Finite Group Databasebeta

← #15754794

Subgroups — #15754794

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114646C211yesmaximal, characteristic, complemented
2#13113443C211yesmaximal, characteristic, complemented
3#13113348C211yesmaximal, characteristic, complemented
4#13113322C211yesmaximal, characteristic, complemented
5#13113270C211yesmaximal, characteristic, complemented
6#13113257C211yesmaximal, characteristic, complemented
7C13×#3515C211yesmaximal, characteristic
8C13×#557C411yescharacteristic, complemented
9C13×#554C411yescharacteristic, complemented
10C13×#554C411yescharacteristic, complemented
11C13×#553—21no—
12C13×#552—21no—
13C13×#552—22no—
14C13×#552—21no—
15C13×#547—21no—
16C13×#547C411yescharacteristic, complemented
17C13×#541—21no—
18C13×#539—22no—
19C13×#533C2211yescharacteristic
20C13×#529—21no—
21C13×#529C2211yescharacteristic
22C2×C13×#125—21no—
23C13×#520—21no—
24C4×C13×#41C2211yescharacteristic
25C2×#88077—21no—
26#11718593C2211yescharacteristic
27#11718587C2211yescharacteristic
28#11718586C2211yescharacteristic
29C4×#6099C2211yescharacteristic
30#11718135—21no—
31#11718132—21no—
32#11718130—22no—
33#11718130—21no—
34#11718129—21no—
35Q8⋊#1055—22no—
36Q8⋊#1055—21no—
37D4⋊#1055—21no—
38#11718124—21no—
39C2×C13×#41—21no—
40C2×C13×#41D411yescharacteristic
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8C2×C411yescharacteristic
43C13×C4⋊Q8C2×C411yescharacteristic
44C13×#126—22no—
45C13×#126—22no—
46C13×#126—22no—
47C13×#126—21no—
48C13×#125—22no—
49C13×#125—22no—
50C13×#125—22no—
51C13×#125—21no—
52C13×#125—21no—
53C13×#125—22no—
54C13×#125—21no—
55C13×#125—21no—
56C13×#125D411yescharacteristic
57C13×#124D411yescharacteristic
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×#123—21no—
62C13×#123—22no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—21no—
67C13×C22⋊Q8—21no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8D411yescharacteristic
70C13×C22⋊Q8D412yes—
71C13×#121—22no—
72C13×#121—21no—
73C13×#121D411yescharacteristic
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13C2×C411yescharacteristic
78C4×Q8×C13C2×C411yescharacteristic
79C4×Q8×C13D411yescharacteristic
80C4×Q8×C13D412yes—
81C4×D4×C13—22no—
82C4×D4×C13—22no—
83C4×D4×C13—21no—
84C4×D4×C13—21no—
85C4×D4×C13—21no—
86C4×D4×C13—21no—
87C4×D4×C13—21no—
88C4×D4×C13C2×C411yescharacteristic
89C4×D4×C13C2×C411yescharacteristic
90C4×D4×C13D411yescharacteristic
91C13×#117—22no—
92C13×#117—22no—
93C13×#117—21no—
94C13×#117—21no—
95C13×#117—21no—
96C13×#117D411yescharacteristic
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4—21no—
101C2×C13×C4⋊C4—21no—
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104C2×C4×Dic13—21no—
105C2×#6099—21no—
106#88077—24no—
107#88071—21no—
108#88071—21no—
109C22⋊#1055—21no—
110C22⋊#1055—21no—
111C4⋊#1055—21no—
112C4⋊#1055—21no—
113#88043—21no—
114#88043—21no—
115C4×#1055—21no—
116C4×#1055—21no—
117#8415—131nomaximal, Sylow
118C13×#41—22no—
119C13×#41—41no—
120C13×#41—42no—
121C13×#41—42no—
122C2×Q8×C13—21no—
123C2×Q8×C13C22⋊C411yescharacteristic
124C2×Q8×C13C22⋊C411yescharacteristic
125C2×Q8×C13C22⋊C412yes—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C22⋊C411yescharacteristic
130C2×D4×C13C22⋊C411yescharacteristic
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×Dic13—41no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—22no—
145C13×C4⋊C4—22no—
146C13×C4⋊C4—22no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4C22⋊C411yescharacteristic
