Finite Group Databasebeta

← #14746145

Subgroups — #14746145

Order 2816.

752 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081247C211yesmaximal, characteristic, complemented
2#13080423C211yesmaximal, characteristic, complemented
3SD16×D44C211yesmaximal, characteristic, complemented
4#13068206C211yesmaximal, characteristic, complemented
5#13068062C211yesmaximal, characteristic, complemented
6#13068051C211yesmaximal, characteristic, complemented
7#13067957C211yesmaximal, characteristic, complemented
8#13067954C211yesmaximal, characteristic, complemented
9#13067863C211yesmaximal, characteristic, complemented
10#13067851C211yesmaximal, characteristic, complemented
11#13067681C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13SD16×C11⋊C8C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3284C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#550C2211yescharacteristic, complemented
18C11×#547C2211yescharacteristic
19C2×SD16×D11—21no—
20Q8×D44C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#492C2211yescharacteristic, complemented
23C11×#465—21no—
24C11×#462C2211yescharacteristic, complemented
25C11×#459C2211yescharacteristic
26C11×#452—21no—
27C11×#449—21no—
28C4×C11×SD16C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic, complemented
30#10622701C2211yescharacteristic
31#10622700C2211yescharacteristic
32#10622691C2211yescharacteristic, complemented
33#10622686C2211yescharacteristic
34#10622685—21no—
35#10622685C2211yescharacteristic
36#10622683—21no—
37#10622683C2211yescharacteristic, complemented
38#10622651—21no—
39#10622649—21no—
40#10622640C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic, complemented
42#10622632C2211yescharacteristic
43#10622628C2211yescharacteristic
44C4×#4323—21no—
45C4×#4323C2211yescharacteristic
46D4×C11⋊C8C2211yescharacteristic
47#10622620—21no—
48#10622620C2211yescharacteristic, complemented
49#10622580—21no—
50C2×#66873—21no—
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×Q8×D11—21no—
70C2×D4×D11—21no—
71C22×D44—21no—
72C11×#135—44no—
73C2×C11×Q16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16D411yescharacteristic
77C2×C11×D8—21no—
78C22×C8×C11—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×#127—21no—
81C11×#127C2311yescharacteristic
82C11×#123—41no—
83C11×C22⋊Q8—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—41no—
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11C2311yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C2×C11×C4⋊C4—21no—
92C2×#4325—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—41no—
97C2×#4323D411yescharacteristic
98#66983—21no—
99C22×C11⋊C8—21no—
100SD16×D11—44no—
101C2×#4314—21no—
102C2×#4314—21no—
103C2×C8×D11—21no—
104#66950—21no—
105#66950—41no—
106#66948—21no—
107#66935—41no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44C2311yescharacteristic
111#66922—21no—
112#66922C2311yescharacteristic
113C11×#106D411yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×#103—21no—
116C11×#103D411yescharacteristic
117C11×#102—21no—
118C11×#102D411yescharacteristic
119C11×C22⋊C8—21no—
120C4×C8×C11C2311yescharacteristic
121#66896—21no—
122#66896—21no—
123#66896—21no—
124#66896—21no—
125#66896D411yescharacteristic
126C22⋊(C11⋊C8)—21no—
127(C2×D11)⋊C8—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—21no—
133#66873—21no—
134#66873D411yescharacteristic
135#66871—21no—
136#66871—21no—
137#66871—41no—
138#66871D411yescharacteristic
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#19970—111nomaximal, Sylow
147C23×D11—41no—
148C11×#41—42no—
149C11×#41—42no—
150C11×#41—81no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C2×C22⋊D11—41no—
167Q8×D11—42no—
168Q8×D11—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×C4×D11—41no—
180C2×Dic22—21no—
181C2×Dic22—41no—
182C11×Q16—42no—
183C11×SD16—42no—
184C11×SD16—81no—
185C11×SD16D814yescomplemented
186C11×D8—42no—
187C2×C8×C11—21no—
188C2×C8×C11—42no—
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×D411yescharacteristic
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
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—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11C2411yescharacteristic
204#4325—42no—
205#4324—42no—
206#4323—22no—
207#4323—42no—
208#4323—81no—
209#4323—82no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—41no—
212(C2×D11)⋊C4—41no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—41no—
216C4⋊Dic11C2×D411yescharacteristic
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—81no—
222C2×C11⋊C8C2×D411yescharacteristic
223C2×C11⋊C8C2×D411yescharacteristic
224#4314—42no—
225#4314—81no—
226C8×D11—42no—
227#3358—111no—
228#3294—111no—
229#3284D1111yescharacteristic, complemented
230D4×SD16—111no—
231#1706—111no—
232#1682—111no—
233#1681—111no—
234#1665—111no—
235#1665—111no—
236#1649—111no—
237#1647—111no—
238#1621—111no—
239#1619—111no—
240C8×SD16—111no—
241C8×D8—111no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—41no—
245C22×D11—21no—
246C22×D11—41no—
247C22×D11—82no—
248C22×D11—82no—
249C22×D11—161no—
250Q8×C11—21no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11C2×D812yes—
254D4×C11—21no—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—82no—
262D4×C11—81no—
263D4×C11—82no—
264D4×C11—161no—
265D4×C11C2×D812yes—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C22⋊D11—82no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283D44—21no—
284D44—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—81no—
289D44—82no—
290D44#13512yescomplemented
291C4×D11—41no—
292C4×D11—41no—
293C4×D11—82no—
294Dic22—41no—
295Dic22—41no—
296Dic22—82no—
297C8×C11—21no—
298C8×C11—41no—
299C8×C11C2×D812yes—
300C11⋊C8—22no—
301C11⋊C8—21no—
302C11⋊C8—21no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C2×#135—21no—
307C22×SD16—221no—
308#550C2×D1111yescharacteristic, complemented
