Finite Group Databasebeta

← #15625337

Subgroups — #15625337

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#13081949C211yesmaximal, characteristic, complemented
3#13079727C218yesmaximal, complemented
4#13079712C218yesmaximal, complemented
5#13079082C212yesmaximal, complemented
6#13079010C212yesmaximal, complemented
7#13078090C212yesmaximal, complemented
8#13078082C212yesmaximal, complemented
9#13077878C212yesmaximal, complemented
10#13077870C212yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C11×#117C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16C2×#66962C2214yescomplemented
17C2×#66961C2214yescomplemented
18#10623065—24no—
19#10623065C2218yescomplemented
20#10623057C2214yescomplemented
21#10623056C2214yescomplemented
22#10623055—24no—
23C2×#66951—21no—
24#10623041—21no—
25#10623041—21no—
26C2×#66949—21no—
27#10623024—21no—
28#10623024—21no—
29C2×#66938—21no—
30C2×#66936—21no—
31#10623008C2212yes—
32#10623008C2212yes—
33C2×#66928C2211yescharacteristic, complemented
34C2×C4×D44C2211yescharacteristic, complemented
35C2×#66922C2211yescharacteristic, complemented
36C2×C4×Dic22C2211yescharacteristic, complemented
37C11×#433C2218yescomplemented
38C11×#423C2212yescomplemented
39C11×#407C2212yes—
40C4×C11×M16C2212yescomplemented
41#10622746C2214yescomplemented
42#10622746C2214yescomplemented
43#10622462C2214yescomplemented
44#10622461C2214yescomplemented
45#10622458C2218yescomplemented
46#10622457C2218yescomplemented
47#10622456C2214yescomplemented
48#10622454C2214yescomplemented
49#10622352C2214yescomplemented
50#10622351C2214yescomplemented
51#10622347C2218yes—
52#10622346C2218yescomplemented
53#10622345C2214yescomplemented
54#10622344C2214yescomplemented
55#10622328C2214yescomplemented
56#10622327C2218yescomplemented
57#10622325C2214yescomplemented
58#10622309C2218yescomplemented
59#10622307C2214yescomplemented
60#10622294C2214yescomplemented
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—22no—
63C22×C22⋊D11—21no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—48no—
67C2×#4339C2314yes—
68C2×#4339C2314yes—
69C22×D44C2311yescharacteristic
70C22×D44C2312yes—
71C22×C4×D11—22no—
72C22×C4×D11—21no—
73C22×Dic22—21no—
74C22×Dic22C2311yescharacteristic
75C22×Dic22C2312yes—
76C2×C11×M16C2314yes—
77C11×#117D414yes—
78C11×#117C2314yes—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86#66983—22no—
87#66983—22no—
88#66983—22no—
89#66983—22no—
90#66983—22no—
91#66983C2314yes—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977C2314yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104#66962—48no—
105#66961—48no—
106C2×Dic44C2318yes—
107C2×D88C2318yes—
108C2×#4314C2318yes—
109C2×#4314C2318yes—
110#66951—28no—
111#66950—24no—
112#66950—24no—
113#66949—28no—
114#66948—24no—
115#66948—24no—
116#66939—24no—
117#66939—24no—
118#66938—28no—
119#66936—28no—
120#66935—24no—
121#66935—24no—
122#66928—22no—
123#66928C2314yes—
124#66928C2314yes—
125#66928C2314yes—
126#66927C2312yes—
127#66927C2312yes—
128C4×D44—22no—
129C4×D44—22no—
130C4×D44—22no—
131C4×D44—22no—
132C4×D44—22no—
133C4×D44C2314yes—
134#66922—22no—
135#66922C2312yes—
136#66922C2312yes—
137#66922C2314yes—
138C4×Dic22—22no—
139C4×Dic22C2314yes—
140C11×C4⋊C8C2314yes—
141C11×C4⋊C8C2314yes—
142C11×C22⋊C8C2314yes—
143C11×C22⋊C8C2314yes—
144C11×#97C2314yes—
145C4×C8×C11C2314yes—
146#66885C2318yes—
147#66885C2318yes—
148#66880C2318yes—
149#66880C2318yes—
150#60810—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C23×D11—22no—
154C22×C4×C11—24no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—24no—
165C2×C22⋊D11—24no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—82no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172#4339—28no—
173#4339—28no—
174#4339—44no—
175#4339—44no—
176#4339—48no—
177#4339—48no—
178C2×D44—21no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—22no—
184C2×D44—24no—
185C2×D44—44no—
186C2×D44C2414yes—
187C2×D44C2412yes—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—48no—
192C2×C4×D11—82no—
193C2×Dic22—21no—
194C2×Dic22—22no—
195C2×Dic22—24no—
196C2×Dic22—24no—
197C2×Dic22—44no—
198C2×Dic22—82no—
199C2×Dic22C2414yes—
200C2×Dic22C2412yes—
201C11×M16—28no—
202C2×C8×C11C2418yes—
