Group #35309188 — subgroups

Subgroups — #35309188

Order 21248.

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

normal subgroups only

This group has 272 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	#24908444	C₂	1	1	yes	maximal, characteristic
2	#24906121	C₂	1	2	yes	maximal
3	#24905360	C₂	1	2	yes	maximal
4	#24905292	C₂	1	1	yes	maximal, characteristic
5	C₈₃×#1832	C₂	1	1	yes	maximal, characteristic
6	#19128258	C₂²	1	1	yes	characteristic
7	#19127754	C₂²	1	2	yes	—
8	#19127725	C₂²	1	1	yes	characteristic
9	#19127461	—	2	2	no	—
10	#19127449	—	2	2	no	—
11	#19127446	—	2	2	no	—
12	C₂×C₄⋊C₈×C₈₃	C₂²	1	2	yes	—
13	#376×C₈₃	C₂²	1	1	yes	characteristic
14	#336×C₈₃	—	2	2	no	—
15	C₂×#13050574	—	2	1	no	—
16	#14581792	D₄	1	2	yes	—
17	#14581784	—	2	1	no	—
18	#14581771	—	2	2	no	—
19	C₄×Dic₁₆₆	—	2	2	no	—
20	#14581751	—	2	1	no	—
21	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
22	C₄⋊(C₈₃⋊C₈)	—	2	2	no	—
23	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
24	C₄×C₈₃⋊C₈	—	2	2	no	—
25	C₂²×C₈×C₈₃	—	2	2	no	—
26	C₂×C₄²×C₈₃	D₄	1	2	yes	—
27	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
28	C₄⋊C₈×C₈₃	—	2	2	no	—
29	C₄⋊C₈×C₈₃	—	2	2	no	—
30	#95×C₈₃	—	2	2	no	—
31	C₂×Dic₁₆₆	—	2	2	no	—
32	#13050574	—	4	2	no	—
33	C₂×C₈₃⋊C₈	—	4	2	no	—
34	C₂×C₈₃⋊C₈	—	4	1	no	—
35	C₄⋊Dic₈₃	—	2	2	no	—
36	C₄⋊Dic₈₃	—	2	2	no	—
37	Dic₈₃⋊C₄	—	4	2	no	—
38	C₂²⋊Dic₈₃	—	4	1	no	—
39	C₄×Dic₈₃	—	4	1	no	—
40	C₂²×C₄×C₈₃	—	2	2	no	—
41	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₈₃	#41	1	2	yes	—
43	C₂×C₈×C₈₃	—	4	2	no	—
44	C₂×C₈×C₈₃	—	4	2	no	—
45	C₂×C₈×C₈₃	—	4	2	no	—
46	C₄²×C₈₃	—	2	2	no	—
47	C₄²×C₈₃	—	2	2	no	—
48	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
49	C₄²×C₈₃	#41	1	1	yes	characteristic
50	C₄²×C₈₃	#41	1	2	yes	—
51	C₂³×C₈₃	#123	1	1	yes	characteristic
52	C₂×C₄×C₈₃	—	4	2	no	—
53	C₂×C₄×C₈₃	—	4	4	no	—
54	C₂×C₄×C₈₃	—	4	2	no	—
55	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
56	C₂×C₄×C₈₃	#123	1	2	yes	—
57	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
58	C₂×C₄×C₈₃	#126	1	2	yes	—
59	C₂×C₄×C₈₃	#135	1	2	yes	—
60	C₂×C₄×C₈₃	#137	1	2	yes	—
61	C₂×Dic₈₃	—	4	2	no	—
62	Dic₁₆₆	—	8	2	no	—
63	C₈×C₈₃	—	8	2	no	—
64	C₈₃⋊C₈	—	8	2	no	—
65	C₈₃⋊C₈	—	8	1	no	—
66	C₂²×C₈₃	—	2	2	no	—
67	C₂²×C₈₃	#397	1	1	yes	characteristic
68	C₂²×C₈₃	#485	1	2	yes	—
69	C₄×C₈₃	—	2	2	no	—
70	C₄×C₈₃	—	2	2	no	—
71	C₄×C₈₃	—	8	2	no	—
