Finite Group Databasebeta

← #14914070

Subgroups — #14914070

Order 2816.

3118 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic, complemented
3C22×#66945C211yesmaximal, characteristic, complemented
4#13071656C214yesmaximal, complemented
5#13071645C214yesmaximal, complemented
6#13071563C214yesmaximal, complemented
7#13071548C214yesmaximal, complemented
8#13071276C214yesmaximal, complemented
9#13071239C211yesmaximal, characteristic, complemented
10#13071204C211yesmaximal, characteristic, complemented
11C4×#66939C214yesmaximal, complemented
12#13070995C211yesmaximal, characteristic, complemented
13C11×#2274C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×C4×C22⋊D11C2214yes—
20C22×(C2×D11)⋊C4C2212yes—
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24#10623055C4116yescomplemented
25C2×#66950C2212yes—
26C2×#66948C2212yes—
27#10623035—28no—
28C2×#66946C2212yescomplemented
29C2×#66945—28no—
30C2×#66945C2214yes—
31C2×#66945C2214yes—
32C2×#66945C2212yescomplemented
33C2×C4⋊C4×D11C2212yescomplemented
34C2×#66940C2212yescomplemented
35C2×#66939C2212yes—
36C2×#66935C2212yes—
37C2×C4×D44C2214yes—
38C4×C11×C4⋊C4C2214yescomplemented
39C4×C11×C4⋊C4C2214yescomplemented
40C4×C11×C22⋊C4C2214yes—
41#10622600C2212yes—
42#10622600C2212yes—
43#10622600C2214yescomplemented
44#10622598C2214yescomplemented
45#10622571C2214yes—
46#10622568C2212yes—
47#10622563C2214yes—
48#10622556C2212yes—
49#10622553C2218yes—
50#10622552C2218yes—
51#10622552C2212yescomplemented
52C4×(C2×D11)⋊C4C2214yes—
53C4×(C2×D11)⋊C4C2218yescomplemented
54#10622549C2212yescomplemented
55#10622548C2212yescomplemented
56C4×C4⋊Dic11C2218yescomplemented
57#10622542C2212yescomplemented
58#10622283C2218yes—
59#10622283C2218yescomplemented
60#10622278C2218yes—
61#10622266C2218yescomplemented
62C24×D11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339C2×C418yes—
71C22×D44C2311yescharacteristic
72C22×D44C2314yes—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11C2×C418yescomplemented
76C22×C4×D11C2312yes—
77C22×C4×D11C2312yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2314yes—
80C22×Dic22C2311yescharacteristic
81C11×#117—24no—
82C11×#117C2×C418yescomplemented
83C2×C11×C4⋊C4D418yescomplemented
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2318yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C4×C22⋊D11—216no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103#66979—24no—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2318yes—
110C2×C4⋊Dic11C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×C4×Dic11—28no—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2318yes—
116#66950C2×C4116yescomplemented
117#66948C2×C4116yescomplemented
118#66946—28no—
119#66945—216no—
120#66945—216no—
121#66945—28no—
122C4⋊C4×D11—28no—
123#66940—28no—
124#66939C2×C4116yescomplemented
125#66935C2×C4116yescomplemented
126C4×D44C2×C4132yescomplemented
127C11×#95C2318yes—
128C11⋊#95C2314yes—
129C11⋊#95C2318yes—
130C11⋊#95C2318yes—
131C11⋊#95C2314yes—
132#34201—111nomaximal, Sylow
133C24×C11C2411yescharacteristic
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—42no—
137C23×D11—42no—
138C23×D11C22×C414yes—
139C23×D11C2412yes—
140C23×D11C2412yes—
141C22×C4×C11—44no—
142C22×C4×C11C22×C414yes—
143C22×C4×C11C2×D418yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11#4114yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—24no—
153C2×C22⋊D11C22×C418yes—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—44no—
158C22×Dic11C22×C414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164#4339—232no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—44no—
168C2×D44—44no—
169C2×D44C22×C414yes—
170C2×D44C22×C4116yes—
171C2×C4×D11—232no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11—28no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—48no—
180C2×C4×D11C22×C418yes—
181C2×C4×D11C22×C418yes—
182C2×C4×D11C22×C418yes—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22C22×C414yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4C22×C418yes—
188C11×C4⋊C4C2×D418yes—
189C11×C4⋊C4C2×D418yes—
190C11×C22⋊C4—24no—
191C11×C22⋊C4C22×C418yes—
192C42×C11—24no—
193C42×C11—48no—
194C42×C11C22×C418yes—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4—44no—
201(C2×D11)⋊C4C22×C4116yes—
202(C2×D11)⋊C4C22×C4116yes—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—24no—