309D4×Q8—111no—
310#547C2×D1111yescharacteristic
311D42—111no—
312#500—111no—
313#493—111no—
314#492—111no—
315#492C2×D1111yescharacteristic, complemented
316#486—111no—
317#486—111no—
318#486—221no—
319#480—221no—
320#474—111no—
321#474—111no—
322#474—221no—
323#466—221no—
324#465—21no—
325#465—221no—
326#462C2×D1111yescharacteristic, complemented
327#461—111no—
328#460—111no—
329#459—111no—
330#459—111no—
331#459—221no—
332#459C2×D1111yescharacteristic
333#452—21no—
334#450—221no—
335#449—21no—
336#448—221no—
337#447—221no—
338C8×Q8—111no—
339C4×SD16C2×D1111yescharacteristic
340C4×D8—111no—
341C4×D8—221no—
342C8×D4—111no—
343C8×D4—111no—
344C8×D4C2×D1111yescharacteristic, complemented
345C2×#102—221no—
346#335—111no—
347#334—111no—
348#332—111no—
349#332—111no—
350#331—111no—
351#331—111no—
352Q8⋊C8—111no—
353D4⋊C8—111no—
354D4⋊C8—111no—
355D4⋊C8—111no—
356C82—111no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11D4211yescharacteristic
367C2×D11—22no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—164no—
374C4×C11—22no—
375C4×C11—21no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11C22×D811yescharacteristic
381C4×C11C2×#13511yescharacteristic
382C4×C11#57611yescharacteristic
383C4×C11#57711yescharacteristic
384Dic11—41no—
385Dic11—81no—
386C2×#41—21no—
387C2×#41—21no—
388C22×Q8—221no—
389C22×D4—221no—
390C22×D4—221no—
391#135—44no—
392C2×Q16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—221no—
396C2×SD16—221no—
397C2×SD16—221no—
398C2×SD16—221no—
399C2×SD16—444no—
400C2×SD16C22⋊D1111yescharacteristic
401C2×D8—21no—
402C2×D8—111no—
403C2×D8—221no—
404C2×D8—221no—
405C2×D8—441no—
406C22×C8—21no—
407C22×C8—221no—
408C22×C8—221no—
409C4⋊Q8—111no—
410C4⋊Q8—221no—
411C4⋊Q8C22×D1111yescharacteristic
412#127—21no—
413#127—111no—
414#127C22×D1111yescharacteristic
415#123—41no—
416C22⋊Q8—21no—
417C22⋊Q8—221no—
418C22⋊Q8—441no—
419#121—21no—
420#121—21no—
421#121—41no—
422#121—221no—
423#121—221no—
424#120—441no—
425C4×Q8C22×D1111yescharacteristic
426C4×D4—21no—
427C4×D4—111no—
428C4×D4—221no—
429C4×D4C22×D1111yescharacteristic
430C4×D4C22×D1111yescharacteristic
431C2×C4⋊C4—21no—
432#107—111no—
433#107—221no—
434#107—221no—
435#107—441no—
436#106C22⋊D1111yescharacteristic
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8—111no—
440C4⋊C8—221no—
441C4⋊C8C22×D1111yescharacteristic
442#103—21no—
443#103—221no—
444#103C22⋊D1111yescharacteristic
445#102—21no—
446#102—111no—
447#102—111no—
448#102—221no—
449#102—221no—
450#102—221no—
451#102—221no—
452#102—221no—
453#102—221no—
454#102—221no—
455#102—221no—
456#102—221no—
457#102C22⋊D1111yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—221no—
460C22⋊C8—221no—
461C4×C8—111no—
462C4×C8—111no—
463C4×C8—221no—
464C4×C8C22×D1111yescharacteristic
465C2×C11—42no—
466C2×C11—81no—
467C2×C11—161no—
468C2×C11D4×D811yescharacteristic
469C2×C11#328211yescharacteristic
470C2×C11#329111yescharacteristic
471D11—42no—
472D11—161no—
473C24—441no—
474#41—42no—
475#41—42no—
476#41—81no—
477#41—81no—
478C2×Q8—21no—
479C2×Q8—221no—
480C2×Q8—441no—
481C2×Q8—442no—
482C2×Q8—881no—
483C2×Q8C2×C22⋊D1111yescharacteristic
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—111no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—441no—
495C2×D4—442no—
496C2×D4—441no—
497C2×D4—442no—
498C2×D4—881no—
499C2×D4—881no—
500C2×D4D4×D1111yescharacteristic
501C2×D4C2×C22⋊D1111yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—221no—
507C22×C4—441no—
508Q16—42no—
509SD16—42no—
510SD16—81no—
511SD16—442no—
512SD16—442no—
513SD16—442no—
514SD16—881no—
515SD16#432314yescomplemented
516D8—42no—
517D8—222no—
518D8—442no—
519D8—882no—
520D8—881no—
521C2×C8—21no—
522C2×C8—42no—
523C2×C8—111no—
524C2×C8—111no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—442no—
530C2×C8—881no—
531C2×C8C2×C22⋊D1111yescharacteristic
532C2×C8C2×C22⋊D1111yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—41no—
537C4⋊C4—111no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—441no—
541C4⋊C4D4×D1111yescharacteristic
542C4⋊C4C2×C22⋊D1111yescharacteristic
543C4⋊C4C2×C22⋊D1111yescharacteristic
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—221no—
549C22⋊C4—441no—
550C22⋊C4—441no—
551C42—21no—
552C42C23×D1111yescharacteristic
553C11#1997011yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—41no—
557C23—221no—
558C23—441no—
559C23—882no—
560C23—882no—
561C23—1761no—
562Q8—21no—
563Q8—41no—
564Q8—41no—
565Q8—441no—
566Q8—441no—
567Q8—882no—
568Q8C2×#432312yes—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—82no—
577D4—81no—
578D4—82no—
579D4—112no—
580D4—161no—
581D4—221no—
582D4—441no—
583D4—441no—
584D4—441no—
585D4—441no—
586D4—881no—
587D4—882no—
588D4—882no—
589D4C2×#432312yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—221no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—882no—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4#6703711yescharacteristic
608C2×C4C22×C22⋊D1111yescharacteristic
609C8—21no—
610C8—41no—
611C8—222no—
612C8—221no—
613C8—221no—
614C8—441no—
615C8—441no—
616C8—441no—
617C8C2×#432312yes—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—222no—
628C22—441no—
629C22—441no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—1764no—
634C22D4×C22⋊D1111yescharacteristic
635C4—21no—
636C4—22no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—81no—
641C4—441no—
642C4—881no—
643C4D11×#13511yescharacteristic
644C4#1062330111yescharacteristic
645C4C22×#432311yescharacteristic
646C4#1062336611yescharacteristic
647C2—42no—
648C2—81no—
649C2—161no—
650C2—442no—
651C2—1761no—
652C2D4×#432311yescharacteristic
653C2#1308031711yescharacteristic
654C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3284C2
socleC22×C11D42
hypercenter#3284D11
hypocenterC11#19970
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3284

