Finite Group Databasebeta

← #14811296

Subgroups — #14811296

Order 2816.

920 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622442C211yesmaximal, characteristic, complemented
2C2×#10622415C211yesmaximal, characteristic
3#13072331C211yesmaximal, characteristic
4#13071450C211yesmaximal, characteristic
5#13070152C211yesmaximal, characteristic, complemented
6#13069995C211yesmaximal, characteristic, complemented
7#13069767C211yesmaximal, characteristic, complemented
8#13068881C211yesmaximal, characteristic, complemented
9#13068869C211yesmaximal, characteristic, complemented
10#13068816C211yesmaximal, characteristic
11#13068797C211yesmaximal, characteristic
12#13068646C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C11×#2066C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622605—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622442—24no—
48#10622415—24no—
49#10622289—21no—
50#10622280—21no—
51#10622279—21no—
52#10622265—21no—
53#10622259—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—41no—
66C2×Q8×D11—41no—
67C2×Q8×D11Q814yes—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—41no—
103#66945—22no—
104#66945—41no—
105#66940—22no—
106#66940—41no—
107#66923—22no—
108#66923—41no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C11×#106—41no—
112C11×C4⋊C8—22no—
113C11×#103—22no—
114C11×#103—41no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—22no—
119#66899—41no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127(C2×D11)⋊C8—22no—
128#66882—22no—
129#66881—22no—
130#66880—22no—
131#66880D414yes—
132Dic11⋊C8—41no—
133#66874—22no—
134#66874—22no—
135#66871—41no—
136#25981—111nomaximal, Sylow
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158Q8×D11—28no—
159Q8×D11—44no—
160Q8×D11—44no—
161Q8×D11—44no—
162C2×C4×D11—24no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11C2×Q812yes—
170C2×C4×D11#4112yes—
171C2×Dic22—24no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—42no—
176C2×Dic22—42no—
177C2×Dic22C2×D412yes—
178C2×Dic22C2×Q812yes—
179C2×Dic22#4112yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11C2×D412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—81no—
193C42×C11—21no—
194C42×C11—21no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D412yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
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—21no—
224#4313—44no—
225C2×#479—111no—
226C2×#419—111no—
227#2441—111no—
228Q8×C22⋊C4—111no—
229#2095—111no—
230#2066—111no—
231#2066D1111yescharacteristic, complemented
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1854—111no—
236#1851—111no—
237#1809—111no—
238#1803—111no—
239#1787—111no—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11C22⋊Q812yes—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—41no—
251Q8×C11—41no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11C22⋊Q812yes—
296C2×Dic11#13712yes—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—48no—
302Dic22—22no—
303Dic22—22no—
304Dic22—22no—
305Dic22—48no—
306Dic22C22⋊Q814yes—
307C8×C11—22no—
308C8×C11—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C23×Q8—111no—
312C22×M16—111no—
313C2×#125—111no—
314C2×C4×Q8—111no—
315C2×C4×Q8—111no—
316C2×#117—111no—
317#479—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106C2×D1111yescharacteristic
322C2×C4⋊C8—111no—
323C2×C4⋊C8C2×D1111yescharacteristic
324#419—224no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103C2×D1111yescharacteristic
332C2×#103C2×D1111yescharacteristic
333C2×C22⋊C8—111no—
334#399—221no—
335#396—221no—
336#391—111no—
337#391—221no—
338#391—221no—
339#391C2×D1111yescharacteristic
340#389—111no—
341#389—221no—
342#389C2×D1111yescharacteristic
343#387—221no—
344#384—111no—
345#380—111no—
346#380—111no—
347#380—221no—
348C4×C22⋊C4—111no—
349C4×C22⋊C4—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340C2×D1111yescharacteristic
354#336—111no—
355#336—111no—
356C22×C11C2×C22⋊Q811yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54611yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57811yescharacteristic
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11C2×C22⋊Q811yescharacteristic
377C4×C11#54311yescharacteristic
378C4×C11#54611yescharacteristic
379C4×C11#55111yescharacteristic
