Finite Group Databasebeta

← #14745231

Subgroups — #14745231

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081034C211yesmaximal, characteristic, complemented
2#13080860C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic, complemented
4#13068207C211yesmaximal, characteristic, complemented
5#13068149C211yesmaximal, characteristic, complemented
6#13068146C211yesmaximal, characteristic, complemented
7#13068013C211yesmaximal, characteristic, complemented
8#13067969C211yesmaximal, characteristic, complemented
9#13067732C211yesmaximal, characteristic, complemented
10#13067731C211yesmaximal, characteristic, complemented
11#13067699C211yesmaximal, characteristic, complemented
12#13067698C211yesmaximal, characteristic, complemented
13#13067499C211yesmaximal, characteristic, complemented
14D8×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3325C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic, complemented
17D42×C11C2211yescharacteristic
18C22×#4323—21no—
19#10623094C2211yescharacteristic, complemented
20D4×D44C2211yescharacteristic
21C11×#486C2211yescharacteristic, complemented
22C11×#482—21no—
23C11×#476C2211yescharacteristic
24C11×#469—21no—
25C11×#459C2211yescharacteristic, complemented
26C11×#447—21no—
27C4×C11×D8C2211yescharacteristic
28C11×#436C2211yescharacteristic, complemented
29C11×#418—21no—
30#10622830—21no—
31#10622769—21no—
32#10622698C2211yescharacteristic, complemented
33#10622697C2211yescharacteristic, complemented
34#10622691C2211yescharacteristic, complemented
35#10622689C2211yescharacteristic, complemented
36#10622686C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622651—21no—
39#10622651—21no—
40#10622649—21no—
41#10622648—21no—
42#10622628C2211yescharacteristic
43#10622628C2211yescharacteristic, complemented
44C4×#4323C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic, complemented
47#10622621C2211yescharacteristic
48#10622621C2211yescharacteristic, complemented
49#10622616—21no—
50#10622611—21no—
51#10622498—21no—
52#10622395—21no—
53#10622383—21no—
54#10622307C2211yescharacteristic, complemented
55#10622301C2211yescharacteristic, complemented
56#10622184C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×D8—21no—
72C2×C11×D8D411yescharacteristic
73C2×C11×M16—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#124—41no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#120—41no—
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117—21no—
87C2×#4325—41no—
88#66991—21no—
89C2×#4324—41no—
90C2×#4323—21no—
91C2×#4323—21no—
92C2×#4323—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—44no—
96C2×#4323D411yescharacteristic
97#66983—21no—
98#66983—21no—
99#66979—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8—21no—
102C2×#4313—21no—
103#66948—21no—
104#66945—21no—
105#66938—41no—
106#66935—41no—
107#66927C2311yescharacteristic
108C4×D44C2311yescharacteristic
109#66922C2311yescharacteristic
110C11×#107D411yescharacteristic
111C11×#106—21no—
112C11×C4⋊C8C2311yescharacteristic
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116C11×#102—21no—
117C11×#102D411yescharacteristic
118C11×#102D411yescharacteristic
119C11×C22⋊C8—21no—
120C4×C8×C11C2311yescharacteristic
121#66896—21no—
122#66896—21no—
123#66896—21no—
124#66896D411yescharacteristic
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127#66885—21no—
128#66885—21no—
129(C2×D11)⋊C8—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873D411yescharacteristic
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66871—21no—
138#66871—21no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19898—111nomaximal, Sylow
146C24×C11—41no—
147C23×D11—41no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—41no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167D4×D11—42no—
168D4×D11—81no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—41no—
173C2×D44—42no—
174C2×D44—81no—
175C2×D44C2×D411yescharacteristic
176C2×C4×D11—21no—
177C2×Dic22—21no—
178C11×D8—22no—
179C11×D8—81no—
180C11×M16—81no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—41no—
193C11×C22⋊C4—41no—
194C11×C22⋊C4—41no—
195C42×C11—41no—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—41no—
