Finite Group Databasebeta

← #16019217

Subgroups — #16019217

Order 3328.

540 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic, complemented
2#13116993C212yesmaximal, complemented
3#13116985C211yesmaximal, characteristic, complemented
4#13116980C211yesmaximal, characteristic, complemented
5#13116930C212yesmaximal, complemented
6#13116920C212yesmaximal, complemented
7#13116891C212yesmaximal, complemented
8#13116873C211yesmaximal, characteristic, complemented
9#13116868C211yesmaximal, characteristic, complemented
10C2×C4⋊#6090C211yesmaximal, characteristic, complemented
11C13×#3169C211yesmaximal, characteristic, complemented
12C13×#532—21no—
13#11719184—21no—
14C13×#500C2211yescharacteristic
15C13×#493C2211yescharacteristic
16C13×#486—21no—
17C13×#466—21no—
18C13×#466C2212yes—
19C4×C13×D8—21no—
20C4×C13×D8C2212yes—
21C2×C4×C8×C13C2211yescharacteristic
22C2×#88067C2212yes—
23C2×#88066C2212yes—
24#11718777C2211yescharacteristic
25#11718776C2211yescharacteristic
26#11718775—21no—
27C22×#6090C2212yes—
28C4×Dic52C2211yescharacteristic
29#11718358—21no—
30#11718357C2211yescharacteristic
31C4×D104C2211yescharacteristic
32C4×#6095—21no—
33#11718344C2211yescharacteristic
34#11718154C2212yes—
35#11718154C2212yes—
36#11718084C2212yes—
37#11718083C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40C4⋊#6090C2211yescharacteristic
41C4⋊#6090C2211yescharacteristic
42C4⋊#6090C2212yes—
43C2×C13×#41—41no—
44C2×C13×D8—21no—
45C2×C13×D8C2312yes—
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×C4⋊Q8—21no—
49C13×#127—21no—
50C13×#124—41no—
51C13×#121—22no—
52C13×#121—41no—
53C4×D4×C13—22no—
54C4×D4×C13—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×#102—22no—
72C13×#102—22no—
73C4×C8×C13D411yescharacteristic
74C4×C8×C13D411yescharacteristic
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77#88067—42no—
78#88066—42no—
79#88061—21no—
80#88061—21no—
81#88058C2311yescharacteristic
82#88058C2311yescharacteristic
83#88057—21no—
84#88056—21no—
85#88056—21no—
86C2×#6090—42no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33813—131nomaximal, Sylow
90C13×#41—84no—
91C2×Q8×C13—41no—
92C2×D4×C13—22no—
93C2×D4×C13—42no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C22×C4×C13—42no—
97C22×C4×C13D811yescharacteristic
98C22×C4×C13D811yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C2×C22⋊D13—41no—
101C2×D52—21no—
102C2×C4×D13—41no—
103C2×Dic26—21no—
104C13×D8—22no—
105C13×D8—22no—
106C13×D8—42no—
107C2×C8×C13—21no—
108C2×C8×C13—21no—
109C2×C8×C13—41no—
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13C2411yescharacteristic
114C13×C4⋊C4—22no—
115C13×C4⋊C4—41no—
116C13×C22⋊C4—42no—
117C13×C22⋊C4—42no—
118C42×C13D811yescharacteristic
119C42×C13D811yescharacteristic
120C42×C13C2×D411yescharacteristic
121C42×C13C2×D411yescharacteristic
122C22⋊Dic13—41no—
123#6103—41no—
124#6103—41no—
125#6103—41no—
126#6103—41no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129#6101—41no—
130#6101—41no—
131#6101—41no—
132#6101—41no—
133C4×Dic13—41no—
134Dic52—21no—
135Dic52—21no—
136D104—21no—
137D104—21no—
138#6095—42no—
139#6090—22no—
140#6090—22no—
141#3169D1311yescharacteristic, complemented
142#3168—131no—
143#2228—132no—
144#2227—131no—
145#2226—131no—
146#2217—132no—
147#2215—132no—
148#2210—132no—
149#2207—131no—
150#2206—131no—
151C2×C4⋊C16—131no—
152C23×C13—42no—
153C23×C13C2×D811yescharacteristic
154C22×D13—41no—
155Q8×C13—82no—
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—82no—
159D4×C13—84no—
160D4×C13—82no—
161C2×C4×C13—22no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—22no—
165C2×C4×C13—42no—
166C2×C4×C13—84no—
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13C22×D411yescharacteristic
173C22⋊D13—82no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177D52—41no—
178D52—41no—
179C4×D13—82no—
180Dic26—41no—
181Dic26—41no—
182C8×C13—21no—
183C8×C13—21no—
184C8×C13—21no—
185C8×C13H(5,𝔽2)11yescharacteristic
186C8×C132−1+411yescharacteristic
187#532—21no—
188#529—261no—
189C2×SD32—132no—
190C2×D16—132no—
191C22×C16—132no—
192#500C2×D1311yescharacteristic
193#499—131no—
194#495—131no—
195#493C2×D1311yescharacteristic
196#488—261no—
197#486—21no—
198#467—131no—
199#466—21no—
200#466—131no—
201#466C2×D1312yes—
202#465—261no—
203C4×Q16—131no—
204C4×SD16—261no—
205C4×D8—21no—
206C4×D8—131no—
207C4×D8C2×D1312yes—
