Finite Group Databasebeta

← #14821910

Subgroups — #14821910

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072966C211yesmaximal, characteristic
2#13071626C211yesmaximal, characteristic, complemented
3#13069817C211yesmaximal, characteristic, complemented
4#13069767C211yesmaximal, characteristic, complemented
5#13069616C211yesmaximal, characteristic
6#13069571C211yesmaximal, characteristic, complemented
7#13069296C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13069221C211yesmaximal, characteristic, complemented
10#13069206C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic, complemented
12#13068930C211yesmaximal, characteristic
13#13068701C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622572—21no—
40#10622570—21no—
41#10622565—21no—
42#10622557—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622281—21no—
46#10622279—21no—
47#10622265—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66999—22no—
78#66999—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81#66991—22no—
82#66991—41no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C4⋊C4×D11—22no—
104C4⋊C4×D11—41no—
105#66923—22no—
106#66923—41no—
107C11×C4⋊C8—41no—
108C11×#103—22no—
109C11×#102—41no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—22no—
113#66899—41no—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124C8×Dic11—41no—
125#66871—22no—
126#26727—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
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—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—81no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C11×SD16—44no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C22⋊C4—81no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—42no—
182C22⋊Dic11—42no—
183C22⋊Dic11—81no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11#4112yes—
195C4⋊Dic11#4112yes—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213#2490—111no—
214#2360—111no—
215#2055D1111yescharacteristic, complemented
216#2036—111no—
217#2026—111no—
218#2000—111no—
219#1989—111no—
220#1934—111no—
221#1925—111no—
222#1923—111no—
223#1921—111no—
224#1880—111no—
225#1874—111no—
226#1823—111no—
227C4×#103—111no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11#13512yes—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C22⋊D11—84no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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#13712yes—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—84no—
299C8×C11—41no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16C2×D1111yescharacteristic
304C2×#125—111no—
305C2×C22⋊Q8—111no—
306C2×#121—111no—
307C2×C4×Q8—111no—
308C22×C4⋊C4—111no—
309C2×#107—111no—
310C2×C4⋊C8C2×D1111yescharacteristic
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#102—111no—
315C2×#102—111no—
316C2×#102C2×D1111yescharacteristic
317C2×C22⋊C8—111no—
318C2×C22⋊C8—111no—
319C2×C4×C8—111no—
320#397—221no—
321#394—221no—
322#391C2×D1111yescharacteristic
323#390—111no—
324#390—221no—
325#390C2×D1111yescharacteristic
326#389—111no—
327#389—221no—
328#388—221no—
329#387—221no—
330#385—221no—
331#380—111no—
332C4×C4⋊C4—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—111no—
335C4×C22⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11#52511yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57711yescharacteristic
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11#52911yescharacteristic
373C4×C11#53811yescharacteristic
374C4×C11#55511yescharacteristic
375C4×C11#55911yescharacteristic
376Dic11—22no—
377Dic11—42no—
378Dic11—41no—
379Dic11—42no—
380Dic11—42no—
381Dic11—41no—
382Dic11—81no—
383C22×Q8C22×D1111yescharacteristic
384C22×D4—221no—
385C22×D4C22×D1111yescharacteristic
386C23×C4—111no—
387C23×C4—221no—
388C2×SD16—22no—
389C2×SD16—41no—
390C2×SD16—41no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#125—222no—
396#125—441no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399#121—222no—
400#121—441no—
401C4×Q8—222no—
402C4×Q8—441no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431#107—222no—
432C4⋊C8—41no—
433#103—22no—
434#103—222no—
435#103—441no—
436#102—41no—
437#102—222no—
438#102—222no—
439C22⋊C8—441no—
440C22⋊C8—441no—
441C4×C8—441no—
442#95—21no—
443#95—21no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450C2×C11—161no—
451C2×C11#245911yescharacteristic
452C2×C11#310811yescharacteristic
453C2×C11#311911yescharacteristic
454C2×C11#329611yescharacteristic
455C2×C11#329711yescharacteristic
456C2×C11#332011yescharacteristic
457C2×C11#333311yescharacteristic
458D11—42no—
459C24—21no—
460C24—111no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8#434112yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4—881no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4D4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498SD16—44no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—112no—
516C4⋊C4—112no—
517C4⋊C4—112no—
518C4⋊C4—224no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—224no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C42—881no—
545C11#2672711yescharacteristic, complemented, Sylow
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—112no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23C2×D4×D1111yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—41no—
564Q8—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—884no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—112no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—221no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—884no—
611C2×C4C2×#434111yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#6703711yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C8—41no—
618C8—41no—
619C8—441no—
620C8—441no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22#1062313711yescharacteristic
636C22#1062314111yescharacteristic
637C22#1062314311yescharacteristic
638C22#1062329311yescharacteristic
639C22D11×#13511yescharacteristic
640C22#1062330511yescharacteristic
641C22D11×#13711yescharacteristic
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—222no—
648C4—442no—
649C4—442no—
650C4—441no—
651C4—442no—
652C4—441no—
653C4—881no—
654C4#1062312411yescharacteristic
655C4#1062318011yescharacteristic
656C4#1062319511yescharacteristic
657C4#1062320111yescharacteristic
658C2—161no—
659C2—442no—
660C2#1307255411yescharacteristic
661C2#1307869511yescharacteristic
662C2#1307881411yescharacteristic
663C2#1308044611yescharacteristic
664C2#1308047311yescharacteristic
665C2#1308079411yescharacteristic
666C2#1308094911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2055D11
hypocenterC11#26727
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. #13071626C2semidirect
3. #13069817C2semidirect
4. #13069767C2semidirect
6. #13069571C2semidirect
7. #13069296C2semidirect
8. #13069233C2semidirect
9. #13069221C2semidirect
10. #13069206C2semidirect
11. #13068973C2semidirect
13. #13068701C2semidirect
14. #103×Dic11C2semidirect
15. C11×#2055C2semidirect
215. #2055D11semidirect
545. C11#26727semidirect

Maximal subgroups

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

subgroupindex
#130729662
#130716262
#130698172
#130697672
#130696162
#130695712
#130692962
#130692332
#130692212
#130692062
#130689732
#130689302
#130687012
#103×Dic112
C11×#20552
#2672711