Finite Group Databasebeta

← #14960585

Subgroups — #14960585

Order 2816.

2326 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×#10623154C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic
3#13076903C211yesmaximal, characteristic
4#13075086C214yesmaximal, complemented
5#13075082C214yesmaximal, complemented
6#13074931C214yesmaximal, complemented
7#13074927C214yesmaximal, complemented
8#13074432C211yesmaximal, characteristic, complemented
9#13074431C211yesmaximal, characteristic, complemented
10#13073771C212yesmaximal
11#13072902C212yesmaximal, complemented
12#13072887C212yesmaximal
13#13072258C212yesmaximal, complemented
14#13071218C211yesmaximal, characteristic, complemented
15C11×#2848C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66997C2212yescomplemented
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977—28no—
25C2×#66977C2211yescharacteristic
26C2×#66977C2214yes—
27C2×#66977C2214yes—
28C2×#66977C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31#10623154—28no—
32C2×#66942C2212yescomplemented
33C2×#66942C2212yescomplemented
34C2×#66941C2212yescomplemented
35C2×#66941C2214yescomplemented
36C2×#66931C2212yes—
37C2×#66930C2212yes—
38C11×#385C2212yes—
39C11×#385C2214yes—
40C11×#380C2211yescharacteristic
41C11×#380C2212yes—
42C11×#379C2212yes—
43#10622860C2212yes—
44#10622842C2212yescomplemented
45#10622825C2211yescharacteristic
46#10622825C2212yes—
47#10622823C2212yes—
48#10622823C2214yes—
49#10622597C2214yescomplemented
50#10622597C2214yescomplemented
51#10622596C2214yescomplemented
52#10622595C2212yescomplemented
53#10622594C2214yescomplemented
54#10622592C2214yescomplemented
55#10622591C2214yescomplemented
56#10622565C2214yes—
57#10622565C2214yes—
58#10622564C2214yes—
59#10622564C2214yes—
60#10622563C2212yes—
61#10622562C2214yes—
62#10622560C2214yes—
63#10622559C2212yes—
64#10622558C2214yes—
65#10622557C2214yes—
66#10622556C2212yes—
67#10622556C2212yes—
68#10622556C2212yes—
69C22⋊C4×Dic11C2212yes—
70#10622273C2214yescomplemented
71#10622272C2212yescomplemented
72#10622269C2212yescomplemented
73#10622269C2214yescomplemented
74#10622268C2214yescomplemented
75#10622268C2214yescomplemented
76#10622259C2214yescomplemented
77C25×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11—24no—
80C23×C4×C11—44no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×Dic22—24no—
90C22×Dic22—44no—
91C22×Dic22C2314yes—
92C22×Dic22C2312yes—
93C22×Dic22C2311yescharacteristic
94C11×C22⋊Q8—24no—
95C11×C22⋊Q8—44no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112#66997—28no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2312yes—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2312yes—
119#66977—24no—
120#66977—216no—
121#66977—216no—
122#66977—44no—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4D418yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×C4×Dic11C2312yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2314yes—
139#66942—28no—
140#66942—28no—
141#66941—28no—
142#66941—48no—
143#66931—28no—
144#66930—28no—
145C11×#95C2314yes—
146C11×#95C2312yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158#36708—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—24no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—42no—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
166C2×Q8×C11—22no—
167C2×Q8×C11—42no—
168C22×C4×C11—22no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—24no—
173C22×C4×C11—24no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—416no—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2414yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2412yes—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11C2×D414yes—
194C22×Dic11C2×D414yes—
195C22×Dic11C2414yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C2×Dic22—28no—
203C2×Dic22—24no—
204C2×Dic22—22no—
205C2×Dic22—28no—
206C2×Dic22—44no—
207C2×Dic22—416no—
208C2×Dic22—44no—
209C2×Dic22—42no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—28no—
213C11×C4⋊C4—42no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—28no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—44no—
218C22⋊Dic11—28no—
