Finite Group Databasebeta

← #14960735

Subgroups — #14960735

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3#13076899C212yesmaximal, complemented
4#13075257C218yesmaximal, complemented
5#13074831C218yesmaximal, complemented
6#13074353C212yesmaximal, complemented
7#13074091C212yesmaximal, complemented
8#13072253C212yesmaximal, complemented
9#13071929C212yesmaximal, complemented
10#13071929C212yesmaximal, complemented
11C11×#2312C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic, complemented
16C23×C4×D11C2211yescharacteristic, complemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
21C22×Dic11⋊C4C2211yescharacteristic, complemented
22C2×#66948C2214yescomplemented
23#10623024—28no—
24C2×#66939C2214yescomplemented
25C2×#66937—28no—
26C2×#66937C2218yescomplemented
27C2×#66935C2214yescomplemented
28C2×#66935C2214yescomplemented
29C2×#66935C2214yescomplemented
30C2×#66935C2214yescomplemented
31C2×#66935C2214yescomplemented
32C2×#66927C2214yescomplemented
33C11×#388C2218yescomplemented
34C11×#380C2212yescomplemented
35C11×#379C2212yes—
36C4×C11×C22⋊C4C2212yescomplemented
37#10622604C2218yescomplemented
38#10622600C2214yescomplemented
39#10622573C2218yescomplemented
40#10622573C2218yescomplemented
41#10622571C2214yescomplemented
42#10622571C2214yescomplemented
43#10622571C2214yescomplemented
44#10622571C2214yescomplemented
45#10622553C2218yescomplemented
46#10622552C2214yescomplemented
47#10622287C2214yescomplemented
48#10622285C2214yescomplemented
49#10622284C2218yescomplemented
50#10622284C2214yescomplemented
51#10622278C2218yescomplemented
52#10622272C2214yescomplemented
53C25×C11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C24×D11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—48no—
65C22×C22⋊D11C2314yes—
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C22×D44—24no—
73C22×D44—44no—
74C22×D44C2314yes—
75C22×D44C2312yes—
76C22×D44C2318yes—
77C22×D44C2312yes—
78C22×D44C2318yes—
79C22×C4×D11—24no—
80C22×C4×D11—44no—
81C22×C4×D11C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4D418yescomplemented
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C42×C11C2314yes—
89#66983—28no—
90#66983—28no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4C2314yes—
103#66948—48no—
104#66939—216no—
105#66937—232no—
106#66935—216no—
107#66935—48no—
108#66935—48no—
109#66935—48no—
110#66935—48no—
111#66927—48no—
112C11×#95C2314yes—
113C11×#95C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116#36717—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11C2×D414yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C23×D11—22no—
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—42no—
130C23×D11—42no—
131C23×D11—42no—
132C23×D11—44no—
133C23×D11—44no—
134C23×D11—44no—
135C23×D11C2414yes—
136C23×D11C2412yes—
137C23×D11C2412yes—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2418yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—44no—
154C2×C22⋊D11—44no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11—416no—
158C2×C22⋊D11—432no—
159C2×C22⋊D11—416no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—42no—
165C22×Dic11—44no—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C2×D44—28no—
170C2×D44—216no—
171C2×D44—28no—
172C2×D44—24no—
173C2×D44—24no—
174C2×D44—44no—
175C2×D44—44no—
176C2×D44—48no—
177C2×D44—48no—
178C2×D44—48no—
179C2×D44—48no—
180C2×D44—44no—
181C2×D44—48no—
182C2×D44—416no—
183C2×C4×D11—28no—
184C2×C4×D11—28no—
185C2×C4×D11—44no—
186C2×C4×D11—416no—
187C11×C4⋊C4—44no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—44no—
190C11×C22⋊C4—44no—
191C11×C22⋊C4C2×D4116yes—
192C42×C11—44no—
193(C2×D11)⋊C4—216no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—48no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200C4⋊Dic11—24no—
201C4⋊Dic11—24no—
202Dic11⋊C4—28no—
203C2×#534—111no—
204C22×#121—111no—
205#2847—112no—
206#2703—118no—
207#2669—118no—
208#2617—112no—
209#2591—112no—
210#2433—112no—
211#2403—112no—
212#2403—112no—
213#2312D1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—28no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—88no—
223C23×C11C22×D414yes—
