Finite Group Databasebeta

← #14743594

Subgroups — #14743594

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080527C211yesmaximal, characteristic, complemented
2#13080431C211yesmaximal, characteristic
3D4×#4325C211yesmaximal, characteristic, complemented
4#13068270C211yesmaximal, characteristic, complemented
5#13068184C211yesmaximal, characteristic, complemented
6#13068041C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067865C211yesmaximal, characteristic, complemented
10#13067850C211yesmaximal, characteristic, complemented
11#13067793C211yesmaximal, characteristic, complemented
12#13067726C211yesmaximal, characteristic, complemented
13#13067450C211yesmaximal, characteristic, complemented
14#13067440C211yesmaximal, characteristic, complemented
15C11×#3367C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19#10623082C2211yescharacteristic
20D4×D44C2211yescharacteristic
21C11×#489—21no—
22C11×#487C2211yescharacteristic, complemented
23C11×#477—21no—
24C11×#474C2211yescharacteristic, complemented
25C11×#463—21no—
26C11×#461C2211yescharacteristic
27C11×#446C2211yescharacteristic, complemented
28C11×#440—21no—
29C4×C11×D8C2211yescharacteristic
30#10622840—21no—
31#10622769—21no—
32#10622706C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622698C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622691C2211yescharacteristic, complemented
38#10622664—21no—
39#10622661—21no—
40#10622660—21no—
41#10622659—21no—
42#10622644C2211yescharacteristic, complemented
43#10622640C2211yescharacteristic
44C4×#4325C2211yescharacteristic
45#10622628C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic, complemented
48#10622620C2211yescharacteristic
49#10622615—21no—
50#10622609—21no—
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic
63#10622121C2211yescharacteristic
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×D4×D11—21no—
69C2×#4339—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×D8D411yescharacteristic
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#126—41no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—41no—
81C4×Q8×C11—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87C2×#4326—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—44no—
93C2×#4325D411yescharacteristic
94#66991—21no—
95C2×#4323—21no—
96#66983—21no—
97#66977—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100C2×C8×D11—21no—
101#66948—21no—
102C4⋊C4×D11—21no—
103#66936—41no—
104#66935—41no—
105#66927C2311yescharacteristic
106C4×D44C2311yescharacteristic
107#66922C2311yescharacteristic
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#103—21no—
114C11×#103—21no—
115C11×#102—21no—
116C11×#102D411yescharacteristic
117C11×#102D411yescharacteristic
118C11×#97—21no—
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66899D411yescharacteristic
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127(C2×D11)⋊C8—21no—
128#66874—21no—
129#66874—21no—
130#66874—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66873—41no—
135#66873D411yescharacteristic
136#66872D411yescharacteristic
137#66871—21no—
138#66871—21no—
139#66871—41no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19787—111nomaximal, Sylow
146C23×D11—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—81no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11C2×D411yescharacteristic
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160D4×D11—42no—
161D4×D11—81no—
162#4339—42no—
163#4339—81no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—41no—
168C2×D44—42no—
169C2×D44—81no—
170C2×D44C2×D411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—41no—
173C2×Dic22—21no—
174C11×SD16—42no—
175C11×D8—22no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C42×C11—21no—
195C42×C11—41no—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—41no—
198#4326—81no—
199#4325—22no—
200#4325—42no—
201#4325—42no—
202#4325—42no—
203#4325—81no—
204#4323—81no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—41no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2×D411yescharacteristic
210Dic11⋊C4—41no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—42no—
216C2×C11⋊C8—81no—
217C2×C11⋊C8C2×D411yescharacteristic
218C2×C11⋊C8C2×D411yescharacteristic
219C8×D11—81no—
220#3367D1111yescharacteristic, complemented
221#3302—111no—
222#3294—111no—
223D4×SD16—111no—
224#1719—111no—
225#1702—111no—
226#1679—111no—
227#1679—111no—
228#1665—111no—
229#1649—111no—
230#1647—111no—
231#1639—111no—
232#1628—111no—
233#1582—111no—
234#1580—111no—
235C23×C11—21no—
236C23×C11—21no—
237C22×D11—21no—
238C22×D11—41no—
239C22×D11—82no—
240C22×D11—82no—
241C22×D11—161no—
242Q8×C11—21no—
243Q8×C11—21no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—82no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11#13512yes—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—82no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—82no—
268C22⋊D11—82no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271D44—21no—
272D44—41no—
273D44—41no—
274D44—41no—
275D44—41no—
276D44—81no—
277D44—82no—
278D44AGL(1,ℤ/8)12yes—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—82no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—41no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C22×SD16—221no—
294#556C2×D1111yescharacteristic, complemented
295D4×Q8C2×D1111yescharacteristic
296#547—111no—
297D42—111no—
298#500—111no—
299#492—111no—
300#489—21no—
301#487—111no—
302#487C2×D1111yescharacteristic, complemented
303#486—111no—
304#486—111no—
305#485—221no—
306#480—221no—
307#477—21no—
308#474—111no—
309#474—111no—
310#474C2×D1111yescharacteristic, complemented
311#467—221no—
312#466—221no—
313#465—221no—
314#463—21no—
315#462—111no—
316#461—111no—
317#461C2×D1111yescharacteristic
318#460—111no—
319#459—111no—
320#452—221no—
321#450—221no—
322#448—221no—
323#447—221no—
324#446C2×D1111yescharacteristic, complemented
325#440—21no—
326C4×SD16—111no—
