Finite Group Databasebeta

← #14960473

Subgroups — #14960473

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C2×#10623155C211yesmaximal, characteristic
3#13076685C212yesmaximal, complemented
4#13076681C212yesmaximal, complemented
5#13076680C212yesmaximal, complemented
6#13076671C212yesmaximal, complemented
7#13076651C211yesmaximal, characteristic, complemented
8#13076646C211yesmaximal, characteristic
9#13076643C211yesmaximal, characteristic
10#13076635C214yesmaximal, complemented
11#13071906C212yesmaximal, complemented
12#13071905C212yesmaximal, complemented
13#13071889C212yesmaximal, complemented
14#13071887C212yesmaximal, complemented
15#13071874C214yesmaximal, complemented
16#13071007C211yesmaximal, characteristic, complemented
17C11×#2817C211yesmaximal, characteristic, complemented
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×#66997C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27#10623155—28no—
28#10623153—28no—
29C2×#66951C2212yes—
30C2×#66946C2211yescharacteristic
31C2×#66945C2212yes—
32C2×#66943C2211yescharacteristic
33C2×#66942C2212yes—
34C2×#66941C2211yescharacteristic
35C2×#66940C2211yescharacteristic
36C2×#66940C2212yes—
37C2×#66939C2212yes—
38C2×(C22⋊D11)⋊C4C2212yes—
39C2×#66931C2212yes—
40C2×#66930C2212yes—
41C11×#400C2212yes—
42C11×#400C2212yes—
43C11×#397C2214yes—
44C11×#395C2212yes—
45C11×#395C2212yes—
46C11×#381C2211yescharacteristic
47#10622844C2212yes—
48#10622842C2212yes—
49#10622824C2211yescharacteristic
50#10622607C2214yes—
51#10622605C2214yes—
52#10622605C2212yes—
53#10622604C2212yes—
54#10622599C2212yes—
55#10622597C2214yes—
56#10622596C2212yes—
57#10622595C2212yes—
58#10622592C2212yes—
59C4⋊C4×Dic11C2214yes—
60#10622574C2214yes—
61#10622572C2214yes—
62#10622565C2214yes—
63#10622555C2212yes—
64C22⋊C4×Dic11C2212yes—
65#10622290C2212yes—
66#10622289C2214yes—
67#10622288C2214yes—
68#10622288C2214yes—
69#10622286C2212yes—
70#10622286C2214yes—
71#10622285C2212yes—
72#10622279C2214yes—
73#10622279C2214yes—
74#10622274C2214yes—
75#10622274C2212yes—
76#10622271C2214yes—
77#10622270C2214yes—
78#10622270C2214yes—
79#10622269C2214yes—
80#10622264C2212yes—
81#10622263C2212yes—
82#10622262C2214yes—
83#10622262C2212yes—
84#10622261C2212yes—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2312yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×D44C2311yescharacteristic
92C22×C4×D11C2312yes—
93C22×Dic22C2312yes—
94C22×Dic22C2311yescharacteristic
95C11×C22⋊Q8—24no—
96C11×C22⋊Q8—24no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2312yes—
107#67000—24no—
108Q8×Dic11—24no—
109Q8×Dic11—24no—
110#66997—24no—
111#66983—24no—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2314yes—
126#66977—24no—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×C4×Dic11D418yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145#66951—28no—
146#66946—24no—
147#66945—28no—
148#66943—24no—
149#66942—28no—
150#66941—24no—
151#66940—24no—
152#66940—28no—
153#66939—28no—
154(C22⋊D11)⋊C4—28no—
155#66931—28no—
156#66930—28no—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11×#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2312yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171#36699—111nomaximal, Sylow
172C24×C11C2411yescharacteristic
173C23×D11C2412yes—
174C2×Q8×C11—22no—
175C2×Q8×C11—22no—
176C2×Q8×C11—42no—
177C2×Q8×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—24no—
188C2×C22⋊D11—44no—
189C22×Dic11—24no—
190C22×Dic11—42no—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2411yescharacteristic
198C22×Dic11C2411yescharacteristic
199C22×Dic11C2411yescharacteristic
200C22×Dic11C2411yescharacteristic
201C2×D44—22no—
202C2×D44—42no—
203C2×C4×D11—24no—
204C2×C4×D11—28no—
205C2×Dic22—24no—
206C2×Dic22—22no—
207C2×Dic22—42no—
208C2×Dic22—42no—
209C2×Dic22—42no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—44no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—42no—
