Finite Group Databasebeta

← #14738811

Subgroups — #14738811

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C211yesmaximal, characteristic, complemented
2#13079066C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068098C211yesmaximal, characteristic, complemented
5#13068093C211yesmaximal, characteristic, complemented
6#13068086C211yesmaximal, characteristic, complemented
7#13068079C211yesmaximal, characteristic, complemented
8#13067974C211yesmaximal, characteristic, complemented
9#13067969C211yesmaximal, characteristic, complemented
10#13067962C211yesmaximal, characteristic, complemented
11#13067955C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067322C211yesmaximal, characteristic, complemented
14#13067284C211yesmaximal, characteristic, complemented
15C11×#3217C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C2×#66985—21no—
19C2×#66985—21no—
20#10623008C2211yescharacteristic
21C11×#496—21no—
22C11×#490—21no—
23C11×#460C2211yescharacteristic
24C11×#460C2211yescharacteristic
25C11×#459C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C11×#450—21no—
28C11×#447—21no—
29C11×#432C2211yescharacteristic
30#10622689C2211yescharacteristic
31#10622689C2211yescharacteristic
32#10622687—21no—
33#10622687—21no—
34#10622686C2211yescharacteristic
35#10622686C2211yescharacteristic
36#10622679—21no—
37#10622670—21no—
38#10622662—21no—
39#10622652—21no—
40#10622640C2211yescharacteristic, complemented
41#10622637C2211yescharacteristic, complemented
42Q8×C11⋊C8C2211yescharacteristic, complemented
43#10622633C2211yescharacteristic, complemented
44#10622628C2211yescharacteristic, complemented
45#10622625—21no—
46#10622625C2211yescharacteristic, complemented
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic, complemented
49#10622620C2211yescharacteristic, complemented
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622182C2211yescharacteristic
56#10622182C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622118C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622117C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×#4339—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×D8—21no—
74C2×C11×D8—21no—
75C11×#127—21no—
76C11×#127—21no—
77C11×#127—21no—
78C11×#127C2311yescharacteristic
79C11×#127C2311yescharacteristic
80C11×#126—21no—
81C11×#125D411yescharacteristic
82C11×#124D411yescharacteristic
83C11×#123—21no—
84C11×C22⋊Q8D411yescharacteristic
85C11×#121D411yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11C2311yescharacteristic
89C11×#117—21no—
90C2×C42×C11C2311yescharacteristic
91C2×#4325—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94C2×#4324—21no—
95C2×#4324—21no—
96#66985—44no—
97#66985—44no—
98C2×#4323—21no—
99C2×#4323—21no—
100C2×#4323—21no—
101C2×#4323—21no—
102C2×#4323—21no—
103#66983—21no—
104#66983—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318D411yescharacteristic
108C2×#4318D411yescharacteristic
109C22×C11⋊C8—21no—
110#66928—21no—
111#66927C2311yescharacteristic
112C4×D44—21no—
113C4×D44—21no—
114#66922C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#102—21no—
118C11×#102—21no—
119C11×#102—21no—
120C11×#102—21no—
121C11×C22⋊C8—21no—
122C11×#97—21no—
123#66899—21no—
124#66896—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128#66873—21no—
129#66873—21no—
130#66872—21no—
131#66871—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140#66867D411yescharacteristic
141#66867D411yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19376—111nomaximal, Sylow
147C24×C11—41no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—42no—
157C2×D4×C11—42no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—81no—
162C2×D4×C11—81no—
163C2×D4×C11—82no—
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C2×C22⋊D11—41no—
170#4339—42no—
171#4339—42no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×C4×D11—41no—
176C2×Dic22—21no—
177C11×SD16—81no—
178C11×SD16—81no—
179C11×D8—81no—
180C11×D8—81no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C42×C11—21no—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11#4111yescharacteristic
