Finite Group Databasebeta

← #13125591

Subgroups — #13125591

Order 1664.

468 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 121 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×#88200C211yesmaximal, characteristic, complemented
2D13×#121C211yesmaximal, characteristic
3C13×#448C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718832C212yesmaximal, complemented
6#11718830C212yesmaximal, complemented
7#11718695C211yesmaximal, characteristic, complemented
8#11718468C212yesmaximal, complemented
9#11718466C212yesmaximal, complemented
10#11718396C211yesmaximal, characteristic, complemented
11D13×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic, complemented
13C2×D4×D13—21no—
14C2×D4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×SD16C2212yescomplemented
17C13×#121C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20#88200C2212yes—
21#88200C2212yescomplemented
22C2×#6106C2212yescomplemented
23#88193—21no—
24#88192C2211yescharacteristic
25#88184C2211yescharacteristic
26C2×#6103—21no—
27C2×C4⋊Dic13C2211yescharacteristic, complemented
28C2×#6101—21no—
29C2×C8×D13C2212yescomplemented
30#88149C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88138—21no—
33C22⋊C4×D13—21no—
34C13×#103C2212yescomplemented
35C13×C22⋊C8C2211yescharacteristic, complemented
36#88075C2212yescomplemented
37#88072C2212yescomplemented
38C22⋊#1055C2211yescharacteristic, complemented
39#88061C2212yescomplemented
40#88060C2212yes—
41#88057C2212yescomplemented
42#88048C2212yescomplemented
43C23×D13—21no—
44C23×D13D411yescharacteristic
45C2×Q8×C13—21no—
46C2×Q8×C13—42no—
47C2×Q8×C13C2312yes—
48C2×D4×C13—21no—
49C2×D4×C13C2311yescharacteristic
50C22×C4×C13—21no—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—21no—
54C2×C22⋊D13—21no—
55C22×Dic13—21no—
56C22×Dic13D411yescharacteristic
57D4×D13—42no—
58D4×D13—44no—
59C2×D52—21no—
60C2×D52C2311yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—42no—
63C2×C4×D13D411yescharacteristic
64C2×C4×D13D411yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C2×C4×D13C2311yescharacteristic
67C13×SD16—42no—
68C2×C8×C13C2312yes—
69C13×C4⋊C4C2311yescharacteristic
70C13×C22⋊C4—21no—
71C22⋊Dic13—21no—
72#6106—42no—
73#6103—22no—
74#6103—22no—
75#6103—21no—
76#6103—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13C2312yes—
79C4⋊Dic13C2311yescharacteristic
80#6101—21no—
81#6101—22no—
82#6101—22no—
83C2×#1055C2312yes—
84C8×D13—42no—
85#3187—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13C2×D411yescharacteristic
88C22×D13—21no—
89C22×D13—41no—
90C22×D13—41no—
91C22×D13—42no—
92C22×D13—42no—
93C22×D13—42no—
94C22×D13SD1614yescomplemented
95C22×D13C2×D411yescharacteristic
96C22×D13C2×D411yescharacteristic
97Q8×C13—22no—
98Q8×C13—22no—
99Q8×C13—42no—
100D4×C13—22no—
101D4×C13—42no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—21no—
105C2×C4×C13—42no—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2411yescharacteristic
108C22⋊D13—42no—
109C22⋊D13—42no—
110C22⋊D13—42no—
111C2×Dic13—22no—
112C2×Dic13—21no—
113C2×Dic13—41no—
114C2×Dic13—42no—
115C2×Dic13C2×D411yescharacteristic
116C2×Dic13C2×D411yescharacteristic
117D52—22no—
118D52—42no—
119C4×D13—22no—
120C4×D13—22no—
121C4×D13—41no—
122C4×D13—41no—
123C4×D13—42no—
124C8×C13—22no—
125#1055—22no—
126C2×C22⋊Q8—131no—
127C2×#121—131no—
128#483—132no—
129#481—131no—
130#481—131no—
131#465—132no—
132#465—132no—
133#450—132no—
134#448—131no—
135#448D1311yescharacteristic, complemented
136C2×C22⋊C8—131no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13C2×SD1612yes—
143C22×C13C22×D411yescharacteristic
144C2×D13—21no—
145C2×D13—21no—
146C2×D13—21no—
147C2×D13—21no—
148C2×D13—44no—
149C2×D13—41no—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—84no—
153C2×D13C2×SD1612yes—
154C2×D13C2×SD1612yes—
155C4×C13—21no—
