Finite Group Databasebeta

← #14914071

Subgroups — #14914071

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×#10623358C211yesmaximal, characteristic, complemented
2C22×#66979C211yesmaximal, characteristic, complemented
3#13071658C214yesmaximal, complemented
4#13071647C214yesmaximal, complemented
5#13071565C214yesmaximal, complemented
6#13071545C214yesmaximal, complemented
7#13071277C214yesmaximal, complemented
8#13071239C211yesmaximal, characteristic, complemented
9#13071208C211yesmaximal, characteristic, complemented
10#123×Dic11C214yesmaximal, complemented
11#13070999C211yesmaximal, characteristic, complemented
12#13070972C211yesmaximal, characteristic, complemented
13C2×C11×#525C211yesmaximal, characteristic
14C22×C11×#41C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C11×#525C4116yescomplemented
17C2×C11×#123C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121C2212yes—
20C2×C11×#120C2212yes—
21C2×C4×D4×C11C2214yes—
22C2×C11×#117C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24#10623358—28no—
25C2×Q8×Dic11C2212yescomplemented
26C2×D4×Dic11C2214yes—
27C2×D4×Dic11C2212yescomplemented
28C2×#66979—28no—
29C2×#66979C2214yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C2×#66979C2214yes—
33C2×#66979C2212yescomplemented
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2212yescomplemented
37C22×C4×Dic11C2212yes—
38#10622860C2212yes—
39#10622843C2212yescomplemented
40#10622834C2218yes—
41#10622834C2212yescomplemented
42#10622833C2214yes—
43#10622833C2218yes—
44#10622825C2212yes—
45#10622825C2212yes—
46#10622825C2214yescomplemented
47#10622824C2212yes—
48C4×C22⋊Dic11C2214yes—
49#10622598C2214yescomplemented
50#10622594C2218yescomplemented
51C4⋊C4×Dic11C2218yescomplemented
52C4⋊C4×Dic11C2214yescomplemented
53#10622564C2218yes—
54#10622564C2218yes—
55#10622564C2218yescomplemented
56#10622563C2214yes—
57C22⋊C4×Dic11C2214yes—
58C22⋊C4×Dic11C2218yescomplemented
59#10622549C2212yescomplemented
60#10622548C2212yescomplemented
61C4×C4⋊Dic11C2214yescomplemented
62C25×C11C2311yescharacteristic
63C2×C11×#41—24no—
64C2×C11×#41—24no—
65C2×C11×#41C2×C418yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11C2312yes—
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2314yes—
70C23×C4×C11—24no—
71C23×C4×C11—24no—
72C23×C4×C11C2×C418yescomplemented
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2312yes—
76C23×C4×C11C2312yes—
77C23×C4×C11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2314yes—
80C23×Dic11C2312yes—
81C11×#123C2×C4116yescomplemented
82C11×C22⋊Q8C2×C4116yescomplemented
83C11×#121C2×C4116yescomplemented
84C11×#120C2×C4116yescomplemented
85C4×D4×C11C2×C4132yescomplemented
86C11×#117C2×C418yescomplemented
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2318yes—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2314yes—
101Q8×Dic11—28no—
102D4×Dic11—216no—
103D4×Dic11—28no—
104#66979—24no—
105#66979—24no—
106#66979—216no—
107#66979—216no—
108#66979—28no—
109C2×C4⋊Dic11—24no—
110C2×C4⋊Dic11—28no—
111C2×C4⋊Dic11D418yescomplemented
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2318yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4×Dic11—28no—
122C2×C4×Dic11C2318yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2318yes—
127C11⋊#95C2318yes—
128C11⋊#95C2318yes—
129C11⋊#95C2314yes—
