Finite Group Databasebeta

← #14743136

Subgroups — #14743136

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4325C211yesmaximal, characteristic, complemented
2D8×D44C211yesmaximal, characteristic, complemented
3#13080236C211yesmaximal, characteristic, complemented
4#13068284C211yesmaximal, characteristic, complemented
5#13068083C211yesmaximal, characteristic, complemented
6#13068050C211yesmaximal, characteristic, complemented
7#13067976C211yesmaximal, characteristic, complemented
8#13067969C211yesmaximal, characteristic, complemented
9#13067794C211yesmaximal, characteristic, complemented
10#13067719C211yesmaximal, characteristic, complemented
11#13067681C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13#13067446C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15C11×#3358C211yesmaximal, characteristic, complemented
16C11×#550C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic, complemented
18C2×#67002—21no—
19C22×#4325—21no—
20C2×D8×D11—21no—
21D4×D44C2211yescharacteristic
22D4×D44C2211yescharacteristic
23C11×#486—21no—
24C11×#486C2211yescharacteristic, complemented
25C11×#474—21no—
26C11×#474C2211yescharacteristic, complemented
27C11×#459—21no—
28C11×#459C2211yescharacteristic, complemented
29C8×Q8×C11C2211yescharacteristic, complemented
30C4×C11×D8—21no—
31C4×C11×D8C2211yescharacteristic
32#10622851—21no—
33#10622840—21no—
34#10622701C2211yescharacteristic, complemented
35#10622698C2211yescharacteristic, complemented
36#10622696C2211yescharacteristic
37#10622686C2211yescharacteristic, complemented
38#10622686C2211yescharacteristic, complemented
39#10622685C2211yescharacteristic
40#10622661—21no—
41#10622659—21no—
42#10622652—21no—
43#10622649—21no—
44#10622640C2211yescharacteristic, complemented
45#10622640C2211yescharacteristic, complemented
46C4×#4325C2211yescharacteristic
47#10622628C2211yescharacteristic
48#10622628C2211yescharacteristic
49#10622625C2211yescharacteristic, complemented
50D4×C11⋊C8C2211yescharacteristic, complemented
51#10622496—21no—
52#10622386—21no—
53#10622386—21no—
54#10622308C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic
64#10622117C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C22×D44—21no—
72C22×D44—21no—
73C2×C11×D8—21no—
74C2×C11×D8D411yescharacteristic
75C11×C4⋊Q8—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127—21no—
78C11×#127C2311yescharacteristic
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—41no—
81C11×#121—21no—
82C11×#121—41no—
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88#67002—44no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4325—44no—
95C2×#4325D411yescharacteristic
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323—21no—
100C2×#4323—21no—
101C2×#4323—41no—
102#66983—21no—
103#66983—21no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106D8×D11—44no—
107C2×D88—21no—
108C2×D88—21no—
109C2×C8×D11—21no—
110#66948—21no—
111#66948—21no—
112#66935—41no—
113#66935—41no—
114#66927C2311yescharacteristic
115#66927C2311yescharacteristic
116C4×D44C2311yescharacteristic
117C11×#107—21no—
118C11×#107D411yescharacteristic
119C11×C4⋊C8—21no—
120C11×C4⋊C8C2311yescharacteristic
121C11×#102—21no—
122C11×#102—21no—
123C11×#102—21no—
124C11×#102—21no—
125C11×#102D411yescharacteristic
126C11×#102D411yescharacteristic
127C4×C8×C11—21no—
128C4×C8×C11C2311yescharacteristic
129#66899—21no—
130#66899D411yescharacteristic
131#66896—21no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)—21no—
134(C2×D11)⋊C8—21no—
135#66873—21no—
136#66873—21no—
137#66873—21no—
138#66873—21no—
139#66873—41no—
140#66873D411yescharacteristic
141#66872D411yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4⋊(C11⋊C8)C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147#19756—111nomaximal, Sylow
148C23×D11—41no—
149C23×D11—41no—
150C11×#41—42no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11—41no—
154C2×Q8×C11—42no—
155C2×Q8×C11—81no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C2×C22⋊D11—41no—
169C2×C22⋊D11—41no—
170D4×D11—42no—
171D4×D11—42no—
172D4×D11—81no—
