Finite Group Databasebeta

← #14788510

Subgroups — #14788510

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic, complemented
4#13069848C212yesmaximal, complemented
5#13069685C212yesmaximal, complemented
6#13069552C211yesmaximal, characteristic, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13068961C212yesmaximal, complemented
9#13068860C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66993C2212yes—
17C22×#4323C2212yes—
18C2×#66983—21no—
19C2×#66977—21no—
20#10623084—24no—
21#10623084—24no—
22C2×#66946C2212yes—
23C2×#66937—22no—
24C2×#66927C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31#10622834C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34C2×#66885C2212yes—
35C2×#66885C2212yes—
36#10622628—24no—
37#10622586C2212yes—
38C2×#66873C2212yes—
39#10622561—22no—
40#10622548C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C2×#4339—28no—
52C2×#4339—44no—
53C2×#4339—44no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2312yes—
57C22×C4×D11—22no—
58C22×Dic22D411yescharacteristic
59C2×C11×D8—22no—
60C2×C11×D8—22no—
61C2×C11×D8—22no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75#66993—24no—
76#66993—24no—
77C2×#4323—24no—
78C2×#4323—24no—
79C2×#4323—42no—
80#66983—28no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2312yes—
86#66977—44no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8C2312yes—
91#66946—24no—
92#66946—24no—
93#66937—216no—
94#66927—22no—
95#66927D414yes—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×#107—22no—
99C11×#102—22no—
100C11×#102—22no—
101C4×C8×C11—22no—
102#66896—42no—
103C11⋊#95—22no—
104#66885—24no—
105#66885—42no—
106#66873—24no—
107C4⋊(C11⋊C8)—22no—
108#24184—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—21no—
111C23×D11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11C2×D412yes—
123C2×D4×C11#4112yescomplemented
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—28no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—82no—
140C2×C22⋊D11—82no—
141C22×Dic11—22no—
142C22×Dic11C2×D412yes—
143C22×Dic11C2×D412yes—
144#4339—432no—
145C2×D44—24no—
146C2×D44—24no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—81no—
155C2×D44—81no—
156C2×D44C2×D414yes—
157C2×C4×D11—28no—
158C2×C4×D11—44no—
159C2×C4×D11—44no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22D814yescomplemented
163C11×D8—28no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11#4112yescomplemented
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—42no—
176C42×C11C2×D412yes—
177C42×C11C2×D412yes—
178C22⋊Dic11—44no—
179C22⋊Dic11—82no—
180#4323—48no—
181(C2×D11)⋊C4—28no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187Dic11⋊C4—24no—
188Dic11⋊C4—44no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×#550—111no—
195C2×#459—111no—
196C2×C4×D8D1111yescharacteristic, complemented
197#2538—111no—
198#2041—112no—
199#2011—112no—
200#1984—111no—
201#1957—111no—
202#1879—112no—
203#1862—112no—
204#1802—111no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11C22×D411yescharacteristic
220C22×D11—24no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—48no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—84no—
245C2×C4×C11#12012yes—
246C2×C4×C11#12012yes—
247C2×C4×C11C2×D812yes—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C22⋊D11—416no—
256C22⋊D11—88no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11C2×D814yes—
266D44—24no—
267D44—24no—
268D44—42no—
269D44—42no—
270D44—48no—
271D44—84no—
272C4×D11—416no—
273Dic22—28no—
274C8×C11—22no—
275C8×C11—41no—
276C11⋊C8—42no—
277C22×#41—221no—
278C22×D8—112no—
279C22×D8C2×D1111yescharacteristic
280#550—224no—
281#550—224no—
282C2×#127—112no—
283C2×#127—111no—
284C2×C22⋊Q8—221no—
285C2×#121—222no—
286C2×#121—221no—
287C2×C4×Q8—111no—
288C2×C4×D4—112no—
289C2×C4×D4C2×D1111yescharacteristic
290C2×C4×D4C2×D1111yescharacteristic
291#459—224no—
292C4×D8—24no—
293C2×#107C2×D1111yescharacteristic
294C2×C4⋊C8—111no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102—112no—
299C2×#102C2×D1111yescharacteristic
300C2×#102C2×D1111yescharacteristic
301C2×C4×C8C2×D1111yescharacteristic
302#396—222no—
303#390—112no—
304#389—112no—
305#384—111no—
306#380—221no—
307#340—112no—
308#336—112no—
309#336—112no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11C2×#12011yescharacteristic
325C22×C11#54811yescharacteristic
326C22×C11#55011yescharacteristic
327C22×C11C22×D811yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11#57611yescharacteristic
330C22×C11#57711yescharacteristic
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11#44714yes—
342C4×C11#52511yescharacteristic
343C4×C11#53711yescharacteristic
