Finite Group Databasebeta

← #15626773

Subgroups — #15626773

Order 2816.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13080003C212yesmaximal, complemented
3#13079994C212yesmaximal, complemented
4#13079972C214yesmaximal, complemented
5#13079936C214yesmaximal, complemented
6#13079932C212yesmaximal, complemented
7#13079923C212yesmaximal, complemented
8#13078425C212yesmaximal, complemented
9#13078413C212yesmaximal, complemented
10#13078231C214yesmaximal, complemented
11#13078092C212yesmaximal, complemented
12#13078080C212yesmaximal, complemented
13C2×#10622537C211yesmaximal, characteristic, complemented
14C2×C11×#532C211yesmaximal, characteristic, complemented
15C22×C11×#41—21no—
16C11×#532—21no—
17C11×#532—21no—
18C11×#532—21no—
19C11×#532—21no—
20C11×#532C2212yes—
21C11×#532C2212yes—
22C11×#532C2212yes—
23C11×#532C2212yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#124—21no—
27C2×C11×#121—21no—
28C2×C11×#121C2212yes—
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2212yes—
31C22×C42×C11C2211yescharacteristic
32C2×#66985C2214yes—
33#10623322—21no—
34#10623322—21no—
35#10623322C2212yes—
36C22×#4318C2212yes—
37#10623010—21no—
38#10623010—21no—
39#10623010—21no—
40#10623010—21no—
41#10623010C2212yescomplemented
42#10623010C2212yescomplemented
43#10623008C2211yescharacteristic
44#10623008C2211yescharacteristic, complemented
45#10623008C2211yescharacteristic, complemented
46C4×#4339—21no—
47C4×#4339—21no—
48C4×#4339C2212yes—
49#10623001C2211yescharacteristic
50#10623001C2211yescharacteristic, complemented
51#10623001C2211yescharacteristic, complemented
52#10622828C2214yes—
53#10622707C2214yescomplemented
54#10622704C2214yescomplemented
55#10622700C2214yescomplemented
56#10622697C2214yescomplemented
57#10622688C2214yescomplemented
58#10622688C2214yescomplemented
59#10622685C2214yescomplemented
60#10622685C2214yescomplemented
61#10622655C2218yescomplemented
62#10622654C2218yescomplemented
63#10622652C2218yescomplemented
64#10622651C2218yescomplemented
65#10622632C2214yescomplemented
66#10622629C2218yescomplemented
67#10622628C2214yescomplemented
68#10622622C2218yescomplemented
69#10622621C2214yescomplemented
70#10622620C2214yescomplemented
71#10622579C2214yes—
72#10622577C2214yes—
73#10622537C2212yes—
74#10622537C2212yes—
75#10622537C2212yescomplemented
76#10622537C2212yescomplemented
77C2×C4⋊(C11⋊C8)C2212yescomplemented
78C2×C4⋊(C11⋊C8)C2212yescomplemented
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—22no—
82C2×C11×#41—22no—
83C2×C11×#41—48no—
84C22×Q8×C11—21no—
85C22×D4×C11—22no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11C2312yes—
89C23×C4×C11—22no—
90C23×C4×C11D411yescharacteristic
91C23×C4×C11D411yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C2×#4339—21no—
94C2×#4339—21no—
95C2×#4339C2312yes—
96C11×C4⋊Q8—21no—
97C11×C4⋊Q8—21no—
98C11×C4⋊Q8C2312yes—
99C11×C4⋊Q8C2312yes—
100C11×#127—21no—
101C11×#127—21no—
102C11×#127C2312yes—
103C11×#127C2312yes—
104C11×#124—22no—
105C11×#124—22no—
106C11×#124—22no—
107C11×#124—22no—
108C11×#121—22no—
109C11×#121—22no—
110C11×#121—22no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121C2314yes—
115C11×#121C2314yes—
116C4×D4×C11—22no—
117C4×D4×C11—22no—
118C4×D4×C11—22no—
119C4×D4×C11—22no—
120C4×D4×C11—22no—
121C4×D4×C11—22no—
122C4×D4×C11C2314yes—
123C4×D4×C11C2314yes—
124C2×C11×C4⋊C4—21no—
125C2×C11×C4⋊C4C2312yes—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C42×C11D411yescharacteristic
129C2×C42×C11D411yescharacteristic
130C2×C42×C11D411yescharacteristic
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11D411yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140#67006—22no—
141C2×#4324C2318yes—
142#66985—48no—
143C2×#4323C2318yes—
144#66983—21no—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983C2312yes—
149#66983C2312yes—
150#66982—22no—
151#66982—22no—
152#66982—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159#66979—21no—
160#66979—21no—
161#66979C2312yes—
