Finite Group Databasebeta

← #14675236

Subgroups — #14675236

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622277C211yesmaximal, characteristic
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×#10622279C211yesmaximal, characteristic
4#13066854C212yesmaximal
5#13066852C212yesmaximal
6#13066843C211yesmaximal, characteristic, complemented
7#13066842C212yesmaximal, complemented
8#13066841C211yesmaximal, characteristic, complemented
9C4×C11⋊#95C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C4×C11×#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4C418yescomplemented
36#10622279C418yescomplemented
37#10622277C418yescomplemented
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×C4×D11—42no—
50C22×C4×D11—42no—
51C22×C4×D11C2×C414yes—
52C22×C4×D11C2×C414yes—
53C22×C4×D11C2×C414yes—
54C2×C42×C11—24no—
55C2×C42×C11—24no—
56C2×C42×C11—42no—
57C2×C42×C11—42no—
58C2×C42×C11C2×C414yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×(C2×D11)⋊C4C2×C414yes—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×(C2×D11)⋊C4C2×C418yes—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11C2×C418yes—
78C2×C4×Dic11C2×C414yes—
79C11×#95—24no—
80C11×#95C2×C414yes—
81C11×#95C2×C414yes—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C414yes—
88C11⋊#95C2×C418yes—
89C11⋊#95C2×C414yes—
90C11⋊#95C2×C414yes—
91C11⋊#95C2×C414yes—
92#13807—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C23×D11—22no—
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—22no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11C22×C412yes—
103C23×D11C22×C412yes—
104C23×D11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C414yes—
130C22×C4×C11#4114yes—
131C22×C4×C11#4114yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C414yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C412yes—
161C22×Dic11#4112yes—
162C22×Dic11#4112yes—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11C42116yescomplemented
168C42×C11—44no—
169C42×C11—48no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—48no—
174C4×Dic11—44no—
175C4×Dic11—48no—
176C4×Dic11—48no—
177C2×#381—111no—
178C2×C4×C22⋊C4—111no—
179C2×C4×C22⋊C4—111no—
180#1437—112no—
181#1437—112no—
182#1434—111no—
183#1434—111no—
184#1434—112no—
185C4×#95—112no—
186C4×#95—111no—
187C4×#95D1111yescharacteristic, complemented
188C23×C11C23×C411yescharacteristic
189C23×C11C23×C411yescharacteristic
190C23×C11C23×C411yescharacteristic
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11H(5,𝔽2)12yes—
198C23×C11H(5,𝔽2)12yes—
199C22×D11—24no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11C2×C4214yes—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11C2×C4214yes—
249C2×C4×C11#11718yes—
250C2×C4×C11#11714yes—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11C2×C4214yes—
279C2×Dic11#11714yes—
280C4×D11—416no—
281C24×C4—111no—
282C22×C22⋊C4—111no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C42—111no—
287C22×C42—112no—
288C22×C42—112no—
289C22×C42C2×D1112yes—
290C22×C42C2×D1111yescharacteristic
291#381—118no—
292C4×C22⋊C4—118no—
293C4×C22⋊C4—118no—
294C2×#95—111no—
295C2×#95—112no—
296C2×#95—111no—
297C2×#95—111no—
298C2×#95—111no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95C2×D1112yes—
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1111yescharacteristic
307C22×C11C22×C4211yescharacteristic
308C22×C11C2×#11712yes—
309C22×C11C2×#11711yescharacteristic
310C22×C11C2×#11711yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11C4×#4111yescharacteristic
313C22×C11C4×#4112yes—
314C22×C11C4×#4111yescharacteristic
315C22×C11C4×#4111yescharacteristic
316C22×C11C4×#4111yescharacteristic
317C22×C11C4×#4111yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#51811yescharacteristic
320C22×C11#51812yes—
321C22×C11#51812yes—
322C22×C11#55112yes—
323C22×C11#55112yes—
324C22×C11#55312yes—
325C22×C11#55312yes—
326C22×C11#55312yes—
327C22×C11#55312yes—
328C22×C11#55912yes—
329C22×C11#55912yes—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—44no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—44no—
340C2×D11—44no—
341C4×C11—28no—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—44no—
346Dic11—24no—
347Dic11—24no—
348Dic11—44no—
349Dic11—42no—
350Dic11—44no—
351C25—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—114no—
355C23×C4—114no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—111no—
359C23×C4—112no—
360C23×C4—442no—
