Finite Group Databasebeta

← #14822269

Subgroups — #14822269

Order 2816.

762 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#13072962C211yesmaximal, characteristic
2#13071639C211yesmaximal, characteristic, complemented
3#13069930C211yesmaximal, characteristic, complemented
4#13069810C211yesmaximal, characteristic, complemented
5#13069765C211yesmaximal, characteristic, complemented
6#13069618C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic, complemented
8#13069313C211yesmaximal, characteristic, complemented
9#13069241C211yesmaximal, characteristic, complemented
10#13069229C211yesmaximal, characteristic, complemented
11#13069201C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068937C211yesmaximal, characteristic
14#13068709C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622591—21no—
37C4⋊C4×Dic11C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622553—21no—
41#10622553—21no—
42#10622552—21no—
43#10622552C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C4×Dic11⋊C4—21no—
46#10622541C2211yescharacteristic
47#10622287—21no—
48#10622285—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74#66999—22no—
75#66999—22no—
76C2×#4325—22no—
77C2×#4325—41no—
78C2×#4325—41no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66948—22no—
102#66948—41no—
103#66945—22no—
104#66945—41no—
105#66943—22no—
106#66943—41no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#97—41no—
110C11×#95—21no—
111#66899—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66885—22no—
120#66885—41no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123Dic11⋊C8—41no—
124#66873—22no—
125#66872—22no—
126#26751—111nomaximal, Sylow
127C23×D11—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—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—42no—
155C2×D44—42no—
156C2×D44—81no—
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×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4#4112yes—
175C11×C4⋊C4#4112yes—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179C42×C11—81no—
180#4325—44no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
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#2490—111no—
212#2362—111no—
213#2055—111no—
214#2035—111no—
215#2026—111no—
216#2000—111no—
217#1989—111no—
218#1936—111no—
219#1926—111no—
220#1924—111no—
221#1920—111no—
222#1880—111no—
223#1875—111no—
224#1825—111no—
225#1763D1111yescharacteristic, complemented
226C23×C11C22×D411yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287D44—41no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—84no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C2×#125—111no—
302C2×C22⋊Q8—111no—
303C2×#121—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305C2×#117—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103C2×D1111yescharacteristic
310C2×#103C2×D1111yescharacteristic
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×#97C2×D1111yescharacteristic
317#397—221no—
318#394—221no—
319#391—111no—
320#390—111no—
321#390—111no—
322#390—221no—
323#389—111no—
324#388—221no—
325#388—221no—
326#388—221no—
327#387—221no—
328#380—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331C4×C4⋊C4C2×D1111yescharacteristic
332C4×C22⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
341#336—111no—
342#336—111no—
343C22×C11#52511yescharacteristic
344C22×C11#54611yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57711yescharacteristic
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11#52911yescharacteristic
371C4×C11#53811yescharacteristic
372C4×C11#55511yescharacteristic
373C4×C11#55911yescharacteristic
374Dic11—42no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8C22×D1111yescharacteristic
381C22×D4—111no—
382C22×D4—221no—
383C23×C4—111no—
384C2×SD16—222no—
385C2×SD16—441no—
386C2×SD16—441no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391#125—222no—
392#125—441no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395#121—222no—
396#121—441no—
397C4×Q8—22no—
398C4×Q8—41no—
399#117—222no—
400#117—441no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—111no—
413C2×C22⋊C4—111no—
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×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—111no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428#106—222no—
429C4⋊C8—441no—
430#103—22no—
431#103—22no—
432#103—441no—
433#102—222no—
434#102—222no—
435#102—441no—
436C22⋊C8—441no—
437C22⋊C8—441no—
438#97—41no—
439#95—21no—
440#95—111no—
441#95—111no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11#245911yescharacteristic
448C2×C11#311111yescharacteristic
449C2×C11#312611yescharacteristic
450C2×C11#330711yescharacteristic
451C2×C11#331111yescharacteristic
452C2×C11#331711yescharacteristic
453C2×C11#332611yescharacteristic
454D11—81no—
455D11—161no—
456C24—111no—
457C24—221no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8#433912yes—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—442no—
471C2×D4—442no—
472C2×D4—881no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492SD16—444no—
493C2×C8—21no—
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—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—112no—
511C4⋊C4—224no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C4⋊C4#433912yes—
521C4⋊C4#433912yes—
522C22⋊C4—224no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C22⋊C4—881no—
531C22⋊C4—881no—
532C42—21no—
533C42—21no—
534C42—42no—
535C42—81no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42—442no—
540C11#2675111yescharacteristic, complemented, Sylow
541C23—221no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C2×D4×D1111yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—441no—
561D4—441no—
562D4—441no—
563D4—441no—
564D4—884no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
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—441no—
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C8—41no—
612C8—41no—
613C8—441no—
614C8—441no—
615C22—441no—
616C22—441no—
617C22—441no—
618C22—441no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22#1062302111yescharacteristic
630C22#1062307811yescharacteristic
631C22#1062308111yescharacteristic
632C22#1062330611yescharacteristic
633C22#1062330811yescharacteristic
634C22#1062330811yescharacteristic
635C22#1062330911yescharacteristic
636C4—41no—
637C4—42no—
638C4—41no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—442no—
646C4—881no—
647C4—881no—
648C4#1062301011yescharacteristic
649C4#1062306311yescharacteristic
650C4#1062309011yescharacteristic
651C4#1062309111yescharacteristic
652C2—881no—
653C2—1761no—
654C2#1307255311yescharacteristic
655C2#1307873111yescharacteristic
656C2#1307890611yescharacteristic
657C2#1308059311yescharacteristic
658C2#1308065711yescharacteristic
659C2#1308074711yescharacteristic
660C2#1308086511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1763D11
hypocenterC11#26751
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. #13071639C2semidirect
3. #13069930C2semidirect
4. #13069810C2semidirect
5. #13069765C2semidirect
7. #13069572C2semidirect
8. #13069313C2semidirect
9. #13069241C2semidirect
10. #13069229C2semidirect
11. #13069201C2semidirect
12. #13068971C2semidirect
14. #13068709C2semidirect
15. C11×#1763C2semidirect
225. #1763D11semidirect
540. C11#26751semidirect

Maximal subgroups

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

subgroupindex
#130729622
#130716392
#130699302
#130698102
#130697652
#130696182
#130695722
#130693132
#130692412
#130692292
#130692012
#130689712
#130689372
#130687092
C11×#17632
#2675111