162#66977—21no—
163#66977—21no—
164#66977—21no—
165#66977—21no—
166#66977C2312yes—
167#66977C2312yes—
168C2×#4318—44no—
169C2×#4318C2314yes—
170C2×#4318C2314yes—
171C22×C11⋊C8C2314yes—
172#66929—22no—
173#66929—22no—
174#66928—21no—
175#66928—21no—
176#66928C2312yes—
177#66927C2311yescharacteristic
178C4×D44—21no—
179C4×D44—21no—
180C4×D44—21no—
181C4×D44—21no—
182C4×D44C2312yes—
183C4×D44C2312yes—
184#66925—22no—
185#66925—22no—
186#66925—22no—
187C42×D11—22no—
188#66923—21no—
189#66923—21no—
190#66923C2312yes—
191#66922C2311yescharacteristic
192#66922C2311yescharacteristic
193#66922C2311yescharacteristic
194C4×Dic22—21no—
195C4×Dic22—21no—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22C2312yes—
199C4×Dic22C2312yes—
200#66896C2318yes—
201#66896C2318yes—
202#66874C2318yes—
203#66873C2318yes—
204#66872C2318yes—
205#66871C2318yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208C4⋊(C11⋊C8)C2314yes—
209C4⋊(C11⋊C8)C2314yes—
210#60916—111nomaximal, Sylow
211C24×C11—22no—
212C24×C11C2×D411yescharacteristic
213C11×#41—48no—
214C11×#41—48no—
215C11×#41—48no—
216C11×#41—48no—
217C2×Q8×C11—22no—
218C2×Q8×C11—22no—
219C2×Q8×C11—44no—
220C2×D4×C11—24no—
221C2×D4×C11—24no—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—24no—
228C2×D4×C11—24no—
229C2×D4×C11—44no—
230C2×D4×C11—44no—
231C2×D4×C11—48no—
232C2×D4×C11C2414yes—
233C22×C4×C11—24no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—42no—
240C22×C4×C11—48no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262#4339—24no—
263#4339—24no—
264#4339—44no—
265#4339—44no—
266C2×D44—21no—
267C2×D44—21no—
268C2×D44C2412yes—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×Dic22—21no—
273C2×Dic22—21no—
274C2×Dic22C2412yes—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4C2414yes—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C11×C22⋊C4—24no—
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C22⋊Dic11—22no—
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302#4324—48no—
303#4323—48no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11C2412yes—
315C4⋊Dic11C2412yes—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322C4×Dic11—22no—
323C4×Dic11—22no—
324C4×Dic11—22no—
325#4318—28no—
326#4318—44no—
327C2×C11⋊C8—44no—
328C2×C11⋊C8C2418yes—
329#3444—111no—
330C2×#532D1111yescharacteristic, complemented
331#3254—112no—
332#3253—112no—
333#3251—114no—
334#3247—114no—
335#3246—112no—
336#3245—112no—
337#3079—112no—
338#3077—112no—
339#3055—114no—
340#3038—112no—
341#3036—112no—
342C2×#423—111no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—24no—
346C23×C11—41no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11—44no—
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C22×D11—22no—
354Q8×C11—44no—
355Q8×C11—44no—
356D4×C11—24no—
357D4×C11—24no—
358D4×C11—44no—
359D4×C11—44no—
360D4×C11—48no—
361D4×C11—48no—
362D4×C11—44no—
363D4×C11—44no—
364D4×C11—44no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—21no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—24no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—48no—
385C2×C4×C11—44no—
386C2×C4×C11—48no—
387C2×C4×C11AGL(1,ℤ/8)14yescomplemented
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11H(5,𝔽2)12yes—
400C2×C4×C112−1+412yes—
401C2×C4×C11C2511yescharacteristic
402C22⋊D11—44no—
403C22⋊D11—44no—
404C22⋊D11—44no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408D44—22no—
409D44—22no—
410D44—42no—
411D44—42no—
412C4×D11—44no—
413C4×D11—44no—
414C4×D11—44no—
415Dic22—22no—
416Dic22—22no—
417Dic22—42no—
418Dic22—42no—
419C11⋊C8—28no—
420C22×#41—21no—
421C2×AGL(1,ℤ/8)—114no—
422C22×M16—112no—
423#533—111no—
424#533—111no—
425#533—111no—
426#532—21no—
427#532—21no—
428#532—21no—
429#532—21no—
430#532—111no—
431#532—111no—
432#532—111no—
433#532C2×D1112yes—
434#532C2×D1112yes—
435#532C2×D1112yes—
436#532C2×D1112yes—
437C2×C4⋊Q8C2×D1111yescharacteristic
438C2×#127C2×D1111yescharacteristic
439#529—112no—
