837157	C₂	1	1	yes	maximal, characteristic
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	C₄	1	2	yes	—
8	C₂×C₄×Dic₅₉	C₄	1	2	yes	—
9	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
11	#14273637	C₄	1	8	yes	complemented
12	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
16	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₅₉	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₅₉	—	2	2	no	—
20	C₂×C₈×C₅₉	—	2	2	no	—
21	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
22	C₄²×C₅₉	—	2	2	no	—
23	C₄×Dic₅₉	—	2	4	no	—
24	C₄×Dic₅₉	—	2	1	no	—
25	C₄×Dic₅₉	—	2	1	no	—
26	C₄×Dic₅₉	—	2	4	no	—
27	C₄×Dic₅₉	C₂×C₄	1	4	yes	—
28	C₂×C₅₉⋊C₈	—	2	2	no	—
29	C₂×C₅₉⋊C₈	—	2	2	no	—
30	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
31	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	—	2	2	no	—
33	C₂×C₄×C₅₉	—	2	2	no	—
34	C₂×C₄×C₅₉	M₁₆	1	4	yes	—
35	C₂×C₄×C₅₉	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₅₉	#41	1	2	yes	—
37	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
38	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
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	C₂×Dic₅₉	C₄²	1	2	yes	—
44	C₂×Dic₅₉	C₄²	1	2	yes	—
45	C₂×Dic₅₉	M₁₆	1	4	yes	—
46	C₈×C₅₉	—	2	4	no	—
47	C₅₉⋊C₈	—	2	4	no	—
48	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
49	C₂²×C₅₉	#117	1	1	yes	characteristic
50	C₂²×C₅₉	#117	1	1	yes	characteristic
51	C₂²×C₅₉	C₂×M₁₆	1	2	yes	—
52	C₂²×C₅₉	C₂×M₁₆	1	2	yes	—
53	C₄×C₅₉	—	2	4	no	—
54	C₄×C₅₉	#117	1	2	yes	—
55	C₄×C₅₉	#117	1	2	yes	—
56	Dic₅₉	—	2	2	no	—
57	Dic₅₉	—	2	2	no	—
58	Dic₅₉	—	2	4	no	—
59	#1745	—	59	1	no	maximal, Sylow
60	C₂×C₅₉	#376	1	1	yes	characteristic
61	C₂×C₅₉	C₄×M₁₆	1	1	yes	characteristic
62	C₂×C₅₉	C₄×M₁₆	1	1	yes	characteristic
63	C₂×C₅₉	#432	1	2	yes	—
64	C₂×C₅₉	#432	1	2	yes	—
65	C₂×#97	—	59	2	no	—
66	C₄³	—	59	1	no	—
67	#336	—	59	2	no	—
68	#336	—	59	1	no	—
69	#336	D₅₉	1	1	yes	characteristic
70	C₅₉	#1745	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₈	—	59	2	no	—
72	C₂²×C₈	C₂×D₅₉	1	2	yes	—
73	C₂×C₄²	—	59	1	no	—
74	C₂×C₄²	—	59	2	no	—
75	C₂×C₄²	—	59	2	no	—
76	C₂×C₄²	—	59	1	no	—
77	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
78	#97	—	59	8	no	—
79	C₂²×C₄	—	59	1	no	—
80	C₂²×C₄	—	59	1	no	—
81	C₂²×C₄	—	59	2	no	—
82	C₂²×C₄	C₄×D₅₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	59	4	no	—
87	C₂×C₈	—	118	2	no	—
88	C₂×C₈	—	118	2	no	—
89	C₂×C₈	C₄×D₅₉	1	4	yes	—
90	C₄²	—	2	2	no	—
91	C₄²	—	59	4	no	—
92	C₄²	—	118	4	no	—
93	C₄²	—	118	4	no	—
94	C₄²	—	118	1	no	—
95	C₄²	—	118	1	no	—
96	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	59	2	no	—
100	C₂×C₄	—	59	2	no	—
101	C₂×C₄	—	59	4	no	—
102	C₂×C₄	—	118	2	no	—
103	C₂×C₄	—	118	2	no	—
104	C₂×C₄	—	118	2	no	—
105	C₂×C₄	—	118	2	no	—
106	C₂×C₄	#11745659	1	4	yes	—
107	C₂×C₄	C₂×C₄×D₅₉	1	2	yes	—
108	C₂×C₄	#11745687	1	1	yes	characteristic
109	C₂×C₄	#11745687	1	2	yes	—
110	C₂×C₄	#11745689	1	1	yes	characteristic
111	C₈	—	2	4	no	—
112	C₈	—	118	4	no	—
113	C₂²	C₄²×D₅₉	1	1	yes	characteristic
114	C₂²	#14273683	1	1	yes	characteristic
115	C₂²	#14273685	1	1	yes	characteristic
116	C₂²	M₁₆×D₅₉	1	2	yes	—
117	C₂²	C₂×#11745659	1	2	yes	—
118	C₄	—	2	4	no	—
119	C₄	—	118	4	no	—
120	C₄	—	118	2	no	—
121	C₄	—	118	2	no	—
122	C₄	#14273683	1	2	yes	—
123	C₄	#14273685	1	2	yes	—
124	C₂	#16837247	1	1	yes	characteristic
125	C₂	C₄×#11745659	1	1	yes	characteristic
126	C₂	#16837354	1	1	yes	characteristic
127	C₂	#16837456	1	2	yes	—
128	C₂	#16837458	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273637

