Finite Group Databasebeta

← #14917005

Subgroups — #14917005

Order 2816.

2090 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623088C211yesmaximal, characteristic
2#13071804C214yesmaximal, complemented
3#13071711C212yesmaximal, complemented
4#13071689C212yesmaximal, complemented
5#13071589C211yesmaximal, characteristic, complemented
6#13071579C211yesmaximal, characteristic, complemented
7#13071533C211yesmaximal, characteristic, complemented
8#13071503C212yesmaximal, complemented
9#13071472C212yesmaximal, complemented
10#13071401C214yesmaximal, complemented
11#13071303C212yesmaximal
12#13071296C212yesmaximal, complemented
13#13071258C212yesmaximal, complemented
14#13071250C212yesmaximal, complemented
15#13071020C211yesmaximal, characteristic, complemented
16#13071009C211yesmaximal, characteristic, complemented
17C11×#2349C211yesmaximal, characteristic, complemented
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×C4×C22⋊D11C2212yes—
23C2×#66979C2212yes—
24#10623088C4116yescomplemented
25C2×#66950C2211yescharacteristic
26C2×#66943C2211yescharacteristic
27C2×#66940C2212yes—
28C2×#66936C2212yes—
29C2×#66932C2212yes—
30C2×#66925C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#389C2212yes—
34C11×#385C2214yes—
35C11×#382C2211yescharacteristic
36C11×#380C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C2×C11×#95C2212yes—
39#10622834C2212yes—
40#10622826C2214yes—
41#10622824C2212yes—
42#10622823C2214yes—
43#10622823C2214yes—
44C4×C22⋊Dic11C2214yes—
45C4×C22⋊Dic11C2212yes—
46#10622603C2214yes—
47#10622600C2212yes—
48#10622600C2212yes—
49#10622591C2214yes—
50#10622589C2212yes—
51C4⋊C4×Dic11C2214yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54#10622586C2212yes—
55#10622586C2214yes—
56#10622585C2214yes—
57#10622570C2214yes—
58#10622564C2214yes—
59#10622558C2214yes—
60#10622558C2214yes—
61#10622557C2214yes—
62#10622549C2211yescharacteristic
63C4×C4⋊Dic11C2212yes—
64C4×C4⋊Dic11C2211yescharacteristic
65C4×Dic11⋊C4C2212yes—
66#10622542C2212yes—
67#10622282C2214yes—
68#10622280C2211yescharacteristic
69#10622280C2211yescharacteristic
70#10622279C2212yes—
71#10622277C2212yes—
72#10622267C2214yes—
73#10622266C2214yes—
74#10622265C2214yes—
75#10622264C2212yes—
76#10622264C2212yes—
77#10622263C2211yescharacteristic
78#10622263C2211yescharacteristic
79#10622263C2212yes—
80#10622262C2212yes—
81#10622261C2212yes—
82#10622261C2212yes—
83#10622260C2214yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2312yes—
87C22×C22⋊D11C2312yes—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C4×D4×C11—44no—
93C4×D4×C11C2×C418yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11C2314yes—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2312yes—
107#66991C2×C418yes—
108#66989C2×C418yes—
109C4×C22⋊D11C2×C4116yescomplemented
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2312yes—
114#66979C2×C4116yescomplemented
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137#66950C2×C418yescomplemented
138#66943C2×C418yescomplemented
139#66940—44no—
140#66936C2×C4116yescomplemented
141#66932C2×C4116yescomplemented
142#66925—44no—
143C42×D11C2×C418yescomplemented
144C4×Dic22C2×C418yescomplemented
145C11×#95C2312yes—
146C11×#95C2311yescharacteristic
147C11×#95C2312yes—
148C11×#95C2311yescharacteristic
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2311yescharacteristic
155C11⋊#95C2311yescharacteristic
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2314yes—
163#34397—111nomaximal, Sylow
164C24×C11C2412yes—
165C23×D11C2411yescharacteristic
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11C22×C414yes—
169C22×C4×C11—44no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11—44no—
173C22×C4×C11C22×C418yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—44no—
182C2×C22⋊D11C22×C418yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C22×Dic11C2411yescharacteristic
190C22×Dic11C2411yescharacteristic
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11C22×C414yes—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×Dic22—22no—
199C2×Dic22—22no—
200C2×Dic22C22×C414yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—44no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4C22×C414yes—
205C11×C22⋊C4—44no—
206C11×C22⋊C4C22×C418yes—
207C42×C11—24no—
208C42×C11C22×C414yes—
