Finite Group Databasebeta

← #14775859

Subgroups — #14775859

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078402C211yesmaximal, characteristic
2#13077562C211yesmaximal, characteristic, complemented
3#13077183C211yesmaximal, characteristic
4#13069595C211yesmaximal, characteristic, complemented
5#13069388C211yesmaximal, characteristic, complemented
6#13069368C211yesmaximal, characteristic, complemented
7#13069217C211yesmaximal, characteristic, complemented
8#13069212C211yesmaximal, characteristic, complemented
9#13068890C211yesmaximal, characteristic
10#13068888C211yesmaximal, characteristic
11#13068474C211yesmaximal, characteristic, complemented
12#13068457C211yesmaximal, characteristic
13#13068453C211yesmaximal, characteristic
14#13068425C211yesmaximal, characteristic
15C11×#1945C211yesmaximal, characteristic, complemented
16C2×#66960C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623053C2211yescharacteristic
19#10623048C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C11×#424C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66889C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622732C2211yescharacteristic
28#10622731C2211yescharacteristic
29M16×Dic11C2211yescharacteristic
30#10622726C2211yescharacteristic
31#10622714C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622615C2211yescharacteristic
35#10622612C2211yescharacteristic
36#10622611C2211yescharacteristic
37#10622610C2211yescharacteristic
38#10622545C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41#10622504C411yescharacteristic, complemented
42#10622503C411yescharacteristic, complemented
43#10622490C411yescharacteristic, complemented
44#10622488C411yescharacteristic, complemented
45#10622484C411yescharacteristic, complemented
46#10622483C411yescharacteristic, complemented
47#10622470C411yescharacteristic, complemented
48#10622467C411yescharacteristic, complemented
49#10622452—21no—
50#10622452—21no—
51#10622450—21no—
52D11×C4⋊C8—21no—
53#10622444—21no—
54#10622443—21no—
55#10622441—21no—
56#10622441—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75#66979C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66960—22no—
83#66960—41no—
84#66954—22no—
85#66954—41no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90#66946C2×C411yescharacteristic
91#66946C2×C411yescharacteristic
92#66943C2×C411yescharacteristic
93#66943C2×C411yescharacteristic
94#66941C2×C411yescharacteristic
95#66941C2×C411yescharacteristic
96#66940C2×C411yescharacteristic
97#66940C2×C411yescharacteristic
98(C22⋊D11)⋊C4—21no—
99(C22⋊D11)⋊C4—21no—
100#66931—21no—
101#66931—21no—
102#66925—21no—
103C42×D11—21no—
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×#108—41no—
107C11×#107C2×C411yescharacteristic
108C11×#107C2×C411yescharacteristic
109C11×#106C2×C411yescharacteristic
110C11×#106C2×C411yescharacteristic
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8—21no—
115C4×C8×C11—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66889—22no—
119#66886—41no—
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8C2×C411yescharacteristic
132Dic11⋊C8C2×C411yescharacteristic
133Dic11⋊C8C2×C411yescharacteristic
134Dic11⋊C8D411yescharacteristic
135Dic11⋊C8D411yescharacteristic
136Dic11⋊C8D411yescharacteristic
137Dic11⋊C8D411yescharacteristic
138C8×Dic11—21no—
139C8×Dic11—21no—
140#66874C2×C411yescharacteristic
141#66874C2×C411yescharacteristic
142#66873C2×C411yescharacteristic
143#66873C2×C411yescharacteristic
144#66872C2×C411yescharacteristic
145#66872C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148#66869Q814yescomplemented
149C4⋊(C11⋊C8)—21no—
150C4⋊(C11⋊C8)—21no—
151#66867—21no—
152#66867—41no—
153C4×C11⋊C8—21no—
154#22984—111nomaximal, Sylow
155C22×C4×C11—21no—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C22×Dic11—21no—
159C22×Dic11#4111yescharacteristic
160C22×Dic11#4111yescharacteristic
161#4339—21no—
162#4339—21no—
163#4339C2×Q812yes—
164#4339#4112yes—
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C411yescharacteristic
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C22×C411yescharacteristic
183C2×C8×C11C22×C411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C2×Q812yes—
196C22⋊Dic11—21no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11C22×C411yescharacteristic
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C2×D411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318C2×Q812yes—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8C22×C411yescharacteristic
229C2×C11⋊C8C22×C411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×D411yescharacteristic
232#4313—42no—
233#4313—42no—
234C8×D11—42no—
235C8×D11—42no—
236#3076—111no—
237#2962—111no—
238#2906—111no—
239#1995—111no—
240#1950—111no—
241#1946—111no—
242#1945D1111yescharacteristic, complemented
243#1922—111no—
244#1922—111no—
245#1866—111no—
246#1866—111no—
247#1768—111no—
248#1765—111no—
249#1764—111no—
250#1759—111no—
251C23×C11C2×#4111yescharacteristic
252C22×D11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×Q811yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C22⋊D11—22no—
267C22⋊D11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11C4×D411yescharacteristic
277C2×Dic11C4×D411yescharacteristic
278C2×Dic11C4×D411yescharacteristic
279C2×Dic11C4×D411yescharacteristic
280D44—21no—
281D44C4×Q812yes—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—42no—
285C4×D11—81no—
286Dic22—21no—
287Dic22—42no—
288Dic22—81no—
289Dic22C4×Q812yes—
290C8×C11—21no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—41no—
295C8×C11—41no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131—111no—
304#533—111no—
305C4×#41—111no—
306#479—111no—
307#479—111no—
308#478—111no—
309#478—111no—
310#477—111no—
