Finite Group Databasebeta

← #14827055

Subgroups — #14827055

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073211C211yesmaximal, characteristic, complemented
2#13071691C211yesmaximal, characteristic, complemented
3#13070139C211yesmaximal, characteristic, complemented
4#13069924C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic, complemented
6#13069472C211yesmaximal, characteristic, complemented
7#13069260C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13069195C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic, complemented
12#13068966C211yesmaximal, characteristic
13#13068629C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2012C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24#10622843C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622566—21no—
41#10622565—21no—
42#10622564—21no—
43#10622564—21no—
44#10622564—21no—
45#10622563—21no—
46#10622557—21no—
47C22⋊C4×Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×D8—22no—
67C2×C11×D8—41no—
68C2×C11×D8—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#124—22no—
72C11×#124—22no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88D4×Dic11—22no—
89D4×Dic11—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#103—41no—
106C11×#102—22no—
107#66899—22no—
108#66899—41no—
109#66896—22no—
110#66896—22no—
111#66896—41no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66881—22no—
123Dic11⋊C8—41no—
124C8×Dic11—41no—
125#66871—41no—
126#27072—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11#4112yes—
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×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—81no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C11×SD16—44no—
164C11×D8—44no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11#4112yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—81no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—42no—
180C22⋊Dic11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183C22⋊Dic11—81no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186C4⋊Dic11—22no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—41no—
195C4⋊Dic11—42no—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211#2513—111no—
212#2367—111no—
213#2092—111no—
214#2054—111no—
215#2042—111no—
216#2012D1111yescharacteristic
217#1968—111no—
218#1928—111no—
219#1925—111no—
220#1919—111no—
221#1916—111no—
222#1880—111no—
223#1879—111no—
224#1805—111no—
225C4×#102—111no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—84no—
295C2×Dic11#13512yes—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16C2×D1111yescharacteristic
301C22×D8C2×D1111yescharacteristic
302C2×#124C2×D1111yescharacteristic
303C2×C4×Q8—111no—
304C2×C4×D4—111no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103C2×D1111yescharacteristic
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102C2×D1111yescharacteristic
316C2×C4×C8—111no—
317#397—221no—
318#397—221no—
319#391—111no—
320#390—111no—
321#390—111no—
322#390—111no—
323#390C2×D1111yescharacteristic
324#389—111no—
325#388—221no—
326#388—221no—
327#388—221no—
328#388—221no—
329#385—221no—
330#382—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—221no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336C2×D1111yescharacteristic
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11#52511yescharacteristic
358C22×C11#54611yescharacteristic
359C22×C11#55011yescharacteristic
360C22×C11C2×#13511yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57611yescharacteristic
363C22×C11#57711yescharacteristic
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#53811yescharacteristic
370C4×C11#55111yescharacteristic
371C4×C11#55311yescharacteristic
372Dic11—22no—
373Dic11—41no—
374Dic11—42no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8C22×D1111yescharacteristic
381C22×D4C22×D1111yescharacteristic
382C22×D4C22×D1111yescharacteristic
383C23×C4—221no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—41no—
387C2×D8—22no—
388C2×D8—41no—
389C2×D8—41no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394#124—22no—
395#124—22no—
396C4×Q8—222no—
397C4×Q8—441no—
398C4×D4—222no—
399C4×D4—441no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#106—222no—
428C4⋊C8—441no—
429#103—41no—
430#103—222no—
431#103—441no—
432#102—22no—
433#102—222no—
434#102—222no—
435#102—441no—
436#102—441no—
437C4×C8—441no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—82no—
448C2×C11—161no—
449C2×C11#246711yescharacteristic
450C2×C11#310211yescharacteristic
451C2×C11#311911yescharacteristic
452C2×C11#329711yescharacteristic
453C2×C11#332111yescharacteristic
454C2×C11#339411yescharacteristic
455C2×C11#340311yescharacteristic
456C24—21no—
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8#434112yes—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4#434112yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492SD16—44no—
493D8—44no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8#434112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—441no—
518C4⋊C4—442no—
519C4⋊C4—881no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C22⋊C4—881no—
531C42—21no—
532C42—21no—
533C42—221no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—442no—
538C42—881no—
539C42—881no—
540C11#2707211yescharacteristic, complemented, Sylow
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D1111yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—884no—
605C2×C4C2×#434111yescharacteristic
606C2×C4C2×#434111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C8—22no—
612C8—41no—
613C8—441no—
614C8—441no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22#1062311711yescharacteristic
630C22#1062314311yescharacteristic
631C22#1062324911yescharacteristic
632C22D11×#13511yescharacteristic
633C22#1062330111yescharacteristic
634C22#1062330411yescharacteristic
635C22#1062330511yescharacteristic
636C4—42no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—222no—
641C4—441no—
642C4—442no—
643C4—441no—
644C4—441no—
645C4—881no—
646C4—881no—
647C4—881no—
648C4#1062311811yescharacteristic
649C4#1062312411yescharacteristic
650C4#1062313111yescharacteristic
651C4#1062313211yescharacteristic
652C2—82no—
653C2—161no—
654C2#1307266211yescharacteristic
655C2#1307862711yescharacteristic
656C2#1307881611yescharacteristic
657C2#1308047311yescharacteristic
658C2#1308080911yescharacteristic
659C2#1308160911yescharacteristic
660C2#1308170111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2012C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenter#2012D11
hypocenterC11#27072
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

Complements

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

NH ≅ G/Ntype
1. #13073211C2semidirect
2. #13071691C2semidirect
3. #13070139C2semidirect
5. #13069852C2semidirect
6. #13069472C2semidirect
7. #13069260C2semidirect
8. #13069233C2semidirect
9. #13069195C2semidirect
10. #13069172C2semidirect
11. #13068973C2semidirect
13. #13068629C2semidirect
14. #102×Dic11C2semidirect
540. C11#27072semidirect

Maximal subgroups

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

subgroupindex
#130732112
#130716912
#130701392
#130699242
#130698522
#130694722
#130692602
#130692332
#130691952
#130691722
#130689732
#130689662
#130686292
#102×Dic112
C11×#20122
#2707211