203C11×C4⋊C4C2×D414yes—
204C11×C4⋊C4C2×D414yes—
205C11×C22⋊C4C2×D414yes—
206C11×C22⋊C4C2×D414yes—
207C42×C11C2×D412yes—
208C42×C11C2×D412yes—
209C42×C11C2412yes—
210C42×C11C2412yes—
211C22⋊Dic11—24no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—24no—
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—24no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—24no—
223C4⋊Dic11—22no—
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—22no—
227C4⋊Dic11C2412yes—
228C4⋊Dic11C2412yes—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231C4×Dic11—24no—
232Dic44—48no—
233D88—48no—
234#4314—48no—
235#4314—48no—
236C2×#542—111no—
237#3449—111no—
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#2921D1111yescharacteristic, complemented
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C22×D412yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—22no—
253C22×D11—24no—
254C22×D11—44no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—82no—
259C22×D11—82no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D412yes—
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D412yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11H(5,𝔽2)14yes—
274C2×C4×C11C2511yescharacteristic
275C22⋊D11—48no—
276C22⋊D11—48no—
277C22⋊D11—84no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—44no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286D44—24no—
287D44—24no—
288D44—24no—
289D44—44no—
290D44—42no—
291D44—82no—
292D44—82no—
293D44—82no—
294D44—82no—
295C4×D11—48no—
296C4×D11—48no—
297C4×D11—84no—
298Dic22—24no—
299Dic22—24no—
300Dic22—24no—
301Dic22—44no—
302Dic22—42no—
303Dic22—84no—
304C8×C11—28no—
305C22×#41—112no—
306C2×#137—114no—
307C2×AGL(1,ℤ/8)—114no—
308#542—118no—
309#542—224no—
310#537—221no—
311#537—221no—
312#536—114no—
313#535—114no—
314#534—221no—
315#534—221no—
316#532—112no—
317#532—112no—
318C2×C4⋊Q8—111no—
319C2×#126—221no—
320C2×#124—111no—
321C2×#124—221no—
322#525—224no—
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#433C2×D1118yescomplemented
349#423C2×D1112yescomplemented
350#417—114no—
351#417—114no—
352#407C2×D1112yes—
353C4×M16C2×D1112yescomplemented
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—82no—
360C22×C11#53512yes—
361C22×C11C23×D411yescharacteristic
362C2×D11—42no—
363C2×D11—44no—
364C2×D11—42no—
365C2×D11—44no—
366C2×D11—44no—
367C2×D11—42no—
368C2×D11—84no—
369C2×D11—88no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11#53512yes—
376C4×C11C2×H(5,𝔽2)12yes—
377Dic11—42no—
378Dic11—42no—
379Dic11—44no—
380Dic11—42no—
381C2×#41—114no—
382C2×#41—114no—
383C2×#41—222no—
384C2×#41—222no—
385C2×#41—448no—
386C22×Q8—111no—
387C22×Q8—112no—
388C22×Q8—221no—
389C22×D4—111no—
390C22×D4—112no—
391C22×D4—222no—
392C22×D4—221no—
393C23×C4—222no—
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×M16C22×D1114yes—
403C4⋊Q8—114no—
404C4⋊Q8—112no—
405C4⋊Q8—112no—
406C4⋊Q8—222no—
407#127—112no—
408#127—112no—
409#126—228no—
410#124—114no—
411#124—114no—
412#124—114no—
413#124—228no—
414#124—222no—
415#123—228no—
416#123—224no—
417#123—224no—
418C22⋊Q8—114no—
419C22⋊Q8—222no—
420C22⋊Q8—228no—
421C22⋊Q8—224no—
422C22⋊Q8—224no—
423#121—114no—
424#121—222no—
425#121—222no—
426#121—222no—
427#121—222no—
428#121—222no—
429#121—224no—
430#121—224no—
431#120—224no—
432#120—224no—
433C4×Q8—114no—
434C4×Q8—222no—
435C4×D4—114no—
436C4×D4—222no—
437C4×D4—222no—
438C4×D4—222no—
439C4×D4—222no—
440C4×D4—222no—
441#117D4414yes—
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⋊C4D4411yescharacteristic
449C2×C4⋊C4D4411yescharacteristic
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4D4411yescharacteristic
456C2×C22⋊C4D4411yescharacteristic
457C2×C42—221no—
458C2×C42C22×D1111yescharacteristic
459C2×C42C22×D1111yescharacteristic
460C4⋊C8C22×D1114yes—
461C4⋊C8C22×D1114yes—
462#103—118no—
463#103—118no—
464#102—118no—
465#102—118no—
466C22⋊C8C22×D1114yes—
467C22⋊C8C22×D1114yes—
468#97C22×D1114yes—
469C4×C8C22×D1114yes—
470C2×C11—22no—
471C2×C11—42no—
472C2×C11C2×#53511yescharacteristic
473C2×C11#358511yescharacteristic
474C2×C11#358611yescharacteristic
475D11—82no—
476D11—84no—
477C24—221no—
478C24—222no—
479C24C2×D4411yescharacteristic
480#41—228no—
481#41—228no—
