Finite Group Databasebeta

← #16018504

Subgroups — #16018504

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#13125422C211yesmaximal, characteristic, complemented
2#13117123C211yesmaximal, characteristic, complemented
3#13117108C211yesmaximal, characteristic, complemented
4#13117083C211yesmaximal, characteristic, complemented
5#13117072C211yesmaximal, characteristic, complemented
6#13116947C212yesmaximal
7#13116942C212yesmaximal, complemented
8C4×#88069C212yesmaximal, complemented
9C4×#88067C212yesmaximal, complemented
10C4×#88052C211yesmaximal, characteristic, complemented
11C13×#3168C211yesmaximal, characteristic
12C13×#529—21no—
13#11719175—21no—
14C13×#499C2211yescharacteristic
15C13×#495C2211yescharacteristic
16C13×#488—21no—
17C13×#467C2211yescharacteristic
18C13×#466C2211yescharacteristic
19C13×#465—21no—
20C4×C13×Q16C2211yescharacteristic
21C4×C13×SD16—21no—
22C4×C13×D8C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×#88069C2212yes—
25C2×#88067C2212yes—
26#11718777—21no—
27#11718777C2212yes—
28C2×#88052C2212yes—
29#11718360C2211yescharacteristic
30C4×Dic52—21no—
31C4×Dic52C2212yes—
32#11718343C2211yescharacteristic
33#11718342—21no—
34#11718156C2212yes—
35#11718154C2212yes—
36#11718084C2212yes—
37#11718084C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40#11718053C2211yescharacteristic
41#11718053C2211yescharacteristic
42C4×#6090C2212yes—
43C2×C13×Q16C2311yescharacteristic
44C2×C13×SD16—21no—
45C2×C13×D8C2311yescharacteristic
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×#126—41no—
49C13×#125—21no—
50C13×#124—21no—
51C13×#123—41no—
52C13×C22⋊Q8—21no—
53C13×#121—21no—
54C4×Q8×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—41no—
57C13×#117—41no—
58C2×C42×C13D411yescharacteristic
59#88180—41no—
60#88178—22no—
61#88178—41no—
62C2×Dic52—21no—
63C2×Dic52C2312yes—
64#88124—41no—
65#88123—21no—
66#88123—21no—
67C4×Dic26—22no—
68C4×Dic26—41no—
69C13×#107C2311yescharacteristic
70C13×#107C2311yescharacteristic
71C13×#106—21no—
72C13×#103—21no—
73C13×#103—21no—
74C13×#102—21no—
75C13×#102—21no—
76C4×C8×C13D411yescharacteristic
77C4×C8×C13D411yescharacteristic
78C4×C8×C13C2311yescharacteristic
79C4×C8×C13C2311yescharacteristic
80#88069—24no—
81#88067—24no—
82#88058—21no—
83#88058C2312yes—
84#88056—22no—
85#88056—22no—
86#88052—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33738—131nomaximal, Sylow
90C2×Q8×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13D811yescharacteristic
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C2×Dic26—22no—
98C2×Dic26—41no—
99C13×Q16—22no—
100C13×SD16—42no—
101C13×D8—22no—
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—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C13×C22⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C42×C13—41no—
120C42×C13D811yescharacteristic
121C42×C13D811yescharacteristic
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C22⋊Dic13—42no—
125C4⋊Dic13—22no—
126C4⋊Dic13—41no—
127C4⋊Dic13—41no—
128C4⋊Dic13—41no—
129#6101—42no—
130#6101—42no—
131C4×Dic13—42no—
132Dic52—22no—
133Dic52—22no—
134Dic52—42no—
135#6090—22no—
136#6090#4114yes—
137#3170—131no—
138#3168D1311yescharacteristic
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×C13—41no—
149C23×C13C2×D811yescharacteristic
150Q8×C13—41no—
151Q8×C13—41no—
152D4×C13—41no—
153D4×C13—41no—
154D4×C13—82no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—22no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—82no—
163C2×C4×C13C2×D811yescharacteristic
164C2×C4×C13C2×D811yescharacteristic
165C2×C4×C13C2×D811yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C2×Dic13—42no—
170C2×Dic13—42no—
171Dic26—42no—
172Dic26—42no—
173Dic26—82no—
174C8×C13—21no—
175C8×C13—21no—
176C8×C13#13512yes—
177C8×C13C2×#4112yes—
178#533—261no—
179#529—21no—
180C2×Q32—132no—
181C2×SD32—132no—
182C2×M32—132no—
