Finite Group Databasebeta

← #14926647

Subgroups — #14926647

Order 2816.

4298 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×#10623024C211yesmaximal, characteristic, complemented
2C2×#10623335C212yesmaximal, complemented
3C22×#66992C212yesmaximal, complemented
4#13076959C214yesmaximal, complemented
5#13074720C214yesmaximal, complemented
6#13073546C214yesmaximal, complemented
7#13073544C214yesmaximal, complemented
8#13073085C214yesmaximal, complemented
9#13072251C214yesmaximal, complemented
10C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#534C211yesmaximal, characteristic, complemented
12C23×D4×C11C2212yes—
13C23×C22⋊D11C2212yes—
14C23×C22⋊D11C2212yescomplemented
15C24×Dic11C2211yescharacteristic
16C11×#534—28no—
17C2×C11×#123C2214yescomplemented
18C2×C11×#121C2214yescomplemented
19C2×C11×#120C2214yescomplemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C2×#67006C2214yescomplemented
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yescomplemented
24#10623335—216no—
25C2×#66993C2214yescomplemented
26C2×#66992—216no—
27C2×#66992C2214yes—
28C2×#66992C2214yes—
29C2×#66992C2214yescomplemented
30C2×#66992C2218yescomplemented
31C2×#66992C2214yescomplemented
32C2×#66990C2214yescomplemented
33C2×#66988C2214yescomplemented
34C2×#66983C2214yescomplemented
35C2×#66982C2214yescomplemented
36C22×(C2×D11)⋊C4C2212yescomplemented
37C22×Dic11⋊C4C2212yescomplemented
38C22×C4×Dic11C2212yescomplemented
39#10623024—28no—
40C2×#66939C2214yescomplemented
41C2×#66935C2214yescomplemented
42#10622836C2218yescomplemented
43#10622834C2214yescomplemented
44C2×C11⋊#95C2212yescomplemented
45#10622605C2218yescomplemented
46#10622601C2214yescomplemented
47#10622589C2214yescomplemented
48#10622573C2218yescomplemented
49#10622570C2218yescomplemented
50#10622570C2218yescomplemented
51#10622562C2218yescomplemented
52C22⋊C4×Dic11C2214yescomplemented
53C22⋊C4×Dic11C2214yescomplemented
54C25×C11C2312yes—
55C25×C11C2311yescharacteristic
56C24×D11C2312yes—
57C22×D4×C11—28no—
58C22×D4×C11—28no—
59C22×D4×C11—28no—
60C22×D4×C11C2314yes—
61C22×D4×C11C2314yes—
62C22×D4×C11C2314yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C22×C22⋊D11—28no—
66C22×C22⋊D11—28no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—48no—
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2314yes—
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2318yes—
74C22×C22⋊D11C2314yes—
75C23×Dic11—44no—
76C23×Dic11D418yescomplemented
77C23×Dic11C2312yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2312yes—
80C23×Dic11C2312yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2312yes—
83C22×D44C2314yes—
84C11×#123—216no—
85C11×#121—216no—
86C11×#120—216no—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4D418yescomplemented
89C2×C11×C22⋊C4C2318yes—
90C2×C11×C22⋊C4C2314yes—
91#67006—216no—
92C2×C22⋊Dic11—28no—
93C2×C22⋊Dic11D418yescomplemented
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2314yes—
98#66993—48no—
99#66992—216no—
100#66992—216no—
101#66992—216no—
102#66992—216no—
103#66992—232no—
104#66990—216no—
105#66988—216no—
106#66983—216no—
107#66982—216no—
108C2×(C2×D11)⋊C4—28no—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2318yes—
113C2×C4⋊Dic11C2314yes—
114C2×Dic11⋊C4—28no—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2318yes—
118C2×C4×Dic11—44no—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2314yes—
121#66939—216no—
122#66935—216no—
123C11⋊#95C2318yes—
124#35001—111nomaximal, Sylow
125C24×C11—24no—
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—42no—
129C24×C11—42no—
130C24×C11—44no—
131C24×C11—44no—
132C24×C11C2×D414yes—
133C24×C11C2×D414yes—
134C24×C11C2×D414yes—
135C24×C11C2414yes—
136C24×C11C2412yes—
137C24×C11C2411yescharacteristic
