Finite Group Databasebeta

← #14775431

Subgroups — #14775431

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#13078525C211yesmaximal, characteristic
2#13077343C211yesmaximal, characteristic
3#13077276C211yesmaximal, characteristic, complemented
4#13069368C211yesmaximal, characteristic, complemented
5#13069317C211yesmaximal, characteristic, complemented
6#13069267C211yesmaximal, characteristic, complemented
7#13069218C211yesmaximal, characteristic, complemented
8#13069213C211yesmaximal, characteristic, complemented
9#13068889C211yesmaximal, characteristic, complemented
10#13068820C211yesmaximal, characteristic, complemented
11#13068494C211yesmaximal, characteristic, complemented
12#13068461C211yesmaximal, characteristic, complemented
13#13068382C211yesmaximal, characteristic, complemented
14#13068326C211yesmaximal, characteristic, complemented
15C11×#1897C211yesmaximal, characteristic
16C11×#525C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#407C2211yescharacteristic
24#10622847C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622846C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30C2×#66886C2211yescharacteristic
31#10622735C2211yescharacteristic
32#10622735C2211yescharacteristic
33#10622732C2211yescharacteristic
34#10622732C2211yescharacteristic
35#10622658C411yescharacteristic, complemented
36#10622658C411yescharacteristic, complemented
37#10622657C411yescharacteristic, complemented
38#10622656C411yescharacteristic, complemented
39#10622648C411yescharacteristic, complemented
40#10622648C411yescharacteristic, complemented
41#10622647C411yescharacteristic, complemented
42#10622646C411yescharacteristic, complemented
43#10622625—21no—
44#10622624—21no—
45#10622624—21no—
46D4×C11⋊C8—21no—
47#10622612C2211yescharacteristic
48#10622611C2211yescharacteristic
49#10622611C2211yescharacteristic
50#10622610C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622333—21no—
54#10622333—21no—
55#10622332—21no—
56#10622331—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C11×#123—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×#121C2×C411yescharacteristic
75C11×#121C2×C411yescharacteristic
76C11×#120—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C11×#117—22no—
80C11×#117—41no—
81C11×#117C2311yescharacteristic
82C2×C11×C4⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87#67001—22no—
88#67001—41no—
89#66979—21no—
90#66979—21no—
91#66979C2×C411yescharacteristic
92#66979C2×C411yescharacteristic
93#66979C2311yescharacteristic
94#66979C2311yescharacteristic
95C2×C4⋊Dic11C2×C411yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4×Dic11—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—22no—
101C2×#4318—41no—
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#104—22no—
111C11×#104—41no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120#66896C2×C411yescharacteristic
121#66896C2×C411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)C2×C411yescharacteristic
125C22⋊(C11⋊C8)C2×C411yescharacteristic
126C22⋊(C11⋊C8)C2×C411yescharacteristic
127C22⋊(C11⋊C8)C2×C411yescharacteristic
128C22⋊(C11⋊C8)D411yescharacteristic
129C22⋊(C11⋊C8)D411yescharacteristic
130C22⋊(C11⋊C8)D411yescharacteristic
131C22⋊(C11⋊C8)D411yescharacteristic
132#66886—22no—
133#66886—41no—
134#66879—21no—
135#66879—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138Dic11⋊C8—21no—
139Dic11⋊C8—21no—
140C8×Dic11—21no—
141C8×Dic11—21no—
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66872C2×C411yescharacteristic
145#66872C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148#66871C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150C4⋊(C11⋊C8)—21no—
151C4⋊(C11⋊C8)—21no—
152#66867—21no—
153#66867—41no—
154C4×C11⋊C8—22no—
155C4×C11⋊C8—21no—
156#22951—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—21no—
181C22×Dic11—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—42no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11#4112yes—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11C22×C411yescharacteristic
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C411yescharacteristic
213C4⋊Dic11C22×C411yescharacteristic
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—42no—
222#4318—42no—
223#4318#4112yes—
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⋊C8—42no—
235C2×C11⋊C8—42no—
236C2×C11⋊C8C22×C411yescharacteristic
237C2×C11⋊C8C22×C411yescharacteristic
238C2×C11⋊C8C22×C411yescharacteristic
239C2×C11⋊C8C22×C411yescharacteristic
240C2×C11⋊C8C2×D411yescharacteristic
241C2×C11⋊C8C2×D411yescharacteristic
242C2×C11⋊C8C2×D411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
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#1897D1111yescharacteristic
253#1866—111no—
254#1855—111no—
255#1772—111no—
256#1765—111no—
257#1750—111no—
258#1733—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11C4×D411yescharacteristic
265C23×C11C4×D411yescharacteristic
266C23×C11C2×#4111yescharacteristic
267Q8×C11—21no—
268Q8×C11—21no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—42no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—81no—
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—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11C4×D411yescharacteristic
297C2×C4×C11C4×D411yescharacteristic
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—42no—
309C2×Dic11—81no—
310C8×C11—41no—
311C8×C11—41no—
