Finite Group Databasebeta

← #14960586

Subgroups — #14960586

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic
3#13076901C212yesmaximal
4#13075087C214yesmaximal, complemented
5#13075083C214yesmaximal, complemented
6#13074932C214yesmaximal, complemented
7#13074928C214yesmaximal, complemented
8#13074435C212yesmaximal, complemented
9#13073771C212yesmaximal
10#13072905C211yesmaximal, characteristic, complemented
11#13072899C211yesmaximal, characteristic, complemented
12#13072890C211yesmaximal, characteristic
13#13072258C212yesmaximal, complemented
14#13071217C211yesmaximal, characteristic, complemented
15C11×#2482C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25#10623050—28no—
26C2×#66943C2212yescomplemented
27C2×#66941C2212yescomplemented
28C2×#66941C2214yescomplemented
29C2×#66931—28no—
30C2×#66931C2212yes—
31C2×#66931C2212yes—
32C2×#66931C2214yes—
33C2×#66931C2214yes—
34C2×#66931C2214yes—
35C2×#66923C2212yescomplemented
36C2×#66922C2212yescomplemented
37C11×#399C2212yes—
38C11×#397C2212yes—
39C11×#388C2214yes—
40C11×#385C2212yes—
41C11×#381C2211yescharacteristic
42C11×#379C2212yes—
43#10622860C2212yes—
44#10622824C2211yescharacteristic
45#10622823C2212yes—
46#10622595C2212yescomplemented
47#10622593C2212yescomplemented
48#10622593C2214yescomplemented
49#10622592C2214yescomplemented
50#10622592C2214yescomplemented
51#10622566C2212yes—
52#10622565C2214yes—
53#10622564C2214yes—
54#10622563C2212yes—
55#10622563C2214yes—
56#10622562C2212yes—
57#10622560C2214yes—
58#10622559C2212yes—
59#10622559C2214yes—
60#10622557C2214yes—
61#10622557C2214yes—
62#10622556C2212yes—
63#10622556C2212yes—
64#10622555C2212yes—
65#10622555C2214yes—
66C22⋊C4×Dic11C2212yes—
67#10622546C2214yescomplemented
68#10622274C2212yescomplemented
69#10622272C2212yescomplemented
70#10622271C2214yescomplemented
71#10622270C2214yescomplemented
72#10622269C2214yescomplemented
73#10622267C2214yescomplemented
74#10622266C2214yescomplemented
75#10622266C2214yescomplemented
76#10622259C2214yescomplemented
77C25×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11—24no—
81C23×Dic11—44no—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×Dic22—24no—
88C22×Dic22—44no—
89C22×Dic22C2314yes—
90C22×Dic22C2312yes—
91C22×Dic22C2312yes—
92C11×#117—24no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C42×C11C2312yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110#66979—24no—
111C2×C4⋊Dic11D418yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2314yes—
133#66943—28no—
134#66941—28no—
135#66941—48no—
136#66931—28no—
137#66931—28no—
138#66931—216no—
139#66931—216no—
140#66931—48no—
141#66923—28no—
142#66922—28no—
143C11×#95C2314yes—
144C11×#95C2312yes—
145C11×#95C2312yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#36708—111nomaximal, Sylow
158C24×C11—22no—
159C24×C11—24no—
160C24×C11—24no—
161C24×C11—42no—
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—42no—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—24no—
175C22×Dic11—28no—
176C22×Dic11—28no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—24no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—44no—
183C22×Dic11—416no—
184C22×Dic11C2×D414yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2414yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C2×Dic22—28no—
194C2×Dic22—28no—
195C2×Dic22—24no—
196C2×Dic22—24no—
197C2×Dic22—44no—
198C2×Dic22—44no—
199C2×Dic22—44no—
200C2×Dic22—416no—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—44no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—28no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—44no—
210C42×C11—24no—
211C22⋊Dic11—28no—
212C22⋊Dic11—24no—
213C22⋊Dic11—28no—
214C22⋊Dic11—24no—
215C22⋊Dic11—44no—
216C4⋊Dic11—24no—
217C4⋊Dic11—24no—