380Dic11—24no—
381Dic11—22no—
382Dic11—22no—
383Dic11—42no—
384Dic11—41no—
385Dic11—81no—
386Dic11—81no—
387C22×Q8—114no—
388C22×Q8—111no—
389C22×Q8—221no—
390C22×Q8—222no—
391C22×Q8—222no—
392C22×Q8—222no—
393C22×Q8—441no—
394C22×Q8—441no—
395C22×Q8C22×D1111yescharacteristic
396C23×C4—111no—
397C23×C4—221no—
398C2×M16—222no—
399C2×M16—222no—
400C2×M16—441no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405#125—222no—
406#125—441no—
407C4×Q8—222no—
408C4×Q8—222no—
409C4×Q8—441no—
410C4×Q8—441no—
411#117—222no—
412#117—441no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—111no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42C22×D1111yescharacteristic
437#107—222no—
438#107—441no—
439#106—41no—
440#106—222no—
441C4⋊C8—22no—
442C4⋊C8—441no—
443#103—22no—
444#103—41no—
445#103—114no—
446#103—222no—
447#103—222no—
448#103—222no—
449#103—222no—
450#103—441no—
451C22⋊C8—222no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11#243711yescharacteristic
463C2×C11#307811yescharacteristic
464C2×C11#308211yescharacteristic
465C2×C11#327111yescharacteristic
466C2×C11#327611yescharacteristic
467C2×C11#332011yescharacteristic
468C2×C11#332711yescharacteristic
469D11—42no—
470C24—111no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—112no—
477C2×Q8—112no—
478C2×Q8—112no—
479C2×Q8—224no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—228no—
484C2×Q8—442no—
485C2×Q8—442no—
486C2×Q8—444no—
487C2×Q8—444no—
488C2×Q8—444no—
489C2×Q8Q8×D1112yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—111no—
499C22×C4—224no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4D4×D1111yescharacteristic
511C22×C4D4×D1111yescharacteristic
512C22×C4C23×D1111yescharacteristic
513M16—444no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8D4×D1112yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—81no—
533C4⋊C4—112no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C22⋊C4—222no—
547C22⋊C4—441no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C42—21no—
552C42—21no—
553C42—221no—
554C42—221no—
555C42—442no—
556C42—442no—
557C42—442no—
558C11#2598111yescharacteristic, complemented, Sylow
559C23—112no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23C2×D4×D1111yescharacteristic
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8—114no—
572Q8—222no—
573Q8—222no—
574Q8—222no—
575Q8—448no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—448no—
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×C4C2×D4×D1111yescharacteristic
621C2×C4#6703711yescharacteristic
622C2×C4C2×Q8×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704211yescharacteristic
626C8—22no—
627C8—41no—
628C8—441no—
629C8—441no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22#1062314011yescharacteristic
638C22#1062314311yescharacteristic
639C22D11×C22⋊Q811yescharacteristic
640C22#1062329311yescharacteristic
641C22#1062329911yescharacteristic
642C22D11×#13711yescharacteristic
643C22#1062331011yescharacteristic
644C4—41no—
645C4—42no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4—222no—
651C4—224no—
652C4—222no—
653C4—441no—
654C4—442no—
655C4—881no—
656C4—881no—
657C4#1062314111yescharacteristic
658C4D11×C22⋊Q811yescharacteristic
659C4#1062316511yescharacteristic
660C4#1062323611yescharacteristic
661C2—442no—
662C2#1307227811yescharacteristic
663C2#1307841911yescharacteristic
664C2#1307845111yescharacteristic
665C2#1308019811yescharacteristic
666C2#1308025911yescharacteristic
667C2#1308079411yescharacteristic
668C2#1308089111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2066C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2066D11
hypocenterC11#25981
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2066

Complements

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

NH ≅ G/Ntype
1. C2×#10622442C2semidirect
5. #13070152C2semidirect
6. #13069995C2semidirect
7. #13069767C2semidirect
8. #13068881C2semidirect
9. #13068869C2semidirect
13. #13068620C2semidirect
15. C11×#2066C2semidirect
231. #2066D11semidirect
558. C11#25981semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
C2×#106224152
#130723312
#130714502
#130701522
#130699952
#130697672
#130688812
#130688692
#130688162
#130687972
#130686462
#130686202
#130685492
C11×#20662
#2598111