Finite Group Databasebeta

← #16019816

Subgroups — #16019816

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127205C211yesmaximal, characteristic, complemented
2#13117067C211yesmaximal, characteristic, complemented
3#13117041C211yesmaximal, characteristic, complemented
4#13117014C211yesmaximal, characteristic, complemented
5#13117000C211yesmaximal, characteristic, complemented
6#13116930C211yesmaximal, characteristic, complemented
7#13116925C211yesmaximal, characteristic, complemented
8#13116895C211yesmaximal, characteristic, complemented
9#13116776C211yesmaximal, characteristic, complemented
10#13116770C211yesmaximal, characteristic, complemented
11C4×#88069C211yesmaximal, characteristic, complemented
12D4×#6090C211yesmaximal, characteristic, complemented
13#13116543C211yesmaximal, characteristic, complemented
14C2×#11718156C211yesmaximal, characteristic, complemented
15C13×#3285C211yesmaximal, characteristic
16C2×C13×#135C2211yescharacteristic
17C22×C13×Q16C2211yescharacteristic
18C13×#548—21no—
19#11719246—21no—
20C13×#495C2211yescharacteristic
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#464—21no—
24C13×#452—21no—
25C13×#448—21no—
26C4×C13×Q16C2211yescharacteristic
27C8×D4×C13C2211yescharacteristic
28C2×#88069C2211yescharacteristic
29C2×#88069C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31#11718777C2211yescharacteristic
32#11718777C2211yescharacteristic
33#11718767C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic
37#11718490—21no—
38#11718384—21no—
39#11718382—21no—
40C4×Dic52C2211yescharacteristic
41#11718344C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718156C2211yescharacteristic
44#11718156C2211yescharacteristic
45#11718156C2211yescharacteristic
46#11718156C2211yescharacteristic
47#11718156C2211yescharacteristic
48#11718154C2211yescharacteristic
49#11718154C2211yescharacteristic
50#11718154C2211yescharacteristic
51C22⋊#6090C2211yescharacteristic
52C22⋊#6090C2211yescharacteristic
53#11718084C2211yescharacteristic
54#11718082C2211yescharacteristic
55#11718081C2211yescharacteristic
56#11718081C2211yescharacteristic
57C4⋊#6090C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×#41—21no—
60C22×Q8×C13—21no—
61C13×#135—22no—
62C13×#135—41no—
63C2×C13×Q16—22no—
64C2×C13×Q16—21no—
65C2×C13×Q16—41no—
66C2×C13×Q16C2311yescharacteristic
67C2×C13×Q16C2311yescharacteristic
68C2×C13×SD16—21no—
69C2×C13×SD16—21no—
70C2×C13×D8C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C13×#124—21no—
74C13×#124—41no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—41no—
77C13×#121—21no—
78C13×#121—41no—
79C4×Q8×C13—21no—
80C4×D4×C13—41no—
81C4×D4×C13D411yescharacteristic
82#88189—41no—
83#88180—21no—
84C2×C4⋊Dic13—21no—
85#88178—21no—
86#88178—21no—
87C2×Dic52C2311yescharacteristic
88#88143—41no—
89#88133—41no—
90#88131—41no—
91#88124—21no—
92C4×Dic26—21no—
93C13×#107C2311yescharacteristic
94C13×C4⋊C8D411yescharacteristic
95C13×#103—21no—
96C13×#103—21no—
97C13×#102—21no—
98C13×C22⋊C8D411yescharacteristic
99C13×C22⋊C8D411yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88069—22no—
102#88069—41no—
103#88067—41no—
104#88058—21no—
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88058C2311yescharacteristic
108#88057—21no—
109#88057—21no—
110#88056—21no—
111#88056—21no—
112#88056—21no—
113C2×#6090—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33867—131nomaximal, Sylow
120C13×#41—42no—
121C13×#41—81no—
122C2×Q8×C13—21no—
123C2×Q8×C13—21no—
124C2×Q8×C13—42no—
125C2×Q8×C13—41no—
126C2×Q8×C13—81no—
127C2×D4×C13—21no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13D811yescharacteristic