327C4×D8C2×D1111yescharacteristic
328C8×D4—111no—
329C8×D4—111no—
330C8×D4—111no—
331#416—221no—
332C2×#102—221no—
333#334—111no—
334#334—111no—
335#332—111no—
336#332—111no—
337#332—111no—
338#331—111no—
339Q8⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343#322—111no—
344C22×C11—22no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11D4211yescharacteristic
351C2×D11—22no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—164no—
358C4×C11—21no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11C2×#13511yescharacteristic
366C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57711yescharacteristic
369Dic11—41no—
370Dic11—81no—
371C2×#41—221no—
372C22×Q8—21no—
373C22×D4—221no—
374C22×D4—221no—
375C2×Q16—221no—
376C2×SD16—21no—
377C2×SD16—111no—
378C2×SD16—221no—
379C2×SD16—221no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×SD16—444no—
383C2×D8—221no—
384C2×D8C22⋊D1111yescharacteristic
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8—21no—
389C4⋊Q8—111no—
390C4⋊Q8C22×D1111yescharacteristic
391C4⋊Q8C22×D1111yescharacteristic
392#127—111no—
393#126—41no—
394#124—21no—
395#123—441no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—221no—
400#121—221no—
401#121—221no—
402#121—221no—
403#120—441no—
404C4×Q8—21no—
405C4×Q8C22×D1111yescharacteristic
406C4×D4—21no—
407C4×D4—111no—
408C4×D4C22×D1111yescharacteristic
409C4×D4C22×D1111yescharacteristic
410#117—21no—
411C2×C4⋊C4—221no—
412#107—21no—
413#107—221no—
414#107—221no—
415#107—441no—
416#107C22⋊D1111yescharacteristic
417#106—111no—
418C4⋊C8—21no—
419C4⋊C8—111no—
420C4⋊C8—111no—
421C4⋊C8—111no—
422C4⋊C8C22×D1111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—111no—
427#103—221no—
428#103—221no—
429#103—221no—
430#103—221no—
431#102—21no—
432#102—111no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102—441no—
440#102C22⋊D1111yescharacteristic
441#102C22⋊D1111yescharacteristic
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445#97—21no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8C22×D1111yescharacteristic
449C2×C11—42no—
450C2×C11—81no—
451C2×C11#326411yescharacteristic
452C2×C11#328211yescharacteristic
453C2×C11#328911yescharacteristic
454D11—42no—
455D11—161no—
456C24—441no—
457#41—442no—
458#41—881no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—221no—
465C2×Q8D4×D1111yescharacteristic
466C2×D4—111no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—441no—
471C2×D4—442no—
472C2×D4—441no—
473C2×D4—442no—
474C2×D4—441no—
475C2×D4—881no—
476C2×D4—881no—
477C2×D4C2×C22⋊D1111yescharacteristic
478C2×D4C2×C22⋊D1111yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—221no—
483C22×C4—441no—
484Q16—881no—
485SD16—42no—
486SD16—222no—
487SD16—442no—
488SD16—442no—
489SD16—442no—
490SD16—881no—
491D8—22no—
492D8—881no—
493C2×C8—21no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—442no—
501C2×C8—881no—
502C2×C8—881no—
503C2×C8C2×C22⋊D1111yescharacteristic
504C2×C8C2×C22⋊D1111yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—111no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—441no—
516C4⋊C4D4×D1111yescharacteristic
517C4⋊C4C2×C22⋊D1111yescharacteristic
518C4⋊C4C2×C22⋊D1111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—221no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C42—21no—
528C42—41no—
529C42C23×D1111yescharacteristic
530C11#1978711yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—221no—
534C23—441no—
535C23—882no—
536C23—882no—
537C23—1761no—
538Q8—21no—
539Q8—21no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—82no—
545Q8—441no—
546Q8—441no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—112no—
551D4—221no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—881no—
557D4—882no—
558D4—882no—
559D4—882no—
560D4#6700312yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—221no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—882no—
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4#6703711yescharacteristic
579C2×C4C22×C22⋊D1111yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—221no—
584C8—221no—
585C8—441no—
586C8—441no—
587C8—441no—
588C8—441no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—222no—
596C22—441no—
597C22—441no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22—1764no—
602C22D4×C22⋊D1111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—441no—
611C4—881no—
612C4D11×AGL(1,ℤ/8)11yescharacteristic
613C4#1062330511yescharacteristic
614C4C2×#6700311yescharacteristic
615C4#1062336811yescharacteristic
616C2—42no—
617C2—81no—
618C2—442no—
619C2—1761no—
620C2#1308009011yescharacteristic
621C2#1308032411yescharacteristic
622C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3367C2
socleC22×C11D42
prime radical#13080431C2
hypercenter#3367D11
hypocenterC11#19787
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3367

Complements

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

NH ≅ G/Ntype
1. #13080527C2semidirect
3. D4×#4325C2semidirect
4. #13068270C2semidirect
5. #13068184C2semidirect
6. #13068041C2semidirect
7. #13068036C2semidirect
8. #13067959C2semidirect
9. #13067865C2semidirect
10. #13067850C2semidirect
11. #13067793C2semidirect
12. #13067726C2semidirect
13. #13067450C2semidirect
14. #13067440C2semidirect
15. C11×#3367C2semidirect
16. C11×#556C22semidirect
22. C11×#487C22semidirect
24. C11×#474C22semidirect
27. C11×#446C22semidirect
32. #10622706C22semidirect
37. #10622691C22semidirect
42. #10622644C22semidirect
47. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. #10622093C22semidirect
220. #3367D11semidirect
294. #556C2×D11semidirect
302. #487C2×D11semidirect
310. #474C2×D11semidirect
324. #446C2×D11semidirect
530. C11#19787semidirect

Maximal subgroups

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

subgroupindex
#130805272
#130804312
D4×#43252
#130682702
#130681842
#130680412
#130680362
#130679592
#130678652
#130678502
#130677932
#130677262
#130674502
#130674402
C11×#33672
#1978711