219C22⋊Dic11—28no—
220C22⋊Dic11—24no—
221C22⋊Dic11—24no—
222C22⋊Dic11—28no—
223C22⋊Dic11—44no—
224C4⋊Dic11—24no—
225C4⋊Dic11—28no—
226C4⋊Dic11—22no—
227C4⋊Dic11—44no—
228C4⋊Dic11—42no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—28no—
237Dic11⋊C4—44no—
238Dic11⋊C4C2×D418yes—
239Dic11⋊C4C2×D418yes—
240C4×Dic11—24no—
241C4×Dic11—24no—
242C4×Dic11—44no—
243C2×#544—111no—
244C22×C22⋊Q8—111no—
245#2848—111no—
246#2848D1111yescharacteristic
247#2690—114no—
248#2690—114no—
249#2677—114no—
250#2677—114no—
251#2627—111no—
252#2627—111no—
253#2561—112no—
254#2484—112no—
255#2482—112no—
256#2434—112no—
257#2313—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—28no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—48no—
268C23×C11—48no—
269C23×C11—44no—
270C23×C11—44no—
271C23×C11C22×D412yes—
272C23×C112−1+412yes—
273C23×C112−1+414yes—
274C23×C112−1+412yes—
275C23×C11C2511yescharacteristic
276Q8×C11—82no—
277C2×C4×C11—28no—
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—24no—
288C2×C4×C11—24no—
289C2×C4×C11—44no—
290C2×C4×C11—48no—
291C2×C4×C11—48no—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D412yes—
294C2×C4×C11H(5,𝔽2)14yes—
295C2×Dic11—28no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
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—22no—
310C2×Dic11—22no—
311C2×Dic11—44no—
312C2×Dic11—44no—
313C2×Dic11—44no—
314C2×Dic11C22×D414yes—
315C2×Dic11C22×D414yes—
316Dic22—416no—
317Dic22—84no—
318Dic22—82no—
319C23×Q8—111no—
320C24×C4C2×D1111yescharacteristic
321#544—228no—
322C2×C4⋊Q8—112no—
323C2×C4⋊Q8—112no—
324C2×C4⋊Q8—114no—
325C2×#125—112no—
326C2×#125—112no—
327C2×C22⋊Q8—111no—
328C2×C22⋊Q8—114no—
329C2×C22⋊Q8—114no—
330C2×C22⋊Q8—112no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8—228no—
333C2×C22⋊Q8C2×D1111yescharacteristic
334C2×C22⋊Q8C2×D1112yes—
335C2×#117—112no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C22⋊C4—111no—
340C22×C22⋊C4—111no—
341#400—112no—
342#400—112no—
343#400—114no—
344#399—114no—
345#398—114no—
346#398—114no—
347#398—114no—
348#397—114no—
349#397—114no—
350#395—112no—
351#395—114no—
352#395—112no—
353#395—114no—
354#393—114no—
355#391—114no—
356#388—114no—
357#388—114no—
358#388—114no—
359#388—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#387—114no—
364#385—114no—
365#385—112no—
366#385—112no—
367#385—112no—
368#385C2×D1114yes—
369#385C2×D1112yes—
370#381—112no—
371#381—112no—
372#381—112no—
373#380—111no—
374#380—112no—
375#380C2×D1111yescharacteristic
376#380C2×D1112yes—
377#379—112no—
378#379C2×D1112yes—
379C4×C22⋊C4—112no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—24no—
383C22×C11—24no—
384C22×C11—24no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—416no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11#53614yes—
393C22×C11C23×D411yescharacteristic
394C22×C11C2×H(5,𝔽2)12yes—
395C22×C11C2×2−1+411yescharacteristic
396C22×C11C2×2−1+411yescharacteristic
397C22×C11C2×2−1+412yes—
398C4×C11—24no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—44no—
404Dic11—24no—
405Dic11—24no—
406Dic11—42no—
407Dic11—42no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C25C22×D1111yescharacteristic
412C22×Q8—114no—
413C22×Q8—111no—
414C22×Q8—112no—
415C22×Q8—224no—
416C22×Q8—444no—
417C22×Q8C22×D1111yescharacteristic
418C23×C4—24no—
419C23×C4—44no—
420C23×C4—111no—
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4C22×D1111yescharacteristic
425C23×C4C22×D1112yes—
426C23×C4C22×D1112yes—
427C23×C4C22×D1111yescharacteristic
428C4⋊Q8—228no—
429C4⋊Q8—228no—
430C4⋊Q8—448no—
431#125—228no—
432#125—228no—
433C22⋊Q8—24no—
434C22⋊Q8—44no—
435C22⋊Q8—228no—
436C22⋊Q8—2216no—
437C22⋊Q8—2216no—
438C22⋊Q8—224no—
439C22⋊Q8—444no—
440#117—228no—
441C2×C4⋊C4—118no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—112no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1112yes—
462C2×C4⋊C4C22×D1114yes—
463C2×C4⋊C4C22×D1112yes—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4C22×D1112yes—
473C2×C22⋊C4C22×D1112yes—
474C2×C22⋊C4C22×D1114yes—
475C2×C22⋊C4C22×D1114yes—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—114no—
479#95—114no—
