Finite Group Databasebeta

← #14745257

Subgroups — #14745257

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081600C211yesmaximal, characteristic, complemented
2#13080849C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic
4#13068220C211yesmaximal, characteristic, complemented
5#13068177C211yesmaximal, characteristic, complemented
6#13068174C211yesmaximal, characteristic, complemented
7#13067979C211yesmaximal, characteristic, complemented
8#13067974C211yesmaximal, characteristic, complemented
9#13067795C211yesmaximal, characteristic, complemented
10#13067794C211yesmaximal, characteristic, complemented
11#13067726C211yesmaximal, characteristic, complemented
12#13067725C211yesmaximal, characteristic, complemented
13#13067499C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3324C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17D42×C11C2211yescharacteristic
18C22×#4323—21no—
19#10623115C2211yescharacteristic, complemented
20D4×D44C2211yescharacteristic
21C11×#486C2211yescharacteristic, complemented
22C11×#482—21no—
23C11×#474C2211yescharacteristic
24C11×#468—21no—
25C11×#460C2211yescharacteristic, complemented
26C11×#450—21no—
27C4×C11×SD16C2211yescharacteristic
28C11×#436C2211yescharacteristic, complemented
29C11×#418—21no—
30#10622830—21no—
31#10622782—21no—
32#10622705C2211yescharacteristic, complemented
33#10622701C2211yescharacteristic, complemented
34#10622696C2211yescharacteristic, complemented
35#10622686C2211yescharacteristic
36#10622685C2211yescharacteristic
37#10622683C2211yescharacteristic, complemented
38#10622672—21no—
39#10622667—21no—
40#10622651—21no—
41#10622649—21no—
42C4×#4326—21no—
43#10622641—21no—
44#10622640C2211yescharacteristic, complemented
45Q8×C11⋊C8C2211yescharacteristic, complemented
46#10622632C2211yescharacteristic, complemented
47#10622628C2211yescharacteristic
48C4×#4323C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622479—21no—
52#10622425—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic, complemented
55#10622301C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16D411yescharacteristic
73C2×C11×M16—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#126—41no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#120—41no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C11×#117—21no—
87#66999—21no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4324—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—44no—
98C2×#4323D411yescharacteristic
99#66983—21no—
100C22×C11⋊C8—21no—
101C2×#4313—21no—
102#66951—41no—
103#66948—21no—
104#66945—21no—
105#66935—41no—
106#66928—21no—
107#66927C2311yescharacteristic
108C4×D44C2311yescharacteristic
109#66922C2311yescharacteristic
110C4×Dic22—21no—
111C11×#107—21no—
112C11×#106D411yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×#103D411yescharacteristic
115C11×#102—21no—
116C11×#102—21no—
117C11×#102—21no—
118C11×#102—21no—
119C11×#102D411yescharacteristic
120C11×C22⋊C8—21no—
121C4×C8×C11C2311yescharacteristic
122#66899—21no—
123#66896—21no—
124#66896—21no—
125#66896—41no—
126#66896D411yescharacteristic
127C22⋊(C11⋊C8)—21no—
128#66885—21no—
129#66885—21no—
130(C2×D11)⋊C8—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66873—41no—
135#66873D411yescharacteristic
136#66871—21no—
137#66871D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19900—111nomaximal, Sylow
146C24×C11—41no—
147C23×D11—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11C2×D411yescharacteristic
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C2×C22⋊D11—41no—
164D4×D11—42no—
165D4×D11—81no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—41no—
170C2×D44—42no—
171C2×D44—81no—
172C2×D44C2×D411yescharacteristic
173C2×C4×D11—21no—
174C2×Dic22—21no—
175C11×SD16—22no—
176C11×SD16—81no—
177C11×M16—81no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C11×C22⋊C4—41no—
193C42×C11—21no—
194C42×C11—41no—
195C42×C11C2411yescharacteristic
196#4326—42no—
197#4326—81no—
198#4325—81no—
199#4325—81no—
200#4324—81no—
201#4323—22no—
202#4323—42no—
203#4323—42no—
204#4323—42no—
205#4323—81no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—41no—
