Finite Group Databasebeta

← #14680288

Subgroups — #14680288

Order 2816.

2718 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C2×#10622278C214yesmaximal, complemented
3C2×#10622280C211yesmaximal, characteristic, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066884C211yesmaximal, characteristic, complemented
6#13066860C214yesmaximal, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic, complemented
9C11×#1445C211yesmaximal, characteristic, complemented
10C23×D44C2212yes—
11C23×D44C2211yescharacteristic
12C23×C4×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×Dic11⋊C4C2212yes—
20C2×#66948—24no—
21C2×#66948—24no—
22C2×#66948C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2214yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2214yes—
30#10622280—24no—
31#10622278—216no—
32D11×#95—24no—
33C24×D11C2312yes—
34C24×D11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2311yescharacteristic
42C22×D44—24no—
43C22×D44—24no—
44C22×D44—28no—
45C22×D44—28no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—44no—
49C22×D44C2×C418yes—
50C22×D44C2×C414yescomplemented
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—44no—
54C22×C4×D11—44no—
55C22×C4×D11—44no—
56C22×C4×D11C2×C414yes—
57C22×C4×D11D414yes—
58C22×C4×D11D414yes—
59C22×C4×D11D418yescomplemented
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2×C414yescomplemented
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—28no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4—44no—
71C2×(C2×D11)⋊C4—44no—
72C2×(C2×D11)⋊C4—44no—
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—44no—
76#66948—232no—
77C11×#95—22no—
78C11×#95—28no—
79C11×#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—28no—
84#14271—111nomaximal, Sylow
85C24×C11C2411yescharacteristic
86C23×D11—24no—
87C23×D11—22no—
88C23×D11—22no—
89C23×D11—24no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—24no—
93C23×D11—24no—
94C23×D11—24no—
95C23×D11—24no—
96C23×D11—24no—
97C23×D11C22×C414yes—
98C23×D11C22×C412yes—
99C23×D11C2×D412yes—
100C23×D11C2×D412yes—
101C23×D11C2×D414yes—
102C23×D11#4114yes—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11C22×C412yes—
133C22×Dic11C2×D414yes—
134C22×Dic11C2×D412yes—
135C22×Dic11C2×D412yes—
136C2×D44—216no—
137C2×D44—232no—
138C2×D44—28no—
139C2×D44—48no—
140C2×D44—48no—
141C2×D44—48no—
142C2×D44—416no—
143C2×D44—48no—
144C2×D44—48no—
145C2×C4×D11—216no—
146C2×C4×D11—48no—
147C2×C4×D11—48no—
148C2×C4×D11—48no—
149C2×C4×D11—416no—
150C2×C4×D11—48no—
151C2×C4×D11—48no—
152C2×C4×D11—416no—
153C2×C4×D11C22⋊C4116yescomplemented
154C11×C4⋊C4—28no—
155(C2×D11)⋊C4—216no—
156(C2×D11)⋊C4—416no—
157(C2×D11)⋊C4—416no—
158(C2×D11)⋊C4—48no—
159Dic11⋊C4—48no—
160C22×#121—111no—
161C2×#386—114no—
162C2×#380—111no—
163C22×#95—111no—
164#1445—111no—
165#1445D1111yescharacteristic, complemented
166#1439—114no—
167#1438—111no—
168#1438—111no—
169C23×C11C23×C411yescharacteristic
170C23×C11C22×D411yescharacteristic
171C23×C11C22×D411yescharacteristic
172C23×C11C22×D412yes—
173C23×C11C2×#4112yes—
174C23×C11H(5,𝔽2)14yes—
175C23×C11H(5,𝔽2)12yes—
176C23×C112−1+412yes—
177C22×D11—24no—
178C22×D11—24no—
179C22×D11—24no—
180C22×D11—24no—
181C22×D11—28no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—24no—
185C22×D11—28no—
186C22×D11—28no—
187C22×D11—28no—
188C22×D11—24no—
189C22×D11—28no—
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—28no—
