Finite Group Databasebeta

← #13124462

Subgroups — #13124462

Order 1664.

496 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#88196C211yesmaximal, characteristic, complemented
3#11719496C211yesmaximal, characteristic
4C22×#6099C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6#11718713C212yesmaximal, complemented
7#11718712C212yesmaximal, complemented
8#11718710C212yesmaximal, complemented
9#11718709C212yesmaximal, complemented
10#11718627C211yesmaximal, characteristic, complemented
11#11718625C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C2×#6127C2211yescharacteristic
15C13×C22⋊Q8—21no—
16C13×C22⋊Q8—21no—
17C13×C22⋊Q8C2212yes—
18C13×C22⋊Q8C2212yes—
19C2×C13×C4⋊C4—21no—
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4—21no—
22#88207—21no—
23C2×#6107C2212yescomplemented
24#88196—24no—
25C2×#6106C2212yescomplemented
26#88184C2211yescharacteristic
27#88184C2211yescharacteristic
28#88183—21no—
29C4×C22⋊D13—21no—
30C4×C22⋊D13—21no—
31#88180C2211yescharacteristic
32#88178C2211yescharacteristic
33#88178C2211yescharacteristic
34C2×#6099—24no—
35C2×#6099C2212yes—
36C2×#6099C2211yescharacteristic
37C2×#6099C2211yescharacteristic
38C22×#1055C2212yes—
39#88075C2212yescomplemented
40#88075C2212yescomplemented
41#88050C2212yescomplemented
42#88049C2212yescomplemented
43#88048C2212yescomplemented
44#88047C2212yescomplemented
45C24×C13D411yescharacteristic
46C2×Q8×C13—21no—
47C2×Q8×C13—22no—
48C2×Q8×C13—22no—
49C2×Q8×C13C2312yes—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13D411yescharacteristic
55C22×C4×C13D411yescharacteristic
56C22×C4×C13D411yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C2×C22⋊D13—21no—
62C2×C22⋊D13—21no—
63#6127—22no—
64#6127—22no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26C2311yescharacteristic
68C13×C4⋊C4—22no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2312yes—
72C13×C22⋊C4—22no—
73C13×C22⋊C4—22no—
74C22⋊Dic13—21no—
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77#6107—24no—
78#6106—24no—
79#6103—21no—
80#6103—21no—
81C4⋊Dic13C2311yescharacteristic
82C4⋊Dic13C2311yescharacteristic
83#6101—21no—
84#6101—21no—
85C4×Dic13—21no—
86#6099—22no—
87#6099—24no—
88#6099D414yescomplemented
89C2×#1055—24no—
90C2×#1055C2312yes—
91C2×#1055C2312yes—
92#3056—131nomaximal, Sylow
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—41no—
96C23×C13C2×D411yescharacteristic
97C23×C13C2×D411yescharacteristic
98C23×C13C2×D411yescharacteristic
99C22×D13—21no—
100Q8×C13—22no—
101Q8×C13—22no—
102Q8×C13—42no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D412yes—
118C2×C4×C13#4112yes—
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—42no—
121C22⋊D13—42no—
122C22⋊D13—42no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126D52—21no—
127D52—21no—
128C4×D13—42no—
129Dic26—21no—
130Dic26—21no—
131#1055—22no—
132#1055C2×D414yes—
133C2×#137—131no—
134C22×M16—131no—
135#525—131no—
136C2×C22⋊Q8D1311yescharacteristic, complemented
137#470—132no—
138#468—132no—
139#467—132no—
140#465—132no—
141#428—131no—
142#419—131no—
143#417—131no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—44no—
152C22×C13#12112yes—
153C22×C13#13712yescomplemented
154C22×C13C22×D411yescharacteristic
155C2×D13—41no—
156C2×D13—41no—
157C2×D13—41no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—42no—
161C4×C13—42no—
162C4×C13#12112yes—
163C4×C13C22×D411yescharacteristic
164C4×C13C2×#4111yescharacteristic
165Dic13—41no—
166Dic13—41no—
167Dic13—41no—
168C2×#41—131no—
169C22×Q8C2×D1311yescharacteristic
170C23×C4C2×D1311yescharacteristic
