Finite Group Databasebeta

← #14726779

Subgroups — #14726779

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C211yesmaximal, characteristic, complemented
2C2×#10622646C211yesmaximal, characteristic, complemented
3#13072924C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067613C214yesmaximal, 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
25C2×#66988—21no—
26C22×C4⋊Dic11C2211yescharacteristic
27C2×#66899—21no—
28C2×#66896—21no—
29#10622825—21no—
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622656—22no—
34#10622656C2214yescomplemented
35#10622646—22no—
36#10622646C2214yes—
37#10622596C2212yescomplemented
38C2×#66872—21no—
39C2×#66871—21no—
40#10622566C2212yescomplemented
41#10622556—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—
109#66988—44no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2312yes—
117C2×Dic11⋊C4—22no—
118C22×C11⋊C8—21no—
119C22×C11⋊C8—21no—
120#66899—24no—
121#66896—24no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95C2312yes—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)C2312yes—
128C22⋊(C11⋊C8)C2312yes—
129#66872—24no—
130#66871—24no—
131#18206—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C11×#41—82no—
136C2×Q8×C11—21no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
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×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—41no—
173C22×Dic11—41no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2×D412yes—
187C11×C4⋊C4C2×D412yes—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—44no—
207C22⋊Dic11—42no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—42no—
211C4⋊Dic11—41no—
212C4⋊Dic11—41no—
213Dic11⋊C4—44no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8—42no—
218#3505D1111yescharacteristic
219C2×#483—111no—
220C2×#480—111no—
221#2486—111no—
222#1612—114no—
223#1609—114no—
224#1520—111no—
225#1519—111no—
226#1459—111no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—81no—
237C23×C11—81no—
238C23×C11#12011yescharacteristic
239C23×C11#12011yescharacteristic
240C23×C11#13512yes—
241C23×C11AGL(1,ℤ/8)12yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—42no—
244Q8×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—44no—
251D4×C11—42no—
252D4×C11—82no—
253D4×C11—82no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—81no—
273C2×C4×C11—81no—
274C2×C4×C11—81no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—82no—
288C2×Dic11—82no—
289C11⋊C8—42no—
290C11⋊C8—42no—
291#553—22no—
292#553—21no—
293#552—21no—
294#551—22no—
295#548—21no—
296#546—21no—
297#539C2×D1112yes—
298#538C2×D1112yes—
299#534—21no—
300#529—21no—
301#525—21no—
302C2×#123—221no—
303C2×C22⋊Q8C2×D1111yescharacteristic
304C2×#121C2×D1111yescharacteristic
305#518—21no—
306C2×C4×D4C2×D1111yescharacteristic
307C22×C4⋊C4—111no—
308#483—114no—
309#483—222no—
310#480—114no—
311#480—222no—
312C2×#107—221no—
313C2×#106—221no—
314C2×#103—221no—
315C2×#102—221no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318#398—112no—
319#397—112no—
320#389—221no—
321#381—221no—
322#380—111no—
323#380—221no—
324#328—114no—
325#327—114no—
326#324—112no—
327#323—112no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—162no—
345C22×C11#44912yes—
346C22×C11#44912yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11#45812yes—
360Dic11—82no—
361Dic11—82no—
362C2×#41—21no—
363C22×Q8C22⋊D1111yescharacteristic
364C22×D4—21no—
365C22×D4C22⋊D1111yescharacteristic
366C22×D4C22⋊D1111yescharacteristic
367C23×C4—221no—
368C23×C4C22⋊D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C22×C8—221no—
371C22×C8—221no—
372#126—22no—
373#126—22no—
374#126—22no—
375#125—21no—
376#125—22no—
377#124—21no—
378#124—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—444no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8C22⋊D1112yes—
390C22⋊Q8C22×D1112yes—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121—21no—
397#121C22⋊D1112yes—
398#121C22×D1112yes—
399#120—22no—
400#120—22no—
401C4×Q8—21no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—22no—
412#117—22no—
413#117—21no—
414#117—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—222no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22⋊D1111yescharacteristic
425C2×C4⋊C4C22⋊D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4C22⋊D1111yescharacteristic
433C2×C22⋊C4C22×D1111yescharacteristic
434C2×C42C22⋊D1111yescharacteristic
435#107—224no—
436#106—224no—
437#103—224no—
438#102—224no—
439C22⋊C8—112no—
440C22⋊C8—112no—
441C22⋊C8—221no—
442C22⋊C8—221no—
443#95—112no—
444#95—222no—
445#95—222no—
446C2×C11—21no—
447C2×C11—21no—
448C2×C11—22no—
449C2×C11—22no—
450C2×C11—81no—
451C2×C11—82no—
452C2×C11C2×#44911yescharacteristic
453C2×C11#302211yescharacteristic
454C2×C11C2×#45811yescharacteristic
455C24—21no—
456C24C2×C22⋊D1111yescharacteristic
457C24C2×C22⋊D1111yescharacteristic
458#41—82no—
459C2×Q8—21no—
460C2×Q8—42no—
461C2×Q8C2×C22⋊D1112yes—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4C2×C22⋊D1112yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—441no—
489C22×C4—441no—
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—442no—
502C2×C8—442no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—444no—
516C4⋊C4—442no—
517C4⋊C4—441no—
518C4⋊C4—441no—
519C4⋊C4C2×C22⋊D1112yes—
520C4⋊C4C2×C22⋊D1112yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—444no—
536C22⋊C4—442no—
537C42—22no—
538C42—22no—
539C42—21no—
540C42—21no—
541C11#1820611yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—22no—
545C23—21no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—42no—
551C23—81no—
552C23—81no—
553C23#6700212yes—
554C23#6700312yes—
555C23#6700611yescharacteristic
556C23#6700611yescharacteristic
557C23C22×C22⋊D1111yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—44no—
566D4—42no—
567D4—82no—
568D4—82no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—81no—
588C2×C4—81no—
589C2×C4—81no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—882no—
599C2×C4—882no—
600C2×C4#6700611yescharacteristic
601C2×C4#6700611yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C2×C4C22×C22⋊D1111yescharacteristic
604C8—442no—
605C8—442no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—81no—
622C22—162no—
623C22#1062285112yes—
624C22#1062285112yes—
625C22C2×#6700211yescharacteristic
626C22C2×#6700311yescharacteristic
627C22C2×#6700611yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—882no—
638C4—882no—
639C4#1062285612yes—
640C2—21no—
641C2—21no—
642C2—22no—
643C2—22no—
644C2—81no—
645C2—82no—
646C2C2×#1062285111yescharacteristic
647C2#1307799511yescharacteristic
648C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3505C2
socleC22×C11C2×#120
hypercenter#3505D11
hypocenterC11#18206
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×#10622656C2semidirect
2. C2×#10622646C2semidirect
3. #13072924C2semidirect
4. #13067630C2semidirect
5. #13067613C2semidirect
6. #13067188C2semidirect
7. #13067184C2semidirect
8. #13066934C2semidirect
34. #10622656C22semidirect
37. #10622596C22semidirect
40. #10622566C22semidirect
43. #10622176C22semidirect
45. #10622166C22semidirect
46. #10622163C22semidirect
541. C11#18206semidirect

Maximal subgroups

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

subgroupindex
C2×#106226562
C2×#106226462
#130729242
#130676302
#130676132
#130671882
#130671842
#130669342
C11×#35052
#1820611