Finite Group Databasebeta

← #14724937

Subgroups — #14724937

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078672C211yesmaximal, characteristic
2#13077739C211yesmaximal, characteristic, complemented
3#13077679C211yesmaximal, characteristic, complemented
4#13067509C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067481C211yesmaximal, characteristic, complemented
7#13067480C211yesmaximal, characteristic, complemented
8#13067473C211yesmaximal, characteristic, complemented
9#13067472C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067406C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic, complemented
13#13066995C211yesmaximal, characteristic, complemented
14#13066898C211yesmaximal, characteristic, complemented
15C8×C11×D8C211yesmaximal, characteristic, complemented
16#10623079C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622771C411yescharacteristic
22#10622763C411yescharacteristic
23#10622724—21no—
24#10622723—21no—
25C8×C22⋊D11—21no—
26C2×Dic11⋊C8—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622498C411yescharacteristic
32#10622488C411yescharacteristic
33#10622450C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446C2211yescharacteristic
36#10622444C2211yescharacteristic
37#10622394C411yescharacteristic
38#10622392C411yescharacteristic
39#10622375C411yescharacteristic
40#10622374C411yescharacteristic
41#10622343—21no—
42#10622342—21no—
43#10622340—21no—
44#10622332—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66991C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×#4314C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66948C2×C411yescharacteristic
90#66945C2×C411yescharacteristic
91#66941C2×C411yescharacteristic
92#66940C2×C411yescharacteristic
93#66938—21no—
94#66937—21no—
95(C22⋊D11)⋊C4—21no—
96#66930—21no—
97C4×D44C2311yescharacteristic
98C42×D11C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66896C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8C2×C411yescharacteristic
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18015—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155#4341—22no—
156#4341—41no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C2×Dic22—21no—
166C2×Dic22C22×C411yescharacteristic
167C11×D8—22no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—81no—
172C2×C8×C11—81no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184#4324—41no—
185#4323—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#4314—41no—
210#4313—81no—
211#4313—81no—
212C8×D11—24no—
213C8×D11—81no—
214#3106—111no—
215#2990—111no—
216#2979—111no—
217#1590—111no—
218#1590—111no—
219#1586—111no—
220#1586—111no—
221#1585—111no—
222#1585—111no—
223C8×D8—111no—
224C8×D8D1111yescharacteristic, complemented
225#1574—111no—
226#1492—111no—
227#1476—111no—
228#1450—111no—
229C23×C11—21no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11#13112yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—81no—
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257C2×Dic11C4×D411yescharacteristic
258D44—21no—
259D44—21no—
260D44—81no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—22no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—21no—
269Dic22—21no—
270Dic22—81no—
271C8×C11—22no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—22no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#532—111no—
286C4×#41—111no—
287#482—111no—
288#482—111no—
289#477—111no—
290#476—111no—
291#460—111no—
292#459—111no—
293#449—111no—
294#449—111no—
295#446—111no—
296#446—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8C2×D1111yescharacteristic
301#436—111no—
302#436—111no—
303#436—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4C2×D1111yescharacteristic
310C8×D4C2×D1111yescharacteristic
311#432—221no—
312#431—111no—
313#431—111no—
314#431—111no—
315#423—111no—
316C2×C4⋊C8—221no—
317#408—221no—
318#408—221no—
319C2×C4×C8—111no—
320#335—111no—
321#335C2×D1111yescharacteristic
322#334—111no—
323#334—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322—111no—
334C82—111no—
335C82C2×D1111yescharacteristic
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11C2×#13111yescharacteristic
353C4×C11#56811yescharacteristic
354C4×C11#57611yescharacteristic
355C4×C11#57711yescharacteristic
356Dic11—21no—
357Dic11—21no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11#44312yes—
362C2×#41—111no—
363C2×#41—221no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8C4×D1111yescharacteristic
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C4⋊Q8—111no—
377#127—111no—
378#124—221no—
379#121—111no—
380#121—111no—
381#121—221no—
382C4×Q8—111no—
383C4×Q8—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390C4×D4C22×D1111yescharacteristic
391#117—111no—
392#117—221no—
393C2×C42—111no—
394C2×C42—221no—
395#107—111no—
396#107C4×D1111yescharacteristic
397#106—111no—
398#106—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102C4×D1111yescharacteristic
417#102C4×D1111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—111no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429#97—221no—
430#97—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8—221no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—42no—
440C2×C11—81no—
441C2×C11#293311yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11C2×#44311yescharacteristic
444D11—41no—
445D11—81no—
446#41—222no—
447#41—441no—
448#41—881no—
449#41—881no—
450C2×Q8—111no—
451C2×Q8—221no—
452C2×D4—111no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4C2×C4×D1111yescharacteristic
459C2×D4C2×C4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468SD16—441no—
469SD16—441no—
470D8—22no—
471D8—222no—
472M16—881no—
473M16—881no—
474M16—881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—81no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—224no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—881no—
489C2×C8—881no—
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8D4×D1111yescharacteristic
493C2×C8D4×D1111yescharacteristic
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4C2×C4×D1111yescharacteristic
500C4⋊C4C2×C4×D1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42—221no—
512C42—221no—
513C42—221no—
514C42C23×D1111yescharacteristic
515C11#1801511yescharacteristic, complemented, Sylow
516C23—21no—
517C23—21no—
518C23—111no—
519C23—221no—
520Q8—221no—
521Q8—221no—
522Q8—881no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—221no—
527D4—221no—
528D4—442no—
529D4—442no—
530D4—881no—
531D4—881no—
532D4—881no—
533D4#6695412yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—111no—
543C2×C4—222no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4C22×C4×D1111yescharacteristic
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—222no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—441no—
571C8—441no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—221no—
579C22—221no—
580C22—221no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22C4×D4×D1111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—112no—
589C4—221no—
590C4—221no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4C2×#6695411yescharacteristic
595C4#1062328111yescharacteristic
596C4#1062328811yescharacteristic
597C4#1062330111yescharacteristic
598C2—42no—
599C2—81no—
600C2—441no—
601C2—881no—
602C2#1307733611yescharacteristic
603C2#1307744111yescharacteristic
604C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×D8C2
socleC22×C11C2×C4×D4
prime radical#13078672C2
cosocleC42×C11C24
hypercenterC8×D8D11
hypocenterC11#18015
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13077739C2semidirect
3. #13077679C2semidirect
4. #13067509C2semidirect
5. #13067508C2semidirect
6. #13067481C2semidirect
7. #13067480C2semidirect
8. #13067473C2semidirect
9. #13067472C2semidirect
10. #13067408C2semidirect
11. #13067406C2semidirect
12. #13067065C2semidirect
13. #13066995C2semidirect
14. #13066898C2semidirect
15. C8×C11×D8C2semidirect
224. C8×D8D11semidirect
515. C11#18015semidirect

Maximal subgroups

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

subgroupindex
#130786722
#130777392
#130776792
#130675092
#130675082
#130674812
#130674802
#130674732
#130674722
#130674082
#130674062
#130670652
#130669952
#130668982
C8×C11×D82
#1801511