Finite Group Databasebeta

← #14787666

Subgroups — #14787666

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic, complemented
4#13069796C212yesmaximal, complemented
5#13069611C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal, complemented
9#13068802C212yesmaximal, 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×#66991C2212yes—
17C2×#66991C2212yes—
18C2×#66983—21no—
19C2×#66977—21no—
20#10623082—24no—
21#10623082—24no—
22C2×C4⋊C4×D11C2212yes—
23C2×#66936—22no—
24C2×C4×D44C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36#10622620—24no—
37#10622600C2212yes—
38C2×#66871C2212yes—
39#10622574—22no—
40#10622548C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
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×D44D411yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11C2312yes—
57C22×Dic22—21no—
58C2×C11×D8—22no—
59C2×C11×D8—22no—
60C2×C11×D8—22no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11D414yescomplemented
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74#66991—24no—
75#66991—24no—
76#66991—24no—
77#66991—42no—
78#66983—44no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4D412yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2312yes—
86C2×C4⋊Dic11C2312yes—
87#66977—28no—
88C2×Dic11⋊C4—22no—
89C22×C11⋊C8C2312yes—
90C4⋊C4×D11—24no—
91C4⋊C4×D11—24no—
92#66936—216no—
93C4×D44—22no—
94C4×D44—22no—
95#66922—22no—
96#66922D414yescomplemented
97C11×#107—22no—
98C11×#102—22no—
99C11×#102—22no—
100C4×C8×C11—22no—
101#66896—24no—
102#66896—42no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105(C2×D11)⋊C8—42no—
106#66871—24no—
107C4⋊(C11⋊C8)—22no—
108#24116—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—21no—
111C23×D11C2×D412yes—
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—44no—
137C2×C22⋊D11—44no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—44no—
140C2×C22⋊D11—82no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11C2×D412yes—
144#4339—432no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44D814yescomplemented
148C2×C4×D11—28no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×Dic22—24no—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C11×D8—28no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11#4112yescomplemented
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—42no—
173C42×C11C2×D412yes—
174C42×C11C2×D412yes—
175C22⋊Dic11—28no—
176C22⋊Dic11—44no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—44no—
179C4⋊Dic11—24no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—42no—
185C4⋊Dic11—81no—
186C4⋊Dic11C2×D414yes—
187Dic11⋊C4—28no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×#547—111no—
192C2×#474—111no—
193C2×C4×D8D1111yescharacteristic, complemented
194#2537—111no—
195#2033—112no—
196#1999—112no—
197#1990—111no—
198#1954—111no—
199#1874—112no—
200#1852—112no—
201#1802—111no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
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×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11C2×D814yes—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—41no—
229D4×C11—41no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—48no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—84no—
242C2×C4×C11#12012yes—
243C2×C4×C11#12012yes—
244C2×C4×C11C2×D812yes—
245C2×C4×C11AGL(1,ℤ/8)12yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C22⋊D11—416no—
253C22⋊D11—88no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263D44—28no—
264C4×D11—416no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—42no—
269Dic22—48no—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—42no—
273C22×#41—221no—
274C22×D8C2×D1111yescharacteristic
275#547—224no—
276#547—224no—
277C2×C4⋊Q8—111no—
278C2×#123—222no—
279C2×C22⋊Q8—221no—
280C2×#121—112no—
281C2×#121—112no—
282C2×#121—221no—
283C2×C4×D4—111no—
284C2×C4×D4C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—112no—
287#474—224no—
288C4×D8—24no—
289C2×#107—112no—
290C2×#107C2×D1111yescharacteristic
291C2×C4⋊C8—111no—
292C2×#102—112no—
293C2×#102—112no—
294C2×#102C2×D1111yescharacteristic
295C2×#102C2×D1111yescharacteristic
296C2×C22⋊C8—112no—
297C2×C22⋊C8—112no—
298C2×C4×C8C2×D1111yescharacteristic
299#394—222no—
300#384—111no—
301#380—112no—
302#380—221no—
303#340—112no—
304#340—112no—
305#340—112no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11C2×#12011yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11#54711yescharacteristic
323C22×C11C22×D811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57811yescharacteristic
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11#44714yes—
338C4×C11#52511yescharacteristic