224C23×C11C22×D412yes—
225C23×C11H(5,𝔽2)14yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—22no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—28no—
235C22×D11—24no—
236C22×D11—28no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—416no—
242C22×D11—44no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—48no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—84no—
249C22×D11—84no—
250C22×D11—88no—
251C22×D11—816no—
252C22×D11H(5,𝔽2)14yes—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—28no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—44no—
259C2×C4×C11—44no—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C22×D414yes—
262C22⋊D11—416no—
263C22⋊D11—416no—
264C22⋊D11—416no—
265C22⋊D11—416no—
266C2×Dic11—28no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—48no—
275C2×Dic11—44no—
276C2×Dic11H(5,𝔽2)14yes—
277D44—416no—
278D44—84no—
279D44—84no—
280D44—816no—
281D44—816no—
282C4×D11—416no—
283C23×D4—111no—
284C23×D4—111no—
285C23×D4—112no—
286C23×D4—111no—
287C24×C4—111no—
288#534—228no—
289C2×#127—114no—
290C2×#123—114no—
291C2×#121—112no—
292C2×#121—112no—
293C2×#121—114no—
294C2×#121—118no—
295C2×#121—228no—
296C2×#120—114no—
297C2×#120—114no—
298C2×#120—114no—
299C2×#120—114no—
300C2×#120—114no—
301C22×C4⋊C4—111no—
302C22×C22⋊C4—111no—
303C22×C22⋊C4C2×D1111yescharacteristic
304#400—114no—
305#397—114no—
306#394—118no—
307#394—114no—
308#392—118no—
309#392—118no—
310#392—114no—
311#392—118no—
312#390—114no—
313#388—118no—
314#388C2×D1118yescomplemented
315#386—114no—
316#386—114no—
317#386—114no—
318#386—114no—
319#386—118no—
320#380—114no—
321#380C2×D1112yescomplemented
322#379C2×D1112yes—
323C4×C22⋊C4C2×D1112yescomplemented
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—28no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—48no—
331C22×C11—88no—
332C22×C11#53514yes—
333C22×C11C23×D411yescharacteristic
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×H(5,𝔽2)12yes—
336C22×C11C2×H(5,𝔽2)12yes—
337C2×D11—24no—
338C2×D11—28no—
339C2×D11—416no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—42no—
344C2×D11—44no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—48no—
350C2×D11—48no—
351C2×D11—48no—
352C2×D11—88no—
353C2×D11—816no—
354C4×C11—24no—
355C4×C11—24no—
356C4×C11—48no—
357Dic11—24no—
358Dic11—44no—
359Dic11—42no—
360C25—111no—
361C25—111no—
362C25—112no—
363C25C22×D1111yescharacteristic
364C22×D4—114no—
365C22×D4—114no—
366C22×D4—114no—
367C22×D4—114no—
368C22×D4—114no—
369C22×D4—112no—
370C22×D4—112no—
371C22×D4—118no—
372C22×D4—118no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—228no—
376C22×D4—224no—
377C22×D4—444no—
378C22×D4—444no—
379C22×D4—448no—
380C22×D4—444no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—112no—
384C23×C4—114no—
385C23×C4—224no—
386C23×C4—444no—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389#127—448no—
390#123—2216no—
391#121—228no—
392#121—228no—
393#121—2232no—
394#121—448no—
395#120—2216no—
396#120—448no—
397#120—448no—
398#120—448no—
399#120—448no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4D4418yescomplemented
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1114yes—
416C2×C22⋊C4C22×D1114yes—
417C2×C22⋊C4C22×D1114yes—
418C2×C42C22×D1114yes—
419#95—118no—
420#95—118no—
421#95C22×D1114yes—
422#95C22×D1114yes—
423C2×C11—24no—
424C2×C11—44no—
425C2×C11C2×#53511yescharacteristic
426C2×C11#348411yescharacteristic
427C2×C11#348411yescharacteristic
428C2×C11#353714yes—
429D11—44no—
430D11—82no—
431D11—84no—
432C24—24no—
433C24—42no—
434C24—42no—
435C24—112no—
436C24—112no—
437C24—114no—
438C24—224no—
439C24—222no—
440C24—222no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24—442no—
445C24—442no—
446C24—442no—
447C24—444no—
448C24—444no—
449C24—444no—
450C24C2×D4414yes—
451C24C23×D1112yes—
452C24C23×D1111yescharacteristic
453C2×D4—228no—
454C2×D4—2216no—
455C2×D4—228no—
456C2×D4—228no—
457C2×D4—228no—
458C2×D4—228no—
459C2×D4—228no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—224no—
465C2×D4—224no—
466C2×D4—444no—
467C2×D4—448no—
468C2×D4—448no—
469C2×D4—448no—
470C2×D4—444no—
