Finite Group Databasebeta

← #15625272

Subgroups — #15625272

Order 2816.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13079649C214yesmaximal, complemented
3#13079640C212yesmaximal, complemented
4#13079631C212yesmaximal, complemented
5#13079588C214yesmaximal, complemented
6#13079577C214yesmaximal, complemented
7#13079080C212yesmaximal, complemented
8#13079019C212yesmaximal, complemented
9#13078088C212yesmaximal, complemented
10#13078080C212yesmaximal, complemented
11#13077874C212yesmaximal, complemented
12#13077866C212yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C2×C11×#529C211yesmaximal, characteristic, complemented
15C22×#4339C2212yes—
16C11×#529—21no—
17C11×#529—21no—
18C11×#529—21no—
19C11×#529—21no—
20C11×#529C2212yes—
21C11×#529C2212yes—
22C11×#529C2212yescomplemented
23C11×#529C2212yescomplemented
24C2×C11×#126—21no—
25C2×C11×#125C2211yescharacteristic, complemented
26C2×C11×#124C2211yescharacteristic, complemented
27C2×C11×#123—21no—
28C2×C11×C22⋊Q8C2211yescharacteristic
29C2×C11×#121C2211yescharacteristic
30C2×C4×Q8×C11C2211yescharacteristic, complemented
31C2×C4×D4×C11—21no—
32C2×C4×D4×C11C2211yescharacteristic, complemented
33C2×C11×#117—21no—
34C22×C42×C11C2211yescharacteristic
35C2×#66995C2214yescomplemented
36C2×#66985C2214yescomplemented
37C2×#66983—21no—
38C2×#66983—21no—
39#10623008—21no—
40#10623008—21no—
41#10623008—21no—
42#10623008—21no—
43#10623008C2212yes—
44#10623008C2212yes—
45#10623008C2212yescomplemented
46#10623008C2212yescomplemented
47C2×#66928C2212yescomplemented
48C2×#66927C2211yescharacteristic, complemented
49C2×C4×D44—21no—
50C2×C4×D44—21no—
51C2×#66922C2211yescharacteristic, complemented
52#10622820C2212yes—
53#10622682C2214yescomplemented
54#10622681C2218yescomplemented
55#10622680C2214yescomplemented
56#10622673C2214yescomplemented
57#10622672C2218yescomplemented
58#10622671C2214yescomplemented
59#10622663C2214yescomplemented
60#10622660C2218yescomplemented
61#10622659C2214yescomplemented
62#10622653C2214yes—
63#10622650C2218yescomplemented
64#10622649C2214yes—
65#10622644C2214yescomplemented
66#10622641C2218yescomplemented
67#10622640C2214yescomplemented
68#10622632C2214yescomplemented
69#10622629C2218yescomplemented
70#10622628C2214yescomplemented
71#10622579C2214yescomplemented
72#10622579C2214yescomplemented
73#10622539C2212yescomplemented
74#10622539C2212yescomplemented
75#10622538C2212yescomplemented
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11D411yescharacteristic
84C23×C4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—22no—
87C2×#4339—22no—
88C2×#4339—22no—
89C2×#4339—48no—
90C2×#4339C2314yes—
91C2×#4339C2314yes—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44C2312yes—
95C22×C4×D11—22no—
96C22×Dic22C2312yes—
97C11×#126—22no—
98C11×#126—22no—
99C11×#126—22no—
100C11×#126—22no—
101C11×#125—21no—
102C11×#125—21no—
103C11×#125C2312yes—
104C11×#125C2312yes—
105C11×#124—21no—
106C11×#124—21no—
107C11×#124C2312yes—
108C11×#124C2312yes—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—22no—
112C11×#123—22no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8C2312yes—
116C11×C22⋊Q8C2312yes—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121C2312yes—
120C11×#121C2312yes—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11—22no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11C2312yes—
132C4×D4×C11C2312yes—
133C11×#117—22no—
134C11×#117—22no—
135C11×#117—22no—
136C11×#117—22no—
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4—21no—
144C2×C11×C22⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C11×C22⋊C4—21no—
147C2×C11×C22⋊C4—21no—
148C2×C42×C11—21no—
149C2×C42×C11D411yescharacteristic
150C2×C42×C11D411yescharacteristic
151C2×C42×C11D411yescharacteristic
152C2×C42×C11D411yescharacteristic
153C2×C42×C11D411yescharacteristic
154C2×C42×C11D411yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×#4326C2318yes—
162#66995—48no—
163C2×#4325C2318yes—
164C2×#4324C2318yes—
165#66985—48no—
166C2×#4323C2318yes—
167#66983—22no—
