Finite Group Databasebeta

← #14775421

Subgroups — #14775421

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078529C211yesmaximal, characteristic
2#13077341C211yesmaximal, characteristic
3#13077274C211yesmaximal, characteristic, complemented
4#13069368C211yesmaximal, characteristic, complemented
5#13069321C211yesmaximal, characteristic, complemented
6#13069262C211yesmaximal, characteristic, complemented
7#13069218C211yesmaximal, characteristic, complemented
8#13069213C211yesmaximal, characteristic, complemented
9#13069064C211yesmaximal, characteristic
10#13068892C211yesmaximal, characteristic, complemented
11#13068821C211yesmaximal, characteristic, complemented
12#13068494C211yesmaximal, characteristic, complemented
13#13068457C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#1733C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10623322C2211yescharacteristic
20C2×#66960C2211yescharacteristic
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622742C2211yescharacteristic
25#10622741—21no—
26#10622740—21no—
27C2×#66886C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29#10622735C2211yescharacteristic
30#10622732C2211yescharacteristic
31#10622724—21no—
32C8×C22⋊D11—21no—
33#10622616C411yescharacteristic, complemented
34#10622616C411yescharacteristic, complemented
35#10622615C2211yescharacteristic
36#10622615C2211yescharacteristic
37#10622613—21no—
38#10622613—21no—
39#10622612C2211yescharacteristic
40#10622612C2211yescharacteristic
41#10622611C2211yescharacteristic
42#10622611C2211yescharacteristic
43#10622610C2211yescharacteristic
44#10622610C2211yescharacteristic
45#10622609C411yescharacteristic, complemented
46#10622609C411yescharacteristic, complemented
47#10622584C411yescharacteristic, complemented
48#10622583C411yescharacteristic, complemented
49#10622581C411yescharacteristic, complemented
50#10622580C411yescharacteristic, complemented
51C2×#66869C2211yescharacteristic
52C2×#66869C2211yescharacteristic
53#10622539—21no—
54#10622538—21no—
55C2×#66867C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#339C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16—41no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—22no—
78C11×#117—41no—
79C11×#117C2×C411yescharacteristic
80C11×#117C2×C411yescharacteristic
81C11×#117C2311yescharacteristic
82C11×#117C2311yescharacteristic
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#67006—21no—
92#66983C2×C411yescharacteristic
93#66983C2×C411yescharacteristic
94#66982—21no—
95C4×C22⋊D11—21no—
96C4×C22⋊D11—21no—
97#66979C2311yescharacteristic
98#66977C2×C411yescharacteristic
99#66977C2×C411yescharacteristic
100C2×#4318C2311yescharacteristic
101C2×#4318C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66960—22no—
107#66960—41no—
108C2×#4313—21no—
109C2×C8×D11—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)C2×C411yescharacteristic
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)C2×C411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117C22⋊(C11⋊C8)D411yescharacteristic
118C22⋊(C11⋊C8)D411yescharacteristic
119C22⋊(C11⋊C8)D411yescharacteristic
120#66886—22no—
121#66886—41no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66874C2×C411yescharacteristic
131#66874C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66872C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141#66871C2×C411yescharacteristic
142#66871C2×C411yescharacteristic
143#66871C2×C411yescharacteristic
144#66869—22no—
145#66869—41no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148C4⋊(C11⋊C8)—21no—
149C4⋊(C11⋊C8)—21no—
150#66867—21no—
151#66867—21no—
152#66867—41no—
153C4×C11⋊C8—22no—
154C4×C11⋊C8—21no—
155C4×C11⋊C8—21no—
156#22951—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—21no—
173C2×C22⋊D11—21no—
174C2×C22⋊D11—21no—
175#4339—21no—
176#4339—21no—
177#4339—21no—
178#4339—21no—
179C2×D44C22×C411yescharacteristic
180C2×C4×D11—21no—
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—42no—
186C11×M16#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—42no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C411yescharacteristic
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—42no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11#4112yes—
