Finite Group Databasebeta

← #14913925

Subgroups — #14913925

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2#13071586C214yesmaximal, complemented
3#13071578C214yesmaximal, complemented
4#13071555C214yesmaximal, complemented
5#13071551C214yesmaximal, complemented
6#13071226C211yesmaximal, characteristic, complemented
7#13071225C211yesmaximal, characteristic, complemented
8#13071224C211yesmaximal, characteristic, complemented
9#13071205C212yesmaximal
10#13071021C211yesmaximal, characteristic, complemented
11#13071012C212yesmaximal, complemented
12#13071011C212yesmaximal, complemented
13D11×#382C211yesmaximal, characteristic, complemented
14#13070970C212yesmaximal, complemented
15C11×#2314C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19#10623053C4116yescomplemented
20C2×#66946C2212yes—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66940C2212yes—
24C2×(C22⋊D11)⋊C4C2212yes—
25C2×(C22⋊D11)⋊C4C2212yes—
26C2×#66925C2211yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C11×#388C2214yes—
31C11×#387C2214yes—
32C11×#384C2211yescharacteristic
33C11×#382C2211yescharacteristic
34C11×#380C2212yes—
35C4×C11×C4⋊C4C2212yes—
36#10622825C2212yes—
37#10622603C2214yes—
38#10622600C2212yes—
39#10622600C2212yes—
40#10622600C2214yes—
41#10622594C2214yes—
42#10622591C2214yes—
43#10622590C2212yes—
44#10622590C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2214yes—
48#10622570C2214yes—
49#10622569C2214yes—
50#10622564C2214yes—
51#10622556C2214yes—
52C22⋊C4×Dic11C2214yes—
53C4×(C2×D11)⋊C4C2214yes—
54C4×(C2×D11)⋊C4C2214yes—
55#10622549C2211yescharacteristic
56#10622548C2211yescharacteristic
57C4×C4⋊Dic11C2212yes—
58#10622545C2214yes—
59C4×Dic11⋊C4C2214yes—
60#10622283C2214yes—
61#10622279C2214yes—
62#10622278C2214yes—
63#10622277C2214yes—
64D11×#95C2214yes—
65#10622268C2214yes—
66#10622264C2214yes—
67#10622264C2214yes—
68#10622263C2214yes—
69#10622262C2214yes—
70#10622261C2214yes—
71#10622259C2214yes—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11C2311yescharacteristic
74C22×C22⋊D11C2311yescharacteristic
75C23×Dic11C2312yes—
76C2×#4339—24no—
77C2×#4339—24no—
78C2×#4339C2×C418yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2314yes—
82C22×C4×D11C2312yes—
83C22×C4×D11C2312yes—
84C22×C4×D11C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C11×#117C2×C418yescomplemented
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2312yes—
101C2×(C2×D11)⋊C4C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2312yes—
107C2×Dic11⋊C4C2312yes—
108C2×C4×Dic11C2×C418yescomplemented
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2312yes—
118#66946C2×C4116yes—
119#66945—28no—
120C4⋊C4×D11—28no—
121#66940C2×C4116yescomplemented
122(C22⋊D11)⋊C4C2×C4116yes—
123(C22⋊D11)⋊C4C2×C4116yescomplemented
124#66925C2×C418yes—
125#66925C2×C418yescomplemented
126C42×D11C2×C418yes—
127C42×D11C2×C418yescomplemented
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142#34189—111nomaximal, Sylow
143C24×C11C2411yescharacteristic
144C23×D11C2411yescharacteristic
145C23×D11C2411yescharacteristic
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11C22×C414yes—
160C2×C22⋊D11C22×C414yes—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11C22×C418yes—
164C22×Dic11C2414yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2411yescharacteristic
168C22×Dic11C2412yes—
169C22×Dic11C2411yescharacteristic
170#4339—232no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44C22×C414yes—
174C2×C4×D11—28no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×C4×D11—42no—
181C2×C4×D11—44no—
182C2×C4×D11—44no—
183C2×C4×D11C22×C414yes—
184C2×C4×D11C22×C418yes—
185C2×C4×D11C22×C418yes—
186C2×C4×D11C22×C414yes—
187C2×C4×D11#4114yes—
188C2×C4×D11#4114yes—
189C2×Dic22—22no—
190C2×Dic22—22no—
191C2×Dic22C22×C414yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—44no—
195C11×C4⋊C4C22×C418yes—
196C11×C22⋊C4—44no—
197C11×C22⋊C4C22×C418yes—
198C42×C11—44no—
199C42×C11C22×C414yes—
200C42×C11C22×C414yes—
201C22⋊Dic11—44no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—44no—
204(C2×D11)⋊C4—44no—
205(C2×D11)⋊C4C22×C418yes—
206(C2×D11)⋊C4C22×C418yes—
