Finite Group Databasebeta

← #14746125

Subgroups — #14746125

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080431C211yesmaximal, characteristic, complemented
2#13080334C211yesmaximal, characteristic, complemented
3D4×#4323C211yesmaximal, characteristic, complemented
4#13068220C211yesmaximal, characteristic, complemented
5#13068053C211yesmaximal, characteristic, complemented
6#13068050C211yesmaximal, characteristic, complemented
7#13067979C211yesmaximal, characteristic, complemented
8#13067969C211yesmaximal, characteristic, complemented
9#13067795C211yesmaximal, characteristic, complemented
10#13067794C211yesmaximal, characteristic, complemented
11#13067705C211yesmaximal, characteristic, complemented
12#13067704C211yesmaximal, characteristic, complemented
13D8×C11⋊C8C211yesmaximal, characteristic, complemented
14C8×#4323C211yesmaximal, characteristic, complemented
15C11×#3294C211yesmaximal, characteristic, complemented
16C11×#547C2211yescharacteristic, complemented
17D42×C11C2211yescharacteristic
18C2×#67003—21no—
19C22×#4323—21no—
20#10623082C2211yescharacteristic, complemented
21D4×D44C2211yescharacteristic
22C11×#486C2211yescharacteristic, complemented
23C11×#480—21no—
24C11×#474C2211yescharacteristic
25C11×#466—21no—
26C11×#459C2211yescharacteristic, complemented
27C11×#447—21no—
28C4×C11×D8C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic, complemented
30C2×C11×#102—21no—
31#10622852—21no—
32#10622830—21no—
33#10622769—21no—
34#10622705C2211yescharacteristic, complemented
35#10622701C2211yescharacteristic, complemented
36#10622696C2211yescharacteristic, complemented
37#10622686C2211yescharacteristic
38#10622685C2211yescharacteristic
39#10622683C2211yescharacteristic, complemented
40#10622664—21no—
41#10622660—21no—
42#10622651—21no—
43#10622649—21no—
44#10622632C2211yescharacteristic, complemented
45#10622628C2211yescharacteristic
46#10622628C2211yescharacteristic, complemented
47C4×#4323C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49D4×C11⋊C8C2211yescharacteristic, complemented
50#10622620C2211yescharacteristic
51#10622495—21no—
52#10622388—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic, complemented
55C8×D44C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×D4×D11—21no—
71C2×#4339—21no—
72C22×D44—21no—
73C2×C11×D8—21no—
74C2×C11×D8D411yescharacteristic
75C22×C8×C11—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C11×#123—41no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#120—41no—
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C2×C11×C4⋊C4—21no—
88#67003—44no—
89C2×#4326—21no—
90C2×#4326—21no—
91C2×#4325—21no—
92#66991—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323—44no—
100C2×#4323D411yescharacteristic
101#66983—21no—
102#66977—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C2×C8×D11—21no—
106#66948—21no—
107C4⋊C4×D11—21no—
108#66936—41no—
109#66935—41no—
110#66927C2311yescharacteristic
111C4×D44C2311yescharacteristic
112#66922C2311yescharacteristic
113C11×#107—21no—
114C11×#107D411yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×#102—21no—
117C11×#102—21no—
118C11×#102—21no—
119C11×#102—21no—
120C11×#102D411yescharacteristic
121C11×#102D411yescharacteristic
122C11×C22⋊C8—21no—
123C4×C8×C11C2311yescharacteristic
124#66899—21no—
125#66896—21no—
126#66896—21no—
127#66896—41no—
128#66896D411yescharacteristic
129C22⋊(C11⋊C8)—21no—
130C22⋊(C11⋊C8)—21no—
131#66885—21no—
132#66885—21no—
133(C2×D11)⋊C8—21no—
134#66874—21no—
135#66873—21no—
136#66873—21no—
137#66873—41no—
138#66873D411yescharacteristic
139#66871—21no—
140#66871D411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19968—111nomaximal, Sylow
147C24×C11—41no—
148C23×D11—41no—
149C11×#41—42no—
150C11×#41—81no—
151C2×Q8×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—41no—
160C2×D4×C11—81no—
161C2×D4×C11—81no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—41no—
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171D4×D11—42no—
172D4×D11—81no—
173#4339—42no—
174#4339—81no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—41no—
179C2×D44—42no—
180C2×D44—81no—
181C2×D44C2×D411yescharacteristic
182C2×C4×D11—21no—
183C2×C4×D11—41no—
184C2×Dic22—21no—
185C11×D8—22no—
186C11×D8—81no—
187C2×C8×C11—21no—
188C2×C8×C11—81no—
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×D411yescharacteristic
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C42×C11C2411yescharacteristic
203C22⋊Dic11—41no—
204#4326—42no—
205#4326—81no—
206#4325—42no—