C₂

yes

maximal

C₄²×Dic₅₉

C₂

yes

maximal, characteristic

#16837157

C₂

yes

maximal, characteristic

#16837156

C₂

yes

maximal

C₅₉×#336

C₂

yes

maximal, characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₄

yes

—

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×Dic₅₉

C₂²

yes

characteristic

#14273637

C₄

yes

complemented

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

C₂×C₄

yes

—

C₄²×C₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₂×C₄

yes

—

C₂³×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

M₁₆

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

—

C₂×C₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

C₄²

yes

—

C₂×Dic₅₉

M₁₆

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

C₂×C₄²

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

C₂×M₁₆

yes

—

C₂²×C₅₉

C₂×M₁₆

yes

—

C₄×C₅₉

—

C₄×C₅₉

#117

yes

—

C₄×C₅₉

#117

yes

—

Dic₅₉

—

Dic₅₉

—

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

C₄×M₁₆

yes

characteristic

C₂×C₅₉

C₄×M₁₆

yes

characteristic

C₂×C₅₉

#432

yes

—

C₂×C₅₉

#432

yes

—

C₂×#97

—

C₄³

—

#336

—

#336

—

#336

D₅₉

yes

characteristic

C₅₉

#1745

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#97

—

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

C₄×D₅₉

yes

—

C₄²

—

C₄²

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

—

118

—

C₂³

C₂×C₄×D₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

118

—

103

C₂×C₄

—

118

—

104

C₂×C₄

—

118

—

105

C₂×C₄

—

118

—

106

C₂×C₄

#11745659

yes

—

107

C₂×C₄

C₂×C₄×D₅₉

yes

—

108

C₂×C₄

#11745687

yes

characteristic

109

C₂×C₄

#11745687

yes

—

110

C₂×C₄

#11745689

yes

characteristic

111

C₈

—

112

C₈

—

118

—

113

C₂²

C₄²×D₅₉

yes

characteristic

114

C₂²

#14273683

yes

characteristic

115

C₂²

#14273685

yes

characteristic

116

C₂²

M₁₆×D₅₉

yes

—

117

C₂²

C₂×#11745659

yes

—

118

C₄

—

119

C₄

—

118

—

120

C₄

—

118

—

121

C₄

—

118

—

122

C₄

#14273683

yes

—

123

C₄

#14273685

yes

—

124

C₂

#16837247

yes

characteristic

125

C₂

C₄×#11745659

yes

characteristic

126

C₂

#16837354

yes

characteristic

127

C₂

#16837456

yes

—

128

C₂

#16837458

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂×C₄²
Fitting	C₅₉×#336	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	#336	D₅₉
hypocenter	C₅₉	#1745
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #336

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅₉

commutator

C₂²×C₅₉

C₂×C₄²

Fitting

C₅₉×#336

C₂

socle

C₂³×C₅₉

C₂²×C₄

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ #336

N	H ≅ G/N	type
11. #14273637	C₄	semidirect
70. C₅₉	#1745	semidirect

H ≅ G/N

type

11. #14273637

C₄

semidirect

70. C₅₉

#1745

semidirect

Subgroups — #21423843

Conjugacy classes of subgroups

Complements