Finite Group Databasebeta

← #13125285

Subgroups — #13125285

Order 1664.

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

normal subgroups only

This group has 656 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
1C2×#88168C212yesmaximal, complemented
2C2×#88165C212yesmaximal, complemented
3D13×#127C211yesmaximal, characteristic, complemented
4#11719373C211yesmaximal, characteristic, complemented
5C13×#496C211yesmaximal, characteristic, complemented
6#11718836C212yesmaximal, complemented
7#11718812C212yesmaximal, complemented
8#11718735C211yesmaximal, characteristic, complemented
9#11718719C211yesmaximal, characteristic, complemented
10#11718373C211yesmaximal, characteristic, complemented
11#11718368C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×#6129C2211yescharacteristic
14C2×D4×D13—22no—
15C2×D4×D13C2212yes—
16C2×C13×SD16C2212yescomplemented
17C2×C13×D8C2212yescomplemented
18C13×#127C2211yescharacteristic
19C13×#124C2211yescharacteristic, complemented
20#88198C2211yescharacteristic, complemented
21C2×#6106C2212yescomplemented
22#88194—22no—
23#88194C2212yes—
24#88194C2211yescharacteristic, complemented
25C2×#6105C2212yescomplemented
26C2×#6104C2212yescomplemented
27C2×#6104C2212yescomplemented
28#88168—28no—
29#88165—28no—
30C2×D104C2212yescomplemented
31C2×#6095C2212yescomplemented
32C2×#6094C2212yes—
33#88138—22no—
34#88135—22no—
35#88129C2211yescharacteristic, complemented
36#88128C2211yescharacteristic
37C42×D13C2211yescharacteristic
38C13×#97C2211yescharacteristic, complemented
39C8×Dic13C2212yescomplemented
40#88043C2211yescharacteristic, complemented
41C23×D13—22no—
42C2×Q8×C13C2311yescharacteristic
43C2×D4×C13—22no—
44C2×D4×C13C2311yescharacteristic
45C2×D4×C13C2312yes—
46C2×C22⋊D13—21no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—24no—
50C22×Dic13—21no—
51#6131—24no—
52#6129—24no—
53D4×D13—24no—
54D4×D13—24no—
55D4×D13—48no—
56C2×D52—21no—
57C2×D52—22no—
58C2×D52C2312yes—
59C2×D52C2311yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13D412yes—
62C2×C4×D13C2311yescharacteristic
63C2×Dic26C2311yescharacteristic
64C13×SD16—24no—
65C13×D8—24no—
66C2×C8×C13C2312yes—
67C13×C22⋊C4—22no—
68C42×C13C2311yescharacteristic
69#6106—24no—
70#6105—24no—
71#6104—24no—
72#6104—24no—
73#6103—22no—
74#6101—22no—
75C4×Dic13D412yes—
76C4×Dic13C2311yescharacteristic
77C2×#1055C2312yes—
78D104—24no—
79#6095—24no—
80#6094D418yescomplemented
81#3151—131nomaximal, Sylow
82C23×C13—21no—
83C23×C13—22no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—48no—
87C22×D13—44no—
88C22×D13C2×D411yescharacteristic
89Q8×C13—22no—
90D4×C13—22no—
91D4×C13—22no—
92D4×C13—22no—
93D4×C13—44no—
94C2×C4×C13—21no—
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2411yescharacteristic
97C22⋊D13—42no—
98C22⋊D13—44no—
99C22⋊D13—48no—
100C22⋊D13—44no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D412yes—
105D52—22no—
106D52—22no—
107D52—22no—
108D52—44no—
109D52—42no—
110C4×D13—24no—
111C4×D13—42no—
112C4×D13C2×D414yes—
113Dic26—22no—
114C8×C13C2×D414yescomplemented
115#1055C2×D414yescomplemented
116C2×AGL(1,ℤ/8)—132no—
117C2×AGL(1,ℤ/8)—132no—
118#532—131no—
119C2×#127—131no—
120#496—131no—
121#496—131no—
122#496—131no—
123#496D1311yescharacteristic, complemented
124#493—132no—
125#492—132no—
126C4×M16—131no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13C22×D411yescharacteristic
132C2×D13—22no—
133C2×D13—41no—
134C2×D13—42no—
135C2×D13—44no—
136C2×D13—42no—
137C2×D13—88no—
138C2×D13#12712yes—
139C4×C13—22no—
140C4×C13—41no—
141C4×C13C22×D412yes—
142Dic13—41no—
143Dic13#12712yes—
144Dic13AGL(1,ℤ/8)14yescomplemented