207#4324—42no—
208#4323—42no—
209#4323—42no—
210#4323—42no—
211#4323—81no—
212#4323—81no—
213#4323D814yescomplemented
214(C2×D11)⋊C4—21no—
215(C2×D11)⋊C4—41no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11C2×D411yescharacteristic
219Dic11⋊C4—41no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—42no—
225C2×C11⋊C8—42no—
226C2×C11⋊C8C2×D411yescharacteristic
227C2×C11⋊C8C2×D411yescharacteristic
228C8×D11—81no—
229#3294—111no—
230#3294D1111yescharacteristic, complemented
231#3283—111no—
232D4×D8—111no—
233#1709—111no—
234#1681—111no—
235#1681—111no—
236#1669—111no—
237#1667—111no—
238#1639—111no—
239#1639—111no—
240#1625—111no—
241#1625—111no—
242C8×D8—111no—
243C8×D8—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—41no—
248C23×C11—82no—
249C23×C11—82no—
250C23×C11—161no—
251C22×D11—21no—
252C22×D11—41no—
253C22×D11—82no—
254C22×D11—82no—
255C22×D11—161no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—21no—
259D4×C11—21no—
260D4×C11—21no—
261D4×C11—21no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—81no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11C2×D812yes—
271D4×C11#13512yescomplemented
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—82no—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C22⋊D11—82no—
287C22⋊D11—82no—
288C2×Dic11—21no—
289C2×Dic11—41no—
290D44—21no—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295D44—81no—
296D44—82no—
297D44C2×D812yes—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—82no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—21no—
304C8×C11—21no—
305C8×C11—41no—
306C11⋊C8—21no—
307C11⋊C8—41no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8C2×D812yes—
312C2×#135—221no—
313C22×D8—221no—
314#547—111no—
315#547C2×D1111yescharacteristic, complemented
316D42—111no—
317D42C2×D1111yescharacteristic
318#494—111no—
319#493—111no—
320#486—111no—
321#486—111no—
322#486—111no—
323#486C2×D1111yescharacteristic, complemented
324#480—21no—
325#480—221no—
326#474—111no—
327#474C2×D1111yescharacteristic
328#467—221no—
329#466—21no—
330#466—221no—
331#466—221no—
332#461—111no—
333#461—111no—
334#459—111no—
335#459—111no—
336#459—111no—
337#459C2×D1111yescharacteristic, complemented
338#452—221no—
339#452—221no—
340#447—21no—
341#447—221no—
342#447—221no—
343#447—221no—
344C4×D8—111no—
345C4×D8C2×D1111yescharacteristic
346C8×D4—111no—
347C8×D4—111no—
348C8×D4—111no—
349C8×D4C2×D1111yescharacteristic, complemented
350C2×#102—21no—
351C2×#102—221no—
352#335—111no—
353#335—111no—
354#332—111no—
355#332—111no—
356#331—111no—
357#331—111no—
358D4⋊C8—111no—
359D4⋊C8—111no—
360D4⋊C8—111no—
361D4⋊C8—111no—
362C82—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—164no—
376C22×C11D4211yescharacteristic
377C2×D11—22no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—164no—
384C4×C11—21no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—81no—
389C4×C11C22×D811yescharacteristic
390C4×C11C2×#13511yescharacteristic
391C4×C11#57611yescharacteristic
392C4×C11#57611yescharacteristic
393Dic11—41no—
394Dic11—81no—
395C2×#41—21no—
396C2×#41—221no—
397C22×D4—21no—
398C22×D4—21no—
399C22×D4—221no—
400C22×D4—221no—
401#135—444no—
402C2×Q16—221no—
403C2×Q16—221no—
404C2×SD16—221no—
405C2×SD16—221no—
406C2×D8—21no—
407C2×D8—111no—
408C2×D8—221no—
409C2×D8—221no—
410C2×D8—221no—
411C2×D8—221no—
412C2×D8—221no—
413C2×D8—444no—
414C2×D8C22⋊D1111yescharacteristic
415C22×C8—21no—
416C22×C8—221no—
417C22×C8—221no—
418C22×C8—221no—
419C4⋊Q8—111no—
420C4⋊Q8C22×D1111yescharacteristic
421#127—111no—
422#127C22×D1111yescharacteristic
423#123—41no—
424#123—441no—
425C22⋊Q8—21no—
426C22⋊Q8—221no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—221no—
431#121—221no—
432#121—221no—
433#120—41no—
434#120—441no—
435C4×D4—111no—
436C4×D4C22×D1111yescharacteristic
437C4×D4C22×D1111yescharacteristic
438C4×D4C22×D1111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C4⋊C4—221no—
441#107—21no—
442#107—111no—
443#107—221no—
444#107C22⋊D1111yescharacteristic
445C4⋊C8—111no—
446C4⋊C8—111no—
447C4⋊C8—111no—
448C4⋊C8C22×D1111yescharacteristic
449#103—221no—
450#103—221no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—111no—
456#102—111no—
457#102—221no—
458#102—221no—
459#102—221no—
460#102—221no—
461#102—221no—
462#102—221no—
463#102—441no—
464#102—441no—
465#102C22⋊D1111yescharacteristic
466#102C22⋊D1111yescharacteristic
467C22⋊C8—21no—
468C22⋊C8—221no—
469C22⋊C8—221no—
470C22⋊C8—221no—
471C4×C8—111no—
472C4×C8—111no—
473C4×C8C22×D1111yescharacteristic
