Finite Group Databasebeta

← #14724940

Subgroups — #14724940

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#13078674C211yesmaximal, characteristic
2#13077740C211yesmaximal, characteristic, complemented
3#13077679C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067506C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067476C211yesmaximal, characteristic, complemented
9#13067410C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067406C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic, complemented
13#13066997C211yesmaximal, characteristic, complemented
14#13066901C211yesmaximal, characteristic, complemented
15C11×#1585C211yesmaximal, characteristic, complemented
16C4×#4343C2211yescharacteristic
17#10623079C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622785C411yescharacteristic
22#10622776C411yescharacteristic
23#10622723—21no—
24C8×C22⋊D11—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622479C411yescharacteristic
31#10622450C2211yescharacteristic
32#10622449—21no—
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446C2211yescharacteristic
36D11×C4⋊C8—21no—
37#10622424C411yescharacteristic
38#10622407C411yescharacteristic
39#10622399C411yescharacteristic
40#10622397C411yescharacteristic
41#10622342—21no—
42#10622340—21no—
43#10622319—21no—
44#10622318—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80C2×D88C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87#66948C2×C411yescharacteristic
88#66946—21no—
89#66946C2×C411yescharacteristic
90#66945—21no—
91#66945C2×C411yescharacteristic
92#66941C2×C411yescharacteristic
93#66938—21no—
94#66937—21no—
95C4×D44—21no—
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98C42×D11—21no—
99C42×D11C2311yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123(C2×D11)⋊C8D411yescharacteristic
124(C2×D11)⋊C8D411yescharacteristic
125#66882C2×C411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11—21no—
133#66873C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18015—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151#4343—22no—
152#4343—41no—
153#4339—81no—
154#4339—81no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11C22×C411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11#4111yescharacteristic
166C2×Dic22—21no—
167C11×SD16—41no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—81no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4325—41no—
184#4323—22no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207D88—22no—
208#4313—81no—
209#4313—81no—
210C8×D11—24no—
211C8×D11—81no—
212C8×D11—81no—
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#1585D1111yescharacteristic, complemented
223C8×D8—111no—
224C8×D8—111no—
225#1574—111no—
226#1492—111no—
227#1476—111no—
228#1450—111no—
229C23×C11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—42no—
246C22⋊D11—81no—
247C22⋊D11—81no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253D44—21no—
254D44—21no—
255D44—21no—
256D44—42no—
257D44—81no—
258D44#13112yes—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—22no—
264C4×D11—42no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—42no—
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#446C2×D1111yescharacteristic
297C4×SD16—111no—
298C4×SD16C2×D1111yescharacteristic
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436—111no—
303#436—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—221no—
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⋊C8C2×D1111yescharacteristic
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8C2×D1111yescharacteristic
332#322—111no—
333#322C2×D1111yescharacteristic
334C82—111no—
335C82—111no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C2×D11—22no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11C2×#13111yescharacteristic
354C4×C11#56811yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—21no—
358Dic11—21no—
359Dic11—41no—
360Dic11—41no—
361Dic11#44312yes—
362C2×#41—111no—
363C2×#41—221no—
364C2×SD16—111no—
365C2×SD16C4×D1111yescharacteristic
366C2×D8—111no—
367C2×D8—111no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—21no—
372C22×C8—221no—
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×Q8C22×D1111yescharacteristic
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391#117—111no—
392#117—221no—
393C2×C42—111no—
394C2×C42—221no—
395#107—111no—
396#107—111no—
397#106—111no—
398#106C4×D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103C4×D1111yescharacteristic
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429#97—21no—
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—81no—
440C2×C11#293311yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11C2×#44311yescharacteristic
443D11—41no—
444D11—42no—
445D11—81no—
446#41—222no—
447#41—441no—
448#41—881no—
449#41—881no—
450C2×Q8—221no—
451C2×Q8C2×C4×D1111yescharacteristic
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4C2×C4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468SD16—41no—
469SD16—441no—
470D8—222no—
471D8—222no—
472M16—881no—
473M16—881no—
474M16—881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—224no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8—881no—
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8D4×D1111yescharacteristic
493C2×C8D4×D1111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4C2×C4×D1111yescharacteristic
500C4⋊C4C2×C4×D1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C42—21no—
509C42—111no—
510C42—111no—
511C42—111no—
512C42—221no—
513C42—221no—
514C42C23×D1111yescharacteristic
515C11#1801511yescharacteristic, complemented, Sylow
516C23—21no—
517C23—111no—
518C23—221no—
519C23—221no—
520Q8—21no—
521Q8—21no—
522Q8—881no—
523D4—21no—
524D4—21no—
525D4—112no—
526D4—221no—
527D4—221no—
528D4—221no—
529D4—442no—
530D4—442no—
531D4—881no—
532D4—881no—
533D4—881no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—111no—
542C2×C4—222no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
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—41no—
573C22—41no—
574C22—41no—
575C22—221no—
576C22—222no—
577C22—221no—
578C22—221no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22C4×D4×D1111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—112no—
590C4—221no—
591C4—221no—
592C4—441no—
593C4—441no—
594C4#1062327611yescharacteristic
595C4D11×#13111yescharacteristic
596C4#1062330511yescharacteristic
597C4#1062330911yescharacteristic
598C2—81no—
599C2—441no—
600C2—442no—
601C2—881no—
602C2#1307733911yescharacteristic
603C2#1307744711yescharacteristic
604C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1585C2
socleC22×C11C2×C4×D4
prime radical#13078674C2
cosocleC42×C11C24
hypercenter#1585D11
hypocenterC11#18015
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #13077740C2semidirect
3. #13077679C2semidirect
4. #13067507C2semidirect
5. #13067506C2semidirect
6. #13067483C2semidirect
7. #13067482C2semidirect
8. #13067476C2semidirect
9. #13067410C2semidirect
10. C8×#4323C2semidirect
11. #13067406C2semidirect
12. #13067065C2semidirect
13. #13066997C2semidirect
14. #13066901C2semidirect
15. C11×#1585C2semidirect
222. #1585D11semidirect
515. C11#18015semidirect

Maximal subgroups

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

subgroupindex
#130786742
#130777402
#130776792
#130675072
#130675062
#130674832
#130674822
#130674762
#130674102
C8×#43232
#130674062
#130670652
#130669972
#130669012
C11×#15852
#1801511