Finite Group Databasebeta

← #14726788

Subgroups — #14726788

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622657C211yesmaximal, characteristic, complemented
2C2×#10622647C211yesmaximal, characteristic, complemented
3#13072933C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067647C214yesmaximal, complemented
6#13067188C211yesmaximal, characteristic, complemented
7#13067184C211yesmaximal, characteristic, complemented
8#13066934C211yesmaximal, characteristic, complemented
9C11×#3505C211yesmaximal, characteristic
10C11×#553—22no—
11C11×#553—21no—
12C11×#552—21no—
13C11×#551—22no—
14C11×#548—21no—
15C11×#546—21no—
16C11×#539C2212yes—
17C11×#538C2212yes—
18C11×#534—21no—
19C11×#529—21no—
20C11×#525—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C2×#66899—21no—
27#10622833—21no—
28C2×#66896—21no—
29#10622825—21no—
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622657—22no—
34#10622657C2214yescomplemented
35#10622647—22no—
36#10622647C2214yes—
37#10622599C2212yescomplemented
38C2×#66872—21no—
39C2×#66871—21no—
40#10622562C2212yescomplemented
41#10622559—21no—
42#10622541—21no—
43#10622176C2214yescomplemented
44#10622175C2214yes—
45#10622166C2212yescomplemented
46#10622163C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C11×#126—22no—
56C11×#126—22no—
57C11×#126—22no—
58C11×#125—21no—
59C11×#125—22no—
60C11×#124—21no—
61C11×#124—22no—
62C11×#123—22no—
63C11×#123—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yes—
72C11×C22⋊Q8C2312yes—
73C11×#121—21no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121D412yes—
80C11×#121C2312yes—
81C11×#120—22no—
82C11×#120—22no—
83C4×Q8×C11—21no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C11×#117—22no—
95C11×#117—21no—
96C11×#117—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C11×C22⋊C4C2311yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—22no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4—22no—
117C22×C11⋊C8—21no—
118C22×C11⋊C8—21no—
119#66899—24no—
120#66896—24no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95C2312yes—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)C2312yes—
127C22⋊(C11⋊C8)C2312yes—
128#66872—24no—
129#66871—24no—
130#18207—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C24×C11C2×D411yescharacteristic
134C11×#41—82no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—41no—
172C22×Dic11—41no—
173C22×Dic11—82no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11—21no—
203C42×C11—21no—
204C22⋊Dic11—42no—
205C22⋊Dic11—82no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—42no—
209C4⋊Dic11—41no—
210C4⋊Dic11—41no—
211Dic11⋊C4—82no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—42no—
215C2×C11⋊C8—42no—
216#3505D1111yescharacteristic
217C2×#484—111no—
218C2×#481—111no—
219#2487—111no—
220#1618—114no—
221#1615—114no—
222#1520—111no—
223#1519—111no—
224#1459—111no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11#12011yescharacteristic
237C23×C11#12011yescharacteristic
238C23×C11#13512yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—42no—
242Q8×C11—42no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—44no—
249D4×C11—42no—
250D4×C11—82no—
251D4×C11—82no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—81no—
271C2×C4×C11—81no—
272C2×C4×C11—81no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—82no—
286C2×Dic11—82no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289#553—22no—
290#553—21no—
291#552—21no—
292#551—22no—
293#548—21no—
294#546—21no—
295#539C2×D1112yes—
296#538C2×D1112yes—
297#534—21no—
298#529—21no—
299#525—21no—
300C2×C22⋊Q8C2×D1111yescharacteristic
301C2×#121C2×D1111yescharacteristic
302#518—21no—
303C2×C4×D4C2×D1111yescharacteristic
304C22×C4⋊C4—111no—
305#484—114no—
306#484—222no—
307#481—114no—
308#481—222no—
309C2×#107—221no—
310C2×#106—221no—
311C2×#103—221no—
312C2×#102—221no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315#400—112no—
316#399—112no—
317#389—221no—
318#386—221no—
319#385—221no—
320#380—111no—
321#380—221no—
322#328—114no—
