Finite Group Databasebeta

← #13125604

Subgroups — #13125604

Order 1664.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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×#88192C211yesmaximal, characteristic, complemented
2#11719332C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4#11718878C211yesmaximal, characteristic, complemented
5#11718833C212yesmaximal, complemented
6#11718832C212yesmaximal, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718440C212yesmaximal, complemented
9#11718436C212yesmaximal, complemented
10#11718396C211yesmaximal, characteristic, complemented
11D13×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13—21no—
14C2×#6131C2211yescharacteristic, complemented
15C22×C4×D13C2211yescharacteristic
16C2×C13×SD16C2212yescomplemented
17C13×C22⋊Q8C2211yescharacteristic
18C2×C22⋊Dic13—21no—
19#88200C2211yescharacteristic, complemented
20#88192—21no—
21#88192—21no—
22#88192C2212yes—
23#88192C2212yes—
24C2×#6104C2212yescomplemented
25#88184C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C8×D13C2212yescomplemented
28#88149C2211yescharacteristic, complemented
29#88148—21no—
30#88147—21no—
31#88146C2211yescharacteristic, complemented
32#88136—21no—
33#88135—21no—
34C13×#102C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic
36#88075C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic
39#88061C2212yescomplemented
40#88060C2212yescomplemented
41#88057C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13—21no—
44C23×D13D411yescharacteristic
45C2×Q8×C13C2311yescharacteristic
46C2×D4×C13—21no—
47C2×D4×C13—42no—
48C2×D4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C2×C22⋊D13—21no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13—44no—
54C22×Dic13—21no—
55C22×Dic13D411yescharacteristic
56#6131—42no—
57C2×D52—21no—
58C2×D52—21no—
59C2×D52C2311yescharacteristic
60C2×C4×D13—21no—
61C2×C4×D13—42no—
62C2×C4×D13D411yescharacteristic
63C2×C4×D13D411yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C13×SD16—42no—
67C2×C8×C13C2312yes—
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2311yescharacteristic
70C13×C22⋊C4—21no—
71C22⋊Dic13—22no—
72C22⋊Dic13—22no—
73#6104—42no—
74#6103—21no—
75#6103—21no—
76#6103—21no—
77#6103—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13C2311yescharacteristic
80C4⋊Dic13C2312yes—
81#6101—21no—
82C4×Dic13—21no—
83C2×#1055C2312yes—
84C8×D13—42no—
85#3188—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13C2×D411yescharacteristic
91C22×D13—22no—
92C22×D13—22no—
93C22×D13—21no—
94C22×D13—41no—
95C22×D13C2×D411yescharacteristic
96C22×D13C2×D411yescharacteristic
97Q8×C13—22no—
98D4×C13—22no—
99D4×C13—22no—
100D4×C13—42no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13C2×D411yescharacteristic
105C2×C4×C13C2411yescharacteristic
106C22⋊D13—44no—
107C22⋊D13—42no—
108C22⋊D13—44no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111C2×Dic13—41no—
112C2×Dic13—42no—
113C2×Dic13C2×D411yescharacteristic
114C2×Dic13C2×D411yescharacteristic
115D52—22no—
116D52—42no—
117D52—42no—
118C4×D13—22no—
119C4×D13—22no—
120C4×D13—41no—
121C4×D13—41no—
122C4×D13—42no—
123C8×C13—22no—
124#1055—22no—
125#525—131no—
126C2×#121—131no—
127#484—131no—
128#482—132no—
129#481—131no—
130#466—132no—
131#465—132no—
132#450D1311yescharacteristic, complemented
133#449—132no—
134#447—131no—
135C2×C22⋊C8—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—84no—
142C22×C13#13512yes—
143C22×C13C22×D411yescharacteristic
144C2×D13—21no—
145C2×D13—21no—
146C2×D13—21no—
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—44no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13AGL(1,ℤ/8)12yes—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13H(5,𝔽2)12yes—
