Finite Group Databasebeta

← #14914710

Subgroups — #14914710

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623103C211yesmaximal, characteristic
2C2×#10623103C211yesmaximal, characteristic
3C2×C4×Q8×D11C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic, complemented
5#13071536C213yesmaximal, complemented
6#13071535C213yesmaximal, complemented
7#13071534C211yesmaximal, characteristic, complemented
8#13071530C213yesmaximal, complemented
9Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
10#13071528C213yesmaximal, complemented
11#13071238C213yesmaximal
12#13071237C213yesmaximal
13#13071097C213yesmaximal
14#13071096C213yesmaximal
15Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23#10623103—28no—
24#10623103C4116yescomplemented
25C4×Q8×D11—28no—
26C2×#66945C2213yes—
27C2×#66945C2213yes—
28C2×C4⋊C4×D11C2213yes—
29C2×#66940C2213yes—
30C2×#66940C2213yes—
31C2×#66940C2213yes—
32C2×#66925C2213yes—
33C2×#66925C2213yes—
34C2×C42×D11C2213yes—
35C2×C4×Dic22C2213yes—
36C2×C4×Dic22C2213yes—
37C2×C4×Dic22C2213yes—
38C11×#389C2213yes—
39C11×#389C2213yes—
40C11×#384C2213yes—
41C4×C11×C4⋊C4C2213yes—
42#10622602C2213yes—
43#10622602C2216yes—
44#10622602C2211yescharacteristic
45#10622598C2213yes—
46#10622598C2213yes—
47#10622590C2213yes—
48#10622589C2213yes—
49#10622589C2216yes—
50C4⋊C4×Dic11C2216yes—
51#10622586C2213yes—
52#10622586C2213yes—
53#10622585C2216yes—
54#10622585C2216yes—
55#10622585C2213yes—
56#10622585C2213yes—
57#10622549C2213yes—
58C4×C4⋊Dic11C2213yes—
59C4×Dic11⋊C4C2213yes—
60C4×Dic11⋊C4C2213yes—
61#10622541C2213yes—
62#10622541C2213yes—
63#10622281C2213yes—
64#10622281C2213yes—
65#10622263C2216yes—
66#10622262C2216yes—
67#10622260C2213yes—
68#10622260C2213yes—
69C22×Q8×C11C2311yescharacteristic
70C2×Q8×D11C2×C418yes—
71C2×Q8×D11D418yes—
72C2×Q8×D11Q818yes—
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2313yes—
75C22×C4×D11C2313yes—
76C22×Dic22C2313yes—
77C4×Q8×C11—24no—
78C4×Q8×C11—24no—
79C4×Q8×C11C2×C418yescomplemented
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2313yes—
84C2×C11×C4⋊C4C2316yes—
85C2×C11×C4⋊C4C2313yes—
86C2×C42×C11C2313yes—
87C2×C42×C11C2313yes—
88C2×C42×C11C2313yes—
89Q8×Dic11—24no—
90Q8×Dic11—24no—
91Q8×Dic11C2×C418yescomplemented
92C2×(C2×D11)⋊C4C2311yescharacteristic
93C2×(C2×D11)⋊C4C2313yes—
94C2×(C2×D11)⋊C4C2311yescharacteristic
95C2×(C2×D11)⋊C4C2313yes—
96C2×C4⋊Dic11C2313yes—
97C2×C4⋊Dic11C2313yes—
98C2×C4⋊Dic11C2313yes—
99C2×C4⋊Dic11C2313yes—
100C2×C4⋊Dic11C2313yes—
101C2×Dic11⋊C4C2313yes—
102C2×Dic11⋊C4C2316yes—
103C2×Dic11⋊C4C2313yes—
104C2×Dic11⋊C4C2311yescharacteristic
105C2×Dic11⋊C4C2313yes—
106C2×Dic11⋊C4C2313yes—
