Finite Group Databasebeta

← #14960741

Subgroups — #14960741

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
2#13076898C212yesmaximal, complemented
3#13075255C218yesmaximal, complemented
4#13074828C218yesmaximal, complemented
5#13074350C212yesmaximal, complemented
6#13074096C212yesmaximal, complemented
7#13072249C212yesmaximal, complemented
8#13071926C212yesmaximal, complemented
9#13071926C212yesmaximal, complemented
10#13071214C211yesmaximal, characteristic, complemented
11C22×C11×#121C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic, complemented
15C24×C4×C11C2211yescharacteristic, complemented
16C23×C22⋊D11C2212yes—
17C2×C11×#121—28no—
18C2×C11×#121C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic, complemented
22C2×#67006C2214yescomplemented
23C2×#67006C2214yescomplemented
24C2×#66993C2214yescomplemented
25C2×#66990C2214yescomplemented
26C2×#66990C2214yescomplemented
27C2×#66983C2212yes—
28C2×#66983C2212yes—
29C2×#66983C2214yescomplemented
30#10623024—28no—
31C2×#66939C2214yescomplemented
32C2×#66935C2214yescomplemented
33#10622860C2212yes—
34#10622836C2218yescomplemented
35#10622836C2218yescomplemented
36#10622836C2218yescomplemented
37#10622834C2214yescomplemented
38#10622833C2214yescomplemented
39#10622833C2214yescomplemented
40#10622826C2214yescomplemented
41#10622826C2214yescomplemented
42#10622826C2218yescomplemented
43#10622825C2214yescomplemented
44#10622825C2212yescomplemented
45C4×C22⋊Dic11C2212yescomplemented
46#10622604C2214yescomplemented
47#10622603C2218yescomplemented
48#10622599C2214yescomplemented
49#10622574C2218yescomplemented
50#10622573C2214yescomplemented
51#10622566C2214yescomplemented
52#10622564C2218yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C24×D11C2312yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11—24no—
60C22×D4×C11—44no—
61C22×D4×C11—44no—
62C22×D4×C11—44no—
63C22×D4×C11C2314yes—
64C22×D4×C11C2314yes—
65C22×D4×C11C2314yes—
66C23×C4×C11—24no—
67C23×C4×C11—44no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2314yes—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—28no—
74C22×C22⋊D11—48no—
75C22×C22⋊D11C2314yes—
76C22×C22⋊D11C2314yes—
77C22×C22⋊D11C2318yes—
78C22×C22⋊D11C2318yes—
79C23×Dic11C2312yes—
80C22×D44C2312yes—
81C22×D44C2312yes—
82C11×#121—232no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4D418yescomplemented
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89#67006—48no—
90#67006—48no—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96#66993—48no—
97#66990—48no—
98#66990—48no—
99#66983—28no—
100#66983—28no—
101#66983—48no—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110#66939—216no—
111#66935—216no—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116#36717—111nomaximal, Sylow
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11—42no—
128C24×C11C2×D414yes—
129C24×C11C2412yes—
130C24×C11C2412yes—
131C24×C11C2412yes—
132C24×C11C2411yescharacteristic
133C23×D11—24no—
134C23×D11—44no—
135C23×D11—44no—
136C23×D11—44no—
137C23×D11C2414yes—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—416no—
148C2×D4×C11—416no—
149C2×D4×C11—416no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—42no—
156C22×C4×C11—44no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—416no—
160C22×C4×C11C2×D414yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—28no—
168C2×C22⋊D11—28no—
169C2×C22⋊D11—28no—
170C2×C22⋊D11—216no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—44no—
173C2×C22⋊D11—48no—
174C2×C22⋊D11—48no—
175C2×C22⋊D11—48no—
176C2×C22⋊D11—48no—
177C2×C22⋊D11—48no—
178C2×C22⋊D11—432no—
179C22×Dic11—24no—
180C22×Dic11—44no—
181C22×Dic11C2418yes—
182C22×Dic11C2414yes—
183C2×D44—24no—
184C2×D44—24no—
185C2×D44—44no—
186C2×D44—44no—
187C11×C4⋊C4—28no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4C2×D4116yes—
190C22⋊Dic11—28no—
191C22⋊Dic11—44no—
192C22⋊Dic11—44no—
193C22⋊Dic11—48no—
194C22⋊Dic11—48no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—48no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—44no—
202C4×Dic11—44no—
203C2×#534—111no—
204C22×#121D1111yescharacteristic, complemented
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#2312—111no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—28no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—22no—
