Finite Group Databasebeta

← #14927239

Subgroups — #14927239

Order 2816.

1986 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076966C212yesmaximal, complemented
2#13076924C212yesmaximal, complemented
3#13074425C214yesmaximal
4#13074286C212yesmaximal, complemented
5#13074283C212yesmaximal, complemented
6#13074281C212yesmaximal, complemented
7#13074277C212yesmaximal, complemented
8#13072330C212yesmaximal, complemented
9#13072323C212yesmaximal, complemented
10#13072308C212yesmaximal, complemented
11#13072301C212yesmaximal, complemented
12#13071344C214yesmaximal, complemented
13#13070999C211yesmaximal, characteristic
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic
15C11×#2280C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66943C2212yescomplemented
25C2×#66941C2212yescomplemented
26C2×#66931C2214yes—
27C11×#381C2212yes—
28C11×#380C2212yes—
29C11×#380C2212yes—
30C11×#379C2212yes—
31C4×C11×C22⋊C4C2212yes—
32C4×C11×C22⋊C4C2212yes—
33#10622860C2212yes—
34#10622825C2212yes—
35#10622825C2212yes—
36#10622824C2212yes—
37C4×C22⋊Dic11C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C4×C22⋊Dic11C2211yescharacteristic
40C4×C22⋊Dic11C2211yescharacteristic
41C4×C22⋊Dic11C2212yes—
42C4×C22⋊Dic11C2212yes—
43C4×C22⋊Dic11C2212yes—
44C4×C22⋊Dic11C2212yes—
45C2×C11⋊#95C2212yes—
46#10622598C2212yescomplemented
47#10622598C2212yescomplemented
48#10622590C2212yescomplemented
49#10622589C2212yescomplemented
50#10622586C2212yescomplemented
51#10622586C2212yescomplemented
52#10622563C2214yes—
53#10622562C2214yes—
54#10622562C2214yes—
55#10622561C2214yes—
56#10622561C2214yes—
57#10622561C2214yes—
58#10622561C2214yes—
59#10622560C2214yes—
60#10622560C2214yes—
61#10622559C2214yes—
62#10622555C2214yes—
63#10622546C2214yescomplemented
64#10622546C2214yescomplemented
65#10622542C2214yescomplemented
66#10622541C2214yescomplemented
67#10622268C2214yescomplemented
68#10622268C2214yescomplemented
69#10622267C2214yescomplemented
70#10622267C2214yescomplemented
71#10622260C2214yescomplemented
72#10622260C2214yescomplemented
73#10622259C2214yescomplemented
74#10622259C2214yescomplemented
75C25×C11C2311yescharacteristic
76C23×C4×C11—42no—
77C23×C4×C11—42no—
78C23×C4×C11Q818yescomplemented
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11C2312yes—
86C23×Dic11C2312yes—
87C22×Dic22C2314yes—
88C11×#117—42no—
89C11×#117—42no—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2312yes—
98C2×C22⋊Dic11—28no—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2314yes—
107#66979—42no—
108#66979—42no—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×C4×Dic11—42no—
121C2×C4×Dic11—42no—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130#66943—44no—
131#66941—44no—
132#66931—216no—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2312yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2312yes—
147#35033—111nomaximal, Sylow
148C24×C11—24no—
149C24×C11—41no—
150C24×C11—41no—
151C24×C11—42no—
152C24×C11C2×Q814yes—
153C24×C11C2411yescharacteristic
154C24×C11C2411yescharacteristic
155C24×C11C2411yescharacteristic
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—416no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11C2×Q814yes—
170C22×C4×C11C2×Q814yes—
171C22×C4×C11C2×Q814yes—
172C22×C4×C11C2×Q814yes—
173C22×C4×C11C2×Q814yes—
174C22×C4×C11C2×Q814yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2414yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C22×Dic11—24no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11#4118yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2414yes—
190C22×Dic11C2414yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C2×Dic22—28no—
194C2×Dic22—44no—
195C2×Dic22—44no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C22⋊C4—28no—
199C11×C22⋊C4—44no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C42×C11—42no—
203C42×C11—42no—
204C22⋊Dic11—24no—
205C22⋊Dic11—24no—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208C22⋊Dic11—28no—
209C22⋊Dic11—42no—
210C22⋊Dic11—42no—
211C22⋊Dic11—44no—
212C4⋊Dic11—28no—
213C4⋊Dic11—24no—
214C4⋊Dic11—24no—
215C4⋊Dic11—44no—
216C4⋊Dic11—44no—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—44no—