130C11⋊#95C2318yes—
131C11⋊#95C2314yes—
132#34201—111nomaximal, Sylow
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—42no—
136C24×C11—42no—
137C24×C11C22×C414yes—
138C24×C11C2412yes—
139C24×C11C2412yes—
140C24×C11C2411yescharacteristic
141C11×#41—232no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11C22×C414yes—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11C22×C418yes—
152C2×D4×C11C22×C414yes—
153C2×D4×C11C22×C4116yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—232no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11C22×C418yes—
164C22×C4×C11C22×C418yes—
165C22×C4×C11C22×C418yes—
166C22×C4×C11C22×C414yes—
167C22×C4×C11C22×C414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11#4114yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11—28no—
176C22×Dic11—24no—
177C22×Dic11—44no—
178C22×Dic11—44no—
179C22×Dic11—48no—
180C22×Dic11C2×D418yes—
181C22×Dic11C2414yes—
182C22×Dic11C2412yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C11×C4⋊C4C22×C418yes—
187C11×C4⋊C4C22×C4116yes—
188C11×C22⋊C4C22×C418yes—
189C11×C22⋊C4C22×C4116yes—
190C11×C22⋊C4C22×C4116yes—
191C42×C11C22×C418yes—
192C22⋊Dic11—216no—
193C22⋊Dic11—28no—
194C22⋊Dic11—24no—
195C22⋊Dic11—24no—
196C22⋊Dic11—48no—
197C22⋊Dic11—44no—
198C22⋊Dic11—44no—
199C4⋊Dic11—28no—
200C4⋊Dic11—22no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11—24no—
205C4⋊Dic11—48no—
206C4⋊Dic11C2×D418yes—
207C4⋊Dic11C2×D418yes—
208C4×Dic11—216no—
209C4×Dic11—28no—
210C4×Dic11—24no—
211C4×Dic11—24no—
212C4×Dic11—48no—
213C2×#525D1111yescharacteristic
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#2274—111no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—28no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—48no—
240C23×C11—44no—
241C23×C11—44no—
242C23×C11—48no—
243C23×C11C23×C414yes—
244C23×C11C23×C414yes—
245C23×C11C23×C412yes—
246C23×C11C22×D412yes—
247C23×C11C2×#4112yes—
248C23×C11C2511yescharacteristic
249Q8×C11—28no—
250D4×C11—216no—
251D4×C11—28no—
252D4×C11—416no—
253C2×C4×C11—28no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—216no—
261C2×C4×C11—216no—
262C2×C4×C11—216no—
263C2×C4×C11C4×D4116yes—
264C2×C4×C11C23×C418yes—
265C2×C4×C11C23×C414yes—
266C2×C4×C11C23×C414yes—
267C2×C4×C11C23×C412yes—
268C2×C4×C11C23×C412yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C2×#4112yes—
272C2×C4×C11C2×#4112yes—
273C2×Dic11—28no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—28no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—48no—
284C2×Dic11—48no—
285C2×Dic11—88no—
286C2×Dic11C22×D418yes—
287C22×#41C2×D1111yescharacteristic
288C24×C4C2×D1111yescharacteristic
289#525Dic11116yescomplemented
290C2×#123C2×D1112yes—
291C2×C22⋊Q8C2×D1112yes—
292C2×#121C2×D1112yes—
293C2×#120C2×D1112yes—
294#520—228no—
295C2×C4×Q8—112no—
296C2×C4×D4—114no—
297C2×C4×D4—112no—
298C2×C4×D4C2×D1114yes—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—114no—
302C2×#117—112no—
303C2×#117—114no—
304C2×#117—228no—
305C2×#117C2×D1111yescharacteristic
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
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⋊C4—114no—
331C4×C4⋊C4—114no—
332C4×C22⋊C4—114no—
333C4×C22⋊C4—114no—
334C4×C22⋊C4—118no—
335C22×C11—24no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—24no—
339C22×C11—24no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11—28no—
