Finite Group Databasebeta

← #13125299

Subgroups — #13125299

Order 1664.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88172C212yesmaximal, complemented
2C2×#88168C212yesmaximal, complemented
3#11719430C211yesmaximal, characteristic, complemented
4D13×#124C211yesmaximal, characteristic, complemented
5C13×#497C211yesmaximal, characteristic, complemented
6#11718852C212yesmaximal, complemented
7#11718829C212yesmaximal, complemented
8#11718747C211yesmaximal, characteristic, complemented
9#11718719C211yesmaximal, characteristic, complemented
10#11718373C211yesmaximal, characteristic, complemented
11#11718368C211yesmaximal, characteristic, complemented
12C2×#6131C2212yes—
13C2×Q8×D13C2211yescharacteristic
14C2×D4×D13C2211yescharacteristic
15C2×C13×Q16C2212yescomplemented
16C2×C13×SD16C2212yes—
17C13×C4⋊Q8C2211yescharacteristic, complemented
18C13×#124C2211yescharacteristic
19#88201C2211yescharacteristic
20#88201C2212yescomplemented
21C2×#6107C2212yescomplemented
22C2×#6106C2212yes—
23C2×#6106C2212yescomplemented
24#88190C2211yescharacteristic
25C2×#6104C2212yes—
26#88172—28no—
27#88168—28no—
28C2×D104C2212yes—
29C2×#6095C2212yescomplemented
30C2×#6094C2212yes—
31#88149—22no—
32#88147—22no—
33#88139—22no—
34C22⋊C4×D13—22no—
35#88129C2211yescharacteristic
36#88128C2211yescharacteristic, complemented
37C42×D13C2211yescharacteristic
38C13×#97C2211yescharacteristic, complemented
39C8×Dic13C2212yescomplemented
40#88043C2211yescharacteristic, complemented
41C23×D13—21no—
42C2×Q8×C13C2312yes—
43C2×Q8×C13C2311yescharacteristic
44C2×D4×C13C2311yescharacteristic
45C2×C22⋊D13—21no—
46#6131—24no—
47#6131—24no—
48Q8×D13—24no—
49D4×D13—24no—
50C2×D52—22no—
51C2×D52—22no—
52C2×D52C2312yes—
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×C4×D13D412yes—
57C2×C4×D13C2311yescharacteristic
58C2×Dic26—21no—
59C2×Dic26C2311yescharacteristic
60C13×Q16—24no—
61C13×SD16—24no—
62C2×C8×C13C2312yes—
63C13×C4⋊C4—22no—
64C13×C22⋊C4—22no—
65C42×C13C2311yescharacteristic
66C22⋊Dic13—22no—
67#6107—24no—
68#6106—24no—
69#6106—24no—
70#6104—24no—
71#6103—22no—
72#6103—22no—
73#6103—24no—
74C4×Dic13D412yes—
75C4×Dic13C2311yescharacteristic
76C2×#1055C2312yes—
77D104—24no—
78#6095—24no—
79#6094D418yescomplemented
80#3153—131nomaximal, Sylow
81C23×C13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13—44no—
85C22×D13—42no—
86C22×D13C2×D411yescharacteristic
87Q8×C13—22no—
88Q8×C13—22no—
89Q8×C13—22no—
90D4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—42no—
96C2×Dic13—21no—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×D411yescharacteristic
99D52—22no—
100D52—22no—
101D52—22no—
102D52—44no—
103D52—44no—
104C4×D13—42no—
105C4×D13—42no—
106C4×D13—44no—
107C4×D13C2×D414yes—
108Dic26—22no—
109Dic26—42no—
110C8×C13C2×D414yes—
111#1055C2×D414yes—
112C2×#137—132no—
113C2×AGL(1,ℤ/8)—132no—
114#532—131no—
115C2×#124—131no—
116#497—131no—
117#497D1311yescharacteristic, complemented
118#496—131no—
119#496—131no—
120#495—132no—
121#495—132no—
122C4×M16—131no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13C22×D411yescharacteristic
126C2×D13—22no—
127C2×D13—42no—
128C2×D13—41no—
129C2×D13—44no—
130C2×D13—42no—
131C2×D13—84no—
132C2×D13#12712yes—
133C4×C13—22no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C13C22×D412yes—
137Dic13—22no—
138Dic13—41no—
139Dic13#12712yes—