168#66983—22no—
169#66983—22no—
170#66983—22no—
171#66983—22no—
172#66983—22no—
173#66983—22no—
174#66983—22no—
175C2×(C2×D11)⋊C4—22no—
176C2×(C2×D11)⋊C4—22no—
177C2×C4⋊Dic11—21no—
178C2×C4⋊Dic11—21no—
179C2×#4318C2314yes—
180#66928—22no—
181#66928—22no—
182#66928C2314yes—
183#66928C2314yes—
184#66927—21no—
185#66927—21no—
186#66927C2312yes—
187#66927C2312yes—
188C4×D44—22no—
189C4×D44—22no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44—22no—
193C4×D44—22no—
194C4×D44—22no—
195C4×D44—22no—
196#66922—21no—
197#66922—21no—
198#66922C2312yes—
199#66922C2312yes—
200C22⋊(C11⋊C8)C2314yes—
201C22⋊(C11⋊C8)C2314yes—
202#66874C2318yes—
203#66874C2318yes—
204#66873C2318yes—
205#66873C2318yes—
206C4⋊(C11⋊C8)C2314yes—
207C4⋊(C11⋊C8)C2314yes—
208#66867C2314yes—
209C4×C11⋊C8C2314yes—
210#60805—111nomaximal, Sylow
211C24×C11—21no—
212C24×C11C2×D411yescharacteristic
213C23×D11—22no—
214C2×Q8×C11—21no—
215C2×Q8×C11—24no—
216C2×Q8×C11C2412yes—
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—21no—
220C2×D4×C11—24no—
221C2×D4×C11—44no—
222C2×D4×C11C2412yes—
223C22×C4×C11—24no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—42no—
230C22×C4×C11—42no—
231C22×C4×C11—44no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—24no—
251C2×C22⋊D11—24no—
252C2×C22⋊D11—48no—
253C22×Dic11—22no—
254#4339—28no—
255#4339—28no—
256#4339—44no—
257#4339—44no—
258#4339—48no—
259#4339—48no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44C2414yes—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—48no—
272C2×Dic22—22no—
273C2×Dic22—44no—
274C2×Dic22C2414yes—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2412yes—
287C11×C22⋊C4—22no—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—22no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C42×C11—22no—
298C42×C11—22no—
299C42×C11C2×D411yescharacteristic
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D411yescharacteristic
302C42×C11C2×D411yescharacteristic
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D411yescharacteristic
306C42×C11C2×D411yescharacteristic
307C42×C11C2×D411yescharacteristic
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2×D411yescharacteristic
311C42×C11C2411yescharacteristic
312C42×C11C2411yescharacteristic
313C42×C11C2411yescharacteristic
314C42×C11C2411yescharacteristic
315#4326—48no—
316#4325—48no—
317#4324—48no—
318#4323—48no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323C4⋊Dic11—22no—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—22no—
327#4318—28no—
328C2×C11⋊C8C2418yes—
329C2×#532—111no—
330C2×#529D1111yescharacteristic, complemented
331#3219—114no—
332#3218—112no—
333#3217—112no—
334#3212—114no—
335#3211—114no—
336#3153—112no—
337#3142—112no—
338#3037—112no—
339#3036—112no—
340#3007—112no—
341#3006—112no—
342#2920—111no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—41no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11—42no—
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C22×D11—24no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357Q8×C11—24no—
358Q8×C11—42no—
359D4×C11—24no—
360D4×C11—44no—
361D4×C11—44no—
362D4×C11—42no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
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—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—44no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—44no—
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)14yes—
400C2×C4×C11C2511yescharacteristic
401C22⋊D11—48no—
402C22⋊D11—48no—
403C2×Dic11—24no—
404C2×Dic11—44no—
405D44—24no—
406D44—24no—
407D44—44no—
408D44—44no—
409D44—44no—
410D44—44no—
411D44—44no—
412C4×D11—48no—
413C4×D11—48no—
414Dic22—24no—
415Dic22—24no—
416Dic22—44no—
417C11⋊C8—28no—
418C22×#41—112no—
419C2×#137—114no—
420C2×AGL(1,ℤ/8)—114no—
421#532—112no—
422#532—112no—
423#532—112no—
424#532—112no—
425#532—221no—
426#532—221no—
427#532—221no—
428#532—221no—
429C2×C4⋊Q8—111no—
430C2×#127—111no—
431#529—21no—
432#529—21no—
433#529—21no—
434#529—21no—
435#529C2×D1112yes—
436#529C2×D1112yes—
