Finite Group Databasebeta

← #15638525

Subgroups — #15638525

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082465C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic, complemented
3#13080546C214yesmaximal, complemented
4#13080530C214yesmaximal, complemented
5#13080349C214yesmaximal, complemented
6#13080337C214yesmaximal, complemented
7#13079566C211yesmaximal, characteristic, complemented
8#13079538C211yesmaximal, characteristic, complemented
9#13079396C214yesmaximal, complemented
10#13078624C211yesmaximal, characteristic, complemented
11#13077829C214yesmaximal, complemented
12#13077639C211yesmaximal, characteristic, complemented
13C11×#3100C211yesmaximal, characteristic, complemented
14C22×#4341C2212yes—
15C11×#532C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17#10623361—21no—
18#10623358—21no—
19C2×#66983—21no—
20C22×C4⋊Dic11—21no—
21C2×#66965C2218yescomplemented
22#10623263C2212yescomplemented
23#10623249C2212yescomplemented
24#10623212—22no—
25#10623148—22no—
26#10623137C2214yes—
27#10623096—22no—
28#10623094C2212yescomplemented
29#10623086—22no—
30#10623086—22no—
31#10623086C2214yes—
32#10623086C2214yes—
33#10623086C2212yescomplemented
34C2×#66950C2212yes—
35C2×#66939—22no—
36C2×C4×D44C2211yescharacteristic
37#10623001C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#480C2212yes—
40C11×#474C2212yescomplemented
41C11×#459C2212yescomplemented
42C11×#447C2212yes—
43C4×C11×D8C2214yescomplemented
44C11×#431C2211yescharacteristic
45#10622831C2212yes—
46#10622771C2218yescomplemented
47#10622706C2212yescomplemented
48#10622689C2212yescomplemented
49#10622653C2214yes—
50#10622632C2212yescomplemented
51#10622632C2214yescomplemented
52C4×#4324C2214yescomplemented
53#10622621C2212yescomplemented
54#10622584C2212yes—
55#10622538C2211yescharacteristic
56#10622501C2218yescomplemented
57#10622500C2218yescomplemented
58#10622462C2214yescomplemented
59#10622447C2214yescomplemented
60#10622396C2218yescomplemented
61#10622396C2218yescomplemented
62#10622391C2218yescomplemented
63#10622385C2218yescomplemented
64#10622352C2214yes—
65D11×C22⋊C8C2214yes—
66#10622312C2212yescomplemented
67C8×D44C2214yescomplemented
68#10622294C2212yescomplemented
69C2×C11×#41—21no—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C22×C22⋊D11—22no—
73C23×Dic11—22no—
74C2×#4341—24no—
75C2×#4341—48no—
76C2×#4341C2318yes—
77C2×#4341C2314yes—
78C22×D44D411yescharacteristic
79C22×C4×D11C2312yes—
80C22×Dic22C2312yes—
81C2×C11×D8C2314yes—
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#124—21no—
85C11×#121—21no—
86C11×#121C2312yes—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11C2312yes—
91C4×D4×C11C2312yes—
92C4×D4×C11C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C42×C11C2311yescharacteristic
96#67000—22no—
97Q8×Dic11—22no—
98#66993—22no—
99#66992—24no—
100#66991C2314yes—
101#66990—24no—
102D4×Dic11—24no—
103D4×Dic11—22no—
104C2×#4324C2314yes—
105C2×#4324C2318yes—
106#66983—24no—
107#66983—24no—
108#66983—22no—
109#66983—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4D412yes—
112#66979—21no—
113#66979—22no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—24no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11—22no—
120C2×C4⋊Dic11D411yescharacteristic
121#66977—21no—
122#66977C2312yes—
123#66965—416no—
124C2×Dic44C2318yes—
125C2×C8×D11C2318yes—
126#66951—24no—
127#66950—24no—
128#66950C2314yes—
129#66950C2318yes—
130#66945C2314yes—
131#66939—28no—
132#66939—28no—
133#66939—24no—
134#66938—24no—
135#66936—24no—
136(C22⋊D11)⋊C4—24no—
137C4×D44D412yes—
138C4×D44D412yes—
139C4×D44C2312yes—
140C4×D44C2312yes—
141#66923—21no—
142#66922—21no—
