Finite Group Databasebeta

← #14960728

Subgroups — #14960728

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623025C211yesmaximal, characteristic
2#13076908C212yesmaximal, complemented
3#13075210C214yesmaximal, complemented
4#13075186C214yesmaximal, complemented
5#13074964C214yesmaximal, complemented
6#13074955C214yesmaximal, complemented
7#13074389C212yesmaximal, complemented
8#13074096C211yesmaximal, characteristic, complemented
9#13073996C211yesmaximal, characteristic, complemented
10#13073963C212yesmaximal, complemented
11#13073104C211yesmaximal, characteristic, complemented
12#13073090C211yesmaximal, characteristic, complemented
13#13071975C212yesmaximal, complemented
14#13071214C211yesmaximal, characteristic, complemented
15C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2214yes—
20C2×C11×C22⋊Q8C2214yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#66999C2214yescomplemented
28C2×#66983C2211yescharacteristic
29C2×#66982C2214yes—
30C2×C4×C22⋊D11C2212yes—
31C2×#66977C2211yescharacteristic
32#10623025—28no—
33C2×#66938C2212yes—
34C2×#66937C2212yes—
35C2×#66936C2212yes—
36C2×#66932C2212yes—
37#10622860C2212yes—
38#10622844C2214yescomplemented
39#10622843C2214yescomplemented
40#10622842C2214yescomplemented
41#10622826C2214yes—
42#10622826C2212yes—
43#10622826C2212yes—
44#10622826C2212yes—
45#10622826C2212yes—
46#10622825C2212yes—
47#10622824C2214yes—
48#10622823C2214yes—
49#10622823C2212yes—
50#10622823C2212yes—
51#10622823C2212yes—
52#10622823C2212yes—
53C4×C22⋊Dic11C2211yescharacteristic
54C4×C22⋊Dic11C2211yescharacteristic
55#10622607C2214yescomplemented
56#10622606C2214yescomplemented
57#10622604C2212yescomplemented
58#10622603C2214yescomplemented
59#10622602C2214yescomplemented
60#10622601C2212yescomplemented
61#10622599C2212yescomplemented
62#10622597C2214yescomplemented
63#10622596C2212yescomplemented
64#10622593C2214yescomplemented
65#10622592C2212yescomplemented
66#10622591C2214yescomplemented
67#10622590C2212yescomplemented
68#10622589C2212yescomplemented
69#10622587C2212yescomplemented
70#10622585C2214yescomplemented
71#10622572C2214yes—
72#10622572C2214yes—
73#10622565C2214yes—
74#10622565C2214yes—
75#10622564C2214yes—
76#10622564C2214yes—
77C25×C11C2311yescharacteristic
78C22×Q8×C11—24no—
79C22×Q8×C11—44no—
80C22×Q8×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—44no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11C2312yes—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C22×D44C2311yescharacteristic
94C22×C4×D11C2312yes—
95C22×Dic22C2311yescharacteristic
96C11×C22⋊Q8—216no—
97C11×C22⋊Q8—216no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4D418yes—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111#67006—28no—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119#66999—48no—
120#66983—24no—
121#66982—48no—
122C4×C22⋊D11—28no—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2314yes—
132#66977—24no—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×C4×Dic11C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2312yes—
142#66938—28no—
143#66937—28no—
144#66936—28no—
145#66932—28no—
146C11⋊#95C2312yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#36716—111nomaximal, Sylow
158C24×C11—24no—
159C24×C11—42no—
160C24×C11—42no—
161C24×C11C2×D414yes—
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C23×D11C2412yes—
165C2×Q8×C11—28no—
166C2×Q8×C11—28no—
167C2×Q8×C11—44no—
168C2×Q8×C11—416no—
169C22×C4×C11—22no—
170C22×C4×C11—24no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—28no—
175C22×C4×C11—28no—
176C22×C4×C11—44no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—416no—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—24no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—44no—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2414yes—
201C22×Dic11C2414yes—
202C22×Dic11C2412yes—
203C2×D44—22no—
204C2×D44—42no—
205C2×C4×D11—24no—
206C2×C4×D11—44no—
207C2×Dic22—22no—
208C2×Dic22—42no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C22⋊C4—28no—
215C11×C22⋊C4C2×D418yes—
216C11×C22⋊C4C2×D418yes—
217C22⋊Dic11—24no—
218C22⋊Dic11—24no—
219C22⋊Dic11—24no—
220C22⋊Dic11—24no—
221C22⋊Dic11—24no—
222C22⋊Dic11—44no—