173D4×D11—81no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—41no—
181C2×D44—41no—
182C2×D44—42no—
183C2×D44—42no—
184C2×D44—81no—
185C2×D44—81no—
186C2×D44C2×D411yescharacteristic
187C2×C4×D11—21no—
188C11×D8—22no—
189C11×D8—42no—
190C2×C8×C11—21no—
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—41no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C42×C11—21no—
205C42×C11C2411yescharacteristic
206#4325—42no—
207#4325—42no—
208#4325—42no—
209#4325—42no—
210#4325—81no—
211#4325D814yescomplemented
212#4323—42no—
213#4323—42no—
214#4323—42no—
215#4323—42no—
216#4323—81no—
217#4323—82no—
218(C2×D11)⋊C4—21no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—41no—
221C4⋊Dic11C2×D411yescharacteristic
222#4318—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8C2×D411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230D88—42no—
231D88—81no—
232C8×D11—42no—
233#3358D1111yescharacteristic, complemented
234D4×SD16—111no—
235D4×D8—111no—
236#3274—111no—
237#1721—111no—
238#1685—111no—
239#1681—111no—
240#1668—111no—
241#1667—111no—
242#1639—111no—
243#1627—111no—
244#1621—111no—
245#1619—111no—
246#1581—111no—
247SD16⋊C8—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—41no—
251C22×D11—21no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—82no—
255C22×D11—82no—
256C22×D11—82no—
257C22×D11—82no—
258C22×D11—161no—
259C22×D11—161no—
260Q8×C11—21no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—82no—
264Q8×C11C2×D812yescomplemented
265D4×C11—21no—
266D4×C11—21no—
267D4×C11—21no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—82no—
273D4×C11—81no—
274D4×C11—161no—
275D4×C11AGL(1,ℤ/8)12yescomplemented
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C22⋊D11—82no—
291C22⋊D11—82no—
292C2×Dic11—21no—
293D44—21no—
294D44—41no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302D44—81no—
303D44—81no—
304D44—82no—
305D44—82no—
306D44C2×D812yes—
307C4×D11—41no—
308C4×D11—41no—
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—41no—
312C11⋊C8—21no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C11⋊C8C2×D812yescomplemented
318C2×AGL(1,ℤ/8)—221no—
319C22×SD16—221no—
320C22×D8—221no—
321#550C2×D1111yescharacteristic, complemented
322D4×Q8C2×D1111yescharacteristic, complemented
323D42—111no—
324D42—111no—
325#493—111no—
326#493—111no—
327#493—111no—
328#492—111no—
329#486—21no—
330#486—111no—
331#486C2×D1111yescharacteristic, complemented
332#474—21no—
333#474C2×D1111yescharacteristic, complemented
334#469—221no—
335#466—221no—
336#465—221no—
337#461—111no—
338#460—111no—
339#460—111no—
340#459—21no—
341#459—111no—
342#459—111no—
343#459—111no—
344#459C2×D1111yescharacteristic, complemented
345#450—221no—
346#449—221no—
347#448—221no—
348#447—221no—
349#447—221no—
350#447—221no—
351C8×Q8C2×D1111yescharacteristic, complemented
352C4×SD16—111no—
353C4×D8—21no—
354C4×D8C2×D1111yescharacteristic
355#436—111no—
356C8×D4—111no—
357C8×D4—111no—
358#335—111no—
359#335—111no—
360#332—111no—
361#331—111no—
362#331—111no—
363#331—111no—
364Q8⋊C8—111no—
365D4⋊C8—111no—
366D4⋊C8—111no—
367D4⋊C8—111no—
368#322—111no—
369C22×C11—22no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11D4211yescharacteristic
379C2×D11—22no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—164no—
389C2×D11—164no—
390C4×C11—22no—
391C4×C11—21no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11C22×D811yescharacteristic
397C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
398C4×C11#57611yescharacteristic
399C4×C11#57711yescharacteristic
400Dic11—41no—
401C2×#41—21no—
402C22×Q8—21no—
403C22×D4—221no—
404C22×D4—221no—
405C22×D4—221no—
406C22×D4—221no—
407AGL(1,ℤ/8)—444no—
408C2×SD16—111no—
409C2×SD16—221no—
410C2×SD16—221no—
411C2×SD16—221no—
412C2×SD16—221no—
413C2×SD16—221no—
414C2×SD16—444no—
415C2×D8—21no—
416C2×D8—221no—
417C2×D8—221no—
418C2×D8—221no—
419C2×D8—221no—
420C2×D8—221no—
421C2×D8—221no—
422C2×D8—221no—
423C2×D8—441no—
424C2×D8—444no—
425C2×D8C22⋊D1111yescharacteristic
426C2×M16—221no—
427C22×C8—221no—
428C22×C8—221no—
429C4⋊Q8—21no—
430C4⋊Q8C22×D1111yescharacteristic
431#127—21no—