339C4×C11#53711yescharacteristic
340C4×C11#54811yescharacteristic
341C4×C11#55011yescharacteristic
342Dic11—42no—
343Dic11—44no—
344Dic11—82no—
345C2×#41—228no—
346C2×#41—444no—
347C2×#41—444no—
348C22×Q8—221no—
349C22×D4—111no—
350C22×D4—222no—
351C22×D4—222no—
352C22×D4C22×D1111yescharacteristic
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—112no—
357C23×C4—222no—
358C2×D8—22no—
359C2×D8—22no—
360C2×D8—22no—
361C22×C8—112no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366#123—2216no—
367C22⋊Q8—228no—
368#121—224no—
369#121—224no—
370#121—224no—
371#121—442no—
372#121—444no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—222no—
377C4×D4—222no—
378C4×D4C22⋊D1114yescomplemented
379C2×C4⋊C4—112no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C22⋊C4—222no—
396C2×C42C22×D1111yescharacteristic
397#107—22no—
398#107—224no—
399C4⋊C8—222no—
400#102—22no—
401#102—22no—
402#102—224no—
403#102—442no—
404C22⋊C8—224no—
405C22⋊C8—442no—
406C4×C8—22no—
407#95—222no—
408C2×C11—82no—
409C2×C11—82no—
410C2×C11#240711yescharacteristic
411C2×C11C2×#44711yescharacteristic
412C2×C11#301311yescharacteristic
413C2×C11#329411yescharacteristic
414C2×C11#333011yescharacteristic
415C2×C11#333411yescharacteristic
416C2×C11#335411yescharacteristic
417D11—44no—
418C24—21no—
419C24—21no—
420C24—112no—
421#41—4432no—
422C2×Q8—224no—
423C2×Q8—442no—
424C2×Q8—442no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—114no—
436C2×D4—228no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—444no—
443C2×D4—882no—
444C2×D4#433912yescomplemented
445C2×D4C2×C22⋊D1112yes—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—112no—
455C22×C4—228no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—444no—
465C22×C4—444no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469D8—28no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8#433912yescomplemented
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—114no—
483C4⋊C4—228no—
484C4⋊C4—222no—
485C4⋊C4—224no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4C2×C22⋊D1112yes—
492C22⋊C4—24no—
493C22⋊C4—42no—
494C22⋊C4—228no—
495C22⋊C4—224no—
496C22⋊C4—444no—
497C22⋊C4—444no—
498C42D4×D1112yes—
499C42C2×C22⋊D1112yes—
500C11#2411611yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—114no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—222no—
522C23C2×D4×D1111yescharacteristic
523Q8—448no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—228no—
533D4—4416no—
534D4—888no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—48no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—84no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—4416no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4D8×D1112yes—
560C2×C4#6696412yes—
561C2×C4#6699012yes—
562C2×C4#6699012yes—
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4#6704211yescharacteristic
567C2×C4#6704311yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—22no—
570C8—41no—
571C8—442no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—224no—
587C22—224no—
588C22—224no—
589C22—442no—
590C22—442no—
591C22—442no—
592C22—442no—
593C22#1062308111yescharacteristic
594C22#1062308211yescharacteristic
595C22C2×D8×D1111yescharacteristic
596C22C2×#6696411yescharacteristic
597C22#1062330111yescharacteristic
598C22#1062330211yescharacteristic
599C22C2×#6699011yescharacteristic
600C4—22no—
601C4—42no—
602C4—81no—
603C4—444no—
604C4—442no—
605C4—882no—
606C4#1062276914yes—
607C4#1062308311yescharacteristic
608C4#1062308411yescharacteristic
609C4#1062332211yescharacteristic
610C4#1062336411yescharacteristic
611C2—82no—
612C2—82no—
613C2—444no—
614C2#1307196111yescharacteristic
615C2C2×#1062276911yescharacteristic
616C2#1307792711yescharacteristic
617C2#1308043111yescharacteristic
618C2#1308092311yescharacteristic
619C2#1308096511yescharacteristic
620C2#1308121311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11#24116
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×#10623082C2semidirect
2. C2×#10622620C2semidirect
3. #13073529C2semidirect
4. #13069796C2semidirect
5. #13069611C2semidirect
6. #13069577C2semidirect
7. #13069410C2semidirect
8. #13068930C2semidirect
9. #13068802C2semidirect
10. #13068616C2semidirect
11. C2×C4×C11×D8C2semidirect
66. C4×D4×C11D4semidirect
96. #66922D4semidirect
123. C2×D4×C11#41semidirect
147. C2×D44D8semidirect
166. C2×C8×C11#41semidirect
193. C2×C4×D8D11semidirect
378. C4×D4C22⋊D11semidirect
444. C2×D4#4339semidirect
478. C2×C8#4339semidirect
500. C11#24116semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226202
#130735292
#130697962
#130696112
#130695772
#130694102
#130689302
#130688022
#130686162
C2×C4×C11×D82
#2411611