223C22⋊Dic11—44no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226(C2×D11)⋊C4—28no—
227(C2×D11)⋊C4—44no—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4—44no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—44no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—28no—
236Dic11⋊C4—44no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239C4×Dic11—24no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C2×#538—111no—
243C22×C22⋊Q8D1111yescharacteristic, complemented
244#2849—112no—
245#2700—114no—
246#2698—114no—
247#2681—114no—
248#2680—114no—
249#2622—112no—
250#2591—111no—
251#2583—111no—
252#2579—112no—
253#2504—111no—
254#2502—111no—
255#2409—112no—
256#2312—111no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—28no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—44no—
264C23×C11—44no—
265C23×C11—416no—
266C23×C11C22×D414yes—
267C23×C11C22×D412yes—
268C23×C112−1+414yes—
269C23×C11C2511yescharacteristic
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274Q8×C11—416no—
275C2×C4×C11—28no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—416no—
290C2×C4×C11—44no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11C22×D414yes—
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C2×C4×C11H(5,𝔽2)14yes—
297C22⋊D11—48no—
298C22⋊D11—84no—
299C22⋊D11—84no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312D44—82no—
313C4×D11—84no—
314Dic22—82no—
315C23×Q8C2×D1111yescharacteristic
316C24×C4C2×D1111yescharacteristic
317#538—228no—
318C2×#126—112no—
319C2×#124—112no—
320C2×#123—114no—
321C2×#123—112no—
322C2×C22⋊Q8—28no—
323C2×C22⋊Q8—111no—
324C2×C22⋊Q8—114no—
325C2×C22⋊Q8C2×D1114yes—
326C2×C22⋊Q8C2×D1114yes—
327C2×#121—111no—
328C2×#121—112no—
329C2×#120—112no—
330C2×C4×D4—112no—
331C22×C4⋊C4C2×D1111yescharacteristic
332C22×C4⋊C4C2×D1111yescharacteristic
333C22×C4⋊C4C2×D1111yescharacteristic
334C22×C22⋊C4C2×D1111yescharacteristic
335C22×C22⋊C4C2×D1111yescharacteristic
336#400—112no—
337#398—114no—
338#398—112no—
339#398—114no—
340#397—114no—
341#397—114no—
342#397—114no—
343#396—114no—
344#395—114no—
345#395—112no—
346#394—112no—
347#394—114no—
348#394—114no—
349#393—114no—
350#391—114no—
351#391—112no—
352#390—112no—
353#389—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#386—112no—
359#386—112no—
360#386—112no—
361#386—114no—
362#386—112no—
363#385—112no—
364#385—112no—
365#385—112no—
366#385—114no—
367#385—112no—
368#385—114no—
369#384—112no—
370#382—112no—
371#381—114no—
372#380—112no—
373#379—112no—
374C4×C22⋊C4—111no—
375C4×C22⋊C4—111no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—28no—
379C22×C11—24no—
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—416no—
383C22×C11—48no—
384C22×C11#53614yes—
385C22×C11C23×D411yescharacteristic
386C22×C11C2×H(5,𝔽2)12yes—
387C22×C11C2×2−1+412yes—
388C22×C11#58512yes—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—48no—
393C4×C11—24no—
394C4×C11—24no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400Dic11—42no—
401Dic11—42no—
402Dic11—42no—
403Dic11—44no—
404Dic11—44no—
405C25C22×D1111yescharacteristic
406C22×Q8—24no—
407C22×Q8—44no—
408C22×Q8—111no—
409C22×Q8C22×D1114yes—
410C22×D4—112no—
411C22×D4—112no—
412C22×D4—112no—
413C22×D4—111no—
414C23×C4—24no—
415C23×C4—44no—
416C23×C4—112no—
417C23×C4C22×D1111yescharacteristic
418C23×C4C22×D1114yes—
419C23×C4C22×D1111yescharacteristic
420C23×C4C22×D1111yescharacteristic
421C23×C4C22×D1111yescharacteristic
422C23×C4C22×D1111yescharacteristic
423C23×C4C22×D1111yescharacteristic
424#126—228no—
425#124—228no—
426#123—228no—
427#123—448no—
428C22⋊Q8—216no—
429C22⋊Q8—216no—
430C22⋊Q8—224no—
431C22⋊Q8—448no—
432#121—224no—
433#121—228no—
434#120—228no—
435C4×D4—228no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4C22×D1112yes—
449C2×C4⋊C4C22×D1112yes—
450C2×C4⋊C4C22×D1114yes—
451C2×C4⋊C4C22×D1112yes—
452C2×C4⋊C4C22×D1112yes—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—112no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4—112no—
459C2×C22⋊C4—112no—
460C2×C22⋊C4—112no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4C22⋊D1118yes—
468C2×C22⋊C4C22×D1114yes—
469C2×C22⋊C4C22×D1112yes—
470C2×C22⋊C4C22×D1112yes—
471C2×C42—112no—
472C2×C42—112no—
473C2×C42—112no—
474#95—112no—