156C4×C13—42no—
157C4×C13—41no—
158C4×C13H(5,𝔽2)12yes—
159Dic13—21no—
160Dic13—21no—
161Dic13—41no—
162Dic13—42no—
163C22×Q8C2×D1311yescharacteristic, complemented
164C22×D4—131no—
165C22×D4—261no—
166C23×C4—131no—
167C2×SD16—132no—
168C2×SD16C2×D1312yescomplemented
169C22×C8—132no—
170C22⋊Q8—132no—
171C22⋊Q8—132no—
172C22⋊Q8—261no—
173C22⋊Q8—261no—
174#121—131no—
175#121—131no—
176#121—131no—
177#121—261no—
178#121—261no—
179#121C2×D1311yescharacteristic
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C22⋊C4—261no—
184C2×C22⋊C4—261no—
185#106—132no—
186#106—132no—
187#103—132no—
188#103C2×D1312yescomplemented
189#102—132no—
190#102—132no—
191C22⋊C8—131no—
192C22⋊C8—132no—
193C22⋊C8C2×D1311yescharacteristic, complemented
194C2×C13—22no—
195C2×C13—81no—
196C2×C13#53411yescharacteristic
197C2×C13C22×SD1611yescharacteristic
198C2×C13#57511yescharacteristic
199D13—22no—
200D13—22no—
201D13—81no—
202C24—131no—
203C24—261no—
204C2×Q8—21no—
205C2×Q8—42no—
206C2×Q8C22×D1312yes—
207C2×D4—21no—
208C2×D4—131no—
209C2×D4—261no—
210C2×D4—261no—
211C2×D4—261no—
212C2×D4—261no—
213C2×D4—522no—
214C2×D4—524no—
215C2×D4C22×D1311yescharacteristic
216C22×C4—21no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—522no—
225C22×C4C22×D1311yescharacteristic
226SD16—42no—
227SD16—522no—
228C2×C8—132no—
229C2×C8—522no—
230C2×C8C22×D1312yes—
231C4⋊C4—132no—
232C4⋊C4—131no—
233C4⋊C4—261no—
234C4⋊C4—262no—
235C4⋊C4—262no—
236C4⋊C4—261no—
237C4⋊C4C22×D1311yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—261no—
240C22⋊C4—262no—
241C22⋊C4—262no—
242C22⋊C4—261no—
243C22⋊C4—261no—
244C13#318711yescharacteristic, complemented, Sylow
245C23—21no—
246C23—131no—
247C23—131no—
248C23—134no—
249C23—261no—
250C23—521no—
251C23—521no—
252C23—522no—
253C23—522no—
254C23—522no—
255C23D4×D1311yescharacteristic
256Q8—22no—
257Q8—22no—
258Q8—42no—
259D4—22no—
260D4—42no—
261D4—262no—
262D4—522no—
263D4—522no—
264D4—522no—
265D4—522no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—261no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—522no—
279C2×C4—521no—
280C2×C4—522no—
281C2×C4D4×D1311yescharacteristic
282C2×C4C23×D1311yescharacteristic
283C8—22no—
284C8—262no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—132no—
291C22—132no—
292C22—261no—
293C22—261no—
294C22—261no—
295C22—261no—
296C22—524no—
297C22—521no—
298C22—521no—
299C22—521no—
300C22—1044no—
301C22SD16×D1312yes—
302C22C2×D4×D1311yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—261no—
307C4—261no—
308C4—521no—
309C4—522no—
310C4#8825112yes—
311C2—22no—
312C2—81no—
313C2—262no—
314C2—262no—
315C2—1041no—
316C2#1171929411yescharacteristic
317C2C2×SD16×D1311yescharacteristic
318C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#448C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#448D13
hypocenterC13#3187
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#448C2semidirect
4. #11718888C2semidirect
5. #11718832C2semidirect
6. #11718830C2semidirect
7. #11718695C2semidirect
8. #11718468C2semidirect
9. #11718466C2semidirect
10. #11718396C2semidirect
11. D13×C22⋊C8C2semidirect
12. C22×Q8×C13C22semidirect
16. C2×C13×SD16C22semidirect
21. #88200C22semidirect
22. C2×#6106C22semidirect
27. C2×C4⋊Dic13C22semidirect
29. C2×C8×D13C22semidirect
34. C13×#103C22semidirect
35. C13×C22⋊C8C22semidirect
36. #88075C22semidirect
37. #88072C22semidirect
38. C22⋊#1055C22semidirect
39. #88061C22semidirect
41. #88057C22semidirect
42. #88048C22semidirect
94. C22×D13SD16semidirect
135. #448D13semidirect
163. C22×Q8C2×D13semidirect
168. C2×SD16C2×D13semidirect
188. #103C2×D13semidirect
193. C22⋊C8C2×D13semidirect
244. C13#3187semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
D13×#1212
C13×#4482
#117188882
#117188322
#117188302
#117186952
#117184682
#117184662
#117183962
D13×C22⋊C82
#318713