Finite Group Databasebeta

← #13124759

Subgroups — #13124759

Order 1664.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2#11719496C211yesmaximal, characteristic
3#11718868C211yesmaximal, characteristic, complemented
4#11718632C212yesmaximal, complemented
5#11718631C212yesmaximal, complemented
6#11718629C212yesmaximal, complemented
7#11718628C212yesmaximal, complemented
8#11718627C212yesmaximal, complemented
9#11718625C212yesmaximal, complemented
10C23×C4×C13—21no—
11C23×C4×C13C2211yescharacteristic
12C2×#6127C2211yescharacteristic
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4—21no—
15C2×C13×C4⋊C4—21no—
16C2×C13×C4⋊C4C2212yes—
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C4⋊C4C2212yes—
19#88207—21no—
20#88184C2211yescharacteristic
21#88184C2211yescharacteristic
22#88183—21no—
23C4×C22⋊D13—21no—
24C4×C22⋊D13—21no—
25#88180C2211yescharacteristic
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28C2×#6099C2212yes—
29C22⋊#1055C2212yes—
30C22⋊#1055C2212yes—
31#88050C2214yescomplemented
32#88049C2214yescomplemented
33#88048C2214yescomplemented
34#88047C2214yescomplemented
35C24×C13D411yescharacteristic
36C22×C4×C13—24no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—22no—
40C22×C4×C13—44no—
41C22×C4×C13D411yescharacteristic
42C22×C4×C13D411yescharacteristic
43C22×C4×C13D411yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—21no—
48C2×C22⋊D13—21no—
49C2×C22⋊D13—21no—
50#6127—24no—
51C2×D52C2311yescharacteristic
52C2×C4×D13—21no—
53C2×Dic26C2311yescharacteristic
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4C2314yes—
58C22⋊Dic13—21no—
59C22⋊Dic13—21no—
60C22⋊Dic13—21no—
61#6103—21no—
62#6103—21no—
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65#6101—21no—
66#6101—21no—
67C4×Dic13—21no—
68#6099—24no—
69C2×#1055C2314yes—
70#3092—131nomaximal, Sylow
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D411yescharacteristic
75C23×C13C2×D411yescharacteristic
76C23×C13C2×D411yescharacteristic
77C22×D13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—24no—
84C2×C4×C13—44no—
85C2×C4×C13—44no—
86C2×C4×C13—44no—
87C2×C4×C13C2×D411yescharacteristic
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13#4114yes—
91C2×C4×C13C2411yescharacteristic
92C22⋊D13—42no—
93C22⋊D13—42no—
94C22⋊D13—42no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98D52—22no—
99C4×D13—42no—
100Dic26—22no—
101#1055—24no—
102#525—131no—
103C22×C4⋊C4D1311yescharacteristic, complemented
104#484—132no—
105#483—132no—
106#481—132no—
107#480—132no—
108#428—132no—
109#417—132no—
110#407—131no—
111C22×C13—28no—
112C22×C13—21no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13—21no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13#12312yes—
119C22×C13AGL(1,ℤ/8)12yes—
120C22×C13#13712yes—
121C22×C13C22×D411yescharacteristic
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—41no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—44no—
128C4×C13#12312yes—
129C4×C13C2×#4112yes—
130Dic13—41no—
131Dic13—41no—
132Dic13—41no—
133C2×#41—131no—
134C23×C4—21no—
135C23×C4C2×D1311yescharacteristic
136C2×M16—132no—
137#123—261no—
138C22⋊Q8—131no—
139C22⋊Q8—131no—
140#121—131no—
141#121—131no—
142#120—261no—
143C4×D4—261no—
144C4×D4—261no—
145#117—131no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4C2×D1312yes—
150C2×C4⋊C4C2×D1312yes—
151C2×C4⋊C4C2×D1312yes—
152#107—134no—
153#106—134no—
154#103—134no—
155#102—134no—
156C22⋊C8—132no—
157C22⋊C8—132no—
158C2×C13—22no—
159C2×C13—22no—
160C2×C13—22no—
161C2×C13C2×#12311yescharacteristic
162C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C13C2×#13711yescharacteristic
164D13—81no—
165C24C22⋊D1311yescharacteristic
166#41—264no—
167C2×Q8—131no—
168C2×D4—131no—
169C2×D4—261no—
170C2×D4—261no—
171C2×D4—261no—
172C22×C4—24no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—44no—
177C22×C4—261no—
178C22×C4C22⋊D1311yescharacteristic
179C22×C4C22⋊D1311yescharacteristic
180C22×C4C22⋊D1311yescharacteristic
181C22×C4C22×D1311yescharacteristic
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1311yescharacteristic
184M16—264no—
185C2×C8—134no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—131no—
190C4⋊C4—131no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4C22×D1314yes—
194C22⋊C4—261no—
195C22⋊C4—261no—
196C22⋊C4—261no—
197C22⋊C4—261no—
198C22⋊C4—261no—
199C42—261no—
200C13#309211yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—261no—
205C23C2×C22⋊D1311yescharacteristic
206C23C2×C22⋊D1311yescharacteristic
207C23C2×C22⋊D1311yescharacteristic
208Q8—262no—
209D4—262no—
210D4—522no—
211D4—522no—
212D4—522no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—522no—
226C2×C4#612714yes—
227C2×C4C2×C22⋊D1311yescharacteristic
228C2×C4C2×C22⋊D1311yescharacteristic
229C2×C4C2×C22⋊D1311yescharacteristic
230C2×C4C23×D1311yescharacteristic
231C8—264no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—521no—
240C22—521no—
241C22—521no—
242C22#8818312yes—
243C22#8818612yes—
244C22#8819612yes—
245C22C22×C22⋊D1311yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—521no—
250C4—521no—
251C4—521no—
252C4#8818312yes—
253C4C2×#612712yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—1041no—
258C2C2×#8818311yescharacteristic
259C2C2×#8818611yescharacteristic
260C2C2×#8819611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC22×C13×C4⋊C4C2
socleC22×C13C22×D4
prime radical#11719496C2
hypercenterC22×C4⋊C4D13
hypocenterC13#3092
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C13×C4⋊C4C2semidirect
3. #11718868C2semidirect
4. #11718632C2semidirect
5. #11718631C2semidirect
6. #11718629C2semidirect
7. #11718628C2semidirect
8. #11718627C2semidirect
9. #11718625C2semidirect
31. #88050C22semidirect
32. #88049C22semidirect
33. #88048C22semidirect
34. #88047C22semidirect
103. C22×C4⋊C4D13semidirect
200. C13#3092semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C4⋊C42
#117194962
#117188682
#117186322
#117186312
#117186292
#117186282
#117186272
#117186252
#309213