Finite Group Databasebeta

← #13125644

Subgroups — #13125644

Order 1664.

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

normal subgroups only

This group has 462 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
1D13×#121C211yesmaximal, characteristic
2C2×#88151C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718701C211yesmaximal, characteristic, complemented
5#11718628C211yesmaximal, characteristic, complemented
6#11718547C212yesmaximal, complemented
7#11718545C212yesmaximal, complemented
8#11718441C212yesmaximal, complemented
9#11718437C212yesmaximal, complemented
10#11718399C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic, complemented
12C2×D4×D13—21no—
13C2×D4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic, complemented
16C13×#121C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic, complemented
18#88193—21no—
19#88192C2211yescharacteristic
20C2×#6105C2212yescomplemented
21#88184C2211yescharacteristic
22C2×#6103—21no—
23C2×C4⋊Dic13—21no—
24C2×#6095C2212yescomplemented
25C2×#6094C2212yescomplemented
26#88151—21no—
27#88151—21no—
28#88151C2212yes—
29#88151C2212yescomplemented
30#88149C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88138—21no—
33C22⋊C4×D13—21no—
34C13×#107C2212yescomplemented
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic, complemented
37C22⋊#1055C2211yescharacteristic, complemented
38#88060C2212yes—
39#88056C2212yescomplemented
40#88050C2212yescomplemented
41#88049C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13—21no—
44C23×D13D411yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13C2311yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—21no—
50C2×C22⋊D13—21no—
51C2×C22⋊D13—21no—
52C22×Dic13—21no—
53C22×Dic13D411yescharacteristic
54D4×D13—42no—
55D4×D13—44no—
56C2×D52—21no—
57C2×D52C2311yescharacteristic
58C2×C4×D13—21no—
59C2×C4×D13—42no—
60C2×C4×D13D411yescharacteristic
61C2×C4×D13D411yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×Dic26—21no—
65C2×Dic26—42no—
66C2×Dic26C2312yes—
67C2×C8×C13C2312yes—
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2312yes—
70C13×C4⋊C4C2311yescharacteristic
71C13×C22⋊C4—21no—
72C22⋊Dic13—21no—
73#6105—42no—
74#6103—22no—
75#6103—22no—
76#6103—21no—
77#6103—21no—
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80C4⋊Dic13C2311yescharacteristic
81#6101—21no—
82C2×#1055C2312yes—
83#6095—42no—
84#6094—42no—
85#3193—131nomaximal, Sylow
86C23×C13—21no—
87C23×C13C2×D411yescharacteristic
88C22×D13—22no—
89C22×D13—22no—
90C22×D13—21no—
91C22×D13—41no—
92C22×D13—42no—
93C22×D13—42no—
94C22×D13—42no—
95C22×D13C2×D411yescharacteristic
96C22×D13C2×D411yescharacteristic
97D4×C13—22no—
98D4×C13—42no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—42no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2411yescharacteristic
105C22⋊D13—42no—
106C22⋊D13—42no—
107C22⋊D13—42no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—42no—
112C2×Dic13C2×D411yescharacteristic
113C2×Dic13C2×D411yescharacteristic
114D52—22no—
115D52—42no—
116C4×D13—22no—
117C4×D13—22no—
118C4×D13—41no—
119C4×D13—41no—
120C4×D13—42no—
121Dic26—22no—
122Dic26—22no—
123Dic26—42no—
124C8×C13—22no—
125#1055—22no—
126C2×C22⋊Q8—131no—
127C2×#121—131no—
128#484—132no—
129#480—131no—
130#480D1311yescharacteristic, complemented
131#468—132no—
132#468—132no—
133#450—132no—
134#448—131no—
135#448—131no—