206C4⋊Dic11—22no—
207C4⋊Dic11—48no—
208C4⋊Dic11C22×C4116yes—
209Dic11⋊C4—28no—
210C4×Dic11—28no—
211C4×Dic11—24no—
212C4×Dic11—216no—
213C2×#525—111no—
214C2×#520—111no—
215C22×#117—111no—
216#2363—114no—
217#2362—114no—
218#2354—114no—
219#2352—114no—
220#2321—114no—
221#2317—111no—
222#2311—111no—
223C4×#123—114no—
224#2280—111no—
225#2274D1111yescharacteristic, complemented
226C23×C11—22no—
227C23×C11—22no—
228C23×C11C23×C412yes—
229C23×C11C22×D412yes—
230C23×C11C2×#4112yes—
231C23×C11C2511yescharacteristic
232C22×D11—28no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—24no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—48no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—48no—
247C22×D11C23×C414yes—
248C22×D11C23×C414yes—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—48no—
256C2×C4×C11C4×D4116yes—
257C2×C4×C11C23×C418yes—
258C2×C4×C11C23×C412yes—
259C2×C4×C11C23×C412yes—
260C2×C4×C11C22×D418yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4112yes—
265C22⋊D11—216no—
266C2×Dic11—28no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—28no—
276C2×Dic11—24no—
277C2×Dic11—48no—
278C2×Dic11C23×C414yes—
279C2×Dic11C23×C414yes—
280D44—28no—
281D44—416no—
282C4×D11—216no—
283C4×D11—216no—
284C4×D11—216no—
285C4×D11—88no—
286Dic22—28no—
287C22×#41—111no—
288C24×C4—111no—
289#525—1116no—
290C2×#123—112no—
291C2×C22⋊Q8—112no—
292C2×#121—112no—
293C2×#120—112no—
294#520—228no—
295C2×C4×Q8—112no—
296C2×C4×D4—114no—
297C2×C4×D4—112no—
298C2×C4×D4—114no—
299C2×#117—111no—
300C2×#117—114no—
301C2×#117—112no—
302C2×#117—114no—
303C2×#117—228no—
304C2×#117C2×D1111yescharacteristic
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—111no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4C2×D1111yescharacteristic
309C22×C22⋊C4—112no—
310C22×C42—112no—
311#391—112no—
312#390—112no—
313#390—118no—
314#389—114no—
315#388—118no—
316#388—118no—
317#388—118no—
318#387—118no—
319#386—114no—
320#386—118no—
321#385—114no—
322#384—112no—
323#382—112no—
324#381—112no—
325#380—114no—
326#380—112no—
327#380—112no—
328#379—112no—
329C4×C4⋊C4—118no—
330C4×C4⋊C4C2×D1114yescomplemented
331C4×C4⋊C4C2×D1114yescomplemented
332C4×C22⋊C4—118no—
333C4×C22⋊C4—114no—
334C4×C22⋊C4C2×D1114yes—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—24no—
339C22×C11C2×C4×D414yes—
340C22×C11C24×C411yescharacteristic
341C22×C11C23×D411yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11#58512yes—
344C22×C11#58512yes—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—28no—
350C2×D11—416no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—44no—
356C2×D11—42no—
357C2×D11—42no—
358C4×C11—28no—
359C4×C11—28no—
360C4×C11—44no—
361C4×C11C2×C4×D414yes—
362C4×C11C2×C4×D414yes—
363Dic11—24no—
364Dic11—24no—
365Dic11—42no—
366Dic11—42no—
367Dic11—44no—
368C25—111no—
369C2×#41—118no—
370C2×#41—224no—
371C2×#41—224no—
372C22×Q8—111no—
373C22×D4—112no—
374C22×D4—111no—
375C22×D4—114no—
376C23×C4—111no—
377C23×C4—118no—
378C23×C4—112no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—112no—
382C23×C4—114no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387#123—1116no—
388C22⋊Q8—1116no—
389#121—1116no—
390#120—1116no—
391C4×Q8—228no—
392C4×D4—1132no—
393C4×D4—2216no—
394C4×D4—228no—
395#117—24no—
396#117—224no—
397#117—2216no—
398#117—2216no—
399#117—228no—
400#117C4×D1118yescomplemented
401C2×C4⋊C4—114no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—118no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—228no—
410C2×C4⋊C4D4418yescomplemented
411C2×C4⋊C4C22×D1112yes—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1112yes—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—112no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—114no—
422C2×C22⋊C4—118no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4C22×D1112yes—
425C2×C22⋊C4C22×D1112yes—
426C2×C42—118no—
427C2×C42—112no—
428C2×C42—114no—
429C2×C42—228no—
430C2×C42C22×D1112yes—
431C2×C42C22×D1118yes—
432C2×C42C22×D1112yes—
433#95—114no—
434#95—114no—
435#95—118no—
436#95—118no—
437#95C22×D1118yes—
438C2×C11—24no—
439C2×C11C22×C4×D411yescharacteristic
440C2×C11#342812yes—
441C2×C11#348511yescharacteristic
442C2×C11#348711yescharacteristic
443C2×C11#349312yes—
444D11—44no—
445D11—44no—
446C24—112no—
447C24—112no—
448C24—114no—
449C24—222no—
450C24—222no—
451C24—442no—
452C24—442no—