198C42×C11C2411yescharacteristic
199#4325—81no—
200#4324—42no—
201#4324—42no—
202#4324—42no—
203#4324—42no—
204#4323—42no—
205#4323—42no—
206#4323—42no—
207#4323—42no—
208#4323—81no—
209(C2×D11)⋊C4—41no—
210(C2×D11)⋊C4—41no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213#4318—22no—
214#4318—22no—
215#4318—42no—
216#4318—81no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—42no—
222C2×C11⋊C8C2×D411yescharacteristic
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×D411yescharacteristic
225C2×C11⋊C8C2×D411yescharacteristic
226#3251—111no—
227#3217D1111yescharacteristic, complemented
228#3151—111no—
229#2969—111no—
230#1688—111no—
231#1687—111no—
232#1686—111no—
233#1685—111no—
234#1668—111no—
235#1667—111no—
236#1666—111no—
237#1665—111no—
238#1569—111no—
239#1553—111no—
240#1545—111no—
241C23×C11—21no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—82no—
245C23×C11—82no—
246C23×C11—82no—
247C23×C11#12111yescharacteristic
248C22×D11—41no—
249Q8×C11—21no—
250Q8×C11—21no—
251D4×C11—21no—
252D4×C11—21no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—81no—
262D4×C11—81no—
263D4×C11—82no—
264D4×C11—82no—
265D4×C11—82no—
266D4×C11—81no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11#12111yescharacteristic
278C2×C4×C11#12111yescharacteristic
279C2×C4×C11#12111yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C22⋊D11—82no—
284C2×Dic11—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—41no—
289D44—81no—
290C4×D11—82no—
291Dic22—41no—
292Dic22—41no—
293C8×C11—41no—
294C8×C11—41no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8AGL(1,ℤ/8)12yes—
302C11⋊C8AGL(1,ℤ/8)12yes—
303C2×AGL(1,ℤ/8)—221no—
304C2×AGL(1,ℤ/8)—221no—
305#532—111no—
306C2×#127C2×D1111yescharacteristic
307#529C2×D1111yescharacteristic
308#496—21no—
309#496—221no—
310#496—221no—
311#493—111no—
312#493—111no—
313#492—111no—
314#492—111no—
315#490—21no—
316#478—221no—
317#475—111no—
318#474—111no—
319#469—221no—
320#468—221no—
321#463—221no—
322#460—111no—
323#460C2×D1111yescharacteristic
324#460C2×D1111yescharacteristic
325#459—111no—
326#459C2×D1111yescharacteristic
327#459C2×D1111yescharacteristic
328#450—21no—
329#447—21no—
330#446—111no—
331C8×Q8—111no—
332#436—111no—
333#436—221no—
334#435—221no—
335C8×D4—111no—
336#433—221no—
337#432C2×D1111yescharacteristic
338#431—111no—
339#423—111no—
340#405—221no—
341C4×M16—111no—
342#335—111no—
343#335—111no—
344#334—111no—
345#334—111no—
346#332—111no—
347#332—111no—
348#331—111no—
349#331—111no—
350#331—111no—
351#331—111no—
352#331—111no—
353#331—111no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—164no—
367C22×C11C2×#12111yescharacteristic
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
379C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
380C4×C11#57611yescharacteristic
381C4×C11#57711yescharacteristic
382Dic11—81no—
383C2×#41—221no—
384C22×D4—21no—
385C22×D4—21no—
386C22×D4—21no—
387AGL(1,ℤ/8)—444no—
388AGL(1,ℤ/8)—444no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—221no—
392C2×SD16—221no—
393C2×SD16—221no—
394C2×SD16—221no—
395C2×SD16—221no—
396C2×D8—21no—
397C2×D8—21no—
398C2×D8—221no—
399C2×D8—221no—
400C2×D8—221no—
401C2×D8—221no—
402C2×D8—221no—
403C2×M16—111no—
404C2×M16—111no—
405C2×M16—221no—
406C2×M16—221no—
407C22×C8—221no—
408C4⋊Q8—111no—
409#127—21no—
410#127—21no—
411#127—21no—
412#127—111no—
413#127C22×D1111yescharacteristic
414#127C22×D1111yescharacteristic
415#126—21no—
416#125C22⋊D1111yescharacteristic
417#124—221no—
418#124C22⋊D1111yescharacteristic
419#123—21no—
420C22⋊Q8C22⋊D1111yescharacteristic
421#121—221no—
422#121—221no—
423#121C22⋊D1111yescharacteristic
424C4×Q8C22×D1111yescharacteristic
425C4×D4—21no—
426C4×D4—221no—
427C4×D4—221no—
428C4×D4C22×D1111yescharacteristic
429#117—21no—
430C2×C42C22×D1111yescharacteristic
431#107—221no—
432#106—221no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8C22×D1111yescharacteristic
441C4⋊C8C22×D1111yescharacteristic
442#103—221no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—221no—
