Finite Group Databasebeta

← #14675111

Subgroups — #14675111

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622603C212yesmaximal
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3#13066852C212yesmaximal
4#13066848C212yesmaximal, complemented
5#13066843C211yesmaximal, characteristic, complemented
6#13066840C212yesmaximal, complemented
7(C2×D11)⋊#95C211yesmaximal, characteristic
8(C2×D11)⋊#95C211yesmaximal, characteristic
9#95×Dic11C211yesmaximal, characteristic, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622603C4116yescomplemented
36C4×(C2×D11)⋊C4C418yescomplemented
37C24×D11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—22no—
50C22×C4×D11—42no—
51C22×C4×D11—42no—
52C22×C4×D11C2×C414yes—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4C2×C418yescomplemented
56C2×C42×C11—42no—
57C2×C42×C11C2×C414yes—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4C2×C414yes—
64C2×(C2×D11)⋊C4C2×C418yes—
65C2×(C2×D11)⋊C4C2×C418yes—
66C2×(C2×D11)⋊C4C2×C414yes—
67C2×(C2×D11)⋊C4C2×C418yes—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11—42no—
72C2×C4×Dic11—42no—
73C2×C4×Dic11—42no—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C418yescomplemented
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—42no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95C2×C414yes—
86C11⋊#95C2×C414yes—
87C11⋊#95C2×C418yescomplemented
88C11⋊#95C2×C418yescomplemented
89#13788—111nomaximal, Sylow
90C24×C11C2411yescharacteristic
91C23×D11—22no—
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—21no—
95C23×D11—21no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11C22×C414yes—
101C23×D11C22×C412yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
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—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11C22×C412yes—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C414yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C412yes—
159C22×Dic11#4114yes—
160C2×C4×D11—28no—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C11×C4⋊C4—48no—
166C42×C11—44no—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—48no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4C42116yescomplemented
171C4×Dic11—44no—
172C4×Dic11—48no—
173C4×Dic11—48no—
174C2×#388—112no—
175C2×C4×C22⋊C4—111no—
176#1437—112no—
177#1436—112no—
178C4⋊#95D1111yescharacteristic, complemented
179#1434—111no—
180#1434—112no—
181C22⋊#95—111no—
182C22⋊#95—111no—
183C4×#95—111no—
184C4×#95—111no—
185C23×C11C23×C411yescharacteristic
186C23×C11C23×C412yes—
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4111yescharacteristic
189C23×C11C2×#4112yes—
190C23×C11H(5,𝔽2)11yescharacteristic
191C23×C11H(5,𝔽2)12yes—
192C23×C11H(5,𝔽2)11yescharacteristic
193C23×C11H(5,𝔽2)12yes—
194C23×C112−1+411yescharacteristic
195C23×C112−1+411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—41no—
213C22×D11—42no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—42no—
218C22×D11C2×C4214yes—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
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—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11C2×C4214yes—
247C2×C4×C11#11714yes—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11C2×C4214yes—
276C2×Dic11#11714yes—
277C4×D11—416no—
278C24×C4—111no—
279C22×C4⋊C4C2×D1112yes—
280C22×C22⋊C4—111no—
281C22×C22⋊C4—111no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C42—111no—
285C22×C42—112no—
286C22×C42—112no—
287C22×C42C2×D1111yescharacteristic
288#388—1116no—
289C4×C22⋊C4—118no—
290C2×#95—112no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—111no—
294C2×#95—111no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1111yescharacteristic
301C2×#95C2×D1111yescharacteristic
302C2×#95C2×D1112yes—
303C22×C11C22×C4211yescharacteristic
304C22×C11C2×#11711yescharacteristic
305C22×C11C2×#11711yescharacteristic
306C22×C11C4×#4112yes—
307C22×C11C4×#4112yes—
308C22×C11#51811yescharacteristic
309C22×C11#51812yes—
310C22×C11#51811yescharacteristic
311C22×C11#51812yes—
312C22×C11#52011yescharacteristic
313C22×C11#52011yescharacteristic
314C22×C11#52012yes—
315C22×C11#52012yes—
316C22×C11#53812yes—
317C22×C11#53812yes—
318C22×C11#53812yes—
319C22×C11#53912yes—
320C22×C11#54011yescharacteristic
321C22×C11#54012yes—
322C22×C11#54111yescharacteristic
323C22×C11#54211yescharacteristic
324C22×C11#54211yescharacteristic
325C22×C11#54212yes—
326C2×D11—24no—
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—44no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C4×C11—24no—
338C4×C11—24no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—44no—
342Dic11—24no—
343Dic11—24no—
344Dic11—42no—
345Dic11—44no—
346Dic11—44no—
