Finite Group Databasebeta

← #14960543

Subgroups — #14960543

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623148C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic, complemented
3#13076907C212yesmaximal, complemented
4#13075062C214yesmaximal, complemented
5#13075036C214yesmaximal, complemented
6#13074896C214yesmaximal, complemented
7#13074862C214yesmaximal, complemented
8#13074393C212yesmaximal, complemented
9#13074097C211yesmaximal, characteristic, complemented
10#13073991C211yesmaximal, characteristic, complemented
11#13073960C212yesmaximal, complemented
12#13072930C212yesmaximal, complemented
13#13072256C211yesmaximal, characteristic, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2436C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#124C2212yescomplemented
19C2×C11×#121C2211yescharacteristic
20C2×#66999—28no—
21C2×#66999C2214yes—
22C2×#66999C2214yes—
23C2×#66997C2212yescomplemented
24C2×#66992C2212yes—
25C2×#66990C2212yes—
26C2×D4×Dic11C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33#10623148—28no—
34C2×#66951C2212yes—
35C2×#66939C2212yes—
36C2×#66938C2212yes—
37C2×#66936C2214yes—
38C11×#393C2214yescomplemented
39C11×#391C2212yescomplemented
40C11×#386C2212yes—
41C11×#386C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622843C2212yescomplemented
44#10622842C2214yescomplemented
45#10622835C2212yescomplemented
46#10622833C2212yes—
47#10622833C2212yes—
48#10622823C2212yes—
49#10622823C2212yes—
50C4×C22⋊Dic11C2211yescharacteristic
51#10622595C2212yescomplemented
52#10622574C2214yes—
53#10622572C2214yes—
54#10622569C2214yes—
55#10622568C2212yes—
56#10622563C2212yes—
57#10622563C2212yes—
58#10622563C2214yescomplemented
59#10622562C2214yescomplemented
60#10622561C2214yescomplemented
61#10622558C2214yescomplemented
62#10622555C2212yes—
63#10622555C2214yescomplemented
64#10622553C2214yes—
65#10622541C2214yescomplemented
66#10622288C2214yes—
67#10622287C2214yes—
68#10622282C2214yes—
69#10622281C2214yes—
70#10622277C2214yes—
71#10622274C2214yescomplemented
72#10622274C2212yescomplemented
73#10622273C2214yescomplemented
74#10622269C2212yescomplemented
75#10622268C2214yescomplemented
76#10622260C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×Q8×C11—24no—
79C22×Q8×C11—44no—
80C22×Q8×C11C2312yes—
81C22×Q8×C11C2312yes—
82C22×D4×C11C2312yes—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11C2312yes—
88C22×C22⋊D11C2312yes—
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—44no—
95C22×C4×D11C2314yes—
96C22×Dic22C2311yescharacteristic
97C11×#124—44no—
98C11×#121—24no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110#66999—216no—
111#66999—216no—
112#66997—44no—
113#66992—28no—
114#66990—28no—
115D4×Dic11—28no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4D418yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2314yes—
131#66977—24no—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143#66951—28no—
144#66939—28no—
145#66938—28no—
146#66936—48no—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158#36705—111nomaximal, Sylow
159C24×C11C2412yes—
160C24×C11C2411yescharacteristic
161C23×D11—24no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11C2×D414yes—
165C23×D11C2412yes—
166C2×Q8×C11—24no—
167C2×Q8×C11—24no—
168C2×Q8×C11—24no—
169C2×Q8×C11—24no—
170C2×Q8×C11—42no—
171C2×Q8×C11—42no—
172C2×Q8×C11—416no—
173C2×D4×C11—24no—
174C2×D4×C11—28no—
175C2×D4×C11—22no—
176C2×D4×C11—42no—
177C22×C4×C11—22no—
178C22×C4×C11—24no—
179C22×C4×C11—22no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D414yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2414yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2412yes—
189C2×C22⋊D11—24no—
190C2×C22⋊D11—24no—
191C2×C22⋊D11—44no—
192C2×C22⋊D11—44no—
193C22×Dic11—24no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—42no—
199C22×Dic11—44no—
200C22×Dic11C2×D414yes—
201C22×Dic11C2414yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C2×C4×D11—28no—
208C2×C4×D11—28no—
209C2×C4×D11—44no—
210C2×C4×D11—416no—
211C2×Dic22—22no—
212C2×Dic22—42no—
213C11×C4⋊C4—22no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—28no—
217C11×C22⋊C4—44no—
218C42×C11—42no—
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)⋊C4C2×D418yes—
230(C2×D11)⋊C4C2×D418yes—
231C4⋊Dic11—24no—
232C4⋊Dic11—28no—
233C4⋊Dic11—22no—
234C4⋊Dic11—44no—
235C4⋊Dic11—44no—
236Dic11⋊C4—28no—
237Dic11⋊C4—24no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—28no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—24no—
244C4×Dic11—42no—
245C2×#538—111no—
246C22×C22⋊Q8—111no—
247#2849—112no—
248#2689—114no—
249#2687—114no—
250#2674—114no—
251#2672—114no—
252#2622—112no—
253#2591—111no—
254#2583—111no—
255#2579—112no—
256#2487—112no—
257#2436D1111yescharacteristic, complemented
258#2434—111no—
259#2312—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11C22×D412yes—
267C23×C112−1+414yes—
268C23×C11C2511yescharacteristic
269C22×D11—28no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—416no—
276C22×D11C22×D414yes—
277Q8×C11—48no—
278Q8×C11—48no—
279D4×C11—48no—
280D4×C11—82no—
281C2×C4×C11—28no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11C22×D412yes—
297C2×C4×C11C22×D412yes—
298C2×C4×C11H(5,𝔽2)14yes—
299C22⋊D11—84no—
300C22⋊D11—84no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—44no—
315C2×Dic11—44no—
316C2×Dic11—44no—
317C2×Dic11—84no—
318C2×Dic11C22×D414yes—
319C4×D11—416no—
320Dic22—82no—
321C23×Q8C2×D1111yescharacteristic
322C24×C4—111no—
323#538—228no—
324C2×C4⋊Q8—112no—
325C2×#126—112no—
326C2×#124—112no—
327C2×#124C2×D1112yescomplemented