107C2×Dic11⋊C4C2316yes—
108C2×Dic11⋊C4C2313yes—
109C2×Dic11⋊C4C2313yes—
110C2×Dic11⋊C4C2313yes—
111C2×C4×Dic11C2313yes—
112C2×C4×Dic11C2316yes—
113C2×C4×Dic11C2313yes—
114C2×C4×Dic11C2313yes—
115C2×C4×Dic11C2313yes—
116C2×C4×Dic11C2316yes—
117C2×C4×Dic11C2313yes—
118#66945—212no—
119#66945C2×C4124yes—
120C4⋊C4×D11—212no—
121#66940—212no—
122#66940—212no—
123#66940C2×C4124yescomplemented
124#66925—212no—
125#66925C2×C4124yes—
126C42×D11—212no—
127C4×Dic22—212no—
128C4×Dic22—212no—
129C4×Dic22C2×C4124yescomplemented
130C11×#95C2313yes—
131C11×#95C2313yes—
132C11⋊#95C2311yescharacteristic
133C11⋊#95C2313yes—
134C11⋊#95C2316yes—
135C11⋊#95C2313yes—
136C11⋊#95C2316yes—
137C11⋊#95C2313yes—
138C11⋊#95C2311yescharacteristic
139C11⋊#95C2313yes—
140#34249—111nomaximal, Sylow
141C23×D11C2411yescharacteristic
142C2×Q8×C11C22×C414yes—
143C2×Q8×C11C2×D414yes—
144C2×Q8×C11C2×Q814yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2413yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2413yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2413yes—
152C22×Dic11C2413yes—
153C22×Dic11C2413yes—
154C22×Dic11C2411yescharacteristic
155C22×Dic11C2411yescharacteristic
156C22×Dic11C2413yes—
157C22×Dic11C2411yescharacteristic
158C22×Dic11C2413yes—
159Q8×D11C4⋊C4164yescomplemented
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—26no—
163C2×C4×D11—22no—
164C2×C4×D11—43no—
165C2×C4×D11—43no—
166C2×C4×D11C22×C4112yes—
167C2×C4×D11C2×D4112yes—
168C2×C4×D11C2×Q8112yes—
169C2×Dic22C22×C4112yes—
170C2×Dic22C2×D4112yes—
171C2×Dic22C2×Q8112yes—
172C11×C4⋊C4—26no—
173C11×C4⋊C4—26no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—46no—
176C11×C4⋊C4—43no—
177C11×C4⋊C4C22×C4112yes—
178C42×C11—26no—
179C42×C11—26no—
180C42×C11C22×C4112yes—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—26no—
183(C2×D11)⋊C4C22×C414yes—
184(C2×D11)⋊C4C22×C4112yes—
185C4⋊Dic11—26no—
186C4⋊Dic11—26no—
187C4⋊Dic11—26no—
188C4⋊Dic11—43no—
189C4⋊Dic11C22×C4112yes—
190Dic11⋊C4—26no—
191Dic11⋊C4—212no—
192Dic11⋊C4—26no—
193Dic11⋊C4—22no—
194Dic11⋊C4—26no—
195Dic11⋊C4—46no—
196Dic11⋊C4—43no—
197Dic11⋊C4—43no—
198Dic11⋊C4C22×C4112yes—
199Dic11⋊C4C22×C4112yes—
200C4×Dic11—26no—
201C4×Dic11—212no—
202C4×Dic11—26no—
203C4×Dic11—26no—
204C4×Dic11—26no—
205C4×Dic11C22×C4124yes—
206C4×Dic11C22×C4112yes—
207C2×#519—111no—
208C2×#519—111no—
209C22×C4×Q8—111no—
210#2351—113no—
211#2351—113no—
212#2351—111no—
213#2351—111no—
214Q8×C4⋊C4—113no—
215Q8×C4⋊C4—113no—
216Q8×C4⋊C4—111no—
217Q8×C4⋊C4D1111yescharacteristic, complemented
218#2317—113no—
219#2317—113no—
220#2296—113no—
221#2296—113no—
222C23×C11C2511yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11C23×C412yes—