218C4⋊Dic11—28no—
219C4⋊Dic11—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11C2×D418yes—
222C4⋊Dic11C2×D418yes—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226Dic11⋊C4—24no—
227Dic11⋊C4—28no—
228Dic11⋊C4—28no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233C4×Dic11—24no—
234C4×Dic11—44no—
235C2×#544—111no—
236C22×C22⋊Q8—111no—
237#2848—112no—
238#2690—114no—
239#2690—114no—
240#2677—114no—
241#2677—114no—
242#2627—112no—
243#2561—112no—
244#2484—111no—
245#2484—111no—
246#2482—111no—
247#2482D1111yescharacteristic
248#2434—112no—
249#2313—111no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—28no—
253C23×C11—22no—
254C23×C11—24no—
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—416no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11C22×D412yes—
261C23×C112−1+414yes—
262C23×C112−1+414yes—
263C23×C11C2511yescharacteristic
264C2×C4×C11—28no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—44no—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D412yes—
279C2×Dic11—28no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—44no—
294C2×Dic11—44no—
295C2×Dic11—416no—
296C2×Dic11—44no—
297C2×Dic11C22×D414yes—
298C2×Dic11C22×D414yes—
299C2×Dic11H(5,𝔽2)14yes—
300Dic22—416no—
301Dic22—84no—
302Dic22—84no—
303C23×Q8—111no—
304C24×C4—111no—
305#544—228no—
306C2×C4⋊Q8—112no—
307C2×C4⋊Q8—114no—
308C2×C4⋊Q8—112no—
309C2×#125—112no—
310C2×#125—112no—
311C2×C22⋊Q8—112no—
312C2×C22⋊Q8—112no—
313C2×C22⋊Q8—114no—
314C2×C22⋊Q8—114no—
315C2×C22⋊Q8—114no—
316C2×C22⋊Q8—228no—
317C2×#117—111no—
318C2×#117C2×D1111yescharacteristic
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4—111no—
322C22×C22⋊C4—111no—
323C22×C22⋊C4C2×D1111yescharacteristic
324#400—112no—
325#400—114no—
326#400—112no—
327#399—112no—
328#399C2×D1112yes—
329#398—114no—
330#398—112no—
331#398—114no—
332#398—112no—
333#397—114no—
334#397—112no—
335#397C2×D1112yes—
336#395—114no—
337#395—114no—
338#395—114no—
339#393—114no—
340#391—114no—
341#388—114no—
342#388—114no—
343#388—114no—
344#388C2×D1114yes—
345#387—114no—
346#387—114no—
347#387—114no—
348#387—114no—
349#385—112no—
350#385—114no—
351#385—112no—
352#385—114no—
353#385—112no—
354#385C2×D1112yes—
355#381—111no—
356#381—112no—
357#381—112no—
358#381C2×D1111yescharacteristic
359#380—112no—
360#380—114no—
361#379—112no—
362#379C2×D1112yes—
363C4×C22⋊C4—112no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—28no—
367C22×C11—24no—
368C22×C11—28no—
369C22×C11—416no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—44no—
373C22×C11#53614yes—
374C22×C11C23×D411yescharacteristic
375C22×C11C2×H(5,𝔽2)12yes—
376C22×C11C2×2−1+412yes—
377C22×C11C2×2−1+412yes—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—44no—
384Dic11—24no—
385Dic11—24no—
386Dic11—24no—
387Dic11—42no—
388Dic11—42no—
389Dic11—42no—
390Dic11—44no—
391C25C22×D1111yescharacteristic
392C22×Q8—114no—
393C22×Q8—112no—
394C22×Q8—112no—
395C22×Q8—224no—
396C22×Q8—444no—
397C23×C4—111no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—111no—
401C23×C4—114no—
402C23×C4—224no—
403C23×C4—444no—
404C23×C4C22×D1111yescharacteristic
405C23×C4C22×D1111yescharacteristic
406C4⋊Q8—228no—
407C4⋊Q8—228no—
408C4⋊Q8—448no—
409#125—228no—
410#125—228no—
411C22⋊Q8—2216no—
412C22⋊Q8—2216no—
413C22⋊Q8—228no—
414C22⋊Q8—228no—
415C22⋊Q8—448no—
416#117—24no—
417#117—224no—
418C2×C4⋊C4—118no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—224no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1114yes—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—114no—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—224no—
448C2×C22⋊C4C22×D1112yes—
449C2×C22⋊C4C22×D1112yes—
450C2×C22⋊C4C22×D1112yes—
451C2×C22⋊C4C22×D1112yes—
452C2×C22⋊C4C22×D1114yes—
