Finite Group Databasebeta

← #16018497

Subgroups — #16018497

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic
2#13117119C211yesmaximal, characteristic, complemented
3#13117105C211yesmaximal, characteristic, complemented
4#13117081C211yesmaximal, characteristic, complemented
5#13117075C211yesmaximal, characteristic, complemented
6#13116951C212yesmaximal
7#13116942C212yesmaximal, complemented
8C4×#88069C212yesmaximal, complemented
9C4×#88068C212yesmaximal, complemented
10C4×#88052C211yesmaximal, characteristic, complemented
11C13×#3170C211yesmaximal, characteristic, complemented
12C13×#533—21no—
13#11719184—21no—
14C13×#500C2211yescharacteristic
15C13×#494C2211yescharacteristic
16C13×#487—21no—
17C13×#467—21no—
18C13×#467C2212yes—
19C4×C13×Q16—21no—
20C4×C13×Q16C2212yes—
21C2×C4×C8×C13C2211yescharacteristic
22C2×#88069C2212yes—
23C2×#88068C2212yes—
24#11718777C2211yescharacteristic
25#11718776C2211yescharacteristic
26#11718775—21no—
27C2×#88052C2212yes—
28C4×Dic52C2211yescharacteristic
29#11718358—21no—
30#11718357C2211yescharacteristic
31C4×D104C2211yescharacteristic
32C4×#6095—21no—
33#11718344C2211yescharacteristic
34#11718156C2212yes—
35#11718156C2212yes—
36#11718084C2212yes—
37#11718083C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40#11718053C2211yescharacteristic
41#11718053C2211yescharacteristic
42C4×#6090C2212yes—
43C2×C13×Q16—21no—
44C2×C13×Q16C2312yes—
45C22×C8×C13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C13×C4⋊Q8—21no—
48C13×C4⋊Q8—21no—
49C13×#125—41no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—41no—
52C4×Q8×C13—22no—
53C4×Q8×C13—41no—
54C13×#117—41no—
55C2×C42×C13D411yescharacteristic
56#88184—21no—
57#88183—41no—
58C4×C22⋊D13—41no—
59#88178—21no—
60C2×Dic52C2311yescharacteristic
61C2×D104C2311yescharacteristic
62C2×#6095—21no—
63#88130—41no—
64#88129—21no—
65C4×D52—21no—
66#88126—41no—
67#88124—21no—
68C4×Dic26—21no—
69C13×#107—21no—
70C13×#107C2312yes—
71C13×#103—22no—
72C13×#103—22no—
73C4×C8×C13D411yescharacteristic
74C4×C8×C13D411yescharacteristic
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77#88069—24no—
78#88068—24no—
79#88061—21no—
80#88061—21no—
81#88058C2311yescharacteristic
82#88058C2311yescharacteristic
83#88057—21no—
84#88056—21no—
85#88056—21no—
86#88052—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33738—131nomaximal, Sylow
90C2×Q8×C13—22no—
91C2×Q8×C13—41no—
92C22×C4×C13D811yescharacteristic
93C22×C4×C13D811yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C2×C22⋊D13—41no—
96C2×D52—21no—
97C2×C4×D13—41no—
98C2×Dic26—21no—
99C13×Q16—22no—
100C13×Q16—22no—
101C13×Q16—42no—
102C2×C8×C13—22no—
103C2×C8×C13—22no—
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2411yescharacteristic
108C13×C4⋊C4—22no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—42no—
112C13×C4⋊C4—42no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—42no—
115C42×C13—42no—
116C42×C13D811yescharacteristic
117C42×C13D811yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C22⋊Dic13—41no—
121#6103—41no—
122#6103—41no—
123#6103—41no—
124#6103—41no—
125C4⋊Dic13—21no—
126C4⋊Dic13—21no—
127#6101—41no—
128#6101—41no—
129#6101—41no—
130#6101—41no—
131C4×Dic13—41no—
132Dic52—22no—
133D104—22no—
134#6095—42no—
135#6090—22no—
136#6090#4114yes—
137#3170D1311yescharacteristic, complemented
138#3168—131no—
139#2255—131no—
140#2251—131no—
141#2245—131no—
142#2243—131no—
143#2220—132no—
144#2219—132no—
145C4×Q32—132no—
146C4×SD32—132no—
147C4×M32—131no—
148C23×C13C2×D811yescharacteristic
149C22×D13—41no—
150Q8×C13—42no—
151Q8×C13—42no—
152Q8×C13—82no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13C2×D811yescharacteristic
160C2×C4×C13C2×D811yescharacteristic
161C2×C4×C13C2×D811yescharacteristic
162C2×C4×C13C2×D811yescharacteristic
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C22×D411yescharacteristic
165C22⋊D13—82no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169D52—41no—
170D52—41no—
171C4×D13—82no—
172Dic26—41no—
173Dic26—41no—
174C8×C13—21no—
175C8×C13—21no—
176C8×C13#13512yes—
177C8×C13C2×#4112yes—
178#533—21no—
179#529—261no—
180C2×Q32—132no—
181C2×SD32—132no—
182C2×M32—132no—
183#500C2×D1311yescharacteristic
