Finite Group Databasebeta

← #14811004

Subgroups — #14811004

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622374C211yesmaximal, characteristic, complemented
2#13072301C211yesmaximal, characteristic, complemented
3#13071446C211yesmaximal, characteristic
4#13070166C211yesmaximal, characteristic, complemented
5#13069995C211yesmaximal, characteristic, complemented
6#13069993C211yesmaximal, characteristic, complemented
7#13069755C211yesmaximal, characteristic, complemented
8#13068879C211yesmaximal, characteristic, complemented
9#13068861C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic, complemented
11#13068794C211yesmaximal, characteristic, complemented
12#13068641C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic
15C2×C11×#416C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C11×#416—24no—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622833—21no—
32#10622833—21no—
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37#10622824—21no—
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C11⋊#95—21no—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622590C2211yescharacteristic
47#10622586C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622561—21no—
51#10622560—21no—
52#10622546—21no—
53#10622542—21no—
54#10622374—24no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41Q814yescomplemented
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C23×Dic11—21no—
74C22×Dic22—21no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#117—22no—
81C11×#117—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11D411yescharacteristic
91C2×C22⋊Dic11D411yescharacteristic
92D4×Dic11—22no—
93D4×Dic11—22no—
94D4×Dic11—41no—
95D4×Dic11—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66941—22no—
108#66941—41no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102D414yes—
113#66899—41no—
114#66899—41no—
115#66896—22no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130#66881—22no—
131#66881—41no—
132Dic11⋊C8—22no—
133Dic11⋊C8—41no—
134#66872—22no—
135#66871—41no—
136#25962—111nomaximal, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C11×#41—28no—
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×Q812yes—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C2×D412yes—
156C2×D4×C11C2×Q812yes—
157C2×D4×C11#4112yes—
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—24no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×Q812yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—42no—
179C22×Dic11—42no—
180C22×Dic11—81no—
181C22×Dic11—81no—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C2×Dic22—42no—
187C2×Dic22—42no—
188C2×Dic22—81no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—44no—
195C2×C8×C11C2×D412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C2×D412yes—
200C11×C22⋊C4—42no—
201C42×C11—42no—
202C22⋊Dic11—22no—
203C22⋊Dic11—41no—
204C22⋊Dic11—42no—
205C22⋊Dic11—42no—
206C22⋊Dic11—81no—
207C22⋊Dic11—81no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—81no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×#476—111no—
230C2×#416D1111yescharacteristic
231#2439—111no—
232#2339—111no—
233#2097—111no—
234#2066—111no—
235#2066—111no—
236#2024—111no—
237#1864—111no—
238#1862—111no—
239#1854—111no—
240#1850—111no—
241#1807—111no—
242#1804—111no—
243#1788—111no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11C22⋊Q812yes—
258C23×C11C22×D411yescharacteristic
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—48no—
267D4×C11C22⋊Q814yes—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—48no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11C22⋊Q812yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×Q811yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—84no—
315C2×Dic11—84no—
316C2×Dic11#13512yes—
317Dic22—84no—
318C8×C11—22no—
319C8×C11—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C22×#41C2×D1111yescharacteristic
323C23×C8C2×D1111yescharacteristic
324C2×C4⋊Q8—111no—
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×#117C2×D1111yescharacteristic
328#476—224no—
329C2×#107—111no—
330C2×#106—111no—
331C2×#106—111no—
332C2×#106—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335#416—24no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×#102—111no—
341C2×#102—111no—
342C2×#102C2×D1111yescharacteristic
343C2×#102C2×D1111yescharacteristic
344C2×C22⋊C8—111no—
345#396—221no—
346#393—221no—
347#391—111no—
348#391—111no—
349#391—221no—
350#389—111no—
351#389—111no—
352#387—221no—
353#386—221no—
354#386—221no—
355#382—111no—
356#381—221no—
357#380—111no—
358#380—111no—
359C4×C22⋊C4—111no—
360C2×#95—221no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#336—111no—
366#336—111no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—24no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—41no—
374C22×C11—42no—
375C22×C11—41no—
376C22×C11—42no—
377C22×C11—41no—
378C22×C11—42no—
379C22×C11—41no—
380C22×C11—42no—
381C22×C11C2×C22⋊Q811yescharacteristic
382C22×C11D4211yescharacteristic
383C22×C11#54611yescharacteristic
