Finite Group Databasebeta

← #14743121

Subgroups — #14743121

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D8×D44C211yesmaximal, characteristic, complemented
2D4×#4323C211yesmaximal, characteristic, complemented
3#13080216C211yesmaximal, characteristic, complemented
4#13068284C211yesmaximal, characteristic, complemented
5#13068093C211yesmaximal, characteristic, complemented
6#13068050C211yesmaximal, characteristic, complemented
7#13067971C211yesmaximal, characteristic, complemented
8#13067959C211yesmaximal, characteristic, complemented
9#13067794C211yesmaximal, characteristic, complemented
10#13067705C211yesmaximal, characteristic, complemented
11#13067670C211yesmaximal, characteristic, complemented
12#13067669C211yesmaximal, characteristic, complemented
13#13067446C211yesmaximal, characteristic, complemented
14#13067438C211yesmaximal, characteristic, complemented
15C11×#3294C211yesmaximal, characteristic, complemented
16C11×#547C2211yescharacteristic, complemented
17D42×C11C2211yescharacteristic, complemented
18C2×#67002—21no—
19C22×#4323—21no—
20C2×D8×D11—21no—
21D4×D44C2211yescharacteristic
22D4×D44C2211yescharacteristic, complemented
23C11×#486C2211yescharacteristic, complemented
24C11×#480—21no—
25C11×#474C2211yescharacteristic, complemented
26C11×#466—21no—
27C11×#459C2211yescharacteristic, complemented
28C11×#447—21no—
29C4×C11×D8C2211yescharacteristic
30C8×D4×C11C2211yescharacteristic, complemented
31C2×C11×#102—21no—
32#10622851—21no—
33#10622830—21no—
34#10622701C2211yescharacteristic, complemented
35#10622698C2211yescharacteristic, complemented
36#10622696C2211yescharacteristic, complemented
37#10622686C2211yescharacteristic, complemented
38#10622686C2211yescharacteristic, complemented
39#10622685C2211yescharacteristic
40#10622662—21no—
41#10622659—21no—
42#10622651—21no—
43#10622649—21no—
44#10622628C2211yescharacteristic
45#10622628C2211yescharacteristic, complemented
46#10622628C2211yescharacteristic, complemented
47#10622628C2211yescharacteristic, complemented
48C4×#4323C2211yescharacteristic
49#10622625C2211yescharacteristic, complemented
50D4×C11⋊C8C2211yescharacteristic, complemented
51#10622496—21no—
52#10622386—21no—
53#10622386—21no—
54#10622308C2211yescharacteristic, complemented
55C8×D44C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic, complemented
59D4⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622121C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622096C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×D4×D11—21no—
71C2×D4×D11—21no—
72C22×D44—21no—
73C22×D44—21no—
74C2×C11×D8—21no—
75C2×C11×D8D411yescharacteristic
76C22×C8×C11—21no—
77C11×C4⋊Q8C2311yescharacteristic
78C11×#127C2311yescharacteristic
79C11×#123—41no—
80C11×C22⋊Q8—21no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#120—41no—
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C2×C11×C4⋊C4—21no—
89#67002—44no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98C2×#4323—21no—
99C2×#4323—21no—
100C2×#4323—41no—
101C2×#4323—44no—
102C2×#4323D411yescharacteristic
103#66983—21no—
104#66983—21no—
105C2×#4318—21no—
106C22×C11⋊C8—21no—
107D8×D11—44no—
108C2×D88—21no—
109C2×D88—21no—
110C2×C8×D11—21no—
111#66948—21no—
112#66948—21no—
113#66935—41no—
114#66935—41no—
115#66927C2311yescharacteristic
116#66927C2311yescharacteristic
117C4×D44C2311yescharacteristic
118C11×#107—21no—
119C11×#107D411yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×#102—21no—
122C11×#102—21no—
123C11×#102—21no—
124C11×#102—21no—
125C11×#102D411yescharacteristic
126C11×#102D411yescharacteristic
127C11×C22⋊C8—21no—
128C4×C8×C11C2311yescharacteristic
129#66899—21no—
130#66896—21no—