183#500—131no—
184#499C2×D1311yescharacteristic
185#495C2×D1311yescharacteristic
186#494—131no—
187#488—21no—
188#487—261no—
189#467—132no—
190#467—261no—
191#467C2×D1311yescharacteristic
192#466C2×D1311yescharacteristic
193#465—21no—
194C4×Q16—132no—
195C4×Q16—261no—
196C4×Q16C2×D1311yescharacteristic
197C4×SD16—21no—
198C4×D8C2×D1311yescharacteristic
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×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13C22×D811yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—81no—
221C4×C13—81no—
222C4×C13—81no—
223C4×C13#51012yes—
224C4×C13#53211yescharacteristic
225C4×C13C2×#13511yescharacteristic
226Dic13—82no—
227Dic13—82no—
228C2×Q16—132no—
229C2×Q16—261no—
230C2×Q16C22×D1311yescharacteristic
231C2×SD16—21no—
232C2×D8C22×D1311yescharacteristic
233C22×C8C22⋊D1311yescharacteristic
234C22×C8C22×D1311yescharacteristic
235C4⋊Q8—261no—
236C4⋊Q8—261no—
237#126—41no—
238#125—21no—
239#125—521no—
240#124—21no—
241#123—41no—
242C22⋊Q8—21no—
243C22⋊Q8—262no—
244C22⋊Q8—521no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—262no—
248C4×Q8—521no—
249C4×D4—21no—
250C4×D4—41no—
251#117—41no—
252#117—521no—
253C2×C42C22⋊D1311yescharacteristic
254Q32—264no—
255SD32—264no—
256M32—264no—
257C2×C16—132no—
258C2×C16—132no—
259#107—132no—
260#107—261no—
261#107C22×D1311yescharacteristic
262#107C22×D1311yescharacteristic
263#106—21no—
264#103—21no—
265#103—21no—
266#103—262no—
267#103—262no—
268#102—21no—
269#102—21no—
270C4×C8C22⋊D1311yescharacteristic
271C4×C8C22⋊D1311yescharacteristic
272C4×C8C22×D1311yescharacteristic
273C4×C8C22×D1311yescharacteristic
274C2×C13—41no—
275C2×C13—161no—
276C2×C13#316911yescharacteristic
277C2×C13C2×#51011yescharacteristic
278C2×C13#341411yescharacteristic
279C2×Q8—21no—
280C2×Q8—262no—
281C2×Q8—521no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4#610411yescharacteristic
286C22×C4#610411yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288Q16—22no—
289Q16—262no—
290Q16—262no—
291Q16—522no—
292SD16—42no—
293D8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1311yescharacteristic
297C2×C8C2×C22⋊D1311yescharacteristic
298C2×C8C2×C22⋊D1311yescharacteristic
299C2×C8C23×D1311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—262no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C4⋊C4—522no—
310C4⋊C4—522no—
311C4⋊C4—521no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—522no—
318C42—41no—
319C42—522no—
320C42#610411yescharacteristic
321C42#610411yescharacteristic
322C42C2×C22⋊D1311yescharacteristic
323C42C2×C22⋊D1311yescharacteristic
324C16—134no—
325C16—262no—
326C13#3373811yescharacteristic, complemented, Sylow
327C23—41no—
328C23C2×#610411yescharacteristic
329Q8—41no—
330Q8—41no—
331Q8—522no—
332Q8—522no—
333Q8—1042no—
334D4—41no—
335D4—41no—
336D4—82no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—522no—
346C2×C4—522no—
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—81no—
361C22—81no—
362C22—81no—
363C22C22×#610411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—1042no—
372C4—1042no—
373C4#1171885612yes—
374C4C2×#8820411yescharacteristic
375C4#1171953711yescharacteristic
376C2—41no—
377C2—161no—
378C2#1312541111yescharacteristic
379C2C2×#1171885611yescharacteristic
380C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
prime radicalC13×#466C22
hypercenter#3168D13
hypocenterC13#33738
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125422C2semidirect
2. #13117123C2semidirect
3. #13117108C2semidirect
4. #13117083C2semidirect
5. #13117072C2semidirect
7. #13116942C2semidirect
8. C4×#88069C2semidirect
9. C4×#88067C2semidirect
10. C4×#88052C2semidirect
326. C13#33738semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131171232
#131171082
#131170832
#131170722
#131169472
#131169422
C4×#880692
C4×#880672
C4×#880522
C13×#31682
#3373813