312C11⋊C8—21no—
313C11⋊C8—21no—
314C11⋊C8—21no—
315C11⋊C8—21no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—22no—
319C11⋊C8—21no—
320C11⋊C8—21no—
321C11⋊C8—41no—
322C2×#131—111no—
323C22×M16—111no—
324#525C2×D1111yescharacteristic
325C2×#117—111no—
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×#104C2×D1111yescharacteristic
351C2×#104C2×D1111yescharacteristic
352#416—111no—
353#416—111no—
354#408—111no—
355#407C2×D1111yescharacteristic
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#339—111no—
368#339—111no—
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—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11C2×C4×D411yescharacteristic
387C22×C11#55111yescharacteristic
388C22×C11#55211yescharacteristic
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11C4×#4111yescharacteristic
397C4×C11#52011yescharacteristic
398C4×C11#54611yescharacteristic
399C4×C11#54711yescharacteristic
400Dic11—41no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404C2×#41C22×D1111yescharacteristic
405C23×C4C22×D1111yescharacteristic
406#131—222no—
407#131—441no—
408C2×M16—111no—
409C2×M16—111no—
410C2×M16—221no—
411C2×M16—221no—
412C2×M16—222no—
413C2×M16—441no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—221no—
421C22×C8—221no—
422#123—21no—
423C22⋊Q8C4×D1111yescharacteristic
424C22⋊Q8C4×D1111yescharacteristic
425#121C4×D1111yescharacteristic
426#121C4×D1111yescharacteristic
427#120—21no—
428C4×D4—21no—
429C4×D4—21no—
430#117—22no—
431#117—41no—
432#117—111no—
433#117—111no—
434#117—111no—
435#117—111no—
436#117—221no—
437#117—221no—
438#117C22×D1111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—221no—
444C2×C42—221no—
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—22no—
464#104—41no—
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—21no—
474C22⋊C8—21no—
475C22⋊C8—111no—
476C22⋊C8—111no—
477C22⋊C8—111no—
478C22⋊C8—111no—
479C22⋊C8—111no—
480C22⋊C8—111no—
481C22⋊C8—111no—
482C22⋊C8—111no—
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—81no—
498C2×C11#235911yescharacteristic
499C2×C11#295511yescharacteristic
500C2×C11#295711yescharacteristic
501C24#434111yescharacteristic
502#41—21no—
503#41—21no—
504#41—21no—
505#41—21no—
506C2×Q8C2×C4×D1111yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4C2×C4×D1111yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—221no—
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—21no—
530M16—112no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—442no—
535M16—442no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—111no—
539C2×C8—111no—
540C2×C8—111no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—221no—
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—442no—
557C2×C8—442no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—111no—
562C4⋊C4—111no—
563C4⋊C4—111no—
564C4⋊C4—111no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4C2×C4×D1111yescharacteristic
568C4⋊C4C2×C4×D1111yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—42no—
575C22⋊C4—221no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—221no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—221no—
584C42—221no—
585C42—221no—
586C42—221no—
587C42#434112yes—
588C11#2295111yescharacteristic, complemented, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23(C22⋊D11)⋊C411yescharacteristic
595C23(C22⋊D11)⋊C411yescharacteristic
596C23C2×#434111yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
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—22no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—442no—
631C2×C4—881no—
632C2×C4(C22⋊D11)⋊C411yescharacteristic
633C2×C4(C22⋊D11)⋊C411yescharacteristic
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704311yescharacteristic
640C8—41no—
641C8—41no—
642C8—221no—
643C8—221no—
644C8—221no—
645C8—221no—
646C8—221no—
647C8—221no—
648C8—222no—
649C8—221no—
650C8—221no—
651C8—441no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×(C22⋊D11)⋊C411yescharacteristic
666C22#1062311811yescharacteristic
667C22#1062318111yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—441no—
676C4—441no—
677C4—441no—
678C4—441no—
679C4C4×#434111yescharacteristic
680C4#1062307711yescharacteristic
681C4#1062314111yescharacteristic
682C4#1062314211yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2#1307161411yescharacteristic
689C2#1307751511yescharacteristic
690C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1897C2
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#1897D11
hypocenterC11#22951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
3. #13077276C2semidirect
4. #13069368C2semidirect
5. #13069317C2semidirect
6. #13069267C2semidirect
7. #13069218C2semidirect
8. #13069213C2semidirect
9. #13068889C2semidirect
10. #13068820C2semidirect
11. #13068494C2semidirect
12. #13068461C2semidirect
13. #13068382C2semidirect
14. #13068326C2semidirect
35. #10622658C4semidirect
36. #10622658C4semidirect
37. #10622657C4semidirect
38. #10622656C4semidirect
39. #10622648C4semidirect
40. #10622648C4semidirect
41. #10622647C4semidirect
42. #10622646C4semidirect
588. C11#22951semidirect

Maximal subgroups

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

subgroupindex
#130785252
#130773432
#130772762
#130693682
#130693172
#130692672
#130692182
#130692132
#130688892
#130688202
#130684942
#130684612
#130683822
#130683262
C11×#18972
#2295111