432#127—111no—
433#127—111no—
434#127C22×D1111yescharacteristic
435C22⋊Q8—21no—
436C22⋊Q8—41no—
437#121—21no—
438#121—41no—
439#121—221no—
440#121—221no—
441#121—221no—
442#121—221no—
443#120—441no—
444#120—441no—
445C4×Q8C22×D1111yescharacteristic
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—111no—
449C4×D4C22×D1111yescharacteristic
450C4×D4C22×D1111yescharacteristic
451#107—21no—
452#107C22⋊D1111yescharacteristic
453#106—111no—
454C4⋊C8—21no—
455C4⋊C8—111no—
456C4⋊C8—111no—
457C4⋊C8—111no—
458C4⋊C8C22×D1111yescharacteristic
459#103—111no—
460#103—221no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102—111no—
466#102—221no—
467#102—221no—
468#102—221no—
469#102—221no—
470#102—221no—
471#102—441no—
472#102C22⋊D1111yescharacteristic
473#102C22⋊D1111yescharacteristic
474C22⋊C8—221no—
475C22⋊C8—221no—
476C22⋊C8—221no—
477C4×C8—21no—
478C4×C8—111no—
479C4×C8—111no—
480C4×C8C22×D1111yescharacteristic
481C2×C11—42no—
482C2×C11—81no—
483C2×C11—161no—
484C2×C11#326511yescharacteristic
485C2×C11D4×D811yescharacteristic
486C2×C11#328811yescharacteristic
487D11—42no—
488D11—161no—
489D11—161no—
490C24—441no—
491C24—441no—
492#41—42no—
493#41—81no—
494C2×Q8—21no—
495C2×Q8—41no—
496C2×Q8—42no—
497C2×Q8—81no—
498C2×Q8D4×D1111yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—111no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C2×D4—441no—
512C2×D4—441no—
513C2×D4—442no—
514C2×D4—442no—
515C2×D4—441no—
516C2×D4—441no—
517C2×D4—442no—
518C2×D4—442no—
519C2×D4—881no—
520C2×D4—881no—
521C2×D4—881no—
522C2×D4—881no—
523C2×D4C2×C22⋊D1111yescharacteristic
524C2×D4C2×C22⋊D1111yescharacteristic
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—221no—
530SD16—114no—
531SD16—442no—
532SD16—442no—
533SD16—442no—
534SD16—442no—
535SD16—881no—
536D8—22no—
537D8—42no—
538D8—442no—
539D8—442no—
540D8—442no—
541D8—442no—
542D8—442no—
543D8—881no—
544D8—881no—
545D8—882no—
546M16—442no—
547C2×C8—21no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—442no—
555C2×C8—442no—
556C2×C8C2×C22⋊D1111yescharacteristic
557C2×C8C2×C22⋊D1111yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—41no—
562C4⋊C4—111no—
563C4⋊C4D4×D1111yescharacteristic
564C4⋊C4C2×C22⋊D1111yescharacteristic
565C4⋊C4C2×C22⋊D1111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—221no—
571C22⋊C4—441no—
572C22⋊C4—441no—
573C42—21no—
574C42C23×D1111yescharacteristic
575C11#1975611yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—41no—
579C23—221no—
580C23—441no—
581C23—441no—
582C23—882no—
583C23—882no—
584C23—882no—
585C23—882no—
586C23—1761no—
587C23—1761no—
588Q8—21no—
589Q8—41no—
590Q8—41no—
591Q8—82no—
592Q8D8×D1112yescomplemented
593D4—21no—
594D4—21no—
595D4—21no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—82no—
601D4—81no—
602D4—112no—
603D4—161no—
604D4—221no—
605D4—441no—
606D4—441no—
607D4—441no—
608D4—441no—
609D4—441no—
610D4—441no—
611D4—441no—
612D4—441no—
613D4—881no—
614D4—881no—
615D4—882no—
616D4—882no—
617D4—882no—
618D4—882no—
619D4#6700212yescomplemented
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—82no—
630C2×C4—82no—
631C2×C4—221no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—21no—
638C8—21no—
639C8—41no—
640C8—112no—
641C8—221no—
642C8—441no—
643C8—441no—
644C8—441no—
645C8—441no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—222no—
656C22—441no—
657C22—441no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22—881no—
662C22—881no—
663C22—881no—
664C22—1764no—
665C22—1764no—
666C22D4×C22⋊D1111yescharacteristic
667C4—21no—
668C4—22no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—81no—
673C4—441no—
674C4C2×D8×D1111yescharacteristic
675C4#1062328811yescharacteristic
676C4C2×#6700211yescharacteristic
677C4#1062336811yescharacteristic
678C2—42no—
679C2—81no—
680C2—161no—
681C2—442no—
682C2—1761no—
683C2—1761no—
684C2#1308011211yescharacteristic
685C2D8×C22⋊D1111yescharacteristic
686C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3358C2
socleC22×C11D42
hypercenter#3358D11
hypocenterC11#19756
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3358