480#95—112no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95C22×D1112yes—
491#95C22×D1114yes—
492C2×C11—24no—
493C2×C11—44no—
494C2×C11C2×#53611yescharacteristic
495C2×C11#348411yescharacteristic
496C2×C11#348611yescharacteristic
497C2×C11#353812yes—
498C2×C11#353812yes—
499C24—22no—
500C24—24no—
501C24—22no—
502C24—22no—
503C24—42no—
504C24C23×D1112yes—
505C24C23×D1111yescharacteristic
506C2×Q8—22no—
507C2×Q8—42no—
508C2×Q8—228no—
509C2×Q8—224no—
510C2×Q8—222no—
511C2×Q8—228no—
512C2×Q8—444no—
513C2×Q8—442no—
514C2×Q8—444no—
515C2×Q8—4416no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—416no—
526C22×C4—114no—
527C22×C4—112no—
528C22×C4—112no—
529C22×C4—114no—
530C22×C4—114no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—442no—
542C22×C4—442no—
543C22×C4D4×D1114yes—
544C22×C4C23×D1114yes—
545C22×C4C23×D1112yes—
546C22×C4C23×D1112yes—
547C22×C4C23×D1111yescharacteristic
548C22×C4C23×D1111yescharacteristic
549C22×C4C23×D1112yes—
550C4⋊C4—22no—
551C4⋊C4—24no—
552C4⋊C4—28no—
553C4⋊C4—42no—
554C4⋊C4—118no—
555C4⋊C4—118no—
556C4⋊C4—228no—
557C4⋊C4—224no—
558C4⋊C4—224no—
559C4⋊C4—224no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—222no—
565C4⋊C4—224no—
566C4⋊C4—228no—
567C4⋊C4—442no—
568C4⋊C4—444no—
569C4⋊C4—444no—
570C22⋊C4—24no—
571C22⋊C4—28no—
572C22⋊C4—24no—
573C22⋊C4—44no—
574C22⋊C4—228no—
575C22⋊C4—228no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—228no—
579C22⋊C4—444no—
580C42—224no—
581C42—224no—
582C42—444no—
583C11#3670811yescharacteristic, complemented, Sylow
584C23—22no—
585C23—22no—
586C23—28no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—48no—
594C23—48no—
595C23—44no—
596C23—44no—
597C23C2×D4×D1112yes—
598C23#6704012yes—
599C23#6704314yes—
600C23#6704312yes—
601C23C24×D1111yescharacteristic
602Q8—82no—
603Q8—4416no—
604Q8—882no—
605Q8—884no—
606C2×C4—28no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—44no—
619C2×C4—48no—
620C2×C4—48no—
621C2×C4—114no—
622C2×C4—114no—
623C2×C4—228no—
624C2×C4—224no—
625C2×C4—222no—
626C2×C4—222no—
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—222no—
636C2×C4—224no—
637C2×C4—224no—
638C2×C4—222no—
639C2×C4—444no—
640C2×C4—444no—
641C2×C4—444no—
642C2×C4C2×D4×D1112yes—
643C2×C4C2×D4×D1112yes—
644C2×C4#6703714yes—
645C22—22no—
646C22—22no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—416no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22#1062315914yes—
658C22C22×D4×D1111yescharacteristic
659C22C2×#6703712yes—
660C22C2×#6704011yescharacteristic
661C22C2×#6704311yescharacteristic
662C22C2×#6704312yes—
663C4—24no—
664C4—22no—
665C4—22no—
666C4—42no—
667C4—42no—
668C4—44no—
669C4—224no—
670C4—224no—
671C4—442no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—444no—
676C2—24no—
677C2—44no—
678C2C2×#1062315911yescharacteristic
679C2#1308224511yescharacteristic
680C2#1308226311yescharacteristic
681C2#1308286112yes—
682C2#1308286512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
prime radicalC25×C11C23
hypercenter#2848D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623154C2semidirect
4. #13075086C2semidirect
5. #13075082C2semidirect
6. #13074931C2semidirect
7. #13074927C2semidirect
8. #13074432C2semidirect
9. #13074431C2semidirect
11. #13072902C2semidirect
13. #13072258C2semidirect
14. #13071218C2semidirect
22. C2×#66997C22semidirect
32. C2×#66942C22semidirect
33. C2×#66942C22semidirect
34. C2×#66941C22semidirect
35. C2×#66941C22semidirect
44. #10622842C22semidirect
49. #10622597C22semidirect
50. #10622597C22semidirect
51. #10622596C22semidirect
52. #10622595C22semidirect
53. #10622594C22semidirect
54. #10622592C22semidirect
55. #10622591C22semidirect
70. #10622273C22semidirect
71. #10622272C22semidirect
72. #10622269C22semidirect
73. #10622269C22semidirect
74. #10622268C22semidirect
75. #10622268C22semidirect
76. #10622259C22semidirect
583. C11#36708semidirect

Maximal subgroups

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

subgroupindex
C2×#106231542
C22×#669772
#130769032
#130750862
#130750822
#130749312
#130749272
#130744322
#130744312
#130737712
#130729022
#130728872
#130722582
#130712182
C11×#28482
#3670811