Finite Group Databasebeta

← #14727389

Subgroups — #14727389

Order 2816.

1068 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
1#13078536C211yesmaximal, characteristic, complemented
2C2×#10622646C211yesmaximal, characteristic, complemented
3#13073109C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067602C214yesmaximal, complemented
6#13067132C211yesmaximal, characteristic, complemented
7#13067107C211yesmaximal, characteristic, complemented
8#13066976C211yesmaximal, characteristic, complemented
9C11×#3537C211yesmaximal, characteristic
10C11×#560—22no—
11C11×#553—21no—
12C11×#553—21no—
13D42×C11—22no—
14D42×C11—21no—
15D42×C11—21no—
16C11×#540—21no—
17C11×#538—21no—
18C11×#538C2212yes—
19C11×#535—21no—
20C11×#534—21no—
21C11×#534C2212yes—
22C11×#525C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic, complemented
26#10622845—21no—
27#10622834—21no—
28#10622833—22no—
29C2×#66896—21no—
30C4×C22⋊Dic11C2211yescharacteristic, complemented
31#10622820C2211yescharacteristic, complemented
32C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
33#10622657—21no—
34#10622656C2212yescomplemented
35#10622647—21no—
36#10622646—22no—
37#10622646C2212yescomplemented
38#10622646C2214yescomplemented
39#10622608—21no—
40#10622590—21no—
41C2×#66871—21no—
42#10622566C2214yescomplemented
43#10622176C2212yescomplemented
44#10622175C2212yescomplemented
45#10622175C2214yescomplemented
46#10622163C2214yescomplemented
47C2×C11×#41D411yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11D412yes—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C11×#127—22no—
58C11×#127—21no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—21no—
62C11×#124—22no—
63C11×#123—22no—
64C11×#123—21no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×C22⋊Q8D411yescharacteristic
69C11×C22⋊Q8C2311yescharacteristic
70C11×#121—22no—
71C11×#121—21no—
72C11×#121—21no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121D412yes—
85C11×#121D411yescharacteristic
86C11×#121C2312yes—
87C11×#121C2311yescharacteristic
88C11×#120—22no—
89C11×#120—22no—
90C11×#120—22no—
91C11×#120—21no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—22no—
101C11×#117—21no—
102C11×#117D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4C2312yes—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—24no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11C2312yes—
115C2×C4×Dic11—21no—
116C2×#4318—21no—
117C22×C11⋊C8—21no—
118#66899—22no—
119#66896—24no—
120#66896—22no—
121C11⋊#95—24no—
122C11⋊#95C2312yes—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)C2312yes—
126C22⋊(C11⋊C8)C2312yes—
127#66872—22no—
128#66871—24no—
129#66871—22no—
130#18264—111nomaximal, Sylow
131C24×C11—22no—
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D412yes—
135C11×#41—42no—
136C2×Q8×C11C2×D411yescharacteristic
137C2×D4×C11—22no—
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—22no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—42no—
153C2×D4×C11—42no—
154C2×D4×C11—44no—
155C2×D4×C11—82no—
156C2×D4×C11—82no—
157C2×D4×C11—84no—
158C2×D4×C11—84no—
159C2×D4×C11C2×D411yescharacteristic
160C2×D4×C11C2×D412yes—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—41no—
176C22×Dic11—41no—
177C22×Dic11—82no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—21no—
202C42×C11—22no—
203C42×C11—21no—
204C22⋊Dic11—42no—
205C22⋊Dic11—84no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—41no—
209C4⋊Dic11—41no—
210C4×Dic11—42no—
211#4318—42no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—42no—
215#3537D1111yescharacteristic
216#3092—111no—
217C2×#480—111no—
218#2504—111no—
219#1612—114no—
220#1607—114no—
221#1507—111no—
222#1501—111no—
223#1471—111no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—21no—
229C23×C11—24no—
230C23×C11—41no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11—82no—
237C23×C11—82no—
238C23×C11—82no—
239C23×C11#12011yescharacteristic
240C23×C11#12011yescharacteristic
241C23×C11C22×D411yescharacteristic
242Q8×C11—41no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—44no—
246D4×C11—42no—
247D4×C11—44no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—81no—
252D4×C11—82no—
253D4×C11—82no—
254D4×C11—81no—
255D4×C11—82no—
256D4×C11—82no—
257D4×C11—82no—
258D4×C11—82no—
259D4×C11—82no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—81no—
274C2×C4×C11—82no—
275C2×C4×C11—82no—
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—44no—
285C2×Dic11—82no—
286C2×Dic11—82no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289#560—22no—
290#553—21no—
291#553—21no—
292D42—22no—
293D42—21no—
294D42—21no—
295#540—21no—
296#538—21no—
297#538C2×D1112yes—
298#535—21no—
299#534—21no—
300#534C2×D1112yes—
301#525C2×D1111yescharacteristic
302C2×#121C2×D1111yescharacteristic
303C2×#121C2×D1111yescharacteristic
