Finite Group Databasebeta

← #14745141

Subgroups — #14745141

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081593C211yesmaximal, characteristic, complemented
2D4×#4325C211yesmaximal, characteristic, complemented
3#13080237C211yesmaximal, characteristic
4#13068209C211yesmaximal, characteristic, complemented
5#13068126C211yesmaximal, characteristic, complemented
6#13068100C211yesmaximal, characteristic, complemented
7#13067966C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067815C211yesmaximal, characteristic, complemented
10#13067794C211yesmaximal, characteristic, complemented
11#13067719C211yesmaximal, characteristic, complemented
12#13067712C211yesmaximal, characteristic, complemented
13#13067506C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3386C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19C2×#66967—21no—
20#10623108C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#501—21no—
23C11×#500C2211yescharacteristic, complemented
24C11×#478—21no—
25C11×#477—21no—
26C11×#475C2211yescharacteristic, complemented
27C11×#474C2211yescharacteristic
28C11×#446C2211yescharacteristic, complemented
29C11×#440—21no—
30C4×C11×SD16C2211yescharacteristic
31#10622840—21no—
32#10622701C2211yescharacteristic
33#10622701C2211yescharacteristic, complemented
34#10622698—21no—
35#10622698C2211yescharacteristic
36#10622698C2211yescharacteristic, complemented
37#10622696—21no—
38#10622696C2211yescharacteristic
39#10622696C2211yescharacteristic
40#10622661—21no—
41#10622659—21no—
42#10622640—21no—
43#10622640C2211yescharacteristic
44#10622640C2211yescharacteristic
45#10622640C2211yescharacteristic, complemented
46C4×#4325—21no—
47C4×#4325C2211yescharacteristic
48Q8×C11⋊C8C2211yescharacteristic, complemented
49#10622628C2211yescharacteristic
50D4×C11⋊C8C2211yescharacteristic
51#10622478—21no—
52#10622424—21no—
53#10622386—21no—
54#10622308C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×#4343—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16D411yescharacteristic
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#125—21no—
77C11×#125—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—41no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4325—21no—
95C2×#4325—44no—
96C2×#4325D411yescharacteristic
97C2×#4323—21no—
98#66983—21no—
99C22×C11⋊C8—21no—
100#66967—44no—
101C2×D88—21no—
102C2×D88—21no—
103C2×#4313—21no—
104#66948—21no—
105#66948—21no—
106#66948—41no—
107#66935—41no—
108#66927—21no—
109#66927C2311yescharacteristic
110#66927C2311yescharacteristic
111C4×D44—21no—
112C4×D44C2311yescharacteristic
113C11×#107—21no—
114C11×#107—21no—
115C11×#107—21no—
116C11×#106—21no—
117C11×#106D411yescharacteristic
118C11×C4⋊C8—21no—
119C11×C4⋊C8C2311yescharacteristic
120C11×#103—21no—
121C11×#103D411yescharacteristic
122C11×#102—21no—
123C11×#102D411yescharacteristic
124C11×#97—21no—
125C4×C8×C11C2311yescharacteristic
126#66899—21no—
127#66899—21no—
128#66899D411yescharacteristic
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66873—21no—
135#66873—41no—
136#66873—41no—
137#66873D411yescharacteristic
138#66872D411yescharacteristic
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8—21no—
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19892—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×Q8×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C2×C22⋊D11—41no—
159#4343—42no—
160#4343—81no—
161D4×D11—42no—
162D4×D11—81no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—41no—
170C2×D44—41no—
171C2×D44—41no—
172C2×D44—42no—
173C2×D44—81no—
174C2×D44C2×D411yescharacteristic
175C2×C4×D11—21no—
176C2×C4×D11—41no—
177C11×SD16SD1614yescomplemented
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—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—41no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—41no—
199C42×C11C2411yescharacteristic
200#4325—22no—
201#4325—42no—
202#4325—42no—
203#4325—42no—
204#4325—42no—
205#4325—42no—
206#4325—81no—
207#4325—81no—
208#4325—81no—
209#4325—81no—
210#4323—42no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—41no—
213(C2×D11)⋊C4—41no—
214C4⋊Dic11C2×D411yescharacteristic
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
222D88—42no—
223D88—81no—
224#4313—42no—
225#3392—111no—
226#3386D1111yescharacteristic, complemented
227D4×SD16—111no—
228#3274—111no—
229#1706—111no—
230#1693—111no—
231#1688—111no—
232#1666—111no—
233#1665—111no—
234#1642—111no—
235#1639—111no—
236#1627—111no—
237#1626—111no—
238#1590—111no—
239C8×SD16—111no—
240C23×C11—21no—
241C22×D11—21no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—82no—
245C22×D11—82no—
246C22×D11—161no—
247Q8×C11—21no—
248Q8×C11—21no—
249Q8×C11—21no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—82no—
255Q8×C11C2×SD1612yescomplemented
256D4×C11—21no—
257D4×C11C2×SD1612yes—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C22⋊D11—82no—
272C2×Dic11—21no—
273D44—21no—
274D44—21no—
275D44—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—41no—
280D44—41no—
281D44—41no—
282D44—41no—
283D44—82no—
284D44—81no—
285D44—81no—
286D44—82no—
287D44—161no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—82no—
291C8×C11—21no—
292C8×C11—41no—
293C8×C11C2×SD1612yescomplemented
294C11⋊C8—21no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8AGL(1,ℤ/8)12yescomplemented
300C2×AGL(1,ℤ/8)—221no—
301C22×SD16—221no—
302#557C2×D1111yescharacteristic, complemented
303#550—111no—