220Dic11⋊C4—44no—
221Dic11⋊C4—44no—
222Dic11⋊C4—44no—
223C4×Dic11—24no—
224C4×Dic11—24no—
225C4×Dic11—41no—
226C4×Dic11—41no—
227C4×Dic11—41no—
228C4×Dic11—41no—
229C4×Dic11—42no—
230C4×Dic11—42no—
231#2857—112no—
232#2851—112no—
233#2626—114no—
234#2608—112no—
235#2608—112no—
236#2607—112no—
237#2607—112no—
238#2441—112no—
239#2441—112no—
240#2439—112no—
241#2439—112no—
242#2329—114no—
243#2280—111no—
244#2280D1111yescharacteristic
245C2×C4×C22⋊C4—111no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—22no—
249C23×C11—28no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—48no—
261C23×C11—48no—
262C23×C11C22×Q812yes—
263C23×C11C22×Q812yes—
264C23×C11C22×Q812yes—
265C23×C11C2×#4114yes—
266C23×C11C2511yescharacteristic
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—28no—
274C2×C4×C11—28no—
275C2×C4×C11—28no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—44no—
283C2×C4×C11—44no—
284C2×C4×C11—44no—
285C2×C4×C11C22×Q812yes—
286C2×C4×C11C22×Q812yes—
287C2×C4×C11C22×Q812yes—
288C2×C4×C11C22×Q812yes—
289C2×C4×C11H(5,𝔽2)12yes—
290C2×C4×C11H(5,𝔽2)12yes—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—22no—
307C2×Dic11—48no—
308C2×Dic11—48no—
309C2×Dic11C2×#4114yes—
310C2×Dic11C2×#4114yes—
311Dic22—88no—
312C24×C4C2×D1111yescharacteristic
313C2×C4⋊Q8—112no—
314C2×#125—112no—
315C2×C22⋊Q8—114no—
316C2×#117—111no—
317C2×#117—111no—
318C2×#117C2×D1111yescharacteristic
319C2×#117C2×D1111yescharacteristic
320C22×C22⋊C4—112no—
321C22×C42—111no—
322C22×C42—111no—
323#399—114no—
324#399—114no—
325#396—114no—
326#396—114no—
327#396—114no—
328#396—114no—
329#393—114no—
330#393—114no—
331#391—114no—
332#391—114no—
333#391—114no—
334#389—112no—
335#389—112no—
336#389—112no—
337#389—112no—
338#389—114no—
339#389—114no—
340#389—114no—
341#387—114no—
342#387—114no—
343#387—114no—
344#387—114no—
345#387—114no—
346#387—114no—
347#385—114no—
348#385—114no—
349#384—112no—
350#382—112no—
351#381—112no—
352#381C2×D1112yes—
353#380—112no—
354#380—112no—
355#380—114no—
356#380C2×D1112yes—
357#380C2×D1112yes—
358#379—112no—
359#379C2×D1112yes—
360C4×C22⋊C4—112no—
361C4×C22⋊C4—111no—
362C4×C22⋊C4—111no—
363C4×C22⋊C4—112no—
364C4×C22⋊C4—111no—
365C4×C22⋊C4—111no—
366C4×C22⋊C4—112no—
367C4×C22⋊C4—112no—
368C4×C22⋊C4C2×D1112yes—
369C4×C22⋊C4C2×D1112yes—
370C2×#95—112no—
371C22×C11—22no—
372C22×C11—22no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—416no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11#53314yes—
387C22×C11C23×Q811yescharacteristic
388C22×C11C22×#4112yes—
389C22×C11C2×H(5,𝔽2)11yescharacteristic
390C22×C11C2×H(5,𝔽2)11yescharacteristic
391C22×C11#58512yes—
392C4×C11—22no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—44no—
396C4×C11—44no—
397C4×C11#54314yes—
398Dic11—24no—
399Dic11—24no—
400Dic11—44no—
401Dic11—44no—
402Dic11—42no—
403Dic11—42no—
404C25C22×D1111yescharacteristic
405C22×Q8—114no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—112no—
409C23×C4—112no—
410C23×C4Dic2218yescomplemented
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1111yescharacteristic
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1111yescharacteristic
415C23×C4C22×D1111yescharacteristic
416C23×C4C22×D1111yescharacteristic
417C4⋊Q8—444no—
418#125—444no—
419C22⋊Q8—2216no—
420#117—42no—
421#117—42no—
422#117—442no—
423#117—442no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4C22×D1112yes—
436C2×C4⋊C4C22×D1112yes—
437C2×C22⋊C4—112no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—112no—
441C2×C22⋊C4—114no—
442C2×C22⋊C4—112no—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—114no—
445C2×C22⋊C4—228no—
446C2×C22⋊C4C22×D1114yes—
447C2×C22⋊C4C22×D1112yes—
448C2×C22⋊C4C22×D1112yes—
449C2×C22⋊C4C22×D1114yes—
450C2×C42—112no—
451C2×C42—112no—
452C2×C42—112no—
453C2×C42—112no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—111no—
458C2×C42—442no—
459C2×C42—442no—
460C2×C42C22×D1112yes—
461C2×C42C22×D1112yes—
462#95—112no—
463#95—112no—
464#95—112no—
465#95—112no—
466#95—114no—
467#95—114no—
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95—114no—
473#95—114no—
474#95C22×D1114yes—
