Finite Group Databasebeta

← #15625335

Subgroups — #15625335

Order 2816.

2098 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13079725C218yesmaximal, complemented
3#13079710C218yesmaximal, complemented
4#13079084C212yesmaximal, complemented
5#13079009C212yesmaximal, complemented
6#13078084C212yesmaximal, complemented
7#13078076C212yesmaximal, complemented
8#13077876C212yesmaximal, complemented
9#13077868C212yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C11×#3449C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C11×#537—21no—
14C11×#537—21no—
15C11×#536C2214yescomplemented
16C11×#535C2214yescomplemented
17C11×#534—21no—
18C11×#534—21no—
19C11×#532C2212yes—
20C11×#532C2212yes—
21C11×#525—24no—
22C2×C11×#117C2211yescharacteristic
23C2×#67004C2214yescomplemented
24C2×#67002C2214yescomplemented
25C2×#66983C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27#10623065—24no—
28#10623065C2218yescomplemented
29C2×#66951—21no—
30C2×#66949—21no—
31C2×#66938—21no—
32C2×#66936—21no—
33C2×#66928C2211yescharacteristic, complemented
34C2×C4×D44C2211yescharacteristic, complemented
35C2×#66922C2211yescharacteristic, complemented
36C2×C4×Dic22C2211yescharacteristic, complemented
37#10622852C2218yescomplemented
38#10622851C2218yes—
39#10622845C2214yescomplemented
40#10622845C2214yescomplemented
41#10622841C2214yescomplemented
42#10622840C2214yescomplemented
43#10622831C2214yescomplemented
44#10622830C2214yescomplemented
45#10622820C2212yes—
46#10622703C2214yescomplemented
47#10622699C2214yescomplemented
48#10622696C2214yescomplemented
49#10622694C2214yescomplemented
50#10622688C2214yescomplemented
51#10622687C2214yescomplemented
52#10622685C2214yescomplemented
53#10622683C2214yescomplemented
54#10622672C2218yescomplemented
55#10622670C2218yescomplemented
56#10622668C2218yescomplemented
57#10622667C2218yescomplemented
58#10622613C2218yescomplemented
59#10622537C2212yescomplemented
60C4×#4318C2212yescomplemented
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—48no—
64C2×C11×#41C2314yes—
65C2×C11×#41C2314yes—
66C22×Q8×C11C2312yes—
67C22×D4×C11—22no—
68C22×D4×C11C2312yes—
69C23×C4×C11—22no—
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22—21no—
75C22×Dic22C2311yescharacteristic
76C11×C4⋊Q8C2312yes—
77C11×C4⋊Q8C2312yes—
78C11×#127C2312yes—
79C11×#127C2312yes—
80C11×#124C2314yes—
81C11×#124C2314yes—
82C11×#123—24no—
83C11×#123—24no—
84C11×C22⋊Q8—24no—
85C11×C22⋊Q8—24no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—24no—
91C11×#121—24no—
92C11×#120—24no—
93C11×#120—24no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C11×#117D414yes—
99C11×#117C2314yes—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#67004—48no—
108#67002—48no—
109C2×#4326C2318yes—
110C2×#4325C2318yes—
111C2×#4324C2318yes—
112C2×#4323C2318yes—
113#66983—22no—
114#66983C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122#66977—22no—
123#66977C2314yes—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×C4×Dic11—21no—
127C2×#4318C2314yes—
128#66951—28no—
129#66949—28no—
130#66938—28no—
131#66936—28no—
132#66928—22no—
133#66928C2314yes—
134C4×D44—22no—
135C4×D44C2314yes—
136#66922—22no—
137#66922C2314yes—
138C4×Dic22—22no—
139C4×Dic22C2314yes—
