Finite Group Databasebeta

← #14745111

Subgroups — #14745111

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080967C211yesmaximal, characteristic, complemented
2D4×#4325C211yesmaximal, characteristic, complemented
3#13080217C211yesmaximal, characteristic
4#13068204C211yesmaximal, characteristic, complemented
5#13068112C211yesmaximal, characteristic, complemented
6#13068088C211yesmaximal, characteristic, complemented
7#13067993C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067899C211yesmaximal, characteristic, complemented
10#13067879C211yesmaximal, characteristic, complemented
11#13067731C211yesmaximal, characteristic, complemented
12#13067688C211yesmaximal, characteristic, complemented
13#13067506C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3384C211yesmaximal, characteristic, complemented
16C11×#554C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19C2×#66964—21no—
20#10623086C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#501—21no—
23C11×#498C2211yescharacteristic, complemented
24C11×#478—21no—
25C11×#476—21no—
26C11×#476C2211yescharacteristic
27C11×#474C2211yescharacteristic, complemented
28C11×#446C2211yescharacteristic, complemented
29C11×#442—21no—
30C4×C11×D8C2211yescharacteristic
31#10622840—21no—
32#10622698C2211yescharacteristic
33#10622698C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622692C2211yescharacteristic, complemented
37#10622692C2211yescharacteristic, complemented
38#10622661—21no—
39#10622661—21no—
40#10622659—21no—
41#10622656—21no—
42#10622640C2211yescharacteristic
43C4×#4325C2211yescharacteristic
44#10622633C2211yescharacteristic, complemented
45#10622632C2211yescharacteristic
46#10622628C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic, complemented
49#10622581—21no—
50C2×#66872—21no—
51#10622499—21no—
52#10622394—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×#4341—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×D8D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#125—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—41no—
79C11×C22⋊Q8—41no—
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—41no—
91C2×#4325—44no—
92C2×#4325D411yescharacteristic
93C2×#4324—21no—
94C2×#4323—21no—
95#66983—21no—
96#66983—21no—
97C2×C4⋊Dic11—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100#66964—44no—
101C2×#4314—21no—
102C2×#4314—21no—
103C2×#4313—21no—
104#66950—21no—
105#66948—21no—
106#66939—41no—
107#66935—41no—
108#66927C2311yescharacteristic
109C4×D44C2311yescharacteristic
110#66922C2311yescharacteristic
111C11×#107—21no—
112C11×#107D411yescharacteristic
113C11×#106—21no—
114C11×#106—21no—
115C11×#106—21no—
116C11×C4⋊C8—21no—
117C11×C4⋊C8C2311yescharacteristic
118C11×#102—21no—
119C11×#102—21no—
120C11×#102D411yescharacteristic
121C11×#102D411yescharacteristic
122C11×#97—21no—
123C4×C8×C11C2311yescharacteristic
124#66899—21no—
125#66899—21no—
126#66899D411yescharacteristic
127C22⋊(C11⋊C8)—21no—
128C22⋊(C11⋊C8)—21no—
129(C2×D11)⋊C8—21no—
130#66874—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66873D411yescharacteristic
135#66872—21no—
136#66872—21no—
137#66872—21no—
138#66872—21no—
139#66872—41no—
140#66872D411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19890—111nomaximal, Sylow
147C23×D11—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—41no—
159C22×C4×C11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C22×Dic11—41no—
163#4341—42no—
164#4341—81no—
165D4×D11—42no—
166D4×D11—81no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—41no—
171C2×D44—42no—
172C2×D44—81no—
173C2×D44C2×D411yescharacteristic
174C2×C4×D11—21no—
175C2×Dic22—21no—
176C11×D8SD1614yescomplemented
177C2×C8×C11—21no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11—21no—
196C42×C11C2411yescharacteristic
197#4325—22no—
198#4325—42no—
199#4325—42no—
200#4325—42no—
201#4325—81no—
202#4325—82no—
203#4324—42no—
204#4323—42no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—41no—
211C4⋊Dic11C2×D411yescharacteristic
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8—42no—