224C23×C11—28no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—44no—
230C23×C11—44no—
231C23×C11—416no—
232C23×C11—44no—
233C23×C11—44no—
234C23×C11—44no—
235C23×C11—44no—
236C23×C11—44no—
237C23×C11—88no—
238C23×C11—88no—
239C23×C11C22×D414yes—
240C23×C11C22×D412yes—
241C23×C11H(5,𝔽2)14yes—
242C23×C11H(5,𝔽2)14yes—
243C23×C11C2511yescharacteristic
244C22×D11—24no—
245C22×D11—28no—
246C22×D11—28no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—48no—
250C22×D11—84no—
251C22×D11—84no—
252C22×D11—816no—
253D4×C11—416no—
254D4×C11—416no—
255D4×C11—416no—
256C2×C4×C11—28no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—44no—
264C2×C4×C11—44no—
265C2×C4×C11—416no—
266C2×C4×C11—44no—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11H(5,𝔽2)14yes—
270C22⋊D11—416no—
271C22⋊D11—416no—
272C22⋊D11—816no—
273C22⋊D11—816no—
274C2×Dic11—24no—
275C2×Dic11—28no—
276C2×Dic11—28no—
277C2×Dic11—28no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281D44—84no—
282D44—84no—
283C23×D4—112no—
284C23×D4C2×D1111yescharacteristic
285C23×D4C2×D1111yescharacteristic
286C23×D4C2×D1111yescharacteristic, complemented
287C24×C4C2×D1111yescharacteristic, complemented
288#534—228no—
289C2×#127—114no—
290C2×#123—114no—
291C2×#121—28no—
292C2×#121—112no—
293C2×#121—112no—
294C2×#121—114no—
295C2×#121C2×D1118yescomplemented
296C2×#120—114no—
297C2×#120—114no—
298C2×#120—114no—
299C2×#120—114no—
300C2×#120—114no—
301C22×C4⋊C4C2×D1111yescharacteristic, complemented
302C22×C22⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4C2×D1111yescharacteristic, complemented
304#400—114no—
305#397—114no—
306#394—114no—
307#394—118no—
308#392—118no—
309#392—118no—
310#392—118no—
311#392—114no—
312#390—114no—
313#388—118no—
314#388—118no—
315#386—114no—
316#386—114no—
317#386—114no—
318#386—114no—
319#386—118no—
320#380—112no—
321#380—114no—
322#379—112no—
323C4×C22⋊C4—112no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—28no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—28no—
332C22×C11—416no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—48no—
336C22×C11—44no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—48no—
341C22×C11—88no—
342C22×C11—88no—
343C22×C11#53514yes—
344C22×C11C23×D411yescharacteristic
345C22×C11C2×H(5,𝔽2)12yes—
346C22×C11C2×H(5,𝔽2)12yes—
347C22×C11C2×H(5,𝔽2)12yes—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—48no—
352C2×D11—48no—
353C2×D11—816no—
354C4×C11—24no—
355C4×C11—24no—
356C4×C11—24no—
357C4×C11—42no—
358Dic11—44no—
359Dic11—48no—
360C25—112no—
361C25C22×D1111yescharacteristic
362C25C22×D1111yescharacteristic
363C25C22×D1111yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—44no—
368C22×D4—44no—
369C22×D4—44no—
370C22×D4—114no—
371C22×D4—118no—
372C22×D4—114no—
373C22×D4—118no—
374C22×D4—112no—
375C22×D4—112no—
376C22×D4—228no—
377C22×D4—448no—
378C22×D4C22×D1114yes—
379C22×D4C22×D1114yes—
380C22×D4C22×D1114yes—
381C23×C4—24no—
382C23×C4—44no—
383C23×C4—112no—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1114yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389#127—448no—
390#123—2216no—
391#121—232no—
392#121—228no—
393#121—228no—
394#121—448no—
395#120—2216no—
396#120—448no—
397#120—448no—
398#120—448no—
399#120—448no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4C22⋊D1118yescomplemented
416C2×C22⋊C4C22×D1114yes—
417C2×C22⋊C4C22×D1114yes—
418C2×C42—114no—
419#95—114no—
420#95—118no—
421#95—114no—
422#95—118no—
423C2×C11—24no—
424C2×C11—44no—
425C2×C11—44no—
426C2×C11—82no—
427C2×C11C2×#53511yescharacteristic
428C2×C11#348411yescharacteristic
429C2×C11#348411yescharacteristic
430C2×C11#353714yes—
431D11—84no—
432C24—24no—
433C24—22no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—24no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—114no—
444C24—224no—
445C24—444no—
446C24—444no—
447C24—444no—
448C24C2×C22⋊D1114yes—
449C24C23×D1112yes—
450C24C23×D1112yes—
451C24C23×D1112yes—
452C24C23×D1111yescharacteristic
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—416no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—228no—
466C2×D4—228no—
467C2×D4—228no—
468C2×D4—228no—
469C2×D4—2216no—
470C2×D4—224no—
