Finite Group Databasebeta

← #14756855

Subgroups — #14756855

Order 2816.

890 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×#10622639C211yesmaximal, characteristic
2#13071267C211yesmaximal, characteristic, complemented
3#13070976C211yesmaximal, characteristic
4#13069260C211yesmaximal, characteristic, complemented
5#13069253C211yesmaximal, characteristic, complemented
6#13069211C211yesmaximal, characteristic, complemented
7#13069190C211yesmaximal, characteristic, complemented
8#13068947C211yesmaximal, characteristic
9#13068947C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic
11#13068864C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13C4×#66885C211yesmaximal, characteristic
14#13068367C211yesmaximal, characteristic, complemented
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30#10622639C418yescomplemented
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622594—21no—
34#10622594—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42C4×(C2×D11)⋊C4—21no—
43#10622550—21no—
44#10622549—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622545C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48#10622279—21no—
49D11×#95—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11C2×C414yescomplemented
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325C2×C414yes—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66946—22no—
97#66946—22no—
98C4×D44—22no—
99C4×D44C2×C414yes—
100C11×#103—22no—
101C11×#103—22no—
102C4×C8×C11—22no—
103C11×#95—21no—
104#66899C2×C414yescomplemented
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885—22no—
119#66885—22no—
120#66873C2×C414yes—
121#66872—22no—
122#66871—22no—
123#66871C2×C414yescomplemented
124#66867C2×C414yescomplemented
125#21125—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44C22×C412yes—
151C2×D44#4112yes—
152C2×D44#4112yes—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—81no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4#4112yes—
174C11×C4⋊C4#4112yes—
175C42×C11—24no—
176C42×C11—81no—
177C42×C11C22×C412yes—
178C42×C11#4112yes—
179#4325—28no—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—24no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—81no—
189C4⋊Dic11—81no—
190C4⋊Dic11C22×C412yes—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×#440—111no—
205#2320—111no—
206#2275—111no—
207#1928—111no—
208#1927—111no—
209#1921—111no—
210#1918—111no—
211#1877—111no—
212#1877—111no—
213#1864—111no—
214#1862—111no—
215#1776—111no—
216C4×#103D1111yescharacteristic, complemented
217C4×#102—111no—
218#1746—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C4×D412yes—
248C2×C4×C11C4×D412yes—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276D44—22no—
277D44—22no—
278D44—22no—
279D44#11714yes—
280C4×D11—84no—
281C4×D11—84no—
282C4×D11—84no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—22no—
287C22×SD16—111no—
288C2×C4×Q8C2×D1111yescharacteristic
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C2×C4×D4—111no—
292#440—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#103—111no—
297C2×#103C2×D1111yescharacteristic
298C2×#103C2×D1111yescharacteristic
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#97—111no—
303C2×C4×C8C2×D1111yescharacteristic
304#391—111no—
305#391—111no—
306#389—111no—
307#389—111no—
308#387—221no—
309#387—221no—
310#383—221no—
311#382—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4C2×D1111yescharacteristic
316C4×C22⋊C4—221no—
317C4×C22⋊C4—221no—
318C4×C22⋊C4—221no—
319#376—111no—
320C2×#95—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340C2×D1111yescharacteristic
326#340C2×D1111yescharacteristic
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331C22×C11C2×C4×D411yescharacteristic
332C22×C11#52511yescharacteristic
333C22×C11#52511yescharacteristic
334C22×C11#57611yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57711yescharacteristic
337C22×C11#57811yescharacteristic
338C2×D11—24no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11C2×#11711yescharacteristic
352C4×C11C4×#4111yescharacteristic
353C4×C11#52911yescharacteristic
354C4×C11#52911yescharacteristic
355Dic11—41no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8C22×D1111yescharacteristic
363C22×D4—111no—
364C23×C4—221no—
365C23×C4—221no—
366C23×C4—221no—
367C2×SD16—114no—
368C2×SD16—222no—
369C2×SD16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4×Q8—22no—
375C4×Q8C4×D1114yescomplemented
376C4×D4—114no—
377C4×D4—222no—
378C4×D4—222no—
379C4×D4—222no—
380C4×D4—222no—
381C4×D4—222no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—114no—
403#107—222no—
404#106—222no—
405#103—22no—
406#103—22no—
407#103—114no—
408#102—114no—
409#102—222no—
410#102—222no—
411#97—114no—
412C4×C8—22no—
413#95—21no—
414#95—111no—
415#95—111no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11#229011yescharacteristic
428C2×C11#294611yescharacteristic
429C2×C11#294711yescharacteristic
430C2×C11#311811yescharacteristic
431C2×C11#312011yescharacteristic
432C2×C11#312311yescharacteristic
433C2×C11#312411yescharacteristic
434D11—44no—
435C24—221no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1112yes—
442C2×D4—112no—
443C2×D4—112no—
444C2×D4—112no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—221no—
459C22×C4—224no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4—881no—
465C22×C4—881no—
466C22×C4—881no—
467C22×C4—881no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—228no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—112no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4C2×C4×D1112yes—
497C4⋊C4#433912yes—
498C4⋊C4#433912yes—
499C22⋊C4—224no—
500C22⋊C4—224no—
501C22⋊C4—224no—
502C42—24no—
503C42—81no—
504C42—221no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—881no—
509C42—881no—
510C42—881no—
511C42C2×C4×D1112yes—
512C42#434112yes—
513C11#2112511yescharacteristic, complemented, Sylow
514C23—222no—
515C23—222no—
516C23—222no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23C2×D4×D1111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—114no—
527D4—222no—
528D4—222no—
529D4—222no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—884no—
568C2×C4—884no—
569C2×C4—884no—
570C2×C4(C22⋊D11)⋊C412yes—
571C2×C4(C22⋊D11)⋊C412yes—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#433911yescharacteristic
575C2×C4C2×#434111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C8—41no—
579C8—41no—
580C8—222no—
581C8—222no—
582C22—224no—
583C22—442no—
584C22—442no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—442no—
589C22C2×(C22⋊D11)⋊C411yescharacteristic
590C22#1062307811yescharacteristic
591C22#1062307811yescharacteristic
592C22#1062329311yescharacteristic
593C22#1062329711yescharacteristic
594C22#1062330011yescharacteristic
595C22#1062330111yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—441no—
603C4—441no—
604C4—441no—
605C4—441no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4C4×#433911yescharacteristic
610C4D11×#11711yescharacteristic
611C4#1062308811yescharacteristic
612C4#1062308811yescharacteristic
613C2—444no—
614C2#1307106211yescharacteristic
615C2#1307745111yescharacteristic
616C2#1307745311yescharacteristic
617C2#1307880611yescharacteristic
618C2#1307883611yescharacteristic
619C2#1307886511yescharacteristic
620C2#1307888411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11#21125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. #13071267C2semidirect
4. #13069260C2semidirect
5. #13069253C2semidirect
6. #13069211C2semidirect
7. #13069190C2semidirect
12. #13068514C2semidirect
14. #13068367C2semidirect
15. C4×C11×#103C2semidirect
30. #10622639C4semidirect
68. C4×Q8×C11C2×C4semidirect
104. #66899C2×C4semidirect
123. #66871C2×C4semidirect
124. #66867C2×C4semidirect
216. C4×#103D11semidirect
375. C4×Q8C4×D11semidirect
513. C11#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#106226392
#130712672
#130709762
#130692602
#130692532
#130692112
#130691902
#130689472
#130688782
#130688642
#130685142
C4×#668852
#130683672
C4×C11×#1032
#2112511