171#137—264no—
172C2×Q16—132no—
173C2×SD16—132no—
174C2×M16—131no—
175C2×M16—131no—
176C2×M16—132no—
177C2×M16—264no—
178C22×C8—132no—
179#123—261no—
180C22⋊Q8—21no—
181C22⋊Q8—21no—
182C22⋊Q8—131no—
183C22⋊Q8—131no—
184C22⋊Q8C2×D1312yes—
185C22⋊Q8C2×D1312yes—
186#121—131no—
187#121—131no—
188#120—261no—
189C4×D4—261no—
190C4×D4—261no—
191#117—131no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×D1311yescharacteristic
194C2×C22⋊C4—21no—
195#107—132no—
196#106—132no—
197#103—132no—
198#103—132no—
199#103—132no—
200#102—132no—
201C2×C13—22no—
202C2×C13—22no—
203C2×C13—41no—
204C2×C13C2×#12111yescharacteristic
205C2×C13C2×#13711yescharacteristic
206C2×C13#57511yescharacteristic
207D13—81no—
208C24C22⋊D1311yescharacteristic
209#41—262no—
210#41—262no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—131no—
215C2×Q8C22×D1312yes—
216C2×D4—131no—
217C2×D4—261no—
218C2×D4—261no—
219C2×D4—261no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—261no—
225C22×C4C22⋊D1311yescharacteristic
226C22×C4C22⋊D1311yescharacteristic
227C22×C4C22⋊D1311yescharacteristic
228C22×C4C22×D1311yescharacteristic
229C22×C4C22×D1311yescharacteristic
230C22×C4C22×D1311yescharacteristic
231Q16—264no—
232SD16—264no—
233M16—134no—
234M16—264no—
235M16—262no—
236C2×C8—132no—
237C2×C8—132no—
238C2×C8—264no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—21no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4C22×D1312yes—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—261no—
255C13#305611yescharacteristic, complemented, Sylow
256C23—22no—
257C23—22no—
258C23—41no—
259C23—261no—
260C23C2×C22⋊D1311yescharacteristic
261C23C2×C22⋊D1311yescharacteristic
262C23C2×C22⋊D1311yescharacteristic
263Q8—22no—
264Q8—22no—
265Q8—42no—
266Q8—261no—
267Q8—261no—
268D4—261no—
269D4—261no—
270D4—522no—
271D4—522no—
272D4—522no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—522no—
288C2×C4D4×D1312yes—
289C2×C4#612912yes—
290C2×C4C2×C22⋊D1311yescharacteristic
291C2×C4C2×C22⋊D1311yescharacteristic
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C23×D1311yescharacteristic
294C8—134no—
295C8—262no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—44no—
304C22—521no—
305C22—521no—
306C22—521no—
307C22#8819312yes—
308C22#8819612yescomplemented
309C22C22×C22⋊D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—42no—
313C4—42no—
314C4—521no—
315C4—521no—
316C4—521no—
317C4#8819312yes—
318C4C2×D4×D1311yescharacteristic
319C4C2×#612911yescharacteristic
320C2—22no—
321C2—22no—
322C2—41no—
323C2—1041no—
324C2C2×#8819311yescharacteristic
325C2C2×#8819611yescharacteristic
326C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×C22⋊Q8C2
socleC22×C13C22×D4
prime radical#11719496C2
hypercenterC2×C22⋊Q8D13
hypocenterC13#3056
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
2. C2×#88196C2semidirect
4. C22×#6099C2semidirect
5. #11718886C2semidirect
6. #11718713C2semidirect
7. #11718712C2semidirect
8. #11718710C2semidirect
9. #11718709C2semidirect
10. #11718627C2semidirect
11. #11718625C2semidirect
23. C2×#6107C22semidirect
25. C2×#6106C22semidirect
39. #88075C22semidirect
40. #88075C22semidirect
41. #88050C22semidirect
42. #88049C22semidirect
43. #88048C22semidirect
44. #88047C22semidirect
88. #6099D4semidirect
136. C2×C22⋊Q8D13semidirect
153. C22×C13#137semidirect
255. C13#3056semidirect
308. C22#88196semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×#881962
#117194962
C22×#60992
#117188862
#117187132
#117187122
#117187102
#117187092
#117186272
#117186252
#305613