138C23×D11—24no—
139C23×D11—24no—
140C23×D11—24no—
141C23×D11—44no—
142C23×D11—44no—
143C23×D11C2414yes—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11—432no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D418yescomplemented
160C22×C4×C11C2414yes—
161C22×C4×C11C2414yes—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—216no—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—48no—
173C2×C22⋊D11—48no—
174C2×C22⋊D11—48no—
175C2×C22⋊D11—432no—
176C2×C22⋊D11—432no—
177C22×Dic11—24no—
178C22×Dic11—28no—
179C22×Dic11—24no—
180C22×Dic11—24no—
181C22×Dic11—24no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—44no—
185C22×Dic11—42no—
186C22×Dic11—416no—
187C22×Dic11C2×D418yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2×D418yes—
190C22×Dic11C2×D414yes—
191C22×Dic11C2×D418yescomplemented
192C22×Dic11C2414yes—
193C22×Dic11C2412yes—
194C22×Dic11C2414yes—
195C22×Dic11C2411yescharacteristic
196C22×Dic11C2411yescharacteristic
197C2×D44—28no—
198C2×D44—44no—
199C2×D44—44no—
200C11×C4⋊C4—28no—
201C11×C22⋊C4—216no—
202C11×C22⋊C4C2×D4116yescomplemented
203C22⋊Dic11—216no—
204C22⋊Dic11—28no—
205C22⋊Dic11—28no—
206C22⋊Dic11C2×D4116yescomplemented
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—216no—
210(C2×D11)⋊C4—216no—
211C4⋊Dic11—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—28no—
214Dic11⋊C4—216no—
215C4×Dic11—28no—
216C4×Dic11—44no—
217C2×#534—112no—
218C2×#534—111no—
219C2×#534D1111yescharacteristic, complemented
220C22×#121—112no—
221#2856—114no—
222#2656—114no—
223#2539—114no—
224#2539—114no—
225#2501—114no—
226#2433—114no—
227C2×C4×C22⋊C4—111no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—22no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—28no—
236C23×C11—28no—
237C23×C11—44no—
238C23×C11—44no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11—48no—
242C23×C11—48no—
243C23×C11—48no—
244C23×C11—88no—
245C23×C11—88no—
246C23×C11#127116yescomplemented
247C23×C11C22×D414yes—
248C23×C11C22×D414yes—
249C23×C11C22×D412yes—
250C23×C11C22×D412yes—
251C23×C11C22×D414yes—
252C23×C11C22×D412yes—
253C23×C11C2511yescharacteristic
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—28no—
258C22×D11—28no—
259C22×D11—48no—
260C22×D11—48no—
261C22×D11—48no—
262C22×D11—88no—
263C22×D11—88no—
264D4×C11—416no—
265D4×C11—416no—
266D4×C11—88no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—48no—
273C2×C4×C11—48no—
274C2×C4×C11C22×D418yes—
275C22⋊D11—416no—
276C22⋊D11—416no—
277C22⋊D11—416no—
278C22⋊D11—416no—
279C22⋊D11—816no—
280C2×Dic11—24no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—28no—
285C2×Dic11—216no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—48no—
290C2×Dic11—44no—
291C2×Dic11—48no—
292C2×Dic11—48no—
293C2×Dic11C22×D418yes—
294C2×Dic11C22×D414yes—
295C2×Dic11C22×D412yes—
296C2×Dic11C22×D412yes—
297C2×Dic11H(5,𝔽2)14yes—
298D44—88no—
299C23×D4—112no—
300C23×D4—112no—
301C23×D4C2×D1112yes—
302C24×C4—111no—
303#534—28no—
304#534—2216no—
305#534—228no—
306C2×#127—114no—
307C2×#123—114no—
308C2×#123—114no—
309C2×#123—114no—
310C2×#123C2×D1114yescomplemented
311C2×#121—114no—
312C2×#121—118no—
313C2×#121—114no—
314C2×#121—114no—
315C2×#121—114no—
316C2×#121—114no—
317C2×#121—2216no—
318C2×#121C2×D1114yescomplemented
319C2×#120—114no—
320C2×#120—114no—
321C2×#120—114no—
322C2×#120C2×D1114yescomplemented
323C22×C4⋊C4—112no—
324C22×C22⋊C4—111no—
325C22×C22⋊C4—112no—
326C22×C22⋊C4—112no—
327C22×C22⋊C4C2×D1111yescharacteristic
328C22×C42—112no—
329#399—118no—
330#399—118no—
331#392—118no—
332#392—118no—
333#390—114no—
334#390—114no—
335#390—118no—
336#390—118no—
337#384—114no—
338C4×C22⋊C4—114no—
339C4×C22⋊C4—114no—
340C2×#95—112no—
341C22×C11—24no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—22no—