228C22×D11C22×D412yes—
229C22×D11C22×Q812yes—
230Q8×C11C2×C4⋊C4116yes—
231C2×C4×C11—21no—
232C2×C4×C11—23no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—23no—
236C2×C4×C11—21no—
237C2×C4×C11—23no—
238C2×C4×C11—23no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—23no—
243C2×C4×C11—23no—
244C2×C4×C11—23no—
245C2×C4×C11—23no—
246C2×C4×C11C23×C416yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C416yes—
249C2×C4×C11C22×D416yes—
250C2×C4×C11C22×Q816yes—
251C2×C4×C112−1+412yes—
252C2×Dic11—21no—
253C2×Dic11—23no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—23no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—23no—
260C2×Dic11—23no—
261C2×Dic11—23no—
262C2×Dic11—23no—
263C2×Dic11—21no—
264C2×Dic11—23no—
265C2×Dic11—23no—
266C2×Dic11—21no—
267C2×Dic11C23×C412yes—
268C2×Dic11C23×C416yes—
269C2×Dic11C23×C416yes—
270C2×Dic11C22×D416yes—
271C2×Dic11C22×Q816yes—
272C2×Dic112−1+412yes—
273C4×D11—28no—
274C4×D11—412no—
275C4×D11C2×C4⋊C4148yes—
276Dic22C2×C4⋊C4148yes—
277C23×Q8—111no—
278#519—1116no—
279#519—228no—
280C2×C4×Q8—111no—
281C2×C4×Q8—111no—
282C2×C4×Q8—111no—
283C2×C4×Q8—113no—
284C2×C4×Q8—113no—
285C2×C4×Q8—113no—
286C2×C4×Q8—113no—
287C2×C4×Q8—113no—
288C2×C4×Q8—113no—
289C2×C4×Q8—228no—
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×Q8C2×D1111yescharacteristic
292C2×C4×Q8C2×D1111yescharacteristic
293C2×#117—113no—
294C2×#117—113no—
295C2×#117—113no—
296C2×#117—113no—
297C22×C4⋊C4—113no—
298C22×C42—113no—
299#389—116no—
300#389—116no—
301#389—113no—
302#389—113no—
303#389—113no—
304#389—113no—
305#389—113no—
306#389—113no—
307#389—113no—
308#389—113no—
309#389—113no—
310#389—113no—
311#389C2×D1113yes—
312#389C2×D1113yes—
313#385—116no—
314#385—113no—
315#385—111no—
316#385—113no—
317#385—113no—
318#384—116no—
319#384—113no—
320#384C2×D1113yes—
321#382—113no—
322#382—113no—
323#382—116no—
324C4×C4⋊C4—116no—
325C4×C4⋊C4—113no—
326C4×C4⋊C4—113no—
327C4×C4⋊C4—113no—
328C4×C4⋊C4—116no—
329C4×C4⋊C4C2×D1113yes—
330C22×C11C24×C411yescharacteristic
331C22×C11C23×D411yescharacteristic
332C22×C11C23×Q811yescharacteristic
333C22×C11C2×2−1+411yescharacteristic
334C22×C11C2×2−1+411yescharacteristic
335C22×C11#58511yescharacteristic
336C22×C11#58511yescharacteristic
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11C22×C4⋊C414yes—
344C4×C11—26no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—43no—
349C4×C11—43no—
350C4×C11C22×C4⋊C4112yes—
351Dic11—22no—
352Dic11—26no—
353Dic11—22no—
354Dic11—43no—
355Dic11—43no—
356Dic11—41no—
357Dic11C22×C4⋊C4112yes—
358C22×Q8—118no—
359C22×Q8—118no—
360C22×Q8—118no—
361C22×Q8—113no—