145C2×#41—131no—
146C2×#41—131no—
147C22×D4—132no—
148C22×D4—262no—
149AGL(1,ℤ/8)—268no—
150AGL(1,ℤ/8)—268no—
151C2×SD16—132no—
152C2×SD16—132no—
153C2×SD16—132no—
154C2×SD16C2×D1312yescomplemented
155C2×D8—132no—
156C2×D8—132no—
157C2×D8—132no—
158C2×D8C2×D1312yescomplemented
159C2×M16—132no—
160C4⋊Q8—131no—
161#127—132no—
162#127—131no—
163#127—131no—
164#127—262no—
165#127C2×D1311yescharacteristic
166#124—131no—
167#124C2×D1311yescharacteristic, complemented
168#121—262no—
169C4×D4—262no—
170C2×C42—131no—
171#97—131no—
172#97C2×D1311yescharacteristic, complemented
173C4×C8—132no—
174C2×C13—82no—
175C2×C13—81no—
176C2×C13C2×#12711yescharacteristic
177C2×C13C2×AGL(1,ℤ/8)12yes—
178D13—22no—
179D13—81no—
180D13—82no—
181C24—262no—
182#41—264no—
183#41—264no—
184C2×Q8—131no—
185C2×Q8C22×D1311yescharacteristic
186C2×D4—22no—
187C2×D4—131no—
188C2×D4—132no—
189C2×D4—261no—
190C2×D4—264no—
191C2×D4—264no—
192C2×D4—262no—
193C2×D4—264no—
194C2×D4—262no—
195C2×D4—261no—
196C2×D4—262no—
197C2×D4—528no—
198C2×D4C22×D1311yescharacteristic
199C2×D4C22×D1312yes—
200C22×C4—131no—
201C22×C4—132no—
202C22×C4—261no—
203C22×C4—261no—
204SD16—24no—
205SD16—264no—
206SD16—264no—
207SD16—264no—
208D8—24no—
209D8—264no—
210D8—264no—
211D8—264no—
212M16—138no—
213C2×C8—132no—
214C2×C8C22×D1312yes—
215C4⋊C4—262no—
216C22⋊C4—22no—
217C22⋊C4—262no—
218C42—132no—
219C42—131no—
220C42C22×D1311yescharacteristic
221C13#315111yescharacteristic, complemented, Sylow
222C23—21no—
223C23—22no—
224C23—131no—
225C23—261no—
226C23—262no—
227C23—524no—
228C23—528no—
229Q8—22no—
230Q8—262no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—262no—
236D4—262no—
237D4—262no—
238D4—524no—
239D4—522no—
240D4—524no—
241D4—524no—
242D4—528no—
243D4—522no—
244C2×C4—21no—
245C2×C4—132no—
246C2×C4—131no—
247C2×C4—134no—
248C2×C4—264no—
249C2×C4—261no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4D4×D1312yes—
253C2×C4C23×D1311yescharacteristic
254C8—134no—
255C8D4×D1314yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—132no—
261C22—262no—
262C22—524no—
263C22—522no—
264C22—521no—
265C22—522no—
266C22—1048no—
267C22C2×D4×D1311yescharacteristic
268C4—22no—
269C4—41no—
270C4—134no—
271C4—132no—
272C4—521no—
273C4C2×D4×D1312yes—
274C2—82no—
275C2—81no—
276C2—262no—
277C2—1042no—
278C2—1041no—
279C2D13×#12711yescharacteristic
280C2D13×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3151
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#88168C2semidirect
2. C2×#88165C2semidirect
3. D13×#127C2semidirect
4. #11719373C2semidirect
5. C13×#496C2semidirect
6. #11718836C2semidirect
7. #11718812C2semidirect
8. #11718735C2semidirect
9. #11718719C2semidirect
10. #11718373C2semidirect
11. #11718368C2semidirect
16. C2×C13×SD16C22semidirect
17. C2×C13×D8C22semidirect
19. C13×#124C22semidirect
20. #88198C22semidirect
21. C2×#6106C22semidirect
24. #88194C22semidirect
25. C2×#6105C22semidirect
26. C2×#6104C22semidirect
27. C2×#6104C22semidirect
30. C2×D104C22semidirect
31. C2×#6095C22semidirect
35. #88129C22semidirect
38. C13×#97C22semidirect
39. C8×Dic13C22semidirect
40. #88043C22semidirect
80. #6094D4semidirect
114. C8×C13C2×D4semidirect
115. #1055C2×D4semidirect
123. #496D13semidirect
144. Dic13AGL(1,ℤ/8)semidirect
154. C2×SD16C2×D13semidirect
158. C2×D8C2×D13semidirect
167. #124C2×D13semidirect
172. #97C2×D13semidirect
221. C13#3151semidirect
255. C8D4×D13semidirect

Maximal subgroups

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

subgroupindex
C2×#881682
C2×#881652
D13×#1272
#117193732
C13×#4962
#117188362
#117188122
#117187352
#117187192
#117183732
#117183682
#315113