208C2×C4×C8C2×D1311yescharacteristic
209#367—132no—
210#366—132no—
211C4⋊C16—131no—
212C4⋊C16—131no—
213C4⋊C16—132no—
214#358—132no—
215#357—132no—
216#357—132no—
217#357—132no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—82no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13#50912yes—
224C22×C13C22×D811yescharacteristic
225C2×D13—81no—
226C2×D13—81no—
227C2×D13—81no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—82no—
233C4×C13#50812yes—
234C4×C13#53711yescharacteristic
235C4×C13#57511yescharacteristic
236Dic13—81no—
237Dic13—81no—
238Dic13—81no—
239C2×#41—41no—
240C2×Q16—131no—
241C2×SD16—261no—
242C2×D8—21no—
243C2×D8—131no—
244C2×D8C22×D1312yes—
245C22×C8C22⋊D1311yescharacteristic
246C22×C8C22×D1311yescharacteristic
247C4⋊Q8—21no—
248#127—21no—
249#126—521no—
250#125—261no—
251#124—41no—
252#124—261no—
253#123—521no—
254C22⋊Q8—261no—
255#121—22no—
256#121—41no—
257#121—261no—
258C4×Q8—261no—
259C4×D4—22no—
260C4×D4—41no—
261C4×D4—261no—
262C4×D4—521no—
263#117—521no—
264C2×C42C22⋊D1311yescharacteristic
265SD32—522no—
266D16—522no—
267C2×C16—132no—
268C2×C16—132no—
269C2×C16—522no—
270#107—21no—
271#107—131no—
272#107—131no—
273#107C22×D1312yes—
274#106—261no—
275#103—261no—
276#103—261no—
277#102—22no—
278#102—22no—
279#102—261no—
280#102—261no—
281C4×C8C22⋊D1311yescharacteristic
282C4×C8C22⋊D1311yescharacteristic
283C4×C8C22×D1311yescharacteristic
284C4×C8C22×D1311yescharacteristic
285C2×C13—22no—
286C2×C13—162no—
287C2×C13#324511yescharacteristic
288C2×C13C2×#50811yescharacteristic
289C2×C13C2×#50911yescharacteristic
290D13—161no—
291#41—84no—
292C2×Q8—41no—
293C2×Q8—261no—
294C2×D4—22no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—261no—
299C2×D4—521no—
300C22×C4—42no—
301C22×C4—521no—
302C22×C4#610411yescharacteristic
303C22×C4#610411yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305Q16—261no—
306Q16—261no—
307SD16—522no—
308D8—22no—
309D8—22no—
310D8—42no—
311D8—261no—
312D8—261no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8C2×C22⋊D1311yescharacteristic
317C2×C8C2×C22⋊D1311yescharacteristic
318C2×C8C2×C22⋊D1311yescharacteristic
319C2×C8C23×D1311yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4—521no—
325C4⋊C4—521no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—521no—
331C22⋊C4—521no—
332C22⋊C4—521no—
333C22⋊C4—521no—
334C22⋊C4—521no—
335C42—521no—
336C42#610411yescharacteristic
337C42#610411yescharacteristic
338C42C2×C22⋊D1311yescharacteristic
339C42C2×C22⋊D1311yescharacteristic
340C16—262no—
341C16—262no—
342C13#3381311yescharacteristic, complemented, Sylow
343C23—42no—
344C23—521no—
345C23C2×#610411yescharacteristic
346Q8—82no—
347Q8—521no—
348Q8—521no—
349D4—42no—
350D4—42no—
351D4—82no—
352D4—84no—
353D4—82no—
354D4—521no—
355D4—521no—
356D4—1042no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—84no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—1042no—
367C2×C4C2×#610411yescharacteristic
368C2×C4C2×#610411yescharacteristic
369C2×C4C2×#610411yescharacteristic
370C2×C4C2×#610411yescharacteristic
371C2×C4C2×#610411yescharacteristic
372C2×C4C22×C22⋊D1311yescharacteristic
373C8—21no—
374C8—21no—
375C8—21no—
376C8#8825611yescharacteristic
377C8#8825711yescharacteristic
378C22—21no—
379C22—21no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22—1041no—
384C22—1041no—
385C22—1041no—
386C22#1171880812yes—
387C22C22×#610411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—1041no—
394C4—1041no—
395C4—1041no—
396C4#1171885512yes—
397C4#1171952711yescharacteristic
398C4#1171953811yescharacteristic
399C2—22no—
400C2—162no—
401C2—2081no—
402C2#1312614311yescharacteristic
403C2C2×#1171885511yescharacteristic
404C2C2×#1171880811yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3169C2
socleC22×C13C22×D8
hypercenter#3169D13
hypocenterC13#33813
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13125406C2semidirect
2. #13116993C2semidirect
3. #13116985C2semidirect
4. #13116980C2semidirect
5. #13116930C2semidirect
6. #13116920C2semidirect
7. #13116891C2semidirect
8. #13116873C2semidirect
9. #13116868C2semidirect
10. C2×C4⋊#6090C2semidirect
11. C13×#3169C2semidirect
141. #3169D13semidirect
342. C13#33813semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131169932
#131169852
#131169802
#131169302
#131169202
#131168912
#131168732
#131168682
C2×C4⋊#60902
C13×#31692
#3381313