361C23×C4—442no—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C2×C22⋊C4—114no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—114no—
384C2×C42—118no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—442no—
388C2×C42—442no—
389C2×C42—442no—
390C2×C42—442no—
391C2×C42C4×D1114yes—
392#95—24no—
393#95—114no—
394#95—114no—
395#95—114no—
396#95—118no—
397#95—114no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—442no—
402#95—442no—
403#95C4×D1114yes—
404#95C4×D1114yes—
405C2×C11C4×#11711yescharacteristic
406C2×C11C4×#11711yescharacteristic
407C2×C11#227311yescharacteristic
408C2×C11#235312yes—
409C2×C11#235311yescharacteristic
410C2×C11#235311yescharacteristic
411C2×C11#235712yes—
412C2×C11#235711yescharacteristic
413C2×C11#235711yescharacteristic
414C2×C11#237412yes—
415C2×C11#237412yes—
416D11—44no—
417C24—112no—
418C24—112no—
419C24—112no—
420C24—222no—
421C24—222no—
422C24—221no—
423C24—222no—
424C24—221no—
425C24—221no—
426C24—221no—
427C24—222no—
428C24C23×D1111yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—1116no—
454C22×C4—114no—
455C22×C4—114no—
456C22×C4—112no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—444no—
478C22×C4—444no—
479C22×C4—448no—
480C22×C4—448no—
481C22×C4C2×C4×D1114yes—
482C22×C4C2×C4×D1112yes—
483C22×C4C2×C4×D1112yes—
484C22×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1114yes—
487C22×C4C2×C4×D1112yes—
488C22×C4#433914yes—
489C22×C4#433914yes—
490C22×C4#434112yes—
491C22×C4#434312yes—
492C22⋊C4—228no—
493C22⋊C4—2216no—
494C22⋊C4—228no—
495C22⋊C4—448no—
496C42—44no—
497C42—48no—
498C42—444no—
499C42—448no—
500C42—448no—
501C11#1380711yescharacteristic, complemented, Sylow
502C23—114no—
503C23—224no—
504C23—224no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—224no—
514C23—224no—
515C23—222no—
516C23—222no—
517C23—442no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23C22×C4×D1111yescharacteristic
526C23C22×C4×D1111yescharacteristic
527C23C22×C4×D1111yescharacteristic
528C23C2×#433912yes—
529C23C2×#433912yes—
530C23C2×#434111yescharacteristic
531C23#6703712yes—
532C23C2×#434311yescharacteristic
533C23#41×D1111yescharacteristic
534C23#41×D1111yescharacteristic
535C23#6704212yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—114no—
563C2×C4—114no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—4416no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4C42×D1114yes—
593C2×C4#6692518yes—
594C2×C4#6694514yes—
595C22—224no—
596C22—224no—
597C22—224no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—442no—
602C22—442no—
603C22—444no—
604C22—442no—
605C22—442no—
606C22C2×C42×D1111yescharacteristic
607C22C2×#6692512yes—
608C22C4×#433912yes—
609C22C4×#433911yescharacteristic
610C22C4×#433911yescharacteristic
611C22#1062301711yescharacteristic
612C22#1062302612yes—
613C22C2×#6694511yescharacteristic
614C22#1062304512yes—
615C22D11×#11711yescharacteristic
616C22#1062305211yescharacteristic
617C22#1062305812yes—
618C22#1062306112yes—
619C22C4×#434111yescharacteristic
620C22C4×#434111yescharacteristic
621C22#1062307112yes—
622C22#1062307612yes—
623C22#1062307612yes—
624C22#1062309012yes—
625C22#1062309612yes—
626C22C4×#434311yescharacteristic
627C22C4×#434311yescharacteristic
628C22#1062311612yes—
629C4—24no—
630C4—28no—
631C4—24no—
632C4—44no—
633C4—42no—
634C4—224no—
635C4—224no—
636C4—444no—
637C4—444no—
638C4—442no—
639C2—444no—
640C2C4×#6694511yescharacteristic
641C2C4×#6692511yescharacteristic
642C2#1307096811yescharacteristic
643C2#1307155012yes—
644C2#1307155211yescharacteristic
645C2#1307155711yescharacteristic
646C2#1307158512yes—
647C2#1307158711yescharacteristic
648C2#1307159011yescharacteristic
649C2#1307174512yes—
650C2#1307175012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4×#95D11
hypocenterC11#13807
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
6. #13066843C2semidirect
7. #13066842C2semidirect
8. #13066841C2semidirect
9. C4×C11⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C4×C11×#95C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
36. #10622279C4semidirect
37. #10622277C4semidirect
167. C2×C4×D11C42semidirect
187. C4×#95D11semidirect
501. C11#13807semidirect

Maximal subgroups

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

subgroupindex
C2×#106222772
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668542
#130668522
#130668432
#130668422
#130668412
C4×C11⋊#952
#95×Dic112
C4×C11×#952
#1380711