218C2×C11⋊C8C2×D411yescharacteristic
219C2×C11⋊C8C2×D411yescharacteristic
220#4314—42no—
221#4314—81no—
222#4313—42no—
223#3384D1111yescharacteristic, complemented
224#3335—111no—
225D4×SD16—111no—
226#3272—111no—
227#1705—111no—
228#1691—111no—
229#1686—111no—
230#1671—111no—
231#1665—111no—
232#1654—111no—
233#1651—111no—
234#1629—111no—
235#1622—111no—
236#1590—111no—
237C8×D8—111no—
238C23×C11—21no—
239C23×C11—21no—
240C22×D11—21no—
241C22×D11—41no—
242C22×D11—82no—
243C22×D11—82no—
244C22×D11—161no—
245Q8×C11—21no—
246Q8×C11—21no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—81no—
250Q8×C11—82no—
251D4×C11—21no—
252D4×C11—21no—
253D4×C11C2×SD1612yes—
254D4×C11C2×SD1612yescomplemented
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—82no—
266C2×C4×C11—161no—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C22⋊D11—82no—
271C22⋊D11—82no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—82no—
275D44—21no—
276D44—21no—
277D44—41no—
278D44—41no—
279D44—41no—
280D44—41no—
281D44—81no—
282D44—82no—
283C4×D11—41no—
284C4×D11—41no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—21no—
288C8×C11—41no—
289C8×C11C2×SD1612yescomplemented
290C11⋊C8—22no—
291C11⋊C8—21no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C11⋊C8AGL(1,ℤ/8)12yescomplemented
296C2×AGL(1,ℤ/8)—221no—
297C22×SD16—221no—
298#554C2×D1111yescharacteristic, complemented
299D4×Q8C2×D1111yescharacteristic
300#547—111no—
301D42—111no—
302#501—21no—
303#498—111no—
304#498—111no—
305#498C2×D1111yescharacteristic, complemented
306#492—111no—
307#492—111no—
308#492—111no—
309#483—221no—
310#481—221no—
311#478—21no—
312#476—21no—
313#476—111no—
314#476C2×D1111yescharacteristic
315#475—111no—
316#474C2×D1111yescharacteristic, complemented
317#468—221no—
318#465—221no—
319#465—221no—
320#461—111no—
321#461—111no—
322#460—111no—
323#459—111no—
324#450—221no—
325#450—221no—
326#449—221no—
327#448—221no—
328#446C2×D1111yescharacteristic, complemented
329#442—21no—
330C4×SD16—111no—
331C4×D8C2×D1111yescharacteristic
332#436—111no—
333C8×D4—111no—
334C8×D4—111no—
335C2×#106—221no—
336#335—111no—
337#334—111no—
338#333—111no—
339#332—111no—
340#332—111no—
341#331—111no—
342Q8⋊C8—111no—
343D4⋊C8—111no—
344D4⋊C8—111no—
345D4⋊C8—111no—
346C82—111no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11D4211yescharacteristic
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—164no—
361C4×C11—21no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11C22×SD1611yescharacteristic
369C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C4×C11#57711yescharacteristic
371C4×C11#57711yescharacteristic
372Dic11—41no—
373Dic11—81no—
374C2×#41—221no—
375C22×Q8—21no—
376C22×D4—221no—
377C22×D4—221no—
378AGL(1,ℤ/8)—444no—
379C2×SD16—111no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×SD16—221no—
383C2×SD16—221no—
384C2×SD16—221no—
385C2×SD16—221no—
386C2×SD16—221no—
387C2×SD16—441no—
388C2×SD16—444no—
389C2×D8—221no—
390C2×D8C22⋊D1111yescharacteristic
391C2×M16—221no—
392C22×C8—221no—
393C22×C8—221no—
394C4⋊Q8—21no—
395C4⋊Q8—111no—
396C4⋊Q8C22×D1111yescharacteristic
397C4⋊Q8C22×D1111yescharacteristic
398#127—111no—
399#125—21no—
400#123—441no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—41no—
405C22⋊Q8—221no—
406#121—221no—
407#121—221no—
408#121—221no—
409#120—441no—
410C4×Q8C22×D1111yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—111no—
414C4×D4C22×D1111yescharacteristic
415C4×D4C22×D1111yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—221no—
418#107—21no—
419#107C22⋊D1111yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—111no—
424#106—221no—
425#106—221no—
426#106—221no—
427#106—221no—
428#106—441no—
429C4⋊C8—21no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8C22×D1111yescharacteristic
434#103—111no—
435#103—221no—
436#103—221no—
437#103—221no—
438#102—21no—
439#102—21no—
440#102—111no—
441#102—221no—
442#102—221no—
443#102—221no—
444#102C22⋊D1111yescharacteristic
445#102C22⋊D1111yescharacteristic
446C22⋊C8—221no—
447C22⋊C8—221no—
448C22⋊C8—221no—
