Finite Group Databasebeta

← #13124929

Subgroups — #13124929

Order 1664.

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

normal subgroups only

This group has 488 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
1#11719430C211yesmaximal, characteristic, complemented
2C4×D4×D13C211yesmaximal, characteristic, complemented
3C13×#476C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718676C211yesmaximal, characteristic, complemented
6#11718530C212yesmaximal, complemented
7#11718524C212yesmaximal, complemented
8#11718504C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic, complemented
10#11718446C212yesmaximal, complemented
11#11718434C212yesmaximal, complemented
12C2×#6131—21no—
13C2×D4×D13C2211yescharacteristic
14C22×C4×D13—21no—
15C13×C4⋊Q8C2211yescharacteristic, complemented
16C4×D4×C13C2211yescharacteristic
17#88201—21no—
18D4×Dic13C2211yescharacteristic
19C2×#6104C2212yes—
20C4×C22⋊D13—21no—
21C2×D104C2212yes—
22#88149—21no—
23#88149C2212yes—
24#88147—21no—
25#88147C2211yescharacteristic
26#88147C2212yescomplemented
27C4⋊C4×D13C2211yescharacteristic
28#88135—21no—
29C22⋊C4×D13—21no—
30#88128C2211yescharacteristic, complemented
31C4×D52C2211yescharacteristic
32C42×D13C2211yescharacteristic
33C13×#106C2212yescomplemented
34C13×C4⋊C8C2211yescharacteristic, complemented
35C13×#102C2212yes—
36#88061C2212yescomplemented
37#88060C2212yes—
38#88055C2212yescomplemented
39#88049C2212yes—
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49#6131—44no—
50D4×D13—22no—
51D4×D13—22no—
52C2×D52—22no—
53C2×D52—21no—
54C2×D52—21no—
55C2×D52C2312yes—
56C2×D52C2311yescharacteristic
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13—22no—
61C2×C4×D13—44no—
62C2×C4×D13D411yescharacteristic
63C2×C4×D13D411yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×C8×C13C2312yes—
66C13×C4⋊C4—21no—
67C13×C4⋊C4C2312yes—
68C13×C4⋊C4C2311yescharacteristic
69C13×C22⋊C4—21no—
70C42×C13C2311yescharacteristic
71C22⋊Dic13—21no—
72#6104—24no—
73#6103—21no—
74#6103—21no—
75#6103—22no—
76#6103—22no—
77C4⋊Dic13C2311yescharacteristic
78#6101—21no—
79C4×Dic13D411yescharacteristic
80C4×Dic13D411yescharacteristic
81C4×Dic13C2311yescharacteristic
82C2×#1055C2312yes—
83D104—24no—
84#3109—131nomaximal, Sylow
85C23×C13—21no—
86C22×D13—24no—
87C22×D13—21no—
88C22×D13—22no—
89C22×D13—42no—
90C22×D13—42no—
91C22×D13C2×D411yescharacteristic
92Q8×C13—42no—
93D4×C13—21no—
94D4×C13#4112yescomplemented
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2×D411yescharacteristic
100C2×C4×C13C2411yescharacteristic
101C22⋊D13—24no—
102C2×Dic13—21no—
103C2×Dic13—42no—
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106C2×Dic13C2×D411yescharacteristic
107D52—21no—
108D52—22no—
109D52—22no—
110D52—42no—
111D52—44no—
112D52—42no—
113D52#4112yescomplemented
114C4×D13—22no—
115C4×D13—22no—
116C4×D13—21no—
117C4×D13—21no—
118C4×D13—42no—
119C4×D13—44no—
120C4×D13—42no—
121C4×D13—42no—
122C8×C13—22no—
123#1055—22no—
124#532—131no—
125C2×C4×D4—131no—
126#481—132no—
127#476—131no—
128#476D1311yescharacteristic, complemented
129#459—131no—
130#459—131no—
131#447—132no—
132#442—132no—
133#442—132no—
134#432—131no—
135C22×C13—22no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13C22×D411yescharacteristic
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—22no—
142C2×D13—48no—
143C2×D13—41no—
144C2×D13—41no—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13AGL(1,ℤ/8)12yes—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13—42no—
152C4×C13AGL(1,ℤ/8)12yes—
153C4×C13C2×#4111yescharacteristic
154C4×C13C2×#4111yescharacteristic
155Dic13—21no—
156Dic13—21no—
157Dic13—21no—
158Dic13—41no—
159C2×#41—261no—
160C22×D4—131no—