210C22⋊Dic11—21no—
211C22⋊Dic11—21no—
212C22⋊Dic11—21no—
213(C2×D11)⋊C4—21no—
214(C2×D11)⋊C4—21no—
215C4⋊Dic11C22×C411yescharacteristic
216C4⋊Dic11C22×C411yescharacteristic
217Dic11⋊C4—21no—
218Dic11⋊C4—21no—
219C4×Dic11—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8C22×C411yescharacteristic
235C2×C11⋊C8C22×C411yescharacteristic
236C2×C11⋊C8C22×C411yescharacteristic
237C2×C11⋊C8C22×C411yescharacteristic
238C2×C11⋊C8C2×D411yescharacteristic
239C2×C11⋊C8C2×D411yescharacteristic
240C2×C11⋊C8C2×D411yescharacteristic
241C2×C11⋊C8C2×D411yescharacteristic
242#4313—42no—
243C8×D11—42no—
244#3091—111no—
245#2933—111no—
246#2924—111no—
247#1946—111no—
248#1937—111no—
249#1929—111no—
250#1922—111no—
251#1922—111no—
252#1897—111no—
253#1866—111no—
254#1855—111no—
255#1772—111no—
256#1765—111no—
257#1750—111no—
258#1733D1111yescharacteristic, complemented
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C4×D411yescharacteristic
264C23×C11C4×D411yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C22×D11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—81no—
289C2×C4×C11C4×D411yescharacteristic
290C2×C4×C11C4×D411yescharacteristic
291C2×C4×C11C23×C411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C112−1+411yescharacteristic
297C22⋊D11—42no—
298C22⋊D11—41no—
299C22⋊D11—41no—
300C22⋊D11—81no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304D44—21no—
305D44—21no—
306C4×D11—41no—
307C4×D11—41no—
308Dic22—21no—
309Dic22—21no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—21no—
313C11⋊C8—21no—
314C11⋊C8—21no—
315C11⋊C8—21no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—21no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C2×#131—111no—
323C22×M16C2×D1111yescharacteristic
324#525—111no—
325C2×#117C2×D1111yescharacteristic
326C2×#117C2×D1111yescharacteristic
327#485—111no—
328#485—111no—
329#484—111no—
330#483—111no—
331#482—111no—
332#482—111no—
333#481—111no—
334#480—111no—
335#436—221no—
336#435—221no—
337#435—221no—
338C8×D4—221no—
339#433—221no—
340#433—221no—
341#432—221no—
342#431—221no—
343C2×#108—111no—
344C2×#108—111no—
345#427—111no—
346#427—111no—
347#424—111no—
348#424—111no—
349#424—111no—
350C2×#104—111no—
351C2×#104—111no—
352#416—111no—
353#416—111no—
354#408—111no—
355#407—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358#405—111no—
359#405—111no—
360#405—111no—
361C2×#97—111no—
362C2×C4×C8—111no—
363#341—111no—
364#341—111no—
365#339—111no—
366#339—111no—
367#339C2×D1111yescharacteristic
368#339C2×D1111yescharacteristic
369#339C2×D1111yescharacteristic
370#339C2×D1111yescharacteristic
371#336—111no—
372#336—111no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×C4×D411yescharacteristic
384C22×C11#55111yescharacteristic
385C22×C11#55211yescharacteristic
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—81no—
397C4×C11C4×#4111yescharacteristic
398C4×C11#52011yescharacteristic
399C4×C11#54611yescharacteristic
400C4×C11#54711yescharacteristic
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404C2×#41—111no—
405C23×C4C22×D1111yescharacteristic
406#131—222no—
407#131—441no—
408C2×M16—21no—
409C2×M16—22no—
410C2×M16—41no—
411C2×M16—111no—
412C2×M16—111no—
413C2×M16—221no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—21no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—221no—
422#123—221no—
423C22⋊Q8—111no—
424C22⋊Q8—111no—
425#121—111no—
426#121—111no—
427#120—221no—
428C4×D4—221no—
429C4×D4—221no—
430#117—21no—
431#117—21no—
432#117—22no—
433#117—41no—
434#117—111no—
435#117C4×D1111yescharacteristic
436#117C4×D1111yescharacteristic
437#117C22×D1111yescharacteristic
438#117C22×D1111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C4⋊C4C4×D1111yescharacteristic
441C2×C4⋊C4C4×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C42—21no—
445C2×C42C22×D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447#108—222no—
448#108—441no—
449#107—111no—
450#107—111no—
451#107—111no—
452#107—111no—
453#106—111no—
454#106—111no—
455#106—111no—
456#106—111no—
457C4⋊C8—221no—
458C4⋊C8—221no—
459C4⋊C8—221no—
460C4⋊C8—221no—
461C4⋊C8—221no—
462C4⋊C8—221no—
463#104—222no—
464#104—441no—
465#103—111no—
466#103—111no—
467#103—111no—