328C2×#123—112no—
329C2×#123—114no—
330C2×C22⋊Q8—114no—
331C2×C22⋊Q8—114no—
332C2×C22⋊Q8—111no—
333C2×C22⋊Q8—228no—
334C2×#121—112no—
335C2×#121C2×D1111yescharacteristic
336C2×#120—112no—
337C2×C4×D4—112no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343#400—112no—
344#400—114no—
345#399—114no—
346#398—114no—
347#398—112no—
348#397—114no—
349#397—114no—
350#396—114no—
351#395—114no—
352#395—112no—
353#394—112no—
354#394—114no—
355#394—114no—
356#393C2×D1114yescomplemented
357#391—112no—
358#391C2×D1112yescomplemented
359#389—114no—
360#389—114no—
361#388—114no—
362#388—114no—
363#388—114no—
364#387—114no—
365#386—112no—
366#386—112no—
367#386—114no—
368#386C2×D1112yes—
369#386C2×D1112yes—
370#385—112no—
371#385—112no—
372#385—112no—
373#385—114no—
374#385—112no—
375#385—114no—
376#381—114no—
377#380—112no—
378#380—114no—
379#379—112no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4C2×D1111yescharacteristic
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—28no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—48no—
389C22×C11#53614yes—
390C22×C11C23×D411yescharacteristic
391C22×C11C2×H(5,𝔽2)12yes—
392C22×C11C2×2−1+412yes—
393C22×C11#58512yes—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—416no—
398C2×D11—48no—
399C4×C11—24no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—44no—
405Dic11—24no—
406Dic11—42no—
407Dic11—42no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C25—111no—
412C22×Q8—24no—
413C22×Q8—44no—
414C22×Q8—111no—
415C22×Q8C22×D1112yes—
416C22×Q8C22×D1112yes—
417C22×D4—112no—
418C22×D4—112no—
419C22×D4C22×D1112yes—
420C22×D4C22×D1111yescharacteristic
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—112no—
425C23×C4—114no—
426C23×C4—224no—
427C23×C4—444no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—444no—
432#126—228no—
433#124—44no—
434#124—228no—
435#123—228no—
436#123—448no—
437C22⋊Q8—2216no—
438C22⋊Q8—2216no—
439C22⋊Q8—224no—
440#121—24no—
441#121—228no—
442#120—228no—
443C4×D4—228no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—111no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C22⋊C4—118no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—112no—
464C2×C22⋊C4—112no—
465C2×C22⋊C4—112no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4C22×D1112yes—
475C2×C22⋊C4C22×D1114yes—
476C2×C22⋊C4C22×D1112yes—
477C2×C22⋊C4C22×D1114yes—
478C2×C42—112no—
479C2×C42—112no—
480C2×C42C22×D1112yes—
481#95—112no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95C22×D1112yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492C2×C11—24no—
493C2×C11—82no—
494C2×C11C2×#53611yescharacteristic
495C2×C11#348411yescharacteristic
496C2×C11#348511yescharacteristic
497C2×C11#354114yes—
498D11—44no—
499C24—112no—
500C24—114no—
501C24—224no—
502C24—442no—
503C24—442no—
504C24C23×D1112yes—
505C24C23×D1111yescharacteristic
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—416no—
513C2×Q8—222no—
514C2×Q8—442no—
515C2×D4—24no—
516C2×D4—28no—
517C2×D4—22no—
518C2×D4—42no—
519C2×D4—224no—
520C2×D4—224no—
521C2×D4—444no—
522C2×D4—444no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—112no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—228no—
536C22×C4—224no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—228no—
540C22×C4—444no—
541C22×C4—4416no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4—442no—
545C22×C4—444no—
546C22×C4D4×D1114yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1114yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1112yes—
553C4⋊C4—22no—
554C4⋊C4—228no—
555C4⋊C4—228no—
556C4⋊C4—224no—
557C4⋊C4—224no—
558C4⋊C4—224no—
559C4⋊C4—224no—
560C4⋊C4—222no—
561C4⋊C4—228no—
562C4⋊C4—444no—
563C4⋊C4—444no—
564C4⋊C4—444no—
565C4⋊C4—444no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—28no—
569C22⋊C4—44no—
570C22⋊C4—118no—
571C22⋊C4—118no—
572C22⋊C4—228no—
573C22⋊C4—224no—
574C22⋊C4—224no—
575C22⋊C4—224no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—444no—
579C22⋊C4—444no—
580C22⋊C4—444no—
581C22⋊C4—444no—
582C42—42no—
583C42—224no—
584C42—442no—
585C11#3670511yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—114no—
593C23—224no—
594C23—224no—
595C23—224no—
596C23—228no—
597C23—444no—
598C23—444no—
599C23—4416no—
600C23C2×D4×D1112yes—
601C23#6704314yes—
602C23C24×D1111yescharacteristic
603Q8—48no—
604Q8—48no—
605Q8—882no—
606D4—48no—
607D4—82no—
608D4—884no—
609D4—884no—
610C2×C4—28no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—114no—
626C2×C4—224no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—224no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—224no—
639C2×C4—4416no—
640C2×C4—444no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4—884no—
644C2×C4C2×D4×D1112yes—
645C2×C4C2×D4×D1112yes—
646C2×C4#6703714yes—
647C22—28no—
648C22—22no—
649C22—22no—
650C22—48no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—224no—
655C22—224no—
656C22—224no—
657C22—4416no—
658C22—448no—
659C22#1062320614yes—
660C22C22×D4×D1111yescharacteristic
661C22C2×#6703712yes—
662C22C2×#6704312yes—
663C22#1062345712yes—
664C4—24no—
665C4—22no—
666C4—22no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—224no—
671C4—444no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—442no—
676C2—24no—
677C2—82no—
678C2—444no—
679C2C2×#1062320611yescharacteristic
680C2#1308224511yescharacteristic
681C2#1308225911yescharacteristic
682C2#1308289514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2436C2
prime radicalC2×#10623148C2
hypercenter#2436D11
hypocenterC11#36705
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2436

