Finite Group Databasebeta

← #14675985

Subgroups — #14675985

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622550C211yesmaximal, characteristic, complemented
2C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066877C212yesmaximal, complemented
5#13066876C212yesmaximal, complemented
6#13066842C211yesmaximal, characteristic, complemented
7#13066841C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C211yesmaximal, characteristic
9(C2×D11)⋊#95C212yesmaximal
10(C2×D11)⋊#95C212yesmaximal
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×#95C2211yescharacteristic
20C2×C11×#95C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4C418yescomplemented
36#10622550—24no—
37D11×#95—24no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—22no—
52C22×C4×D11—24no—
53C22×C4×D11—22no—
54C22×C4×D11—24no—
55C22×C4×D11—24no—
56C22×C4×D11—24no—
57C22×C4×D11—42no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11C2×C414yes—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11C2×C414yescomplemented
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4C2×C414yes—
71C2×(C2×D11)⋊C4C2×C414yes—
72C2×C4×Dic11—42no—
73C2×C4×Dic11C2×C414yescomplemented
74C11×#95—22no—
75C11×#95—24no—
76C11×#95—22no—
77C11×#95—42no—
78C11⋊#95—22no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C414yescomplemented
88C11⋊#95C2×C414yescomplemented
89C11⋊#95D414yes—
90#13901—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11C22×C412yes—
99C23×D11#4112yes—
100C23×D11#4114yes—
101C23×D11#4112yes—
102C23×D11#4114yes—
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—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4112yes—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C2×D414yes—
163C2×C4×D11—216no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—44no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—48no—
174C2×C4×D11—48no—
175C42×C11—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179C4×Dic11—44no—
180C2×#383—111no—
181C2×C4×C22⋊C4—111no—
182C22×#95—111no—
183#1443—112no—
184#1443—112no—
185#1434—111no—
186#1434—111no—
187#1434D1111yescharacteristic, complemented
188C22⋊#95—112no—
189C22⋊#95—112no—
190C22⋊#95—111no—
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C2×#4112yes—
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4112yes—
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4112yes—
198C23×C11C2×#4111yescharacteristic
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)12yes—
201C23×C112−1+411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—22no—
220C22×D11#11714yes—
221C22×D11#11714yes—
222C22×D11#11714yes—
223C22×D11#12618yes—
224C22×D11#12618yes—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
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—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C4×D414yes—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
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×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C4×D11—416no—
286C4×D11—432no—
287C24×C4—111no—
288C24×C4—112no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C42—111no—
293C22×C42C2×D1111yescharacteristic
294#383—224no—
295C4×C22⋊C4—118no—
296C2×#95—111no—
297C2×#95—111no—
298C2×#95—111no—
299C2×#95—112no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—224no—
309C2×#95C2×D1111yescharacteristic
310C2×#95C2×D1112yes—
311C2×#95C2×D1111yescharacteristic
312C2×#95C2×D1112yes—
313C22×C11C2×#11711yescharacteristic
314C22×C11C2×#11711yescharacteristic
315C22×C11C2×#11711yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11C4×#4111yescharacteristic
318C22×C11#51811yescharacteristic
319C22×C11#52011yescharacteristic
320C22×C11#52512yes—
321C22×C11C2×#12612yes—
322C22×C11C2×#12612yes—
323C22×C11#52912yes—
324C22×C11#53812yes—
325C22×C11#53912yes—
326C22×C11#54611yescharacteristic
327C22×C11#54612yes—
328C22×C11#54811yescharacteristic
329C22×C11#55112yes—
330C22×C11#55112yes—
331C22×C11#55112yes—
332C22×C11#55212yes—
333C22×C11#55211yescharacteristic
334C22×C11#55312yes—
335C22×C11#55311yescharacteristic
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—28no—
342C2×D11—28no—
343C2×D11—28no—
344C2×D11—28no—
345C2×D11—24no—
346C2×D11#38318yescomplemented
347C4×C11—24no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11—42no—
351C4×C11—82no—
352Dic11—42no—
353Dic11—42no—
354Dic11—42no—
355Dic11—44no—
356Dic11—82no—
357C25—111no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—112no—
362C23×C4—114no—