304D4×Q8C2×D1111yescharacteristic
305D42—111no—
306#501—21no—
307#500C2×D1111yescharacteristic, complemented
308#493—111no—
309#492—111no—
310#492—111no—
311#492—221no—
312#486—111no—
313#486—111no—
314#478—21no—
315#477—21no—
316#475C2×D1111yescharacteristic, complemented
317#474C2×D1111yescharacteristic
318#469—221no—
319#465—221no—
320#461—111no—
321#461—111no—
322#461—221no—
323#460—111no—
324#460—111no—
325#460—111no—
326#460—221no—
327#459—111no—
328#450—221no—
329#449—221no—
330#448—221no—
331#447—221no—
332#446C2×D1111yescharacteristic, complemented
333C8×Q8—111no—
334#440—21no—
335C4×SD16—111no—
336C4×SD16—221no—
337C4×SD16C2×D1111yescharacteristic
338#436—111no—
339C8×D4—111no—
340#334—111no—
341#334—111no—
342#332—111no—
343#332—111no—
344#331—111no—
345#331—111no—
346Q8⋊C8—111no—
347Q8⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350C82—111no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11D4211yescharacteristic
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—164no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11C22×SD1611yescharacteristic
374C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C4×C11#57611yescharacteristic
376C4×C11#57711yescharacteristic
377Dic11—41no—
378C2×#41—221no—
379C22×Q8—21no—
380C22×D4—221no—
381C22×D4—221no—
382AGL(1,ℤ/8)—444no—
383C2×SD16—111no—
384C2×SD16—221no—
385C2×SD16—221no—
386C2×SD16—221no—
387C2×SD16—221no—
388C2×SD16—221no—
389C2×SD16—221no—
390C2×SD16—221no—
391C2×SD16—221no—
392C2×SD16—221no—
393C2×SD16—444no—
394C2×SD16C22⋊D1111yescharacteristic
395C2×D8—221no—
396C2×D8—221no—
397C2×D8—221no—
398C2×M16—221no—
399C22×C8—221no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8C22×D1111yescharacteristic
403C4⋊Q8C22×D1111yescharacteristic
404#127—111no—
405#127—111no—
406#127—221no—
407#125—21no—
408#125—41no—
409C22⋊Q8—21no—
410C22⋊Q8—41no—
411#121—221no—
412#121—221no—
413#121—221no—
414#121—441no—
415#120—441no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8C22×D1111yescharacteristic
419C4×Q8C22×D1111yescharacteristic
420C4×D4—21no—
421C4×D4—111no—
422C4×D4—221no—
423C4×D4C22×D1111yescharacteristic
424#107—21no—
425#107—21no—
426#107—21no—
427#106—21no—
428#106—111no—
429#106C22⋊D1111yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—221no—
435C4⋊C8C22×D1111yescharacteristic
436#103—21no—
437#103—111no—
438#103—221no—
439#103—221no—
440#103C22⋊D1111yescharacteristic
441#102—21no—
442#102—111no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—441no—
448#102—441no—
449#102C22⋊D1111yescharacteristic
450C22⋊C8—221no—
451C22⋊C8—221no—
452#97—21no—
453C4×C8—111no—
454C4×C8—111no—
455C4×C8—221no—
456C4×C8C22×D1111yescharacteristic
457C2×C11—42no—
458C2×C11#327411yescharacteristic
459C2×C11D4×SD1611yescharacteristic
460C2×C11#329011yescharacteristic
461D11—81no—
462D11—161no—
463D11—161no—
464C24—441no—
465#41—442no—
466#41—881no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8D4×D1111yescharacteristic
473C2×Q8C2×C22⋊D1111yescharacteristic
474C2×D4—111no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—441no—
482C2×D4—441no—
483C2×D4—441no—
484C2×D4—442no—
485C2×D4—441no—
486C2×D4—442no—
487C2×D4—881no—
488C2×D4—881no—
489C2×D4C2×C22⋊D1111yescharacteristic
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—221no—
493C22×C4—441no—
494SD16—222no—
495SD16—442no—
496SD16—442no—
497SD16—442no—
498SD16—442no—
499SD16—442no—
500SD16—881no—
501SD16—881no—
502SD16—881no—
503SD16—881no—
504SD16#432514yescomplemented
505D8—442no—
506D8—442no—
507D8—881no—
508M16—442no—
509C2×C8—21no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—442no—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—111no—
530C4⋊C4D4×D1111yescharacteristic
531C4⋊C4C2×C22⋊D1111yescharacteristic
532C4⋊C4C2×C22⋊D1111yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—221no—
536C22⋊C4—441no—
537C22⋊C4—441no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42C23×D1111yescharacteristic
542C11#1989211yescharacteristic, complemented, Sylow
543C23—21no—
544C23—221no—
545C23—441no—
546C23—441no—
547C23—882no—
548C23—882no—
549C23—1761no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—82no—
558Q8C2×#432512yescomplemented
559D4—21no—
560D4—221no—
561D4—221no—
562D4—441no—
563D4—441no—
564D4—441no—
565D4—441no—
566D4—441no—
567D4—441no—
568D4—441no—
569D4—441no—
570D4—882no—
571D4—881no—
572D4—881no—
573D4—882no—
574D4—882no—
575D4—1761no—
576D4C2×#432512yes—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—221no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—882no—
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—21no—
595C8—41no—
596C8—112no—
597C8—221no—
598C8—441no—
599C8—441no—
600C8—441no—
601C8—441no—
602C8C2×#432512yescomplemented
603C22—22no—
604C22—41no—
605C22—41no—
606C22—441no—
607C22—441no—
608C22—441no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—1764no—
616C22D4×C22⋊D1111yescharacteristic
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—441no—
626C4D11×AGL(1,ℤ/8)11yescharacteristic
627C4#1062330511yescharacteristic
628C4C22×#432511yescharacteristic
629C4#1062336811yescharacteristic
630C2—42no—
631C2—881no—
632C2—1761no—
633C2—1761no—
634C2#1308023011yescharacteristic
635C2D4×#432511yescharacteristic
636C2#1308040211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3386C2
socleC22×C11D42
prime radical#13080237C2
hypercenter#3386D11
hypocenterC11#19892
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3386