323#327—114no—
324#324—112no—
325#323—112no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—81no—
342C22×C11—162no—
343C22×C11#45212yes—
344C22×C11#45212yes—
345C22×C11C2×#12011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11#45812yes—
358Dic11—82no—
359Dic11—82no—
360C2×#41—21no—
361C22×Q8C22⋊D1111yescharacteristic
362C22×D4—21no—
363C22×D4C22⋊D1111yescharacteristic
364C22×D4C22⋊D1111yescharacteristic
365C23×C4—221no—
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C22×C8—221no—
369C22×C8—221no—
370#126—22no—
371#126—22no—
372#126—22no—
373#125—21no—
374#125—22no—
375#124—21no—
376#124—22no—
377#123—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8C22⋊D1112yes—
387C22⋊Q8C22×D1112yes—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121C22⋊D1112yes—
395#121C22×D1112yes—
396#120—22no—
397#120—22no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—22no—
409#117—22no—
410#117—21no—
411#117—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4C22⋊D1111yescharacteristic
422C2×C4⋊C4C22⋊D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4C22⋊D1111yescharacteristic
430C2×C22⋊C4C22×D1111yescharacteristic
431C2×C42C22⋊D1111yescharacteristic
432#107—224no—
433#106—224no—
434#103—224no—
435#102—224no—
436C22⋊C8—112no—
437C22⋊C8—112no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440#95—112no—
441#95—222no—
442#95—222no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—22no—
446C2×C11—22no—
447C2×C11—81no—
448C2×C11—82no—
449C2×C11C2×#45211yescharacteristic
450C2×C11#302111yescharacteristic
451C2×C11C2×#45811yescharacteristic
452C24—21no—
453C24C2×C22⋊D1111yescharacteristic
454C24C2×C22⋊D1111yescharacteristic
455#41—82no—
456C2×Q8—21no—
457C2×Q8—42no—
458C2×Q8C2×C22⋊D1112yes—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4C2×C22⋊D1112yes—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—441no—
484C22×C4—441no—
485C22×C4—882no—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—442no—
498C2×C8—442no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—442no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4—882no—
515C4⋊C4C2×C22⋊D1112yes—
516C4⋊C4C2×C22⋊D1112yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—442no—
532C22⋊C4—882no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C11#1820711yescharacteristic, complemented, Sylow
538C23—21no—
539C23—21no—
540C23—22no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23#6700312yes—
550C23#6700412yes—
551C23#6700611yescharacteristic
552C23#6700611yescharacteristic
553C23C22×C22⋊D1111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—82no—
564D4—82no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—882no—
595C2×C4—882no—
596C2×C4#6700611yescharacteristic
597C2×C4#6700611yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—442no—
601C8—442no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—81no—
618C22—162no—
619C22#1062285212yes—
620C22#1062285212yes—
621C22C2×#6700311yescharacteristic
622C22C2×#6700411yescharacteristic
623C22C2×#6700611yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—882no—
634C4—882no—
635C4#1062285612yes—
636C2—21no—
637C2—21no—
638C2—22no—
639C2—22no—
640C2—81no—
641C2—82no—
642C2C2×#1062285211yescharacteristic
643C2#1307798811yescharacteristic
644C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3505C2
socleC22×C11C2×#120
hypercenter#3505D11
hypocenterC11#18207
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×#10622657C2semidirect
2. C2×#10622647C2semidirect
3. #13072933C2semidirect
4. #13067664C2semidirect
5. #13067647C2semidirect
6. #13067188C2semidirect
7. #13067184C2semidirect
8. #13066934C2semidirect
34. #10622657C22semidirect
37. #10622599C22semidirect
40. #10622562C22semidirect
43. #10622176C22semidirect
45. #10622166C22semidirect
46. #10622163C22semidirect
537. C11#18207semidirect

Maximal subgroups

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

subgroupindex
C2×#106226572
C2×#106226472
#130729332
#130676642
#130676472
#130671882
#130671842
#130669342
C11×#35052
#1820711