Finite Group Databasebeta

← #14743165

Subgroups — #14743165

Order 2816.

736 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#13080959C211yesmaximal, characteristic, complemented
2#13080423C211yesmaximal, characteristic, complemented
3#13080217C211yesmaximal, characteristic, complemented
4#13068288C211yesmaximal, characteristic, complemented
5#13068102C211yesmaximal, characteristic, complemented
6#13068055C211yesmaximal, characteristic, complemented
7#13068003C211yesmaximal, characteristic, complemented
8#13067957C211yesmaximal, characteristic, complemented
9#13067851C211yesmaximal, characteristic, complemented
10#13067849C211yesmaximal, characteristic, complemented
11#13067793C211yesmaximal, characteristic, complemented
12#13067705C211yesmaximal, characteristic, complemented
13#13067445C211yesmaximal, characteristic, complemented
14#13067440C211yesmaximal, characteristic, complemented
15C11×#3283C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#547C2211yescharacteristic
18C11×#547C2211yescharacteristic, complemented
19C2×#66964—21no—
20#10623086C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#494C2211yescharacteristic, complemented
23C11×#467—21no—
24C11×#461C2211yescharacteristic
25C11×#461C2211yescharacteristic, complemented
26C11×#452—21no—
27C11×#452—21no—
28C4×C11×D8C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic, complemented
30#10622701C2211yescharacteristic
31#10622701C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622691C2211yescharacteristic, complemented
35#10622691C2211yescharacteristic, complemented
36#10622651—21no—
37#10622651—21no—
38#10622649—21no—
39#10622646—21no—
40#10622632C2211yescharacteristic
41#10622628C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic, complemented
46#10622620C2211yescharacteristic, complemented
47#10622580—21no—
48#10622580—21no—
49C2×#66873—21no—
50C2×#66871—21no—
51#10622499—21no—
52#10622394—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×#4341—21no—
70C2×D4×D11—21no—
71C22×D44—21no—
72C11×#135—44no—
73C2×C11×Q16—21no—
74C2×C11×Q16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×D8D411yescharacteristic
78C22×C8×C11—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#123—41no—
82C11×#123—41no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×#121—21no—
86C11×#121—21no—
87C4×D4×C11C2311yescharacteristic
88C4×D4×C11C2311yescharacteristic
89C4×D4×C11C2311yescharacteristic
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×#4324—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323D411yescharacteristic
96#66983—21no—
97#66983—21no—
98C2×C4⋊Dic11—21no—
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101#66964—44no—
102C2×#4314—21no—
103C2×#4314—21no—
104C2×#4313—21no—
105#66950—21no—
106#66948—21no—
107#66939—41no—
108#66935—41no—
109#66927C2311yescharacteristic
110C4×D44C2311yescharacteristic
111#66922C2311yescharacteristic
112C11×#107D411yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×#103—21no—
115C11×#103—21no—
116C11×#102D411yescharacteristic
117C11×#102D411yescharacteristic
118C11×C22⋊C8—21no—
119C4×C8×C11C2311yescharacteristic
120#66896—21no—
121#66896D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124(C2×D11)⋊C8—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—21no—
139#66871—41no—
140#66871D411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19758—111nomaximal, Sylow
147C23×D11—41no—
148C11×#41—42no—
149C11×#41—42no—
150C11×#41—81no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C2×D4×C11C2×D411yescharacteristic
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C22×Dic11—41no—
167#4341—42no—
168#4341—81no—
169D4×D11—42no—
170D4×D11—81no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—41no—
175C2×D44—42no—
176C2×D44—81no—
177C2×D44C2×D411yescharacteristic
178C2×C4×D11—21no—
179C2×Dic22—21no—
180C11×Q16—42no—
181C11×Q16—81no—
182C11×SD16—42no—
183C11×SD16—42no—
184C11×D8D814yescomplemented
185C2×C8×C11—21no—
186C2×C8×C11—42no—