440#529—112no—
441#529—221no—
442#529—221no—
443#529—221no—
444#529—221no—
445C2×#124—21no—
446#525—112no—
447#525—221no—
448#525—221no—
449C2×#121—21no—
450C2×#121C2×D1112yes—
451C4×#41—112no—
452C4×#41—221no—
453C4×#41—221no—
454C2×C4×D4—21no—
455C2×C4×D4C2×D1112yes—
456C22×C42C2×D1111yescharacteristic
457#478—118no—
458#477—114no—
459#476—114no—
460#476—114no—
461#475—114no—
462#474—114no—
463#474—114no—
464#469—118no—
465#468—118no—
466#466—118no—
467#465—118no—
468#463—118no—
469#461—114no—
470#460—114no—
471#460—114no—
472#459—114no—
473#459—114no—
474#459—114no—
475#428—114no—
476#423—112no—
477#423—112no—
478#423—112no—
479#423—112no—
480C2×C4⋊C8—112no—
481C2×C4⋊C8—112no—
482#418—114no—
483#417—114no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—44no—
492C22×C11—44no—
493C22×C11—44no—
494C22×C11—44no—
495C22×C11—88no—
496C22×C11#53712yes—
497C22×C11C2×AGL(1,ℤ/8)12yes—
498C22×C11C23×D411yescharacteristic
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—44no—
510C4×C11#53712yes—
511C4×C11C2×AGL(1,ℤ/8)12yes—
512C4×C11C2×AGL(1,ℤ/8)12yes—
513C4×C11#57512yes—
514C4×C11C2×H(5,𝔽2)11yescharacteristic
515C4×C11C2×2−1+411yescharacteristic
516Dic11—42no—
517Dic11—42no—
518Dic11—42no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—48no—
524C2×#41—112no—
525C2×#41—221no—
526C2×#41—221no—
527C22×Q8—21no—
528C22×D4—22no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4C22×D1112yes—
532C23×C4—22no—
533C23×C4C22⋊D1111yescharacteristic
534C23×C4C22⋊D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536AGL(1,ℤ/8)—448no—
537C2×SD16—118no—
538C2×D8—118no—
539C2×M16—114no—
540C2×M16—114no—
541C2×M16—444no—
542C22×C8—114no—
543C4⋊Q8—21no—
544C4⋊Q8—21no—
545C4⋊Q8—111no—
546C4⋊Q8—111no—
547C4⋊Q8—111no—
548C4⋊Q8C22×D1112yes—
549C4⋊Q8C22×D1112yes—
550#127—21no—
551#127—21no—
552#127—111no—
553#127C22×D1112yes—
554#127C22×D1112yes—
555#126—222no—
556#126—222no—
557#125—112no—
558#125—221no—
559#125—221no—
560#124—22no—
561#124—22no—
562#124—22no—
563#124—22no—
564#124—112no—
565#124—221no—
566#124—221no—
567#123—222no—
568#123—222no—
569#123—222no—
570C22⋊Q8—112no—
571C22⋊Q8—112no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8—221no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—112no—
583#121—112no—
584#121—221no—
585#121—221no—
586#121—221no—
587#121—221no—
588#121C22×D1114yes—
589#121C22×D1114yes—
590#120—222no—
591C4×Q8—112no—
592C4×Q8—112no—
593C4×Q8—221no—
594C4×Q8—221no—
595C4×Q8—221no—
596C4×Q8—221no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—112no—
604C4×D4—112no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—221no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4C22×D1114yes—
616C4×D4C22×D1114yes—
617#117—112no—
618#117—221no—
619#117—221no—
620#117—222no—
621#117—222no—
622#117—222no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4C22×D1112yes—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C42—222no—
628C2×C42C22⋊D1111yescharacteristic
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640#107—118no—
641#106—118no—
642C4⋊C8—114no—
643C4⋊C8—114no—
644C4⋊C8—114no—
645C4⋊C8—114no—
646#103—118no—
647#102—118no—
648#102—118no—
649#102—118no—
650C2×C11—22no—
651C2×C11—22no—
652C2×C11—41no—
653C2×C11—84no—
654C2×C11C2×#53711yescharacteristic
655C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
656C2×C11C2×#57511yescharacteristic
657D11—82no—
658C24—22no—
659C24C2×C22⋊D1111yescharacteristic
660#41—48no—
661#41—48no—
662#41—48no—
663#41—48no—
664#41—224no—
665#41—224no—
666#41—444no—
667#41—444no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—44no—
671C2×Q8—112no—
672C2×Q8—221no—
673C2×Q8—221no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—48no—
686C2×D4—112no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—221no—
691C2×D4—221no—
692C2×D4C23×D1114yes—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—42no—
700C22×C4—48no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4C2×C22⋊D1111yescharacteristic
