Finite Group Databasebeta

← #13125303

Subgroups — #13125303

Order 1664.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#137C211yesmaximal, characteristic, complemented
2#11719537C211yesmaximal, characteristic, complemented
3C2×#88203C211yesmaximal, characteristic, complemented
4C2×#88201C211yesmaximal, characteristic, complemented
5C2×#88196C211yesmaximal, characteristic, complemented
6C2×#88162C211yesmaximal, characteristic, complemented
7#11718852C212yesmaximal, complemented
8#11718851C212yesmaximal, complemented
9#11718837C212yesmaximal, complemented
10#11718829C212yesmaximal, complemented
11M16×Dic13C211yesmaximal, characteristic, complemented
12C2×C13×#41C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C22×D52C2211yescharacteristic
16C13×#137—24no—
17C2×C13×Q16C2212yescomplemented
18C2×C13×SD16C2212yescomplemented
19C2×C13×M16C2211yescharacteristic
20#88203—24no—
21#88201—22no—
22#88201C2212yes—
23#88201C2212yes—
24#88201C2211yescharacteristic, complemented
25#88198C2211yescharacteristic, complemented
26C2×#6107C2212yescomplemented
27#88196—24no—
28C2×#6106C2212yes—
29C2×#6106C2212yescomplemented
30#88194C2211yescharacteristic, complemented
31#88193—22no—
32#88190C2211yescharacteristic, complemented
33C2×#6104C2212yes—
34C4×C22⋊D13—22no—
35C2×#6103—22no—
36C2×C4×Dic13C2211yescharacteristic
37C2×#6099C2211yescharacteristic
38#88162—24no—
39C2×D104C2212yes—
40C2×#6095C2212yes—
41#88055C2212yescomplemented
42C8×Dic13C2212yescomplemented
43C23×D13—21no—
44C13×#41—22no—
45C13×#41—22no—
46C2×Q8×C13—21no—
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13C2311yescharacteristic
50C2×Q8×C13C2312yes—
51C2×D4×C13—21no—
52C2×D4×C13C2311yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C2311yescharacteristic
56C2×C22⋊D13—21no—
57C2×C22⋊D13—22no—
58C22×Dic13D412yes—
59#6127—22no—
60#6127—22no—
61C2×D52—22no—
62C2×D52—22no—
63C2×D52—21no—
64C2×D52C2312yes—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26C2311yescharacteristic
68C13×Q16—24no—
69C13×SD16—24no—
70C13×M16D414yescomplemented
71C2×C8×C13C2312yes—
72C22⋊Dic13—22no—
73#6107—24no—
74#6106—24no—
75#6106—24no—
76#6104—24no—
77#6103—24no—
78#6103—24no—
79#6103—22no—
80#6101—22no—
81C4×Dic13D412yes—
82C4×Dic13C2311yescharacteristic
83C4×Dic13C2311yescharacteristic
84#6099D414yescomplemented
85C2×#1055C2312yes—
86D104—24no—
87#6095—24no—
88#3153—131nomaximal, Sylow
89C23×C13—21no—
90C23×C13C2×D411yescharacteristic
91C22×D13—22no—
92C22×D13—21no—
93C22×D13—44no—
94C22×D13—42no—
95Q8×C13—21no—
96Q8×C13—22no—
97Q8×C13—22no—
98Q8×C13—21no—
99Q8×C13—42no—
100D4×C13—21no—
101D4×C13—21no—
102D4×C13—42no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2×D412yes—
109C2×C4×C13C2×D412yes—
110C2×C4×C13C2411yescharacteristic
111C22⋊D13—44no—
112C22⋊D13—42no—
113C2×Dic13—21no—
114C2×Dic13—42no—
115C2×Dic13C2×D412yes—
116C2×Dic13C2×D412yes—
117D52—22no—
118D52—21no—
119D52—22no—
120D52—21no—
121D52—42no—
122C4×D13—42no—
123Dic26—21no—
124Dic26—21no—
125C8×C13C2×D414yes—
126#1055C2×D414yes—
127C2×#137—131no—
128C2×#137D1311yescharacteristic, complemented
129C2×AGL(1,ℤ/8)—131no—
130C2×AGL(1,ℤ/8)—131no—
131#532—131no—
132C2×#124—131no—
133#497—132no—
134#496—132no—
135#495—132no—
136#495—132no—
137C4×M16—131no—
138C22×C13—22no—
139C22×C13—41no—
140C22×C13—42no—
141C22×C13#12712yes—
142C22×C13C22×D411yescharacteristic
143C2×D13—41no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—44no—
147C2×D13—84no—
148C4×C13—41no—
149C4×C13—42no—
150C4×C13#12712yes—
151C4×C13C22×D411yescharacteristic
152C4×C13C22×D411yescharacteristic
153Dic13—22no—
154Dic13—22no—
155Dic13—41no—