140C2×#41—132no—
141C22×Q8—131no—
142C22×D4—131no—
143#137—268no—
144AGL(1,ℤ/8)—268no—
145C2×Q16—132no—
146C2×Q16C2×D1312yescomplemented
147C2×SD16—132no—
148C2×SD16—132no—
149C2×SD16—132no—
150C2×SD16C2×D1312yes—
151C2×D8—132no—
152C2×D8—132no—
153C2×M16—132no—
154C4⋊Q8C2×D1311yescharacteristic, complemented
155#127—131no—
156#124—131no—
157#124—132no—
158#124—131no—
159#124—131no—
160#124—262no—
161#124C2×D1311yescharacteristic
162#121—262no—
163C4×D4—262no—
164C2×C22⋊C4—262no—
165C2×C42—131no—
166#97—131no—
167#97C2×D1311yescharacteristic, complemented
168C4×C8—132no—
169C2×C13—81no—
170C2×C13C2×#12711yescharacteristic
171C2×C13#57512yes—
172D13—22no—
173D13—82no—
174D13—81no—
175C24—261no—
176#41—264no—
177#41—264no—
178C2×Q8—131no—
179C2×Q8—261no—
180C2×Q8—264no—
181C2×Q8C22×D1311yescharacteristic
182C2×Q8C22×D1312yes—
183C2×D4—131no—
184C2×D4—132no—
185C2×D4—262no—
186C2×D4—264no—
187C2×D4—261no—
188C2×D4—262no—
189C2×D4C22×D1311yescharacteristic
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—262no—
193C22×C4—261no—
194Q16—24no—
195Q16—264no—
196SD16—24no—
197SD16—264no—
198SD16—264no—
199SD16—264no—
200D8—264no—
201D8—264no—
202M16—138no—
203C2×C8—132no—
204C2×C8C22×D1312yes—
205C4⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—262no—
208C22⋊C4—264no—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C42—132no—
212C42—131no—
213C42C22×D1311yescharacteristic
214C13#315311yescharacteristic, complemented, Sylow
215C23—21no—
216C23—131no—
217C23—261no—
218C23—262no—
219C23—522no—
220C23—524no—
221Q8—22no—
222Q8—22no—
223Q8—22no—
224Q8—262no—
225Q8—522no—
226D4—22no—
227D4—262no—
228D4—262no—
229D4—262no—
230D4—524no—
231D4—524no—
232D4—522no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—131no—
236C2×C4—134no—
237C2×C4—132no—
238C2×C4—261no—
239C2×C4—522no—
240C2×C4—524no—
241C2×C4—522no—
242C2×C4D4×D1312yes—
243C2×C4C23×D1311yescharacteristic
244C8—134no—
245C8D4×D1314yes—
246C22—42no—
247C22—41no—
248C22—132no—
249C22—262no—
250C22—524no—
251C22—522no—
252C22—522no—
253C22—521no—
254C22—1044no—
255C22C2×D4×D1311yescharacteristic
256C4—22no—
257C4—42no—
258C4—41no—
259C4—132no—
260C4—262no—
261C4—521no—
262C4C2×D4×D1312yes—
263C2—81no—
264C2—262no—
265C2—1041no—
266C2—1042no—
267C2D13×#12711yescharacteristic
268C2#1171948212yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
hypercenter#497D13
hypocenterC13#3153
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#88172C2semidirect
2. C2×#88168C2semidirect
3. #11719430C2semidirect
4. D13×#124C2semidirect
5. C13×#497C2semidirect
6. #11718852C2semidirect
7. #11718829C2semidirect
8. #11718747C2semidirect
9. #11718719C2semidirect
10. #11718373C2semidirect
11. #11718368C2semidirect
15. C2×C13×Q16C22semidirect
17. C13×C4⋊Q8C22semidirect
20. #88201C22semidirect
21. C2×#6107C22semidirect
23. C2×#6106C22semidirect
29. C2×#6095C22semidirect
36. #88128C22semidirect
38. C13×#97C22semidirect
39. C8×Dic13C22semidirect
40. #88043C22semidirect
79. #6094D4semidirect
117. #497D13semidirect
146. C2×Q16C2×D13semidirect
154. C4⋊Q8C2×D13semidirect
167. #97C2×D13semidirect
214. C13#3153semidirect

Maximal subgroups

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

subgroupindex
C2×#881722
C2×#881682
#117194302
D13×#1242
C13×#4972
#117188522
#117188292
#117187472
#117187192
#117183732
#117183682
#315313