Group #21425679 — subgroups

Subgroups — #21425679

Order 7552.

148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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	#16837450	C₂	1	1	yes	maximal, characteristic
2	#16837429	C₂	1	1	yes	maximal, characteristic
3	#16837172	C₂	1	1	yes	maximal, characteristic
4	#16837166	C₂	1	1	yes	maximal, characteristic
5	#16837166	C₂	1	1	yes	maximal, characteristic
6	C₅₉⋊#338	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×#11745664	C₂²	1	1	yes	characteristic
9	C₂×#11745664	C₂²	1	1	yes	characteristic
10	C₂×#11745664	C₂²	1	1	yes	characteristic
11	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
12	#14273662	—	2	2	no	—
13	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
14	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
16	#117×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
18	M₁₆×C₅₉	—	2	1	no	—
19	M₁₆×C₅₉	—	2	1	no	—
20	M₁₆×C₅₉	—	2	1	no	—
21	M₁₆×C₅₉	—	2	1	no	—
22	C₂×C₈×C₅₉	—	2	1	no	—
23	C₂×C₈×C₅₉	—	2	1	no	—
24	C₄⋊C₄×C₅₉	—	2	1	no	—
25	C₂²⋊C₄×C₅₉	Q₈	1	2	yes	—
26	C₄²×C₅₉	—	2	1	no	—
27	#11745664	—	2	1	no	—
28	#11745664	—	2	1	no	—
29	#11745664	—	2	1	no	—
30	#11745664	—	2	1	no	—
31	#11745664	—	2	1	no	—
32	#11745664	—	2	1	no	—
33	C₂×C₅₉⋊C₈	—	2	1	no	—
34	C₂×C₅₉⋊C₈	—	2	1	no	—
35	C₂×C₅₉⋊C₈	—	2	1	no	—
36	C₂×C₅₉⋊C₈	—	2	1	no	—
37	C₂×C₅₉⋊C₈	—	2	1	no	—
38	C₂×C₅₉⋊C₈	D₄	1	2	yes	—
39	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₅₉	—	2	2	no	—
41	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
43	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
44	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
47	C₈×C₅₉	—	4	1	no	—
48	C₈×C₅₉	—	4	1	no	—
49	C₅₉⋊C₈	—	2	2	no	—
50	C₅₉⋊C₈	—	4	1	no	—
51	C₅₉⋊C₈	—	4	1	no	—
52	C₅₉⋊C₈	—	4	1	no	—
53	C₂²×C₅₉	—	4	1	no	—
54	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂²×C₅₉	#125	1	1	yes	characteristic
56	C₂²×C₅₉	#125	1	1	yes	characteristic
57	C₄×C₅₉	—	4	2	no	—
58	C₄×C₅₉	#123	1	1	yes	characteristic
59	C₄×C₅₉	#124	1	1	yes	characteristic
60	C₄×C₅₉	#126	1	1	yes	characteristic
61	C₄×C₅₉	#126	1	1	yes	characteristic
62	#2103	—	59	1	no	maximal, Sylow
63	C₂×C₅₉	—	2	1	no	—
64	C₂×C₅₉	—	2	1	no	—
65	C₂×C₅₉	—	2	1	no	—
66	C₂×C₅₉	#400	1	1	yes	characteristic
67	#430	—	59	1	no	—
68	#424	—	59	1	no	—
69	#344	—	59	1	no	—
70	#344	D₅₉	1	1	yes	characteristic
71	#341	—	59	1	no	—
72	#341	—	59	1	no	—
73	#338	—	59	1	no	—
74	C₅₉	#2103	1	1	yes	characteristic, complemented, Sylow
75	C₂×M₁₆	—	59	1	no	—
76	C₂×M₁₆	—	59	1	no	—
77	C₂×M₁₆	—	59	1	no	—
78	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
79	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
80	C₂²×C₈	—	59	1	no	—
81	#117	C₂×D₅₉	1	1	yes	characteristic
82	#108	—	118	2	no	—
83	C₄⋊C₈	—	118	2	no	—
84	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	2	1	no	—
87	M₁₆	—	2	1	no	—
88	M₁₆	—	2	1	no	—
89	M₁₆	—	118	1	no	—
90	M₁₆	—	118	1	no	—
91	M₁₆	—	118	1	no	—
92	M₁₆	—	118	1	no	—
93	M₁₆	—	118	1	no	—
94	M₁₆	—	118	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	59	2	no	—
98	C₂×C₈	—	118	1	no	—
99	C₂×C₈	—	118	1	no	—
100	C₂×C₈	—	118	1	no	—
101	C₂×C₈	—	118	1	no	—
102	C₂×C₈	—	118	1	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₂²⋊C₄	Dic₁₁₈	1	2	yes	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×Dic₁₁₈	1	1	yes	characteristic
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	#11745685	1	1	yes	characteristic
109	C₂×C₄	#11745685	1	1	yes	characteristic
110	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
111	C₂×C₄	#11745687	1	1	yes	characteristic
112	C₂×C₄	#11745687	1	1	yes	characteristic
113	C₂×C₄	#11745689	1	1	yes	characteristic
114	C₈	—	4	1	no	—
115	C₈	—	4	1	no	—
116	C₈	—	118	2	no	—
117	C₈	—	236	1	no	—
118	C₈	—	236	1	no	—
119	C₈	—	236	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	#14273704	1	1	yes	characteristic
122	C₂²	#14273718	1	1	yes	characteristic
123	C₂²	#14273719	1	1	yes	characteristic
124	C₄	—	4	2	no	—
125	C₄	#14273712	1	1	yes	characteristic
126	C₄	#14273713	1	1	yes	characteristic
127	C₄	#14273720	1	1	yes	characteristic
128	C₄	#14273722	1	1	yes	characteristic
129	C₂	—	2	1	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	#16837344	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837450

