Finite Group Databasebeta

← #14960616

Subgroups — #14960616

Order 2816.

2910 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic, complemented
2#13076898C212yesmaximal, complemented
3#13075162C218yesmaximal, complemented
4#13074882C218yesmaximal, complemented
5#13074350C212yesmaximal, complemented
6#13074096C212yesmaximal, complemented
7#13072249C212yesmaximal, complemented
8#13071935C212yesmaximal, complemented
9#13071935C212yesmaximal, complemented
10#13071219C211yesmaximal, characteristic, complemented
11C22×C11×#123C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C22×#4339C2212yes—
15C2×C11×#123—28no—
16C2×C11×#123C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C2×#67006C2214yes—
23C2×#67006C2214yes—
24C2×#66993C2214yes—
25C2×#66983C2212yes—
26C2×#66983C2212yes—
27C2×#66983C2214yescomplemented
28#10623041—28no—
29C2×#66950C2214yescomplemented
30C2×#66948C2214yescomplemented
31#10622836C2218yes—
32#10622834C2214yes—
33#10622826C2214yes—
34#10622826C2214yes—
35#10622826C2218yescomplemented
36#10622825C2212yes—
37#10622825C2214yescomplemented
38#10622824C2212yes—
39C4×C22⋊Dic11C2212yes—
40#10622604C2214yescomplemented
41#10622603C2218yescomplemented
42#10622599C2214yescomplemented
43#10622594C2218yescomplemented
44#10622574C2218yescomplemented
45#10622573C2214yescomplemented
46#10622573C2214yescomplemented
47#10622573C2214yescomplemented
48#10622569C2218yescomplemented
49#10622569C2218yescomplemented
50#10622566C2214yescomplemented
51#10622560C2214yescomplemented
52#10622560C2214yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C22×D4×C11—24no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2318yes—
68C22×C22⋊D11C2318yes—
69C2×#4339—28no—
70C2×#4339—48no—
71C22×D44C2312yes—
72C22×D44C2312yes—
73C22×D44C2312yes—
74C22×C4×D11C2314yes—
75C22×Dic22C2312yes—
76C11×#123—232no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4D418yescomplemented
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87#67006—48no—
88#67006—48no—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92#66993—48no—
93#66983—28no—
94#66983—28no—
95#66983—48no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2314yes—
103C2×C4×Dic11C2314yes—
104#66950—216no—
105#66948—216no—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112#36710—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11—42no—
121C24×C11C2412yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11C2414yes—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—44no—
128C2×D4×C11—416no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—42no—
135C22×C4×C11—44no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—416no—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C2×C22⋊D11—28no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—48no—
157C22×Dic11C2418yes—
158C22×Dic11C2414yes—
159#4339—432no—
160C2×D44—24no—
161C2×D44—24no—
162C2×D44—24no—
163C2×D44—44no—
164C2×D44—44no—
165C2×D44—44no—
166C2×C4×D11—28no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×Dic22—24no—
170C2×Dic22—44no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4C2×D4116yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—48no—
178C22⋊Dic11—48no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—24no—
184C4⋊Dic11—24no—
185C4⋊Dic11—44no—
186C4×Dic11—44no—
187C2×#537—111no—
188C22×#123D1111yescharacteristic, complemented
189#2847—112no—
190#2696—118no—
191#2673—118no—
192#2617—112no—
193#2591—112no—
194#2433—112no—
195#2404—112no—
196#2404—112no—
197#2313—111no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—28no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—416no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—88no—
216C23×C11C22×D412yes—
217C23×C11H(5,𝔽2)14yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11C2511yescharacteristic
220C22×D11—24no—
221C22×D11—28no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—28no—
225D4×C11—416no—
226C2×C4×C11—28no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—416no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×D414yes—
242C22⋊D11—416no—
243C22⋊D11—816no—
244C22⋊D11—816no—
245C2×Dic11—24no—
246C2×Dic11—28no—
247C2×Dic11—28no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—28no—
251D44—48no—
252D44—84no—
253D44—84no—
254C4×D11—416no—
255Dic22—48no—
256C22×#41—112no—
257C23×D4C2×D1111yescharacteristic
258C24×C4C2×D1111yescharacteristic
259#537—228no—
260C2×#127—114no—
261C2×#123—28no—
262C2×#123C2×D1118yes—
263C2×C22⋊Q8—114no—
264C2×#121—112no—
265C2×#121—112no—
266C2×#121—114no—
267C2×#121—114no—
268C2×#120—114no—
269C2×#120—114no—
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4C2×D1111yescharacteristic
273C22×C22⋊C4C2×D1111yescharacteristic
274C22×C22⋊C4C2×D1111yescharacteristic
275#400—114no—
276#397—114no—
277#394—114no—
278#394—118no—
279#393—114no—
280#393—114no—
281#392—118no—
282#392—114no—
283#392—114no—
284#392—114no—
285#390—114no—
286#388—118no—
287#387—118no—
288#386—114no—
289#386—114no—
290#386—118no—
291#386—118no—
292#386—118no—
293#381—112no—
294#380—112no—
295#380—114no—
296C4×C22⋊C4—112no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—28no—
300C22×C11—24no—
301C22×C11—28no—
302C22×C11—416no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—48no—
310C22×C11—88no—