143#66922—21no—
144#66922C2312yes—
145#66922C2312yes—
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150C11×#107C2314yes—
151C11×C4⋊C8C2312yes—
152C11×#102C2314yes—
153C11×#102C2314yes—
154C11×C22⋊C8C2312yes—
155C4×C8×C11C2312yes—
156#66896C2314yes—
157C22⋊(C11⋊C8)C2312yes—
158(C2×D11)⋊C8C2318yes—
159#66880C2318yes—
160#66874C2314yes—
161#66874C2318yes—
162#66872C2314yes—
163C4⋊(C11⋊C8)C2312yes—
164C4×C11⋊C8C2312yes—
165#61565—111nomaximal, Sylow
166C24×C11—21no—
167C23×D11C2×D412yes—
168C11×#41—44no—
169C2×Q8×C11—21no—
170C2×D4×C11—24no—
171C2×D4×C11—22no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11C2412yes—
176C2×D4×C11C2412yes—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—44no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—28no—
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—48no—
189C22×Dic11—28no—
190C22×Dic11—24no—
191C22×Dic11—22no—
192C22×Dic11—48no—
193C22×Dic11C2×D412yes—
194#4341—216no—
195#4341—48no—
196#4341—48no—
197#4341—416no—
198C2×D44—24no—
199C2×D44C2×D412yes—
200C2×D44C2×D412yes—
201C2×C4×D11—44no—
202C2×C4×D11C2×D414yes—
203C2×C4×D11C2414yes—
204C2×Dic22—22no—
205C2×Dic22—21no—
206C2×Dic22—44no—
207C2×Dic22C2414yes—
208C2×Dic22C2412yes—
209C11×D8—28no—
210C2×C8×C11C2414yes—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4C2412yes—
214C11×C4⋊C4C2412yes—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2411yescharacteristic
222C42×C11C2411yescharacteristic
223C22⋊Dic11—24no—
224C22⋊Dic11—22no—
225#4324—28no—
226#4324—48no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—24no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4C2×D414yes—
231(C2×D11)⋊C4C2×D414yes—
232C4⋊Dic11—24no—
233C4⋊Dic11—28no—
234C4⋊Dic11—21no—
235C4⋊Dic11—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—22no—
238C4⋊Dic11—22no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11C2×D412yes—
242C4⋊Dic11C2×D412yes—
243C4⋊Dic11C2412yes—
244Dic11⋊C4—22no—
245Dic11⋊C4—22no—
246C4×Dic11—24no—
247C4×Dic11—22no—
248C2×C11⋊C8C2414yes—
249Dic44—48no—
250C8×D11—48no—
251#3506—111no—
252C2×#547—111no—
253#3303—114no—
254#3302—114no—
255#3284—114no—
256#3283—114no—
257#3209—111no—
258#3206—111no—
259#3190—114no—
260#3101—111no—
261#3100D1111yescharacteristic, complemented
262#3002—114no—
263#2972—111no—
264C23×C11—24no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11C22×D411yescharacteristic
270C22×D11—24no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11C22×D414yes—
274Q8×C11—42no—
275D4×C11—24no—
276D4×C11—22no—
277D4×C11—24no—
278D4×C11—44no—
279D4×C11—42no—
280D4×C11—81no—
281D4×C11H(5,𝔽2)14yes—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—41no—
286C2×C4×C11—42no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11#13514yescomplemented
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C2511yescharacteristic
297C22⋊D11—416no—
298C22⋊D11—84no—
299C22⋊D11—84no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—24no—
303C2×Dic11—42no—
304C2×Dic11—416no—
305C2×Dic11—44no—
306C2×Dic11—84no—
307C2×Dic11C22×D414yes—
308D44—24no—
309D44—24no—
310C4×D11—28no—
311C4×D11—44no—
312Dic22—24no—
313Dic22—28no—
314Dic22—44no—
315Dic22—81no—
316C8×C11—24no—
317C11⋊C8—24no—
318C22×#41—112no—
319C2×#135—118no—
320#559—222no—
321#556—112no—
322#555—112no—
323#553—222no—
324#550—112no—
325#547—114no—
326#547—114no—
327#547—112no—
328#547—222no—
329#547—222no—
330#538—222no—
331#535—221no—
332#533—111no—
333#532C2×D1111yescharacteristic
334C2×C4⋊Q8—111no—
335#525—114no—
336C2×#123—222no—
337C2×C22⋊Q8—112no—
338C2×#121—221no—
339#520—221no—
340C2×C4×D4—111no—
341C2×C4×D4C2×D1111yescharacteristic
