Finite Group Databasebeta

← #16019259

Subgroups — #16019259

Order 3328.

534 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#13125415C211yesmaximal, characteristic, complemented
2#13116990C212yesmaximal, complemented
3#13116978C211yesmaximal, characteristic, complemented
4#13116973C211yesmaximal, characteristic, complemented
5#13116951C212yesmaximal, complemented
6#13116937C212yesmaximal, complemented
7#13116888C212yesmaximal, complemented
8#13116876C211yesmaximal, characteristic, complemented
9#13116871C211yesmaximal, characteristic, complemented
10#13116592C211yesmaximal, characteristic, complemented
11C13×#3168C211yesmaximal, characteristic, complemented
12C13×#529—21no—
13#11719182—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×#88068C2212yes—
25C2×#88066C2212yes—
26#11718776—21no—
27#11718776C2212yes—
28C2×#88052C2212yes—
29#11718356C2211yescharacteristic
30#11718355—21no—
31C4×D104—21no—
32C4×D104C2212yes—
33#11718343C2211yescharacteristic
34#11718156C2212yes—
35#11718154C2212yes—
36#11718083C2212yes—
37#11718083C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40C4⋊#6090C2211yescharacteristic
41C4⋊#6090C2211yescharacteristic
42C4⋊#6090C2212yes—
43C2×#6127—41no—
44C2×C13×Q16C2311yescharacteristic
45C2×C13×SD16—21no—
46C2×C13×D8C2311yescharacteristic
47C22×C8×C13D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C13×#126—41no—
50C13×#125—21no—
51C13×#124—21no—
52C13×#123—41no—
53C13×C22⋊Q8—21no—
54C13×#121—21no—
55C4×Q8×C13—21no—
56C4×D4×C13—21no—
57C4×D4×C13—41no—
58C13×#117—41no—
59C2×C42×C13D411yescharacteristic
60#88184—22no—
61#88184—41no—
62C2×D104—21no—
63C2×D104C2312yes—
64#88129—41no—
65#88128—21no—
66C4×D52—22no—
67C4×D52—41no—
68#88123—21no—
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#88068—42no—
81#88066—42no—
82#88061—22no—
83#88061—22no—
84#88058—21no—
85#88058C2312yes—
86#88052—42no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33817—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×C22⋊D13—42no—
98#6127—84no—
99C2×D52—22no—
100C2×D52—41no—
101C2×D52—41no—
102C2×C4×D13—42no—
103C2×Dic26—41no—
104C13×Q16—21no—
105C13×Q16—21no—
106C13×SD16—42no—
107C13×D8—21no—
108C13×D8—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—41no—
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13C2×D411yescharacteristic
114C2×C8×C13C2×D411yescharacteristic
115C2×C8×C13C2411yescharacteristic
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C42×C13—41no—
128C42×C13D811yescharacteristic
129C42×C13D811yescharacteristic
130C42×C13C2×D411yescharacteristic
131C42×C13C2×D411yescharacteristic
132#6103—42no—
133#6103—42no—
134C4⋊Dic13—22no—
135C4⋊Dic13—41no—
136D104—22no—
137D104—22no—
138D104—42no—
139#6090—22no—
140#6090—22no—
141#3169—131no—
142#3168D1311yescharacteristic, complemented
143#2228—132no—
144#2225—131no—
145#2224—131no—
146#2220—132no—
147#2218—132no—
148#2210—132no—
149#2207—131no—
150#2206—131no—
151#2150—131no—
152C23×C13—41no—
153C23×C13C2×D811yescharacteristic
154C22×D13—42no—
155Q8×C13—41no—
156Q8×C13—41no—
157D4×C13—41no—
158D4×C13—41no—
159D4×C13—82no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—22no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—82no—
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13C2×D811yescharacteristic
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13C22×D411yescharacteristic
174C22⋊D13—84no—
175C2×Dic13—42no—
176D52—42no—
177D52—42no—
178D52—82no—
179D52—82no—
180C4×D13—84no—
181Dic26—82no—
182C8×C13—21no—
183C8×C13—21no—
184C8×C13—21no—
185C8×C13H(5,𝔽2)11yescharacteristic
186C8×C132−1+411yescharacteristic
187#532—261no—
188#529—21no—
189C2×SD32—132no—
190C2×D16—132no—
191C2×M32—132no—
192#500—131no—
193#499C2×D1311yescharacteristic
194#495C2×D1311yescharacteristic
195#493—131no—
196#488—21no—
197#486—261no—
198#467C2×D1311yescharacteristic
199#466—132no—
