Finite Group Databasebeta

← #14960554

Subgroups — #14960554

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623175C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic, complemented
3#13076911C212yesmaximal, complemented
4#13075066C214yesmaximal, complemented
5#13075032C214yesmaximal, complemented
6#13074892C214yesmaximal, complemented
7#13074866C214yesmaximal, complemented
8#13074394C212yesmaximal, complemented
9#13074091C211yesmaximal, characteristic, complemented
10#13073997C211yesmaximal, characteristic, complemented
11#13073966C212yesmaximal, complemented
12#13072932C212yesmaximal, complemented
13#13072270C211yesmaximal, characteristic, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2434C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×C4⋊Q8C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#67000C2212yes—
21C2×#67000C2212yescomplemented
22C2×#66999—28no—
23C2×#66999C2214yes—
24C2×#66999C2214yes—
25C2×#66983C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31#10623175—28no—
32C2×#66951C2212yes—
33C2×#66948C2212yes—
34C2×#66947C2212yes—
35C2×#66947C2214yes—
36C2×#66935C2212yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C11×#395C2214yescomplemented
39C11×#391C2212yescomplemented
40C11×#385C2212yes—
41C11×#385C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622844C2214yescomplemented
44#10622843C2212yescomplemented
45#10622842C2212yescomplemented
46#10622826C2212yes—
47#10622826C2212yes—
48C4×C22⋊Dic11C2211yescharacteristic
49#10622607C2214yescomplemented
50#10622606C2214yes—
51#10622605C2214yescomplemented
52#10622604C2214yes—
53#10622602C2214yes—
54#10622594C2214yescomplemented
55#10622593C2212yescomplemented
56#10622585C2214yescomplemented
57#10622585C2214yescomplemented
58#10622571C2212yes—
59#10622571C2212yes—
60#10622568C2212yes—
61#10622559C2212yes—
62#10622559C2212yes—
63#10622555C2212yes—
64#10622553C2214yes—
65#10622553C2214yescomplemented
66#10622288C2214yes—
67#10622285C2214yes—
68#10622285C2212yescomplemented
69#10622282C2214yes—
70#10622281C2214yescomplemented
71#10622280C2214yescomplemented
72#10622278C2214yes—
73#10622277C2214yes—
74#10622272C2212yescomplemented
75#10622271C2214yescomplemented
76#10622270C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×Q8×C11—24no—
79C22×Q8×C11—44no—
80C22×Q8×C11C2312yes—
81C22×Q8×C11C2312yes—
82C22×Q8×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×D44C2312yes—
91C22×D44C2312yes—
92C22×D44C2311yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—44no—
95C22×C4×D11C2314yes—
96C22×C4×D11C2312yes—
97C11×C4⋊Q8—44no—
98C11×C22⋊Q8—24no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C42×C11C2312yes—
106C2×C22⋊Dic11C2312yes—
107#67000—28no—
108#67000—44no—
109#66999—216no—
110#66999—216no—
111#66983—24no—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4D418yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×C4⋊Dic11—24no—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4—24no—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141#66951—28no—
142#66948—28no—
143#66947—28no—
144#66947—48no—
145#66935—28no—
146(C22⋊D11)⋊C4—28no—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158#36705—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—24no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11C2×D414yes—
164C23×D11C2412yes—
165C23×D11C2412yes—
166C2×Q8×C11—24no—
167C2×Q8×C11—24no—
168C2×Q8×C11—22no—
169C2×Q8×C11—24no—
170C2×Q8×C11—24no—
171C2×Q8×C11—42no—
172C2×Q8×C11—42no—
173C2×Q8×C11—42no—
174C2×Q8×C11—416no—
175C22×C4×C11—22no—
176C22×C4×C11—24no—
177C22×C4×C11—22no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2412yes—
188C2×C22⋊D11—24no—
189C2×C22⋊D11—28no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C22×Dic11C2×D414yes—
196C22×Dic11C2412yes—
197C22×Dic11C2414yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—22no—
204C2×D44—44no—
205C2×D44—42no—
206C2×D44—44no—
207C2×C4×D11—24no—
208C2×C4×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—44no—
211C2×C4×D11—44no—
212C2×C4×D11—416no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—28no—
216C11×C4⋊C4—44no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C42×C11—42no—
220C22⋊Dic11—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—28no—
227(C2×D11)⋊C4—44no—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4—44no—
230(C2×D11)⋊C4—44no—
231(C2×D11)⋊C4—44no—
232(C2×D11)⋊C4C2×D418yes—
233(C2×D11)⋊C4C2×D418yes—
234C4⋊Dic11—28no—
235C4⋊Dic11—22no—
236Dic11⋊C4—24no—
237Dic11⋊C4—28no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—24no—
244C4×Dic11—42no—
245C2×#538—111no—
246C22×C22⋊Q8—111no—
247#2849—112no—
248#2689—114no—
249#2687—114no—
250#2674—114no—
251#2672—114no—
252#2622—112no—
253#2591—111no—
254#2583—111no—
255#2579—112no—
256#2487—112no—
257#2436—111no—
258#2434D1111yescharacteristic, complemented
259#2312—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11C22×D412yes—
263C23×C112−1+414yes—
264C23×C11C2511yescharacteristic
265C22×D11—28no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—22no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—416no—
276C22×D11C22×D414yes—
277Q8×C11—48no—
278Q8×C11—48no—
279Q8×C11—82no—
280C2×C4×C11—28no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—44no—
296C2×C4×C11—44no—
297C2×C4×C11C22×D412yes—
298C2×C4×C11C22×D412yes—
299C2×C4×C11H(5,𝔽2)14yes—
300C22⋊D11—48no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—44no—
313C2×Dic11—44no—
314C2×Dic11—44no—
315C2×Dic11C22×D414yes—
316D44—82no—
317D44—84no—
318D44—84no—
319C4×D11—416no—
320C4×D11—84no—
321C23×Q8C2×D1111yescharacteristic
322C24×C4—111no—
323#538—228no—
324C2×C4⋊Q8C2×D1112yescomplemented
325C2×#126—112no—
326C2×#124—112no—
327C2×#124—112no—
