Finite Group Databasebeta

← #15632596

Subgroups — #15632596

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic
2C2×#10623110C211yesmaximal, characteristic, complemented
3#13081244C212yesmaximal, complemented
4#13081233C212yesmaximal, complemented
5#13081106C214yesmaximal, complemented
6#13081076C214yesmaximal, complemented
7#13081010C212yesmaximal, complemented
8#13080975C212yesmaximal, complemented
9#13079162C211yesmaximal, characteristic, complemented
10#13078562C212yesmaximal, complemented
11#13078537C212yesmaximal, complemented
12#13078431C211yesmaximal, characteristic, complemented
13#13078421C211yesmaximal, characteristic, complemented
14#13078240C212yesmaximal, complemented
15M16×D44C211yesmaximal, characteristic, complemented
16D11×#428C212yesmaximal, complemented
17C4×C11×#137C211yesmaximal, characteristic, complemented
18C2×C11×#137C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21#10623359C2212yes—
22C2×#66999C2212yes—
23C2×M16×D11C2212yes—
24#10623115C2211yescharacteristic
25#10623112C2212yes—
26#10623110—21no—
27#10623110—21no—
28#10623110—22no—
29#10623110C2214yes—
30#10623110C2212yes—
31#10623110C2212yes—
32#10623110C2211yescharacteristic
33#10623094C2211yescharacteristic
34#10623089C2212yes—
35#10623087—22no—
36#10623082C2211yescharacteristic
37#10623081—21no—
38#10623072—21no—
39#10623059—22no—
40D11×#117C2212yes—
41C2×#66949—22no—
42C2×C4⋊C4×D11C2212yes—
43#10623010—21no—
44C4×#4339—21no—
45C2×C4×D44—21no—
46C2×C4×D44C2211yescharacteristic
47#10623001C2211yescharacteristic
48C2×#66923—21no—
49C2×#66922C2211yescharacteristic
50C11×#441C2212yescomplemented
51C11×#440C2212yescomplemented
52C4×C11×Q16C2212yescomplemented
53C4×C11×SD16C2212yescomplemented
54C11×#428C2211yescharacteristic
55C11×#419C2211yescharacteristic
56C11×#417C2211yescharacteristic
57C4×C11×M16C2211yescharacteristic
58#10622845C2212yes—
59#10622838C2212yes—
60#10622802C2214yescomplemented
61#10622801C2214yescomplemented
62#10622787C2214yescomplemented
63#10622784C2214yescomplemented
64#10622739C2212yes—
65#10622734C2212yes—
66#10622734C2212yes—
67#10622635C2214yescomplemented
68#10622634C2212yescomplemented
69#10622634C2212yescomplemented
70#10622633C2212yescomplemented
71#10622633C2212yescomplemented
72#10622621C2212yescomplemented
73#10622620C2212yescomplemented
74#10622608C2212yes—
75#10622577C2212yes—
76#10622537C2211yescharacteristic
77#10622494C2214yescomplemented
78D11×#107C2214yescomplemented
79#10622474C2214yescomplemented
80D11×#106C2214yescomplemented
81#10622428C2214yescomplemented
82#10622427C2214yescomplemented
83#10622422C2214yescomplemented
84#10622422C2214yescomplemented
85#10622418C2214yescomplemented
86#10622418C2214yescomplemented
87#10622390C2214yescomplemented
88#10622387C2214yescomplemented
89#10622319C2214yes—
90#10622315C2214yescomplemented
91#10622301C2212yes—
92C8×D44C2212yes—
93#10622295C2212yescomplemented
94#10622293C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C2×#4339—21no—
98C22×D44D411yescharacteristic
99C22×C4×D11—22no—
100C22×C4×D11C2312yes—
101C22×Dic22—21no—
102C11×#137—24no—