705C22×C4C2×C22⋊D1111yescharacteristic
706C22×C4C2×C22⋊D1111yescharacteristic
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C2×C22⋊D1111yescharacteristic
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722SD16—448no—
723D8—448no—
724M16—228no—
725M16—444no—
726C2×C8—118no—
727C2×C8—444no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—112no—
732C4⋊C4—112no—
733C4⋊C4—222no—
734C4⋊C4—222no—
735C4⋊C4—221no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4C23×D1114yes—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C42—222no—
758C42—222no—
759C42—222no—
760C42C2×C22⋊D1111yescharacteristic
761C42C2×C22⋊D1111yescharacteristic
762C42C2×C22⋊D1111yescharacteristic
763C42C2×C22⋊D1111yescharacteristic
764C42C2×C22⋊D1111yescharacteristic
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C11#6091611yescharacteristic, complemented, Sylow
777C23—22no—
778C23—22no—
779C23—24no—
780C23—41no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—222no—
785C23C22×C22⋊D1111yescharacteristic
786C23C22×C22⋊D1111yescharacteristic
787C23C22×C22⋊D1111yescharacteristic
788Q8—44no—
789Q8—44no—
790Q8—222no—
791Q8—222no—
792Q8—442no—
793Q8—442no—
794D4—24no—
795D4—24no—
796D4—44no—
797D4—44no—
798D4—48no—
799D4—48no—
800D4—44no—
801D4—44no—
802D4—44no—
803D4—222no—
804D4—222no—
805D4—442no—
806D4—444no—
807D4—444no—
808D4—444no—
809D4—442no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—24no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—48no—
830C2×C4—44no—
831C2×C4—48no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4#6698514yescomplemented
839C2×C4#6704212yes—
840C2×C4#6704312yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C2×C4C22×C22⋊D1111yescharacteristic
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C24×D1111yescharacteristic
853C8—228no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—88no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22C2×#6698512yes—
870C22#1062336412yes—
871C22C23×C22⋊D1111yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—44no—
880C4—442no—
881C4—442no—
882C4—442no—
883C4C2×#6698512yes—
884C4C2×#6698512yes—
885C4#1062335312yes—
886C4#1062336412yes—
887C4C2×#6704211yescharacteristic
888C4C2×#6704311yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—84no—
893C2—882no—
894C2C2×#1062336411yescharacteristic
895C2C22×#6698511yescharacteristic
896C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#532C2
socleC22×C11C23×D4
hypercenterC2×#532D11
hypocenterC11#60916
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13080003C2semidirect
3. #13079994C2semidirect
4. #13079972C2semidirect
5. #13079936C2semidirect
6. #13079932C2semidirect
7. #13079923C2semidirect
8. #13078425C2semidirect
9. #13078413C2semidirect
10. #13078231C2semidirect
11. #13078092C2semidirect
12. #13078080C2semidirect
13. C2×#10622537C2semidirect
14. C2×C11×#532C2semidirect
41. #10623010C22semidirect
42. #10623010C22semidirect
44. #10623008C22semidirect
45. #10623008C22semidirect
50. #10623001C22semidirect
51. #10623001C22semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622700C22semidirect
56. #10622697C22semidirect
57. #10622688C22semidirect
58. #10622688C22semidirect
59. #10622685C22semidirect
60. #10622685C22semidirect
61. #10622655C22semidirect
62. #10622654C22semidirect
63. #10622652C22semidirect
64. #10622651C22semidirect
65. #10622632C22semidirect
66. #10622629C22semidirect
67. #10622628C22semidirect
68. #10622622C22semidirect
69. #10622621C22semidirect
70. #10622620C22semidirect
75. #10622537C22semidirect
76. #10622537C22semidirect
77. C2×C4⋊(C11⋊C8)C22semidirect
78. C2×C4⋊(C11⋊C8)C22semidirect
330. C2×#532D11semidirect
387. C2×C4×C11AGL(1,ℤ/8)semidirect
776. C11#60916semidirect
838. C2×C4#66985semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130800032
#130799942
#130799722
#130799362
#130799322
#130799232
#130784252
#130784132
#130782312
#130780922
#130780802
C2×#106225372
C2×C11×#5322
#6091611