328C2×#123—112no—
329C2×#123—114no—
330C2×C22⋊Q8—114no—
331C2×C22⋊Q8—114no—
332C2×C22⋊Q8—228no—
333C2×C22⋊Q8C2×D1111yescharacteristic
334C2×#121—111no—
335C2×#121—112no—
336C2×#120—112no—
337C2×C4×D4—112no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343#400—112no—
344#400—114no—
345#399—114no—
346#398—112no—
347#398—114no—
348#397—114no—
349#397—114no—
350#396—114no—
351#395—112no—
352#395C2×D1114yescomplemented
353#394—114no—
354#394—112no—
355#394—114no—
356#393—114no—
357#391—112no—
358#391C2×D1112yescomplemented
359#389—114no—
360#389—114no—
361#388—114no—
362#388—114no—
363#388—114no—
364#387—114no—
365#386—112no—
366#386—112no—
367#386—112no—
368#386—112no—
369#386—114no—
370#385—114no—
371#385—112no—
372#385—112no—
373#385—114no—
374#385C2×D1112yes—
375#385C2×D1112yes—
376#381—114no—
377#380—112no—
378#380—114no—
379#379—112no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4C2×D1111yescharacteristic
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—28no—
385C22×C11#53614yes—
386C22×C11C23×D411yescharacteristic
387C22×C11C2×H(5,𝔽2)12yes—
388C22×C11C2×2−1+412yes—
389C22×C11#58512yes—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—416no—
394C2×D11—48no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—48no—
399C4×C11—24no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—44no—
406Dic11—24no—
407Dic11—42no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C25—111no—
412C22×Q8—24no—
413C22×Q8—44no—
414C22×Q8C22×D1112yes—
415C22×Q8C22×D1112yes—
416C22×Q8C22×D1111yescharacteristic
417C22×D4—112no—
418C22×D4—112no—
419C22×D4—112no—
420C22×D4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—114no—
425C23×C4—112no—
426C23×C4—224no—
427C23×C4—444no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—44no—
432#126—228no—
433#124—228no—
434#124—444no—
435#123—228no—
436#123—448no—
437C22⋊Q8—24no—
438C22⋊Q8—2216no—
439C22⋊Q8—2216no—
440#121—228no—
441#121—224no—
442#120—228no—
443C4×D4—228no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—224no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4C22×D1112yes—
457C2×C4⋊C4C22×D1111yescharacteristic
458C2×C4⋊C4C22×D1114yes—
459C2×C4⋊C4C22×D1114yes—
460C2×C22⋊C4—118no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—112no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—112no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4C22×D1112yes—
477C2×C22⋊C4C22×D1112yes—
478C2×C42—112no—
479C2×C42—112no—
480C2×C42C22×D1112yes—
481#95—112no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95C22×D1112yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492C2×C11—24no—
493C2×C11C2×#53611yescharacteristic
494C2×C11#348411yescharacteristic
495C2×C11#348511yescharacteristic
496C2×C11#354114yes—
497D11—44no—
498D11—82no—
499C24—112no—
500C24—114no—
501C24—112no—
502C24—224no—
503C24—442no—
504C24—442no—
505C24C23×D1111yescharacteristic
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—416no—
515C2×D4—224no—
516C2×D4—224no—
517C2×D4—224no—
518C2×D4—228no—
519C2×D4—222no—
520C2×D4—444no—
521C2×D4—442no—
522C2×D4—444no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—112no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—114no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—224no—
535C22×C4—228no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—228no—
539C22×C4—444no—
540C22×C4—444no—
541C22×C4—4416no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4—442no—
545C22×C4D4×D1114yes—
546C22×C4C23×D1114yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1112yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1112yes—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—28no—
556C4⋊C4—44no—
557C4⋊C4—228no—
558C4⋊C4—228no—
559C4⋊C4—224no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—222no—
563C4⋊C4—444no—
564C4⋊C4—444no—
565C4⋊C4—444no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—118no—
569C22⋊C4—118no—
570C22⋊C4—224no—
571C22⋊C4—228no—
572C22⋊C4—224no—
573C22⋊C4—224no—
574C22⋊C4—224no—
575C22⋊C4—224no—
576C22⋊C4—228no—
577C22⋊C4—444no—
578C22⋊C4—444no—
579C22⋊C4—444no—
580C22⋊C4—444no—
581C22⋊C4—444no—
582C42—42no—
583C42—224no—
584C42—442no—
585C11#3670511yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—114no—
589C23—228no—
590C23—224no—
591C23—224no—
592C23—224no—
593C23—222no—
594C23—224no—
595C23—224no—
596C23—224no—
597C23—444no—
598C23—444no—
599C23—4416no—
600C23C2×D4×D1112yes—
601C23#6704014yes—
602C23C24×D1111yescharacteristic
603Q8—48no—
604Q8—48no—
605Q8—82no—
606D4—448no—
607D4—882no—
608D4—884no—
609D4—884no—
610C2×C4—28no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—114no—
628C2×C4—224no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—222no—
637C2×C4—224no—
638C2×C4—222no—
639C2×C4—4416no—
640C2×C4—444no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4—884no—
644C2×C4C2×D4×D1112yes—
645C2×C4C2×D4×D1112yes—
646C2×C4#6703714yes—
647C22—28no—
648C22—22no—
649C22—22no—
650C22—224no—
651C22—224no—
652C22—224no—
653C22—4416no—
654C22—448no—
655C22—448no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22#1062325514yes—
660C22C22×D4×D1111yescharacteristic
661C22C2×#6703712yes—
662C22C2×#6704012yes—
663C22#1062345712yes—
664C4—24no—
665C4—22no—
666C4—22no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—224no—
672C4—444no—
673C4—442no—
674C4—442no—
675C4—442no—
676C2—24no—
677C2—444no—
678C2—882no—
679C2C2×#1062325511yescharacteristic
680C2#1308224511yescharacteristic
681C2#1308225911yescharacteristic
682C2#1308291414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2434C2
prime radicalC2×#10623175C2
hypercenter#2434D11
hypocenterC11#36705
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2434

