Finite Group Databasebeta

← #14682970

Subgroups — #14682970

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622556C211yesmaximal, characteristic
2#13066876C212yesmaximal, complemented
3#13066875C212yesmaximal, complemented
4#13066861C211yesmaximal, characteristic
5#13066853C212yesmaximal
6#13066850C212yesmaximal, complemented
7#13066842C212yesmaximal, complemented
8#13066838C212yesmaximal
9C11×#1439C211yesmaximal, characteristic
10C24×Dic11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622556C418yescomplemented
32C25×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×Dic11—22no—
38C23×Dic11—22no—
39C23×Dic11—41no—
40C23×Dic11—41no—
41C23×Dic11—41no—
42C23×Dic11—41no—
43C23×Dic11C2×C414yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—41no—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4—42no—
55C2×C11×C22⋊C4C2×C414yes—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—41no—
59C2×C22⋊Dic11—41no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11C2×C414yes—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11—41no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—42no—
66C2×C4×Dic11—42no—
67C11×#95—24no—
68C11×#95—41no—
69C11⋊#95—24no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—41no—
78C11⋊#95C2×C418yes—
79C11⋊#95C2×C418yes—
80#14508—111nomaximal, Sylow
81C24×C11—22no—
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—21no—
87C24×C11—21no—
88C24×C11—22no—
89C24×C11C22×C412yes—
90C24×C11#4112yes—
91C24×C11#4112yes—
92C24×C11C2411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11#4114yes—
117C22×Dic11—28no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—44no—
144C22×Dic11—44no—
145C22×Dic11—44no—
146C22×Dic11—44no—
147C22×Dic11—44no—
148C22×Dic11—44no—
149C22×Dic11C22×C414yes—
150C22×Dic11C22×C414yes—
151C22×Dic11#4114yes—
152C11×C4⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—48no—
155C22⋊Dic11—44no—
156C22⋊Dic11—48no—
157C4⋊Dic11—44no—
158C4×Dic11—48no—
159C2×#381—111no—
160#1443—112no—
161#1442—112no—
162#1439—111no—
163#1439D1111yescharacteristic
164#1437—112no—
165#1436—112no—
166#1434—112no—
167C22⋊#95—112no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—24no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—41no—
185C23×C11—42no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—41no—
190C23×C11#11714yes—
191C23×C11C23×C411yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4112yes—
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4112yes—
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C11H(5,𝔽2)12yes—
199C23×C11H(5,𝔽2)11yescharacteristic
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C112−1+412yes—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—416no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C24×C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4C2×D1111yescharacteristic
258C22×C22⋊C4—111no—
259C22×C22⋊C4—112no—
260C22×C22⋊C4C2×D1112yes—
261C22×C22⋊C4C2×D1111yescharacteristic
262C22×C42—112no—
263#381—118no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—111no—
275C2×#95C2×D1112yes—
276C2×#95C2×D1111yescharacteristic
277C22×C11—24no—
278C22×C11—28no—
279C22×C11—44no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×#11711yescharacteristic
289C22×C11C4×#4112yes—
290C22×C11#51811yescharacteristic
291C22×C11#51811yescharacteristic
292C22×C11#52012yes—
293C22×C11#53811yescharacteristic
294C22×C11#53811yescharacteristic
295C22×C11#53811yescharacteristic
296C22×C11#53811yescharacteristic
297C22×C11#53812yes—
298C22×C11#53912yes—
299C22×C11#54012yes—
300C22×C11#54212yes—
301C22×C11#55112yes—
302C22×C11#55112yes—
303C22×C11#55111yescharacteristic
304C22×C11#55212yes—
305C22×C11#55212yes—
306C22×C11#55312yes—
307C22×C11#55911yescharacteristic
308C22×C11#56011yescharacteristic
309C22×C11#56212yes—
310C22×C11#56311yescharacteristic
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—82no—
315Dic11—44no—
316Dic11—44no—
317Dic11—44no—
318Dic11—82no—
319C25C22×D1111yescharacteristic