471C2×D4—448no—
472C2×D4—444no—
473C2×D4—448no—
474C2×D4—4416no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—444no—
478C2×D4—444no—
479C2×D4—4416no—
480C2×D4—4432no—
481C2×D4—4416no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—228no—
488C22×C4—224no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—224no—
492C22×C4—228no—
493C22×C4—444no—
494C22×C4—4416no—
495C22×C4—444no—
496C22×C4—442no—
497C22×C4C2×D4414yes—
498C22×C4C2×D4414yes—
499C22×C4C23×D1118yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C4⋊C4—44no—
503C4⋊C4—228no—
504C4⋊C4—224no—
505C4⋊C4—224no—
506C22⋊C4—28no—
507C22⋊C4—44no—
508C22⋊C4—44no—
509C22⋊C4—2216no—
510C22⋊C4—228no—
511C22⋊C4—228no—
512C22⋊C4—228no—
513C22⋊C4—448no—
514C22⋊C4—448no—
515C22⋊C4—448no—
516C22⋊C4C2×D44116yes—
517C42—44no—
518C11#3671711yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—28no—
525C23—44no—
526C23—44no—
527C23—88no—
528C23—114no—
529C23—228no—
530C23—222no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—224no—
535C23—222no—
536C23—224no—
537C23—224no—
538C23—224no—
539C23—228no—
540C23—228no—
541C23—224no—
542C23—224no—
543C23—4416no—
544C23—444no—
545C23—444no—
546C23—444no—
547C23—448no—
548C23—444no—
549C23—444no—
550C23—888no—
551C23—884no—
552C23—884no—
553C23—8816no—
554C23C22×D4414yes—
555C23C22×D4412yes—
556C23#6704214yes—
557C23C24×D1111yescharacteristic
558D4—4416no—
559D4—4416no—
560D4—4416no—
561D4—4416no—
562D4—4416no—
563D4—884no—
564D4—884no—
565D4—8816no—
566D4—8816no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—114no—
575C2×C4—228no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—4416no—
584C2×C4—448no—
585C2×C4—444no—
586C2×C4C22×D4414yes—
587C2×C4C22×D4414yes—
588C22—22no—
589C22—22no—
590C22—28no—
591C22—24no—
592C22—24no—
593C22—24no—
594C22—48no—
595C22—88no—
596C22—224no—
597C22—228no—
598C22—4416no—
599C22—442no—
600C22—442no—
601C22—444no—
602C22—444no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—444no—
607C22—444no—
608C22—448no—
609C22—448no—
610C22—448no—
611C22—888no—
612C22—8816no—
613C22#1062305614yes—
614C22C23×D4411yescharacteristic
615C22C2×#6704212yes—
616C22D11×H(5,𝔽2)12yes—
617C22D11×H(5,𝔽2)12yes—
618C4—24no—
619C4—24no—
620C4—48no—
621C4—224no—
622C4—444no—
623C4—442no—
624C2—24no—
625C2—44no—
626C2—444no—
627C2—884no—
628C2—882no—
629C2C2×#1062305611yescharacteristic
630C2#1308225211yescharacteristic
631C2#1308225211yescharacteristic
632C2#1308284814yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2312C2
hypercenter#2312D11
hypocenterC11#36717
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2312

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C22×#66937C2semidirect
3. #13076899C2semidirect
4. #13075257C2semidirect
5. #13074831C2semidirect
6. #13074353C2semidirect
7. #13074091C2semidirect
8. #13072253C2semidirect
9. #13071929C2semidirect
10. #13071929C2semidirect
11. C11×#2312C2semidirect
15. C23×D44C22semidirect
16. C23×C4×D11C22semidirect
20. C22×(C2×D11)⋊C4C22semidirect
21. C22×Dic11⋊C4C22semidirect
22. C2×#66948C22semidirect
24. C2×#66939C22semidirect
26. C2×#66937C22semidirect
27. C2×#66935C22semidirect
28. C2×#66935C22semidirect
29. C2×#66935C22semidirect
30. C2×#66935C22semidirect
31. C2×#66935C22semidirect
32. C2×#66927C22semidirect
33. C11×#388C22semidirect
34. C11×#380C22semidirect
36. C4×C11×C22⋊C4C22semidirect
37. #10622604C22semidirect
38. #10622600C22semidirect
39. #10622573C22semidirect
40. #10622573C22semidirect
41. #10622571C22semidirect
42. #10622571C22semidirect
43. #10622571C22semidirect
44. #10622571C22semidirect
45. #10622553C22semidirect
46. #10622552C22semidirect
47. #10622287C22semidirect
48. #10622285C22semidirect
49. #10622284C22semidirect
50. #10622284C22semidirect
51. #10622278C22semidirect
52. #10622272C22semidirect
83. C2×C11×C22⋊C4D4semidirect
213. #2312D11semidirect
314. #388C2×D11semidirect
321. #380C2×D11semidirect
323. C4×C22⋊C4C2×D11semidirect
413. C2×C22⋊C4D44semidirect
518. C11#36717semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C22×#669372
#130768992
#130752572
#130748312
#130743532
#130740912
#130722532
#130719292
C11×#23122
#3671711