Complements

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

NH ≅ G/Ntype
1. D4×#4325C2semidirect
2. D8×D44C2semidirect
3. #13080236C2semidirect
4. #13068284C2semidirect
5. #13068083C2semidirect
6. #13068050C2semidirect
7. #13067976C2semidirect
8. #13067969C2semidirect
9. #13067794C2semidirect
10. #13067719C2semidirect
11. #13067681C2semidirect
12. #13067669C2semidirect
13. #13067446C2semidirect
14. #13067426C2semidirect
15. C11×#3358C2semidirect
16. C11×#550C22semidirect
17. D4×Q8×C11C22semidirect
24. C11×#486C22semidirect
26. C11×#474C22semidirect
28. C11×#459C22semidirect
29. C8×Q8×C11C22semidirect
34. #10622701C22semidirect
35. #10622698C22semidirect
37. #10622686C22semidirect
38. #10622686C22semidirect
44. #10622640C22semidirect
45. #10622640C22semidirect
49. #10622625C22semidirect
50. D4×C11⋊C8C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622123C22semidirect
64. #10622117C22semidirect
65. #10622096C22semidirect
66. #10622092C22semidirect
211. #4325D8semidirect
233. #3358D11semidirect
264. Q8×C11C2×D8semidirect
275. D4×C11AGL(1,ℤ/8)semidirect
317. C11⋊C8C2×D8semidirect
321. #550C2×D11semidirect
322. D4×Q8C2×D11semidirect
331. #486C2×D11semidirect
333. #474C2×D11semidirect
344. #459C2×D11semidirect
351. C8×Q8C2×D11semidirect
575. C11#19756semidirect
592. Q8D8×D11semidirect
619. D4#67002semidirect

Maximal subgroups

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

subgroupindex
D4×#43252
D8×D442
#130802362
#130682842
#130680832
#130680502
#130679762
#130679692
#130677942
#130677192
#130676812
#130676692
#130674462
#130674262
C11×#33582
#1975611