162C13×C4⋊C4C22⋊C411yescharacteristic
163C13×C4⋊C4C22⋊C411yescharacteristic
164C13×C4⋊C4C22⋊C411yescharacteristic
165C13×C4⋊C4C22⋊C412yes—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—21no—
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C42×C13—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—22no—
184C42×C13C22×C411yescharacteristic
185C42×C13C2×D411yescharacteristic
186C42×C13C2×D411yescharacteristic
187C42×C13C2×D411yescharacteristic
188C4×Dic13—22no—
189C4×Dic13—41no—
190#6099—22no—
191#6099—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195#3515D1311yescharacteristic
196#1759—131no—
197#1529—131no—
198#1506—131no—
199#1500—131no—
200#1488—131no—
201#1485—131no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13#12011yescharacteristic
205Q8×C13—21no—
206Q8×C13—21no—
207Q8×C13—42no—
208Q8×C13—41no—
209Q8×C13—41no—
210Q8×C13—41no—
211D4×C13—21no—
212D4×C13—41no—
213D4×C13—42no—
214D4×C13—44no—
215D4×C13—81no—
216D4×C13#10412yes—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—44no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—81no—
235C2×C4×C13—82no—
236C2×C4×C13—82no—
237C2×C4×C13C2×C22⋊C411yescharacteristic
238C2×C4×C13C2×C22⋊C411yescharacteristic
239C2×C4×C13C2×C22⋊C411yescharacteristic
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13#12011yescharacteristic
243C2×Dic13—42no—
244C2×Dic13—81no—
245C2×Dic13—81no—
246#1055—42no—
247#1055—81no—
248#1055—81no—
249#557Dic1311yescharacteristic, complemented
250#554Dic1311yescharacteristic, complemented
251#554Dic1311yescharacteristic, complemented
252#553—21no—
253#552—21no—
254#552—22no—
255#552—21no—
256#547—21no—
257#547Dic1311yescharacteristic, complemented
258#541—21no—
259#539—22no—
260#533C2×D1311yescharacteristic
261#529—21no—
262#529C2×D1311yescharacteristic
263C2×#125—21no—
264#520—21no—
265C4×#41C2×D1311yescharacteristic
266#432—131no—
267#431—131no—
268C2×#104—261no—
269C4×M16—131no—
270#376—131no—
271#339—261no—
272#330—261no—
273#329—261no—
274#328—261no—
275#328—262no—
276#327—261no—
277Q8⋊C8—262no—
278Q8⋊C8—261no—
279D4⋊C8—261no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—22no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13#37911yescharacteristic
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—41no—
296C4×C13—41no—
297C4×C13—42no—
298C4×C13—41no—
299C4×C13—41no—
300C4×C13—41no—
301C4×C13—41no—
302C4×C13—42no—
303C4×C13C2×#10411yescharacteristic
304C4×C13#42111yescharacteristic
305Dic13—82no—
306C2×#41—21no—
307C2×#41C22⋊D1311yescharacteristic
308C2×M16—261no—
309C4⋊Q8—21no—
310C4⋊Q8C2×Dic1311yescharacteristic
311C4⋊Q8C2×Dic1311yescharacteristic
312#126—22no—
313#126—22no—
314#126—22no—
315#126—21no—
316#125—22no—
317#125—22no—
318#125—22no—
319#125—21no—
320#125—21no—
321#125—22no—
322#125—21no—
323#125—21no—
324#125C22⋊D1311yescharacteristic
325#124C22⋊D1311yescharacteristic
326#123—22no—
327#123—22no—
328#123—22no—
329#123—21no—
330#123—22no—
331C22⋊Q8—21no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8C22⋊D1311yescharacteristic
338C22⋊Q8C22⋊D1312yes—
339#121—22no—
340#121—21no—
341#121C22⋊D1311yescharacteristic
342C4×Q8—21no—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8C2×Dic1311yescharacteristic
346C4×Q8C2×Dic1311yescharacteristic
347C4×Q8C22⋊D1311yescharacteristic
348C4×Q8C22⋊D1312yes—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4C2×Dic1311yescharacteristic
357C4×D4C2×Dic1311yescharacteristic