344C4×C11#54611yescharacteristic
345C4×C11#54711yescharacteristic
346Dic11—24no—
347Dic11—42no—
348Dic11—82no—
349C2×#41—228no—
350C2×#41—444no—
351C2×#41—444no—
352C22×Q8—111no—
353C22×D4—112no—
354C22×D4—222no—
355C22×D4—222no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4C22×D1111yescharacteristic
359C22×D4C22×D1111yescharacteristic
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—222no—
363C2×D8—22no—
364C2×D8—22no—
365C2×D8—22no—
366C2×D8—224no—
367C2×D8—224no—
368C2×D8—442no—
369C22×C8—112no—
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372#127—114no—
373#127—224no—
374#127—224no—
375#127—222no—
376C22⋊Q8—444no—
377#121—2216no—
378#121—228no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—224no—
385C4×D4—224no—
386C4×D4C22⋊D1114yes—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C42—112no—
401C2×C42C22×D1111yescharacteristic
402#107—22no—
403C4⋊C8—222no—
404#102—22no—
405#102—22no—
406#102—224no—
407#102—224no—
408#102—442no—
409#102—442no—
410C4×C8—22no—
411#95—222no—
412C2×C11—82no—
413C2×C11—82no—
414C2×C11#240711yescharacteristic
415C2×C11C2×#44711yescharacteristic
416C2×C11#301211yescharacteristic
417C2×C11#335811yescharacteristic
418C2×C11#336611yescharacteristic
419C2×C11#339111yescharacteristic
420C2×C11#339711yescharacteristic
421D11—84no—
422C24—21no—
423C24—21no—
424C24—222no—
425#41—4432no—
426C2×Q8—114no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—114no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—222no—
448C2×D4—222no—
449C2×D4—444no—
450C2×D4—444no—
451C2×D4—442no—
452C2×D4—442no—
453C2×D4—881no—
454C2×D4—881no—
455C2×D4—882no—
456C2×D4—882no—
457C2×D4#433912yescomplemented
458C2×D4C2×C22⋊D1112yes—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—228no—
470C22×C4—222no—
471C22×C4—444no—
472C22×C4—444no—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476D8—28no—
477D8—448no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8#433912yescomplemented
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—444no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4C2×C22⋊D1112yes—
498C22⋊C4—24no—
499C22⋊C4—42no—
500C22⋊C4—228no—
501C22⋊C4—444no—
502C22⋊C4—882no—
503C42—222no—
504C42—222no—
505C42D4×D1112yes—
506C42C2×C22⋊D1112yes—
507C11#2418411yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—224no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23C2×D4×D1111yescharacteristic
530Q8—228no—
531D4—22no—
532D4—22no—
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—224no—
540D4—224no—
541D4—4416no—
542D4—448no—
543D4—442no—
544D4—442no—
545D4—884no—
546D4—888no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—48no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—84no—
557C2×C4—114no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—4416no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4D8×D1112yes—
568C2×C4#6696412yes—
569C2×C4#6699012yes—
570C2×C4#6699012yes—
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6704211yescharacteristic
575C2×C4#6704311yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—22no—
578C8—41no—
579C8—442no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—882no—
598C22—882no—
599C22—882no—
600C22—882no—
601C22#1062308311yescharacteristic
602C22#1062308411yescharacteristic
603C22C2×D8×D1111yescharacteristic
604C22C2×#6696411yescharacteristic
605C22#1062330011yescharacteristic
606C22#1062330111yescharacteristic
607C22C2×#6699011yescharacteristic
608C4—22no—
609C4—42no—
610C4—81no—
611C4—224no—
612C4—442no—
613C4—882no—
614C4#1062276914yes—
615C4#1062308111yescharacteristic
616C4#1062308211yescharacteristic
617C4#1062332211yescharacteristic
618C4#1062336411yescharacteristic
619C2—82no—
620C2—82no—
621C2—884no—
622C2#1307196111yescharacteristic
623C2C2×#1062276911yescharacteristic
624C2#1307791611yescharacteristic
625C2#1308124911yescharacteristic
626C2#1308132111yescharacteristic
627C2#1308159011yescharacteristic
628C2#1308163411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11#24184
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. C2×#10622628C2semidirect
3. #13073538C2semidirect
4. #13069848C2semidirect
5. #13069685C2semidirect
6. #13069552C2semidirect
7. #13069422C2semidirect
8. #13068961C2semidirect
9. #13068860C2semidirect
10. #13068616C2semidirect
11. C2×C4×C11×D8C2semidirect
123. C2×D4×C11#41semidirect
162. C2×Dic22D8semidirect
169. C2×C8×C11#41semidirect
196. C2×C4×D8D11semidirect
457. C2×D4#4339semidirect
486. C2×C8#4339semidirect
507. C11#24184semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106226282
#130735382
#130698482
#130696852
#130695522
#130694222
#130689612
#130688602
#130686162
C2×C4×C11×D82
#2418411