72	C₄×C₈₃	#464	1	2	yes	—
73	C₄×C₈₃	#488	1	1	yes	characteristic
74	C₄×C₈₃	#491	1	1	yes	characteristic
75	Dic₈₃	—	8	2	no	—
76	#10630	—	83	1	no	maximal, Sylow
77	C₂×C₈₃	—	2	2	no	—
78	C₂×C₈₃	#2074	1	1	yes	characteristic
79	C₂×C₈₃	#2080	1	2	yes	—
80	#1995	—	83	1	no	—
81	#1832	D₈₃	1	1	yes	characteristic
82	#1542	—	83	2	no	—
83	#1301	—	83	2	no	—
84	#1274	—	83	1	no	—
85	C₈₃	#10630	1	1	yes	characteristic, complemented, Sylow
86	#533	—	83	1	no	—
87	#431	—	83	2	no	—
88	#423	—	83	1	no	—
89	C₂×C₄⋊C₈	C₂×D₈₃	1	2	yes	—
90	#376	C₂×D₈₃	1	1	yes	characteristic
91	#339	—	166	2	no	—
92	#336	—	2	2	no	—
93	#333	—	166	2	no	—
94	#332	—	166	2	no	—
95	C₂×M₁₆	—	166	1	no	—
96	C₂²×C₈	—	2	2	no	—
97	C₄⋊Q₈	—	83	2	no	—
98	#125	—	166	1	no	—
99	C₂²⋊Q₈	—	166	2	no	—
100	C₄×Q₈	—	166	2	no	—
101	#117	—	166	1	no	—
102	C₂×C₄²	C₂²⋊D₈₃	1	2	yes	—
103	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	2	2	no	—
106	C₄⋊C₈	—	166	2	no	—
107	C₄⋊C₈	—	166	2	no	—
108	C₂²⋊C₈	—	166	2	no	—
109	C₄×C₈	—	166	2	no	—
110	#95	—	2	2	no	—
111	C₂×Q₈	—	166	2	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
114	C₂²×C₄	#13050590	1	2	yes	—
115	M₁₆	—	332	2	no	—
116	C₂×C₈	—	4	2	no	—
117	C₂×C₈	—	4	2	no	—
118	C₂×C₈	—	4	2	no	—
119	C₂×C₈	—	332	2	no	—
120	C₂×C₈	—	332	1	no	—
121	C₄⋊C₄	—	332	2	no	—
122	C₄⋊C₄	—	166	2	no	—
123	C₄⋊C₄	—	166	2	no	—
124	C₂²⋊C₄	—	332	1	no	—
125	C₄²	—	2	2	no	—
126	C₄²	—	2	2	no	—
127	C₄²	—	332	1	no	—
128	C₄²	D₄×D₈₃	1	1	yes	characteristic
129	C₄²	#13050589	1	1	yes	characteristic
130	C₄²	#13050591	1	2	yes	—
131	C₂³	#14581775	1	1	yes	characteristic
132	Q₈	—	664	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	4	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	—	332	2	no	—
137	C₂×C₄	#14581763	1	1	yes	characteristic
138	C₂×C₄	#14581777	1	2	yes	—
139	C₂×C₄	#14581781	1	1	yes	characteristic
140	C₂×C₄	#14581787	1	2	yes	—
141	C₂×C₄	#14581812	1	2	yes	—
142	C₂×C₄	#14581822	1	2	yes	—
143	C₈	—	8	2	no	—
144	C₈	—	664	2	no	—
145	C₈	—	664	1	no	—
146	C₂²	—	2	2	no	—
147	C₂²	#19127627	1	1	yes	characteristic
148	C₂²	#19128042	1	2	yes	—
149	C₄	—	2	2	no	—
150	C₄	—	2	2	no	—
151	C₄	—	8	2	no	—
152	C₄	—	664	2	no	—
153	C₄	#19127920	1	2	yes	—
154	C₄	#19128058	1	1	yes	characteristic
155	C₄	#19128071	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	#24908882	1	1	yes	characteristic
158	C₂	#24908914	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#24908444