103C2×C11×Q16C2312yes—
104C2×C11×SD16C2312yes—
105C2×C11×M16C2311yescharacteristic
106C2×C11×M16C2311yescharacteristic
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11C2312yes—
110C4×Q8×C11C2312yes—
111C4×Q8×C11C2311yescharacteristic
112C4×Q8×C11C2311yescharacteristic
113C4×D4×C11—21no—
114C4×D4×C11—21no—
115C4×D4×C11C2311yescharacteristic
116C4×D4×C11C2311yescharacteristic
117C11×#117—21no—
118C11×#117C2311yescharacteristic
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124#66999—22no—
125#66999—22no—
126#66999C2314yes—
127#66999C2314yes—
128#66999C2312yes—
129#66999C2312yes—
130#66991C2312yes—
131#66991C2312yes—
132#66990—22no—
133#66988—22no—
134#66983—21no—
135#66982—22no—
136C4×C22⋊D11—22no—
137C4×C22⋊D11—22no—
138C4×C22⋊D11—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4D412yes—
141#66979—21no—
142#66979C2312yes—
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11D411yescharacteristic
145C2×C4⋊Dic11C2312yes—
146#66977—21no—
147#66977—21no—
148#66977—21no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×#4318C2312yes—
152M16×D11—28no—
153C2×#4313C2314yes—
154C2×C8×D11C2314yes—
155#66951—22no—
156#66949—24no—
157#66949—24no—
158#66949—24no—
159#66949—24no—
160#66949—22no—
161#66947—22no—
162#66945C2312yes—
163#66945C2312yes—
164C4⋊C4×D11—22no—
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2312yes—
167C4⋊C4×D11C2314yes—
168C4⋊C4×D11C2314yes—
169C4⋊C4×D11C2312yes—
170#66942—22no—
171#66938—22no—
172#66937—22no—
173#66936—22no—
174C22⋊C4×D11—22no—
175#66932—22no—
176#66930—22no—
177#66929—22no—
178#66928—21no—
179C4×D44—22no—
180C4×D44—24no—
181C4×D44—22no—
182C4×D44—21no—
183C4×D44D411yescharacteristic
184C4×D44D411yescharacteristic
185C4×D44D412yes—
186C4×D44C2311yescharacteristic
187C4×D44C2311yescharacteristic
188C4×D44C2312yes—
189#66925—22no—
190#66925—22no—
191C42×D11—22no—
192#66923—22no—
193#66923—22no—
194#66923—24no—
195#66923—21no—
196#66923C2312yes—
197#66922—21no—
198#66922—21no—
199#66922C2312yes—
200#66922C2312yes—
201#66922C2311yescharacteristic
202#66922C2311yescharacteristic
203C4×Dic22—21no—
204C4×Dic22—21no—
205C4×Dic22—21no—
206C11×#107C2312yes—
207C11×#106C2312yes—
208C11×#103C2312yes—
209C11×#103C2312yes—
210C11×#103C2312yes—
211C11×#102C2312yes—
212C11×#97C2312yes—
213C4×C8×C11C2312yes—
214#66899C2314yes—
215#66899C2314yes—
216#66899C2314yes—
217#66896C2314yes—
218(C2×D11)⋊C8C2314yes—
219(C2×D11)⋊C8C2314yes—
220#66882C2314yes—
221#66882C2314yes—
222#66881C2314yes—
223#66881C2314yes—
224#66872C2314yes—
225#66872C2314yes—
226#66871C2314yes—
227#66871C2314yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230#61254—111nomaximal, Sylow
231C23×D11C2×D412yes—
232C11×#41—22no—
233C11×#41—22no—
234C2×Q8×C11—21no—
235C2×Q8×C11—22no—
236C2×Q8×C11—22no—
237C2×Q8×C11C2412yes—
238C2×Q8×C11C2411yescharacteristic
239C2×D4×C11—21no—
240C2×D4×C11C2411yescharacteristic
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—22no—
250C2×C22⋊D11—22no—
251C22×Dic11—22no—
252C22×Dic11C2×D412yes—
253#4339—44no—
254C2×D44—24no—
255C2×D44C2×D411yescharacteristic
256C2×D44C2×D412yes—