198#4325—82no—
199#4324—82no—
200#4323—22no—
201#4323—42no—
202#4323—42no—
203#4323—42no—
204#4323—81no—
205#4323—81no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—41no—
208(C2×D11)⋊C4—41no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C2×D411yescharacteristic
212C4×Dic11—41no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—42no—
218C2×C11⋊C8—42no—
219C2×C11⋊C8C2×D411yescharacteristic
220C2×C11⋊C8C2×D411yescharacteristic
221#4313—81no—
222#3341—111no—
223#3325—111no—
224#3325D1111yescharacteristic, complemented
225D4×D8—111no—
226#1706—111no—
227#1697—111no—
228#1697—111no—
229#1675—111no—
230#1667—111no—
231#1629—111no—
232#1629—111no—
233#1624—111no—
234#1624—111no—
235#1589—111no—
236C8×D8—111no—
237C23×C11—21no—
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—81no—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11—21no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—81no—
260D4×C11—82no—
261D4×C11—82no—
262D4×C11—161no—
263D4×C11#13512yes—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C22⋊D11—82no—
278C22⋊D11—161no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281D44—21no—
282D44—21no—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—41no—
287D44—81no—
288D44—82no—
289C4×D11—41no—
290C4×D11—41no—
291Dic22—81no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—21no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8AGL(1,ℤ/8)12yes—
301C22×D8—221no—
302#555—111no—
303#555C2×D1111yescharacteristic, complemented
304D42—111no—
305D42C2×D1111yescharacteristic
306#500—111no—
307#493—111no—
308#492—111no—
309#492—111no—
310#486—111no—
311#486C2×D1111yescharacteristic, complemented
312#482—21no—
313#482—221no—
314#482—221no—
315#482—221no—
316#476—111no—
317#476—111no—
318#476—111no—
319#476C2×D1111yescharacteristic
320#469—21no—
321#469—221no—
322#466—221no—
323#466—221no—
324#459—111no—
325#459—111no—
326#459—111no—
327#459C2×D1111yescharacteristic, complemented
328#447—21no—
329#447—221no—
330#447—221no—
331#447—221no—
332C4×D8—111no—
333C4×D8C2×D1111yescharacteristic
334#436—111no—
335#436C2×D1111yescharacteristic, complemented
336C8×D4—111no—
337C8×D4—111no—
338#427—221no—
339#418—21no—
340#418—221no—
341#335—111no—
342#335—111no—
343#333—111no—
344#333—111no—
345#331—111no—
346#331—111no—
347D4⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350D4⋊C8—111no—
351C82—111no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—164no—
365C22×C11D4211yescharacteristic
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—164no—
373C4×C11—21no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11C2×#13511yescharacteristic
379C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
380C4×C11#57611yescharacteristic
381C4×C11#57711yescharacteristic
382Dic11—41no—
383Dic11—81no—
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—221no—
387C22×D4—221no—
388C2×SD16—441no—
389C2×SD16—441no—
390C2×D8—21no—
391C2×D8—111no—
392C2×D8—221no—
393C2×D8—221no—
394C2×D8—221no—
395C2×D8—221no—
396C2×D8—221no—
397C2×D8—444no—
398C2×D8C22⋊D1111yescharacteristic
399C2×M16—21no—
400C2×M16—221no—
401C22×C8—221no—
402C22×C8—221no—
403C4⋊Q8—111no—
404C4⋊Q8C22×D1111yescharacteristic
405#127—111no—
406#127C22×D1111yescharacteristic
407#124—41no—
408#124—441no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—21no—
413#121—221no—
414#121—221no—
415#121—221no—
416#121—221no—
417#120—41no—
418#120—441no—
419C4×D4—111no—
420C4×D4C22×D1111yescharacteristic
421C4×D4C22×D1111yescharacteristic
422C4×D4C22×D1111yescharacteristic
423#117—21no—
424#117—21no—
425#117—221no—
426#117—221no—
427#107—111no—
428#107—221no—
429#107—221no—
430#107C22⋊D1111yescharacteristic
431#106—21no—
432#106—221no—
433#106—221no—
434#106—221no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8C22×D1111yescharacteristic
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—111no—
444#102—111no—
445#102—221no—
446#102—221no—
447#102—221no—
448#102—221no—
449#102—221no—
450#102—221no—
451#102—221no—
452#102—221no—
453#102C22⋊D1111yescharacteristic
454#102C22⋊D1111yescharacteristic
455C22⋊C8—21no—
456C22⋊C8—221no—
457C22⋊C8—221no—
458C22⋊C8—221no—
459C4×C8—111no—
460C4×C8—111no—
