Finite Group Databasebeta

← #15638527

Subgroups — #15638527

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#13082468C211yesmaximal, characteristic, complemented
2#13080544C214yesmaximal, complemented
3#13080533C214yesmaximal, complemented
4#13080342C214yesmaximal, complemented
5#13080334C214yesmaximal, complemented
6#13079564C211yesmaximal, characteristic, complemented
7#13079541C211yesmaximal, characteristic, complemented
8#13079397C214yesmaximal, complemented
9#13078624C211yesmaximal, characteristic, complemented
10#13078616C211yesmaximal, characteristic, complemented
11#13077834C214yesmaximal, complemented
12#13077640C211yesmaximal, characteristic, complemented
13C2×C11×#547C211yesmaximal, characteristic, complemented
14C22×C11×#41C2212yes—
15C11×#547—22no—
16C11×#547—22no—
17C11×#547C2214yes—
18C11×#547C2214yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#123—22no—
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4—21no—
26C2×#67003C2218yescomplemented
27#10623336—21no—
28#10623322C2214yes—
29#10623094C2212yescomplemented
30#10623090—22no—
31#10623089—22no—
32#10623084C2212yescomplemented
33#10623082C2212yescomplemented
34#10623073C2212yescomplemented
35#10623035—21no—
36#10623025—22no—
37#10623008C2211yescharacteristic
38#10623001C2211yescharacteristic
39#10622852C2218yescomplemented
40#10622851C2218yescomplemented
41#10622846C2218yescomplemented
42#10622841C2214yes—
43#10622840C2214yes—
44#10622831C2212yes—
45#10622830C2212yes—
46C2×C22⋊(C11⋊C8)C2214yes—
47#10622705C2212yescomplemented
48#10622703C2214yescomplemented
49#10622698C2212yescomplemented
50#10622696C2214yescomplemented
51#10622694C2212yescomplemented
52#10622694C2212yescomplemented
53#10622664C2218yescomplemented
54#10622661C2218yescomplemented
55#10622660C2218yescomplemented
56#10622658C2218yescomplemented
57#10622632C2212yescomplemented
58C4×#4324C2214yescomplemented
59#10622628C2212yescomplemented
60C4×#4323C2214yescomplemented
61D4×C11⋊C8C2214yescomplemented
62D4×C11⋊C8C2214yescomplemented
63#10622621C2212yescomplemented
64#10622620C2212yescomplemented
65#10622584C2212yes—
66#10622580C2212yes—
67#10622538C2211yescharacteristic
68#10622538C2211yescharacteristic
69C2×C11×#41—24no—
70C2×C11×#41—48no—
71C2×C11×#41C2318yes—
72C22×Q8×C11C2312yes—
73C22×D4×C11—22no—
74C22×D4×C11D411yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11—21no—
77C23×C4×C11—22no—
78C23×C4×C11C2312yes—
79C2×#4339—21no—
80C2×#4339C2314yes—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8C2312yes—
84C11×C4⋊Q8C2312yes—
85C11×#123—28no—
86C11×#123—28no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8C2318yes—
89C11×#121—24no—
90C11×#121—24no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11D412yes—
94C4×D4×C11D412yes—
95C4×D4×C11C2312yes—
96C4×D4×C11C2312yes—
97C4×D4×C11C2312yes—
98C4×D4×C11C2312yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4D412yes—
109C2×C42×C11C2311yescharacteristic
110#67006—24no—
111#67003—416no—
112C2×#4326C2318yes—
113C2×#4325C2318yes—
114#66993—22no—
115#66991—22no—
116#66991—22no—
117#66989—22no—
118C2×#4324C2314yes—
119C2×#4323C2314yes—
120#66983—21no—
121#66983C2312yes—
122#66983C2314yes—
123#66982—24no—
124C4×C22⋊D11—24no—
125C4×C22⋊D11—24no—
126#66979—21no—
127#66979C2314yes—
128#66977—21no—
129#66977C2312yes—
130#66977C2314yes—
131C22×C11⋊C8C2318yes—
132#66946—22no—
133#66945—22no—
134C4⋊C4×D11—22no—
135#66940—22no—
136#66938—24no—
137#66937—24no—
138#66936—24no—
139#66932—24no—
140#66928—21no—
141#66927C2311yescharacteristic
142C4×D44—21no—
143C4×D44C2312yes—
144#66923—21no—
145#66922C2311yescharacteristic