C₂

yes

maximal, characteristic

#24906121

C₂

yes

maximal

#24905360

C₂

yes

maximal

#24905292

C₂

yes

maximal, characteristic

C₈₃×#1832

C₂

yes

maximal, characteristic

#19128258

C₂²

yes

characteristic

#19127754

C₂²

yes

—

#19127725

C₂²

yes

—

—

—

C₂×C₄⋊C₈×C₈₃

C₂²

yes

—

#376×C₈₃

C₂²

yes

characteristic

#336×C₈₃

—

C₂×#13050574

—

#14581792

D₄

yes

—

#14581784

—

#14581771

—

C₄×Dic₁₆₆

—

#14581751

—

C₄⋊(C₈₃⋊C₈)

—

C₄⋊(C₈₃⋊C₈)

—

C₂²⋊(C₈₃⋊C₈)

—

C₄×C₈₃⋊C₈

—

C₂²×C₈×C₈₃

—

C₂×C₄²×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

C₄⋊C₈×C₈₃

—

C₄⋊C₈×C₈₃

—

#95×C₈₃

—

C₂×Dic₁₆₆

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₃

#41

yes

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

—

C₄²×C₈₃

C₂×D₄

yes

C₄²×C₈₃

yes

C₄²×C₈₃

yes

—

C₂³×C₈₃

#123

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#121

yes

characteristic

C₂×C₄×C₈₃

#123

yes

—

C₂×C₄×C₈₃

#124

yes

characteristic

C₂×C₄×C₈₃

#126

yes

—

C₂×C₄×C₈₃

#135

yes

—

C₂×C₄×C₈₃

#137

yes

—

C₂×Dic₈₃

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

#397

yes

characteristic

C₂²×C₈₃

#485

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#464

yes

—

C₄×C₈₃

yes

C₄×C₈₃

yes

Dic₈₃

—

#10630

—

maximal, Sylow

C₂×C₈₃

—

C₂×C₈₃

#2074

yes

characteristic

C₂×C₈₃

#2080

yes

—

#1995

—

#1832

D₈₃

yes

—

—

—

C₈₃

#10630

yes

characteristic, complemented, Sylow

#533

—

#431

—

#423

—

C₂×C₄⋊C₈

C₂×D₈₃

yes

—

#376

C₂×D₈₃

yes

characteristic

#339

—

166

—

#336

—

#333

—

166

—

#332

—

166

—

C₂×M₁₆

—

166

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

166

—

C₂²⋊Q₈

—

166

—

100

C₄×Q₈

—

166

—

101

#117

—

166

—

102

C₂×C₄²

C₂²⋊D₈₃

yes

—

103

C₂×C₄²

C₂²×D₈₃

yes

characteristic

104

C₄⋊C₈

—

105

C₄⋊C₈

—

106

C₄⋊C₈

—

166

—

107

C₄⋊C₈

—

166

—

108

C₂²⋊C₈

—

166

—

109

C₄×C₈

—

166

—

110

#95

—

111

C₂×Q₈

—

166

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

characteristic

114

C₂²×C₄

#13050590

yes

—

115

M₁₆

—

332

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

332

—

120

C₂×C₈

—

332

—

121

C₄⋊C₄

—

332

—

122

C₄⋊C₄

—

166

—

123

C₄⋊C₄

—

166

—

124

C₂²⋊C₄

—

332

—

125

C₄²

—

126

C₄²

—

127

C₄²

—

332

—

128

C₄²

D₄×D₈₃

yes

characteristic

129

C₄²

#13050589

yes

characteristic

130

C₄²

#13050591

yes

—

131

C₂³

#14581775

yes

characteristic

132

Q₈

—

664

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

332

—

137

C₂×C₄

#14581763

yes

characteristic

138

C₂×C₄

#14581777

yes

—

139

C₂×C₄

#14581781

yes

characteristic

140

C₂×C₄

#14581787

yes

—

141

C₂×C₄

#14581812

yes

—

142

C₂×C₄

#14581822

yes

—

143

C₈

—

144

C₈

—

664

—

145

C₈

—

664

—

146

C₂²

—

147

C₂²

#19127627

yes

characteristic

148

C₂²

#19128042

yes

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

664

—

153

C₄

#19127920

yes

—

154

C₄

#19128058

yes

characteristic

155

C₄

#19128071

yes

characteristic

156

C₂

—

157

C₂

#24908882

yes

characteristic

158

C₂

#24908914

yes

—

	subgroup	G/H
center	C₂×C₄	#14581781
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#1832	C₂
socle	C₂²×C₈₃	#397
prime radical	C₂³×C₈₃	#123
hypercenter	#1832	D₈₃
hypocenter	C₈₃	#10630
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1832

subgroup

G/H

center

C₂×C₄

#14581781

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#1832

C₂

C₂²×C₈₃

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1832

N	H ≅ G/N	type
85. C₈₃	#10630	semidirect

H ≅ G/N

type

85. C₈₃

#10630

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#24908444	2
#24906121	2
#24905360	2
#24905292	2
C₈₃×#1832	2
#10630	83

subgroup

index

C₈₃×#1832

Subgroups — #35309188

Conjugacy classes of subgroups

Complements

Maximal subgroups