Complements

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

NH ≅ G/Ntype
1. #13081247C2semidirect
2. #13080423C2semidirect
3. SD16×D44C2semidirect
4. #13068206C2semidirect
5. #13068062C2semidirect
6. #13068051C2semidirect
7. #13067957C2semidirect
8. #13067954C2semidirect
9. #13067863C2semidirect
10. #13067851C2semidirect
11. #13067681C2semidirect
12. #13067669C2semidirect
13. SD16×C11⋊C8C2semidirect
14. C8×#4323C2semidirect
15. C11×#3284C2semidirect
17. C11×#550C22semidirect
22. C11×#492C22semidirect
24. C11×#462C22semidirect
29. C8×D4×C11C22semidirect
32. #10622691C22semidirect
37. #10622683C22semidirect
41. Q8×C11⋊C8C22semidirect
48. #10622620C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
185. C11×SD16D8semidirect
229. #3284D11semidirect
290. D44#135semidirect
308. #550C2×D11semidirect
315. #492C2×D11semidirect
326. #462C2×D11semidirect
344. C8×D4C2×D11semidirect
515. SD16#4323semidirect
553. C11#19970semidirect

Maximal subgroups

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

subgroupindex
#130812472
#130804232
SD16×D442
#130682062
#130680622
#130680512
#130679572
#130679542
#130678632
#130678512
#130676812
#130676692
SD16×C11⋊C82
C8×#43232
C11×#32842
#1997011