437#529C2×D1112yescomplemented
438#529C2×D1112yescomplemented
439C2×#126—21no—
440C2×#125C2×D1111yescharacteristic, complemented
441C2×#124—112no—
442C2×#124C2×D1111yescharacteristic, complemented
443C2×#123—21no—
444C2×C22⋊Q8C2×D1111yescharacteristic
445C2×#121—221no—
446C2×#121—221no—
447C2×#121C2×D1111yescharacteristic
448C2×C4×Q8C2×D1111yescharacteristic, complemented
449C2×C4×D4—21no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4C2×D1111yescharacteristic, complemented
453C2×#117—21no—
454C22×C42C2×D1111yescharacteristic
455#497—114no—
456#496—114no—
457#495—118no—
458#491—114no—
459#490—114no—
460#488—118no—
461#464—118no—
462#463—118no—
463#462—114no—
464#461—114no—
465#460—114no—
466#459—114no—
467#452—118no—
468#451—114no—
469#450—114no—
470#449—118no—
471#448—114no—
472#447—114no—
473#432—112no—
474#432—112no—
475#431—112no—
476#431—112no—
477#423—112no—
478#417—114no—
479#417—114no—
480#407—112no—
481C4×M16—112no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—44no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—84no—
494C22×C11#53512yes—
495C22×C11#57512yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—44no—
498C2×D11—44no—
499C2×D11—44no—
500C2×D11—88no—
501C4×C11—21no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11#53512yes—
514C4×C11#57512yes—
515C4×C11C2×H(5,𝔽2)12yes—
516Dic11—44no—
517C2×#41—114no—
518C2×#41—114no—
519C2×#41—222no—
520C2×#41—222no—
521C2×#41—448no—
522C22×Q8—112no—
523C22×Q8C22×D1111yescharacteristic
524C22×D4—21no—
525C22×D4—112no—
526C22×D4—222no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4C22×D1111yescharacteristic
530C23×C4—21no—
531C23×C4—222no—
532C23×C4C22⋊D1111yescharacteristic
533C23×C4C22⋊D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535#137—448no—
536AGL(1,ℤ/8)—448no—
537C2×Q16—118no—
538C2×SD16—118no—
539C2×SD16—118no—
540C2×D8—118no—
541C2×M16—114no—
542C4⋊Q8—112no—
543C4⋊Q8—112no—
544C4⋊Q8—221no—
545C4⋊Q8—221no—
546#127—112no—
547#127—112no—
548#127—221no—
549#127—221no—
550#126—22no—
551#126—22no—
552#126—22no—
553#126—22no—
554#125—21no—
555#125—21no—
556#125C22×D1112yes—
557#125C22×D1112yes—
558#124—21no—
559#124—21no—
560#124—114no—
561#124—114no—
562#124—222no—
563#124—222no—
564#124C22×D1112yes—
565#124C22×D1112yes—
566#123—22no—
567#123—22no—
568#123—22no—
569#123—22no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8C22×D1112yes—
573C22⋊Q8C22×D1112yes—
574#121—21no—
575#121—21no—
576#121—222no—
577#121—222no—
578#121—222no—
579#121—222no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121—222no—
584#121C22×D1112yes—
585#121C22×D1112yes—
586C4×Q8—21no—
587C4×Q8—21no—
588C4×Q8C22×D1112yes—
589C4×Q8C22×D1112yes—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4C22×D1112yes—
605C4×D4C22×D1112yes—
606#117—22no—
607#117—22no—
608#117—22no—
609#117—22no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4C22×D1111yescharacteristic
617C2×C4⋊C4C22×D1111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C42—21no—
626C2×C42C22⋊D1111yescharacteristic
627C2×C42C22⋊D1111yescharacteristic
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
638C4⋊C8—114no—
639C4⋊C8—114no—
640#103—118no—
641#103—118no—
642#102—118no—
643#102—118no—
644C22⋊C8—114no—
645C22⋊C8—114no—
646#97—114no—
647C4×C8—114no—
648C2×C11—22no—
649C2×C11—22no—
650C2×C11—41no—
651C2×C11—82no—
652C2×C11C2×#53511yescharacteristic
653C2×C11C2×#57511yescharacteristic
654C2×C11C2×#57511yescharacteristic
655D11—84no—
656C24—21no—
657C24—222no—
658C24C2×C22⋊D1111yescharacteristic
659#41—228no—
660#41—228no—
661#41—444no—
662#41—444no—
663#41—448no—
664#41—448no—
665C2×Q8—21no—
666C2×Q8—24no—
667C2×Q8—114no—
668C2×Q8—222no—
669C2×Q8—444no—
670C2×Q8C23×D1112yes—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—24no—
674C2×D4—21no—
675C2×D4—44no—
676C2×D4—114no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—222no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—448no—
688C2×D4C23×D1112yes—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—44no—
698C22×C4—222no—