161C23×C4—261no—
162C2×D8—132no—
163C2×D8—132no—
164C4⋊Q8C2×D1311yescharacteristic, complemented
165#127—131no—
166#124—261no—
167#121—132no—
168#121—261no—
169C4×D4—131no—
170C4×D4—131no—
171C4×D4—132no—
172C4×D4—131no—
173C4×D4—261no—
174C4×D4—261no—
175C4×D4—261no—
176C4×D4C2×D1311yescharacteristic
177C2×C4⋊C4—131no—
178C2×C22⋊C4—261no—
179C2×C42—131no—
180#106—132no—
181#106C2×D1312yescomplemented
182C4⋊C8—131no—
183C4⋊C8C2×D1311yescharacteristic, complemented
184#102—132no—
185#102—132no—
186#102—132no—
187#102C2×D1312yes—
188C22⋊C8—132no—
189#97—132no—
190C2×C13—42no—
191C2×C13#52511yescharacteristic
192C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
194D13—22no—
195D13—42no—
196D13—82no—
197C24—261no—
198#41—524no—
199C2×Q8—21no—
200C2×D4—131no—
201C2×D4—132no—
202C2×D4—262no—
203C2×D4—261no—
204C2×D4—262no—
205C2×D4—262no—
206C2×D4—261no—
207C2×D4—261no—
208C2×D4C22×D1311yescharacteristic
209C22×C4—21no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—261no—
214C22×C4—262no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4—524no—
219D8—264no—
220D8—264no—
221C2×C8—132no—
222C2×C8C22×D1312yes—
223C4⋊C4—21no—
224C4⋊C4—131no—
225C4⋊C4—261no—
226C4⋊C4C22×D1311yescharacteristic
227C4⋊C4C22×D1312yes—
228C22⋊C4—21no—
229C22⋊C4—261no—
230C22⋊C4—262no—
231C22⋊C4—262no—
232C22⋊C4—261no—
233C22⋊C4—261no—
234C42—131no—
235C42—131no—
236C42—131no—
237C42C22×D1311yescharacteristic
238C13#310911yescharacteristic, complemented, Sylow
239C23—21no—
240C23—131no—
241C23—264no—
242C23—261no—
243C23—262no—
244C23—522no—
245C23—522no—
246Q8—42no—
247D4—21no—
248D4—132no—
249D4—264no—
250D4—261no—
251D4—262no—
252D4—262no—
253D4—522no—
254D4—524no—
255D4—522no—
256D4#613112yescomplemented
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—131no—
261C2×C4—131no—
262C2×C4—131no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—522no—
269C2×C4—524no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—522no—
273C2×C4D4×D1311yescharacteristic
274C2×C4D4×D1311yescharacteristic
275C2×C4C23×D1311yescharacteristic
276C8—22no—
277C8—262no—
278C22—22no—
279C22—41no—
280C22—41no—
281C22—132no—
282C22—261no—
283C22—261no—
284C22—262no—
285C22—528no—
286C22—521no—
287C22—521no—
288C22—522no—
289C22—522no—
290C22—522no—
291C22C2×D4×D1311yescharacteristic
292C4—21no—
293C4—41no—
294C4—42no—
295C4—261no—
296C4—261no—
297C4—261no—
298C4—521no—
299C4#8816812yes—
300C4C2×#613111yescharacteristic
301C4#41×D1311yescharacteristic
302C2—42no—
303C2—262no—
304C2—522no—
305C2—1042no—
306C2#1171933211yescharacteristic
307C2C2×#8816811yescharacteristic
308C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#476C2
socleC22×C13C22×D4
hypercenter#476D13
hypocenterC13#3109
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #11719430C2semidirect
2. C4×D4×D13C2semidirect
3. C13×#476C2semidirect
4. #11718745C2semidirect
5. #11718676C2semidirect
6. #11718530C2semidirect
7. #11718524C2semidirect
8. #11718504C2semidirect
9. #11718496C2semidirect
10. #11718446C2semidirect
11. #11718434C2semidirect
15. C13×C4⋊Q8C22semidirect
26. #88147C22semidirect
30. #88128C22semidirect
33. C13×#106C22semidirect
34. C13×C4⋊C8C22semidirect
36. #88061C22semidirect
38. #88055C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. C4⋊#1055C22semidirect
94. D4×C13#41semidirect
113. D52#41semidirect
128. #476D13semidirect
164. C4⋊Q8C2×D13semidirect
181. #106C2×D13semidirect
183. C4⋊C8C2×D13semidirect
238. C13#3109semidirect
256. D4#6131semidirect

Maximal subgroups

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

subgroupindex
#117194302
C4×D4×D132
C13×#4762
#117187452
#117186762
#117185302
#117185242
#117185042
#117184962
#117184462
#117184342
#310913