471C2×D4—224no—
472C2×D4—444no—
473C2×D4—444no—
474C2×D4—444no—
475C2×D4—444no—
476C2×D4—448no—
477C2×D4—448no—
478C2×D4—448no—
479C2×D4—448no—
480C2×D4—448no—
481C2×D4—4432no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—42no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—416no—
492C22×C4—118no—
493C22×C4—114no—
494C22×C4—224no—
495C22×C4—444no—
496C22×C4C2×C22⋊D1114yes—
497C22×C4C2×C22⋊D1114yes—
498C22×C4C23×D1112yes—
499C22×C4C23×D1112yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C4⋊C4—28no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—444no—
506C22⋊C4—28no—
507C22⋊C4—228no—
508C22⋊C4—2216no—
509C22⋊C4—228no—
510C22⋊C4—228no—
511C22⋊C4—448no—
512C22⋊C4—444no—
513C22⋊C4—444no—
514C22⋊C4—448no—
515C22⋊C4—448no—
516C22⋊C4C2×C22⋊D11116yes—
517C42—444no—
518C11#3671711yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—28no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—22no—
526C23—24no—
527C23—24no—
528C23—22no—
529C23—28no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—22no—
534C23—44no—
535C23—44no—
536C23—416no—
537C23—44no—
538C23—44no—
539C23—44no—
540C23—44no—
541C23—44no—
542C23—88no—
543C23—88no—
544C23—228no—
545C23—228no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—448no—
550C23—884no—
551C23—884no—
552C23—8816no—
553C23#6703714yes—
554C23#6704214yes—
555C23C22×C22⋊D1114yes—
556C23C22×C22⋊D1112yes—
557C23C24×D1111yescharacteristic
558D4—416no—
559D4—416no—
560D4—416no—
561D4—4416no—
562D4—4416no—
563D4—884no—
564D4—884no—
565D4—8816no—
566D4—8816no—
567C2×C4—28no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—416no—
577C2×C4—44no—
578C2×C4—228no—
579C2×C4—228no—
580C2×C4—228no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—448no—
585C2×C4#6703714yes—
586C2×C4C22×C22⋊D1114yes—
587C2×C4C22×C22⋊D1114yes—
588C22—22no—
589C22—22no—
590C22—28no—
591C22—24no—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—28no—
596C22—416no—
597C22—42no—
598C22—42no—
599C22—44no—
600C22—48no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—48no—
605C22—88no—
606C22—88no—
607C22—444no—
608C22—444no—
609C22—444no—
610C22—448no—
611C22—448no—
612C22—8816no—
613C22#1062336114yes—
614C22C2×#6703712yes—
615C22C2×#6703712yes—
616C22C2×#6704212yes—
617C22C23×C22⋊D1111yescharacteristic
618C4—24no—
619C4—24no—
620C4—24no—
621C4—42no—
622C4—444no—
623C4—448no—
624C2—24no—
625C2—44no—
626C2—44no—
627C2—82no—
628C2—884no—
629C2C2×#1062336111yescharacteristic
630C2#1308225111yescharacteristic
631C2#1308225111yescharacteristic
632C2#1308285114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#121C2
hypercenterC22×#121D11
hypocenterC11#36717
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. #13076898C2semidirect
3. #13075255C2semidirect
4. #13074828C2semidirect
5. #13074350C2semidirect
6. #13074096C2semidirect
7. #13072249C2semidirect
8. #13071926C2semidirect
9. #13071926C2semidirect
10. #13071214C2semidirect
11. C22×C11×#121C2semidirect
14. C23×D4×C11C22semidirect
15. C24×C4×C11C22semidirect
18. C2×C11×#121C22semidirect
19. C22×C11×C4⋊C4C22semidirect
21. C22×C11×C22⋊C4C22semidirect
22. C2×#67006C22semidirect
23. C2×#67006C22semidirect
24. C2×#66993C22semidirect
25. C2×#66990C22semidirect
26. C2×#66990C22semidirect
29. C2×#66983C22semidirect
31. C2×#66939C22semidirect
32. C2×#66935C22semidirect
34. #10622836C22semidirect
35. #10622836C22semidirect
36. #10622836C22semidirect
37. #10622834C22semidirect
38. #10622833C22semidirect
39. #10622833C22semidirect
40. #10622826C22semidirect
41. #10622826C22semidirect
42. #10622826C22semidirect
43. #10622825C22semidirect
44. #10622825C22semidirect
45. C4×C22⋊Dic11C22semidirect
46. #10622604C22semidirect
47. #10622603C22semidirect
48. #10622599C22semidirect
49. #10622574C22semidirect
50. #10622573C22semidirect
51. #10622566C22semidirect
52. #10622564C22semidirect
86. C2×C11×C22⋊C4D4semidirect
204. C22×#121D11semidirect
286. C23×D4C2×D11semidirect
287. C24×C4C2×D11semidirect
295. C2×#121C2×D11semidirect
301. C22×C4⋊C4C2×D11semidirect
303. C22×C22⋊C4C2×D11semidirect
415. C2×C22⋊C4C22⋊D11semidirect
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
#130768982
#130752552
#130748282
#130743502
#130740962
#130722492
#130719262
#130712142
C22×C11×#1212
#3671711