131#66896D411yescharacteristic
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#66871D411yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4⋊(C11⋊C8)C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147#19755—111nomaximal, Sylow
148C24×C11—41no—
149C23×D11—41no—
150C23×D11—41no—
151C11×#41—42no—
152C11×#41—81no—
153C2×Q8×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—41no—
162C2×D4×C11—81no—
163C2×D4×C11—81no—
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173D4×D11—42no—
174D4×D11—42no—
175D4×D11—81no—
176D4×D11—81no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—41no—
184C2×D44—41no—
185C2×D44—42no—
186C2×D44—42no—
187C2×D44—81no—
188C2×D44—81no—
189C2×D44C2×D411yescharacteristic
190C2×C4×D11—21no—
191C11×D8—22no—
192C11×D8—81no—
193C2×C8×C11—21no—
194C2×C8×C11—81no—
195C2×C8×C11C2×D411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11C2411yescharacteristic
209#4325—42no—
210#4325—42no—
211#4325—81no—
212#4323—42no—
213#4323—42no—
214#4323—42no—
215#4323—42no—
216#4323—42no—
217#4323—42no—
218#4323—81no—
219#4323—82no—
220#4323D814yescomplemented
221(C2×D11)⋊C4—21no—
222(C2×D11)⋊C4—41no—
223(C2×D11)⋊C4—41no—
224C4⋊Dic11C2×D411yescharacteristic
225#4318—42no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—42no—
231C2×C11⋊C8C2×D411yescharacteristic
232C2×C11⋊C8C2×D411yescharacteristic
233D88—42no—
234D88—81no—
235C8×D11—42no—
236#3294D1111yescharacteristic, complemented
237D4×D8—111no—
238D4×D8—111no—
239#3272—111no—
240#1721—111no—
241#1687—111no—
242#1681—111no—
243#1667—111no—
244#1665—111no—
245#1639—111no—
246#1625—111no—
247#1619—111no—
248#1619—111no—
249#1581—111no—
250#1580—111no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—41no—
255C23×C11—82no—
256C23×C11—82no—
257C23×C11—161no—
258C22×D11—21no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—82no—
262C22×D11—82no—
263C22×D11—82no—
264C22×D11—82no—
265C22×D11—161no—
266C22×D11—161no—
267Q8×C11—41no—
268Q8×C11—41no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—21no—
272D4×C11—21no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—81no—
278D4×C11—82no—
279D4×C11—82no—
280D4×C11—82no—
281D4×C11C2×D812yescomplemented
282D4×C11AGL(1,ℤ/8)12yescomplemented
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—82no—
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C22⋊D11—82no—
298C22⋊D11—82no—
299C2×Dic11—21no—
300D44—21no—
301D44—41no—
302D44—41no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—81no—
310D44—81no—
311D44—82no—
312D44—82no—
313D44C2×D812yes—
314C4×D11—41no—
315C4×D11—41no—
316C8×C11—21no—
317C8×C11—21no—
318C8×C11—41no—
319C11⋊C8—21no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C11⋊C8C2×D812yescomplemented
325C2×AGL(1,ℤ/8)—221no—
326C22×D8—221no—
327C22×D8—221no—
328#547C2×D1111yescharacteristic, complemented
329D42—111no—
330D42—111no—
331D42C2×D1111yescharacteristic, complemented
332#493—111no—
333#493—111no—
334#493—111no—
335#492—111no—
336#486—111no—
337#486C2×D1111yescharacteristic, complemented
338#480—21no—
339#474C2×D1111yescharacteristic, complemented
340#468—221no—
341#466—21no—
342#466—221no—
343#466—221no—
344#461—111no—
345#459—111no—
346#459—111no—
347#459—111no—
348#459—111no—
349#459—111no—
350#459C2×D1111yescharacteristic, complemented
351#450—221no—
352#449—221no—
353#447—21no—
354#447—221no—
355#447—221no—
356#447—221no—
357#447—221no—
358C4×D8—111no—
359C4×D8C2×D1111yescharacteristic
360#436—111no—
361C8×D4—111no—
362C8×D4—111no—
363C8×D4C2×D1111yescharacteristic, complemented
364C2×#102—21no—
365#335—111no—
366#334—111no—
367#332—111no—
368#331—111no—
369#331—111no—
370#331—111no—
371D4⋊C8—111no—
372D4⋊C8—111no—
373D4⋊C8—111no—
