Finite Group Databasebeta

← #14925725

Subgroups — #14925725

Order 2816.

1900 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073893C214yesmaximal, complemented
2#13073824C211yesmaximal, characteristic, complemented
3#13073785C211yesmaximal, characteristic
4#13073539C211yesmaximal, characteristic
5#13073156C212yesmaximal, complemented
6#13073047C212yesmaximal, complemented
7#13072484C212yesmaximal
8#13072144C212yesmaximal, complemented
9#13071893C214yesmaximal, complemented
10#13071183C211yesmaximal, characteristic, complemented
11#125×Dic11C212yesmaximal, complemented
12#13071146C212yesmaximal, complemented
13#13071074C212yesmaximal
14#13071021C212yesmaximal, complemented
15C4×#66940C211yesmaximal, characteristic, complemented
16C4×#66946C211yesmaximal, characteristic
17C11×#2552C211yesmaximal, characteristic, complemented
18C2×C11×#125C2212yes—
19C2×#66950C2212yes—
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×#66945C2214yes—
23C2×#66940C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66940C2212yes—
26C2×C4×D44C2211yescharacteristic
27C2×C42×D11C2212yes—
28C2×#66922C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C11×#398C2214yes—
31C11×#389C2212yes—
32C11×#389C2212yes—
33C11×#384C2212yes—
34C11×#384C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37#10622607C2214yes—
38#10622607C2214yes—
39#10622605C2214yes—
40#10622603C2214yes—
41#10622602C2214yes—
42#10622601C2212yes—
43#10622600C2212yes—
44#10622600C2212yes—
45#10622600C2214yes—
46#10622600C2212yes—
47#10622598C2212yes—
48#10622598C2212yes—
49#10622598C2212yes—
50#10622597C2214yes—
51#10622594C2214yes—
52#10622594C2214yes—
53#10622590C2214yes—
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2214yes—
56C4⋊C4×Dic11C2214yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2211yescharacteristic
59C4⋊C4×Dic11C2212yes—
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62#10622587C2212yes—
63#10622586C2212yes—
64#10622586C2212yes—
65#10622552C2212yes—
66C4×(C2×D11)⋊C4C2212yes—
67#10622549C2212yes—
68#10622548C2212yes—
69C4×Dic11⋊C4C2212yes—
70C42×Dic11C2212yes—
71C42×Dic11C2211yescharacteristic
72#10622542C2212yes—
73#10622286C2214yes—
74#10622283C2214yes—
75#10622279C2212yes—
76#10622279C2214yes—
77#10622279C2212yes—
78#10622273C2214yes—
79#10622269C2214yes—
80#10622267C2214yes—
81#10622262C2212yes—
82#10622262C2212yes—
83C22×D44C2311yescharacteristic
84C22×C4×D11C2312yes—
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2312yes—
89C11×#125—28no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C42×C11C2312yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2311yescharacteristic
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2311yescharacteristic
135#66950—28no—
136#66946—24no—
137#66946Q818yescomplemented
138#66945—48no—
139#66940—24no—
140#66940—24no—
141#66940—44no—
142C4×D44—24no—
143C42×D11—28no—
144#66922—24no—
145C4×Dic22—24no—
146C11×#95C2312yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160#34941—111nomaximal, Sylow
161C23×D11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2412yes—
174C22×Dic11C2411yescharacteristic
175C22×Dic11C2411yescharacteristic
176C22×Dic11C2412yes—
177C22×Dic11C2411yescharacteristic
178C2×D44—22no—
179C2×D44—22no—
180C2×D44C2×Q814yes—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—42no—
189C2×C4×D11C2×Q818yes—
190C2×Dic22—22no—
191C2×Dic22—22no—
192C2×Dic22—24no—
193C2×Dic22—42no—
194C2×Dic22—42no—
195C2×Dic22#4114yes—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—28no—
200C11×C4⋊C4—28no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—44no—
204C11×C4⋊C4C2×Q814yes—
205C11×C4⋊C4#4114yes—
206C42×C11—24no—
207C42×C11—24no—
208C42×C11#4114yes—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—44no—
213(C2×D11)⋊C4—44no—
214(C2×D11)⋊C4—44no—
215(C2×D11)⋊C4C2×Q818yes—
216C4⋊Dic11—28no—
217C4⋊Dic11—22no—
218C4⋊Dic11—24no—
219C4⋊Dic11—24no—
220C4⋊Dic11—22no—
221C4⋊Dic11—44no—
222C4⋊Dic11—44no—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225Dic11⋊C4—24no—
226Dic11⋊C4—44no—
227C4×Dic11—24no—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231C4×Dic11—22no—