358C4×D4C22⋊D1311yescharacteristic
359#117—22no—
360#117—22no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117C22⋊D1311yescharacteristic
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C42—21no—
371C2×C42—261no—
372C2×C42C22×D1311yescharacteristic
373C4⋊C8—261no—
374C4⋊C8—261no—
375#104—264no—
376C22⋊C8—261no—
377C22⋊C8—261no—
378#97—261no—
379#97—261no—
380C4×C8—261no—
381C4×C8—261no—
382#95—261no—
383#95—261no—
384C2×C13—41no—
385C2×C13—42no—
386C2×C13—81no—
387C2×C13#178911yescharacteristic
388C2×C13#179411yescharacteristic
389C2×C13#179611yescharacteristic
390#41—22no—
391#41—41no—
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8C22⋊Dic1311yescharacteristic
396C2×Q8C22⋊Dic1311yescharacteristic
397C2×Q8C22⋊Dic1312yes—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4C22⋊Dic1311yescharacteristic
402C2×D4C22⋊Dic1311yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—521no—
411C22×C4C2×C22⋊D1311yescharacteristic
412C22×C4C2×C22⋊D1311yescharacteristic
413C22×C4C2×C22⋊D1311yescharacteristic
414M16—262no—
415M16—521no—
416C2×C8—521no—
417C2×C8—521no—
418C2×C8—521no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4C22⋊Dic1311yescharacteristic
439C4⋊C4C22⋊Dic1311yescharacteristic
440C4⋊C4C22⋊Dic1311yescharacteristic
441C4⋊C4C22⋊Dic1311yescharacteristic
442C4⋊C4C22⋊Dic1312yes—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C42—22no—
456C42—21no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—22no—
461C42—262no—
462C42—521no—
463C42C22×Dic1311yescharacteristic
464C42C2×C22⋊D1311yescharacteristic
465C42C2×C22⋊D1311yescharacteristic
466C42C2×C22⋊D1311yescharacteristic
467C13#841511yescharacteristic, complemented, Sylow
468C23—21no—
469C23—21no—
470C23#8820711yescharacteristic
471Q8—21no—
472Q8—21no—
473Q8—42no—
474Q8—41no—
475Q8—41no—
476Q8—41no—
477D4—21no—
478D4—41no—
479D4—42no—
480D4—44no—
481D4—81no—
482D4#8807712yes—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—522no—
504C2×C4—1041no—
505C2×C4—1041no—
506C2×C4C2×C22⋊Dic1311yescharacteristic
507C2×C4C2×C22⋊Dic1311yescharacteristic
508C2×C4C2×C22⋊Dic1311yescharacteristic
509C2×C4#8820711yescharacteristic
510C2×C4#8820711yescharacteristic
511C2×C4#8820711yescharacteristic
512C8—522no—
513C8—1041no—
514C8—1041no—
515C22—21no—
516C22—22no—
517C22—21no—
518C22—21no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22#1171890811yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—42no—
533C4—41no—
534C4—41no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—1042no—
539C4C2×#8807711yescharacteristic
540C4#1171889711yescharacteristic
541C2—41no—
542C2—42no—
543C2—81no—
544C2#1311478011yescharacteristic
545C2#1311480011yescharacteristic
546C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3515C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenter#3515D13
hypocenterC13#8415
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #13114646C2semidirect
2. #13113443C2semidirect
3. #13113348C2semidirect
4. #13113322C2semidirect
5. #13113270C2semidirect
6. #13113257C2semidirect
8. C13×#557C4semidirect
9. C13×#554C4semidirect
10. C13×#554C4semidirect
16. C13×#547C4semidirect
249. #557Dic13semidirect
250. #554Dic13semidirect
251. #554Dic13semidirect
257. #547Dic13semidirect
467. C13#8415semidirect

Maximal subgroups

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

subgroupindex
#131146462
#131134432
#131133482
#131133222
#131132702
#131132572
C13×#35152
#841513