C₂

yes

maximal, characteristic

#16837429

C₂

yes

maximal, characteristic

#16837172

C₂

yes

maximal, characteristic

#16837166

C₂

yes

maximal, characteristic

#16837166

C₂

yes

maximal, characteristic

C₅₉⋊#338

C₂

yes

maximal, characteristic

C₅₉×#344

C₂

yes

maximal, characteristic

C₂×#11745664

C₂²

yes

characteristic

C₂×#11745664

C₂²

yes

characteristic

C₂×#11745664

C₂²

yes

characteristic

C₂²×C₅₉⋊C₈

C₂²

yes

characteristic

#14273662

—

C₄⋊(C₅₉⋊C₈)

—

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

#117×C₅₉

C₂²

yes

characteristic

C₂²×C₄×C₅₉

C₂³

yes

characteristic

M₁₆×C₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

Q₈

yes

—

C₄²×C₅₉

—

—

—

—

—

—

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

D₄

yes

—

C₂³×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²⋊Q₈

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

yes

—

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

—

—

—

D₅₉

yes

—

—

—

C₅₉

#2103

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

—

#117

C₂×D₅₉

yes

characteristic

#108

—

118

—

C₄⋊C₈

—

118

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

118

—

M₁₆

—

118

—

M₁₆

—

118

—

M₁₆

—

118

—

M₁₆

—

118

—

M₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

100

C₂×C₈

—

118

—

101

C₂×C₈

—

118

—

102

C₂×C₈

—

118

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

Dic₁₁₈

yes

—

105

C₄²

—

106

C₂³

C₂×Dic₁₁₈

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

#11745685

yes

characteristic

109

C₂×C₄

#11745685

yes

characteristic

110

C₂×C₄

D₄×D₅₉

yes

characteristic

111

C₂×C₄

#11745687

yes

characteristic

112

C₂×C₄

#11745687

yes

characteristic

113

C₂×C₄

#11745689

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

118

—

117

C₈

—

236

—

118

C₈

—

236

—

119

C₈

—

236

—

120

C₂²

—

121

C₂²

#14273704

yes

characteristic

122

C₂²

#14273718

yes

characteristic

123

C₂²

#14273719

yes

characteristic

124

C₄

—

125

C₄

#14273712

yes

characteristic

126

C₄

#14273713

yes

characteristic

127

C₄

#14273720

yes

characteristic

128

C₄

#14273722

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

—

132

C₂

#16837344

yes

characteristic

	subgroup	G/H
center	C₄	#14273713
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#344	C₂
socle	C₂×C₅₉	#400
hypercenter	#344	D₅₉
hypocenter	C₅₉	#2103
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₄

#14273713

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#344

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
74. C₅₉	#2103	semidirect

H ≅ G/N

type

74. C₅₉

#2103

semidirect

Subgroups — #21425679

Conjugacy classes of subgroups

Complements