345C22×C11—24no—
346C22×C11—28no—
347C22×C11—28no—
348C22×C11—24no—
349C22×C11—416no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11—44no—
353C22×C11—48no—
354C22×C11—48no—
355C22×C11—816no—
356C22×C11C2×#12718yes—
357C22×C11C2×#12714yes—
358C22×C11C23×D411yescharacteristic
359C22×C11C23×D411yescharacteristic
360C22×C11C23×D411yescharacteristic
361C22×C11C2×H(5,𝔽2)12yes—
362C22×C11#58512yes—
363C2×D11—44no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—48no—
367C2×D11—48no—
368C2×D11—816no—
369C4×C11—28no—
370C4×C11—44no—
371Dic11—22no—
372Dic11—24no—
373Dic11—28no—
374Dic11—44no—
375Dic11#53414yescomplemented
376C25—112no—
377C25C22×D1112yes—
378C25C22×D1111yescharacteristic
379C22×D4—28no—
380C22×D4—28no—
381C22×D4—28no—
382C22×D4—114no—
383C22×D4—114no—
384C22×D4—114no—
385C22×D4—118no—
386C22×D4—114no—
387C22×D4—114no—
388C22×D4—228no—
389C22×D4—228no—
390C22×D4—228no—
391C22×D4—228no—
392C22×D4—448no—
393C22×D4C22×D1114yes—
394C22×D4C22×D1114yes—
395C22×D4C22×D1114yes—
396C23×C4—112no—
397C23×C4—111no—
398C23×C4—118no—
399C23×C4—112no—
400C23×C4—112no—
401C23×C4—111no—
402C23×C4—112no—
403C23×C4—444no—
404C23×C4C22×D1112yes—
405C23×C4C22×D1112yes—
406#127—448no—
407#123—216no—
408#123—2216no—
409#123—2216no—
410#123—2216no—
411#121—216no—
412#121—2216no—
413#121—2216no—
414#121—2216no—
415#121—2216no—
416#121—2232no—
417#121—2216no—
418#120—216no—
419#120—2216no—
420#120—2216no—
421#120—2216no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—118no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—228no—
427C2×C4⋊C4C22×D1114yes—
428C2×C22⋊C4—118no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4—118no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4—114no—
435C2×C22⋊C4—118no—
436C2×C22⋊C4—118no—
437C2×C22⋊C4—228no—
438C2×C22⋊C4—228no—
439C2×C22⋊C4C22⋊D1118yescomplemented
440C2×C22⋊C4C22×D1118yes—
441C2×C22⋊C4C22×D1114yes—
442C2×C42—114no—
443C2×C42—114no—
444C2×C42—444no—
445#95—118no—
446C2×C11—28no—
447C2×C11—24no—
448C2×C11—84no—
449C2×C11C22×#12711yescharacteristic
450C2×C11C2×#53411yescharacteristic
451C2×C11#344911yescharacteristic
452C2×C11#349612yes—
453C2×C11#349612yes—
454D11—84no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—42no—
459C24—42no—
460C24—44no—
461C24—44no—
462C24—114no—
463C24—224no—
464C24—224no—
465C24—224no—
466C24—444no—
467C24—444no—
468C24D4×D1114yes—
469C24D4×D1114yes—
470C24C2×C22⋊D1114yes—
471C24C23×D1114yes—
472C24C23×D1112yes—
473C24C23×D1111yescharacteristic
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—432no—
484C2×D4—228no—
485C2×D4—228no—
486C2×D4—2216no—
487C2×D4—2216no—
488C2×D4—228no—
489C2×D4—228no—
490C2×D4—228no—
491C2×D4—228no—
492C2×D4—228no—
493C2×D4—228no—
494C2×D4—228no—
495C2×D4—444no—
496C2×D4—444no—
497C2×D4—448no—
498C2×D4—4432no—
499C2×D4—448no—
500C2×D4—448no—
501C2×D4—4432no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—111no—
508C22×C4—118no—
509C22×C4—114no—
510C22×C4—112no—
511C22×C4—114no—
512C22×C4—111no—
513C22×C4—118no—
514C22×C4—118no—
515C22×C4—114no—
516C22×C4—114no—
517C22×C4—224no—
518C22×C4—228no—
519C22×C4—224no—
520C22×C4—224no—
521C22×C4—224no—
522C22×C4—4416no—
523C22×C4—442no—
524C22×C4—444no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4C2×C22⋊D1118yescomplemented
528C22×C4C23×D1114yes—
529C22×C4C23×D1114yes—
530C4⋊C4—28no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4—2216no—
534C4⋊C4—228no—
535C22⋊C4—216no—
536C22⋊C4—1116no—
537C22⋊C4—228no—
538C22⋊C4—228no—
539C22⋊C4—2216no—
540C22⋊C4—228no—
541C22⋊C4—228no—
542C22⋊C4—2216no—
543C22⋊C4—2216no—
544C22⋊C4C2×C22⋊D11116yescomplemented
545C42—228no—
546C42—444no—
547C11#3500111yescharacteristic, complemented, Sylow
548C23—22no—
