Finite Group Databasebeta

← #14810937

Subgroups — #14810937

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622409C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic
3#13072341C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic
5#13070162C211yesmaximal, characteristic, complemented
6#13070009C211yesmaximal, characteristic, complemented
7#13069993C211yesmaximal, characteristic, complemented
8#13069765C211yesmaximal, characteristic, complemented
9#13068882C211yesmaximal, characteristic, complemented
10#13068872C211yesmaximal, characteristic, complemented
11#13068806C211yesmaximal, characteristic
12#13068793C211yesmaximal, characteristic
13#13068639C211yesmaximal, characteristic
14#13068629C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622843—21no—
29#10622843—21no—
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32C2×#66899—24no—
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622825—21no—
38#10622825C2211yescharacteristic
39C4×C22⋊Dic11—21no—
40C4×C22⋊Dic11C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66882C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622590C2211yescharacteristic
47#10622586C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622563—21no—
51#10622555—21no—
52#10622409—24no—
53#10622274—21no—
54#10622273—21no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—41no—
66C22×Q8×C11—41no—
67C22×Q8×C11Q814yes—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80C2×C22⋊Dic11D411yescharacteristic
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83Q8×Dic11—41no—
84Q8×Dic11—41no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66943—22no—
108#66943—41no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103—41no—
112C11×#103—41no—
113C11×C22⋊C8—22no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117#66899—22no—
118#66899D414yes—
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⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66882—22no—
131#66882—41no—
132Dic11⋊C8—22no—
133Dic11⋊C8—41no—
134#66872—22no—
135#66872—41no—
136#25957—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—28no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—42no—
149C2×Q8×C11—42no—
150C2×Q8×C11—44no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2×Q812yes—
155C2×Q8×C11C2×Q812yes—
156C2×Q8×C11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
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—81no—
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C22⋊C4—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196C22⋊Dic11—42no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—81no—
209C4⋊Dic11C2×D412yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—42no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—44no—
224C2×C11⋊C8C2×D412yes—
225C2×#479—111no—
226C22×#103—111no—
227#2442—111no—
228Q8×C22⋊C4—111no—
229#2097—111no—
230#2068—111no—
231#2066—111no—
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1852—111no—
236#1850—111no—
237#1807—111no—
238#1805—111no—
239#1787D1111yescharacteristic
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11C22⋊Q812yes—
245C23×C11#13512yes—
246C23×C11#13712yes—
247C23×C11C22×D411yescharacteristic
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—48no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11C22⋊Q814yes—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—48no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C22⋊Q812yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×Q811yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—84no—
308C8×C11—41no—
309C8×C11—41no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C23×Q8C2×D1111yescharacteristic
313C23×C8—111no—
314C2×#125—111no—
315C2×C4×Q8—111no—
316C2×C4×Q8—111no—
317C22×C4⋊C4—111no—
318#479—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—224no—
330C2×#103C2×D1111yescharacteristic
331C2×#103C2×D1111yescharacteristic
332C2×#103C2×D1111yescharacteristic
333C2×#103C2×D1111yescharacteristic
334C2×C22⋊C8C2×D1111yescharacteristic
335#400—221no—
336#398—221no—
337#391—111no—
338#391—111no—
339#391—221no—
340#391—221no—
341#389—111no—
342#389—111no—
343#385—221no—
344#382—111no—
345#380—111no—
346#380—221no—
347#380—221no—
348#380C2×D1111yescharacteristic
349C4×C22⋊C4—111no—
350C4×C22⋊C4—221no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11#47914yescomplemented
364C22×C11C2×C22⋊Q811yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11C2×#13711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—24no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11C2×C22⋊Q811yescharacteristic
377C4×C11#54311yescharacteristic
378C4×C11#54611yescharacteristic
379C4×C11#55111yescharacteristic
380Dic11—41no—
381Dic11—41no—
382Dic11—42no—
383Dic11—41no—
384Dic11—41no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8Dic2214yes—
395C22×Q8C22×D1111yescharacteristic
396C22×Q8C22×D1111yescharacteristic
397C23×C4—21no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8—441no—
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407#125—222no—
408#125—441no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—441no—
412C4×Q8—441no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—441no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42—221no—
436#107—222no—
437#107—441no—
438#106—222no—
439#106—441no—
440C4⋊C8—222no—
441C4⋊C8—441no—
442#103—22no—
443#103—22no—
444#103—41no—
445#103—41no—
446#103—114no—
447#103—222no—
448#103—222no—
449#103—222no—
450C22⋊C8—22no—
451#95—21no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—24no—
464C2×C11#243711yescharacteristic
465C2×C11C2×#47911yescharacteristic
466C2×C11#308211yescharacteristic
467C2×C11#327011yescharacteristic
468C2×C11#328211yescharacteristic
469C2×C11#330011yescharacteristic
470C2×C11#332011yescharacteristic
471C24D4×D1111yescharacteristic
472C2×Q8—24no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—28no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C2×Dic2212yes—
488C2×Q8C2×Dic2212yes—
489C2×Q8D4×D1112yes—
490C2×Q8#434112yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—881no—
513C22×C4C2×Dic2212yes—
514C22×C4D4×D1111yescharacteristic
515C22×C4#434112yes—
516C22×C4C23×D1111yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—112no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—444no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—112no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—42no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—442no—
553C42—221no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—442no—
558C42—442no—
559C11#2595711yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#6693112yes—
565C23#6696812yes—
566C23#6697212yes—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8#6693114yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—48no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—884no—
621C2×C4#6693112yes—
622C2×C4C22×Dic2211yescharacteristic
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#6703711yescharacteristic
628C8—41no—
629C8—41no—
630C8—222no—
631C8—441no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1062240914yescomplemented
639C22C2×#6693111yescharacteristic
640C22#1062312111yescharacteristic
641C22#1062312211yescharacteristic
642C22C2×#6696811yescharacteristic
643C22C2×#6697211yescharacteristic
644C22#1062330911yescharacteristic
645C22#1062331011yescharacteristic
646C4—22no—
647C4—24no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4—441no—
655C4—442no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4C2×#6693111yescharacteristic
660C4#1062301411yescharacteristic
661C4#1062311811yescharacteristic
662C4#1062312211yescharacteristic
663C2—24no—
664C2#1307228211yescharacteristic
665C2C2×#1062240911yescharacteristic
666C2#1307846011yescharacteristic
667C2#1308017911yescharacteristic
668C2#1308031611yescharacteristic
669C2#1308050711yescharacteristic
670C2#1308079111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1787D11
hypocenterC11#25957
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
1. C2×#10622409C2semidirect
5. #13070162C2semidirect
6. #13070009C2semidirect
7. #13069993C2semidirect
8. #13069765C2semidirect
9. #13068882C2semidirect
10. #13068872C2semidirect
14. #13068629C2semidirect
363. C22×C11#479semidirect
559. C11#25957semidirect
638. C22#10622409semidirect

Maximal subgroups

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

subgroupindex
C2×#106224092
C22×#668992
#130723412
Q8×C22⋊Dic112
#130701622
#130700092
#130699932
#130697652
#130688822
#130688722
#130688062
#130687932
#130686392
#130686292
C11×#17872
#2595711