363C23×C4—112no—
364C23×C4—224no—
365C23×C4—224no—
366C23×C4—224no—
367C23×C4—224no—
368C23×C4—224no—
369C23×C4—224no—
370C23×C4—222no—
371C23×C4—222no—
372C23×C4—442no—
373C23×C4—442no—
374C23×C4—442no—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1112yes—
379C23×C4C22×D1111yescharacteristic
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—114no—
391C2×C42—442no—
392C2×C42C4×D1114yescomplemented
393#95—24no—
394#95—22no—
395#95—22no—
396#95—42no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95—224no—
401#95—224no—
402#95—224no—
403#95—224no—
404#95—222no—
405#95—442no—
406#95—442no—
407#95—442no—
408#95—442no—
409C2×C11C2×#38311yescharacteristic
410C2×C11#229011yescharacteristic
411C2×C11#231811yescharacteristic
412C2×C11#234211yescharacteristic
413C2×C11#234311yescharacteristic
414C2×C11#235211yescharacteristic
415C2×C11#235311yescharacteristic
416C2×C11#248012yes—
417C2×C11#248112yes—
418C2×C11#249312yes—
419C2×C11#251012yes—
420D11—28no—
421C24—112no—
422C24—112no—
423C24—114no—
424C24—114no—
425C24—112no—
426C24—222no—
427C24—221no—
428C24—221no—
429C24—221no—
430C24—221no—
431C24—222no—
432C24C23×D1111yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—114no—
462C22×C4—228no—
463C22×C4—2216no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—222no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—228no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—444no—
491C22×C4—448no—
492C22×C4—448no—
493C22×C4—448no—
494C22×C4—448no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4—448no—
498C22×C4—448no—
499C22×C4C2×C4×D1112yes—
500C22×C4C2×C4×D1112yes—
501C22×C4C2×C4×D1112yes—
502C22×C4#433914yes—
503C22×C4D4×D1112yes—
504C22×C4#434112yes—
505C22⋊C4—228no—
506C22⋊C4—228no—
507C22⋊C4—448no—
508C42—28no—
509C42—444no—
510C11#1390111yescharacteristic, complemented, Sylow
511C23—118no—
512C23—118no—
513C23—114no—
514C23—114no—
515C23—114no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—222no—
527C23—222no—
528C23—222no—
529C23—222no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23C22×C4×D1111yescharacteristic
535C23C2×#433912yes—
536C23C2×D4×D1111yescharacteristic
537C23C2×#434111yescharacteristic
538C23#6703711yescharacteristic
539C23#6704011yescharacteristic
540C23#41×D1111yescharacteristic
541C23#41×D1111yescharacteristic
542C23#41×D1112yes—
543C23#41×D1112yes—
544C23#6704212yes—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—4416no—
588C2×C4—4432no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4(C22⋊D11)⋊C414yes—
607C22—118no—
608C22—228no—
609C22—224no—
610C22—228no—
611C22—224no—
612C22—224no—
613C22—224no—
614C22—224no—
615C22—224no—
616C22—228no—
617C22—228no—
618C22C4×#433911yescharacteristic
619C22C2×(C22⋊D11)⋊C411yescharacteristic
620C22#1062303511yescharacteristic
621C22D11×#11711yescharacteristic
622C22D11×#11711yescharacteristic
623C22D11×#11711yescharacteristic
624C22#1062305211yescharacteristic
625C22#1062305812yes—
626C22#1062306112yes—
627C22#1062307812yes—
628C22#1062308712yes—
629C22#1062308812yes—
630C22#1062311212yes—
631C22#1062314311yescharacteristic
632C22#1062314511yescharacteristic
633C22#1062316411yescharacteristic
634C22#1062317011yescharacteristic
635C22#1062318512yes—
636C22#1062318912yes—
637C22#1062320912yes—
638C22#1062322312yes—
639C22D11×#12612yes—
640C22D11×#12612yes—
641C4—24no—
642C4—42no—
643C4—42no—
644C4—44no—
645C4—82no—
646C4—442no—
647C4—442no—
648C4—442no—
649C4—444no—
650C4—882no—
651C2—228no—
652C2D11×#38311yescharacteristic
653C2#1307106211yescharacteristic
654C2#1307125211yescharacteristic
655C2#1307145811yescharacteristic
656C2#1307147911yescharacteristic
657C2#1307153811yescharacteristic
658C2#1307155711yescharacteristic
659C2#1307286612yes—
660C2#1307288112yes—
661C2#1307300012yes—
662C2#1307318112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13901
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#10622550C2semidirect
4. #13066877C2semidirect
5. #13066876C2semidirect
6. #13066842C2semidirect
7. #13066841C2semidirect
11. C11×#1434C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
63. C2×C42×C11C2×C4semidirect
73. C2×C4×Dic11C2×C4semidirect
87. C11⋊#95C2×C4semidirect
88. C11⋊#95C2×C4semidirect
187. #1434D11semidirect
346. C2×D11#383semidirect
392. C2×C42C4×D11semidirect
510. C11#13901semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
C2×C4×(C2×D11)⋊C42
C2×D11×#952
#130668772
#130668762
#130668422
#130668412
(C2×D11)⋊#952
C11×#14342
#1390111