Finite Group Databasebeta

← #14960927

Subgroups — #14960927

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076898C212yesmaximal, complemented
2#13075826C214yesmaximal, complemented
3#13075731C214yesmaximal, complemented
4#13075259C214yesmaximal, complemented
5#13074849C214yesmaximal, complemented
6#13074718C211yesmaximal, characteristic, complemented
7#13074586C211yesmaximal, characteristic, complemented
8#13072351C214yesmaximal, complemented
9#13072152C214yesmaximal, complemented
10#13071319C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C22⋊C4C2212yes—
15C2×#67006C2214yes—
16C2×#66983C2212yes—
17C2×#66983C2214yes—
18C2×#66983C2212yes—
19C2×#66983C2212yes—
20C2×C4×C22⋊D11C2214yes—
21C2×#66947C2214yescomplemented
22C2×#66937C2214yes—
23C11×#380C2214yes—
24C11×#380C2214yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27#10622826C2214yes—
28#10622826C2214yes—
29#10622826C2214yes—
30#10622826C2214yes—
31#10622825C2212yes—
32#10622825C2212yes—
33#10622825C2212yes—
34#10622823C2214yes—
35#10622606C2214yescomplemented
36#10622605C2214yescomplemented
37#10622604C2214yescomplemented
38#10622603C2214yescomplemented
39#10622602C2214yescomplemented
40#10622597C2214yescomplemented
41#10622594C2214yescomplemented
42#10622573C2214yes—
43#10622572C2214yes—
44#10622572C2214yes—
45#10622570C2214yes—
46#10622569C2214yes—
47#10622564C2214yes—
48#10622561C2214yes—
49#10622290C2214yescomplemented
50#10622284C2214yescomplemented
51#10622283C2214yescomplemented
52#10622281C2214yescomplemented
53#10622278C2214yescomplemented
54#10622273C2214yescomplemented
55#10622270C2214yescomplemented
56#10622266C2214yescomplemented
57C25×C11C2311yescharacteristic
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C22×D44C2312yes—
70C22×D44C2314yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—44no—
73C2×C11×C4⋊C4C2314yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2314yes—
78#67006—48no—
79C2×C22⋊Dic11C2314yes—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2314yes—
82#66983—28no—
83#66983—44no—
84#66983—44no—
85#66983—48no—
86C4×C22⋊D11—48no—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×C4×Dic11C2314yes—
103#66947—48no—
104#66937—48no—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114#36727—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—42no—
120C24×C11C2411yescharacteristic
121C24×C11C2411yescharacteristic
122C24×C11C2411yescharacteristic
123C23×D11C2414yes—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—416no—
140C22×C4×C11#4114yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2414yes—
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—44no—
151C2×C22⋊D11—44no—
152C2×C22⋊D11—44no—
153C2×C22⋊D11—44no—
154C22×Dic11C2414yes—
155C22×Dic11C2414yes—
156C22×Dic11C2414yes—
157C2×D44—24no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—44no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—44no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—44no—
168C11×C22⋊C4—28no—
169C11×C22⋊C4—44no—
170C22⋊Dic11—28no—
171C22⋊Dic11—44no—
172C22⋊Dic11—44no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—44no—
178(C2×D11)⋊C4—44no—
179(C2×D11)⋊C4—44no—
180(C2×D11)⋊C4—44no—
181C4⋊Dic11—24no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184C4⋊Dic11—44no—
185Dic11⋊C4—44no—
186Dic11⋊C4—44no—
187Dic11⋊C4—44no—
188C4×Dic11—44no—
189#2847—112no—
190#2748—114no—
191#2741—114no—
192#2703—114no—
193#2671—114no—
194#2656—111no—
195#2646—111no—
196#2443—114no—
197#2424—114no—
198#2325—112no—
199C2×#380D1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—28no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—21no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11C2×#4112yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C112−1+412yes—
220C23×C11C2511yescharacteristic
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C2×C4×C11—28no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—44no—
240C2×C4×C11—48no—
241C2×C4×C11—48no—
242C2×C4×C11—84no—
243C2×C4×C11—84no—
244C2×C4×C11C2×#4114yes—
245C2×C4×C11H(5,𝔽2)14yes—
246C22⋊D11—416no—
247C22⋊D11—88no—
248C22⋊D11—88no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258D44—84no—
259D44—88no—
260C4×D11—88no—
261C24×C4C2×D1111yescharacteristic
262C2×#123—114no—
263C2×#121—112no—
264C2×#121—112no—
265C2×#121—112no—
266C2×#121—114no—
267C2×#121—114no—
268C2×#120—114no—
269C2×C4×D4—114no—
270C22×C4⋊C4C2×D1112yes—
271C22×C22⋊C4C2×D1112yes—
272#400—114no—
273#399—114no—
274#399—114no—
275#398—114no—
276#398—114no—
277#397—114no—
278#396—114no—
279#394—114no—
280#394—114no—
281#394—114no—
282#392—114no—
283#392—114no—
284#390—114no—
285#388—114no—
286#388—114no—
287#388—114no—
288#387—114no—
289#387—114no—
290#386—114no—
291#386—114no—
292#386—114no—
293#386—114no—
294#386—114no—
295#386—114no—
296#385—114no—
297#385—114no—
298#385—114no—
299#380—112no—
300#380—112no—
301#380—112no—
302#380C2×D1114yes—
303#380C2×D1114yes—