482#41—444no—
483#41—444no—
484#41—448no—
485#41—448no—
486C2×Q8—114no—
487C2×Q8—112no—
488C2×Q8—221no—
489C2×Q8—222no—
490C2×Q8—224no—
491C2×Q8—224no—
492C2×Q8—444no—
493C2×Q8—882no—
494C2×D4—114no—
495C2×D4—112no—
496C2×D4—224no—
497C2×D4—224no—
498C2×D4—224no—
499C2×D4—221no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—222no—
505C2×D4—224no—
506C2×D4—444no—
507C2×D4—448no—
508C2×D4—882no—
509C22×C4—24no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—448no—
518C22×C4—882no—
519C22×C4C2×D4411yescharacteristic
520C22×C4C2×D4412yes—
521C22×C4C2×D4411yescharacteristic
522C22×C4C2×D4411yescharacteristic
523C22×C4C2×D4411yescharacteristic
524C22×C4C2×D4411yescharacteristic
525C22×C4C23×D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—448no—
528SD16—448no—
529SD16—448no—
530D8—448no—
531M16—28no—
532C2×C8C23×D1118yes—
533C4⋊C4—112no—
534C4⋊C4—112no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—222no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4C2×D4414yes—
545C4⋊C4C2×D4414yes—
546C22⋊C4—224no—
547C22⋊C4—224no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—224no—
555C22⋊C4C2×D4414yes—
556C22⋊C4C2×D4414yes—
557C42—224no—
558C42C2×D4412yes—
559C42C2×D4412yes—
560C42C23×D1112yes—
561C42C23×D1112yes—
562C11#6081011yescharacteristic, complemented, Sylow
563C23—22no—
564C23—41no—
565C23—41no—
566C23—222no—
567C23—224no—
568C23—444no—
569C23—442no—
570C23—442no—
571C23—442no—
572C23—882no—
573C23—882no—
574C23C22×D4412yes—
575C23C22×D4411yescharacteristic
576Q8—224no—
577Q8—224no—
578Q8—224no—
579Q8—444no—
580Q8—442no—
581Q8—884no—
582D4—224no—
583D4—224no—
584D4—224no—
585D4—444no—
586D4—448no—
587D4—448no—
588D4—442no—
589D4—882no—
590D4—882no—
591D4—882no—
592D4—882no—
593D4—884no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—224no—
605C2×C4—448no—
606C2×C4—444no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—448no—
611C2×C4—884no—
612C2×C4C22×D4412yes—
613C2×C4C22×D4412yes—
614C2×C4C22×D4412yes—
615C2×C4C22×D4412yes—
616C2×C4C22×D4412yes—
617C2×C4C22×D4411yescharacteristic
618C2×C4#6704214yes—
619C2×C4C24×D1111yescharacteristic
620C8—28no—
621C22—21no—
622C22—21no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—82no—
627C22—442no—
628C22—444no—
629C22—444no—
630C22—442no—
631C22—444no—
632C22—442no—
633C22—884no—
634C22—888no—
635C22#1062305612yes—
636C22C23×D4411yescharacteristic
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—442no—
643C4—442no—
644C4—444no—
645C4—442no—
646C4#1062305612yes—
647C4C2×#6704212yes—
648C2—22no—
649C2—42no—
650C2—882no—
651C2—884no—
652C2C2×#1062305611yescharacteristic
653C2#1308339711yescharacteristic
654C2#1308340411yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2921C2
socleC22×C11C23×D4
hypercenter#2921D11
hypocenterC11#60810
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13081949C2semidirect
3. #13079727C2semidirect
4. #13079712C2semidirect
5. #13079082C2semidirect
6. #13079010C2semidirect
7. #13078090C2semidirect
8. #13078082C2semidirect
9. #13077878C2semidirect
10. #13077870C2semidirect
11. C11×#2921C2semidirect
16. C2×#66962C22semidirect
17. C2×#66961C22semidirect
19. #10623065C22semidirect
20. #10623057C22semidirect
21. #10623056C22semidirect
33. C2×#66928C22semidirect
34. C2×C4×D44C22semidirect
35. C2×#66922C22semidirect
36. C2×C4×Dic22C22semidirect
37. C11×#433C22semidirect
38. C11×#423C22semidirect
40. C4×C11×M16C22semidirect
41. #10622746C22semidirect
42. #10622746C22semidirect
43. #10622462C22semidirect
44. #10622461C22semidirect
45. #10622458C22semidirect
46. #10622457C22semidirect
47. #10622456C22semidirect
48. #10622454C22semidirect
49. #10622352C22semidirect
50. #10622351C22semidirect
52. #10622346C22semidirect
53. #10622345C22semidirect
54. #10622344C22semidirect
55. #10622328C22semidirect
56. #10622327C22semidirect
57. #10622325C22semidirect
58. #10622309C22semidirect
59. #10622307C22semidirect
60. #10622294C22semidirect
246. #2921D11semidirect
348. #433C2×D11semidirect
349. #423C2×D11semidirect
353. C4×M16C2×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
#130819492
#130797272
#130797122
#130790822
#130790102
#130780902
#130780822
#130778782
#130778702
C11×#29212
#6081011