343C22×C11—24no—
344C22×C11—416no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—44no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11C2×C4×D414yes—
353C22×C11C24×C411yescharacteristic
354C22×C11C23×D411yescharacteristic
355C22×C11C22×#4111yescharacteristic
356C22×C11#58512yes—
357C22×C11#58512yes—
358C4×C11—24no—
359C4×C11—24no—
360C4×C11—28no—
361C4×C11C2×C4×D414yes—
362C4×C11C2×C4×D414yes—
363Dic11—28no—
364Dic11—42no—
365Dic11—42no—
366Dic11—44no—
367Dic11—44no—
368C25C22×D1111yescharacteristic
369C2×#41—24no—
370C2×#41—24no—
371C2×#41C2×Dic1118yes—
372C22×Q8C22×D1111yescharacteristic
373C22×D4C22×D1112yes—
374C22×D4C22×D1111yescharacteristic
375C22×D4C22×D1114yes—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—112no—
379C23×C4—112no—
380C23×C4—114no—
381C23×C4C2×Dic1118yescomplemented
382C23×C4C22×D1112yes—
383C23×C4C22×D1112yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387#123C2×Dic11116yescomplemented
388C22⋊Q8C2×Dic11116yescomplemented
389#121C2×Dic11116yescomplemented
390#120C2×Dic11116yescomplemented
391C4×Q8—228no—
392C4×D4—228no—
393C4×D4—2216no—
394C4×D4C2×Dic11132yescomplemented
395#117—2216no—
396#117—2216no—
397#117—228no—
398#117—224no—
399#117—224no—
400#117C2×Dic1118yescomplemented
401C2×C4⋊C4—118no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—118no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4C22×D1112yes—
414C2×C4⋊C4C22×D1114yes—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—112no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4C22×D1112yes—
424C2×C22⋊C4C22×D1114yes—
425C2×C22⋊C4C22×D1114yes—
426C2×C42—118no—
427C2×C42—112no—
428C2×C42—114no—
429C2×C42—112no—
430C2×C42—118no—
431C2×C42—228no—
432C2×C42C22×D1112yes—
433#95—114no—
434#95—114no—
435#95—118no—
436#95—118no—
437#95—118no—
438C2×C11—24no—
439C2×C11—44no—
440C2×C11—44no—
441C2×C11C22×C4×D411yescharacteristic
442C2×C11#342812yes—
443C2×C11#348511yescharacteristic
444C2×C11#348711yescharacteristic
445C2×C11#349312yes—
446C24—22no—
447C24—22no—
448C24—42no—
449C24—42no—
450C24C22×Dic1114yes—
451C24C23×D1112yes—
452C24C23×D1112yes—
453C24C23×D1111yescharacteristic
454#41—232no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8C22×Dic1114yes—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4C22×Dic1118yes—
465C2×D4C22×Dic1114yes—
466C2×D4C22×Dic11116yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—232no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—114no—
477C22×C4—118no—
478C22×C4—114no—
479C22×C4—112no—
480C22×C4—114no—
481C22×C4—112no—
482C22×C4—228no—
483C22×C4—224no—
484C22×C4—444no—
485C22×C4—444no—
486C22×C4—448no—
487C22×C4D4×D1114yes—
488C22×C4#434114yes—
489C22×C4C22×Dic1118yes—
490C22×C4C22×Dic1118yes—
491C22×C4C22×Dic1118yes—
492C22×C4C22×Dic1114yes—
493C22×C4C22×Dic1114yes—
494C22×C4C23×D1112yes—
495C22×C4C23×D1114yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C4⋊C4—118no—
500C4⋊C4—118no—
501C4⋊C4—228no—
502C4⋊C4—222no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—222no—
506C4⋊C4—224no—
507C4⋊C4—448no—
508C4⋊C4C22×Dic1118yes—
509C4⋊C4C22×Dic11116yes—
510C22⋊C4—2216no—
511C22⋊C4—228no—
512C22⋊C4—224no—
513C22⋊C4—224no—
514C22⋊C4—444no—
515C22⋊C4—444no—
516C22⋊C4—448no—
517C22⋊C4C22×Dic1118yes—
518C22⋊C4C22×Dic11116yes—
519C22⋊C4C22×Dic11116yes—