374D4⋊C8—111no—
375#322—111no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—164no—
389C22×C11D4211yescharacteristic
390C2×D11—22no—
391C2×D11—41no—
392C2×D11—41no—
393C2×D11—81no—
394C2×D11—81no—
395C2×D11—81no—
396C2×D11—81no—
397C2×D11—81no—
398C2×D11—81no—
399C2×D11—164no—
400C2×D11—164no—
401C4×C11—21no—
402C4×C11—41no—
403C4×C11—41no—
404C4×C11—41no—
405C4×C11—81no—
406C4×C11C22×D811yescharacteristic
407C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C4×C11#57611yescharacteristic
409C4×C11#57611yescharacteristic
410Dic11—41no—
411C2×#41—21no—
412C22×D4—21no—
413C22×D4—21no—
414C22×D4—221no—
415C22×D4—221no—
416C22×D4—221no—
417C22×D4—221no—
418AGL(1,ℤ/8)—444no—
419C2×SD16—221no—
420C2×SD16—221no—
421C2×SD16—221no—
422C2×D8—21no—
423C2×D8—111no—
424C2×D8—221no—
425C2×D8—221no—
426C2×D8—221no—
427C2×D8—221no—
428C2×D8—221no—
429C2×D8—221no—
430C2×D8—221no—
431C2×D8—221no—
432C2×D8—221no—
433C2×D8—441no—
434C2×D8—444no—
435C2×D8—444no—
436C2×D8C22⋊D1111yescharacteristic
437C2×M16—221no—
438C22×C8—21no—
439C22×C8—221no—
440C22×C8—221no—
441C4⋊Q8C22×D1111yescharacteristic
442#127—111no—
443#127—111no—
444#127C22×D1111yescharacteristic
445#123—41no—
446C22⋊Q8—21no—
447#121—21no—
448#121—21no—
449#121—21no—
450#121—221no—
451#121—221no—
452#121—221no—
453#121—221no—
454#120—41no—
455#120—441no—
456#120—441no—
457C4×D4—111no—
458C4×D4C22×D1111yescharacteristic
459C4×D4C22×D1111yescharacteristic
460C4×D4C22×D1111yescharacteristic
461C2×C4⋊C4—21no—
462#107—21no—
463#107—111no—
464#107C22⋊D1111yescharacteristic
465C4⋊C8—111no—
466C4⋊C8—111no—
467C4⋊C8—111no—
468C4⋊C8C22×D1111yescharacteristic
469#103—221no—
470#102—21no—
471#102—21no—
472#102—21no—
473#102—21no—
474#102—111no—
475#102—111no—
476#102—221no—
477#102—221no—
478#102—221no—
479#102—221no—
480#102—221no—
481#102—441no—
482#102C22⋊D1111yescharacteristic
483#102C22⋊D1111yescharacteristic
484C22⋊C8—21no—
485C22⋊C8—221no—
486C22⋊C8—221no—
487C22⋊C8—221no—
488C4×C8—111no—
489C4×C8—111no—
490C4×C8C22×D1111yescharacteristic
491C2×C11—42no—
492C2×C11—42no—
493C2×C11—81no—
494C2×C11—161no—
495C2×C11#326411yescharacteristic
496C2×C11D4×D811yescharacteristic
497C2×C11#328811yescharacteristic
498D11—42no—
499D11—161no—
500D11—161no—
501C24—41no—
502C24—441no—
503C24—441no—
504#41—42no—
505#41—81no—
506C2×Q8—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—41no—
515C2×D4—81no—
516C2×D4—81no—
517C2×D4—111no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—221no—
521C2×D4—221no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—441no—
525C2×D4—441no—
526C2×D4—442no—
527C2×D4—442no—
528C2×D4—441no—
529C2×D4—441no—
530C2×D4—442no—
531C2×D4—442no—
532C2×D4—881no—
533C2×D4—881no—
534C2×D4—881no—
535C2×D4—881no—
536C2×D4D4×D1111yescharacteristic
537C2×D4C2×C22⋊D1111yescharacteristic
538C2×D4C2×C22⋊D1111yescharacteristic
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—41no—
543C22×C4—221no—
544SD16—442no—
545SD16—442no—
546SD16—881no—
547D8—22no—
548D8—81no—
549D8—114no—
550D8—442no—
551D8—442no—
552D8—442no—
553D8—442no—
554D8—442no—
555D8—442no—
556D8—442no—
557D8—881no—
558D8—881no—
559D8—882no—
560M16—442no—
561C2×C8—21no—
562C2×C8—81no—
563C2×C8—111no—
564C2×C8—111no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—442no—
570C2×C8—442no—
571C2×C8C2×C22⋊D1111yescharacteristic
572C2×C8C2×C22⋊D1111yescharacteristic
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—41no—
576C4⋊C4—111no—
577C4⋊C4D4×D1111yescharacteristic
578C4⋊C4C2×C22⋊D1111yescharacteristic
579C4⋊C4C2×C22⋊D1111yescharacteristic
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—41no—
584C22⋊C4—41no—
585C22⋊C4—221no—
586C22⋊C4—441no—
587C22⋊C4—441no—