136#407—131no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13AGL(1,ℤ/8)12yes—
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×D13—84no—
154C2×D13#13712yes—
155C4×C13—21no—
156C4×C13—41no—
157C4×C13—42no—
158C4×C13H(5,𝔽2)12yes—
159Dic13—21no—
160Dic13—21no—
161Dic13—42no—
162Dic13—41no—
163C22×Q8—131no—
164C22×D4—131no—
165C22×D4—261no—
166C23×C4—131no—
167C2×SD16—132no—
168C2×SD16—132no—
169C2×M16—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—261no—
182C2×C4⋊C4C2×D1311yescharacteristic, complemented
183C2×C22⋊C4—261no—
184C2×C22⋊C4—261no—
185#107—132no—
186#107C2×D1312yescomplemented
187#103—132no—
188#103—132no—
189#102—132no—
190#102C2×D1312yescomplemented
191C22⋊C8—131no—
192C22⋊C8—132no—
193C22⋊C8C2×D1311yescharacteristic, complemented
194C2×C13—22no—
195C2×C13—81no—
196C2×C13#53411yescharacteristic
197C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C13C2×#13711yescharacteristic
199D13—22no—
200D13—41no—
201D13—81no—
202C24—131no—
203C24—261no—
204C2×Q8—132no—
205C2×Q8—261no—
206C2×Q8—522no—
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—522no—
227SD16—522no—
228M16—522no—
229C2×C8—132no—
230C2×C8C22×D1312yes—
231C4⋊C4—21no—
232C4⋊C4—131no—
233C4⋊C4—261no—
234C4⋊C4—262no—
235C4⋊C4—262no—
236C4⋊C4C22×D1312yes—
237C4⋊C4C22×D1311yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—261no—
240C22⋊C4—262no—
241C22⋊C4—262no—
242C22⋊C4—261no—
243C22⋊C4—261no—
244C13#319311yescharacteristic, complemented, Sylow
245C23—21no—
246C23—131no—
247C23—131no—
248C23—262no—
249C23—262no—
250C23—261no—
251C23—521no—
252C23—522no—
253C23—522no—
254C23—522no—
255C23D4×D1311yescharacteristic
256Q8—262no—
257Q8—262no—
258Q8—522no—
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—261no—
275C2×C4—262no—
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—261no—
292C22—261no—
293C22—261no—
294C22—261no—
295C22—261no—
296C22—524no—
297C22—521no—
298C22—521no—
299C22—521no—
300C22—1044no—
301C22#8816512yes—
302C22C2×D4×D1311yescharacteristic
303C4—21no—
304C4—42no—
305C4—41no—
306C4—261no—
307C4—261no—
308C4—521no—
309C4—522no—
310C4#8825612yes—
311C2—22no—
312C2—81no—
313C2—262no—
314C2—521no—
315C2—1041no—
316C2#1171935811yescharacteristic
317C2C2×#8816511yescharacteristic
318C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radicalD13×#121C2
hypercenter#480D13
hypocenterC13#3193
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#88151C2semidirect
3. C13×#480C2semidirect
4. #11718701C2semidirect
5. #11718628C2semidirect
6. #11718547C2semidirect
7. #11718545C2semidirect
8. #11718441C2semidirect
9. #11718437C2semidirect
10. #11718399C2semidirect
11. #11718387C2semidirect
15. C22×Dic26C22semidirect
17. C2×C13×C4⋊C4C22semidirect
20. C2×#6105C22semidirect
24. C2×#6095C22semidirect
25. C2×#6094C22semidirect
29. #88151C22semidirect
34. C13×#107C22semidirect
35. C13×#102C22semidirect
36. C13×C22⋊C8C22semidirect
37. C22⋊#1055C22semidirect
39. #88056C22semidirect
40. #88050C22semidirect
41. #88049C22semidirect
42. #88047C22semidirect
130. #480D13semidirect
182. C2×C4⋊C4C2×D13semidirect
186. #107C2×D13semidirect
190. #102C2×D13semidirect
193. C22⋊C8C2×D13semidirect
244. C13#3193semidirect

Maximal subgroups

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

subgroupindex
D13×#1212
C2×#881512
C13×#4802
#117187012
#117186282
#117185472
#117185452
#117184412
#117184372
#117183992
#117183872
#319313