384C22×C11C2×#13511yescharacteristic
385C22×C11#57511yescharacteristic
386C22×C11#57711yescharacteristic
387C22×C11#57711yescharacteristic
388C4×C11—22no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11—81no—
392C4×C11C2×C22⋊Q811yescharacteristic
393C4×C11#54311yescharacteristic
394C4×C11#54611yescharacteristic
395C4×C11#55111yescharacteristic
396Dic11—22no—
397Dic11—41no—
398Dic11—41no—
399Dic11—41no—
400Dic11—81no—
401Dic11—81no—
402Dic11—81no—
403Dic11—81no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—41no—
408C2×#41—41no—
409C2×#41Dic2214yescomplemented
410C22×Q8—221no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—21no—
413C22×D4C22×D1111yescharacteristic
414C23×C4—21no—
415C23×C4—221no—
416C23×C4—221no—
417C23×C4C22×D1111yescharacteristic
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8—111no—
422C22×C8—111no—
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C4⋊Q8—222no—
426C4⋊Q8—441no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—441no—
431#117—22no—
432#117—41no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—21no—
450C2×C42—111no—
451C2×C42—111no—
452#107—441no—
453#106—222no—
454#106—222no—
455#106—441no—
456C4⋊C8—222no—
457C4⋊C8—441no—
458#103—22no—
459#103—22no—
460#103—441no—
461#103—441no—
462#102—22no—
463#102—222no—
464#102—222no—
465#102C22⋊D1114yes—
466C22⋊C8—222no—
467#95—111no—
468#95—111no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11—42no—
480C2×C11—44no—
481C2×C11#243711yescharacteristic
482C2×C11#307611yescharacteristic
483C2×C11#308411yescharacteristic
484C2×C11#326711yescharacteristic
485C2×C11#328211yescharacteristic
486C2×C11#330311yescharacteristic
487C2×C11#331111yescharacteristic
488C24—21no—
489C24D4×D1111yescharacteristic
490#41—28no—
491#41—44no—
492#41—44no—
493#41—44no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—442no—
500C2×Q8—442no—
501C2×Q8—881no—
502C2×Q8C2×Dic2212yes—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×Dic2212yes—
510C2×D4#433912yes—
511C2×D4C2×C22⋊D1112yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—881no—
535C22×C4—881no—
536C22×C4C2×Dic2212yes—
537C22×C4D4×D1111yescharacteristic
538C22×C4#434112yes—
539C22×C4C23×D1111yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—44no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8C2×C22⋊D1112yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—442no—
565C4⋊C4—442no—
566C4⋊C4—881no—
567C4⋊C4C2×C22⋊D1112yes—
568C22⋊C4—42no—
569C22⋊C4—222no—
570C22⋊C4—441no—
571C22⋊C4—442no—
572C22⋊C4—442no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—42no—
576C42—221no—
577C42—221no—
578C42—221no—
579C42—221no—
580C11#2596211yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23#6693112yes—
595C23C2×D4×D1111yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—884no—
601D4—22no—
602D4—22no—
603D4—22no—
604D4—48no—
605D4#6697714yes—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—48no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—112no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—884no—
647C2×C4—884no—
648C2×C4#6693112yes—
649C2×C4C22×Dic2211yescharacteristic
650C2×C4C2×#433911yescharacteristic
651C2×C4C2×#434111yescharacteristic
652C2×C4#6703711yescharacteristic
653C2×C4#6703711yescharacteristic
654C2×C4C22×C22⋊D1111yescharacteristic
655C8—22no—
656C8—41no—
657C8—441no—
658C8—441no—
659C22—22no—
660C22—22no—
661C22—24no—
662C22—22no—
663C22—42no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—41no—
673C22C2×#6693111yescharacteristic
674C22#1062302111yescharacteristic
675C22D11×#13511yescharacteristic
676C22#1062329911yescharacteristic
677C22#1062330111yescharacteristic
678C22#1062330111yescharacteristic
679C22D4×C22⋊D1111yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—81no—
684C4—222no—
685C4—441no—
686C4—441no—
687C4—441no—
688C4—881no—
689C4—881no—
690C4—881no—
691C4—881no—
692C4#1062301411yescharacteristic
693C4#1062302611yescharacteristic
694C4C2×#6697711yescharacteristic
695C4#1062333711yescharacteristic
696C2—42no—
697C2—44no—
698C2#1307227711yescharacteristic
699C2#1307840011yescharacteristic
700C2#1307847611yescharacteristic
701C2#1308014111yescharacteristic
702C2#1308031711yescharacteristic
703C2#1308054011yescharacteristic
704C2#1308064811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11#25962
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10622374C2semidirect
2. #13072301C2semidirect
4. #13070166C2semidirect
5. #13069995C2semidirect
6. #13069993C2semidirect
7. #13069755C2semidirect
8. #13068879C2semidirect
9. #13068861C2semidirect
10. #13068815C2semidirect
11. #13068794C2semidirect
12. #13068641C2semidirect
13. #13068624C2semidirect
66. C2×C11×#41Q8semidirect
409. C2×#41Dic22semidirect
580. C11#25962semidirect

Maximal subgroups

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

subgroupindex
C2×#106223742
#130723012
#130714462
#130701662
#130699952
#130699932
#130697552
#130688792
#130688612
#130688152
#130687942
#130686412
#130686242
#130685562
C2×C11×#4162
#2596211