Finite Group Databasebeta

← #14803668

Subgroups — #14803668

Order 2816.

790 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×#10622405C211yesmaximal, characteristic
2C2×#10622795C211yesmaximal, characteristic
3#13073833C211yesmaximal, characteristic
4#13071670C211yesmaximal, characteristic
5#13070037C211yesmaximal, characteristic
6#13070036C211yesmaximal, characteristic
7#13069938C211yesmaximal, characteristic
8#13069936C211yesmaximal, characteristic
9#13069566C211yesmaximal, characteristic
10#13069333C211yesmaximal, characteristic
11#13068954C211yesmaximal, characteristic
12#13068631C211yesmaximal, characteristic
13#13068630C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622795—24no—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622591—21no—
38#10622590C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42#10622549C2211yescharacteristic
43#10622546—21no—
44C4×Dic11⋊C4—21no—
45C4×Dic11⋊C4C2211yescharacteristic
46#10622542C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622405—24no—
49#10622273—21no—
50#10622273—21no—
51#10622259—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79#66997—22no—
80#66997D414yes—
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326—41no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941—22no—
103#66940—22no—
104#66940—41no—
105C11×#103—22no—
106C11×#103—22no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
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—
127Dic11⋊C8—22no—
128Dic11⋊C8—41no—
129C8×Dic11—22no—
130#66874—22no—
131C4⋊(C11⋊C8)—41no—
132#25323—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×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—42no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22C2×D412yes—
169C11×Q16—44no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4#4112yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184#4326—44no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—22no—
195Dic11⋊C4—22no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11C2×D412yes—
204C4×Dic11#4112yes—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×#487—111no—
212C2×#462—111no—
213#2568—111no—
214#2365—111no—
215#2074—111no—
216#2074—111no—
217#2056—111no—
218#2056—111no—
219#1988—111no—
220#1939—111no—
221#1878—111no—
222#1878D1111yescharacteristic
223#1805—111no—
224#1805—111no—
225C4×#103—111no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
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—41no—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
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—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11#12112yes—
280C2×Dic11#12112yes—
281C2×Dic11#13512yes—
282C2×Dic11#13712yes—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287Dic22—84no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16—111no—
293C22×Q16C2×D1111yescharacteristic
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8C2×D1111yescharacteristic
299#487—224no—
300#462—224no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103C2×D1111yescharacteristic
311C2×#103C2×D1111yescharacteristic
312C2×C4×C8—111no—
313#400—221no—
314#400—221no—
315#391—111no—
316#391—111no—
317#391—111no—
318#391—221no—
319#391—221no—
320#391C2×D1111yescharacteristic
321#389—221no—
322#387—221no—
323#387—221no—
324#382—111no—
325#382—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#336—111no—
336#336C2×D1111yescharacteristic
337C22×C11C2×#12111yescharacteristic
338C22×C11#54611yescharacteristic
339C22×C11#54811yescharacteristic
340C22×C11C2×#13511yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57811yescharacteristic
343C22×C11#57811yescharacteristic
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11#52911yescharacteristic
351C4×C11#54211yescharacteristic
352C4×C11#54611yescharacteristic
353C4×C11#54711yescharacteristic
354Dic11—22no—
355Dic11—41no—
356Dic11—42no—
357Dic11—41no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361Dic11#46414yes—
362C22×Q8—111no—
363C22×Q8—221no—
364C22×Q8C22×D1111yescharacteristic
365C22×Q8C22×D1111yescharacteristic
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—41no—
369C2×Q16—222no—
370C2×Q16—222no—
371C2×Q16—441no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C4⋊Q8—114no—
377C4⋊Q8—222no—
378C4⋊Q8—222no—
379C4⋊Q8—222no—
380C4×Q8—22no—
381C4×Q8—41no—
382C4×Q8—222no—
383C4×Q8—222no—
384C4×Q8—222no—
385C4×Q8—441no—
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—21no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406C4⋊C8—222no—
407C4⋊C8—441no—
408C4⋊C8—441no—
409#103—22no—
410#103—22no—
411#103—222no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—222no—
417C4×C8—222no—
418#95—21no—
419#95—21no—
420#95—111no—
421#95—111no—
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#242711yescharacteristic
434C2×C11C2×#46411yescharacteristic
435C2×C11#304411yescharacteristic
436C2×C11#330211yescharacteristic
437C2×C11#332811yescharacteristic
438C2×C11#336411yescharacteristic
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—112no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—442no—
459C2×Q8#433912yes—
460C2×Q8D4×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—44no—
477Q16—444no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—224no—
497C4⋊C4—224no—
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#434112yes—
508C42—21no—
509C42—21no—
510C42—42no—
511C42—112no—
512C42—112no—
513C42—221no—
514C42—221no—
515C42—442no—
516C42—442no—
517C42—442no—
518C11#2532311yescharacteristic, complemented, Sylow
519C23C2×D4×D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—222no—
529Q8—222no—
530Q8—441no—
531Q8—441no—
532Q8—884no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—222no—
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—441no—
574C2×C4—441no—
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4#6703711yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—41no—
582C8—41no—
583C8—441no—
584C8—441no—
585C22#1062308311yescharacteristic
586C22#1062312211yescharacteristic
587C22D11×#12111yescharacteristic
588C22#1062329711yescharacteristic
589C22D11×#13511yescharacteristic
590C22D11×#13711yescharacteristic
591C22#1062331011yescharacteristic
592C4—41no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—114no—
599C4—222no—
600C4—441no—
601C4—442no—
602C4—441no—
603C4—881no—
604C4—881no—
605C4—881no—
606C4#1062302111yescharacteristic
607C4#1062306911yescharacteristic
608C4#1062314211yescharacteristic
609C4#1062319311yescharacteristic
610C2#1307219011yescharacteristic
611C2D11×#46411yescharacteristic
612C2#1307814111yescharacteristic
613C2#1308052611yescharacteristic
614C2#1308089211yescharacteristic
615C2#1308130211yescharacteristic
616C2#1308142011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
hypercenter#1878D11
hypocenterC11#25323
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
518. C11#25323semidirect

Maximal subgroups

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

subgroupindex
C2×#106224052
C2×#106227952
#130738332
#130716702
#130700372
#130700362
#130699382
#130699362
#130695662
#130693332
#130689542
#130686312
#130686302
#103×Dic112
C11×#18782
#2532311