184#499—131no—
185#495—131no—
186#494C2×D1311yescharacteristic
187#488—261no—
188#487—21no—
189#467—21no—
190#467—131no—
191#467C2×D1312yes—
192#466—131no—
193#465—261no—
194C4×Q16—21no—
195C4×Q16—131no—
196C4×Q16C2×D1312yes—
197C4×SD16—261no—
198C4×D8—131no—
199C2×C4×C8C2×D1311yescharacteristic
200#367—132no—
201#366—132no—
202#358—132no—
203#358—132no—
204#358—132no—
205#357—132no—
206#346—131no—
207#346—131no—
208C4×C16—132no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13C22×D811yescharacteristic
213C2×D13—81no—
214C2×D13—81no—
215C2×D13—81no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—82no—
221C4×C13—82no—
222C4×C13#51012yes—
223C4×C13#53211yescharacteristic
224C4×C13C2×#13511yescharacteristic
225Dic13—81no—
226Dic13—81no—
227Dic13—81no—
228C2×Q16—21no—
229C2×Q16—131no—
230C2×Q16C22×D1312yes—
231C2×SD16—261no—
232C2×D8—131no—
233C22×C8C22⋊D1311yescharacteristic
234C22×C8C22×D1311yescharacteristic
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237#126—521no—
238#125—41no—
239#125—261no—
240#124—261no—
241#123—521no—
242C22⋊Q8—22no—
243C22⋊Q8—41no—
244C22⋊Q8—261no—
245#121—261no—
246C4×Q8—22no—
247C4×Q8—41no—
248C4×Q8—261no—
249C4×D4—261no—
250C4×D4—521no—
251#117—41no—
252#117—521no—
253C2×C42C22⋊D1311yescharacteristic
254Q32—264no—
255SD32—264no—
256M32—264no—
257C2×C16—132no—
258C2×C16—132no—
259#107—21no—
260#107—131no—
261#107—131no—
262#107C22×D1312yes—
263#106—261no—
264#103—22no—
265#103—22no—
266#103—261no—
267#103—261no—
268#102—261no—
269#102—261no—
270C4×C8C22⋊D1311yescharacteristic
271C4×C8C22⋊D1311yescharacteristic
272C4×C8C22×D1311yescharacteristic
273C4×C8C22×D1311yescharacteristic
274C2×C13—41no—
275C2×C13#316911yescharacteristic
276C2×C13C2×#51011yescharacteristic
277C2×C13#341411yescharacteristic
278D13—161no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—261no—
282C2×D4—261no—
283C2×D4—521no—
284C22×C4—521no—
285C22×C4#610411yescharacteristic
286C22×C4#610411yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288Q16—22no—
289Q16—22no—
290Q16—42no—
291Q16—262no—
292SD16—522no—
293D8—262no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1311yescharacteristic
297C2×C8C2×C22⋊D1311yescharacteristic
298C2×C8C2×C22⋊D1311yescharacteristic
299C2×C8C23×D1311yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C22⋊C4—42no—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C22⋊C4—521no—
318C42—42no—
319C42—521no—
320C42#610411yescharacteristic
321C42#610411yescharacteristic
322C42C2×C22⋊D1311yescharacteristic
323C42C2×C22⋊D1311yescharacteristic
324C16—134no—
325C16—262no—
326C13#3373811yescharacteristic, complemented, Sylow
327C23—521no—
328C23C2×#610411yescharacteristic
329Q8—42no—
330Q8—42no—
331Q8—82no—
332Q8—521no—
333Q8—521no—
334D4—521no—
335D4—521no—
336D4—1042no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—1042no—
347C2×C4C2×#610411yescharacteristic
348C2×C4C2×#610411yescharacteristic
349C2×C4C2×#610411yescharacteristic
350C2×C4C2×#610411yescharacteristic
351C2×C4C2×#610411yescharacteristic
352C2×C4C22×C22⋊D1311yescharacteristic
353C8—21no—
354C8—21no—
355C8#8820412yes—
356C8#41×D1312yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—1041no—
361C22—1041no—
362C22—1041no—
363C22C22×#610411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—82no—
370C4—1041no—
371C4—1041no—
372C4—1041no—
373C4#1171884012yes—
374C4C2×#8820411yescharacteristic
375C4#1171953711yescharacteristic
376C2—41no—
377C2—2081no—
378C2#1312541111yescharacteristic
379C2C2×#1171884011yescharacteristic
380C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3170C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenter#3170D13
hypocenterC13#33738
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #13117119C2semidirect
3. #13117105C2semidirect
4. #13117081C2semidirect
5. #13117075C2semidirect
7. #13116942C2semidirect
8. C4×#88069C2semidirect
9. C4×#88068C2semidirect
10. C4×#88052C2semidirect
11. C13×#3170C2semidirect
137. #3170D13semidirect
326. C13#33738semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171192
#131171052
#131170812
#131170752
#131169512
#131169422
C4×#880692
C4×#880682
C4×#880522
C13×#31702
#3373813