218C22⋊Dic11—24no—
219C22⋊Dic11—42no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—44no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4—44no—
228C4⋊Dic11—24no—
229C4⋊Dic11—24no—
230C4⋊Dic11—24no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11—44no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—24no—
244C4×Dic11—24no—
245C4×Dic11—24no—
246C4×Dic11—28no—
247C4×Dic11C2×D414yes—
248C4×Dic11C2×D414yes—
249C4×Dic11C2×D414yes—
250C4×Dic11C2×D414yes—
251C2×#533—111no—
252C2×#529—111no—
253#2822—112no—
254#2821—112no—
255#2821—112no—
256#2820—112no—
257#2817—111no—
258#2817D1111yescharacteristic, complemented
259#2816—111no—
260#2816—111no—
261#2814—114no—
262#2399—112no—
263#2398—112no—
264#2396—112no—
265#2396—112no—
266#2395—114no—
267#2283—111no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11C22×D412yes—
272C23×C11C2511yescharacteristic
273C22×D11—22no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277Q8×C11—44no—
278Q8×C11—44no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—44no—
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C22⋊D11—48no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—28no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—44no—
312C2×Dic11C22×D412yes—
313C2×Dic11C22×D412yes—
314C2×Dic11C22×D412yes—
315C2×Dic11C22×D412yes—
316C2×Dic112−1+414yes—
317D44—44no—
318C4×D11—48no—
319Dic22—48no—
320Dic22—44no—
321#533—228no—
322C2×C4⋊Q8—111no—
323C2×C4⋊Q8—111no—
324#529—228no—
325C2×#126—112no—
326C2×#125—112no—
327C2×#125—111no—
328C2×#124—111no—
329C2×#123—112no—
330C2×C22⋊Q8—111no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8C2×D1111yescharacteristic
333C2×C22⋊Q8C2×D1111yescharacteristic
334C2×#121—111no—
335C2×C4×Q8—111no—
336C2×C4×Q8—111no—
337C2×C4×Q8—111no—
338C2×C4×Q8—112no—
339C2×C4×D4—111no—
340C2×C4×D4—112no—
341C2×#117—112no—
342C2×#117—112no—
343C22×C42—111no—
344#400—112no—
345#400—112no—
346#400—114no—
347#400C2×D1112yes—
348#400C2×D1112yes—
349#399—112no—
350#399—114no—
351#399—112no—
352#398—112no—
353#398—114no—
354#398—112no—
355#398—114no—
356#398—114no—
357#398—114no—
358#397—114no—
359#397—114no—
360#397—114no—
361#397C2×D1114yes—
362#396—114no—
363#396—114no—
364#395—112no—
365#395—112no—
366#395—114no—
367#395C2×D1112yes—
368#395C2×D1112yes—
369#394—112no—
370#394—114no—
371#394—114no—
372#394—112no—
373#393—112no—
374#393—112no—
375#393—114no—
376#383—112no—
377#382—112no—
378#381—111no—
379#381C2×D1111yescharacteristic
380#380—112no—
381C4×C4⋊C4—114no—
382C4×C4⋊C4—114no—
383C4×C4⋊C4—112no—
384C4×C22⋊C4—112no—
385C4×C22⋊C4—114no—
386C4×C22⋊C4—114no—
387#376—112no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—44no—
392C22×C11C23×D411yescharacteristic
393C22×C11C2×2−1+412yes—
394C22×C11#58512yes—
395C22×C11#58512yes—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—48no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—44no—
407Dic11—22no—
408Dic11—22no—
409Dic11—22no—
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413Dic11—44no—
414Dic11#53614yes—
415C22×Q8—112no—
416C22×Q8—111no—
417C22×Q8C22×D1111yescharacteristic
418C22×Q8C22×D1111yescharacteristic
419C22×D4—112no—
420C22×D4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—112no—
424C23×C4C22×D1111yescharacteristic
425C4⋊Q8—224no—
426C4⋊Q8—224no—
427#126—228no—
428#125—224no—
429#125—228no—
430#124—224no—
431#123—228no—
432C22⋊Q8—24no—
433C22⋊Q8—24no—
434C22⋊Q8—228no—
435C22⋊Q8—224no—
436#121—224no—
437C4×Q8—224no—
438C4×Q8—228no—
439C4×Q8—224no—
440C4×Q8—224no—
441C4×D4—224no—
442C4×D4—228no—
443#117—228no—
444#117—228no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4C22×D1112yes—
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C4⋊C4C22×D1112yes—
463C2×C4⋊C4C22×D1111yescharacteristic
464C2×C4⋊C4C22×D1114yes—
465C2×C22⋊C4—112no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—112no—
470C2×C22⋊C4—112no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4C22×D1112yes—
