Finite Group Databasebeta

← #14960928

Subgroups — #14960928

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#13076899C212yesmaximal, complemented
2#13075828C214yesmaximal, complemented
3#13075738C214yesmaximal, complemented
4#13075258C214yesmaximal, complemented
5#13074859C214yesmaximal, complemented
6#13074718C211yesmaximal, characteristic, complemented
7#13072355C214yesmaximal, complemented
8#13072150C214yesmaximal, complemented
9#13071316C212yesmaximal, complemented
10C2×#10622280C211yesmaximal, characteristic, complemented
11C11×#2646C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×#66983C2212yes—
14C2×#66983C2214yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C2×#66948C2214yes—
18C2×#66948C2212yes—
19C2×#66948C2212yes—
20C2×#66947C2214yescomplemented
21C2×#66935C2214yes—
22C2×(C22⋊D11)⋊C4C2214yes—
23C11×#400C2214yescomplemented
24C11×#398C2214yescomplemented
25C11×#385C2214yes—
26C11×#380C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29#10622607C2214yes—
30#10622605C2214yescomplemented
31#10622604C2214yes—
32#10622603C2214yescomplemented
33#10622602C2214yescomplemented
34#10622602C2214yescomplemented
35#10622601C2214yes—
36#10622600C2212yes—
37#10622600C2212yes—
38#10622597C2214yescomplemented
39#10622571C2214yes—
40#10622571C2214yes—
41#10622290C2214yescomplemented
42#10622288C2214yescomplemented
43#10622285C2214yes—
44#10622285C2214yescomplemented
45#10622284C2214yes—
46#10622284C2214yescomplemented
47#10622283C2214yes—
48#10622282C2214yescomplemented
49#10622280C2214yes—
50#10622280C2214yes—
51#10622278C2214yes—
52#10622278C2214yes—
53#10622278C2214yes—
54#10622278C2214yescomplemented
55#10622268C2214yescomplemented
56#10622267C2214yescomplemented
57C24×D11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2314yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C22×D44C2314yes—
64C22×D44C2314yes—
65C22×D44C2312yes—
66C22×D44C2314yes—
67C22×C4×D11—24no—
68C22×C4×D11—44no—
69C22×C4×D11C2312yes—
70C22×C4×D11C2312yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C22⋊C4C2314yes—
77#66983—28no—
78#66983—48no—
79C2×(C2×D11)⋊C4—44no—
80C2×(C2×D11)⋊C4C2314yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×C4×Dic11C2314yes—
99#66948—44no—
100#66948—44no—
101#66948—48no—
102#66947—48no—
103#66935—48no—
104(C22⋊D11)⋊C4—48no—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11×#95C2314yes—
108C11×#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114#36727—111nomaximal, Sylow
115C24×C11C2411yescharacteristic
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—42no—
121C23×D11C2414yes—
122C23×D11C2411yescharacteristic
123C23×D11C2411yescharacteristic
124C22×C4×C11—24no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11#4114yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C2×C22⋊D11—28no—
134C2×C22⋊D11—28no—
135C2×C22⋊D11—28no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11C2414yes—
142C22×Dic11C2414yes—
143C22×Dic11C2412yes—
144C2×D44—28no—
145C2×D44—28no—
146C2×D44—24no—
147C2×D44—44no—
148C2×D44—44no—
149C2×D44—44no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—44no—
153C2×D44—44no—
154C2×D44—44no—
155C2×D44—44no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—416no—
166C11×C4⋊C4—44no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—44no—
170C11×C22⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—44no—
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—
181(C2×D11)⋊C4—44no—
182(C2×D11)⋊C4—44no—
183C4⋊Dic11—24no—
184C4⋊Dic11—44no—
185Dic11⋊C4—28no—
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#2646D1111yescharacteristic, complemented
196#2443—114no—
197#2424—114no—
198#2325—112no—
199C2×#380—111no—
200C23×C11—22no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11C2×#4112yes—
204C23×C11H(5,𝔽2)14yes—
205C23×C11C2511yescharacteristic
206C22×D11—28no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—21no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—48no—
223C22×D11—48no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11H(5,𝔽2)12yes—
227C22×D112−1+412yes—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
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—84no—
241C2×C4×C11C2×#4114yes—
242C22⋊D11—416no—
243C2×Dic11—28no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—84no—
253C2×Dic11H(5,𝔽2)14yes—
254D44—84no—
255D44—88no—
256D44—88no—
257D44—88no—
258C4×D11—48no—
259C4×D11—48no—
260C4×D11—88no—
261C24×C4—111no—
262C2×#123—114no—
263C2×#121—112no—
264C2×#121—114no—
265C2×#121—112no—
266C2×#121—112no—
267C2×#121—114no—
268C2×#120—114no—
269C2×C4×D4—114no—
270C22×C4⋊C4—112no—
271C22×C22⋊C4—112no—
272#400C2×D1114yescomplemented
273#399—114no—
274#399—114no—
275#398—114no—
276#398C2×D1114yescomplemented
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#385C2×D1114yes—
299#380—112no—
300#380—112no—
301#380—114no—
302#380—114no—
303#380C2×D1112yes—
304C2×#95—111no—
305C2×#95C2×D1111yescharacteristic
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11#54014yes—
311C22×C11C22×#4111yescharacteristic
312C22×C11C2×H(5,𝔽2)12yes—
313C22×C11C2×H(5,𝔽2)12yes—
314C22×C11C2×H(5,𝔽2)11yescharacteristic
315C22×C11C2×2−1+411yescharacteristic
316C2×D11—22no—
317C2×D11—22no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—416no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—42no—
326C2×D11—42no—
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—44no—
336C4×C11—44no—
337C4×C11—44no—
338Dic11—24no—
339Dic11—44no—
340Dic11—44no—
341C25—111no—
342C22×D4—114no—
343C22×D4—114no—
344C22×D4—114no—
345C22×D4—112no—
346C22×D4—114no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4—114no—
352C23×C4—224no—
353C23×C4—444no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356#123—448no—
357#121—228no—
358#121—444no—
359#121—444no—
360#121—448no—
361#121—448no—
362#120—448no—
363C4×D4—448no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—444no—
370C2×C4⋊C4C22×D1112yes—
371C2×C4⋊C4C22×D1112yes—
372C2×C4⋊C4C22×D1114yes—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—114no—
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⋊C4—444no—
387C2×C22⋊C4C22×D1114yes—
388C2×C42—114no—
389#95—114no—
390#95—114no—
391#95—114no—
392#95—114no—
393#95—114no—
394#95C22×D1114yes—
395#95C22×D1114yes—
396#95C22×D1114yes—
397#95C22×D1114yes—
398C2×C11—24no—
399C2×C11C2×#54011yescharacteristic
400C2×C11#349011yescharacteristic
401C2×C11#349211yescharacteristic
402C2×C11#353612yes—
403C2×C11#353712yes—
404D11—42no—
405D11—42no—
406D11—84no—
407C24—111no—
408C24—111no—
409C24—114no—
410C24—222no—
411C24—222no—
412C24—222no—
413C24—224no—
414C24—442no—
415C24C23×D1111yescharacteristic
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—224no—
422C2×D4—444no—
423C2×D4—444no—
424C2×D4—442no—
425C2×D4—442no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—444no—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—444no—
448C22×C4—444no—
449C22×C4—444no—
450C22×C4—4416no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4#434314yes—
454C22×C4C23×D1114yes—
455C22×C4C23×D1114yes—
456C22×C4C23×D1114yes—
457C22×C4C23×D1112yes—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—44no—
461C4⋊C4—44no—
462C4⋊C4—228no—
463C4⋊C4—224no—
464C4⋊C4—444no—
465C4⋊C4—444no—
466C4⋊C4—444no—
467C22⋊C4—28no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C22⋊C4—444no—
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—112no—
486C23—112no—
487C23—228no—
488C23—221no—
489C23—221no—
490C23—222no—
491C23—222no—
492C23—221no—
493C23—222no—
494C23—222no—
495C23—221no—
496C23—224no—
497C23—224no—
498C23—224no—
499C23—224no—
500C23—224no—
501C23—224no—
502C23—224no—
503C23—448no—
504C23—448no—
505C23—444no—
506C23—444no—
507C23C2×#434312yes—
508C23#6704214yes—
509C23C24×D1111yescharacteristic
510D4—4416no—
511D4—884no—
512D4—888no—
513D4—888no—
514D4—888no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—44no—
527C2×C4—84no—
528C2×C4—114no—
529C2×C4—228no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—448no—
539C2×C4—448no—
540C2×C4—888no—
541C2×C4—884no—
542C2×C4C2×#434314yes—
543C22—22no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—222no—
548C22—222no—
549C22—224no—
550C22—224no—
551C22—4416no—
552C22—441no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—442no—
557C22—442no—
558C22—444no—
559C22—444no—
560C22—444no—
561C22—444no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22#1062322914yes—
566C22C22×#434311yescharacteristic
567C22C2×#6704212yes—
568C22D11×H(5,𝔽2)12yes—
569C22D11×H(5,𝔽2)11yescharacteristic
570C22D11×2−1+411yescharacteristic
571C4—24no—
572C4—44no—
573C4—44no—
574C4—44no—
575C4—224no—
576C4—444no—
577C4—444no—
578C2—24no—
579C2—442no—
580C2—442no—
581C2—884no—
582C2C2×#1062322911yescharacteristic
583C2#1308230611yescharacteristic
584C2#1308232611yescharacteristic
585C2#1308284012yes—
586C2#1308284812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2646C2
hypercenter#2646D11
hypocenterC11#36727
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2646