207C4⋊Dic11—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—44no—
210Dic11⋊C4—28no—
211Dic11⋊C4C22×C418yes—
212Dic11⋊C4C22×C418yes—
213C4×Dic11—28no—
214C4×Dic11—44no—
215C4×Dic11—44no—
216C4×Dic11—44no—
217C4×Dic11C22×C414yes—
218C4×Dic11C22×C418yes—
219C4×Dic11C22×C418yes—
220C4×Dic11C22×C414yes—
221C4×Dic11C22×C418yes—
222C2×C4×#41—111no—
223#2357—114no—
224#2356—114no—
225#2353—114no—
226#2353—114no—
227#2314—111no—
228#2314—111no—
229#2314—111no—
230#2314D1111yescharacteristic, complemented
231#2311—112no—
232#2285—111no—
233#2283—112no—
234#2283—112no—
235C2×#382—111no—
236#2274—112no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11C23×C412yes—
242C23×C11C2511yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11C23×C412yes—
250C22×D11C23×C412yes—
251C22×D11C2×#4112yes—
252C22×D11C2×#4112yes—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11C23×C412yes—
267C2×C4×C11C23×C414yes—
268C2×C4×C11C23×C414yes—
269C2×C4×C11C23×C412yes—
270C2×C4×C11C2×#4112yes—
271C2×C4×C11C2×#4112yes—
272C22⋊D11—28no—
273C22⋊D11—28no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—48no—
287C2×Dic11C23×C414yes—
288C2×Dic11C23×C414yes—
289C2×Dic11C23×C412yes—
290C2×Dic11C23×C412yes—
291C2×Dic11C2×#4112yes—
292C2×Dic11C2×#4112yes—
293D44—28no—
294C4×D11—28no—
295C4×D11—48no—
296C4×D11—48no—
297C4×D11—88no—
298C4×D11#117116yes—
299Dic22—28no—
300C22×#41—111no—
301C4×#41—1116no—
302C2×C4×Q8—112no—
303C2×C4×D4—112no—
304C2×C4×D4—112no—
305C2×C4×D4—112no—
306C2×#117—112no—
307C2×#117—111no—
308C2×#117—111no—
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—112no—
311C22×C42—111no—
312C22×C42—111no—
313C22×C42—111no—
314#391—114no—
315#390—114no—
316#388—114no—
317#388—114no—
318#388—114no—
319#388C2×D1114yes—
320#387—114no—
321#387—114no—
322#387—114no—
323#387C2×D1114yes—
324#386—114no—
325#386—114no—
326#384—111no—
327#384C2×D1111yescharacteristic
328#383—114no—
329#383—114no—
330#382—112no—
331#382—112no—
332#382—111no—
333#382—114no—
334#382C2×D1111yescharacteristic
335#381—114no—
336#381—114no—
337#380—112no—
338#380—112no—
339#380—112no—
340#380—114no—
341#380C2×D1112yes—
342C4×C4⋊C4—112no—
343C4×C4⋊C4—112no—
344C4×C4⋊C4—114no—
345C4×C4⋊C4—112no—
346C4×C4⋊C4—114no—
347C4×C4⋊C4—114no—
348C4×C4⋊C4C2×D1112yes—
349C4×C22⋊C4—114no—
350C4×C22⋊C4—114no—
351C4×C22⋊C4—114no—
352C4×C22⋊C4—114no—
353#376—114no—
354#376—114no—
355C2×#95—114no—
356C22×C11—22no—
357C22×C11—24no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11C24×C411yescharacteristic
362C22×C11C22×#4111yescharacteristic
363C22×C11C22×#4111yescharacteristic
364C22×C11#58512yes—
365C22×C11#58512yes—
366C2×D11—24no—
367C2×D11—24no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—24no—
372C2×D11—42no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11C2×#11714yes—
376C4×C11—22no—
377C4×C11—24no—
378C4×C11—24no—
379C4×C11—44no—
380C4×C11—44no—
381C4×C11C2×#11714yes—
382Dic11—22no—
383Dic11—24no—
384Dic11—24no—
385Dic11—44no—
386Dic11—44no—
387Dic11C2×#11714yes—
388C2×#41—118no—
389C2×#41—224no—
390C2×#41—224no—
391C22×Q8—111no—
392C22×D4—111no—
393C22×D4—111no—
394C22×D4—111no—
395C23×C4—111no—
396C23×C4—112no—
397C23×C4—111no—
398C23×C4—112no—
399C23×C4—112no—
400C23×C4—114no—
401C23×C4C22×D1111yescharacteristic
402C4×Q8—1116no—
403C4×D4—1116no—
404C4×D4—1116no—
405C4×D4—1116no—
406#117—118no—
407#117—118no—
408#117—228no—
409#117C4×D1118yescomplemented
410C2×C4⋊C4—112no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—112no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—228no—
417C2×C4⋊C4C22×D1112yes—
418C2×C4⋊C4C22×D1112yes—
419C2×C4⋊C4C22×D1114yes—
420C2×C4⋊C4C22×D1112yes—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—112no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4C22×D1114yes—
428C2×C22⋊C4C22×D1112yes—
429C2×C42—118no—
430C2×C42—111no—
431C2×C42—112no—
432C2×C42—112no—
433C2×C42—112no—
434C2×C42—111no—
435C2×C42—118no—
436C2×C42—118no—
437C2×C42—114no—
438C2×C42—114no—
439C2×C42—114no—
440C2×C42—114no—
441C2×C42C22×D1114yes—
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95—114no—
452#95—114no—
453#95—114no—
454#95—114no—