320C23×C4—112no—
321C23×C4—112no—
322C23×C4—112no—
323C23×C4—114no—
324C23×C4—112no—
325C23×C4—222no—
326C23×C4—222no—
327C23×C4—441no—
328C23×C4—441no—
329C23×C4—441no—
330C23×C4—441no—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1112yes—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—441no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—114no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—224no—
347C2×C22⋊C4—441no—
348C2×C22⋊C4—441no—
349C2×C22⋊C4—442no—
350C2×C22⋊C4C4×D1114yes—
351C2×C42—224no—
352C2×C42—442no—
353C2×C42—442no—
354#95—24no—
355#95—41no—
356#95—118no—
357#95—118no—
358#95—224no—
359#95—442no—
360#95—441no—
361#95—442no—
362#95—442no—
363#95—442no—
364#95—442no—
365#95—442no—
366#95—442no—
367C2×C11—44no—
368C2×C11#231211yescharacteristic
369C2×C11#233512yes—
370C2×C11#234312yes—
371C2×C11#237411yescharacteristic
372C2×C11#237611yescharacteristic
373C2×C11#275012yes—
374C2×C11#275211yescharacteristic
375C2×C11#276011yescharacteristic
376C2×C11#276112yes—
377C2×C11#276411yescharacteristic
378C2×C11#277111yescharacteristic
379C24—22no—
380C24—22no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—21no—
386C24—22no—
387C24C2×C4×D1112yes—
388C24#434112yes—
389C24#434312yes—
390C24C23×D1111yescharacteristic
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—114no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—228no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—444no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4—444no—
447C22×C4C2×C4×D1112yes—
448C22×C4C2×C4×D1112yes—
449C22×C4#434114yes—
450C4⋊C4—44no—
451C4⋊C4—444no—
452C22⋊C4—44no—
453C22⋊C4—48no—
454C22⋊C4—444no—
455C22⋊C4—448no—
456C42—448no—
457C11#1450811yescharacteristic, complemented, Sylow
458C23—22no—
459C23—22no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—22no—
464C23—22no—
465C23—24no—
466C23—24no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23#6694514yes—
481C23C22×C4×D1111yescharacteristic
482C23C2×#434112yes—
483C23C2×#434111yescharacteristic
484C23#6703711yescharacteristic
485C23#6703711yescharacteristic
486C23#6703712yes—
487C23C2×#434311yescharacteristic
488C23#41×D1112yes—
489C23#6704211yescharacteristic
490C23#6704211yescharacteristic
491C23#6704312yes—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—4416no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C22—24no—
546C22—28no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—44no—
554C22—42no—
555C22—42no—
556C22#1062301711yescharacteristic
557C22C2×#6694511yescharacteristic
558C22#1062305211yescharacteristic
559C22C4×#434112yes—
560C22#1062307712yes—
561C22#1062311812yes—
562C22#1062312611yescharacteristic
563C22#1062313212yes—
564C22#1062314811yescharacteristic
565C22#1062314811yescharacteristic
566C22#1062315012yes—
567C22#1062315212yes—
568C22#1062316812yes—
569C22#1062317312yes—
570C22#1062317511yescharacteristic
571C22#1062317511yescharacteristic
572C22#1062318112yes—
573C22#1062318211yescharacteristic
574C22#1062319612yes—
575C22#1062320912yes—
576C22#1062321011yescharacteristic
577C22#1062324112yes—
578C22#1062324411yescharacteristic
579C4—42no—
580C4—42no—
581C4—44no—
582C4—82no—
583C4—444no—
584C4—444no—
585C4—444no—
586C4—882no—
587C2—44no—
588C2#1307121311yescharacteristic
589C2#1307141112yes—
590C2#1307147412yes—
591C2#1307175111yescharacteristic
592C2#1307175911yescharacteristic
593C2#1307585612yes—
594C2#1307588411yescharacteristic
595C2#1307599111yescharacteristic
596C2#1307600912yes—
597C2#1307604311yescharacteristic
598C2#1307613611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14508
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13066876C2semidirect
3. #13066875C2semidirect
6. #13066850C2semidirect
7. #13066842C2semidirect
31. #10622556C4semidirect
457. C11#14508semidirect

Maximal subgroups

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

subgroupindex
C2×#106225562
#130668762
#130668752
#130668612
#130668532
#130668502
#130668422
#130668382
C11×#14392
#1450811