Complements

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

NH ≅ G/Ntype
1. #13076899C2semidirect
2. #13075828C2semidirect
3. #13075738C2semidirect
4. #13075258C2semidirect
5. #13074859C2semidirect
6. #13074718C2semidirect
7. #13072355C2semidirect
8. #13072150C2semidirect
9. #13071316C2semidirect
10. C2×#10622280C2semidirect
11. C11×#2646C2semidirect
20. C2×#66947C22semidirect
23. C11×#400C22semidirect
24. C11×#398C22semidirect
30. #10622605C22semidirect
32. #10622603C22semidirect
33. #10622602C22semidirect
34. #10622602C22semidirect
38. #10622597C22semidirect
41. #10622290C22semidirect
42. #10622288C22semidirect
44. #10622285C22semidirect
46. #10622284C22semidirect
48. #10622282C22semidirect
54. #10622278C22semidirect
55. #10622268C22semidirect
56. #10622267C22semidirect
195. #2646D11semidirect
272. #400C2×D11semidirect
276. #398C2×D11semidirect
481. C11#36727semidirect

Maximal subgroups

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

subgroupindex
#130768992
#130758282
#130757382
#130752582
#130748592
#130747182
#130723552
#130721502
#130713162
C2×#106222802
C11×#26462
#3672711