474C2×C11—42no—
475C2×C11—42no—
476C2×C11—81no—
477C2×C11—161no—
478C2×C11D4×D811yescharacteristic
479C2×C11#328011yescharacteristic
480C2×C11#329011yescharacteristic
481D11—42no—
482D11—161no—
483C24—41no—
484C24—441no—
485#41—42no—
486#41—81no—
487#41—442no—
488#41—881no—
489C2×Q8—21no—
490C2×Q8—221no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—41no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—111no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—441no—
506C2×D4—442no—
507C2×D4—441no—
508C2×D4—442no—
509C2×D4—441no—
510C2×D4—881no—
511C2×D4—881no—
512C2×D4D4×D1111yescharacteristic
513C2×D4C2×C22⋊D1111yescharacteristic
514C2×D4C2×C22⋊D1111yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—41no—
519C22×C4—221no—
520C22×C4—441no—
521Q16—442no—
522Q16—881no—
523SD16—442no—
524SD16—442no—
525D8—22no—
526D8—81no—
527D8—114no—
528D8—442no—
529D8—442no—
530D8—442no—
531D8—881no—
532D8—881no—
533C2×C8—21no—
534C2×C8—81no—
535C2×C8—111no—
536C2×C8—111no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—442no—
542C2×C8—442no—
543C2×C8—881no—
544C2×C8C2×C22⋊D1111yescharacteristic
545C2×C8C2×C22⋊D1111yescharacteristic
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—41no—
549C4⋊C4—111no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—441no—
553C4⋊C4D4×D1111yescharacteristic
554C4⋊C4C2×C22⋊D1111yescharacteristic
555C4⋊C4C2×C22⋊D1111yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—221no—
562C22⋊C4—441no—
563C22⋊C4—441no—
564C42C23×D1111yescharacteristic
565C11#1996811yescharacteristic, complemented, Sylow
566C23—21no—
567C23—21no—
568C23—21no—
569C23—41no—
570C23—82no—
571C23—82no—
572C23—161no—
573C23—221no—
574C23—441no—
575C23—882no—
576C23—882no—
577C23—1761no—
578Q8—41no—
579Q8—41no—
580Q8—441no—
581Q8—441no—
582D4—21no—
583D4—21no—
584D4—21no—
585D4—21no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—81no—
591D4—82no—
592D4—82no—
593D4—82no—
594D4—112no—
595D4—221no—
596D4—441no—
597D4—441no—
598D4—441no—
599D4—441no—
600D4—881no—
601D4—882no—
602D4—882no—
603D4—882no—
604D4D8×D1112yes—
605D4#6700312yescomplemented
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—82no—
617C2×C4—221no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—882no—
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4C22×C22⋊D1111yescharacteristic
625C8—21no—
626C8—21no—
627C8—41no—
628C8—112no—
629C8—221no—
630C8—441no—
631C8—441no—
632C8—441no—
633C8—441no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—164no—
647C22—222no—
648C22—441no—
649C22—441no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—1764no—
654C22D4×C22⋊D1111yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—441no—
661C4—881no—
662C4C2×D8×D1111yescharacteristic
663C4#1062328811yescharacteristic
664C4C2×#6700311yescharacteristic
665C4#1062336611yescharacteristic
666C2—42no—
667C2—42no—
668C2—81no—
669C2—161no—
670C2—442no—
671C2—1761no—
672C2D8×C22⋊D1111yescharacteristic
673C2#1308029711yescharacteristic
674C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3294C2
socleC22×C11D42
hypercenter#3294D11
hypocenterC11#19968
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #13080431C2semidirect
2. #13080334C2semidirect
3. D4×#4323C2semidirect
4. #13068220C2semidirect
5. #13068053C2semidirect
6. #13068050C2semidirect
7. #13067979C2semidirect
8. #13067969C2semidirect
9. #13067795C2semidirect
10. #13067794C2semidirect
11. #13067705C2semidirect
12. #13067704C2semidirect
13. D8×C11⋊C8C2semidirect
14. C8×#4323C2semidirect
15. C11×#3294C2semidirect
16. C11×#547C22semidirect
20. #10623082C22semidirect
22. C11×#486C22semidirect
26. C11×#459C22semidirect
29. C8×D4×C11C22semidirect
34. #10622705C22semidirect
35. #10622701C22semidirect
36. #10622696C22semidirect
39. #10622683C22semidirect
44. #10622632C22semidirect
46. #10622628C22semidirect
49. D4×C11⋊C8C22semidirect
54. #10622307C22semidirect
55. C8×D44C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
62. #10622123C22semidirect
63. #10622121C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. C8×C11⋊C8C22semidirect
213. #4323D8semidirect
230. #3294D11semidirect
271. D4×C11#135semidirect
315. #547C2×D11semidirect
323. #486C2×D11semidirect
337. #459C2×D11semidirect
349. C8×D4C2×D11semidirect
565. C11#19968semidirect
605. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130804312
#130803342
D4×#43232
#130682202
#130680532
#130680502
#130679792
#130679692
#130677952
#130677942
#130677052
#130677042
D8×C11⋊C82
C8×#43232
C11×#32942
#1996811