342C22×C4⋊C4—221no—
343#494—112no—
344#492—112no—
345#487—112no—
346#487—112no—
347#485—118no—
348#483—112no—
349#480C2×D1112yes—
350#476—112no—
351#474C2×D1112yescomplemented
352#467—118no—
353#465—118no—
354#462—114no—
355#461—112no—
356#461—114no—
357#459C2×D1112yescomplemented
358#452—118no—
359#452—118no—
360#451—114no—
361#450—112no—
362#449—118no—
363#448—114no—
364#447C2×D1112yes—
365C4×SD16—114no—
366C4×D8C2×D1114yescomplemented
367C8×D4—114no—
368C8×D4—114no—
369#431—111no—
370#431C2×D1111yescharacteristic
371#416—118no—
372C2×C22⋊C8—114no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—24no—
376C22×C11—48no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11C2×#13512yes—
383C22×C11C23×D411yescharacteristic
384C2×D11—24no—
385C2×D11—24no—
386C2×D11—24no—
387C2×D11—84no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—42no—
392C4×C11—42no—
393C4×C11C2×#13512yes—
394C4×C11C2×#13512yes—
395C4×C11C2×H(5,𝔽2)12yes—
396Dic11—24no—
397Dic11—42no—
398Dic11—44no—
399Dic11—42no—
400C2×#41—21no—
401C2×#41—118no—
402C2×#41—114no—
403C2×#41—224no—
404C2×#41—448no—
405C22×Q8—112no—
406C22×D4—111no—
407C22×D4—222no—
408C22×D4C22×D1111yescharacteristic
409C23×C4—21no—
410C23×C4—112no—
411C23×C4—222no—
412#135—4416no—
413C2×Q16—118no—
414C2×SD16—114no—
415C2×SD16—118no—
416C2×D8C22×D1114yes—
417C22×C8—118no—
418C4⋊Q8—111no—
419C4⋊Q8—112no—
420C4⋊Q8—112no—
421C4⋊Q8—111no—
422C4⋊Q8—221no—
423C4⋊Q8—221no—
424C4⋊Q8C22×D1111yescharacteristic
425#127—222no—
426#127C22×D1111yescharacteristic
427#126—224no—
428#125—221no—
429#124—21no—
430#124—224no—
431#124—222no—
432#123—228no—
433#123—228no—
434#123—224no—
435#123—224no—
436C22⋊Q8—112no—
437C22⋊Q8—118no—
438C22⋊Q8—114no—
439C22⋊Q8—224no—
440C22⋊Q8—221no—
441#121—21no—
442#121—114no—
443#121—224no—
444#121—224no—
445#121—224no—
446#121—222no—
447#121—222no—
448#121C22×D1112yes—
449#120—224no—
450C4×Q8—112no—
451C4×Q8—222no—
452C4×Q8—221no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—112no—
457C4×D4—112no—
458C4×D4—112no—
459C4×D4—112no—
460C4×D4—224no—
461C4×D4—222no—
462C4×D4—224no—
463C4×D4C22×D1112yes—
464C4×D4C22×D1112yes—
465C4×D4C22×D1112yes—
466#117—114no—
467#117—222no—
468#117—221no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—224no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—222no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—112no—
479C2×C22⋊C4—222no—
480C2×C42C22×D1111yescharacteristic
481#107C22×D1114yes—
482#106—114no—
483C4⋊C8—112no—
484C4⋊C8C22×D1112yes—
485#103—118no—
486#103—118no—
487#103—114no—
488#102—114no—
489#102C22×D1114yes—
490#102C22×D1114yes—
491C22⋊C8—112no—
492C22⋊C8—118no—
493C22⋊C8C22×D1112yes—
494C4×C8—112no—
495C4×C8C22×D1112yes—
496C2×C11—22no—
497C2×C11—44no—
498C2×C11—82no—
499C2×C11#348411yescharacteristic
500C2×C11C22×#13511yescharacteristic
501C2×C11#358611yescharacteristic
502D11—44no—
503C24—21no—
504C24—112no—
505#41—44no—
506#41—2216no—
507#41—448no—
508#41—448no—
509#41—4416no—
510C2×Q8—21no—
511C2×Q8—114no—
512C2×Q8—112no—
513C2×Q8—222no—
514C2×Q8—221no—
515C2×Q8—444no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—112no—
522C2×D4—112no—
523C2×D4—228no—
524C2×D4—224no—
525C2×D4—224no—
526C2×D4—224no—
527C2×D4—448no—
528C2×D4C23×D1112yes—
529C2×D4C23×D1112yes—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—112no—
536C22×C4—114no—
537C22×C4—114no—
538C22×C4—228no—
539C22×C4—224no—
540C22×C4—222no—
541C22×C4—444no—
542C22×C4—448no—
543C22×C4D4×D1111yescharacteristic
544C22×C4D4×D1111yescharacteristic
545C22×C4C23×D1111yescharacteristic
546Q16—448no—
547SD16—228no—
548SD16—448no—
549D8—28no—
550C2×C8—114no—
551C2×C8—448no—