209C22⋊Dic11—44no—
210C22⋊Dic11—44no—
211C22⋊Dic11C22×C418yes—
212C22⋊Dic11C22×C418yes—
213C22⋊Dic11C22×C418yes—
214(C2×D11)⋊C4—42no—
215(C2×D11)⋊C4—42no—
216(C2×D11)⋊C4—44no—
217(C2×D11)⋊C4C22×C418yes—
218C4⋊Dic11—24no—
219C4⋊Dic11—42no—
220C4⋊Dic11C22×C414yes—
221C4⋊Dic11C22×C418yes—
222C4⋊Dic11C22×C418yes—
223Dic11⋊C4—42no—
224Dic11⋊C4—42no—
225Dic11⋊C4—44no—
226Dic11⋊C4—44no—
227Dic11⋊C4—42no—
228Dic11⋊C4—42no—
229Dic11⋊C4C22×C418yes—
230Dic11⋊C4C22×C418yes—
231C4×Dic11—24no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234C4×Dic11—44no—
235C4×Dic11—44no—
236C4×Dic11C22×C418yes—
237C4×Dic11C22×C414yes—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C414yes—
240C2×#529—111no—
241#2383—114no—
242#2370—112no—
243#2367—112no—
244#2357—111no—
245#2356—111no—
246#2351—111no—
247#2349D1111yescharacteristic, complemented
248#2346—112no—
249#2343—112no—
250#2335—114no—
251#2324—112no—
252#2323—112no—
253#2319—112no—
254#2318—112no—
255#2285—111no—
256#2283—111no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11C23×C414yes—
262C23×C11C2511yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11C23×C412yes—
268D4×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—48no—
282C2×C4×C11—88no—
283C2×C4×C11C23×C412yes—
284C2×C4×C11C23×C412yes—
285C2×C4×C11C23×C414yes—
286C2×C4×C11C23×C412yes—
287C2×C4×C11H(5,𝔽2)12yes—
288C2×C4×C112−1+412yes—
289C22⋊D11—48no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11C23×C412yes—
307C2×Dic11C23×C412yes—
308C2×Dic11C23×C412yes—
309C2×Dic11C23×C414yes—
310C2×Dic11C23×C414yes—
311C4×D11—28no—
312C4×D11—44no—
313C4×D11—44no—
314Dic22—28no—
315#529—1116no—
316C2×#126—112no—
317C2×#125—111no—
318C2×#124—111no—
319C2×#123—112no—
320C2×C22⋊Q8—111no—
321C2×#121—111no—
322C2×C4×Q8—112no—
323C2×C4×Q8—111no—
324C2×C4×D4—112no—
325C2×C4×D4C2×D1112yes—
326C2×C4×D4C2×D1111yescharacteristic
327C2×#117—112no—
328C2×#117—112no—
329C22×C42—111no—
330#391—112no—
331#390—112no—
332#390—114no—
333#389—114no—
334#389—114no—
335#389—112no—
336#389—114no—
337#389C2×D1112yes—
338#388—114no—
339#388—114no—
340#388—114no—
341#388—114no—
342#388—114no—
343#388—114no—
344#387—114no—
345#387—114no—
346#387—114no—
347#387—114no—
348#386—114no—
349#385—114no—
350#385—114no—
351#385C2×D1114yes—
352#384—112no—
353#383—112no—
354#383—112no—
355#382—111no—
356#382—112no—
357#382—111no—
358#382—111no—
359#382C2×D1111yescharacteristic
360#381—112no—
361#381—112no—
362#380—112no—
363#380—112no—
364#380—111no—
365#380—111no—
366#380C2×D1112yes—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—112no—
370C4×C4⋊C4—112no—
371C4×C4⋊C4—111no—
372C4×C4⋊C4—112no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4C2×D1111yescharacteristic
375C4×C22⋊C4—112no—
376C4×C22⋊C4—114no—
377C4×C22⋊C4—112no—
378#376—112no—
379#376—112no—
380C2×#95C2×D1112yes—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—24no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11C24×C411yescharacteristic
387C22×C11C2×H(5,𝔽2)11yescharacteristic
388C22×C11C2×2−1+411yescharacteristic
389C22×C11#58512yes—
390C22×C11#58512yes—
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—42no—
395C2×D11—42no—
396C4×C11—22no—
397C4×C11—24no—
398C4×C11—22no—
399C4×C11—42no—
400C4×C11—44no—
401C4×C11—42no—
402C4×C11#52014yes—
403Dic11—24no—
404Dic11—22no—
405Dic11—22no—
406Dic11—22no—
407Dic11—24no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C22×Q8—111no—
412C22×D4—112no—
413C22×D4C22×D1111yescharacteristic
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C23×C4C22×D1114yes—
418C23×C4C22×D1112yes—
419#126—1116no—
420#125—118no—
421#124—118no—
422#123—1116no—
423C22⋊Q8—118no—
424#121—118no—
425C4×Q8—118no—
426C4×Q8—444no—
427C4×D4—44no—
428C4×D4—1116no—
429C4×D4C4×D1118yes—
430#117—1116no—
431#117—444no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4C22×D1112yes—
446C2×C4⋊C4C22×D1114yes—
447C2×C4⋊C4C22×D1112yes—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C22⋊C4—112no—
450C2×C22⋊C4—112no—
451C2×C22⋊C4—112no—
452C2×C22⋊C4—112no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—112no—
457C2×C22⋊C4—114no—
458C2×C22⋊C4C22×D1114yes—
459C2×C22⋊C4C22×D1112yes—
460C2×C42—111no—
461C2×C42—112no—
462C2×C42—111no—
463C2×C42—111no—
464C2×C42—118no—
465C2×C42—112no—
466C2×C42—114no—
467C2×C42—114no—