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150#66899C2318yes—
151#66899C2318yes—
152#66896C2314yes—
153#66896C2314yes—
154C22⋊(C11⋊C8)C2312yes—
155C22⋊(C11⋊C8)C2312yes—
156C22⋊(C11⋊C8)C2318yes—
157#66874C2314yes—
158#66873C2314yes—
159#66872C2314yes—
160#66871C2314yes—
161C4⋊(C11⋊C8)C2312yes—
162C4⋊(C11⋊C8)C2312yes—
163C4×C11⋊C8C2312yes—
164C4×C11⋊C8C2312yes—
165#61565—111nomaximal, Sylow
166C24×C11—21no—
167C24×C11C2×D412yes—
168C11×#41—216no—
169C11×#41—48no—
170C11×#41—416no—
171C2×Q8×C11—22no—
172C2×Q8×C11—44no—
173C2×Q8×C11C2414yes—
174C2×D4×C11—24no—
175C2×D4×C11—28no—
176C2×D4×C11—24no—
177C2×D4×C11—21no—
178C2×D4×C11—48no—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C2×D4×C11C2412yes—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—28no—
187C22×C4×C11—44no—
188C22×C4×C11—48no—
189C22×C4×C11—44no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D414yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2414yes—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199#4339—48no—
200#4339—44no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44C2412yes—
204C2×C4×D11—22no—
205C2×C4×D11—24no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22C2412yes—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—28no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2412yes—
218C11×C22⋊C4—28no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4C2×D414yes—
222C11×C22⋊C4C2×D414yes—
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2411yescharacteristic
226C42×C11C2411yescharacteristic
227C22⋊Dic11—24no—
228C22⋊Dic11—24no—
229C22⋊Dic11—22no—
230#4326—48no—
231#4325—48no—
232#4324—28no—
233#4323—28no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—24no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11C2412yes—
242C4⋊Dic11C2412yes—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4—24no—
246C4×Dic11—22no—
247C4×Dic11—24no—
248C2×C11⋊C8—48no—
249C2×C11⋊C8C2414yes—
250C2×C11⋊C8C2414yes—
251#3506—111no—
252C2×#547D1111yescharacteristic, complemented
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#3100—111no—
262#3002—114no—
263#2972—111no—
264C23×C11—24no—
265C23×C11—22no—
266C23×C11—24no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11C22×D414yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274Q8×C11—28no—
275Q8×C11—44no—
276D4×C11—24no—
277D4×C11—24no—
278D4×C11—24no—
279D4×C11—22no—
280D4×C11—416no—
281D4×C11H(5,𝔽2)14yes—
282C2×C4×C11—28no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—42no—
287C2×C4×C11—44no—
288C2×C4×C11—41no—
289C2×C4×C11—416no—
290C2×C4×C11—44no—
291C2×C4×C11—42no—
292C2×C4×C11—44no—
293C2×C4×C11—44no—
294C2×C4×C11#13514yescomplemented
295C2×C4×C11C22×D414yes—
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2511yescharacteristic
302C22⋊D11—44no—
303C22⋊D11—84no—
304C22⋊D11—84no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308D44—24no—
309D44—42no—
310D44—81no—
311C4×D11—44no—
312C4×D11—84no—
313Dic22—24no—
314Dic22—42no—
315Dic22—81no—
316C11⋊C8—24no—
317C11⋊C8—24no—
318C22×#41C2×D1112yes—
319C2×#135—118no—
320#559—222no—
321#556—112no—
322#555—112no—
323#553—222no—
324#550—112no—
325#547—22no—
326#547—22no—
327#547—112no—
328#547C2×D1114yes—
329#547C2×D1114yes—
330#538—222no—
331#535—221no—
332#533—111no—
333#532—111no—
334C2×C4⋊Q8C2×D1111yescharacteristic
335#525—114no—
336C2×#123—22no—
337C2×C22⋊Q8C2×D1112yes—
338C2×#121—21no—
339#520—221no—
340C2×C4×D4C2×D1111yescharacteristic
341C2×C4×D4C2×D1111yescharacteristic
342C22×C4⋊C4—21no—
343#494—112no—
344#492—112no—
345#487—112no—
346#487—112no—
347#485—118no—
348#483—112no—
349#480—112no—
350#476—112no—
351#474—112no—