449#97—21no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8C22×D1111yescharacteristic
453C2×C11—42no—
454C2×C11—42no—
455C2×C11#327211yescharacteristic
456C2×C11D4×SD1611yescharacteristic
457C2×C11#329111yescharacteristic
458D11—81no—
459D11—161no—
460C24—441no—
461#41—442no—
462#41—881no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—41no—
466C2×Q8—42no—
467C2×Q8—81no—
468C2×Q8—221no—
469C2×Q8D4×D1111yescharacteristic
470C2×D4—111no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—441no—
475C2×D4—442no—
476C2×D4—441no—
477C2×D4—442no—
478C2×D4—441no—
479C2×D4—881no—
480C2×D4—881no—
481C2×D4C2×C22⋊D1111yescharacteristic
482C2×D4C2×C22⋊D1111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—221no—
488C22×C4—441no—
489SD16—222no—
490SD16—442no—
491SD16—442no—
492SD16—442no—
493SD16—442no—
494SD16—442no—
495SD16—881no—
496SD16—881no—
497SD16—882no—
498D8—442no—
499D8#432514yescomplemented
500M16—442no—
501C2×C8—21no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—442no—
509C2×C8—442no—
510C2×C8C2×C22⋊D1111yescharacteristic
511C2×C8C2×C22⋊D1111yescharacteristic
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—111no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—441no—
524C4⋊C4D4×D1111yescharacteristic
525C4⋊C4C2×C22⋊D1111yescharacteristic
526C4⋊C4C2×C22⋊D1111yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—221no—
532C22⋊C4—441no—
533C22⋊C4—441no—
534C42—21no—
535C42C23×D1111yescharacteristic
536C11#1989011yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—221no—
540C23—441no—
541C23—882no—
542C23—882no—
543C23—1761no—
544Q8—21no—
545Q8—21no—
546Q8—41no—
547Q8—41no—
548Q8—81no—
549Q8—82no—
550Q8—441no—
551Q8—441no—
552D4—21no—
553D4—21no—
554D4—221no—
555D4—221no—
556D4—441no—
557D4—441no—
558D4—441no—
559D4—441no—
560D4—881no—
561D4—882no—
562D4—882no—
563D4—882no—
564D4C2×#432512yes—
565D4C2×#432512yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4—221no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—882no—
583C2×C4C2×D4×D1111yescharacteristic
584C2×C4#6703711yescharacteristic
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—21no—
587C8—41no—
588C8—112no—
589C8—222no—
590C8—221no—
591C8—441no—
592C8—441no—
593C8—441no—
594C8C2×#432512yescomplemented
595C22—22no—
596C22—22no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—1764no—
608C22D4×C22⋊D1111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—441no—
617C4—881no—
618C4D11×AGL(1,ℤ/8)11yescharacteristic
619C4#1062330611yescharacteristic
620C4C22×#432511yescharacteristic
621C4#1062336811yescharacteristic
622C2—42no—
623C2—42no—
624C2—881no—
625C2—1761no—
626C2#1308021011yescharacteristic
627C2D4×#432511yescharacteristic
628C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3384C2
socleC22×C11D42
prime radical#13080217C2
hypercenter#3384D11
hypocenterC11#19890
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #13080967C2semidirect
2. D4×#4325C2semidirect
4. #13068204C2semidirect
5. #13068112C2semidirect
6. #13068088C2semidirect
7. #13067993C2semidirect
8. #13067959C2semidirect
9. #13067899C2semidirect
10. #13067879C2semidirect
11. #13067731C2semidirect
12. #13067688C2semidirect
13. #13067506C2semidirect
14. D8×C11⋊C8C2semidirect
15. C11×#3384C2semidirect
16. C11×#554C22semidirect
23. C11×#498C22semidirect
27. C11×#474C22semidirect
28. C11×#446C22semidirect
36. #10622692C22semidirect
37. #10622692C22semidirect
44. #10622633C22semidirect
48. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
176. C11×D8SD16semidirect
223. #3384D11semidirect
254. D4×C11C2×SD16semidirect
289. C8×C11C2×SD16semidirect
295. C11⋊C8AGL(1,ℤ/8)semidirect
298. #554C2×D11semidirect
305. #498C2×D11semidirect
316. #474C2×D11semidirect
328. #446C2×D11semidirect
499. D8#4325semidirect
536. C11#19890semidirect
565. D4C2×#4325semidirect
594. C8C2×#4325semidirect

Maximal subgroups

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

subgroupindex
#130809672
D4×#43252
#130802172
#130682042
#130681122
#130680882
#130679932
#130679592
#130678992
#130678792
#130677312
#130676882
#130675062
D8×C11⋊C82
C11×#33842
#1989011