208(C2×D11)⋊C4—41no—
209(C2×D11)⋊C4—41no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11C2×D411yescharacteristic
213Dic11⋊C4—41no—
214C4×Dic11—41no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—42no—
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#4313—81no—
223#3393—111no—
224#3324—111no—
225#3324D1111yescharacteristic, complemented
226D4×D8—111no—
227#1709—111no—
228#1701—111no—
229#1701—111no—
230#1669—111no—
231#1668—111no—
232#1639—111no—
233#1639—111no—
234#1628—111no—
235#1628—111no—
236#1589—111no—
237C8×SD16—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—41no—
241C23×C11—82no—
242C23×C11—82no—
243C23×C11—161no—
244C22×D11—21no—
245C22×D11—41no—
246C22×D11—82no—
247C22×D11—82no—
248C22×D11—161no—
249Q8×C11—21no—
250Q8×C11—21no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—21no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—81no—
261D4×C11—82no—
262D4×C11—82no—
263D4×C11#13512yes—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C22⋊D11—82no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279D44—21no—
280D44—21no—
281D44—41no—
282D44—41no—
283D44—41no—
284D44—41no—
285D44—81no—
286D44—82no—
287C4×D11—41no—
288C4×D11—41no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—41no—
294C11⋊C8—21no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8AGL(1,ℤ/8)12yes—
300C22×D8—221no—
301#556—111no—
302#556C2×D1111yescharacteristic, complemented
303D42—111no—
304D42C2×D1111yescharacteristic
305#495—221no—
306#494—111no—
307#493—111no—
308#486—111no—
309#486—111no—
310#486—111no—
311#486C2×D1111yescharacteristic, complemented
312#482—21no—
313#482—221no—
314#474—111no—
315#474C2×D1111yescharacteristic
316#468—21no—
317#468—221no—
318#466—221no—
319#464—221no—
320#464—221no—
321#461—111no—
322#461—111no—
323#460—111no—
324#460C2×D1111yescharacteristic, complemented
325#459—111no—
326#459—111no—
327#450—21no—
328#450—221no—
329#447—221no—
330#447—221no—
331C8×Q8—111no—
332C4×Q16—221no—
333C4×SD16C2×D1111yescharacteristic
334C4×D8—111no—
335#436—111no—
336#436C2×D1111yescharacteristic, complemented
337C8×D4—111no—
338#418—21no—
339#418—221no—
340#335—111no—
341#334—111no—
342#332—111no—
343#332—111no—
344#331—111no—
345#331—111no—
346Q8⋊C8—111no—
347D4⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350C82—111no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—164no—
361C22×C11D4211yescharacteristic
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—164no—
369C4×C11—21no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11C2×#13511yescharacteristic
376C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C4×C11#57611yescharacteristic
378C4×C11#57611yescharacteristic
379Dic11—41no—
380Dic11—81no—
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—221no—
384C22×D4—221no—
385C2×Q16—221no—
386C2×Q16—221no—
387C2×SD16—21no—
388C2×SD16—221no—
389C2×SD16—221no—
390C2×SD16—221no—
391C2×SD16C22⋊D1111yescharacteristic
392C2×D8—111no—
393C2×D8—221no—
394C2×D8—221no—
395C2×D8—221no—
396C2×D8—221no—
397C2×D8—444no—
398C2×M16—21no—
399C2×M16—221no—
400C22×C8—221no—
401C4⋊Q8—111no—
402C4⋊Q8C22×D1111yescharacteristic
403#127—111no—
404#127C22×D1111yescharacteristic
405#126—41no—
406#126—441no—
407#124—21no—
408#124—221no—
409C22⋊Q8—21no—
410C22⋊Q8—221no—
411#121—21no—
412#121—21no—
413#121—221no—
414#121—221no—
415#120—41no—
416#120—441no—
417C4×Q8—21no—
418C4×Q8—221no—
419C4×Q8C22×D1111yescharacteristic
420C4×D4—111no—
421C4×D4C22×D1111yescharacteristic
422C4×D4C22×D1111yescharacteristic
423#117—21no—
424#117—221no—
425#107—21no—
426#107—111no—
427#107—221no—
428#106C22⋊D1111yescharacteristic
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—221no—
433C4⋊C8C22×D1111yescharacteristic
434#103—221no—
435#103—221no—
436#103C22⋊D1111yescharacteristic
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—111no—
442#102—111no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—221no—
448#102—221no—
449#102—441no—
450#102—441no—
451#102C22⋊D1111yescharacteristic
452C22⋊C8—21no—
453C22⋊C8—221no—
454C22⋊C8—221no—
455C4×C8—111no—
456C4×C8—111no—
457C4×C8—221no—