549C23—24no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—28no—
555C23—28no—
556C23—24no—
557C23—44no—
558C23—48no—
559C23—44no—
560C23—48no—
561C23—48no—
562C23—48no—
563C23—48no—
564C23—88no—
565C23—88no—
566C23—224no—
567C23—224no—
568C23—228no—
569C23—228no—
570C23—224no—
571C23—448no—
572C23—448no—
573C23—448no—
574C23—888no—
575C23—888no—
576C23#66993116yescomplemented
577C23C2×D4×D1114yes—
578C23C2×D4×D1114yes—
579C23C2×D4×D1112yes—
580C23C2×D4×D1112yes—
581C23C22×C22⋊D1114yes—
582C23C22×C22⋊D1112yes—
583C23C24×D1111yescharacteristic
584D4—416no—
585D4—416no—
586D4—88no—
587D4—4416no—
588D4—4416no—
589D4—4416no—
590D4—4416no—
591D4—888no—
592D4—8816no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—48no—
599C2×C4—48no—
600C2×C4—112no—
601C2×C4—114no—
602C2×C4—118no—
603C2×C4—112no—
604C2×C4—114no—
605C2×C4—2216no—
606C2×C4—228no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—444no—
615C2×C4—448no—
616C2×C4—448no—
617C2×C4—448no—
618C2×C4C22×C22⋊D1118yes—
619C22—24no—
620C22—28no—
621C22—24no—
622C22—28no—
623C22—24no—
624C22—22no—
625C22—24no—
626C22—22no—
627C22—416no—
628C22—48no—
629C22—48no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—816no—
634C22—448no—
635C22—448no—
636C22—444no—
637C22—444no—
638C22—444no—
639C22—8816no—
640C22C2×#6699318yes—
641C22C2×#6699314yes—
642C22C22×D4×D1111yescharacteristic
643C22C22×D4×D1111yescharacteristic
644C22D11×H(5,𝔽2)12yes—
645C22#1062345512yes—
646C22C23×C22⋊D1111yescharacteristic
647C4—28no—
648C4—44no—
649C4—114no—
650C4—228no—
651C4—224no—
652C4—222no—
653C4—444no—
654C2—28no—
655C2—24no—
656C2—84no—
657C2—884no—
658C2C22×#6699311yescharacteristic
659C2D11×#53411yescharacteristic
660C2#1308194211yescharacteristic
661C2#1308237512yes—
662C2#1308237712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#534C2
hypercenterC2×#534D11
hypocenterC11#35001
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10623335C2semidirect
3. C22×#66992C2semidirect
4. #13076959C2semidirect
5. #13074720C2semidirect
6. #13073546C2semidirect
7. #13073544C2semidirect
8. #13073085C2semidirect
9. #13072251C2semidirect
10. C2×C22⋊C4×Dic11C2semidirect
11. C2×C11×#534C2semidirect
14. C23×C22⋊D11C22semidirect
17. C2×C11×#123C22semidirect
18. C2×C11×#121C22semidirect
19. C2×C11×#120C22semidirect
21. C2×#67006C22semidirect
23. C22×C22⋊Dic11C22semidirect
25. C2×#66993C22semidirect
29. C2×#66992C22semidirect
30. C2×#66992C22semidirect
31. C2×#66992C22semidirect
32. C2×#66990C22semidirect
33. C2×#66988C22semidirect
34. C2×#66983C22semidirect
35. C2×#66982C22semidirect
36. C22×(C2×D11)⋊C4C22semidirect
37. C22×Dic11⋊C4C22semidirect
38. C22×C4×Dic11C22semidirect
40. C2×#66939C22semidirect
41. C2×#66935C22semidirect
42. #10622836C22semidirect
43. #10622834C22semidirect
44. C2×C11⋊#95C22semidirect
45. #10622605C22semidirect
46. #10622601C22semidirect
47. #10622589C22semidirect
48. #10622573C22semidirect
49. #10622570C22semidirect
50. #10622570C22semidirect
51. #10622562C22semidirect
52. C22⋊C4×Dic11C22semidirect
53. C22⋊C4×Dic11C22semidirect
76. C23×Dic11D4semidirect
88. C2×C11×C22⋊C4D4semidirect
93. C2×C22⋊Dic11D4semidirect
159. C22×C4×C11C2×D4semidirect
191. C22×Dic11C2×D4semidirect
202. C11×C22⋊C4C2×D4semidirect
206. C22⋊Dic11C2×D4semidirect
219. C2×#534D11semidirect
246. C23×C11#127semidirect
310. C2×#123C2×D11semidirect
318. C2×#121C2×D11semidirect
322. C2×#120C2×D11semidirect
375. Dic11#534semidirect
439. C2×C22⋊C4C22⋊D11semidirect
527. C22×C4C2×C22⋊D11semidirect
544. C22⋊C4C2×C22⋊D11semidirect
547. C11#35001semidirect
576. C23#66993semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106233352
C22×#669922
#130769592
#130747202
#130735462
#130735442
#130730852
#130722512
C2×C22⋊C4×Dic112
C2×C11×#5342
#3500111