461C4×C8C22×D1111yescharacteristic
462C2×C11—42no—
463C2×C11—81no—
464C2×C11—81no—
465C2×C11—161no—
466C2×C11#327211yescharacteristic
467C2×C11#328011yescharacteristic
468C2×C11#329211yescharacteristic
469D11—81no—
470D11—161no—
471C24—41no—
472C24—441no—
473C2×Q8—21no—
474C2×Q8—221no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—41no—
483C2×D4—81no—
484C2×D4—81no—
485C2×D4—111no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—441no—
490C2×D4—442no—
491C2×D4—441no—
492C2×D4—442no—
493C2×D4—441no—
494C2×D4—881no—
495C2×D4—881no—
496C2×D4D4×D1111yescharacteristic
497C2×D4C2×C22⋊D1111yescharacteristic
498C2×D4C2×C22⋊D1111yescharacteristic
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—221no—
503SD16—882no—
504SD16—882no—
505D8—22no—
506D8—81no—
507D8—222no—
508D8—442no—
509D8—442no—
510D8—442no—
511D8—881no—
512D8—881no—
513M16—81no—
514M16—881no—
515C2×C8—21no—
516C2×C8—111no—
517C2×C8—111no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—442no—
523C2×C8—442no—
524C2×C8C2×C22⋊D1111yescharacteristic
525C2×C8C2×C22⋊D1111yescharacteristic
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—111no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4D4×D1111yescharacteristic
532C4⋊C4C2×C22⋊D1111yescharacteristic
533C4⋊C4C2×C22⋊D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—221no—
541C22⋊C4—441no—
542C22⋊C4—441no—
543C22⋊C4—441no—
544C42—41no—
545C42—441no—
546C42C23×D1111yescharacteristic
547C11#1989811yescharacteristic, complemented, Sylow
548C23—21no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—82no—
553C23—82no—
554C23—161no—
555C23—221no—
556C23—441no—
557C23—882no—
558C23—882no—
559C23—1761no—
560Q8—81no—
561Q8—881no—
562D4—21no—
563D4—21no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—81no—
572D4—82no—
573D4—82no—
574D4—161no—
575D4—221no—
576D4—221no—
577D4—441no—
578D4—441no—
579D4—441no—
580D4—441no—
581D4—881no—
582D4—882no—
583D4—882no—
584D4—1761no—
585D4#6700312yes—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—221no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—21no—
604C8—21no—
605C8—41no—
606C8—112no—
607C8—222no—
608C8—221no—
609C8—441no—
610C8—441no—
611C8—441no—
612C22—22no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22—1764no—
632C22D4×C22⋊D1111yescharacteristic
633C4—21no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—441no—
639C4—881no—
640C4D11×AGL(1,ℤ/8)11yescharacteristic
641C4#1062330611yescharacteristic
642C4C2×#6700311yescharacteristic
643C4#1062336611yescharacteristic
644C2—42no—
645C2—81no—
646C2—81no—
647C2—161no—
648C2—881no—
649C2—1761no—
650C2#1308021011yescharacteristic
651C2#1308029711yescharacteristic
652C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3325C2
socleC22×C11D42
hypercenter#3325D11
hypocenterC11#19898
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #13081034C2semidirect
2. #13080860C2semidirect
3. D4×#4323C2semidirect
4. #13068207C2semidirect
5. #13068149C2semidirect
6. #13068146C2semidirect
7. #13068013C2semidirect
8. #13067969C2semidirect
9. #13067732C2semidirect
10. #13067731C2semidirect
11. #13067699C2semidirect
12. #13067698C2semidirect
13. #13067499C2semidirect
14. D8×C11⋊C8C2semidirect
15. C11×#3325C2semidirect
16. C11×#555C22semidirect
19. #10623094C22semidirect
21. C11×#486C22semidirect
25. C11×#459C22semidirect
28. C11×#436C22semidirect
32. #10622698C22semidirect
33. #10622697C22semidirect
34. #10622691C22semidirect
35. #10622689C22semidirect
43. #10622628C22semidirect
46. D4×C11⋊C8C22semidirect
48. #10622621C22semidirect
54. #10622307C22semidirect
55. #10622301C22semidirect
56. #10622184C22semidirect
57. #10622182C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622121C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
224. #3325D11semidirect
303. #555C2×D11semidirect
311. #486C2×D11semidirect
327. #459C2×D11semidirect
335. #436C2×D11semidirect
547. C11#19898semidirect

Maximal subgroups

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

subgroupindex
#130810342
#130808602
D4×#43232
#130682072
#130681492
#130681462
#130680132
#130679692
#130677322
#130677312
#130676992
#130676982
#130674992
D8×C11⋊C82
C11×#33252
#1989811