232C4×Dic11—28no—
233C4×Dic11—24no—
234C4×Dic11—24no—
235C4×Dic11—22no—
236C4×Dic11—22no—
237C4×Dic11—41no—
238C4×Dic11—42no—
239C4×Dic11C2×Q814yes—
240C4×Dic11#4114yes—
241#2574—114no—
242#2567—111no—
243#2563—111no—
244#2552D1111yescharacteristic, complemented
245#2538—111no—
246#2508—112no—
247#2497—112no—
248#2454—112no—
249#2423—112no—
250#2396—114no—
251C4×C4⋊Q8—111no—
252C4×#125—112no—
253C4×C22⋊Q8—112no—
254#2293—112no—
255#2285—112no—
256C42×Q8—111no—
257C42×D4—111no—
258C23×C11C2511yescharacteristic
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11C22×Q814yes—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11C22×Q814yes—
282C2×C4×C11C22×Q812yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11C2×#4112yes—
285C2×C4×C11C2×#4112yes—
286C2×C4×C11C2×#4112yes—
287C2×C4×C11C2×#4112yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4112yes—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—22no—
297C2×Dic11—21no—
298C2×Dic11—22no—
299C2×Dic11—21no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—21no—
304C2×Dic11—24no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11C22×Q812yes—
309C2×Dic11C22×Q812yes—
310C2×Dic11C2×#4112yes—
311C2×Dic11C2×#4114yes—
312C2×Dic11C2×#4112yes—
313C2×Dic11H(5,𝔽2)12yes—
314D44—28no—
315C4×D11—216no—
316C4×D11—48no—
317C4×D11—48no—
318Dic22—28no—
319Dic22—48no—
320C2×C4⋊Q8—111no—
321C2×#125C2×D1112yes—
322C2×C22⋊Q8—112no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—112no—
326C2×C4×Q8—111no—
327C2×C4×D4—111no—
328C2×C4×D4—111no—
329C2×C4×D4—111no—
330C2×#117—114no—
331C22×C42—112no—
332#400—114no—
333#399—114no—
334#398—114no—
335#398C2×D1114yes—
336#396—114no—
337#396—114no—
338#395—114no—
339#393—114no—
340#391—112no—
341#391—112no—
342#390—112no—
343#390—112no—
344#389—112no—
345#389—112no—
346#389—112no—
347#389—112no—
348#389—112no—
349#389C2×D1112yes—
350#389C2×D1112yes—
351#388—114no—
352#388—114no—
353#387—114no—
354#387—114no—
355#387—114no—
356#385—114no—
357#384—112no—
358#384C2×D1111yescharacteristic
359#384C2×D1112yes—
360#382—114no—
361#382—112no—
362#380—112no—
363#380—112no—
364#380—114no—
365#380—112no—
366C4×C4⋊C4—111no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—114no—
370C4×C4⋊C4—112no—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—111no—
373C4×C4⋊C4—111no—
374C4×C4⋊C4—112no—
375C4×C4⋊C4—112no—
376C4×C4⋊C4—112no—
377C4×C4⋊C4C2×D1111yescharacteristic
378C4×C4⋊C4C2×D1111yescharacteristic
379C4×C22⋊C4—112no—
380C4×C22⋊C4—112no—
381C4×C22⋊C4—112no—
382C4×C22⋊C4—114no—
383C43—112no—
384C43—111no—
385C22×C11C23×Q811yescharacteristic
386C22×C11C22×#4111yescharacteristic
387C22×C11C22×#4111yescharacteristic
388C22×C11C22×#4111yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C2×H(5,𝔽2)11yescharacteristic
391C22×C11#58511yescharacteristic
392C2×D11—24no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C4×C11—22no—
400C4×C11—24no—
401C4×C11—24no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—44no—
405C4×C11#52914yes—
406C4×C11#53314yes—
407Dic11—24no—
408Dic11—22no—
409Dic11—22no—
410Dic11—42no—
411Dic11—44no—
412Dic11—42no—
413Dic11—41no—
414Dic11#55414yes—
415C22×Q8—111no—
416C22×Q8—112no—
417C22×D4—111no—
418C23×C4—112no—
419C23×C4—112no—
420C23×C4—112no—
421C4⋊Q8—224no—
422#125—28no—
423C22⋊Q8—228no—
424C4×Q8—224no—
425C4×Q8—224no—
426C4×Q8—224no—
427C4×Q8—444no—
428C4×D4—118no—
429C4×D4—224no—
430C4×D4—224no—
431#117—448no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C4⋊C4C22×D1111yescharacteristic
445C2×C4⋊C4C22×D1112yes—
446C2×C4⋊C4C22×D1114yes—
447C2×C4⋊C4C22×D1112yes—
448C2×C4⋊C4C22×D1114yes—
449C2×C4⋊C4C22×D1114yes—
450C2×C4⋊C4C22×D1112yes—
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C22⋊C4—112no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—114no—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—112no—
463C2×C42—114no—
464C2×C42—111no—
465C2×C42—111no—
466C2×C42—112no—
467C2×C42—111no—
468C2×C42—112no—
469C2×C42—112no—
470C2×C42—112no—
471C2×C42—112no—
472C2×C42—111no—
473C2×C42—112no—
474C2×C42—228no—
475C2×C42C22×D1112yes—
476C2×C42C22×D1112yes—
477C2×C42C22×D1111yescharacteristic