476C2×C22⋊C4C22×D1112yes—
477C2×C22⋊C4C22×D1112yes—
478C2×C42—118no—
479C2×C42—111no—
480C2×C42—111no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—112no—
484C2×C42—112no—
485C2×C42—112no—
486C2×C42—114no—
487#95—114no—
488#95—112no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—112no—
493#95—114no—
494#95—114no—
495#95—114no—
496#95C22×D1112yes—
497#95C22×D1114yes—
498#95C22×D1114yes—
499#95C22×D1112yes—
500#95C22×D1114yes—
501C2×C11—42no—
502C2×C11C2×#53611yescharacteristic
503C2×C11#344911yescharacteristic
504C2×C11#344911yescharacteristic
505C2×C11#353114yes—
506D11—82no—
507C24—112no—
508C24C23×D1111yescharacteristic
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—224no—
514C2×Q8—222no—
515C2×Q8—442no—
516C2×Q8—442no—
517C2×Q8—442no—
518C2×D4—224no—
519C2×D4—222no—
520C2×D4—442no—
521C2×D4—444no—
522C22×C4—42no—
523C22×C4—111no—
524C22×C4—114no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—224no—
534C22×C4—228no—
535C22×C4—224no—
536C22×C4—442no—
537C22×C4D4×D1114yes—
538C22×C4C23×D1112yes—
539C22×C4C23×D1114yes—
540C22×C4C23×D1112yes—
541C22×C4C23×D1112yes—
542C22×C4C23×D1112yes—
543C22×C4C23×D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—44no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—224no—
554C4⋊C4—224no—
555C4⋊C4—224no—
556C4⋊C4—224no—
557C4⋊C4—224no—
558C4⋊C4—222no—
559C4⋊C4—224no—
560C4⋊C4—222no—
561C4⋊C4—444no—
562C4⋊C4—444no—
563C4⋊C4—444no—
564C4⋊C4—444no—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—224no—
569C22⋊C4—224no—
570C22⋊C4—224no—
571C22⋊C4—224no—
572C22⋊C4—224no—
573C22⋊C4—444no—
574C22⋊C4—444no—
575C22⋊C4—444no—
576C22⋊C4—444no—
577C22⋊C4—442no—
578C42—114no—
579C42—114no—
580C42—114no—
581C42—114no—
582C42—224no—
583C42—224no—
584C42—224no—
585C42—228no—
586C11#3669911yescharacteristic, complemented, Sylow
587C23—22no—
588C23—22no—
589C23—22no—
590C23—222no—
591C23—224no—
592C23—224no—
593C23—224no—
594C23C2×D4×D1112yes—
595C23C24×D1111yescharacteristic
596Q8—44no—
597Q8—44no—
598Q8—444no—
599Q8—448no—
600D4—444no—
601D4—448no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—44no—
617C2×C4—112no—
618C2×C4—114no—
619C2×C4—112no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—228no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—224no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—222no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—222no—
636C2×C4—448no—
637C2×C4—444no—
638C2×C4C2×D4×D1112yes—
639C2×C4C2×D4×D1112yes—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—44no—
644C22—442no—
645C22—442no—
646C22—442no—
647C22—448no—
648C22C22×D4×D1111yescharacteristic
649C22#1062345512yes—
650C22D11×2−1+412yes—
651C22#1062345712yes—
652C4—22no—
653C4—22no—
654C4—42no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—44no—
659C4—114no—
660C4—222no—
661C4—222no—
662C4—222no—
663C4—442no—
664C4—442no—
665C4—442no—
666C4—444no—
667C2—42no—
668C2—882no—
669C2D11×#53611yescharacteristic
670C2#1308194211yescharacteristic
671C2#1308194811yescharacteristic
672C2#1308276214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2817C2
prime radicalC2×#66983C22
hypercenter#2817D11
hypocenterC11#36699
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2817

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
3. #13076685C2semidirect
4. #13076681C2semidirect
5. #13076680C2semidirect
6. #13076671C2semidirect
7. #13076651C2semidirect
10. #13076635C2semidirect
11. #13071906C2semidirect
12. #13071905C2semidirect
13. #13071889C2semidirect
14. #13071887C2semidirect
15. #13071874C2semidirect
16. #13071007C2semidirect
17. C11×#2817C2semidirect
258. #2817D11semidirect
586. C11#36699semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106231552
#130766852
#130766812
#130766802
#130766712
#130766512
#130766462
#130766432
#130766352
#130719062
#130719052
#130718892
#130718872
#130718742
#130710072
C11×#28172
#3669911