257C2×D44C2×D411yescharacteristic
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—24no—
261C2×C4×D11—24no—
262C2×C4×D11—24no—
263C2×C4×D11—24no—
264C2×C4×D11—84no—
265C2×C4×D11C2×D412yes—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2412yes—
268C2×C4×D11C2412yes—
269C2×Dic22—21no—
270C2×Dic22—21no—
271C2×Dic22—22no—
272C2×Dic22—22no—
273C2×Dic22—82no—
274C11×Q16—24no—
275C11×SD16—24no—
276C11×M16—22no—
277C11×M16#4114yescomplemented
278C2×C8×C11C2412yes—
279C2×C8×C11C2412yes—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4C2411yescharacteristic
286C11×C4⋊C4C2412yes—
287C11×C4⋊C4C2411yescharacteristic
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C42×C11—21no—
292C42×C11—22no—
293C42×C11—22no—
294C42×C11—21no—
295C42×C11—21no—
296C42×C11C2×D411yescharacteristic
297C42×C11C2×D411yescharacteristic
298C42×C11C2411yescharacteristic
299C42×C11C2411yescharacteristic
300C22⋊Dic11—22no—
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4C2×D412yes—
310(C2×D11)⋊C4C2×D412yes—
311(C2×D11)⋊C4C2×D412yes—
312(C2×D11)⋊C4C2×D412yes—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11C2×D411yescharacteristic
319C4⋊Dic11C2×D411yescharacteristic
320C4⋊Dic11C2×D412yes—
321C4⋊Dic11C2412yes—
322C4⋊Dic11C2414yes—
323C4⋊Dic11C2412yes—
324Dic11⋊C4—22no—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336C4×Dic11—22no—
337#4318—24no—
338C2×C11⋊C8C2414yes—
339#4313—28no—
340C8×D11—28no—
341#3475—111no—
342C2×#554—111no—
343#3357—112no—
344#3356—112no—
345#3346—114no—
346#3344—114no—
347#3338—112no—
348#3335—112no—
349#3165—111no—
350#3095—112no—
351#3092—112no—
352#3079—111no—
353#3078—111no—
354#3056—112no—
355C4×#137D1111yescharacteristic, complemented
356D4×M16—111no—
357C2×#428—112no—
358C23×C11—21no—
359C23×C11C22×D411yescharacteristic
360C22×D11—24no—
361C22×D11—24no—
362C22×D11—42no—
363C22×D11C22×D412yes—
364C22×D11C22×D412yes—
365Q8×C11—22no—
366Q8×C11—21no—
367Q8×C11—22no—
368Q8×C11—21no—
369Q8×C11—42no—
370D4×C11—21no—
371D4×C11—21no—
372D4×C11—42no—
373C2×C4×C11—22no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—41no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11—42no—
383C2×C4×C11—42no—
384C2×C4×C11—81no—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C2×#4112yes—
391C2×C4×C112−1+412yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—44no—
394C22⋊D11—82no—
395C2×Dic11—24no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—24no—
399C2×Dic11—44no—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402D44—24no—
403D44—22no—
404D44#13714yescomplemented
405C4×D11—24no—
406C4×D11—24no—
407C4×D11—22no—
408C4×D11—22no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—44no—
412C4×D11—82no—
413C4×D11—84no—
414C4×D11—84no—
415Dic22—42no—
416Dic22—81no—
417Dic22—82no—
418Dic22—82no—
419C8×C11—22no—
420C8×C11C2×#4114yes—
421C11⋊C8—24no—
422C2×#137C2×D1111yescharacteristic
423C22×M16—112no—
424#556—111no—
425#555—111no—
426#554—112no—
427#554—111no—
428#554—114no—
429#554—112no—
430#554—221no—
431#554—222no—
432#554—221no—
433#553—112no—
434#552—112no—
435#552—221no—
436#551—222no—
437#547—111no—
