Finite Group Databasebeta

← #13124970

Subgroups — #13124970

Order 1664.

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

normal subgroups only

This group has 450 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.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#529C211yesmaximal, characteristic, complemented
2C2×C4×D52C211yesmaximal, characteristic, complemented
3#11718727C212yesmaximal, complemented
4#11718718C212yesmaximal, complemented
5#11718707C211yesmaximal, characteristic, complemented
6#11718704C211yesmaximal, characteristic, complemented
7#11718697C211yesmaximal, characteristic
8#11718694C211yesmaximal, characteristic, complemented
9#11718687C212yesmaximal, complemented
10#11718675C212yesmaximal, complemented
11#11718587C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13—21no—
14C13×#126—21no—
15C13×#125C2211yescharacteristic, complemented
16C13×#124C2211yescharacteristic, complemented
17C13×#123—21no—
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic, complemented
21C4×D4×C13—21no—
22C4×D4×C13C2211yescharacteristic, complemented
23C13×#117—21no—
24C2×C42×C13C2211yescharacteristic
25C2×#6106C2212yes—
26C2×#6104C2212yes—
27C2×#6103—21no—
28C2×C4⋊Dic13C2211yescharacteristic
29C4×D52—21no—
30C4×D52—21no—
31C4×D52C2212yes—
32C4×D52C2212yes—
33#88075C2212yescomplemented
34#88072C2212yescomplemented
35C22⋊#1055C2211yescharacteristic
36C22⋊#1055C2211yescharacteristic
37#88049C2212yes—
38#88049C2212yes—
39#88048C2212yescomplemented
40#88047C2212yescomplemented
41C4⋊#1055C2212yescomplemented
42#88043C2212yescomplemented
43C23×D13—21no—
44C2×Q8×C13C2311yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13D411yescharacteristic
49C22×C4×C13D411yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C22×Dic13—21no—
52C2×D52—21no—
53C2×D52—24no—
54C2×D52C2312yes—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—44no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—21no—
62C13×C4⋊C4C2311yescharacteristic
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C13×C22⋊C4—21no—
66C13×C22⋊C4—21no—
67C13×C22⋊C4—21no—
68C13×C22⋊C4—21no—
69C42×C13—21no—
70C42×C13D411yescharacteristic
71C42×C13D411yescharacteristic
72C42×C13C2311yescharacteristic
73C42×C13C2311yescharacteristic
74#6106—24no—
75#6104—24no—
76#6103—22no—
77#6103—22no—
78C4⋊Dic13—21no—
79C4⋊Dic13C2312yes—
80C2×#1055C2312yes—
81C2×#1055C2312yes—
82#3114—131nomaximal, Sylow
83C23×C13—21no—
84C23×C13C2×D411yescharacteristic
85C22×D13—24no—
86C22×D13—22no—
87C22×D13—42no—
88C22×D13—42no—
89Q8×C13—22no—
90D4×C13—22no—
91D4×C13—42no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2×D411yescharacteristic
101C2×C4×C13C2×D411yescharacteristic
102C2×C4×C13C2×D411yescharacteristic
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—42no—
107D52—24no—
108D52—22no—
109D52#4114yes—
110C4×D13—44no—
111C4×D13—44no—
112#1055—22no—
113#1055—22no—
114#529D1311yescharacteristic, complemented
115C2×C4×D4—131no—
116#483—131no—
117#480—131no—
118#478—132no—
119#463—132no—
120#450—131no—
121#447—131no—
122#442—132no—
123#440—132no—
124#432—131no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13—41no—
128C22×C13—41no—
129C22×C13—41no—
130C22×C13AGL(1,ℤ/8)12yes—
131C22×C13C22×D411yescharacteristic
132C2×D13—24no—
133C2×D13—48no—
134C2×D13—42no—
135C2×D13—42no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—41no—
142C4×C13—41no—
143C4×C13—41no—
144C4×C13C2×#4112yes—
145Dic13—42no—
146C22×D4—131no—
147C23×C4—261no—
148C2×SD16—132no—
149C2×D8—132no—
150#126—21no—