475#95C22×D1114yes—
476C2×C11—24no—
477C2×C11—42no—
478C2×C11—42no—
479C2×C11C2×#53311yescharacteristic
480C2×C11C2×#54311yescharacteristic
481C2×C11#345811yescharacteristic
482C2×C11#350512yes—
483C2×C11#350612yes—
484C24—24no—
485C24—41no—
486C24—41no—
487C24—42no—
488C24C2×Dic2214yes—
489C24C23×D1111yescharacteristic
490C24C23×D1111yescharacteristic
491C24C23×D1111yescharacteristic
492C2×Q8—228no—
493C2×Q8—444no—
494C2×Q8—444no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—416no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—118no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—114no—
514C22×C4—114no—
515C22×C4—224no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4C2×Dic2214yes—
521C22×C4C2×Dic2214yes—
522C22×C4C2×Dic2214yes—
523C22×C4C2×Dic2214yes—
524C22×C4C2×Dic2214yes—
525C22×C4C2×Dic2214yes—
526C22×C4C23×D1114yes—
527C22×C4C23×D1114yes—
528C22×C4C23×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—228no—
535C4⋊C4—228no—
536C4⋊C4—228no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—444no—
540C4⋊C4—444no—
541C4⋊C4—444no—
542C4⋊C4—444no—
543C4⋊C4—444no—
544C4⋊C4—444no—
545C22⋊C4—28no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—44no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—228no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—444no—
557C42—42no—
558C42—42no—
559C42—224no—
560C42—224no—
561C42—441no—
562C42—441no—
563C42—441no—
564C42—441no—
565C42—442no—
566C42—442no—
567C11#3503311yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—22no—
571C23—28no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—44no—
581C23—44no—
582C23—48no—
583C23—48no—
584C23C22×Dic2212yes—
585C23C22×Dic2212yes—
586C23C22×Dic2212yes—
587C23#41×D1114yes—
588C23C24×D1111yescharacteristic
589Q8—888no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—28no—
597C2×C4—28no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—114no—
609C2×C4—114no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—448no—
627C2×C4—448no—
628C2×C4C22×Dic2212yes—
629C2×C4C22×Dic2212yes—
630C2×C4C22×Dic2212yes—
631C2×C4C22×Dic2212yes—
632C2×C4#6703712yes—
633C2×C4#6703712yes—
634C22—24no—
635C22—24no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—416no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22#1062304814yes—
650C22C23×Dic2211yescharacteristic
651C22C2×#6703711yescharacteristic
652C22C2×#6703711yescharacteristic
653C22C2×#41×D1112yes—
654C22#1062345312yes—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—44no—
659C4—44no—
660C4—224no—
661C4—224no—
662C4—444no—
663C4—442no—
664C4—442no—
665C4—444no—
666C4#1062301414yes—
667C2—24no—
668C2—42no—
669C2—42no—
670C2C2×#1062304811yescharacteristic
671C2C2×#1062301411yescharacteristic
672C2#1308202111yescharacteristic
673C2#1308244412yes—
674C2#1308245912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2280C2
prime radicalC25×C11C23
hypercenter#2280D11
hypocenterC11#35033
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #13076966C2semidirect
2. #13076924C2semidirect
4. #13074286C2semidirect
5. #13074283C2semidirect
6. #13074281C2semidirect
7. #13074277C2semidirect
8. #13072330C2semidirect
9. #13072323C2semidirect
10. #13072308C2semidirect
11. #13072301C2semidirect
12. #13071344C2semidirect
24. C2×#66943C22semidirect
25. C2×#66941C22semidirect
46. #10622598C22semidirect
47. #10622598C22semidirect
48. #10622590C22semidirect
49. #10622589C22semidirect
50. #10622586C22semidirect
51. #10622586C22semidirect
63. #10622546C22semidirect
64. #10622546C22semidirect
65. #10622542C22semidirect
66. #10622541C22semidirect
67. #10622268C22semidirect
68. #10622268C22semidirect
69. #10622267C22semidirect
70. #10622267C22semidirect
71. #10622260C22semidirect
72. #10622260C22semidirect
73. #10622259C22semidirect
74. #10622259C22semidirect
78. C23×C4×C11Q8semidirect
410. C23×C4Dic22semidirect
567. C11#35033semidirect

Maximal subgroups

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

subgroupindex
#130769662
#130769242
#130744252
#130742862
#130742832
#130742812
#130742772
#130723302
#130723232
#130723082
#130723012
#130713442
#130709992
C2×C4×C22⋊Dic112
C11×#22802
#3503311