438#546—221no—
439#533—111no—
440C2×C4⋊Q8—111no—
441#529—221no—
442#529—222no—
443C2×#125—221no—
444#525—112no—
445C2×C22⋊Q8—112no—
446C2×C22⋊Q8—222no—
447C4×#41—221no—
448C4×#41C2×D1111yescharacteristic
449C2×C4×Q8C2×D1111yescharacteristic
450C2×C4×D4—111no—
451C2×C4×D4—221no—
452C2×#117—112no—
453C22×C4⋊C4—112no—
454#501—114no—
455#500—112no—
456#498—112no—
457#485—114no—
458#485—114no—
459#484—114no—
460#484—114no—
461#483—114no—
462#483—114no—
463#481—114no—
464#480—114no—
465#479—114no—
466#477—112no—
467#477—112no—
468#476—112no—
469#475—112no—
470#475—112no—
471#474—112no—
472#470—114no—
473#468—114no—
474#467—114no—
475#465—114no—
476#441C2×D1112yescomplemented
477#440C2×D1112yescomplemented
478C4×Q16C2×D1112yescomplemented
479C4×SD16C2×D1112yescomplemented
480#436—112no—
481#435—114no—
482C8×D4—112no—
483#428—112no—
484#428—112no—
485#428—112no—
486#428—112no—
487#428—114no—
488#428—114no—
489#428C2×D1111yescharacteristic
490C2×#107—114no—
491C2×#106—114no—
492#423—111no—
493#419—112no—
494#419C2×D1111yescharacteristic
495#417—112no—
496#417C2×D1111yescharacteristic
497#407—112no—
498C4×M16C2×D1111yescharacteristic
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—41no—
502C22×C11—41no—
503C22×C11—41no—
504C22×C11#54712yes—
505C22×C11C23×D411yescharacteristic
506C2×D11—22no—
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—48no—
512C2×D11C2×#13714yes—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11—42no—
517C4×C11—41no—
518C4×C11—41no—
519C4×C11—42no—
520C4×C11—41no—
521C4×C11#54712yes—
522C4×C11C2×#13712yes—
523C4×C11C22×#4111yescharacteristic
524C4×C11C2×2−1+411yescharacteristic
525Dic11—22no—
526Dic11—22no—
527Dic11—44no—
528Dic11—42no—
529Dic11—42no—
530C2×#41—221no—
531C2×#41C22×D1111yescharacteristic
532C22×Q8—221no—
533C22×Q8C22×D1111yescharacteristic
534C22×D4—111no—
535C23×C4—112no—
536C23×C4—222no—
537#137—24no—
538C2×Q16C22×D1112yes—
539C2×SD16C22×D1112yes—
540C2×M16—112no—
541C2×M16—114no—
542C2×M16—228no—
543C2×M16C22×D1111yescharacteristic
544C2×M16C22×D1111yescharacteristic
545C22×C8—114no—
546C4⋊Q8—112no—
547C4⋊Q8—112no—
548C4⋊Q8—111no—
549C4⋊Q8—111no—
550C4⋊Q8—221no—
551C4⋊Q8—221no—
552#126—222no—
553#126—222no—
554#126—222no—
555#125—112no—
556#125—222no—
557#125—222no—
558#125—224no—
559#125—221no—
560#125—222no—
561#124—221no—
562#124—222no—
563#123—222no—
564#123—222no—
565#123—222no—
566#123—222no—
567C22⋊Q8—114no—
568C22⋊Q8—114no—
569C22⋊Q8—112no—
570C22⋊Q8—112no—
571C22⋊Q8—224no—
572C22⋊Q8—224no—
573C22⋊Q8—224no—
574C22⋊Q8—224no—
575C22⋊Q8—222no—
576C22⋊Q8—221no—
577C22⋊Q8—222no—
578C22⋊Q8—222no—
579C22⋊Q8—221no—
580C22⋊Q8—221no—
581#121—112no—
582#121—112no—
583#121—222no—
584#121—221no—
585#120—222no—
586C4×Q8—21no—
587C4×Q8—21no—
588C4×Q8—221no—
589C4×Q8—221no—
590C4×Q8—221no—
591C4×Q8C22×D1112yes—
592C4×Q8C22×D1112yes—
593C4×Q8C22×D1111yescharacteristic
594C4×Q8C22×D1111yescharacteristic
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—111no—
598C4×D4—111no—
599C4×D4—112no—
600C4×D4—111no—
601C4×D4—112no—
602C4×D4—111no—
603C4×D4—222no—
604C4×D4—224no—
605C4×D4—222no—