347C25—111no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—112no—
351C23×C4—112no—
352C23×C4—111no—
353C23×C4—114no—
354C23×C4—222no—
355C23×C4—222no—
356C23×C4—442no—
357C23×C4—442no—
358C23×C4C22×D1112yes—
359C23×C4C22×D1112yes—
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4C4×D1118yescomplemented
366C2×C22⋊C4—114no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—442no—
373C2×C22⋊C4—442no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C42—42no—
377C2×C42—114no—
378C2×C42—118no—
379C2×C42—224no—
380C2×C42—442no—
381C2×C42—442no—
382C2×C42—442no—
383C2×C42—442no—
384C2×C42—442no—
385C2×C42C4×D1114yes—
386#95—22no—
387#95—22no—
388#95—42no—
389#95—114no—
390#95—114no—
391#95—118no—
392#95—118no—
393#95—224no—
394#95—222no—
395#95—222no—
396#95—442no—
397#95—442no—
398#95—442no—
399C2×C11C4×#11711yescharacteristic
400C2×C11#227511yescharacteristic
401C2×C11#227511yescharacteristic
402C2×C11#231211yescharacteristic
403C2×C11#231411yescharacteristic
404C2×C11#231811yescharacteristic
405C2×C11#231911yescharacteristic
406C2×C11#233312yes—
407C2×C11#233412yes—
408C2×C11#233512yes—
409C2×C11#233712yes—
410D11—44no—
411C24—114no—
412C24—112no—
413C24—221no—
414C24—221no—
415C24—221no—
416C24—222no—
417C24—221no—
418C24—221no—
419C24—221no—
420C24—222no—
421C24—222no—
422C24C23×D1111yescharacteristic
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—114no—
448C22×C4—114no—
449C22×C4—112no—
450C22×C4—114no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—228no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4—448no—
477C22×C4—448no—
478C22×C4C2×C4×D1112yes—
479C22×C4C2×C4×D1114yes—
480C22×C4C2×C4×D1114yes—
481C22×C4C2×C4×D1112yes—
482C22×C4C2×C4×D1114yes—
483C22×C4C2×C4×D1112yes—
484C22×C4#434112yes—
485C22×C4#434312yes—
486C4⋊C4—48no—
487C22⋊C4—1116no—
488C22⋊C4—228no—
489C22⋊C4—448no—
490C22⋊C4—448no—
491C42—44no—
492C42—444no—
493C42—448no—
494C42—448no—
495C11#1378811yescharacteristic, complemented, Sylow
496C23—114no—
497C23—224no—
498C23—222no—
499C23—222no—
500C23—224no—
501C23—222no—
502C23—222no—
503C23—222no—
504C23—222no—
505C23—224no—
506C23—224no—
507C23—224no—
508C23—224no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23C22×C4×D1111yescharacteristic
520C23C22×C4×D1112yes—
521C23C2×#434111yescharacteristic
522C23#6703711yescharacteristic
523C23#6703711yescharacteristic
524C23#6703712yes—
525C23C2×#434311yescharacteristic
526C23#6704011yescharacteristic
527C23#6704011yescharacteristic
528C23#41×D1112yes—
529C23#6704212yes—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—4416no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4C42×D1114yes—
588C2×C4#6694514yes—
589C22—224no—
590C22—224no—
591C22—224no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—442no—
597C22—442no—
598C22—442no—
599C22—442no—
600C22C2×C42×D1111yescharacteristic
601C22#1062301712yes—
602C22#1062301711yescharacteristic
603C22C2×#6694511yescharacteristic
604C22#1062303512yes—
605C22#1062303511yescharacteristic
606C22#1062303511yescharacteristic
607C22D11×#11711yescharacteristic
608C22#1062305211yescharacteristic
609C22C4×#434112yes—
610C22#1062307612yes—
611C22C4×#434312yes—
612C22#1062310512yes—
613C22#1062314612yes—
614C22#1062314812yes—
615C22#1062317112yes—
616C22#1062317512yes—
617C22#1062320912yes—
618C22#1062322312yes—
619C22#1062325011yescharacteristic
620C22#1062326211yescharacteristic
621C22#1062326411yescharacteristic
622C22#1062326411yescharacteristic
623C4—24no—
624C4—24no—
625C4—44no—
626C4—44no—
627C4—42no—
628C4—224no—
629C4—224no—
630C4—444no—
631C4—444no—
632C4—442no—
633C2—444no—
634C2C4×#6694511yescharacteristic
635C2#1307097411yescharacteristic
636C2#1307097611yescharacteristic
637C2#1307121311yescharacteristic
638C2#1307122411yescharacteristic
639C2#1307125211yescharacteristic
640C2#1307125811yescharacteristic
641C2#1307137512yes—
642C2#1307138412yes—
643C2#1307140912yes—
644C2#1307142812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13788
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. #13066848C2semidirect
5. #13066843C2semidirect
6. #13066840C2semidirect
9. #95×Dic11C2semidirect
10. #95×Dic11C2semidirect
11. C11×C4⋊#95C2semidirect
35. #10622603C4semidirect
36. C4×(C2×D11)⋊C4C4semidirect
55. C2×C11×C4⋊C4C2×C4semidirect
75. C2×C4×Dic11C2×C4semidirect
87. C11⋊#95C2×C4semidirect
88. C11⋊#95C2×C4semidirect
170. (C2×D11)⋊C4C42semidirect
178. C4⋊#95D11semidirect
365. C2×C4⋊C4C4×D11semidirect
495. C11#13788semidirect

Maximal subgroups

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

subgroupindex
C2×#106226032
C2×C4×(C2×D11)⋊C42
#130668522
#130668482
#130668432
#130668402
(C2×D11)⋊#952
#95×Dic112
C11×C4⋊#952
#1378811