468#103—111no—
469#102—111no—
470#102—111no—
471#102—111no—
472#102—111no—
473C22⋊C8—111no—
474C22⋊C8—111no—
475C22⋊C8—111no—
476C22⋊C8—111no—
477C22⋊C8—111no—
478C22⋊C8—111no—
479C22⋊C8—111no—
480C22⋊C8—111no—
481C22⋊C8—221no—
482C22⋊C8—221no—
483C22⋊C8—221no—
484C22⋊C8—221no—
485#97—221no—
486#97—221no—
487#97—221no—
488#97—441no—
489C4×C8—221no—
490C4×C8—221no—
491C4×C8—221no—
492C4×C8—222no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—41no—
496C2×C11—41no—
497C2×C11#235911yescharacteristic
498C2×C11#295511yescharacteristic
499C2×C11#295711yescharacteristic
500D11—81no—
501C24#434111yescharacteristic
502#41—221no—
503#41—221no—
504#41—221no—
505#41—221no—
506C2×Q8—111no—
507C2×D4—111no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—221no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—221no—
520C22×C4C2×C4×D1111yescharacteristic
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4D4×D1111yescharacteristic
524C22×C4#434111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—221no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—442no—
535M16#433912yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—42no—
539C2×C8—111no—
540C2×C8—111no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—111no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—442no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—111no—
562C4⋊C4—111no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4C2×C4×D1111yescharacteristic
566C4⋊C4C2×C4×D1111yescharacteristic
567C4⋊C4C2×C4×D1111yescharacteristic
568C4⋊C4C2×C4×D1111yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—42no—
574C22⋊C4—221no—
575C22⋊C4—221no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—221no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—221no—
587C42#433912yes—
588C11#2295111yescharacteristic, complemented, Sylow
589C23—21no—
590C23—21no—
591C23—41no—
592C23—41no—
593C23—221no—
594C23(C22⋊D11)⋊C411yescharacteristic
595C23(C22⋊D11)⋊C411yescharacteristic
596C23C2×#434111yescharacteristic
597Q8—221no—
598Q8—221no—
599D4—221no—
600D4—221no—
601D4—442no—
602D4—441no—
603D4—441no—
604D4—881no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—81no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4(C22⋊D11)⋊C411yescharacteristic
633C2×C4(C22⋊D11)⋊C411yescharacteristic
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C2×#433911yescharacteristic
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#6704011yescharacteristic
640C8—22no—
641C8—41no—
642C8—221no—
643C8—221no—
644C8—221no—
645C8—221no—
646C8—221no—
647C8—221no—
648C8—221no—
649C8—221no—
650C8—441no—
651C8—441no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—81no—
661C22—81no—
662C22—441no—
663C22—441no—
664C22—441no—
665C22C2×(C22⋊D11)⋊C411yescharacteristic
666C22#1062302611yescharacteristic
667C22#1062304411yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—81no—
676C4—441no—
677C4—441no—
678C4—441no—
679C4C4×#433911yescharacteristic
680C4#1062302111yescharacteristic
681C4#1062303511yescharacteristic
682C4#1062303811yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—881no—
688C2#1307160411yescharacteristic
689C2#1307751511yescharacteristic
690C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1733C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1733D11
hypocenterC11#22951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
3. #13077274C2semidirect
4. #13069368C2semidirect
5. #13069321C2semidirect
6. #13069262C2semidirect
7. #13069218C2semidirect
8. #13069213C2semidirect
10. #13068892C2semidirect
11. #13068821C2semidirect
12. #13068494C2semidirect
13. #13068457C2semidirect
14. #13068382C2semidirect
15. C11×#1733C2semidirect
33. #10622616C4semidirect
34. #10622616C4semidirect
45. #10622609C4semidirect
46. #10622609C4semidirect
47. #10622584C4semidirect
48. #10622583C4semidirect
49. #10622581C4semidirect
50. #10622580C4semidirect
258. #1733D11semidirect
588. C11#22951semidirect

Maximal subgroups

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

subgroupindex
#130785292
#130773412
#130772742
#130693682
#130693212
#130692622
#130692182
#130692132
#130690642
#130688922
#130688212
#130684942
#130684572
#130683822
C11×#17332
#2295111