453C24C23×D1111yescharacteristic
454#41—2232no—
455C2×Q8—114no—
456C2×Q8—222no—
457C2×Q8—222no—
458C2×D4—118no—
459C2×D4—114no—
460C2×D4—1116no—
461C2×D4—224no—
462C2×D4—224no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—444no—
466C2×D4—444no—
467C22×C4—44no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—118no—
472C22×C4—118no—
473C22×C4—118no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—2232no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—228no—
488C22×C4—448no—
489C22×C4—444no—
490C22×C4C2×C4×D1114yes—
491C22×C4C2×D4418yes—
492C22×C4C2×D4414yes—
493C22×C4#433914yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1114yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C4⋊C4—24no—
500C4⋊C4—1116no—
501C4⋊C4—222no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—228no—
505C4⋊C4—222no—
506C4⋊C4—448no—
507C4⋊C4C2×C4×D1118yes—
508C4⋊C4C2×D4418yes—
509C4⋊C4C2×D4418yes—
510C22⋊C4—24no—
511C22⋊C4—1116no—
512C22⋊C4—1116no—
513C22⋊C4—224no—
514C22⋊C4—2216no—
515C22⋊C4—228no—
516C22⋊C4—444no—
517C22⋊C4—444no—
518C22⋊C4—448no—
519C22⋊C4C2×C4×D1118yes—
520C42—24no—
521C42—48no—
522C42—2216no—
523C42—228no—
524C42—224no—
525C42C2×C4×D1118yes—
526C11#3420111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—114no—
530C23—114no—
531C23—228no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—224no—
538C23—222no—
539C23—224no—
540C23—222no—
541C23—222no—
542C23—448no—
543C23—444no—
544C23—444no—
545C23—448no—
546C23C22×C4×D1112yes—
547C23C22×D4412yes—
548C23C2×#433912yes—
549C23C24×D1111yescharacteristic
550Q8—228no—
551D4—2216no—
552D4—228no—
553D4—4416no—
554C2×C4—24no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—114no—
562C2×C4—114no—
563C2×C4—228no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—2216no—
569C2×C4—2216no—
570C2×C4—2216no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—228no—
577C2×C4—448no—
578C2×C4—888no—
579C2×C4C4×D44116yes—
580C2×C4C22×C4×D1118yes—
581C2×C4C22×C4×D1112yes—
582C2×C4C22×C4×D1112yes—
583C2×C4C22×D4418yes—
584C2×C4C22×D4412yes—
585C2×C4C22×D4412yes—
586C2×C4C2×#433912yes—
587C2×C4C2×#433912yes—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—24no—
592C22—224no—
593C22—224no—
594C22—224no—
595C22—228no—
596C22—224no—
597C22—4416no—
598C22—442no—
599C22—442no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—442no—
604C22—444no—
605C22C2×C4×D4414yes—
606C22C23×C4×D1111yescharacteristic
607C22C23×D4411yescharacteristic
608C22C22×#433911yescharacteristic
609C22#1062345512yes—
610C22#1062345712yes—
611C4—28no—
612C4—28no—
613C4—44no—
614C4—224no—
615C4—224no—
616C4—442no—
617C4—444no—
618C4—442no—
619C4C2×C4×D4414yes—
620C4C2×C4×D4414yes—
621C2—24no—
622C2—444no—
623C2—444no—
624C2C22×C4×D4411yescharacteristic
625C2#1308181612yes—
626C2#1308226111yescharacteristic
627C2#1308227511yescharacteristic
628C2#1308232912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2274D11
hypocenterC11#34201
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. C2×#10623035C2semidirect
3. C22×#66945C2semidirect
4. #13071656C2semidirect
5. #13071645C2semidirect
6. #13071563C2semidirect
7. #13071548C2semidirect
8. #13071276C2semidirect
9. #13071239C2semidirect
10. #13071204C2semidirect
11. C4×#66939C2semidirect
12. #13070995C2semidirect
13. C11×#2274C2semidirect
24. #10623055C4semidirect
28. C2×#66946C22semidirect
32. C2×#66945C22semidirect
33. C2×C4⋊C4×D11C22semidirect
34. C2×#66940C22semidirect
38. C4×C11×C4⋊C4C22semidirect
39. C4×C11×C4⋊C4C22semidirect
43. #10622600C22semidirect
44. #10622598C22semidirect
51. #10622552C22semidirect
53. C4×(C2×D11)⋊C4C22semidirect
54. #10622549C22semidirect
55. #10622548C22semidirect
56. C4×C4⋊Dic11C22semidirect
57. #10622542C22semidirect
59. #10622283C22semidirect
61. #10622266C22semidirect
75. C22×C4×D11C2×C4semidirect
82. C11×#117C2×C4semidirect
83. C2×C11×C4⋊C4D4semidirect
116. #66950C2×C4semidirect
117. #66948C2×C4semidirect
124. #66939C2×C4semidirect
125. #66935C2×C4semidirect
126. C4×D44C2×C4semidirect
225. #2274D11semidirect
330. C4×C4⋊C4C2×D11semidirect
331. C4×C4⋊C4C2×D11semidirect
400. #117C4×D11semidirect
410. C2×C4⋊C4D44semidirect
526. C11#34201semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106230352
C22×#669452
#130716562
#130716452
#130715632
#130715482
#130712762
#130712392
#130712042
C4×#669392
#130709952
C11×#22742
#3420111