Complements

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

NH ≅ G/Ntype
2. C22×#66999C2semidirect
3. #13076911C2semidirect
4. #13075066C2semidirect
5. #13075032C2semidirect
6. #13074892C2semidirect
7. #13074866C2semidirect
8. #13074394C2semidirect
9. #13074091C2semidirect
10. #13073997C2semidirect
11. #13073966C2semidirect
12. #13072932C2semidirect
13. #13072270C2semidirect
14. #13071211C2semidirect
15. C11×#2434C2semidirect
18. C2×C11×C4⋊Q8C22semidirect
21. C2×#67000C22semidirect
38. C11×#395C22semidirect
39. C11×#391C22semidirect
43. #10622844C22semidirect
44. #10622843C22semidirect
45. #10622842C22semidirect
49. #10622607C22semidirect
51. #10622605C22semidirect
54. #10622594C22semidirect
55. #10622593C22semidirect
56. #10622585C22semidirect
57. #10622585C22semidirect
65. #10622553C22semidirect
68. #10622285C22semidirect
70. #10622281C22semidirect
71. #10622280C22semidirect
74. #10622272C22semidirect
75. #10622271C22semidirect
76. #10622270C22semidirect
258. #2434D11semidirect
324. C2×C4⋊Q8C2×D11semidirect
352. #395C2×D11semidirect
358. #391C2×D11semidirect
585. C11#36705semidirect

Maximal subgroups

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

subgroupindex
C2×#106231752
C22×#669992
#130769112
#130750662
#130750322
#130748922
#130748662
#130743942
#130740912
#130739972
#130739662
#130729322
#130722702
#130712112
C11×#24342
#3670511