Finite Group Databasebeta

← #13124469

Subgroups — #13124469

Order 1664.

496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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#11719533C211yesmaximal, characteristic
2C2×#88205C211yesmaximal, characteristic, complemented
3C2×M16×D13C211yesmaximal, characteristic, complemented
4C2×#88151C211yesmaximal, characteristic, complemented
5C13×#417C211yesmaximal, characteristic, complemented
6#11718781C211yesmaximal, characteristic, complemented
7#11718625C211yesmaximal, characteristic, complemented
8#11718477C212yesmaximal, complemented
9#11718474C212yesmaximal, complemented
10#11718441C212yesmaximal, complemented
11#11718439C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C2×C13×M16C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88205—24no—
18#88200C2211yescharacteristic
19#88200C2211yescharacteristic
20C2×#6107C2212yescomplemented
21#88192C2211yescharacteristic
22#88192C2211yescharacteristic
23#88191—21no—
24#88189—21no—
25C2×#6105C2212yescomplemented
26C4×C22⋊D13—21no—
27C4×C22⋊D13—21no—
28C2×#6103—21no—
29#88180C2211yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×#6099C2211yescharacteristic
32M16×D13—24no—
33C2×#6094C2212yes—
34C2×C8×D13C2212yes—
35#88151—21no—
36#88151—21no—
37#88151C2212yes—
38#88151C2212yes—
39C13×#103C2212yescomplemented
40C13×#102C2212yescomplemented
41#88056C2212yescomplemented
42#88056C2212yescomplemented
43#88048C2212yescomplemented
44#88047C2212yescomplemented
45C23×D13D411yescharacteristic
46C13×#41—22no—
47C13×#41—22no—
48C2×Q8×C13C2311yescharacteristic
49C2×D4×C13—21no—
50C2×D4×C13C2311yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C2311yescharacteristic
54C2×C22⋊D13—21no—
55C2×C22⋊D13—21no—
56C22×Dic13—21no—
57C22×Dic13D411yescharacteristic
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13D411yescharacteristic
61C2×C4×D13D411yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×Dic26—22no—
65C2×Dic26—22no—
66C2×Dic26—21no—
67C2×Dic26C2312yes—
68C13×M16—22no—
69C2×C8×C13C2312yes—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2312yes—
72C22⋊Dic13—21no—
73C22⋊Dic13—21no—
74C22⋊Dic13—21no—
75#6107—24no—
76#6105—24no—
77#6103—22no—
78#6103—22no—
79#6103—21no—
80#6103—21no—
81C4⋊Dic13—22no—
82C4⋊Dic13—22no—
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87C4×Dic13—21no—
88#6099D414yescomplemented
89C2×#1055C2312yes—
90#6094—24no—
91C8×D13—24no—
92#3056—131nomaximal, Sylow
93C23×C13—21no—
94C23×C13C2×D411yescharacteristic
95C22×D13—22no—
96C22×D13—22no—
97C22×D13—41no—
98C22×D13C2×D411yescharacteristic
99C22×D13C2×D411yescharacteristic
100Q8×C13—21no—
101Q8×C13—21no—
102D4×C13—21no—
103D4×C13—21no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D412yes—
111C2×C4×C13#4112yes—
112C2×C4×C13C2411yescharacteristic
113C22⋊D13—42no—
114C22⋊D13—42no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—22no—
119C2×Dic13—42no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C4×D13—22no—
123C4×D13—22no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—21no—
127C4×D13—21no—
128Dic26—22no—
129Dic26—22no—
130Dic26—42no—
131C8×C13—22no—
132#1055C2×D414yes—
133C2×#137—131no—
134C22×M16—131no—
135#525—131no—
136C2×C22⋊Q8—131no—
137#470—132no—
138#468—132no—
139#467—132no—
140#465—132no—
141#428—131no—
142#419—131no—
143#417D1311yescharacteristic, complemented
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13#12112yes—
150C22×C13C22×D411yescharacteristic
151C2×D13—21no—
152C2×D13—21no—
153C2×D13—21no—
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—44no—
157C2×D13#13712yescomplemented
158C4×C13—41no—
159C4×C13—42no—
160C4×C13#12112yes—