304C22×C4⋊C4—111no—
305#484—221no—
306#483—112no—
307#481—221no—
308#480—114no—
309#480—112no—
310#480—222no—
311#428—221no—
312C2×#107—221no—
313#417—221no—
314C2×#102—221no—
315#407—111no—
316C2×C22⋊C8—111no—
317#397—114no—
318#390—221no—
319#386—222no—
320#382—221no—
321C4×C22⋊C4—111no—
322#328—112no—
323#327—112no—
324#327—114no—
325#323—114no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—84no—
344C22×C11—162no—
345C22×C11—164no—
346C22×C11#45512yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11#57612yes—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#45812yes—
358Dic11—82no—
359Dic11—82no—
360C2×#41C22⋊D1111yescharacteristic
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—22no—
365C22×D4C22⋊D1112yes—
366C22×D4C22⋊D1111yescharacteristic
367C22×D4C22⋊D1111yescharacteristic
368C23×C4—221no—
369C23×C4C22×D1111yescharacteristic
370C2×M16—221no—
371C22×C8—221no—
372#127—22no—
373#127—21no—
374#126—22no—
375#126—22no—
376#125—21no—
377#124—22no—
378#123—22no—
379#123—21no—
380#123—22no—
381#123—22no—
382#123—22no—
383C22⋊Q8C22⋊D1111yescharacteristic
384C22⋊Q8C22×D1111yescharacteristic
385#121—22no—
386#121—21no—
387#121—21no—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—22no—
399#121C22⋊D1112yes—
400#121C22⋊D1111yescharacteristic
401#121C22×D1112yes—
402#121C22×D1111yescharacteristic
403#120—22no—
404#120—22no—
405#120—22no—
406#120—21no—
407#120—22no—
408#120—22no—
409#120—22no—
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—22no—
416#117—21no—
417#117C22⋊D1111yescharacteristic
418C2×C4⋊C4—112no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22⋊D1111yescharacteristic
425C2×C4⋊C4C22⋊D1111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—224no—
429C2×C22⋊C4C22×D1112yes—
430C2×C42—221no—
431#107—224no—
432#107—222no—
433#106—222no—
434#103—222no—
435#102—224no—
436#102—222no—
437C22⋊C8—112no—
438C22⋊C8—112no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441#95—112no—
442#95—224no—
443C2×C11—22no—
444C2×C11—22no—
445C2×C11—41no—
446C2×C11—82no—
447C2×C11—82no—
448C2×C11—81no—
449C2×C11#300811yescharacteristic
450C2×C11C2×#45511yescharacteristic
451C2×C11C2×#45811yescharacteristic
452C24—22no—
453C24—21no—
454C24C2×C22⋊D1111yescharacteristic
455C24C2×C22⋊D1112yes—
456#41—42no—
457C2×Q8C2×C22⋊D1111yescharacteristic
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—82no—
477C2×D4—82no—
478C2×D4—84no—
479C2×D4—84no—
480C2×D4C2×C22⋊D1111yescharacteristic
481C2×D4C2×C22⋊D1112yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—441no—
490C22×C4—441no—
491C22×C4—882no—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499M16—442no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—442no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4C2×C22⋊D1111yescharacteristic
515C4⋊C4C2×C22⋊D1112yes—
516C4⋊C4C2×C22⋊D1111yescharacteristic
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—442no—
532C22⋊C4—884no—
533C42—22no—
534C42—21no—
535C42—442no—
536C11#1826411yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—24no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23#6700611yescharacteristic
553C23#6700611yescharacteristic
554C23C22×C22⋊D1111yescharacteristic
555Q8—41no—
556D4—42no—
557D4—41no—
558D4—44no—
559D4—42no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—81no—
565D4—82no—
566D4—82no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—81no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—444no—
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—21no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—84no—
620C22—162no—
621C22—164no—
622C22#1062285512yes—
623C22#1062336612yes—
624C22C2×#6700611yescharacteristic
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—882no—
634C4—882no—
635C4#1062285612yes—
636C2—22no—
637C2—22no—
638C2—41no—
639C2—82no—
640C2—82no—
641C2—81no—
642C2#1307788411yescharacteristic
643C2C2×#1062285511yescharacteristic
644C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3537C2
socleC22×C11C2×#120
hypercenter#3537D11
hypocenterC11#18264
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #13078536C2semidirect
2. C2×#10622646C2semidirect
3. #13073109C2semidirect
4. #13067630C2semidirect
5. #13067602C2semidirect
6. #13067132C2semidirect
7. #13067107C2semidirect
8. #13066976C2semidirect
25. C22×C4⋊Dic11C22semidirect
30. C4×C22⋊Dic11C22semidirect
31. #10622820C22semidirect
32. C2×C22⋊(C11⋊C8)C22semidirect
34. #10622656C22semidirect
37. #10622646C22semidirect
38. #10622646C22semidirect
42. #10622566C22semidirect
43. #10622176C22semidirect
44. #10622175C22semidirect
45. #10622175C22semidirect
46. #10622163C22semidirect
536. C11#18264semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106226462
#130731092
#130676302
#130676022
#130671322
#130671072
#130669762
C11×#35372
#1826411