606C4×D4—221no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4C22×D1111yescharacteristic
611C4×D4C22×D1111yescharacteristic
612#117—21no—
613#117—112no—
614#117—112no—
615#117—112no—
616#117—222no—
617#117—222no—
618#117—222no—
619#117—221no—
620#117C22×D1111yescharacteristic
621C2×C4⋊C4—21no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—114no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4—222no—
631C2×C4⋊C4—222no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C22⋊C4—112no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—222no—
640C2×C42C22×D1111yescharacteristic
641#107—114no—
642#107—114no—
643#107—114no—
644#107—114no—
645#107C22×D1112yes—
646#106—114no—
647#106—114no—
648#106—114no—
649#106—114no—
650#106C22×D1112yes—
651C4⋊C8—112no—
652C4⋊C8—112no—
653#103—114no—
654#103—114no—
655#103—114no—
656#103C22×D1112yes—
657#103C22×D1112yes—
658#103C22×D1112yes—
659#102—114no—
660#102C22×D1112yes—
661C22⋊C8—114no—
662C22⋊C8—114no—
663#97C22×D1112yes—
664C4×C8C22×D1112yes—
665C2×C11—22no—
666C2×C11—81no—
667C2×C11C2×#54711yescharacteristic
668C2×C11C22×#13711yescharacteristic
669C2×C11#358511yescharacteristic
670D11—24no—
671D11—42no—
672C24—112no—
673#41—22no—
674#41—22no—
675#41—444no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—221no—
680C2×Q8—221no—
681C2×Q8—222no—
682C2×Q8—222no—
683C2×Q8—882no—
684C2×Q8C23×D1112yes—
685C2×Q8C23×D1111yescharacteristic
686C2×D4—21no—
687C2×D4—111no—
688C2×D4—112no—
689C2×D4—111no—
690C2×D4—224no—
691C2×D4—222no—
692C2×D4—222no—
693C2×D4C23×D1111yescharacteristic
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—224no—
707C22×C4—224no—
708C22×C4—224no—
709C22×C4—224no—
710C22×C4—222no—
711C22×C4—884no—
712C22×C4D4×D1111yescharacteristic
713C22×C4D4×D1111yescharacteristic
714C22×C4C23×D1111yescharacteristic
715Q16—24no—
716SD16—24no—
717M16—22no—
718M16—224no—
719M16—228no—
720M16#433914yescomplemented
721C2×C8—114no—
722C2×C8—228no—
723C2×C8C23×D1112yes—
724C2×C8C23×D1112yes—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—111no—
731C4⋊C4—111no—
732C4⋊C4—112no—
733C4⋊C4—114no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—221no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—221no—
751C4⋊C4C23×D1112yes—
752C4⋊C4C23×D1111yescharacteristic
753C4⋊C4C23×D1111yescharacteristic
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—112no—
758C22⋊C4—112no—
759C22⋊C4—112no—
760C22⋊C4—112no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—222no—
766C22⋊C4—222no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—22no—
774C42—22no—
775C42—222no—
776C42—222no—
777C42—222no—
778C42D4×D1111yescharacteristic
779C42D4×D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C42C23×D1111yescharacteristic
782C11#6125411yescharacteristic, complemented, Sylow
783C23—21no—
784C23—112no—
785C23—112no—
786C23—224no—
787C23—224no—
788C23—442no—
789C23C2×D4×D1111yescharacteristic
790Q8—22no—
791Q8—21no—
792Q8—22no—
793Q8—21no—
794Q8—42no—
795Q8—442no—
796Q8—882no—
797Q8—882no—
798Q8—881no—
799D4—21no—
800D4—21no—
801D4—42no—
802D4—114no—
803D4—224no—
804D4—222no—