362C22×Q8C22×D1111yescharacteristic
363C23×C4—113no—
364C23×C4—111no—
365C23×C4—113no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—118no—
369C4×Q8—1124no—
370C4×Q8—1124no—
371C4×Q8—2212no—
372C4×Q8—2212no—
373C4×Q8—2212no—
374C4×Q8—2212no—
375C4×Q8—224no—
376C4×Q8—224no—
377C4×Q8C4×D1118yescomplemented
378#117—1124no—
379#117—1124no—
380#117—2212no—
381#117—2212no—
382C2×C4⋊C4—113no—
383C2×C4⋊C4—113no—
384C2×C4⋊C4—113no—
385C2×C4⋊C4—116no—
386C2×C4⋊C4—113no—
387C2×C4⋊C4—113no—
388C2×C4⋊C4—113no—
389C2×C4⋊C4—113no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—113no—
392C2×C4⋊C4—113no—
393C2×C4⋊C4—113no—
394C2×C4⋊C4—116no—
395C2×C4⋊C4—113no—
396C2×C4⋊C4—113no—
397C2×C4⋊C4—2212no—
398C2×C4⋊C4C22×D1113yes—
399C2×C4⋊C4C22×D1113yes—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1116yes—
402C2×C4⋊C4C22×D1113yes—
403C2×C4⋊C4C22×D1113yes—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—113no—
406C2×C22⋊C4—113no—
407C2×C22⋊C4—111no—
408C2×C42—116no—
409C2×C42—113no—
410C2×C42—116no—
411C2×C42—113no—
412C2×C42—113no—
413C2×C42—113no—
414C2×C42—113no—
415C2×C42—2212no—
416C2×C42C22×D1113yes—
417C2×C42C22×D1113yes—
418C2×C42C22×D1113yes—
419#95—113no—
420#95—111no—
421#95—111no—
422#95—113no—
423#95—116no—
424#95—113no—
425#95—113no—
426#95—116no—
427#95C22×D1113yes—
428#95C22×D1113yes—
429C2×C11C23×C4⋊C411yescharacteristic
430C2×C11C4×2−1+411yescharacteristic
431C2×C11C4×2−1+411yescharacteristic
432C2×C11#348611yescharacteristic
433C2×C11#348711yescharacteristic
434C2×C11#350211yescharacteristic
435C2×C11#350211yescharacteristic
436D11—24no—
437C24—111no—
438C2×Q8—1164no—
439C2×Q8—1112no—
440C2×Q8—1112no—
441C2×Q8—1112no—
442C2×Q8C2×C4×D1114yes—
443C2×Q8D4×D1114yes—
444C2×Q8Q8×D1114yes—
445C22×C4—113no—
446C22×C4—1112no—
447C22×C4—1112no—
448C22×C4—1112no—
449C22×C4—111no—
450C22×C4—113no—
451C22×C4—111no—
452C22×C4—113no—
453C22×C4—113no—
454C22×C4—111no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—226no—
458C22×C4—222no—
459C22×C4—443no—
460C22×C4—443no—
461C22×C4C23×D1111yescharacteristic
462C22×C4C23×D1113yes—
463C22×C4C23×D1113yes—
464C22×C4C23×D1111yescharacteristic
465C22×C4C23×D1113yes—
466C22×C4C23×D1111yescharacteristic
467C22×C4C23×D1113yes—
468C4⋊C4—26no—
469C4⋊C4—26no—
470C4⋊C4—22no—
471C4⋊C4—43no—
472C4⋊C4—46no—
473C4⋊C4—1112no—
474C4⋊C4—1112no—
475C4⋊C4—1112no—
476C4⋊C4—2212no—
477C4⋊C4—226no—
478C4⋊C4—226no—
479C4⋊C4—222no—
480C4⋊C4—226no—
481C4⋊C4—226no—
482C4⋊C4—226no—
483C4⋊C4—226no—
484C4⋊C4—446no—
485C4⋊C4—443no—
486C4⋊C4—443no—
487C4⋊C4—443no—
488C4⋊C4C2×C4×D11112yes—
489C22⋊C4—1112no—
490C22⋊C4—114no—
491C22⋊C4—222no—
492C22⋊C4—226no—
493C42—26no—