352#467—118no—
353#465—118no—
354#462—114no—
355#461—114no—
356#461—112no—
357#459—112no—
358#452—118no—
359#452—118no—
360#451—114no—
361#450—112no—
362#449—118no—
363#448—114no—
364#447—112no—
365C4×SD16—114no—
366C4×D8—114no—
367C8×D4—114no—
368C8×D4—114no—
369#431—111no—
370#431—111no—
371#416—118no—
372C2×C22⋊C8—114no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11—48no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—84no—
383C22×C11C2×#13512yes—
384C22×C11C23×D411yescharacteristic
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—42no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—24no—
391C4×C11—21no—
392C4×C11—44no—
393C4×C11—42no—
394C4×C11C2×#13512yes—
395C4×C11C2×#13512yes—
396C4×C11C2×H(5,𝔽2)12yes—
397Dic11—42no—
398Dic11—42no—
399Dic11—42no—
400C2×#41—24no—
401C2×#41—48no—
402C2×#41—114no—
403C2×#41—221no—
404C2×#41C22×D1118yes—
405C22×Q8C22×D1112yes—
406C22×D4—22no—
407C22×D4C22⋊D1111yescharacteristic
408C22×D4C22×D1111yescharacteristic
409C23×C4—21no—
410C23×C4—22no—
411C23×C4C22×D1112yes—
412#135—4416no—
413C2×Q16—118no—
414C2×SD16—114no—
415C2×SD16—118no—
416C2×D8—114no—
417C22×C8—118no—
418C4⋊Q8—21no—
419C4⋊Q8—21no—
420C4⋊Q8—111no—
421C4⋊Q8—111no—
422C4⋊Q8—111no—
423C4⋊Q8C22×D1112yes—
424C4⋊Q8C22×D1112yes—
425#127—111no—
426#127—222no—
427#126—224no—
428#125—221no—
429#124—222no—
430#124—224no—
431#124—221no—
432#123—28no—
433#123—28no—
434#123—224no—
435#123—224no—
436C22⋊Q8—24no—
437C22⋊Q8—112no—
438C22⋊Q8—114no—
439C22⋊Q8—221no—
440C22⋊Q8C22×D1118yes—
441#121—24no—
442#121—24no—
443#121—112no—
444#121—114no—
445#121—222no—
446#121—222no—
447#121—221no—
448#121—224no—
449#120—224no—
450C4×Q8—112no—
451C4×Q8—222no—
452C4×Q8—221no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—112no—
456C4×D4—224no—
457C4×D4—224no—
458C4×D4—222no—
459C4×D4—221no—
460C4×D4C22⋊D1112yes—
461C4×D4C22⋊D1112yes—
462C4×D4C22×D1112yes—
463C4×D4C22×D1112yes—
464C4×D4C22×D1112yes—
465C4×D4C22×D1112yes—
466#117—114no—
467#117—221no—
468#117—222no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—222no—
475C2×C4⋊C4C22⋊D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—22no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4C22⋊D1112yes—
480C2×C42C22×D1111yescharacteristic
481#107—114no—
482#106—114no—
483C4⋊C8—112no—
484C4⋊C8—112no—
485#103—118no—
486#103—118no—
487#103—114no—
488#102—114no—
489#102—114no—
490#102—114no—
491C22⋊C8—112no—
492C22⋊C8—112no—
493C22⋊C8—118no—
494C4×C8—112no—
495C4×C8—112no—
496C2×C11—22no—
497C2×C11—44no—
498C2×C11—44no—
499C2×C11#348411yescharacteristic
500C2×C11C22×#13511yescharacteristic
501C2×C11#358611yescharacteristic
502D11—82no—
503C24—21no—
504C24C2×C22⋊D1112yes—
505#41—216no—
506#41—48no—
507#41—416no—
508#41—448no—
509#41—444no—
510C2×Q8—22no—
511C2×Q8—44no—
512C2×Q8—112no—
513C2×Q8—221no—
514C2×Q8—221no—
515C2×Q8C23×D1114yes—
516C2×D4—24no—
517C2×D4—28no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—48no—
521C2×D4—112no—
522C2×D4—222no—
523C2×D4—224no—
524C2×D4—224no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4C2×C22⋊D1112yes—
528C2×D4C2×C22⋊D1112yes—
529C2×D4C23×D1112yes—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—28no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—44no—
538C22×C4—222no—
539C22×C4—224no—
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C2×C22⋊D1112yes—
542C22×C4C2×C22⋊D1114yes—
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C22×C4C23×D1114yes—
546Q16—448no—
547SD16—228no—
548SD16—448no—
549D8—228no—
550C2×C8—114no—
551C2×C8—114no—
552C2×C8—448no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—28no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—112no—