311C22×C11#53514yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C2×H(5,𝔽2)12yes—
314C22×C11C2×H(5,𝔽2)12yes—
315C22×C11#58512yes—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—48no—
320C2×D11—48no—
321C4×C11—24no—
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—42no—
325C4×C11—42no—
326Dic11—44no—
327Dic11—48no—
328C25C22×D1111yescharacteristic
329C25C22×D1111yescharacteristic
330C2×#41—228no—
331C2×#41—448no—
332C22×Q8—112no—
333C22×D4—24no—
334C22×D4—44no—
335C22×D4—114no—
336C22×D4—118no—
337C22×D4—118no—
338C22×D4—112no—
339C22×D4—112no—
340C22×D4—112no—
341C22×D4C22×D1114yes—
342C23×C4—24no—
343C23×C4—44no—
344C23×C4—114no—
345C23×C4C22×D1114yes—
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1111yescharacteristic
351#127—448no—
352#123—232no—
353C22⋊Q8—2216no—
354#121—228no—
355#121—228no—
356#121—2216no—
357#121—448no—
358#120—448no—
359#120—448no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4C22⋊D1118yescomplemented
365C2×C4⋊C4C22×D1114yes—
366C2×C4⋊C4C22×D1114yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—118no—
375C2×C22⋊C4—118no—
376C2×C22⋊C4—118no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1114yes—
379C2×C22⋊C4C22×D1114yes—
380C2×C42—114no—
381#95—114no—
382#95—118no—
383#95—114no—
384#95—114no—
385#95—114no—
386#95—118no—
387C2×C11—24no—
388C2×C11—44no—
389C2×C11—82no—
390C2×C11C2×#53511yescharacteristic
391C2×C11#348411yescharacteristic
392C2×C11#348711yescharacteristic
393C2×C11#353414yes—
394D11—84no—
395C24—24no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—24no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—114no—
404C24C23×D1112yes—
405C24C23×D1112yes—
406C24C23×D1111yescharacteristic
407#41—4432no—
408C2×Q8—224no—
409C2×Q8—444no—
410C2×D4—28no—
411C2×D4—28no—
412C2×D4—44no—
413C2×D4—416no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—228no—
417C2×D4—2216no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—224no—
421C2×D4—444no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—448no—
425C2×D4—448no—
426C2×D4—448no—
427C2×D4—448no—
428C2×D4—448no—
429C22×C4—24no—
430C22×C4—28no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—42no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—416no—
440C22×C4—118no—
441C22×C4—114no—
442C22×C4—228no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4C2×C22⋊D1114yes—
446C22×C4C2×C22⋊D1114yes—
447C22×C4C2×C22⋊D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—28no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—444no—
457C4⋊C4C2×C22⋊D11116yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C22⋊C4—448no—
468C42—444no—
469C11#3671011yescharacteristic, complemented, Sylow
470C23—22no—
471C23—22no—
472C23—28no—
473C23—22no—
474C23—24no—
475C23—24no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—22no—
481C23—416no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—44no—
487C23—88no—
488C23—228no—
489C23—224no—
490C23—224no—
491C23—228no—
492C23—224no—
493C23#6703714yes—
494C23#6704214yes—
495C23C22×C22⋊D1112yes—
496C23C24×D1111yescharacteristic
497Q8—448no—
498D4—416no—
499D4—448no—
500D4—4416no—
501D4—884no—
502D4—884no—
503D4—8816no—
504D4—8816no—
505C2×C4—28no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—416no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—228no—
519C2×C4—228no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—228no—
523C2×C4—224no—
524C2×C4—4416no—
525C2×C4C22×C22⋊D1114yes—
526C2×C4C22×C22⋊D1114yes—
527C2×C4C22×C22⋊D1114yes—
528C22—22no—
529C22—22no—
530C22—28no—
531C22—24no—
532C22—28no—
533C22—416no—
534C22—42no—
535C22—42no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—48no—
541C22—88no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—448no—
546C22—448no—
547C22#1062336114yes—
548C22C2×#6703712yes—
549C22C2×#6704212yes—
550C22#1062345312yes—
551C22C23×C22⋊D1111yescharacteristic
552C4—24no—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—444no—
558C4—448no—
559C2—24no—
560C2—44no—
561C2—82no—
562C2—884no—
563C2C2×#1062336111yescharacteristic
564C2#1308225111yescharacteristic
565C2#1308227411yescharacteristic
566C2#1308281014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×#123C2
hypercenterC22×#123D11
hypocenterC11#36710
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10623041C2semidirect
2. #13076898C2semidirect
3. #13075162C2semidirect
4. #13074882C2semidirect
5. #13074350C2semidirect
6. #13074096C2semidirect
7. #13072249C2semidirect
8. #13071935C2semidirect
9. #13071935C2semidirect
10. #13071219C2semidirect
11. C22×C11×#123C2semidirect
27. C2×#66983C22semidirect
29. C2×#66950C22semidirect
30. C2×#66948C22semidirect
35. #10622826C22semidirect
37. #10622825C22semidirect
40. #10622604C22semidirect
41. #10622603C22semidirect
42. #10622599C22semidirect
43. #10622594C22semidirect
44. #10622574C22semidirect
45. #10622573C22semidirect
46. #10622573C22semidirect
47. #10622573C22semidirect
48. #10622569C22semidirect
49. #10622569C22semidirect
50. #10622566C22semidirect
51. #10622560C22semidirect
52. #10622560C22semidirect
78. C2×C11×C4⋊C4D4semidirect
188. C22×#123D11semidirect
364. C2×C4⋊C4C22⋊D11semidirect
469. C11#36710semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130768982
#130751622
#130748822
#130743502
#130740962
#130722492
#130719352
#130712192
C22×C11×#1232
#3671011