478#95—112no—
479#95—112no—
480#95—114no—
481#95—112no—
482#95—112no—
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×D1112yes—
492C2×C11C2×#52911yescharacteristic
493C2×C11C2×#53311yescharacteristic
494C2×C11#346011yescharacteristic
495C2×C11C2×#55411yescharacteristic
496C2×C11#347511yescharacteristic
497C2×C11Q8×#4111yescharacteristic
498C2×C11#348311yescharacteristic
499D11—44no—
500C24—112no—
501C2×Q8—114no—
502C2×Q8—222no—
503C2×Q8—224no—
504C2×Q8—222no—
505C2×Q8—442no—
506C2×Q8—442no—
507C2×D4—114no—
508C2×D4—222no—
509C2×D4—222no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—112no—
514C22×C4—118no—
515C22×C4—112no—
516C22×C4—114no—
517C22×C4—111no—
518C22×C4—112no—
519C22×C4—224no—
520C22×C4—224no—
521C22×C4—224no—
522C22×C4—224no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—224no—
526C22×C4—442no—
527C22×C4C23×D1112yes—
528C22×C4C23×D1112yes—
529C22×C4C23×D1114yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C22×C4C23×D1111yescharacteristic
535C4⋊C4—28no—
536C4⋊C4—28no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—24no—
541C4⋊C4—44no—
542C4⋊C4—42no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—228no—
546C4⋊C4—222no—
547C4⋊C4—224no—
548C4⋊C4—222no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—444no—
552C4⋊C4—444no—
553C4⋊C4—444no—
554C4⋊C4#434114yes—
555C4⋊C4Q8×D1114yes—
556C22⋊C4—118no—
557C22⋊C4—228no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—444no—
561C22⋊C4—444no—
562C22⋊C4—444no—
563C42—24no—
564C42—24no—
565C42—114no—
566C42—114no—
567C42—224no—
568C42—224no—
569C42—224no—
570C42—228no—
571C42—224no—
572C42—224no—
573C42—222no—
574C42—222no—
575C42—224no—
576C42—222no—
577C42—441no—
578C42—442no—
579C42#434314yes—
580C11#3494111yescharacteristic, complemented, Sylow
581C23—114no—
582C23—222no—
583C23—222no—
584C23—222no—
585C23—222no—
586C23—222no—
587C23—222no—
588C23C24×D1111yescharacteristic
589Q8—228no—
590Q8—448no—
591D4—228no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—114no—
613C2×C4—2216no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—224no—
624C2×C4—222no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—224no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—224no—
632C2×C4—448no—
633C2×C4—448no—
634C2×C4C2×#434114yes—
635C2×C4C2×#434112yes—
636C2×C4C2×Q8×D1114yes—
637C2×C4C2×Q8×D1112yes—
638C2×C4C2×#434312yes—
639C2×C4C2×#434312yes—
640C2×C4C2×#434312yes—
641C2×C4#41×D1112yes—
642C2×C4#41×D1112yes—
643C22—224no—
644C22—224no—
645C22—224no—
646C22—442no—
647C22—442no—
648C22—442no—
649C22—442no—
650C22C22×#434111yescharacteristic
651C22C22×Q8×D1111yescharacteristic
652C22C22×#434311yescharacteristic
653C22C2×#41×D1111yescharacteristic
654C22C2×#41×D1111yescharacteristic
655C22D11×H(5,𝔽2)11yescharacteristic
656C22#1062345711yescharacteristic
657C4—24no—
658C4—24no—
659C4—22no—
660C4—42no—
661C4—42no—
662C4—44no—
663C4—114no—
664C4—224no—
665C4—222no—
666C4—222no—
667C4—442no—
668C4—441no—
669C4—444no—
670C4—442no—
671C4#1062322214yes—
672C4#1062325914yes—
673C2—444no—
674C2C2×#1062322211yescharacteristic
675C2C2×#1062325911yescharacteristic
676C2#1308203911yescharacteristic
677C2D11×#55411yescharacteristic
678C2#1308217911yescharacteristic
679C2#1308219811yescharacteristic
680C2#1308223911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2552C2
prime radicalC22×D44C23
hypercenter#2552D11
hypocenterC11#34941
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
1. #13073893C2semidirect
2. #13073824C2semidirect
5. #13073156C2semidirect
6. #13073047C2semidirect
8. #13072144C2semidirect
9. #13071893C2semidirect
10. #13071183C2semidirect
11. #125×Dic11C2semidirect
12. #13071146C2semidirect
14. #13071021C2semidirect
15. C4×#66940C2semidirect
17. C11×#2552C2semidirect
137. #66946Q8semidirect
244. #2552D11semidirect
580. C11#34941semidirect

Maximal subgroups

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

subgroupindex
#130738932
#130738242
#130737852
#130735392
#130731562
#130730472
#130724842
#130721442
#130718932
#130711832
#125×Dic112
#130711462
#130710742
#130710212
C4×#669402
C4×#669462
C11×#25522
#3494111