560C4⋊C4—112no—
561C4⋊C4—221no—
562C4⋊C4—224no—
563C4⋊C4—221no—
564C4⋊C4—222no—
565C4⋊C4—221no—
566C4⋊C4—222no—
567C4⋊C4—221no—
568C4⋊C4C2×C22⋊D1112yes—
569C4⋊C4C2×C22⋊D1112yes—
570C4⋊C4C23×D1112yes—
571C22⋊C4—28no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—224no—
575C22⋊C4—222no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—222no—
579C22⋊C4—222no—
580C22⋊C4C2×C22⋊D1114yes—
581C22⋊C4C2×C22⋊D1114yes—
582C42—224no—
583C42—222no—
584C42C2×C22⋊D1111yescharacteristic
585C42C2×C22⋊D1111yescharacteristic
586C42C23×D1111yescharacteristic
587C42C23×D1111yescharacteristic
588C11#6156511yescharacteristic, complemented, Sylow
589C23—24no—
590C23—22no—
591C23—24no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—222no—
597C23C22×C22⋊D1114yes—
598C23C22×C22⋊D1111yescharacteristic
599Q8—28no—
600Q8—44no—
601Q8—224no—
602Q8—442no—
603Q8—881no—
604D4—24no—
605D4—24no—
606D4—24no—
607D4—22no—
608D4—416no—
609D4—224no—
610D4—444no—
611D4—442no—
612D4—881no—
613D4—884no—
614D4—884no—
615D4#6703714yes—
616C2×C4—28no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—42no—
621C2×C4—44no—
622C2×C4—41no—
623C2×C4—416no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—44no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—444no—
632C2×C4—884no—
633C2×C4#6700314yescomplemented
634C2×C4C22×C22⋊D1114yes—
635C2×C4C22×C22⋊D1111yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C2×C4C22×C22⋊D1111yescharacteristic
638C2×C4C22×C22⋊D1111yescharacteristic
639C2×C4C22×C22⋊D1111yescharacteristic
640C2×C4C24×D1111yescharacteristic
641C8—224no—
642C8—224no—
643C22—21no—
644C22—21no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—24no—
649C22—48no—
650C22—42no—
651C22—42no—
652C22—84no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22C2×#6700312yes—
657C22C23×C22⋊D1111yescharacteristic
658C4—21no—
659C4—21no—
660C4—24no—
661C4—21no—
662C4—44no—
663C4—42no—
664C4—442no—
665C4—442no—
666C4—442no—
667C4C2×#6700312yes—
668C4C2×#6700312yes—
669C4C2×#6703712yes—
670C2—22no—
671C2—44no—
672C2—44no—
673C2—882no—
674C2#1308225111yescharacteristic
675C2C22×#6700311yescharacteristic
676C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC22×C11C23×D4
hypercenterC2×#547D11
hypocenterC11#61565
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. #13080544C2semidirect
3. #13080533C2semidirect
4. #13080342C2semidirect
5. #13080334C2semidirect
6. #13079564C2semidirect
7. #13079541C2semidirect
8. #13079397C2semidirect
9. #13078624C2semidirect
10. #13078616C2semidirect
11. #13077834C2semidirect
12. #13077640C2semidirect
13. C2×C11×#547C2semidirect
26. C2×#67003C22semidirect
29. #10623094C22semidirect
32. #10623084C22semidirect
33. #10623082C22semidirect
34. #10623073C22semidirect
39. #10622852C22semidirect
40. #10622851C22semidirect
41. #10622846C22semidirect
47. #10622705C22semidirect
48. #10622703C22semidirect
49. #10622698C22semidirect
50. #10622696C22semidirect
51. #10622694C22semidirect
52. #10622694C22semidirect
53. #10622664C22semidirect
54. #10622661C22semidirect
55. #10622660C22semidirect
56. #10622658C22semidirect
57. #10622632C22semidirect
58. C4×#4324C22semidirect
59. #10622628C22semidirect
60. C4×#4323C22semidirect
61. D4×C11⋊C8C22semidirect
62. D4×C11⋊C8C22semidirect
63. #10622621C22semidirect
64. #10622620C22semidirect
252. C2×#547D11semidirect
294. C2×C4×C11#135semidirect
588. C11#61565semidirect
633. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130805442
#130805332
#130803422
#130803342
#130795642
#130795412
#130793972
#130786242
#130786162
#130778342
#130776402
C2×C11×#5472
#6156511