311#476—111no—
312#475—111no—
313#474—111no—
314#446—221no—
315#446—221no—
316#446—221no—
317C8×Q8—221no—
318C2×#108—111no—
319C2×#108C2×D1111yescharacteristic
320#427—111no—
321#427C2×D1111yescharacteristic
322#424—111no—
323#424—111no—
324#424—221no—
325#424—221no—
326#424C2×D1111yescharacteristic
327#424C2×D1111yescharacteristic
328#423—111no—
329#423—221no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—221no—
333C2×#104—111no—
334C2×#104—111no—
335#416—111no—
336#416—111no—
337#405—111no—
338#405—111no—
339C4×M16—111no—
340C2×#97—111no—
341C2×C4×C8C2×D1111yescharacteristic
342#376—111no—
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339C2×D1111yescharacteristic
350#339C2×D1111yescharacteristic
351#336—111no—
352#336—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11C2×C4×D411yescharacteristic
356C22×C11#55211yescharacteristic
357C22×C11#55411yescharacteristic
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C2×C4×Q811yescharacteristic
367C4×C11#52011yescharacteristic
368C4×C11#54611yescharacteristic
369C4×C11D4×Q811yescharacteristic
370Dic11—22no—
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—21no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378C2×#41—111no—
379#131—222no—
380#131—222no—
381#131—441no—
382#131—441no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16C22×D1111yescharacteristic
388C2×M16C22×D1111yescharacteristic
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—221no—
392C22×C8—221no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8—111no—
396C4⋊Q8—111no—
397#125—111no—
398#125—111no—
399C22⋊Q8—221no—
400C22⋊Q8—221no—
401C4×Q8—111no—
402C4×Q8—111no—
403C4×Q8—221no—
404C4×Q8—221no—
405C4×D4—111no—
406C4×D4—111no—
407C4×D4—221no—
408C4×D4—221no—
409#117—111no—
410#117—221no—
411#117C22×D1111yescharacteristic
412#117C22×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#108—41no—
418#108—441no—
419#107—111no—
420#107—111no—
421#107C4×D1111yescharacteristic
422#107C4×D1111yescharacteristic
423#106—111no—
424#106—111no—
425#106C4×D1111yescharacteristic
426#106C4×D1111yescharacteristic
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
435C4⋊C8—111no—
436C4⋊C8—111no—
437C4⋊C8—111no—
438C4⋊C8—111no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8—221no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445#104—114no—
446#104—222no—
447#103—111no—
448#103—111no—
449#103—111no—
450#103—111no—
451#102—111no—
452#102—111no—
453#102—111no—
454#102—111no—
455#97—221no—
456#97—221no—
457#97—221no—
458#97—441no—
459C4×C8—41no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—221no—
463#95—221no—
464#95—221no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11#236011yescharacteristic
468C2×C11#295511yescharacteristic
469C2×C11#295711yescharacteristic
470D11—42no—
471#41—112no—
472#41—112no—
473#41—221no—
474#41—221no—
475C2×Q8—111no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×D4—111no—
479C2×D4—221no—
480C22×C4—21no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4C23×D1111yescharacteristic
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—112no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—442no—
497M16—442no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—442no—
515C2×C8—442no—
516C2×C8C2×C4×D1111yescharacteristic
517C2×C8C2×C4×D1111yescharacteristic
518C2×C8D4×D1111yescharacteristic
519C2×C8D4×D1111yescharacteristic
520C4⋊C4—111no—
521C4⋊C4—111no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4C2×C4×D1111yescharacteristic
531C4⋊C4C2×C4×D1111yescharacteristic
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42Q8×D1112yes—
552C11#2298411yescharacteristic, complemented, Sylow
553C23—221no—
554C23#41×D1111yescharacteristic
555Q8—112no—
556Q8—221no—
557Q8—442no—
558Q8—881no—
559D4—112no—
560D4—222no—
561D4—222no—
562D4—221no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—111no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—111no—
574C2×C4—221no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—442no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—881no—
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4#6703711yescharacteristic
589C2×C4C2×Q8×D1111yescharacteristic
590C2×C4#6704011yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—222no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—222no—
607C22—441no—
608C22—441no—
609C22C4×D4×D1111yescharacteristic
610C22#1062316711yescharacteristic
611C22#1062322411yescharacteristic
612C4—42no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—222no—
618C4—221no—
619C4—221no—
620C4—221no—
621C4—221no—
622C4—441no—
623C4—441no—
624C4—881no—
625C4#1062303511yescharacteristic
626C4C4×Q8×D1111yescharacteristic
627C4#1062314111yescharacteristic
628C4#1062325811yescharacteristic
629C2—21no—
630C2—21no—
631C2—442no—
632C2#1307161811yescharacteristic
633C2#1307751411yescharacteristic
634C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1945C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1945D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #13077562C2semidirect
4. #13069595C2semidirect
5. #13069388C2semidirect
6. #13069368C2semidirect
7. #13069217C2semidirect
8. #13069212C2semidirect
11. #13068474C2semidirect
15. C11×#1945C2semidirect
41. #10622504C4semidirect
42. #10622503C4semidirect
43. #10622490C4semidirect
44. #10622488C4semidirect
45. #10622484C4semidirect
46. #10622483C4semidirect
47. #10622470C4semidirect
48. #10622467C4semidirect
148. #66869Q8semidirect
242. #1945D11semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130784022
#130775622
#130771832
#130695952
#130693882
#130693682
#130692172
#130692122
#130688902
#130688882
#130684742
#130684572
#130684532
#130684252
C11×#19452
#2298411