158Dic13—21no—
159Dic13—21no—
160Dic13—41no—
161Dic13—42no—
162C2×#41—131no—
163C22×D4—261no—
164C22×D4C2×D1311yescharacteristic
165C23×C4—131no—
166C2×SD16C2×D1312yescomplemented
167C2×D8—132no—
168C22×C8—132no—
169#123—261no—
170C22⋊Q8—131no—
171C22⋊Q8C2×D1311yescharacteristic
172#121—132no—
173#121—132no—
174#121—131no—
175#121—131no—
176#121—261no—
177#121—261no—
178#120—261no—
179C4×D4—261no—
180C4×D4—261no—
181#117—131no—
182C2×C4⋊C4—131no—
183C2×C22⋊C4—261no—
184#107—132no—
185#106—132no—
186#103—132no—
187#102—132no—
188#102—132no—
189#102C2×D1312yescomplemented
190C22⋊C8—131no—
191C22⋊C8—132no—
192C22⋊C8C2×D1311yescharacteristic
193C2×C13—22no—
194C2×C13—82no—
195C2×C13#53411yescharacteristic
196C2×C13C2×#13511yescharacteristic
197C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
198D13—22no—
199D13—41no—
200D13—81no—
201C24—21no—
202C24—131no—
203#41—522no—
204C2×Q8C22×D1311yescharacteristic
205C2×D4—21no—
206C2×D4—42no—
207C2×D4—131no—
208C2×D4—261no—
209C2×D4—261no—
210C2×D4—262no—
211C2×D4—262no—
212C2×D4—261no—
213C2×D4—524no—
214C2×D4C22×D1312yes—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—522no—
223C22×C4C22×D1311yescharacteristic
224SD16—42no—
225D8—522no—
226C2×C8—132no—
227C2×C8—522no—
228C2×C8C22×D1312yes—
229C4⋊C4—21no—
230C4⋊C4—131no—
231C4⋊C4—132no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4C22×D1311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—261no—
237C22⋊C4—261no—
238C22⋊C4—261no—
239C22⋊C4—262no—
240C22⋊C4—262no—
241C22⋊C4—261no—
242C42—261no—
243C13#318811yescharacteristic, complemented, Sylow
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—131no—
249C23—131no—
250C23—262no—
251C23—262no—
252C23—261no—
253C23—521no—
254C23D4×D1311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—262no—
260D4—522no—
261D4—522no—
262D4—524no—
263D4—524no—
264D4—522no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—261no—
273C2×C4—262no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—522no—
277C2×C4—521no—
278C2×C4—522no—
279C2×C4D4×D1311yescharacteristic
280C2×C4C23×D1311yescharacteristic
281C8—22no—
282C8—262no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—132no—
290C22—261no—
291C22—261no—
292C22—261no—
293C22—261no—
294C22—261no—
295C22—524no—
296C22—521no—
297C22—521no—
298C22—521no—
299C22#8817012yes—
300C22C2×D4×D1311yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—261no—
305C4—261no—
306C4—521no—
307C4—522no—
308C4#8825112yes—
309C2—22no—
310C2—82no—
311C2—262no—
312C2—521no—
313C2—1041no—
314C2#1171929411yescharacteristic
315C2C2×#8817011yescharacteristic
316C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
hypercenter#450D13
hypocenterC13#3188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#88192C2semidirect
2. #11719332C2semidirect
3. C13×#450C2semidirect
4. #11718878C2semidirect
5. #11718833C2semidirect
6. #11718832C2semidirect
7. #11718705C2semidirect
8. #11718440C2semidirect
9. #11718436C2semidirect
10. #11718396C2semidirect
11. D13×C22⋊C8C2semidirect
14. C2×#6131C22semidirect
16. C2×C13×SD16C22semidirect
19. #88200C22semidirect
24. C2×#6104C22semidirect
27. C2×C8×D13C22semidirect
28. #88149C22semidirect
31. #88146C22semidirect
34. C13×#102C22semidirect
36. #88075C22semidirect
37. #88072C22semidirect
39. #88061C22semidirect
40. #88060C22semidirect
41. #88057C22semidirect
42. #88047C22semidirect
132. #450D13semidirect
166. C2×SD16C2×D13semidirect
189. #102C2×D13semidirect
243. C13#3188semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
#117193322
C13×#4502
#117188782
#117188332
#117188322
#117187052
#117184402
#117184362
#117183962
D13×C22⋊C82
#318813