588C42C23×D1111yescharacteristic
589C11#1975511yescharacteristic, complemented, Sylow
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—82no—
595C23—82no—
596C23—161no—
597C23—221no—
598C23—441no—
599C23—441no—
600C23—882no—
601C23—882no—
602C23—882no—
603C23—882no—
604C23—1761no—
605C23—1761no—
606Q8—41no—
607Q8—41no—
608D4—21no—
609D4—21no—
610D4—21no—
611D4—21no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—81no—
617D4—82no—
618D4—82no—
619D4—82no—
620D4—112no—
621D4—221no—
622D4—441no—
623D4—441no—
624D4—441no—
625D4—441no—
626D4—441no—
627D4—441no—
628D4—441no—
629D4—441no—
630D4—881no—
631D4—881no—
632D4—882no—
633D4—882no—
634D4—882no—
635D4—882no—
636D4D8×D1112yescomplemented
637D4#6700212yescomplemented
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—82no—
649C2×C4—221no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4C2×D4×D1111yescharacteristic
653C2×C4#6703711yescharacteristic
654C2×C4C22×C22⋊D1111yescharacteristic
655C8—21no—
656C8—21no—
657C8—41no—
658C8—112no—
659C8—221no—
660C8—441no—
661C8—441no—
662C8—441no—
663C8—441no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—164no—
677C22—222no—
678C22—441no—
679C22—441no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22—881no—
684C22—881no—
685C22—881no—
686C22—1764no—
687C22—1764no—
688C22D4×C22⋊D1111yescharacteristic
689C4—21no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—441no—
695C4C2×D8×D1111yescharacteristic
696C4#1062328811yescharacteristic
697C4C2×#6700211yescharacteristic
698C4#1062336611yescharacteristic
699C2—42no—
700C2—42no—
701C2—81no—
702C2—161no—
703C2—442no—
704C2—1761no—
705C2—1761no—
706C2#1308009711yescharacteristic
707C2D8×C22⋊D1111yescharacteristic
708C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3294C2
socleC22×C11D42
hypercenter#3294D11
hypocenterC11#19755
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. D8×D44C2semidirect
2. D4×#4323C2semidirect
3. #13080216C2semidirect
4. #13068284C2semidirect
5. #13068093C2semidirect
6. #13068050C2semidirect
7. #13067971C2semidirect
8. #13067959C2semidirect
9. #13067794C2semidirect
10. #13067705C2semidirect
11. #13067670C2semidirect
12. #13067669C2semidirect
13. #13067446C2semidirect
14. #13067438C2semidirect
15. C11×#3294C2semidirect
16. C11×#547C22semidirect
17. D42×C11C22semidirect
22. D4×D44C22semidirect
23. C11×#486C22semidirect
25. C11×#474C22semidirect
27. C11×#459C22semidirect
30. C8×D4×C11C22semidirect
34. #10622701C22semidirect
35. #10622698C22semidirect
36. #10622696C22semidirect
37. #10622686C22semidirect
38. #10622686C22semidirect
45. #10622628C22semidirect
46. #10622628C22semidirect
47. #10622628C22semidirect
49. #10622625C22semidirect
50. D4×C11⋊C8C22semidirect
54. #10622308C22semidirect
55. C8×D44C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. D4⋊(C11⋊C8)C22semidirect
59. D4⋊(C11⋊C8)C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622123C22semidirect
62. #10622123C22semidirect
63. #10622121C22semidirect
64. #10622118C22semidirect
65. #10622096C22semidirect
66. #10622092C22semidirect
220. #4323D8semidirect
236. #3294D11semidirect
281. D4×C11C2×D8semidirect
282. D4×C11AGL(1,ℤ/8)semidirect
324. C11⋊C8C2×D8semidirect
328. #547C2×D11semidirect
331. D42C2×D11semidirect
337. #486C2×D11semidirect
339. #474C2×D11semidirect
350. #459C2×D11semidirect
363. C8×D4C2×D11semidirect
589. C11#19755semidirect
636. D4D8×D11semidirect
637. D4#67002semidirect

Maximal subgroups

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

subgroupindex
D8×D442
D4×#43232
#130802162
#130682842
#130680932
#130680502
#130679712
#130679592
#130677942
#130677052
#130676702
#130676692
#130674462
#130674382
C11×#32942
#1975511