Complements

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

NH ≅ G/Ntype
1. #13081593C2semidirect
2. D4×#4325C2semidirect
4. #13068209C2semidirect
5. #13068126C2semidirect
6. #13068100C2semidirect
7. #13067966C2semidirect
8. #13067959C2semidirect
9. #13067815C2semidirect
10. #13067794C2semidirect
11. #13067719C2semidirect
12. #13067712C2semidirect
13. #13067506C2semidirect
14. SD16×C11⋊C8C2semidirect
15. C11×#3386C2semidirect
16. C11×#557C22semidirect
23. C11×#500C22semidirect
26. C11×#475C22semidirect
28. C11×#446C22semidirect
33. #10622701C22semidirect
36. #10622698C22semidirect
45. #10622640C22semidirect
48. Q8×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
62. #10622123C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
177. C11×SD16SD16semidirect
226. #3386D11semidirect
255. Q8×C11C2×SD16semidirect
293. C8×C11C2×SD16semidirect
299. C11⋊C8AGL(1,ℤ/8)semidirect
302. #557C2×D11semidirect
307. #500C2×D11semidirect
316. #475C2×D11semidirect
332. #446C2×D11semidirect
504. SD16#4325semidirect
542. C11#19892semidirect
558. Q8C2×#4325semidirect
602. C8C2×#4325semidirect

Maximal subgroups

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

subgroupindex
#130815932
D4×#43252
#130802372
#130682092
#130681262
#130681002
#130679662
#130679592
#130678152
#130677942
#130677192
#130677122
#130675062
SD16×C11⋊C82
C11×#33862
#1989211