494C42—26no—
495C42—1124no—
496C42—1112no—
497C42—226no—
498C42—226no—
499C42—2212no—
500C42—226no—
501C42—226no—
502C42C2×C4×D11112yes—
503C11#3424911yescharacteristic, complemented, Sylow
504C23—112no—
505C23—112no—
506C23—112no—
507C23—221no—
508C23—221no—
509C23—221no—
510C23—221no—
511C23C24×D1111yescharacteristic
512Q8—1148no—
513Q8C4⋊C4×D11116yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—21no—
524C2×C4—23no—
525C2×C4—23no—
526C2×C4—23no—
527C2×C4—23no—
528C2×C4—21no—
529C2×C4—116no—
530C2×C4—116no—
531C2×C4—116no—
532C2×C4—1148no—
533C2×C4—112no—
534C2×C4—116no—
535C2×C4—112no—
536C2×C4—228no—
537C2×C4—221no—
538C2×C4—223no—
539C2×C4—221no—
540C2×C4—223no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—223no—
544C2×C4—221no—
545C2×C4—223no—
546C2×C4—223no—
547C2×C4—221no—
548C2×C4—223no—
549C2×C4—221no—
550C2×C4—223no—
551C2×C4—223no—
552C2×C4—4412no—
553C2×C4C22×C4×D1116yes—
554C2×C4C22×C4×D1112yes—
555C2×C4C22×C4×D1116yes—
556C2×C4C2×D4×D1116yes—
557C2×C4C2×Q8×D1116yes—
558C2×C4#6704012yes—
559C22—114no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—222no—
564C22—222no—
565C22—222no—
566C22C23×C4×D1111yescharacteristic
567C22C22×D4×D1111yescharacteristic
568C22C22×Q8×D1111yescharacteristic
569C22C2×#6704011yescharacteristic
570C22#1062345311yescharacteristic
571C22#1062345511yescharacteristic
572C22D11×2−1+411yescharacteristic
573C4—22no—
574C4—26no—
575C4—22no—
576C4—41no—
577C4—43no—
578C4—43no—
579C4—1112no—
580C4—222no—
581C4—222no—
582C4—226no—
583C4—443no—
584C4—443no—
585C4—441no—
586C4C2×C4⋊C4×D11112yes—
587C2—224no—
588C2C22×C4⋊C4×D1111yescharacteristic
589C2#1308182711yescharacteristic
590C2C4×#6704011yescharacteristic
591C2#1308226611yescharacteristic
592C2#1308226911yescharacteristic
593C2#1308242311yescharacteristic
594C2#1308242511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11#34249
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13071537C2semidirect
5. #13071536C2semidirect
6. #13071535C2semidirect
7. #13071534C2semidirect
8. #13071530C2semidirect
9. Q8×Dic11⋊C4C2semidirect
10. #13071528C2semidirect
15. Q8×C11×C4⋊C4C2semidirect
24. #10623103C4semidirect
79. C4×Q8×C11C2×C4semidirect
91. Q8×Dic11C2×C4semidirect
123. #66940C2×C4semidirect
129. C4×Dic22C2×C4semidirect
159. Q8×D11C4⋊C4semidirect
217. Q8×C4⋊C4D11semidirect
377. C4×Q8C4×D11semidirect
503. C11#34249semidirect

Maximal subgroups

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

subgroupindex
C2×#106231032
C2×C4×Q8×D112
#130715372
#130715362
#130715352
#130715342
#130715302
Q8×Dic11⋊C42
#130715282
#130712382
#130712372
#130710972
#130710962
Q8×C11×C4⋊C42
#3424911