520C42—2216no—
521C42—228no—
522C42—224no—
523C42—224no—
524C42—448no—
525C42C22×Dic1118yes—
526C11#3420111yescharacteristic, complemented, Sylow
527C23—22no—
528C23—22no—
529C23—28no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—24no—
535C23—22no—
536C23—22no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—48no—
541C23—44no—
542C23—44no—
543C23—48no—
544C23C2×D4×D1112yes—
545C23C2×#434112yes—
546C23C23×Dic1114yes—
547C23C23×Dic1114yes—
548C23C23×Dic1112yes—
549C23C24×D1111yescharacteristic
550Q8—28no—
551D4—216no—
552D4—28no—
553D4—416no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—216no—
562C2×C4—216no—
563C2×C4—216no—
564C2×C4—118no—
565C2×C4—228no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—228no—
574C2×C4—224no—
575C2×C4—448no—
576C2×C4—448no—
577C2×C4—888no—
578C2×C4D4×Dic11116yes—
579C2×C4C2×D4×D1112yes—
580C2×C4C2×D4×D1112yes—
581C2×C4C2×#434112yes—
582C2×C4C2×#434112yes—
583C2×C4C23×Dic1118yes—
584C2×C4C23×Dic1114yes—
585C2×C4C23×Dic1114yes—
586C2×C4C23×Dic1112yes—
587C2×C4C23×Dic1112yes—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—28no—
596C22—24no—
597C22—416no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—44no—
605C22C2×D4×Dic1114yes—
606C22C22×D4×D1111yescharacteristic
607C22C22×#434111yescharacteristic
608C22#1062345312yes—
609C22#1062345312yes—
610C22C24×Dic1111yescharacteristic
611C4—24no—
612C4—24no—
613C4—28no—
614C4—228no—
615C4—442no—
616C4—444no—
617C4—442no—
618C4—444no—
619C4C2×D4×Dic1114yes—
620C4C2×D4×Dic1114yes—
621C2—24no—
622C2—44no—
623C2—44no—
624C2C22×D4×Dic1111yescharacteristic
625C2#1308181912yes—
626C2#1308225811yescharacteristic
627C2#1308227011yescharacteristic
628C2#1308233312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#525C2
socle, cosocleC23×C11C25
hypercenterC2×#525D11
hypocenterC11#34201
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
2. C22×#66979C2semidirect
3. #13071658C2semidirect
4. #13071647C2semidirect
5. #13071565C2semidirect
6. #13071545C2semidirect
7. #13071277C2semidirect
8. #13071239C2semidirect
9. #13071208C2semidirect
10. #123×Dic11C2semidirect
11. #13070999C2semidirect
12. #13070972C2semidirect
16. C11×#525C4semidirect
25. C2×Q8×Dic11C22semidirect
27. C2×D4×Dic11C22semidirect
33. C2×#66979C22semidirect
36. C22×C4⋊Dic11C22semidirect
39. #10622843C22semidirect
41. #10622834C22semidirect
46. #10622825C22semidirect
49. #10622598C22semidirect
50. #10622594C22semidirect
51. C4⋊C4×Dic11C22semidirect
52. C4⋊C4×Dic11C22semidirect
55. #10622564C22semidirect
58. C22⋊C4×Dic11C22semidirect
59. #10622549C22semidirect
60. #10622548C22semidirect
61. C4×C4⋊Dic11C22semidirect
72. C23×C4×C11C2×C4semidirect
81. C11×#123C2×C4semidirect
82. C11×C22⋊Q8C2×C4semidirect
83. C11×#121C2×C4semidirect
84. C11×#120C2×C4semidirect
85. C4×D4×C11C2×C4semidirect
86. C11×#117C2×C4semidirect
111. C2×C4⋊Dic11D4semidirect
289. #525Dic11semidirect
381. C23×C4C2×Dic11semidirect
387. #123C2×Dic11semidirect
388. C22⋊Q8C2×Dic11semidirect
389. #121C2×Dic11semidirect
390. #120C2×Dic11semidirect
394. C4×D4C2×Dic11semidirect
400. #117C2×Dic11semidirect
526. C11#34201semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C22×#669792
#130716582
#130716472
#130715652
#130715452
#130712772
#130712392
#130712082
#123×Dic112
#130709992
#130709722
C2×C11×#5252
#3420111