468C2×C42—114no—
469C2×C42—114no—
470C2×C42C22×D1112yes—
471C2×C42C22×D1111yescharacteristic
472#95—112no—
473#95—114no—
474#95—114no—
475#95—111no—
476#95—112no—
477#95—112no—
478#95—114no—
479#95—111no—
480#95—112no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95C22×D1111yescharacteristic
486#95C22×D1112yes—
487#95C22×D1114yes—
488#95C22×D1111yescharacteristic
489#95C22×D1112yes—
490C2×C11—44no—
491C2×C11C2×#52011yescharacteristic
492C2×C11#342811yescharacteristic
493C2×C11#342811yescharacteristic
494C2×C11#355112yes—
495C2×C11#355712yes—
496D11—42no—
497C24—111no—
498C24C23×D1112yes—
499C2×Q8—114no—
500C2×Q8—222no—
501C2×Q8—222no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—118no—
505C2×D4—444no—
506C2×D4C2×C4×D1114yes—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—114no—
517C22×C4—114no—
518C22×C4—114no—
519C22×C4—114no—
520C22×C4—112no—
521C22×C4—112no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4C2×C4×D1118yes—
527C22×C4C23×D1112yes—
528C22×C4C23×D1114yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1111yescharacteristic
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C4⋊C4—24no—
535C4⋊C4—42no—
536C4⋊C4—44no—
537C4⋊C4—118no—
538C4⋊C4—118no—
539C4⋊C4—118no—
540C4⋊C4—114no—
541C4⋊C4—118no—
542C4⋊C4—224no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—444no—
546C4⋊C4—444no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4C2×C4×D1114yes—
551C22⋊C4—44no—
552C22⋊C4—118no—
553C22⋊C4—118no—
554C22⋊C4—118no—
555C22⋊C4—118no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—444no—
559C22⋊C4—444no—
560C22⋊C4—444no—
561C22⋊C4C2×C4×D1118yes—
562C42—24no—
563C42—114no—
564C42—114no—
565C42—114no—
566C42—118no—
567C42—224no—
568C42—444no—
569C42—444no—
570C42—444no—
571C42—444no—
572C42C2×C4×D1114yes—
573C11#3439711yescharacteristic, complemented, Sylow
574C23—22no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23—112no—
579C23—221no—
580C23—221no—
581C23—222no—
582C23—222no—
583C23C22×C4×D1114yes—
584C23C24×D1111yescharacteristic
585Q8—228no—
586D4—28no—
587D4—448no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—48no—
601C2×C4—88no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—114no—
606C2×C4—114no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—228no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—224no—
623C2×C4—222no—
624C2×C4—444no—
625C2×C4—444no—
626C2×C4C22×C4×D1112yes—
627C2×C4C22×C4×D1112yes—
628C2×C4C22×C4×D1114yes—
629C2×C4C22×C4×D1112yes—
630C2×C4#6703712yes—
631C2×C4#6704012yes—
632C22—24no—
633C22—24no—
634C22—24no—
635C22—44no—
636C22—44no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—442no—
641C22—442no—
642C22C23×C4×D1111yescharacteristic
643C22C2×#6703711yescharacteristic
644C22C2×#6704011yescharacteristic
645C22#1062345312yes—
646C22#1062345512yes—
647C4—22no—
648C4—24no—
649C4—22no—
650C4—42no—
651C4—44no—
652C4—42no—
653C4—222no—
654C4—224no—
655C4—222no—
656C4—222no—
657C4—224no—
658C4—442no—
659C4—442no—
660C4—444no—
661C4#1062303514yes—
662C2—44no—
663C2—442no—
664C2C2×#1062303511yescharacteristic
665C2#1308181411yescharacteristic
666C2#1308181511yescharacteristic
667C2#1308303612yes—
668C2#1308311712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2349C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenter#2349D11
hypocenterC11#34397
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #13071804C2semidirect
3. #13071711C2semidirect
4. #13071689C2semidirect
5. #13071589C2semidirect
6. #13071579C2semidirect
7. #13071533C2semidirect
8. #13071503C2semidirect
9. #13071472C2semidirect
10. #13071401C2semidirect
12. #13071296C2semidirect
13. #13071258C2semidirect
14. #13071250C2semidirect
15. #13071020C2semidirect
16. #13071009C2semidirect
17. C11×#2349C2semidirect
24. #10623088C4semidirect
109. C4×C22⋊D11C2×C4semidirect
114. #66979C2×C4semidirect
137. #66950C2×C4semidirect
138. #66943C2×C4semidirect
140. #66936C2×C4semidirect
141. #66932C2×C4semidirect
143. C42×D11C2×C4semidirect
144. C4×Dic22C2×C4semidirect
247. #2349D11semidirect
573. C11#34397semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130718042
#130717112
#130716892
#130715892
#130715792
#130715332
#130715032
#130714722
#130714012
#130713032
#130712962
#130712582
#130712502
#130710202
#130710092
C11×#23492
#3439711