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×Dic13—41no—
136C2×Dic26—21no—
137C13×Q16—21no—
138C13×Q16—21no—
139C13×Q16—21no—
140C13×Q16—42no—
141C13×Q16#4112yes—
142C13×SD16—42no—
143C13×SD16—81no—
144C13×D8—21no—
145C13×D8—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13C2×D411yescharacteristic
151C2×C8×C13C2×D411yescharacteristic
152C2×C8×C13C2×D411yescharacteristic
153C2×C8×C13C2411yescharacteristic
154C13×C4⋊C4—21no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4D811yescharacteristic
163C13×C22⋊C4D811yescharacteristic
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C22⋊Dic13—41no—
167C22⋊Dic13—41no—
168C22⋊Dic13—41no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—41no—
173#6101—41no—
174#6101—41no—
175#6101—41no—
176#6101—41no—
177#6101—41no—
178C4×Dic13—41no—
179C4×Dic13—41no—
180Dic52—21no—
181Dic52—21no—
182#6090—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#3336—131no—
187#3285D1311yescharacteristic
188#2242—131no—
189#2237—131no—
190#2232—131no—
191#2229—131no—
192#2217—131no—
193#2216—131no—
194#2211—131no—
195#2189—131no—
196#2188—131no—
197C4×Q32—131no—
198D4×C16—131no—
199#2138—131no—
200C2×#358—131no—
201C23×C13—41no—
202C23×C13C2×D811yescharacteristic
203C23×C13C2×D811yescharacteristic
204Q8×C13—22no—
205Q8×C13—41no—
206Q8×C13—41no—
207Q8×C13—41no—
208Q8×C13—82no—
209D4×C13—22no—
210D4×C13—41no—
211D4×C13—41no—
212D4×C13—82no—
213D4×C13—82no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—82no—
222C2×C4×C13—82no—
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C2×Dic13—41no—
229C2×Dic13—41no—
230C2×Dic13—41no—
231C2×Dic13—41no—
232C2×Dic13—82no—
233Dic26—41no—
234Dic26—41no—
235C8×C13—21no—
236C8×C13—21no—
237C8×C13—21no—
238C8×C13C2×#4111yescharacteristic
239C8×C13H(5,𝔽2)11yescharacteristic
240C2×#135C2×D1311yescharacteristic
241C22×Q16C2×D1311yescharacteristic
242#552—261no—
243#548—21no—
244C2×Q32—131no—
245C2×Q32—131no—
246C2×SD32—131no—
247C22×C16—131no—
248C22×C16—131no—
249#499—131no—
250#495C2×D1311yescharacteristic
251#485—261no—
252#483—261no—
253#479—261no—
254#467—131no—
255#467—131no—
256#467C2×D1311yescharacteristic
257#466C2×D1311yescharacteristic
258#464—21no—
259#452—21no—
260#448—21no—
261C4×Q16—131no—
262C4×Q16C2×D1311yescharacteristic
263C8×D4C2×D1311yescharacteristic
264#427—131no—
265C2×#107—131no—
266#367—131no—
267#366—131no—
268#366—131no—
269C4⋊C16—131no—
270#358—131no—
271#358—131no—
272#358—131no—
273#358—131no—
274#358—131no—
275#358—131no—
276#358—131no—
277#357—131no—
278#357—131no—
279#357—131no—
280C22⋊C16—131no—
281C22⋊C16—131no—
282C4×C16—131no—
283C22×C13—21no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—81no—
291C22×C13#50812yes—
292C22×C13C22×D811yescharacteristic
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—42no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13#54611yescharacteristic
301C4×C13#57711yescharacteristic
302Dic13—81no—
303Dic13—81no—
304Dic13—81no—
305Dic13—81no—
306C2×#41—21no—
307C22×Q8—21no—
308#135—22no—
309#135—41no—
310C2×Q16—22no—
311C2×Q16—21no—
312C2×Q16—41no—
313C2×Q16—131no—
314C2×Q16C22×D1311yescharacteristic
315C2×Q16C22×D1311yescharacteristic
316C2×SD16—21no—
317C2×SD16—21no—
318C2×D8C22×D1311yescharacteristic
319C22×C8C22×D1311yescharacteristic
320C22×C8C22×D1311yescharacteristic
321#126—521no—
322#125—261no—
323#125—521no—
324#124—21no—
325#124—41no—
326#123—521no—
327C22⋊Q8—21no—
328C22⋊Q8—41no—
329C22⋊Q8—261no—
330C22⋊Q8—261no—
331#121—21no—
332#121—41no—
333C4×Q8—21no—
334C4×Q8—261no—
335C4×D4—41no—
336C4×D4C22⋊D1311yescharacteristic
337#117—261no—
338#117—521no—
339C2×C4⋊C4—261no—
340Q32—262no—
341Q32—521no—