200#466—261no—
201#466C2×D1311yescharacteristic
202#465—21no—
203C4×Q16C2×D1311yescharacteristic
204C4×SD16—21no—
205C4×D8—132no—
206C4×D8—261no—
207C4×D8C2×D1311yescharacteristic
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—21no—
221C22×C13—81no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13C22×D811yescharacteristic
225C2×D13—82no—
226C2×D13—82no—
227C2×D13—82no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13#50912yes—
236C4×C13#53711yescharacteristic
237C4×C13#57511yescharacteristic
238Dic13—82no—
239C2×#41—521no—
240C2×Q16C22×D1311yescharacteristic
241C2×SD16—21no—
242C2×D8—132no—
243C2×D8—261no—
244C2×D8C22×D1311yescharacteristic
245C22×C8C22⋊D1311yescharacteristic
246C22×C8C22×D1311yescharacteristic
247C4⋊Q8—261no—
248#127—261no—
249#126—41no—
250#125—21no—
251#124—21no—
252#124—521no—
253#123—41no—
254C22⋊Q8—21no—
255#121—21no—
256#121—262no—
257#121—521no—
258C4×Q8—21no—
259C4×D4—21no—
260C4×D4—41no—
261C4×D4—262no—
262C4×D4—521no—
263#117—41no—
264C2×C42C22⋊D1311yescharacteristic
265SD32—522no—
266D16—522no—
267M32—522no—
268C2×C16—132no—
269C2×C16—132no—
270#107—132no—
271#107—261no—
272#107C22×D1311yescharacteristic
273#107C22×D1311yescharacteristic
274#106—21no—
275#103—21no—
276#103—21no—
277#102—21no—
278#102—21no—
279#102—262no—
280#102—262no—
281C4×C8C22⋊D1311yescharacteristic
282C4×C8C22⋊D1311yescharacteristic
283C4×C8C22×D1311yescharacteristic
284C4×C8C22×D1311yescharacteristic
285C2×C13—41no—
286C2×C13—161no—
287C2×C13#324511yescharacteristic
288C2×C13C2×#50911yescharacteristic
289C2×C13#341411yescharacteristic
290D13—162no—
291#41—1044no—
292C2×Q8—21no—
293C2×Q8—521no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—262no—
297C2×D4—522no—
298C2×D4—521no—
299C2×D4—521no—
300C22×C4—41no—
301C22×C4—522no—
302C22×C4#610411yescharacteristic
303C22×C4#610411yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305Q16—21no—
306Q16—21no—
307SD16—42no—
308D8—21no—
309D8—21no—
310D8—262no—
311D8—262no—
312D8—522no—
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—21no—
321C4⋊C4—21no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—262no—
327C4⋊C4—521no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—522no—
334C22⋊C4—522no—
335C42—41no—
336C42#610411yescharacteristic
337C42#610411yescharacteristic
338C42C2×C22⋊D1311yescharacteristic
339C42C2×C22⋊D1311yescharacteristic
340C16—262no—
341C16—262no—
342C13#3381711yescharacteristic, complemented, Sylow
343C23—41no—
344C23—522no—
345C23C2×#610411yescharacteristic
346Q8—41no—
347Q8—41no—
348Q8—1042no—
349D4—41no—
350D4—41no—
351D4—82no—
352D4—522no—
353D4—522no—
354D4—1042no—
355D4—1044no—
356D4—1042no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—522no—
366C2×C4—1044no—
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—21no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—1042no—
385C22—1042no—
386C22—1042no—
387C22C22×#610411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—1042no—
396C4#1171885412yes—
397C4#1171952711yescharacteristic
398C4#1171953811yescharacteristic
399C2—41no—
400C2—161no—
401C2—2082no—
402C2#1312614311yescharacteristic
403C2C2×#1171885411yescharacteristic
404C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
hypercenter#3168D13
hypocenterC13#33817
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125415C2semidirect
2. #13116990C2semidirect
3. #13116978C2semidirect
4. #13116973C2semidirect
5. #13116951C2semidirect
6. #13116937C2semidirect
7. #13116888C2semidirect
8. #13116876C2semidirect
9. #13116871C2semidirect
10. #13116592C2semidirect
11. C13×#3168C2semidirect
142. #3168D13semidirect
342. C13#33817semidirect

Maximal subgroups

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

subgroupindex
#131254152
#131169902
#131169782
#131169732
#131169512
#131169372
#131168882
#131168762
#131168712
#131165922
C13×#31682
#3381713