448#102—221no—
449#102—221no—
450C22⋊C8—21no—
451C22⋊C8—221no—
452C22⋊C8—221no—
453C22⋊C8—221no—
454#97—21no—
455#97—111no—
456#97—111no—
457#97—221no—
458C4×C8—111no—
459C4×C8—111no—
460C4×C8—221no—
461C4×C8—221no—
462C2×C11—41no—
463C2×C11—81no—
464C2×C11—161no—
465C2×C11—161no—
466C2×C11#303811yescharacteristic
467C2×C11#306211yescharacteristic
468C2×C11#306811yescharacteristic
469D11—161no—
470C24—41no—
471#41—442no—
472#41—442no—
473C2×Q8—221no—
474C2×Q8C2×C22⋊D1111yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4—82no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—441no—
494C2×D4C2×C22⋊D1111yescharacteristic
495C22×C4—21no—
496C22×C4—441no—
497C22×C4D4×D1111yescharacteristic
498C22×C4#434111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500SD16—81no—
501SD16—81no—
502SD16—442no—
503SD16—442no—
504SD16—442no—
505SD16—442no—
506SD16—881no—
507D8—81no—
508D8—81no—
509D8—442no—
510D8—442no—
511D8—442no—
512D8—442no—
513D8—881no—
514M16—222no—
515M16—222no—
516M16—442no—
517M16—881no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—111no—
521C2×C8—111no—
522C2×C8—111no—
523C2×C8—111no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—442no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4C2×C22⋊D1111yescharacteristic
536C4⋊C4C2×C22⋊D1111yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—441no—
543C22⋊C4—441no—
544C42—21no—
545C42D4×D1111yescharacteristic
546C42#434111yescharacteristic
547C42C2×C22⋊D1111yescharacteristic
548C42C23×D1111yescharacteristic
549C11#1937611yescharacteristic, complemented, Sylow
550C23—21no—
551C23—41no—
552C23—41no—
553C23—82no—
554C23—82no—
555C23—82no—
556C23—441no—
557C23#6699211yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—441no—
561Q8—441no—
562D4—21no—
563D4—21no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—81no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—81no—
578D4—441no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—881no—
583D4—882no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—441no—
595C2×C4—882no—
596C2×C4#6699211yescharacteristic
597C2×C4#6699211yescharacteristic
598C2×C4#6699211yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4C22×C22⋊D1111yescharacteristic
602C8—41no—
603C8—41no—
604C8—112no—
605C8—112no—
606C8—221no—
607C8—221no—
608C8—441no—
609C8—441no—
610C8—441no—
611C8—441no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—164no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22C2×#6699211yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—881no—
637C4D11×AGL(1,ℤ/8)11yescharacteristic
638C4D11×AGL(1,ℤ/8)11yescharacteristic
639C4#1062336611yescharacteristic
640C4#1062336711yescharacteristic
641C2—41no—
642C2—81no—
643C2—161no—
644C2—161no—
645C2—1761no—
646C2#1307809411yescharacteristic
647C2#1307829211yescharacteristic
648C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19376
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #13079978C2semidirect
2. #13079066C2semidirect
3. #13077621C2semidirect
4. #13068098C2semidirect
5. #13068093C2semidirect
6. #13068086C2semidirect
7. #13068079C2semidirect
8. #13067974C2semidirect
9. #13067969C2semidirect
10. #13067962C2semidirect
11. #13067955C2semidirect
12. #13067384C2semidirect
13. #13067322C2semidirect
14. #13067284C2semidirect
15. C11×#3217C2semidirect
40. #10622640C22semidirect
41. #10622637C22semidirect
42. Q8×C11⋊C8C22semidirect
43. #10622633C22semidirect
44. #10622628C22semidirect
46. #10622625C22semidirect
48. D4×C11⋊C8C22semidirect
49. #10622620C22semidirect
59. #10622124C22semidirect
60. #10622124C22semidirect
61. #10622123C22semidirect
62. #10622123C22semidirect
63. #10622118C22semidirect
64. #10622118C22semidirect
65. #10622117C22semidirect
66. #10622117C22semidirect
227. #3217D11semidirect
549. C11#19376semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130790662
#130776212
#130680982
#130680932
#130680862
#130680792
#130679742
#130679692
#130679622
#130679552
#130673842
#130673222
#130672842
C11×#32172
#1937611