475#95—112no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485C2×C11—24no—
486C2×C11—44no—
487C2×C11C2×#53611yescharacteristic
488C2×C11#348411yescharacteristic
489C2×C11#348511yescharacteristic
490C2×C11#354114yes—
491D11—82no—
492C24—24no—
493C24—42no—
494C24—42no—
495C24—112no—
496C24C2×C22⋊D1114yes—
497C24C23×D1112yes—
498C24C23×D1111yescharacteristic
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—44no—
502C2×Q8—416no—
503C2×Q8—222no—
504C2×Q8—442no—
505C2×D4—228no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—224no—
509C2×D4—222no—
510C2×D4—442no—
511C2×D4—444no—
512C2×D4—444no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—44no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—416no—
527C22×C4—112no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—224no—
533C22×C4—444no—
534C22×C4C2×C22⋊D1114yes—
535C22×C4C2×C22⋊D1114yes—
536C22×C4C23×D1112yes—
537C22×C4C23×D1112yes—
538C22×C4C23×D1112yes—
539C22×C4C23×D1112yes—
540C22×C4C23×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542C22×C4C23×D1112yes—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—28no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—228no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—222no—
552C4⋊C4—222no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C22⋊C4—28no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C22⋊C4—224no—
562C22⋊C4—224no—
563C22⋊C4—228no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—444no—
567C22⋊C4—444no—
568C22⋊C4—444no—
569C22⋊C4—444no—
570C22⋊C4—444no—
571C22⋊C4C2×C22⋊D1118yes—
572C22⋊C4C2×C22⋊D1118yes—
573C42—224no—
574C42—442no—
575C42—442no—
576C11#3671611yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—28no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—44no—
584C23—44no—
585C23—416no—
586C23—224no—
587C23—224no—
588C23—224no—
589C23—222no—
590C23#6704014yes—
591C23C22×C22⋊D1114yes—
592C23C22×C22⋊D1112yes—
593C23C24×D1111yescharacteristic
594Q8—416no—
595Q8—882no—
596D4—448no—
597D4—882no—
598D4—884no—
599D4—884no—
600C2×C4—28no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—416no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—884no—
631C2×C4#6703714yes—
632C2×C4C22×C22⋊D1114yes—
633C2×C4C22×C22⋊D1112yes—
634C2×C4C22×C22⋊D1112yes—
635C22—28no—
636C22—22no—
637C22—22no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—416no—
642C22—48no—
643C22—448no—
644C22—442no—
645C22—442no—
646C22—442no—
647C22#1062334714yes—
648C22C2×#6703712yes—
649C22C2×#6704012yes—
650C22#1062345312yes—
651C22C23×C22⋊D1111yescharacteristic
652C4—24no—
653C4—24no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—444no—
660C4—444no—
661C4—442no—
662C4—442no—
663C4—442no—
664C2—24no—
665C2—44no—
666C2—882no—
667C2C2×#1062334711yescharacteristic
668C2#1308225111yescharacteristic
669C2#1308226011yescharacteristic
670C2#1308291314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×C22⋊Q8C2
prime radicalC2×#10623025C2
hypercenterC22×C22⋊Q8D11
hypocenterC11#36716
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13076908C2semidirect
3. #13075210C2semidirect
4. #13075186C2semidirect
5. #13074964C2semidirect
6. #13074955C2semidirect
7. #13074389C2semidirect
8. #13074096C2semidirect
9. #13073996C2semidirect
10. #13073963C2semidirect
11. #13073104C2semidirect
12. #13073090C2semidirect
13. #13071975C2semidirect
14. #13071214C2semidirect
15. C22×C11×C22⋊Q8C2semidirect
27. C2×#66999C22semidirect
38. #10622844C22semidirect
39. #10622843C22semidirect
40. #10622842C22semidirect
55. #10622607C22semidirect
56. #10622606C22semidirect
57. #10622604C22semidirect
58. #10622603C22semidirect
59. #10622602C22semidirect
60. #10622601C22semidirect
61. #10622599C22semidirect
62. #10622597C22semidirect
63. #10622596C22semidirect
64. #10622593C22semidirect
65. #10622592C22semidirect
66. #10622591C22semidirect
67. #10622590C22semidirect
68. #10622589C22semidirect
69. #10622587C22semidirect
70. #10622585C22semidirect
243. C22×C22⋊Q8D11semidirect
576. C11#36716semidirect

Maximal subgroups

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

subgroupindex
C2×#106230252
#130769082
#130752102
#130751862
#130749642
#130749552
#130743892
#130740962
#130739962
#130739632
#130731042
#130730902
#130719752
#130712142
C22×C11×C22⋊Q82
#3671611