453C2×C22⋊C4C22×D1114yes—
454C2×C42—112no—
455C2×C42—114no—
456C2×C42C22×D1112yes—
457#95—114no—
458#95—114no—
459#95—114no—
460#95—114no—
461#95—112no—
462#95—112no—
463#95—114no—
464#95—114no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95C22×D1112yes—
469#95C22×D1112yes—
470#95C22×D1114yes—
471C2×C11—24no—
472C2×C11—44no—
473C2×C11C2×#53611yescharacteristic
474C2×C11#348411yescharacteristic
475C2×C11#348611yescharacteristic
476C2×C11#353814yes—
477C24—22no—
478C24—24no—
479C24—24no—
480C24—42no—
481C24C23×D1112yes—
482C24C23×D1111yescharacteristic
483C2×Q8—228no—
484C2×Q8—228no—
485C2×Q8—224no—
486C2×Q8—224no—
487C2×Q8—444no—
488C2×Q8—444no—
489C2×Q8—444no—
490C2×Q8—4416no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—224no—
504C22×C4—228no—
505C22×C4—228no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—224no—
509C22×C4—442no—
510C22×C4—444no—
511C22×C4—442no—
512C22×C4—4416no—
513C22×C4D4×D1114yes—
514C22×C4C23×D1114yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1112yes—
517C22×C4C23×D1112yes—
518C22×C4C23×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—44no—
523C4⋊C4—118no—
524C4⋊C4—118no—
525C4⋊C4—228no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—222no—
537C4⋊C4—222no—
538C4⋊C4—444no—
539C4⋊C4—444no—
540C22⋊C4—24no—
541C22⋊C4—28no—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—24no—
545C22⋊C4—44no—
546C22⋊C4—228no—
547C22⋊C4—224no—
548C22⋊C4—228no—
549C22⋊C4—224no—
550C22⋊C4—444no—
551C42—24no—
552C42—224no—
553C42—444no—
554C11#3670811yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—28no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—416no—
563C23—44no—
564C23—44no—
565C23C2×D4×D1112yes—
566C23#6704314yes—
567C23#6704314yes—
568C23C24×D1111yescharacteristic
569Q8—4416no—
570Q8—884no—
571Q8—884no—
572C2×C4—28no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—114no—
588C2×C4—228no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—4416no—
605C2×C4—444no—
606C2×C4C2×D4×D1112yes—
607C2×C4C2×D4×D1112yes—
608C22—22no—
609C22—22no—
610C22—28no—
611C22—24no—
612C22—28no—
613C22—416no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22#1062317914yes—
618C22C22×D4×D1111yescharacteristic
619C22C2×#6704312yes—
620C22C2×#6704312yes—
621C22D11×H(5,𝔽2)12yes—
622C4—22no—
623C4—22no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—44no—
628C4—224no—
629C4—224no—
630C4—224no—
631C4—442no—
632C4—442no—
633C4—442no—
634C4—444no—
635C2—24no—
636C2—44no—
637C2C2×#1062317911yescharacteristic
638C2#1308225011yescharacteristic
639C2#1308226311yescharacteristic
640C2#1308285614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2482C2
prime radicalC25×C11C23
hypercenter#2482D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
4. #13075087C2semidirect
5. #13075083C2semidirect
6. #13074932C2semidirect
7. #13074928C2semidirect
8. #13074435C2semidirect
10. #13072905C2semidirect
11. #13072899C2semidirect
13. #13072258C2semidirect
14. #13071217C2semidirect
26. C2×#66943C22semidirect
27. C2×#66941C22semidirect
28. C2×#66941C22semidirect
35. C2×#66923C22semidirect
36. C2×#66922C22semidirect
46. #10622595C22semidirect
47. #10622593C22semidirect
48. #10622593C22semidirect
49. #10622592C22semidirect
50. #10622592C22semidirect
67. #10622546C22semidirect
68. #10622274C22semidirect
69. #10622272C22semidirect
70. #10622271C22semidirect
71. #10622270C22semidirect
72. #10622269C22semidirect
73. #10622267C22semidirect
74. #10622266C22semidirect
75. #10622266C22semidirect
76. #10622259C22semidirect
554. C11#36708semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C22×#669312
#130769012
#130750872
#130750832
#130749322
#130749282
#130744352
#130737712
#130729052
#130728992
#130728902
#130722582
#130712172
C11×#24822
#3670811