156C2×#41—131no—
157C2×#41C2×D1311yescharacteristic
158C22×Q8C2×D1311yescharacteristic
159C22×D4—131no—
160#137—24no—
161#137—264no—
162AGL(1,ℤ/8)—264no—
163AGL(1,ℤ/8)—264no—
164C2×Q16—132no—
165C2×Q16C2×D1312yescomplemented
166C2×SD16—132no—
167C2×SD16—132no—
168C2×SD16—132no—
169C2×SD16C2×D1312yescomplemented
170C2×D8—132no—
171C2×D8—132no—
172C2×M16—131no—
173C2×M16C2×D1311yescharacteristic
174C4⋊Q8—131no—
175#127—131no—
176#124—132no—
177#124—132no—
178#124—131no—
179#124—131no—
180#124—262no—
181#121—262no—
182C4×D4—262no—
183C2×C22⋊C4—262no—
184C2×C42—131no—
185#97—132no—
186C4×C8—132no—
187C2×C13—22no—
188C2×C13—81no—
189C2×C13C2×#12711yescharacteristic
190C2×C13#57512yes—
191D13—81no—
192D13—82no—
193C24—261no—
194#41—22no—
195#41—22no—
196#41—262no—
197#41—262no—
198C2×Q8—21no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—131no—
202C2×Q8C22×D1312yes—
203C2×Q8C22×D1311yescharacteristic
204C2×D4—21no—
205C2×D4—132no—
206C2×D4—131no—
207C2×D4—262no—
208C2×D4—261no—
209C2×D4—262no—
210C2×D4—261no—
211C2×D4—262no—
212C2×D4C22×D1311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—132no—
216C22×C4—261no—
217C22×C4C22×D1311yescharacteristic
218Q16—24no—
219Q16—264no—
220SD16—24no—
221SD16—264no—
222SD16—264no—
223SD16—264no—
224D8—264no—
225D8—264no—
226M16—134no—
227M16C22⋊D1314yescomplemented
228C2×C8—132no—
229C2×C8C22×D1312yes—
230C4⋊C4—262no—
231C22⋊C4—264no—
232C22⋊C4—264no—
233C22⋊C4—262no—
234C22⋊C4—262no—
235C42—132no—
236C42—131no—
237C42—131no—
238C13#315311yescharacteristic, complemented, Sylow
239C23—21no—
240C23—262no—
241C23—261no—
242C23—524no—
243C23—522no—
244C23D4×D1311yescharacteristic
245Q8—21no—
246Q8—22no—
247Q8—22no—
248Q8—21no—
249Q8—42no—
250Q8—261no—
251Q8—261no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—262no—
256D4—261no—
257D4—261no—
258D4—262no—
259D4—524no—
260D4—522no—
261D4—522no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—132no—
267C2×C4—132no—
268C2×C4—261no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4D4×D1311yescharacteristic
272C2×C4D4×D1312yes—
273C2×C4C2×C22⋊D1312yes—
274C2×C4C23×D1311yescharacteristic
275C8—134no—
276C8C2×C22⋊D1314yes—
277C22—22no—
278C22—42no—
279C22—41no—
280C22—522no—
281C22—524no—
282C22—521no—
283C22—522no—
284C22—1044no—
285C22#8819412yes—
286C22C2×D4×D1311yescharacteristic
287C4—41no—
288C4—42no—
289C4—262no—
290C4—262no—
291C4—521no—
292C4#8819412yes—
293C4C2×D4×D1311yescharacteristic
294C4C22×C22⋊D1311yescharacteristic
295C2—22no—
296C2—81no—
297C2—1042no—
298C2—1041no—
299C2#1171948212yes—
300C2C2×#8819411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#137C2
socleC22×C13C22×D4
hypercenterC2×#137D13
hypocenterC13#3153
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C13×#137C2semidirect
2. #11719537C2semidirect
3. C2×#88203C2semidirect
4. C2×#88201C2semidirect
5. C2×#88196C2semidirect
6. C2×#88162C2semidirect
7. #11718852C2semidirect
8. #11718851C2semidirect
9. #11718837C2semidirect
10. #11718829C2semidirect
11. M16×Dic13C2semidirect
17. C2×C13×Q16C22semidirect
18. C2×C13×SD16C22semidirect
24. #88201C22semidirect
25. #88198C22semidirect
26. C2×#6107C22semidirect
29. C2×#6106C22semidirect
30. #88194C22semidirect
32. #88190C22semidirect
41. #88055C22semidirect
42. C8×Dic13C22semidirect
70. C13×M16D4semidirect
84. #6099D4semidirect
128. C2×#137D13semidirect
165. C2×Q16C2×D13semidirect
169. C2×SD16C2×D13semidirect
227. M16C22⋊D13semidirect
238. C13#3153semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1372
#117195372
C2×#882032
C2×#882012
C2×#881962
C2×#881622
#117188522
#117188512
#117188372
#117188292
M16×Dic132
#315313