161C4×C13C22×D411yescharacteristic
162C4×C13C2×#4111yescharacteristic
163Dic13—21no—
164Dic13—21no—
165Dic13—42no—
166Dic13—41no—
167Dic13—41no—
168C2×#41C2×D1311yescharacteristic
169C22×Q8—131no—
170C23×C4—131no—
171#137—264no—
172C2×Q16—132no—
173C2×SD16—132no—
174C2×M16—131no—
175C2×M16—132no—
176C2×M16—264no—
177C2×M16C2×D1311yescharacteristic
178C22×C8—132no—
179#123—261no—
180C22⋊Q8—131no—
181C22⋊Q8—131no—
182C22⋊Q8—132no—
183C22⋊Q8—132no—
184C22⋊Q8—261no—
185C22⋊Q8—261no—
186#121—131no—
187#121—131no—
188#120—261no—
189C4×D4—261no—
190C4×D4—261no—
191#117—131no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4C2×D1311yescharacteristic
194C2×C22⋊C4—261no—
195#107—132no—
196#106—132no—
197#103—132no—
198#103—132no—
199#103C2×D1312yescomplemented
200#102C2×D1312yescomplemented
201C2×C13—22no—
202C2×C13—81no—
203C2×C13C2×#12111yescharacteristic
204C2×C13C2×#13711yescharacteristic
205C2×C13#57511yescharacteristic
206D13—22no—
207D13—41no—
208C24—131no—
209#41—22no—
210#41—22no—
211C2×Q8—132no—
212C2×Q8—261no—
213C2×Q8—262no—
214C2×Q8—262no—
215C2×Q8C22×D1311yescharacteristic
216C2×D4—21no—
217C2×D4—261no—
218C2×D4—261no—
219C2×D4C22×D1311yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—261no—
230C22×C4C22×D1311yescharacteristic
231Q16—264no—
232SD16—264no—
233M16—22no—
234M16—134no—
235M16—264no—
236C2×C8—132no—
237C2×C8—264no—
238C2×C8C22×D1312yes—
239C4⋊C4—21no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—262no—
243C4⋊C4—262no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4C22×D1312yes—
247C22⋊C4—262no—
248C22⋊C4—262no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—261no—
255C13#305611yescharacteristic, complemented, Sylow
256C23—21no—
257C23—131no—
258C23—131no—
259C23—262no—
260C23—262no—
261C23—521no—
262C23D4×D1311yescharacteristic
263Q8—21no—
264Q8—21no—
265Q8—262no—
266Q8—262no—
267Q8—522no—
268D4—21no—
269D4—21no—
270D4—42no—
271D4—522no—
272D4—522no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—262no—
289C2×C4—522no—
290C2×C4#612712yes—
291C2×C4D4×D1311yescharacteristic
292C2×C4D4×D1312yes—
293C2×C4C23×D1311yescharacteristic
294C8—22no—
295C8—134no—
296C22—21no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—132no—
302C22—261no—
303C22—261no—
304C22—261no—
305C22—261no—
306C22—261no—
307C22—524no—
308C22#8813812yes—
309C22C2×D4×D1311yescharacteristic
310C4—41no—
311C4—42no—
312C4—261no—
313C4—261no—
314C4—522no—
315C4—521no—
316C4—521no—
317C4#8813812yes—
318C4C2×#612711yescharacteristic
319C4C2×D4×D1311yescharacteristic
320C2—22no—
321C2—81no—
322C2—262no—
323C2—521no—
324C2C2×#8813811yescharacteristic
325C2#1171947811yescharacteristic
326C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
prime radical#11719533C2
hypercenter#417D13
hypocenterC13#3056
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#88205C2semidirect
3. C2×M16×D13C2semidirect
4. C2×#88151C2semidirect
5. C13×#417C2semidirect
6. #11718781C2semidirect
7. #11718625C2semidirect
8. #11718477C2semidirect
9. #11718474C2semidirect
10. #11718441C2semidirect
11. #11718439C2semidirect
20. C2×#6107C22semidirect
25. C2×#6105C22semidirect
39. C13×#103C22semidirect
40. C13×#102C22semidirect
41. #88056C22semidirect
42. #88056C22semidirect
43. #88048C22semidirect
44. #88047C22semidirect
88. #6099D4semidirect
143. #417D13semidirect
157. C2×D13#137semidirect
199. #103C2×D13semidirect
200. #102C2×D13semidirect
255. C13#3056semidirect

Maximal subgroups

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

subgroupindex
#117195332
C2×#882052
C2×M16×D132
C2×#881512
C13×#4172
#117187812
#117186252
#117184772
#117184742
#117184412
#117184392
#305613