193C22×D11—44no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—44no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11C2×C22⋊C414yes—
210C22×D11C4×D418yes—
211C22×D11#12118yes—
212C22×D11#12414yes—
213C22×D11#12714yes—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—28no—
219C2×C4×C11—24no—
220C2×C4×C11—28no—
221C2×C4×C11—44no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11—44no—
232C2×C4×C11C2×C22⋊C414yes—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—28no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—44no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11C2×C22⋊C414yes—
247D44—416no—
248D44—432no—
249C4×D11—416no—
250C4×D11—432no—
251C23×D4—112no—
252C23×D4—111no—
253C24×C4—111no—
254C24×C4—112no—
255C2×#121—118no—
256C2×#121—224no—
257C2×#121—224no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C22⋊C4—112no—
261C22×C22⋊C4—112no—
262C22×C22⋊C4—114no—
263C22×C22⋊C4—114no—
264#386—2216no—
265#380—224no—
266C2×#95—111no—
267C2×#95—111no—
268C2×#95—112no—
269C2×#95—114no—
270C2×#95—224no—
271C2×#95C2×D1111yescharacteristic
272C2×#95C2×D1111yescharacteristic
273C2×#95C2×D1114yes—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C2×C4×D412yes—
276C22×C11#51812yes—
277C22×C11#52012yes—
278C22×C11C2×#12112yes—
279C22×C11C2×#12411yescharacteristic
280C22×C11C2×#12711yescharacteristic
281C22×C11#53412yes—
282C22×C11#53412yes—
283C22×C11#53414yes—
284C22×C11#53511yescharacteristic
285C22×C11#53611yescharacteristic
286C22×C11#53712yes—
287C22×C11#53714yes—
288C22×C11#53814yes—
289C22×C11#53914yes—
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—216no—
293C2×D11—28no—
294C2×D11—28no—
295C2×D11—28no—
296C2×D11—28no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—48no—
300C2×D11—48no—
301C2×D11—44no—
302C2×D11—84no—
303C2×D11—84no—
304C2×D11—84no—
305C2×D11—84no—
306C2×D11#39018yes—
307C4×C11—24no—
308C4×C11—44no—
309C4×C11—44no—
310C4×C11—82no—
311Dic11—24no—
312Dic11—44no—
313Dic11—82no—
314C25—111no—
315C25—112no—
316C22×D4—118no—
317C22×D4—114no—
318C22×D4—224no—
319C22×D4—224no—
320C22×D4—228no—
321C22×D4—228no—
322C22×D4—222no—
323C22×D4—222no—
324C22×D4—444no—
325C23×C4—111no—
326C23×C4—114no—
327C23×C4—114no—
328C23×C4—114no—
329C23×C4—112no—
330C23×C4—118no—
331C23×C4—112no—
332C23×C4—224no—
333C23×C4—224no—
334C23×C4—444no—
335C23×C4—444no—
336C23×C4—444no—
337C23×C4C22×D1112yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1112yes—
340C23×C4C22×D1111yescharacteristic
341#121—2232no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—444no—
346C2×C4⋊C4C4×D1114yescomplemented
347C2×C22⋊C4—118no—
348C2×C22⋊C4—224no—
349C2×C22⋊C4—224no—
350C2×C22⋊C4—228no—
351C2×C22⋊C4—224no—
352C2×C22⋊C4—228no—
353C2×C22⋊C4—228no—
354C2×C22⋊C4—444no—
355C2×C22⋊C4—444no—
356C2×C22⋊C4—444no—
357C2×C22⋊C4—444no—
358#95—22no—
359#95—22no—
360#95—28no—
361#95—224no—
362#95—228no—
363#95—222no—
364#95—222no—
365C2×C11C2×#39011yescharacteristic
366C2×C11#230811yescharacteristic
367C2×C11#231111yescharacteristic
368C2×C11#232514yes—
369C2×C11#261712yes—
370C2×C11#261812yes—
371C2×C11#263912yes—
372C2×C11#265612yes—
373D11—28no—
374D11—84no—
375C24—112no—
376C24—112no—
377C24—114no—
378C24—112no—
379C24—114no—
380C24—114no—
381C24—222no—
382C24—222no—
383C24—224no—
384C24—224no—
385C24—222no—
386C24—222no—
387C24—224no—
388C24—224no—
389C24—224no—
390C24—224no—
391C24—224no—
392C24C23×D1111yescharacteristic
393C2×D4—2216no—
394C2×D4—2232no—