458C4×C8C22×D1111yescharacteristic
459C2×C11—42no—
460C2×C11—81no—
461C2×C11—161no—
462C2×C11#327411yescharacteristic
463C2×C11#328011yescharacteristic
464C2×C11#329011yescharacteristic
465D11—81no—
466D11—161no—
467C24—41no—
468C24—441no—
469C2×Q8—21no—
470C2×Q8—221no—
471C2×Q8C2×C22⋊D1111yescharacteristic
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—111no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—441no—
486C2×D4—442no—
487C2×D4—441no—
488C2×D4—442no—
489C2×D4—881no—
490C2×D4—881no—
491C2×D4D4×D1111yescharacteristic
492C2×D4C2×C22⋊D1111yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—221no—
496Q16—442no—
497Q16—881no—
498SD16—22no—
499SD16—81no—
500SD16—881no—
501SD16—881no—
502SD16—881no—
503D8—222no—
504D8—442no—
505D8—442no—
506D8—442no—
507D8—881no—
508M16—81no—
509M16—881no—
510C2×C8—21no—
511C2×C8—111no—
512C2×C8—111no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—442no—
518C2×C8C2×C22⋊D1111yescharacteristic
519C2×C8C2×C22⋊D1111yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—111no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—441no—
528C4⋊C4D4×D1111yescharacteristic
529C4⋊C4C2×C22⋊D1111yescharacteristic
530C4⋊C4C2×C22⋊D1111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—221no—
537C22⋊C4—441no—
538C22⋊C4—441no—
539C22⋊C4—441no—
540C42—21no—
541C42—41no—
542C42—441no—
543C42C23×D1111yescharacteristic
544C11#1990011yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—221no—
552C23—441no—
553C23—882no—
554C23—882no—
555C23—1761no—
556Q8—21no—
557Q8—21no—
558Q8—41no—
559Q8—41no—
560Q8—441no—
561Q8—441no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—81no—
570D4—82no—
571D4—82no—
572D4—221no—
573D4—221no—
574D4—441no—
575D4—441no—
576D4—441no—
577D4—441no—
578D4—881no—
579D4—882no—
580D4—882no—
581D4#6700312yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—221no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4#6703711yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—21no—
599C8—21no—
600C8—41no—
601C8—112no—
602C8—221no—
603C8—441no—
604C8—441no—
605C8—441no—
606C8—441no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—164no—
617C22—441no—
618C22—441no—
619C22—441no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22—1764no—
624C22D4×C22⋊D1111yescharacteristic
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—441no—
632C4—881no—
633C4D11×AGL(1,ℤ/8)11yescharacteristic
634C4#1062330511yescharacteristic
635C4C2×#6700311yescharacteristic
636C4#1062336611yescharacteristic
637C2—42no—
638C2—81no—
639C2—161no—
640C2—881no—
641C2—1761no—
642C2#1308023011yescharacteristic
643C2#1308029711yescharacteristic
644C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3324C2
socleC22×C11D42
prime radicalD4×#4323C2
hypercenter#3324D11
hypocenterC11#19900
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #13081600C2semidirect
2. #13080849C2semidirect
4. #13068220C2semidirect
5. #13068177C2semidirect
6. #13068174C2semidirect
7. #13067979C2semidirect
8. #13067974C2semidirect
9. #13067795C2semidirect
10. #13067794C2semidirect
11. #13067726C2semidirect
12. #13067725C2semidirect
13. #13067499C2semidirect
14. SD16×C11⋊C8C2semidirect
15. C11×#3324C2semidirect
16. C11×#556C22semidirect
19. #10623115C22semidirect
21. C11×#486C22semidirect
25. C11×#460C22semidirect
28. C11×#436C22semidirect
32. #10622705C22semidirect
33. #10622701C22semidirect
34. #10622696C22semidirect
37. #10622683C22semidirect
44. #10622640C22semidirect
45. Q8×C11⋊C8C22semidirect
46. #10622632C22semidirect
54. #10622307C22semidirect
55. #10622301C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
62. #10622123C22semidirect
63. #10622121C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
225. #3324D11semidirect
302. #556C2×D11semidirect
311. #486C2×D11semidirect
324. #460C2×D11semidirect
336. #436C2×D11semidirect
544. C11#19900semidirect

Maximal subgroups

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

subgroupindex
#130816002
#130808492
D4×#43232
#130682202
#130681772
#130681742
#130679792
#130679742
#130677952
#130677942
#130677262
#130677252
#130674992
SD16×C11⋊C82
C11×#33242
#1990011