151#125C2×D1311yescharacteristic, complemented
152#124C2×D1311yescharacteristic, complemented
153#123—21no—
154C22⋊Q8C2×D1311yescharacteristic
155#121C2×D1311yescharacteristic
156C4×Q8C2×D1311yescharacteristic, complemented
157C4×D4—21no—
158C4×D4—132no—
159C4×D4—132no—
160C4×D4—261no—
161C4×D4—261no—
162C4×D4C2×D1311yescharacteristic, complemented
163#117—21no—
164C2×C4⋊C4—131no—
165C2×C22⋊C4—261no—
166C2×C42C2×D1311yescharacteristic
167#107—132no—
168#106—132no—
169C4⋊C8—132no—
170#103—132no—
171#102—132no—
172#102—132no—
173#102—132no—
174C22⋊C8—131no—
175C22⋊C8—131no—
176#97—132no—
177C2×C13—22no—
178C2×C13—81no—
179C2×C13#52511yescharacteristic
180C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C13#57511yescharacteristic
182D13—44no—
183C24—261no—
184C2×Q8C22×D1311yescharacteristic
185C2×D4—21no—
186C2×D4—132no—
187C2×D4—264no—
188C2×D4—261no—
189C2×D4C22×D1311yescharacteristic
190C22×C4—21no—
191C22×C4—261no—
192C22×C4—262no—
193C22×C4—262no—
194C22×C4—524no—
195C22×C4C22⋊D1311yescharacteristic
196C22×C4C22⋊D1311yescharacteristic
197C22×C4C22×D1311yescharacteristic
198SD16—264no—
199D8—264no—
200C2×C8—132no—
201C2×C8—132no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—132no—
207C4⋊C4—261no—
208C4⋊C4C22×D1311yescharacteristic
209C4⋊C4C22×D1311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—262no—
216C22⋊C4—262no—
217C42—21no—
218C42C22⋊D1311yescharacteristic
219C42C22⋊D1311yescharacteristic
220C42C22×D1311yescharacteristic
221C42C22×D1311yescharacteristic
222C13#311411yescharacteristic, complemented, Sylow
223C23—21no—
224C23—264no—
225C23—262no—
226C23—522no—
227C23—522no—
228C23C2×C22⋊D1311yescharacteristic
229Q8—22no—
230D4—22no—
231D4—42no—
232D4—134no—
233D4—264no—
234D4—262no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—262no—
243C2×C4—524no—
244C2×C4—524no—
245C2×C4—522no—
246C2×C4C2×C22⋊D1311yescharacteristic
247C2×C4C2×C22⋊D1311yescharacteristic
248C2×C4C2×C22⋊D1311yescharacteristic
249C2×C4C2×C22⋊D1311yescharacteristic
250C2×C4C2×C22⋊D1311yescharacteristic
251C2×C4C23×D1311yescharacteristic
252C8—262no—
253C8—262no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—264no—
260C22—528no—
261C22—522no—
262C22—522no—
263C22#8820312yes—
264C22C22×C22⋊D1311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—522no—
274C4#41×D1312yes—
275C2—22no—
276C2—81no—
277C2—524no—
278C2C2×#8820311yescharacteristic
279C2#1171952711yescharacteristic
280C2#1171953311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#529C2
socleC22×C13C22×D4
prime radical#11718697C2
hypercenter#529D13
hypocenterC13#3114
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C13×#529C2semidirect
2. C2×C4×D52C2semidirect
3. #11718727C2semidirect
4. #11718718C2semidirect
5. #11718707C2semidirect
6. #11718704C2semidirect
8. #11718694C2semidirect
9. #11718687C2semidirect
10. #11718675C2semidirect
11. #11718587C2semidirect
15. C13×#125C22semidirect
16. C13×#124C22semidirect
20. C4×Q8×C13C22semidirect
22. C4×D4×C13C22semidirect
33. #88075C22semidirect
34. #88072C22semidirect
39. #88048C22semidirect
40. #88047C22semidirect
41. C4⋊#1055C22semidirect
42. #88043C22semidirect
114. #529D13semidirect
151. #125C2×D13semidirect
152. #124C2×D13semidirect
156. C4×Q8C2×D13semidirect
162. C4×D4C2×D13semidirect
222. C13#3114semidirect

Maximal subgroups

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

subgroupindex
C13×#5292
C2×C4×D522
#117187272
#117187182
#117187072
#117187042
#117186972
#117186942
#117186872
#117186752
#117185872
#311413