140#66899C2318yes—
141#66899C2318yes—
142#66896C2318yes—
143#66896C2318yes—
144C22⋊(C11⋊C8)C2314yes—
145C22⋊(C11⋊C8)C2314yes—
146C4⋊(C11⋊C8)C2314yes—
147C4⋊(C11⋊C8)C2314yes—
148#66867C2314yes—
149C4×C11⋊C8C2314yes—
150#60810—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C11×#41—28no—
155C11×#41—28no—
156C11×#41—44no—
157C11×#41—44no—
158C11×#41—48no—
159C11×#41—48no—
160C2×Q8×C11—22no—
161C2×Q8×C11—44no—
162C2×Q8×C11C2414yes—
163C2×D4×C11—24no—
164C2×D4×C11—24no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—44no—
171C2×D4×C11—48no—
172C2×D4×C11C2414yes—
173C22×C4×C11—24no—
174C22×C4×C11—22no—
175C22×C4×C11—24no—
176C22×C4×C11—24no—
177C22×C4×C11—48no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—82no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C2×D44—21no—
192C2×D44—24no—
193C2×D44C2412yes—
194C2×C4×D11—24no—
195C2×C4×D11—82no—
196C2×Dic22—21no—
197C2×Dic22—24no—
198C2×Dic22—24no—
199C2×Dic22—82no—
200C2×Dic22C2412yes—
201C11×C4⋊C4—22no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4C2×D414yes—
206C11×C4⋊C4C2×D414yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4C2×D414yes—
212C11×C22⋊C4C2×D414yes—
213C42×C11C2×D412yes—
214C42×C11C2×D412yes—
215C42×C11C2412yes—
216C42×C11C2412yes—
217C22⋊Dic11—24no—
218#4326—48no—
219#4325—48no—
220#4324—48no—
221#4323—48no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—24no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—24no—
229C4⋊Dic11C2412yes—
230C4⋊Dic11C2412yes—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233C4×Dic11—24no—
234#4318—28no—
235C2×C11⋊C8C2418yes—
236C2×#542—111no—
237#3449D1111yescharacteristic, complemented
238#3225—118no—
239#3224—118no—
240#3153—112no—
241#3141—112no—
242#3037—112no—
243#3036—112no—
244#3007—112no—
245#3006—112no—
246#2921—111no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—44no—
252C23×C11—82no—
253C23×C11—82no—
254C23×C11C22×D412yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—22no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260Q8×C11—24no—
261Q8×C11—24no—
262Q8×C11—44no—
263D4×C11—24no—
264D4×C11—24no—
265D4×C11—44no—
266D4×C11—48no—
267D4×C11—48no—
268D4×C11—82no—
269D4×C11—82no—
270D4×C11—82no—
271D4×C11—82no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—48no—
281C2×C4×C11—44no—
282C2×C4×C11—48no—
283C2×C4×C11C22×D412yes—
284C2×C4×C11C22×D412yes—
285C2×C4×C11C22×D412yes—
286C2×C4×C11C22×D412yes—
287C2×C4×C11C22×D412yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11H(5,𝔽2)14yes—
290C2×C4×C11C2511yescharacteristic
291C22⋊D11—84no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298D44—24no—
299D44—42no—
300C4×D11—84no—
301Dic22—24no—
302Dic22—42no—
303Dic22—84no—
304C11⋊C8—28no—
305C22×#41C2×D1112yes—
306C2×#137—114no—
307C2×AGL(1,ℤ/8)—114no—
308#542—118no—
309#542—224no—
310#537—21no—
311#537—21no—
312#536C2×D1114yescomplemented
313#535C2×D1114yescomplemented
314#534—21no—
315#534—21no—
316#532C2×D1112yes—
317#532C2×D1112yes—
318C2×C4⋊Q8—111no—
319C2×#126—221no—
320C2×#124—111no—
321C2×#124—221no—
322#525—24no—
323C2×#123—221no—
324C2×C22⋊Q8—111no—
325C2×C22⋊Q8—221no—
326C2×#121—111no—
327C2×C4×Q8—111no—
328C2×C4×D4—111no—
329C2×#117C2×D1111yescharacteristic