455#95C22×D1114yes—
456#95C22×D1114yes—
457#95C22×D1114yes—
458C2×C11—42no—
459C2×C11C22×#11711yescharacteristic
460C2×C11#342812yes—
461C2×C11#351012yes—
462C2×C11#351211yescharacteristic
463C2×C11#351211yescharacteristic
464D11—24no—
465D11—42no—
466C24—111no—
467C24—111no—
468C24C23×D1111yescharacteristic
469#41—2232no—
470C2×Q8—114no—
471C2×Q8—222no—
472C2×Q8—222no—
473C2×D4—114no—
474C2×D4—114no—
475C2×D4—114no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—222no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—111no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—114no—
488C22×C4—112no—
489C22×C4—111no—
490C22×C4—112no—
491C22×C4—118no—
492C22×C4—114no—
493C22×C4—118no—
494C22×C4—118no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—228no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—444no—
505C22×C4—444no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4C2×C4×D1114yes—
509C22×C4C23×D1114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1111yescharacteristic
512C22×C4C23×D1112yes—
513C22×C4C23×D1112yes—
514C22×C4C23×D1111yescharacteristic
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—44no—
518C4⋊C4—118no—
519C4⋊C4—118no—
520C4⋊C4—228no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—444no—
524C4⋊C4C2×C4×D1118yes—
525C22⋊C4—44no—
526C22⋊C4—118no—
527C22⋊C4—118no—
528C22⋊C4—228no—
529C22⋊C4—444no—
530C22⋊C4—444no—
531C22⋊C4—444no—
532C22⋊C4C2×C4×D1118yes—
533C42—44no—
534C42—114no—
535C42—114no—
536C42—118no—
537C42—118no—
538C42—118no—
539C42—228no—
540C42—444no—
541C42—444no—
542C42—444no—
543C42C2×C4×D1114yes—
544C42C2×C4×D1114yes—
545C11#3418911yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—22no—
549C23—22no—
550C23—112no—
551C23—112no—
552C23—112no—
553C23—112no—
554C23—222no—
555C23—222no—
556C23—221no—
557C23—221no—
558C23—222no—
559C23—222no—
560C23C22×C4×D1112yes—
561C23C24×D1111yescharacteristic
562Q8—228no—
563D4—228no—
564D4—228no—
565D4—228no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—28no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—1116no—
583C2×C4—114no—
584C2×C4—114no—
585C2×C4—112no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—228no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—448no—
600C2×C4—448no—
601C2×C4—448no—
602C2×C4—888no—
603C2×C4C22×C4×D1112yes—
604C2×C4C22×C4×D1114yes—
605C2×C4C22×C4×D1114yes—
606C2×C4C22×C4×D1112yes—
607C2×C4#41×D1112yes—
608C2×C4#41×D1112yes—
609C22—22no—
610C22—24no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—114no—
615C22—224no—
616C22—222no—
617C22—222no—
618C22—224no—
619C22—222no—
620C22—224no—
621C22—442no—
622C22—441no—
623C22—441no—
624C22C23×C4×D1111yescharacteristic
625C22C2×#41×D1111yescharacteristic
626C22C2×#41×D1111yescharacteristic
627C22#1062345512yes—
628C22#1062345712yes—
629C4—22no—
630C4—24no—
631C4—24no—
632C4—44no—
633C4—44no—
634C4—114no—
635C4—222no—
636C4—224no—
637C4—224no—
638C4—444no—
639C4—444no—
640C4D11×#11714yes—
641C2—42no—
642C2—224no—
643C2—442no—
644C2C2×D11×#11711yescharacteristic
645C2#1308181612yes—
646C2#1308250812yes—
647C2#1308253511yescharacteristic
648C2#1308253911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2314C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2314D11
hypocenterC11#34189
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #13071586C2semidirect
3. #13071578C2semidirect
4. #13071555C2semidirect
5. #13071551C2semidirect
6. #13071226C2semidirect
7. #13071225C2semidirect
8. #13071224C2semidirect
10. #13071021C2semidirect
11. #13071012C2semidirect
12. #13071011C2semidirect
13. D11×#382C2semidirect
14. #13070970C2semidirect
15. C11×#2314C2semidirect
19. #10623053C4semidirect
86. C11×#117C2×C4semidirect
108. C2×C4×Dic11C2×C4semidirect
121. #66940C2×C4semidirect
123. (C22⋊D11)⋊C4C2×C4semidirect
125. #66925C2×C4semidirect
127. C42×D11C2×C4semidirect
230. #2314D11semidirect
409. #117C4×D11semidirect
545. C11#34189semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
#130715862
#130715782
#130715552
#130715512
#130712262
#130712252
#130712242
#130712052
#130710212
#130710122
#130710112
D11×#3822
#130709702
C11×#23142
#3418911