Finite Group Databasebeta

← #13124193

Subgroups — #13124193

Order 1664.

762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 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
1C2×C13×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#11719527C212yesmaximal, complemented
3#11719510C211yesmaximal, characteristic, complemented
4#11718903C214yesmaximal, complemented
5#11718902C214yesmaximal, complemented
6#11718897C212yesmaximal, complemented
7C2×#88073C211yesmaximal, characteristic, complemented
8C13×H(5,𝔽2)—24no—
9C13×H(5,𝔽2)—22no—
10C13×H(5,𝔽2)C2214yes—
11C2×C13×#41—22no—
12C2×C13×#41C2212yes—
13C22×D4×C13—22no—
14C22×D4×C13—22no—
15C22×D4×C13C2211yescharacteristic
16C2×#6127C2211yescharacteristic, complemented
17#88207—22no—
18#88205C2214yescomplemented
19#88204—24no—
20#88203C2214yescomplemented
21#88196—22no—
22#88194C2212yescomplemented
23#88192—22no—
24#88190C2212yescomplemented
25#88186—22no—
26#88180C2211yescharacteristic, complemented
27C2×#6099C2212yescomplemented
28#88077C2218yescomplemented
29#88073C2214yescomplemented
30C24×C13—22no—
31C24×C13D412yes—
32C13×#41—28no—
33C13×#41—28no—
34C13×#41—22no—
35C13×#41—22no—
36C13×#41D414yescomplemented
37C13×#41C2314yes—
38C2×Q8×C13D412yescomplemented
39C2×D4×C13—24no—
40C2×D4×C13—28no—
41C2×D4×C13—28no—
42C2×D4×C13—22no—
43C2×D4×C13—28no—
44C2×D4×C13—28no—
45C2×D4×C13—22no—
46C2×D4×C13—22no—
47C2×D4×C13D412yes—
48C2×D4×C13D412yescomplemented
49C2×D4×C13C2312yes—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13C2311yescharacteristic
53C2×C22⋊D13—21no—
54C2×C22⋊D13—24no—
55#6127—22no—
56#6127—22no—
57C2×D52C2311yescharacteristic, complemented
58C2×C4×D13—21no—
59C2×Dic26C2311yescharacteristic, complemented
60C22⋊Dic13—21no—
61C22⋊Dic13—24no—
62#6107—24no—
63#6106—24no—
64#6105—24no—
65#6104—24no—
66C4⋊Dic13—21no—
67C4×Dic13C2312yescomplemented
68#6099—22no—
69#6099C2314yescomplemented
70C2×#1055—22no—
71#3019—131nomaximal, Sylow
72C23×C13—28no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—82no—
77C23×C13—84no—
78C23×C13C2×D414yes—
79C23×C13C2×D411yescharacteristic
80C22×D13—21no—
81Q8×C13—22no—
82Q8×C13C2×D414yes—
83D4×C13—216no—
84D4×C13—24no—
85D4×C13—24no—
86D4×C13—24no—
87D4×C13—22no—
88D4×C13—24no—
89D4×C13C2×D414yes—
90C2×C4×C13—28no—
91C2×C4×C13—22no—
92C2×C4×C13—24no—
93C2×C4×C13—24no—
94C2×C4×C13C2×D411yescharacteristic
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2×D412yes—
97C2×C4×C13C2411yescharacteristic
98C22⋊D13—41no—
99C22⋊D13—41no—
100C22⋊D13—84no—
101C2×Dic13—22no—
102C2×Dic13—21no—
103D52—22no—
104C4×D13—42no—
105Dic26—22no—
106#1055—24no—
107C2×H(5,𝔽2)D1311yescharacteristic, complemented
108#575—132no—
109#535—131no—
110#455—134no—
111#453—134no—
112#421—132no—
113C2×#100—131no—
114C22×C13—24no—
115C22×C13—24no—
116C22×C13—41no—
117C22×C13—44no—
118C22×C13—44no—
119C22×C13—44no—
120C22×C13—82no—
121C22×C13—88no—
122C22×C13#12011yescharacteristic
123C22×C13#12011yescharacteristic
124C22×C13C22×D411yescharacteristic
125C2×D13—42no—
126C2×D13—41no—
127C4×C13—24no—
128C4×C13#12012yes—
129C4×C13C22×D412yes—
130Dic13—42no—
131Dic13—41no—
132H(5,𝔽2)—24no—
133H(5,𝔽2)—22no—
134H(5,𝔽2)C2×D1314yes—
135C2×#41—22no—
136C2×#41—131no—
137C2×#41C2×D1312yes—
138C22×D4—22no—
139C22×D4—22no—