330#497—114no—
331#496—114no—
332#495—118no—
333#489—118no—
334#487—114no—
335#486—114no—
336#464—118no—
337#463—118no—
338#462—114no—
339#461—114no—
340#460—114no—
341#459—114no—
342#452—118no—
343#451—114no—
344#450—114no—
345#449—118no—
346#448—114no—
347#447—114no—
348#433—118no—
349#423—112no—
350#417—114no—
351#417—114no—
352#407—112no—
353C4×M16—112no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—44no—
360C22×C11—44no—
361C22×C11—44no—
362C22×C11—82no—
363C22×C11—88no—
364C22×C11#53512yes—
365C22×C11C23×D411yescharacteristic
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—84no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—44no—
376C4×C11#53512yes—
377C4×C11C2×H(5,𝔽2)12yes—
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—48no—
384C2×#41C22×D1114yes—
385C2×#41C22×D1114yes—
386C22×Q8—111no—
387C22×Q8—221no—
388C22×Q8C22×D1112yes—
389C22×D4—22no—
390C22×D4—111no—
391C22×D4—221no—
392C22×D4C22×D1112yes—
393C23×C4—22no—
394C23×C4—221no—
395C23×C4C22×D1111yescharacteristic
396#137—448no—
397AGL(1,ℤ/8)—448no—
398C2×Q16—118no—
399C2×SD16—118no—
400C2×SD16—118no—
401C2×D8—118no—
402C2×M16—114no—
403C4⋊Q8—114no—
404C4⋊Q8—222no—
405C4⋊Q8C22×D1112yes—
406C4⋊Q8C22×D1112yes—
407#127C22×D1112yes—
408#127C22×D1112yes—
409#126—228no—
410#124—114no—
411#124—228no—
412#124—222no—
413#124C22×D1114yes—
414#124C22×D1114yes—
415#123—24no—
416#123—24no—
417#123—228no—
418C22⋊Q8—24no—
419C22⋊Q8—24no—
420C22⋊Q8—114no—
421C22⋊Q8—222no—
422C22⋊Q8—228no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—24no—
428#121—24no—
429#121—114no—
430#121—222no—
431#120—24no—
432#120—24no—
433C4×Q8—114no—
434C4×Q8—222no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—114no—
440C4×D4—222no—
441#117C22⋊D1114yes—
442#117C22×D1114yes—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4C22⋊D1111yescharacteristic
449C2×C4⋊C4C22⋊D1111yescharacteristic
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4C22⋊D1111yescharacteristic
456C2×C22⋊C4C22⋊D1111yescharacteristic
457C2×C42—221no—
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460C4⋊C8—114no—
461C4⋊C8—114no—
462#103—118no—
463#103—118no—
464#102—118no—
465#102—118no—
466C22⋊C8—114no—
467C22⋊C8—114no—
468#97—114no—
469C4×C8—114no—
470C2×C11—22no—
471C2×C11—42no—
472C2×C11—84no—
473C2×C11C2×#53511yescharacteristic
474C2×C11#358511yescharacteristic
475C2×C11#358611yescharacteristic
476D11—82no—
477C24—22no—
478C24—221no—
479C24C2×C22⋊D1111yescharacteristic
480#41—28no—
481#41—28no—
482#41—44no—
483#41—44no—
484#41—48no—
485#41—48no—
486C2×Q8—22no—
487C2×Q8—44no—
488C2×Q8—112no—
489C2×Q8—221no—
490C2×Q8—224no—
491C2×Q8—224no—
492C2×Q8—882no—
493C2×Q8C23×D1114yes—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—112no—
504C2×D4—224no—
505C2×D4—224no—
506C2×D4—221no—
507C2×D4—882no—
508C2×D4C23×D1114yes—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—48no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—224no—
518C22×C4—882no—
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1112yes—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C23×D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—448no—
528SD16—448no—
529SD16—448no—
530D8—448no—
531M16—228no—