342SD32—521no—
343C2×C16—131no—
344C2×C16—131no—
345C2×C16—131no—
346C2×C16—131no—
347C2×C16—521no—
348C2×C16—521no—
349#107—131no—
350#107—131no—
351#107—131no—
352#107—261no—
353#107C22×D1311yescharacteristic
354#106—261no—
355#106—261no—
356C4⋊C8C22⋊D1311yescharacteristic
357#103—21no—
358#103—21no—
359#103—261no—
360#103—261no—
361#103—261no—
362#102—21no—
363C22⋊C8C22⋊D1311yescharacteristic
364C22⋊C8C22⋊D1311yescharacteristic
365C4×C8C22×D1311yescharacteristic
366C2×C13—22no—
367C2×C13—41no—
368C2×C13—161no—
369C2×C13#329411yescharacteristic
370C2×C13C2×#50811yescharacteristic
371C2×C13#341711yescharacteristic
372#41—42no—
373#41—81no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—42no—
377C2×Q8—41no—
378C2×Q8—81no—
379C2×Q8—261no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4#610411yescharacteristic
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—521no—
387C22×C4C2×C22⋊D1311yescharacteristic
388C22×C4C2×C22⋊D1311yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—42no—
393Q16—261no—
394Q16—261no—
395Q16#612912yes—
396SD16—42no—
397SD16—81no—
398D8—21no—
399D8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×C22⋊D1311yescharacteristic
405C2×C8C2×C22⋊D1311yescharacteristic
406C2×C8C2×C22⋊D1311yescharacteristic
407C2×C8C23×D1311yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C4⋊C4—261no—
414C4⋊C4—521no—
415C4⋊C4—521no—
416C4⋊C4—521no—
417C4⋊C4—521no—
418C4⋊C4—521no—
419C4⋊C4—521no—
420C4⋊C4#610411yescharacteristic
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—521no—
426C22⋊C4—521no—
427C22⋊C4—521no—
428C22⋊C4#610411yescharacteristic
429C22⋊C4#610411yescharacteristic
430C42—41no—
431C42—521no—
432C42—521no—
433C42C2×C22⋊D1311yescharacteristic
434C16—261no—
435C16—261no—
436C16—261no—
437C16—261no—
438C13#3386711yescharacteristic, complemented, Sylow
439C23—41no—
440C23C2×#610411yescharacteristic
441C23C2×#610411yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—82no—
447Q8—521no—
448Q8—521no—
449D4—22no—
450D4—41no—
451D4—41no—
452D4—82no—
453D4—82no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4—521no—
464C2×C4—521no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—1042no—
468C2×C4C2×#610411yescharacteristic
469C2×C4C2×#610411yescharacteristic
470C2×C4C2×#610411yescharacteristic
471C2×C4C2×#610411yescharacteristic
472C2×C4C22×C22⋊D1311yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#612911yescharacteristic
477C8#8825111yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22#1171885512yes—
487C22C22×#610411yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—1041no—
496C4—1041no—
497C4—1041no—
498C4—1041no—
499C4#1171951111yescharacteristic
500C4#1171954111yescharacteristic
501C2—22no—
502C2—41no—
503C2—161no—
504C2#1312664911yescharacteristic
505C2C2×#1171885511yescharacteristic
506C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3285C2
socleC22×C13C22×D8
hypercenter#3285D13
hypocenterC13#33867
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #13127205C2semidirect
2. #13117067C2semidirect
3. #13117041C2semidirect
4. #13117014C2semidirect
5. #13117000C2semidirect
6. #13116930C2semidirect
7. #13116925C2semidirect
8. #13116895C2semidirect
9. #13116776C2semidirect
10. #13116770C2semidirect
11. C4×#88069C2semidirect
12. D4×#6090C2semidirect
13. #13116543C2semidirect
14. C2×#11718156C2semidirect
438. C13#33867semidirect

Maximal subgroups

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

subgroupindex
#131272052
#131170672
#131170412
#131170142
#131170002
#131169302
#131169252
#131168952
#131167762
#131167702
C4×#880692
D4×#60902
#131165432
C2×#117181562
C13×#32852
#3386713