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C42×C11C2411yescharacteristic
204#4324—42no—
205#4323—41no—
206#4323—42no—
207#4323—81no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—41no—
210(C2×D11)⋊C4—41no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—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⋊C8—81no—
221C2×C11⋊C8C2×D411yescharacteristic
222C2×C11⋊C8C2×D411yescharacteristic
223#4314—42no—
224#4314—81no—
225#4313—42no—
226#3334—111no—
227#3294—111no—
228#3283D1111yescharacteristic, complemented
229#3272—111no—
230#1722—111no—
231#1689—111no—
232#1681—111no—
233#1673—111no—
234#1665—111no—
235#1647—111no—
236#1647—111no—
237#1639—111no—
238#1625—111no—
239#1581—111no—
240#1580—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C22×D11—21no—
245C22×D11—41no—
246C22×D11—82no—
247C22×D11—82no—
248C22×D11—161no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—82no—
258D4×C11—82no—
259D4×C11C2×D812yes—
260D4×C11C2×D812yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C22⋊D11—82no—
278C22⋊D11—82no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—82no—
282D44—21no—
283D44—21no—
284D44—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—81no—
289D44—82no—
290C4×D11—41no—
291C4×D11—41no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—21no—
295C8×C11—41no—
296C8×C11C2×D812yes—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C2×AGL(1,ℤ/8)—221no—
304C2×#135—21no—
305#547—111no—
306#547C2×D1111yescharacteristic
307#547C2×D1111yescharacteristic, complemented
308D42—111no—
309#500—111no—
310#500—111no—
311#494C2×D1111yescharacteristic, complemented
312#492—111no—
313#486—111no—
314#486—111no—
315#480—221no—
316#480—221no—
317#480—221no—
318#474—111no—
319#474—111no—
320#474—111no—
321#468—221no—
322#467—21no—
323#466—221no—
324#466—221no—
325#461—111no—
326#461C2×D1111yescharacteristic
327#461C2×D1111yescharacteristic, complemented
328#459—111no—
329#459—111no—
330#452—21no—
331#452—21no—
332#450—221no—
333#449—221no—
334#447—221no—
335C4×D8—111no—
336C4×D8C2×D1111yescharacteristic
337#436—111no—
338C8×D4—111no—
339C8×D4—111no—
340C8×D4C2×D1111yescharacteristic, complemented
341C2×#107—221no—
342C2×#102—221no—
343#335—111no—
344#334—111no—
345#332—111no—
346#332—111no—
347#332—111no—
348#331—111no—
349D4⋊C8—111no—
350D4⋊C8—111no—
351D4⋊C8—111no—
352D4⋊C8—111no—
353#322—111no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11D4211yescharacteristic
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—164no—
371C4×C11—21no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11C22×D811yescharacteristic
378C4×C11#57511yescharacteristic
379C4×C11#57611yescharacteristic
380C4×C11#57711yescharacteristic
381Dic11—41no—
382Dic11—81no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—221no—
386C22×D4—221no—
387C22×D4—221no—
388AGL(1,ℤ/8)—444no—
389#135—44no—
390C2×Q16—21no—
391C2×Q16—21no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—221no—
395C2×SD16—221no—
396C2×SD16—221no—
397C2×D8—111no—
398C2×D8—221no—
399C2×D8—221no—
400C2×D8C22⋊D1111yescharacteristic
401C2×M16—221no—
402C22×C8—21no—
403C22×C8—221no—
404C22×C8—221no—
405C4⋊Q8—111no—
406C4⋊Q8C22×D1111yescharacteristic
407C4⋊Q8C22×D1111yescharacteristic
408#127—111no—
409#123—41no—
410#123—41no—
411#123—441no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—221no—
415#121—21no—
416#121—21no—
417#121—221no—
418#121—221no—
419#121—221no—
420#120—441no—
421C4×D4—111no—
422C4×D4C22×D1111yescharacteristic
423C4×D4C22×D1111yescharacteristic
424C4×D4C22×D1111yescharacteristic
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—221no—
428#107—111no—
429#107—221no—
430#107—221no—
431#107—221no—
432#107—221no—
433#107—221no—
434#107—441no—
435#107C22⋊D1111yescharacteristic
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8C22×D1111yescharacteristic
440#103—21no—
441#103—21no—
442#103—221no—
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—441no—
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—42no—