Complements

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

NH ≅ G/Ntype
2. C22×#66999C2semidirect
3. #13076907C2semidirect
4. #13075062C2semidirect
5. #13075036C2semidirect
6. #13074896C2semidirect
7. #13074862C2semidirect
8. #13074393C2semidirect
9. #13074097C2semidirect
10. #13073991C2semidirect
11. #13073960C2semidirect
12. #13072930C2semidirect
13. #13072256C2semidirect
14. #13071211C2semidirect
15. C11×#2436C2semidirect
18. C2×C11×#124C22semidirect
23. C2×#66997C22semidirect
38. C11×#393C22semidirect
39. C11×#391C22semidirect
43. #10622843C22semidirect
44. #10622842C22semidirect
45. #10622835C22semidirect
51. #10622595C22semidirect
58. #10622563C22semidirect
59. #10622562C22semidirect
60. #10622561C22semidirect
61. #10622558C22semidirect
63. #10622555C22semidirect
65. #10622541C22semidirect
71. #10622274C22semidirect
72. #10622274C22semidirect
73. #10622273C22semidirect
74. #10622269C22semidirect
75. #10622268C22semidirect
76. #10622260C22semidirect
257. #2436D11semidirect
327. C2×#124C2×D11semidirect
356. #393C2×D11semidirect
358. #391C2×D11semidirect
585. C11#36705semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
C22×#669992
#130769072
#130750622
#130750362
#130748962
#130748622
#130743932
#130740972
#130739912
#130739602
#130729302
#130722562
#130712112
C11×#24362
#3670511