552C2×C8C23×D1114yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—112no—
556C4⋊C4—112no—
557C4⋊C4—112no—
558C4⋊C4—228no—
559C4⋊C4—224no—
560C4⋊C4—222no—
561C4⋊C4—222no—
562C4⋊C4—221no—
563C4⋊C4—222no—
564C4⋊C4—222no—
565C4⋊C4—221no—
566C4⋊C4—222no—
567C4⋊C4—222no—
568C4⋊C4—221no—
569C4⋊C4C23×D1112yes—
570C4⋊C4C23×D1112yes—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—114no—
576C22⋊C4—114no—
577C22⋊C4—228no—
578C22⋊C4—224no—
579C22⋊C4—224no—
580C22⋊C4—224no—
581C22⋊C4—222no—
582C42—224no—
583C42—222no—
584C42D4×D1111yescharacteristic
585C42D4×D1111yescharacteristic
586C42C23×D1111yescharacteristic
587C42C23×D1111yescharacteristic
588C11#6156511yescharacteristic, complemented, Sylow
589C23—24no—
590C23—22no—
591C23—22no—
592C23—42no—
593C23—42no—
594C23—114no—
595C23—224no—
596C23—442no—
597C23—442no—
598C23C2×D4×D1111yescharacteristic
599Q8—42no—
600Q8—224no—
601Q8—228no—
602Q8—444no—
603Q8—881no—
604D4—24no—
605D4—22no—
606D4—24no—
607D4—44no—
608D4—42no—
609D4—81no—
610D4—224no—
611D4—224no—
612D4—4416no—
613D4—884no—
614D4—884no—
615D4#6704214yes—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—114no—
625C2×C4—228no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—224no—
629C2×C4—444no—
630C2×C4—442no—
631C2×C4—4416no—
632C2×C4—444no—
633C2×C4—884no—
634C2×C4#6696514yescomplemented
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4C2×D4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C24×D1111yescharacteristic
641C8—24no—
642C8—224no—
643C22—21no—
644C22—21no—
645C22—24no—
646C22—48no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—224no—
653C22—224no—
654C22—224no—
655C22—884no—
656C22C2×#6696512yes—
657C22C22×D4×D1111yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—42no—
662C4—42no—
663C4—224no—
664C4—442no—
665C4—444no—
666C4—442no—
667C4C2×#6696512yes—
668C4C2×#6696512yes—
669C4C2×#6704212yes—
670C2—22no—
671C2—44no—
672C2—82no—
673C2—444no—
674C2#1308224911yescharacteristic
675C2C22×#6696511yescharacteristic
676C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3100C2
socleC22×C11C23×D4
hypercenter#3100D11
hypocenterC11#61565
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13082465C2semidirect
2. C2×#10623086C2semidirect
3. #13080546C2semidirect
4. #13080530C2semidirect
5. #13080349C2semidirect
6. #13080337C2semidirect
7. #13079566C2semidirect
8. #13079538C2semidirect
9. #13079396C2semidirect
10. #13078624C2semidirect
11. #13077829C2semidirect
12. #13077639C2semidirect
13. C11×#3100C2semidirect
21. C2×#66965C22semidirect
22. #10623263C22semidirect
23. #10623249C22semidirect
28. #10623094C22semidirect
33. #10623086C22semidirect
40. C11×#474C22semidirect
41. C11×#459C22semidirect
43. C4×C11×D8C22semidirect
46. #10622771C22semidirect
47. #10622706C22semidirect
48. #10622689C22semidirect
50. #10622632C22semidirect
51. #10622632C22semidirect
52. C4×#4324C22semidirect
53. #10622621C22semidirect
56. #10622501C22semidirect
57. #10622500C22semidirect
58. #10622462C22semidirect
59. #10622447C22semidirect
60. #10622396C22semidirect
61. #10622396C22semidirect
62. #10622391C22semidirect
63. #10622385C22semidirect
66. #10622312C22semidirect
67. C8×D44C22semidirect
68. #10622294C22semidirect
261. #3100D11semidirect
290. C2×C4×C11#135semidirect
351. #474C2×D11semidirect
357. #459C2×D11semidirect
366. C4×D8C2×D11semidirect
588. C11#61565semidirect
634. C2×C4#66965semidirect

Maximal subgroups

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

subgroupindex
#130824652
C2×#106230862
#130805462
#130805302
#130803492
#130803372
#130795662
#130795382
#130793962
#130786242
#130778292
#130776392
C11×#31002
#6156511