464C2×C11—81no—
465C2×C11#326711yescharacteristic
466C2×C11D4×D811yescharacteristic
467C2×C11#328911yescharacteristic
468D11—81no—
469D11—161no—
470C24—441no—
471#41—42no—
472#41—42no—
473#41—81no—
474#41—81no—
475#41—442no—
476#41—881no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—221no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—111no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—441no—
487C2×D4—442no—
488C2×D4—441no—
489C2×D4—442no—
490C2×D4—441no—
491C2×D4—881no—
492C2×D4—881no—
493C2×D4D4×D1111yescharacteristic
494C2×D4C2×C22⋊D1111yescharacteristic
495C2×D4C2×C22⋊D1111yescharacteristic
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—221no—
502C22×C4—441no—
503Q16—42no—
504Q16—81no—
505SD16—42no—
506SD16—42no—
507SD16—442no—
508SD16—442no—
509SD16—881no—
510D8—441no—
511D8—442no—
512D8—881no—
513D8#432314yescomplemented
514M16—442no—
515C2×C8—21no—
516C2×C8—42no—
517C2×C8—111no—
518C2×C8—111no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—442no—
524C2×C8—881no—
525C2×C8C2×C22⋊D1111yescharacteristic
526C2×C8C2×C22⋊D1111yescharacteristic
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—111no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—441no—
537C4⋊C4D4×D1111yescharacteristic
538C4⋊C4C2×C22⋊D1111yescharacteristic
539C4⋊C4C2×C22⋊D1111yescharacteristic
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—221no—
546C22⋊C4—441no—
547C22⋊C4—441no—
548C42C23×D1111yescharacteristic
549C11#1975811yescharacteristic, complemented, Sylow
550C23—21no—
551C23—21no—
552C23—21no—
553C23—221no—
554C23—441no—
555C23—882no—
556C23—882no—
557C23—1761no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—441no—
563Q8—441no—
564D4—21no—
565D4—21no—
566D4—21no—
567D4—21no—
568D4—82no—
569D4—82no—
570D4—221no—
571D4—221no—
572D4—441no—
573D4—441no—
574D4—441no—
575D4—441no—
576D4—881no—
577D4—882no—
578D4—882no—
579D4—882no—
580D4C2×#432312yes—
581D4C2×#432312yes—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—221no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—882no—
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—21no—
604C8—41no—
605C8—221no—
606C8—221no—
607C8—441no—
608C8—441no—
609C8—441no—
610C8—441no—
611C8C2×#432312yes—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—1764no—
628C22D4×C22⋊D1111yescharacteristic
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—441no—
636C4—881no—
637C4#1062329911yescharacteristic
638C4#1062330111yescharacteristic
639C4C22×#432311yescharacteristic
640C4#1062336611yescharacteristic
641C2—42no—
642C2—42no—
643C2—81no—
644C2—881no—
645C2—1761no—
646C2#1308014111yescharacteristic
647C2D4×#432311yescharacteristic
648C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3283C2
socleC22×C11D42
hypercenter#3283D11
hypocenterC11#19758
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. #13080959C2semidirect
2. #13080423C2semidirect
3. #13080217C2semidirect
4. #13068288C2semidirect
5. #13068102C2semidirect
6. #13068055C2semidirect
7. #13068003C2semidirect
8. #13067957C2semidirect
9. #13067851C2semidirect
10. #13067849C2semidirect
11. #13067793C2semidirect
12. #13067705C2semidirect
13. #13067445C2semidirect
14. #13067440C2semidirect
15. C11×#3283C2semidirect
18. C11×#547C22semidirect
22. C11×#494C22semidirect
25. C11×#461C22semidirect
29. C8×D4×C11C22semidirect
34. #10622691C22semidirect
35. #10622691C22semidirect
45. D4×C11⋊C8C22semidirect
46. #10622620C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622093C22semidirect
184. C11×D8D8semidirect
228. #3283D11semidirect
307. #547C2×D11semidirect
311. #494C2×D11semidirect
327. #461C2×D11semidirect
340. C8×D4C2×D11semidirect
513. D8#4323semidirect
549. C11#19758semidirect

Maximal subgroups

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

subgroupindex
#130809592
#130804232
#130802172
#130682882
#130681022
#130680552
#130680032
#130679572
#130678512
#130678492
#130677932
#130677052
#130674452
#130674402
C11×#32832
#1975811