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1111yescharacteristic
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—416no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11#54014yes—
322C22×C11C22×#4111yescharacteristic
323C22×C11C2×H(5,𝔽2)12yes—
324C22×C11C2×H(5,𝔽2)11yescharacteristic
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2×2−1+411yescharacteristic
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C4×C11—24no—
335C4×C11—24no—
336C4×C11—44no—
337C4×C11—44no—
338Dic11—44no—
339Dic11—44no—
340Dic11—44no—
341C25C22×D1111yescharacteristic
342C22×D4—114no—
343C22×D4—114no—
344C22×D4—114no—
345C22×D4—112no—
346C22×D4—114no—
347C23×C4—24no—
348C23×C4—44no—
349C23×C4—114no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1112yes—
352C23×C4C22×D1112yes—
353C23×C4C22×D1112yes—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356#123—448no—
357#121—228no—
358#121—448no—
359#121—444no—
360#121—444no—
361#121—448no—
362#120—448no—
363C4×D4—448no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4C22×D1114yes—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1114yes—
388C2×C42—114no—
389#95—114no—
390#95—114no—
391#95—114no—
392#95—114no—
393#95—114no—
394#95—114no—
395#95—114no—
396#95C22×D1114yes—
397#95C22×D1114yes—
398C2×C11—24no—
399C2×C11—42no—
400C2×C11—42no—
401C2×C11C2×#54011yescharacteristic
402C2×C11#349011yescharacteristic
403C2×C11#349211yescharacteristic
404C2×C11#353612yes—
405C2×C11#353712yes—
406D11—84no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—24no—
411C24—42no—
412C24—114no—
413C24C23×D1111yescharacteristic
414C24C23×D1111yescharacteristic
415C24C23×D1111yescharacteristic
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—224no—
422C2×D4—442no—
423C2×D4—442no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—444no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—416no—
447C22×C4—114no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4#433914yes—
454C22×C4C23×D1114yes—
455C22×C4C23×D1114yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1112yes—
458C4⋊C4—28no—
459C4⋊C4—44no—
460C4⋊C4—224no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C4⋊C4—442no—
464C4⋊C4—442no—
465C4⋊C4—444no—
466C4⋊C4—444no—
467C22⋊C4—28no—
468C22⋊C4—44no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—444no—
474C22⋊C4—444no—
475C22⋊C4—444no—
476C22⋊C4—444no—
477C22⋊C4—444no—
478C22⋊C4—444no—
479C22⋊C4—444no—
480C42—444no—
481C11#3672711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—21no—
484C23—21no—
485C23—28no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—21no—
492C23—22no—
493C23—22no—
494C23—48no—
495C23—48no—
496C23—44no—
497C23—44no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—224no—
503C23—224no—
504C23—224no—
505C23C2×#433912yes—
506C23#6703712yes—
507C23#6704012yes—
508C23#6704214yes—
509C23C24×D1111yescharacteristic
510D4—4416no—
511D4—884no—
512D4—888no—
513D4—888no—
514D4—888no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4—48no—
529C2×C4—84no—
530C2×C4—84no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—888no—
541C2×C4C2×#433914yes—
542C2×C4#6703714yes—
543C22—22no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—24no—
550C22—24no—
551C22—416no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—42no—
557C22—42no—
558C22—444no—
559C22—444no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22#1062306614yes—
566C22C22×#433911yescharacteristic
567C22C2×#6703712yes—
568C22C2×#6703711yescharacteristic
569C22C2×#6704011yescharacteristic
570C22C2×#6704212yes—
571C4—24no—
572C4—24no—
573C4—44no—
574C4—44no—
575C4—444no—
576C4—444no—
577C4—444no—
578C2—24no—
579C2—42no—
580C2—42no—
581C2—884no—
582C2C2×#1062306611yescharacteristic
583C2#1308230511yescharacteristic
584C2#1308232511yescharacteristic
585C2#1308284512yes—
586C2#1308285112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#380C2
hypercenterC2×#380D11
hypocenterC11#36727
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. #13076898C2semidirect
2. #13075826C2semidirect
3. #13075731C2semidirect
4. #13075259C2semidirect
5. #13074849C2semidirect
6. #13074718C2semidirect
7. #13074586C2semidirect
8. #13072351C2semidirect
9. #13072152C2semidirect
10. #13071319C2semidirect
11. C2×C11×#380C2semidirect
21. C2×#66947C22semidirect
35. #10622606C22semidirect
36. #10622605C22semidirect
37. #10622604C22semidirect
38. #10622603C22semidirect
39. #10622602C22semidirect
40. #10622597C22semidirect
41. #10622594C22semidirect
49. #10622290C22semidirect
50. #10622284C22semidirect
51. #10622283C22semidirect
52. #10622281C22semidirect
53. #10622278C22semidirect
54. #10622273C22semidirect
55. #10622270C22semidirect
56. #10622266C22semidirect
199. C2×#380D11semidirect
481. C11#36727semidirect

Maximal subgroups

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

subgroupindex
#130768982
#130758262
#130757312
#130752592
#130748492
#130747182
#130745862
#130723512
#130721522
#130713192
C2×C11×#3802
#3672711