699C22×C4—224no—
700C22×C4—224no—
701C22×C4—448no—
702C22×C4C2×C22⋊D1111yescharacteristic
703C22×C4C2×C22⋊D1111yescharacteristic
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×C4C23×D1111yescharacteristic
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720Q16—448no—
721SD16—448no—
722SD16—448no—
723D8—448no—
724M16—228no—
725C2×C8—118no—
726C4⋊C4—22no—
727C4⋊C4—22no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4C23×D1112yes—
741C4⋊C4C23×D1112yes—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—224no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C42—22no—
757C42—22no—
758C42C2×C22⋊D1111yescharacteristic
759C42C2×C22⋊D1111yescharacteristic
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
770C42C23×D1111yescharacteristic
771C42C23×D1111yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C11#6080511yescharacteristic, complemented, Sylow
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—224no—
783C23—444no—
784C23—444no—
785C23—444no—
786C23C22×C22⋊D1111yescharacteristic
787C23C22×C22⋊D1111yescharacteristic
788C23C22×C22⋊D1111yescharacteristic
789Q8—24no—
790Q8—42no—
791Q8—224no—
792Q8—224no—
793Q8—444no—
794D4—24no—
795D4—44no—
796D4—44no—
797D4—42no—
798D4—224no—
799D4—224no—
800D4—444no—
801D4—444no—
802D4—444no—
803D4—444no—
804D4—448no—
805D4—448no—
806D4—444no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
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—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—224no—
833C2×C4—448no—
834C2×C4—444no—
835C2×C4—448no—
836C2×C4#6704214yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
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×C4C24×D1111yescharacteristic
849C8—228no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—444no—
863C22—444no—
864C22—444no—
865C22—888no—
866C22#1062335312yes—
867C22#1062336112yes—
868C22C23×C22⋊D1111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—444no—
882C4#1062335312yes—
883C4#1062336112yes—
884C4C2×#6704212yes—
885C2—22no—
886C2—22no—
887C2—41no—
888C2—82no—
889C2—884no—
890C2C2×#1062336111yescharacteristic
891C2C2×#1062335311yescharacteristic
892C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC22×C11C23×D4
hypercenterC2×#529D11
hypocenterC11#60805
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079649C2semidirect
3. #13079640C2semidirect
4. #13079631C2semidirect
5. #13079588C2semidirect
6. #13079577C2semidirect
7. #13079080C2semidirect
8. #13079019C2semidirect
9. #13078088C2semidirect
10. #13078080C2semidirect
11. #13077874C2semidirect
12. #13077866C2semidirect
13. #13077249C2semidirect
14. C2×C11×#529C2semidirect
22. C11×#529C22semidirect
23. C11×#529C22semidirect
25. C2×C11×#125C22semidirect
26. C2×C11×#124C22semidirect
30. C2×C4×Q8×C11C22semidirect
32. C2×C4×D4×C11C22semidirect
35. C2×#66995C22semidirect
36. C2×#66985C22semidirect
45. #10623008C22semidirect
46. #10623008C22semidirect
47. C2×#66928C22semidirect
48. C2×#66927C22semidirect
51. C2×#66922C22semidirect
53. #10622682C22semidirect
54. #10622681C22semidirect
55. #10622680C22semidirect
56. #10622673C22semidirect
57. #10622672C22semidirect
58. #10622671C22semidirect
59. #10622663C22semidirect
60. #10622660C22semidirect
61. #10622659C22semidirect
63. #10622650C22semidirect
65. #10622644C22semidirect
66. #10622641C22semidirect
67. #10622640C22semidirect
68. #10622632C22semidirect
69. #10622629C22semidirect
70. #10622628C22semidirect
71. #10622579C22semidirect
72. #10622579C22semidirect
73. #10622539C22semidirect
74. #10622539C22semidirect
75. #10622538C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
330. C2×#529D11semidirect
437. #529C2×D11semidirect
438. #529C2×D11semidirect
440. C2×#125C2×D11semidirect
442. C2×#124C2×D11semidirect
448. C2×C4×Q8C2×D11semidirect
452. C2×C4×D4C2×D11semidirect
774. C11#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130796492
#130796402
#130796312
#130795882
#130795772
#130790802
#130790192
#130780882
#130780802
#130778742
#130778662
#130772492
C2×C11×#5292
#6080511