395C2×D4—228no—
396C2×D4—448no—
397C2×D4—448no—
398C2×D4—448no—
399C2×D4—448no—
400C2×D4—4416no—
401C2×D4—448no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—1116no—
420C22×C4—114no—
421C22×C4—2216no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—448no—
433C22×C4—448no—
434C22×C4—448no—
435C22×C4—4416no—
436C22×C4—4416no—
437C22×C4—448no—
438C22×C4—448no—
439C22×C4C2×C4×D1114yes—
440C22×C4C2×C4×D1112yes—
441C22×C4D4×D1114yes—
442C22×C4D4×D1112yes—
443C22×C4D4×D1112yes—
444C4⋊C4—28no—
445C4⋊C4—448no—
446C22⋊C4—2216no—
447C22⋊C4—4416no—
448C22⋊C4—4416no—
449C22⋊C4—448no—
450C11#1427111yescharacteristic, complemented, Sylow
451C23—114no—
452C23—114no—
453C23—118no—
454C23—118no—
455C23—114no—
456C23—228no—
457C23—222no—
458C23—224no—
459C23—224no—
460C23—224no—
461C23—228no—
462C23—224no—
463C23—224no—
464C23—228no—
465C23—222no—
466C23—228no—
467C23—224no—
468C23—224no—
469C23—224no—
470C23—228no—
471C23—228no—
472C23—444no—
473C23—444no—
474C23—442no—
475C23—442no—
476C23—444no—
477C23—444no—
478C23—444no—
479C23—444no—
480C23—444no—
481C23—444no—
482C23—444no—
483C23—444no—
484C23—442no—
485C23—442no—
486C23—444no—
487C23—444no—
488C23C22×C4×D1111yescharacteristic
489C23C2×D4×D1111yescharacteristic
490C23C2×D4×D1112yes—
491C23C2×D4×D1111yescharacteristic
492C23#6704012yes—
493C23#41×D1112yes—
494C23#6704212yes—
495C23#6704214yes—
496D4—4416no—
497D4—4432no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—28no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—114no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—228no—
522C2×C4—4416no—
523C2×C4—4432no—
524C2×C4—444no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—444no—
530C2×C4—444no—
531C2×C4—442no—
532C2×C4C22⋊C4×D1114yes—
533C22—118no—
534C22—228no—
535C22—224no—
536C22—224no—
537C22—228no—
538C22—228no—
539C22—228no—
540C22—2216no—
541C22—444no—
542C22—444no—
543C22—448no—
544C22—448no—
545C22—444no—
546C22—884no—
547C22—884no—
548C22—884no—
549C22—884no—
550C22C2×C22⋊C4×D1111yescharacteristic
551C22#1062305212yes—
552C22C4×D4×D1112yes—
553C22#1062310512yes—
554C22D11×#12112yes—
555C22#1062316012yes—
556C22#1062316014yes—
557C22#1062318412yes—
558C22#1062318414yes—
559C22#1062318412yes—
560C22D11×#12411yescharacteristic
561C22#1062320511yescharacteristic
562C22#1062322314yes—
563C22#1062323514yes—
564C22D11×#12711yescharacteristic
565C22#1062325511yescharacteristic
566C4—24no—
567C4—44no—
568C4—44no—
569C4—82no—
570C4—224no—
571C4—444no—
572C4—882no—
573C2—228no—
574C2—884no—
575C2D11×#39011yescharacteristic
576C2#1307119311yescharacteristic
577C2#1307120711yescharacteristic
578C2#1307131514yes—
579C2#1307435112yes—
580C2#1307435912yes—
581C2#1307454812yes—
582C2#1307471912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenter#1445D11
hypocenterC11#14271
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622280C2semidirect
4. C2×D11×#95C2semidirect
5. #13066884C2semidirect
6. #13066860C2semidirect
7. #13066856C2semidirect
8. #13066856C2semidirect
9. C11×#1445C2semidirect
22. C2×#66948C4semidirect
50. C22×D44C2×C4semidirect
59. C22×C4×D11D4semidirect
62. C2×C11×C4⋊C4C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
153. C2×C4×D11C22⋊C4semidirect
165. #1445D11semidirect
346. C2×C4⋊C4C4×D11semidirect
450. C11#14271semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×#106222782
C2×#106222802
C2×D11×#952
#130668842
#130668602
#130668562
C11×#14452
#1427111