805D4—444no—
806D4—882no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—81no—
819C2×C4—112no—
820C2×C4—112no—
821C2×C4—224no—
822C2×C4—224no—
823C2×C4—224no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—224no—
831C2×C4—444no—
832C2×C4—444no—
833C2×C4—884no—
834C2×C4—884no—
835C2×C4—882no—
836C2×C4C2×#433912yes—
837C2×C4C2×D4×D1111yescharacteristic
838C2×C4C2×D4×D1111yescharacteristic
839C2×C4C2×D4×D1111yescharacteristic
840C2×C4C2×D4×D1111yescharacteristic
841C2×C4C2×D4×D1111yescharacteristic
842C2×C4#6704312yes—
843C2×C4C24×D1111yescharacteristic
844C8—22no—
845C8—224no—
846C8C2×#433914yes—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—114no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—448no—
859C22#1062308212yes—
860C22C22×D4×D1111yescharacteristic
861C4—21no—
862C4—21no—
863C4—21no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—42no—
869C4—222no—
870C4—222no—
871C4—444no—
872C4—442no—
873C4—442no—
874C4#1062308212yes—
875C4D11×#13712yes—
876C4C22×#433911yescharacteristic
877C4C2×#6704311yescharacteristic
878C2—22no—
879C2—81no—
880C2—224no—
881C2—442no—
882C2C2×#1062308211yescharacteristic
883C2C2×D11×#13711yescharacteristic
884C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radical#13082180C2
hypercenterC4×#137D11
hypocenterC11#61254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10623110C2semidirect
3. #13081244C2semidirect
4. #13081233C2semidirect
5. #13081106C2semidirect
6. #13081076C2semidirect
7. #13081010C2semidirect
8. #13080975C2semidirect
9. #13079162C2semidirect
10. #13078562C2semidirect
11. #13078537C2semidirect
12. #13078431C2semidirect
13. #13078421C2semidirect
14. #13078240C2semidirect
15. M16×D44C2semidirect
16. D11×#428C2semidirect
17. C4×C11×#137C2semidirect
50. C11×#441C22semidirect
51. C11×#440C22semidirect
52. C4×C11×Q16C22semidirect
53. C4×C11×SD16C22semidirect
60. #10622802C22semidirect
61. #10622801C22semidirect
62. #10622787C22semidirect
63. #10622784C22semidirect
67. #10622635C22semidirect
68. #10622634C22semidirect
69. #10622634C22semidirect
70. #10622633C22semidirect
71. #10622633C22semidirect
72. #10622621C22semidirect
73. #10622620C22semidirect
77. #10622494C22semidirect
78. D11×#107C22semidirect
79. #10622474C22semidirect
80. D11×#106C22semidirect
81. #10622428C22semidirect
82. #10622427C22semidirect
83. #10622422C22semidirect
84. #10622422C22semidirect
85. #10622418C22semidirect
86. #10622418C22semidirect
87. #10622390C22semidirect
88. #10622387C22semidirect
90. #10622315C22semidirect
93. #10622295C22semidirect
94. #10622293C22semidirect
277. C11×M16#41semidirect
355. C4×#137D11semidirect
404. D44#137semidirect
476. #441C2×D11semidirect
477. #440C2×D11semidirect
478. C4×Q16C2×D11semidirect
479. C4×SD16C2×D11semidirect
720. M16#4339semidirect
782. C11#61254semidirect

Maximal subgroups

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

subgroupindex
#130821802
C2×#106231102
#130812442
#130812332
#130811062
#130810762
#130810102
#130809752
#130791622
#130785622
#130785372
#130784312
#130784212
#130782402
M16×D442
D11×#4282
C4×C11×#1372
#6125411