532C2×C8—118no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—112no—
538C4⋊C4—112no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4C2×C22⋊D1114yes—
545C4⋊C4C2×C22⋊D1114yes—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4C2×C22⋊D1114yes—
556C22⋊C4C2×C22⋊D1114yes—
557C42—224no—
558C42C2×C22⋊D1112yes—
559C42C2×C22⋊D1112yes—
560C42C23×D1112yes—
561C42C23×D1112yes—
562C11#6081011yescharacteristic, complemented, Sylow
563C23—22no—
564C23—24no—
565C23—41no—
566C23—41no—
567C23—44no—
568C23—82no—
569C23—82no—
570C23—222no—
571C23—442no—
572C23—442no—
573C23—442no—
574C23C22×C22⋊D1112yes—
575C23C22×C22⋊D1111yescharacteristic
576Q8—24no—
577Q8—24no—
578Q8—44no—
579Q8—224no—
580Q8—442no—
581Q8—884no—
582D4—24no—
583D4—24no—
584D4—44no—
585D4—48no—
586D4—48no—
587D4—82no—
588D4—82no—
589D4—82no—
590D4—82no—
591D4—224no—
592D4—442no—
593D4—884no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—48no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—884no—
612C2×C4#6703714yes—
613C2×C4C22×C22⋊D1112yes—
614C2×C4C22×C22⋊D1112yes—
615C2×C4C22×C22⋊D1112yes—
616C2×C4C22×C22⋊D1112yes—
617C2×C4C22×C22⋊D1112yes—
618C2×C4C22×C22⋊D1111yescharacteristic
619C2×C4C24×D1111yescharacteristic
620C8—228no—
621C22—21no—
622C22—21no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—82no—
630C22—88no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—884no—
635C22#1062333612yes—
636C22C23×C22⋊D1111yescharacteristic
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—44no—
643C4—442no—
644C4—442no—
645C4—442no—
646C4#1062333612yes—
647C4C2×#6703712yes—
648C2—22no—
649C2—42no—
650C2—84no—
651C2—882no—
652C2C2×#1062333611yescharacteristic
653C2#1308339511yescharacteristic
654C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3449C2
socleC22×C11C23×D4
hypercenter#3449D11
hypocenterC11#60810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13079725C2semidirect
3. #13079710C2semidirect
4. #13079084C2semidirect
5. #13079009C2semidirect
6. #13078084C2semidirect
7. #13078076C2semidirect
8. #13077876C2semidirect
9. #13077868C2semidirect
10. #13077254C2semidirect
11. C11×#3449C2semidirect
15. C11×#536C22semidirect
16. C11×#535C22semidirect
23. C2×#67004C22semidirect
24. C2×#67002C22semidirect
28. #10623065C22semidirect
33. C2×#66928C22semidirect
34. C2×C4×D44C22semidirect
35. C2×#66922C22semidirect
36. C2×C4×Dic22C22semidirect
37. #10622852C22semidirect
39. #10622845C22semidirect
40. #10622845C22semidirect
41. #10622841C22semidirect
42. #10622840C22semidirect
43. #10622831C22semidirect
44. #10622830C22semidirect
46. #10622703C22semidirect
47. #10622699C22semidirect
48. #10622696C22semidirect
49. #10622694C22semidirect
50. #10622688C22semidirect
51. #10622687C22semidirect
52. #10622685C22semidirect
53. #10622683C22semidirect
54. #10622672C22semidirect
55. #10622670C22semidirect
56. #10622668C22semidirect
57. #10622667C22semidirect
58. #10622613C22semidirect
59. #10622537C22semidirect
60. C4×#4318C22semidirect
237. #3449D11semidirect
312. #536C2×D11semidirect
313. #535C2×D11semidirect
562. C11#60810semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130797252
#130797102
#130790842
#130790092
#130780842
#130780762
#130778762
#130778682
#130772542
C11×#34492
#6081011