140C22×D4C2×D1311yescharacteristic
141#137—134no—
142#137—262no—
143AGL(1,ℤ/8)—134no—
144AGL(1,ℤ/8)—262no—
145#135—264no—
146C2×M16—132no—
147#127—132no—
148#124—132no—
149#121—262no—
150#120—262no—
151#117—131no—
152#104—138no—
153#100—134no—
154C2×C13—21no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13—44no—
158C2×C13—44no—
159C2×C13C2×#12011yescharacteristic
160D13—81no—
161C24—22no—
162C24C22⋊D1312yes—
163#41—28no—
164#41—28no—
165#41—22no—
166#41—22no—
167#41—262no—
168#41—262no—
169#41C22⋊D1314yescomplemented
170#41C22×D1314yes—
171C2×Q8—131no—
172C2×Q8C22⋊D1312yescomplemented
173C2×D4—24no—
174C2×D4—28no—
175C2×D4—28no—
176C2×D4—22no—
177C2×D4—28no—
178C2×D4—28no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—131no—
182C2×D4—261no—
183C2×D4—264no—
184C2×D4C22⋊D1312yes—
185C2×D4C22⋊D1312yescomplemented
186C2×D4C22×D1312yes—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—261no—
190C22×C4C22×D1311yescharacteristic
191Q16—264no—
192SD16—264no—
193SD16—264no—
194D8—264no—
195M16—134no—
196M16—262no—
197C2×C8—262no—
198C4⋊C4—261no—
199C22⋊C4—261no—
200C22⋊C4—264no—
201C42—132no—
202C13#301911yescharacteristic, complemented, Sylow
203C23—28no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—82no—
208C23—84no—
209C23—261no—
210C23C2×C22⋊D1314yes—
211C23C2×C22⋊D1311yescharacteristic
212Q8—22no—
213Q8—262no—
214Q8C2×C22⋊D1314yes—
215D4—216no—
216D4—24no—
217D4—24no—
218D4—24no—
219D4—22no—
220D4—24no—
221D4—262no—
222D4—521no—
223D4—521no—
224D4—1044no—
225D4C2×C22⋊D1314yes—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—262no—
231C2×C4—261no—
232C2×C4—522no—
233C2×C4C2×C22⋊D1311yescharacteristic
234C2×C4C2×C22⋊D1312yes—
235C2×C4C2×C22⋊D1312yes—
236C2×C4C23×D1311yescharacteristic
237C8—264no—
238C22—24no—
239C22—24no—
240C22—41no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—88no—
246C22—522no—
247C22—521no—
248C22#8820711yescharacteristic
249C22#8820711yescharacteristic
250C22C22×C22⋊D1311yescharacteristic
251C4—24no—
252C4—522no—
253C4—521no—
254C4#8820712yes—
255C4C22×C22⋊D1312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—44no—
261C2—1041no—
262C2C2×#8820711yescharacteristic
subgroupG/H
centerC2C2×#88207
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×H(5,𝔽2)C2
socleC2×C13C2×#120
hypercenterC2×H(5,𝔽2)D13
hypocenterC13#3019
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C13×H(5,𝔽2)C2semidirect
2. #11719527C2semidirect
3. #11719510C2semidirect
4. #11718903C2semidirect
5. #11718902C2semidirect
6. #11718897C2semidirect
7. C2×#88073C2semidirect
16. C2×#6127C22semidirect
18. #88205C22semidirect
20. #88203C22semidirect
22. #88194C22semidirect
24. #88190C22semidirect
26. #88180C22semidirect
27. C2×#6099C22semidirect
28. #88077C22semidirect
29. #88073C22semidirect
36. C13×#41D4semidirect
38. C2×Q8×C13D4semidirect
48. C2×D4×C13D4semidirect
57. C2×D52C23semidirect
59. C2×Dic26C23semidirect
67. C4×Dic13C23semidirect
69. #6099C23semidirect
107. C2×H(5,𝔽2)D13semidirect
169. #41C22⋊D13semidirect
172. C2×Q8C22⋊D13semidirect
185. C2×D4C22⋊D13semidirect
202. C13#3019semidirect

Maximal subgroups

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

subgroupindex
C2×C13×H(5,𝔽2)2
#117195272
#117195102
#117189032
#117189022
#117188972
C2×#880732
#301913