Finite Group Databasebeta

← #14823570

Subgroups — #14823570

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622402C211yesmaximal, characteristic
2#13072451C211yesmaximal, characteristic
3#13072388C211yesmaximal, characteristic
4#13069993C211yesmaximal, characteristic
5#13069946C211yesmaximal, characteristic
6#13069937C211yesmaximal, characteristic
7#13069716C211yesmaximal, characteristic
8#13069484C211yesmaximal, characteristic
9#13069308C211yesmaximal, characteristic
10#13069303C211yesmaximal, characteristic
11#13069292C211yesmaximal, characteristic
12#13068954C211yesmaximal, characteristic
13#13068882C211yesmaximal, characteristic
14#13068490C211yesmaximal, characteristic
15C2×C11×#487C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C11×#487—24no—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622843—21no—
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32#10622842—21no—
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622599—21no—
41#10622598C2211yescharacteristic
42#10622597—21no—
43#10622596—21no—
44#10622591—21no—
45#10622591—21no—
46#10622591—21no—
47#10622587C2211yescharacteristic
48#10622586C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C4×Dic11⋊C4C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622402—24no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C11×C4⋊Q8—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—41no—
79C2×#4326—22no—
80C2×#4326—22no—
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—41no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66940—22no—
102#66940—41no—
103C11×#103—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#103D414yes—
107C4×C8×C11—22no—
108#66899—22no—
109#66899—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66880—22no—
126#66880—22no—
127#66879—22no—
128#66879—22no—
129Dic11⋊C8—22no—
130#66872—22no—
131#66872—41no—
132#26838—111nomaximal, Sylow
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C2×Q8×C11—81no—
147C2×Q8×C11C2×D412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C2×D412yes—
182C42×C11—21no—
183C42×C11—21no—
184#4326—28no—
185#4326—44no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11—81no—
194Dic11⋊C4—22no—
195Dic11⋊C4—22no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8#4112yes—
210C2×C11⋊C8#4112yes—
211C2×#487D1111yescharacteristic
212C2×#441—111no—
213#2451—111no—
214#2446—111no—
215#2066—111no—
216#2058—111no—
217#2056—111no—
218#2016—111no—
219#1971—111no—
220#1935—111no—
221#1935—111no—
222#1933—111no—
223#1878—111no—
224#1865—111no—
225#1771—111no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#13712yes—
253C2×C4×C11#13712yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288C8×C11—22no—
289C8×C11—41no—
290C11⋊C8—22no—
291C11⋊C8—22no—
292C22×Q16—111no—
293C22×Q16—111no—
294C2×C4⋊Q8C2×D1111yescharacteristic
295C2×C4⋊Q8C2×D1111yescharacteristic
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298#487—24no—
299#441—224no—
300C2×#106—111no—
301C2×#106—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×#103C2×D1111yescharacteristic
311C2×#97—111no—
312C2×#97—111no—
313C2×C4×C8C2×D1111yescharacteristic
314#400—221no—
315#398—221no—
316#398—221no—
317#395—221no—
318#391—111no—
319#391—111no—
320#391—111no—
321#391—111no—
322#391—111no—
323#391—221no—
324#389—111no—
325#389—111no—
326#389—111no—
327#387—221no—
328#387—221no—
329#387—221no—
330C4×C4⋊C4—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336—111no—
336#336—111no—
337C22×C11#53211yescharacteristic
338C22×C11D4211yescharacteristic
339C22×C11#54811yescharacteristic
340C22×C11C2×#13711yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57811yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11#52511yescharacteristic
351C4×C11#54211yescharacteristic
352C4×C11#54711yescharacteristic
353C4×C11#55111yescharacteristic
354Dic11—41no—
355Dic11—41no—
356Dic11—42no—
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—21no—
363C22×Q8—111no—
364C22×Q8C22×D1111yescharacteristic
365C22×Q8C22×D1111yescharacteristic
366C2×Q16—222no—
367C2×Q16—222no—
368C2×Q16—222no—
369C2×Q16—222no—
370C2×Q16—222no—
371C2×Q16—441no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—41no—
379C4⋊Q8—41no—
380C4×Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#106—222no—
405#106—441no—
406C4⋊C8—222no—
407#103—22no—
408#103—22no—
409#103—22no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—222no—
414#103C22⋊D1114yes—
415#97—222no—
416#97—222no—
417C4×C8—22no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11#246111yescharacteristic
434C2×C11#317811yescharacteristic
435C2×C11#318511yescharacteristic
436C2×C11#326611yescharacteristic
437C2×C11#327011yescharacteristic
438C2×C11#336911yescharacteristic
439C2×C11#337411yescharacteristic
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8—112no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8C2×C22⋊D1112yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476Q16—228no—
477Q16—444no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—112no—
484C2×C8—112no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8C2×C22⋊D1112yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4C2×C22⋊D1112yes—
510C42—21no—
511C42—21no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—221no—
516C42—442no—
517C42—442no—
518C11#2683811yescharacteristic, complemented, Sylow
519C23C2×D4×D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—84no—
529Q8—222no—
530Q8—222no—
531Q8—441no—
532Q8—441no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
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—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4#6696812yes—
574C2×C4#6697112yes—
575C2×C4#6703711yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#6704311yescharacteristic
580C2×C4C22×C22⋊D1111yescharacteristic
581C8—22no—
582C8—41no—
583C8—222no—
584C8—222no—
585C22#1062319911yescharacteristic
586C22#1062320811yescharacteristic
587C22C2×#6696811yescharacteristic
588C22#1062329311yescharacteristic
589C22C2×#6697111yescharacteristic
590C22#1062329711yescharacteristic
591C22D4×C22⋊D1111yescharacteristic
592C4—22no—
593C4—22no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—81no—
598C4—441no—
599C4—441no—
600C4—441no—
601C4—442no—
602C4—441no—
603C4—881no—
604C4—881no—
605C4—881no—
606C4#1062320011yescharacteristic
607C4#1062321011yescharacteristic
608C4#1062335511yescharacteristic
609C4#1062335911yescharacteristic
610C2#1307257911yescharacteristic
611C2#1307929111yescharacteristic
612C2#1307936011yescharacteristic
613C2#1308012611yescharacteristic
614C2#1308018611yescharacteristic
615C2#1308136111yescharacteristic
616C2#1308142411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#487C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#487D11
hypocenterC11#26838
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
518. C11#26838semidirect

Maximal subgroups

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

subgroupindex
C2×#106224022
#130724512
#130723882
#130699932
#130699462
#130699372
#130697162
#130694842
#130693082
#130693032
#130692922
#130689542
#130688822
#130684902
C2×C11×#4872
#2683811