Finite Group Databasebeta

← #15633699

Subgroups — #15633699

Order 2816.

1878 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic, complemented
2#13081426C212yesmaximal, complemented
3#13081404C212yesmaximal, complemented
4#13081378C214yesmaximal, complemented
5#13081363C214yesmaximal, complemented
6#13081308C212yesmaximal, complemented
7#13081272C212yesmaximal, complemented
8#13079002C212yesmaximal, complemented
9#13078990C211yesmaximal, characteristic, complemented
10#13078421C211yesmaximal, characteristic, complemented
11#13078413C212yesmaximal, complemented
12#13078106C212yesmaximal, complemented
13#13078092C211yesmaximal, characteristic
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66995C211yesmaximal, characteristic, complemented
16C4×#66985C212yesmaximal, complemented
17C2×C11×#559C211yesmaximal, characteristic, complemented
18C11×#559—21no—
19C11×#559—21no—
20C11×#559—22no—
21C11×#559C2214yes—
22C11×#559C2212yes—
23C11×#559C2212yes—
24C2×C11×#127C2211yescharacteristic
25C2×C11×#124—21no—
26C2×C11×#124C2212yes—
27C2×C11×#123—22no—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2212yes—
32Q8×C22⋊D11—21no—
33C2×#66995C2211yescharacteristic
34C2×#66985C2212yes—
35#10623110C2212yescomplemented
36#10623110C2211yescharacteristic, complemented
37#10623109—22no—
38#10623109—21no—
39Q8×D44C2211yescharacteristic, complemented
40C4×Q8×D11—21no—
41#10623098C2212yescomplemented
42#10623098C2211yescharacteristic, complemented
43Q8×Dic22C2211yescharacteristic, complemented
44#10623042—21no—
45#10623042—22no—
46C4×#4339C2211yescharacteristic
47C4×#4339C2212yes—
48#10623001C2212yes—
49#10623001C2211yescharacteristic
50#10622838C2212yes—
51#10622838C2211yescharacteristic
52#10622828C2212yes—
53#10622828C2212yes—
54#10622828C2212yes—
55#10622688C2212yes—
56#10622688C2212yes—
57#10622685C2212yes—
58#10622685C2212yes—
59#10622684C2214yes—
60#10622683C2212yes—
61#10622683C2212yes—
62#10622670C2214yescomplemented
63#10622670C2214yescomplemented
64#10622669C2214yescomplemented
65#10622669C2214yescomplemented
66#10622668C2214yescomplemented
67#10622668C2214yescomplemented
68#10622667C2214yescomplemented
69#10622667C2214yescomplemented
70#10622643C2212yescomplemented
71C4×#4326C2212yescomplemented
72#10622639C2212yescomplemented
73C4×#4325C2212yescomplemented
74#10622637C2214yescomplemented
75#10622637C2212yescomplemented
76Q8×C11⋊C8C2212yescomplemented
77#10622635C2214yescomplemented
78#10622634C2212yescomplemented
79#10622633C2212yescomplemented
80#10622631C2214yescomplemented
81C4×#4324C2214yescomplemented
82#10622627C2214yescomplemented
83C4×#4323C2214yescomplemented
84#10622622C2214yescomplemented
85#10622622C2214yescomplemented
86#10622621C2214yescomplemented
87#10622620C2214yescomplemented
88#10622579C2211yescharacteristic
89#10622577C2211yescharacteristic
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2212yes—
94C4×#4318C2211yescharacteristic
95C22×Q8×C11D411yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11C2312yes—
100C23×C4×C11—22no—
101C2×Q8×D11—21no—
102C2×#4339C2311yescharacteristic
103C11×#127—21no—
104C11×#127—21no—
105C11×#127C2312yes—
106C11×#127C2312yes—
107C11×#124—22no—
108C11×#124—22no—
109C11×#124—24no—
110C11×#124—22no—
111C11×#124—22no—
112C11×#124C2314yes—
113C11×#124C2314yes—
114C11×#123—24no—
115C11×#123—24no—
116C11×#123—24no—
117C11×#123—24no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11D411yescharacteristic
121C4×Q8×C11D412yes—
122C4×Q8×C11D411yescharacteristic
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×Q8×C11C2311yescharacteristic
126C4×Q8×C11C2311yescharacteristic
127C4×Q8×C11C2312yes—
128C4×D4×C11—22no—
129C4×D4×C11—22no—
130C4×D4×C11—24no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11C2314yes—
134C4×D4×C11C2314yes—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4D412yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4—22no—
140C2×C11×C22⋊C4—22no—
141C2×C11×C22⋊C4—22no—
142C2×C42×C11—21no—
143C2×C42×C11C2312yes—
144C2×C42×C11C2311yescharacteristic
145#66999—21no—
146#66999—22no—
147Q8×Dic11—21no—
148#66997—21no—
149#66997—22no—
150C2×#4326C2312yes—
151#66995—24no—
152C2×#4325C2312yes—
153C2×#4324C2314yes—
154#66985—28no—
155C2×#4323C2314yes—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—21no—
158C4×C22⋊D11—21no—
159C4×C22⋊D11—22no—
160#66979C2311yescharacteristic
161#66979C2312yes—
162#66977—22no—
163#66977—21no—
164#66977—21no—
165#66977—22no—
166C2×#4318C2311yescharacteristic
167C2×#4318C2312yes—
168C2×#4318C2311yescharacteristic
169#66950—21no—
170#66950—22no—
171#66949—22no—
172#66949—22no—
173#66949—22no—
174C4⋊C4×D11—21no—
175C4⋊C4×D11—22no—
176#66942—22no—
177#66942—22no—
178#66942—22no—
179#66941—21no—
180#66941—22no—
181#66940—21no—
182#66940—22no—
183C4×D44C2312yes—
184C4×D44C2311yescharacteristic
185C4×D44C2312yes—
186C4×D44C2311yescharacteristic
187#66925—22no—
188#66925—21no—
189C42×D11—22no—
190C42×D11—21no—
191#66923C2312yes—
192#66923C2312yes—
193#66923C2312yes—
194#66922C2312yes—
195#66922C2311yescharacteristic
196#66922C2312yes—
197#66922C2311yescharacteristic
198C4×Dic22—22no—
199C4×Dic22—21no—
200C4×Dic22—22no—
201C4×Dic22—21no—
202C4×Dic22C2312yes—
203C4×Dic22C2311yescharacteristic
204C4×Dic22C2312yes—
205C4×Dic22C2311yescharacteristic
206#66899C2314yes—
207#66899C2314yes—
208#66899C2312yes—
209#66899C2312yes—
210#66896C2314yes—
211#66896C2314yes—
212#66896C2314yes—
213#66896C2314yes—
214#66896C2314yes—
215#66896C2314yes—
216#66874C2312yes—
217#66873C2312yes—
218#66872C2312yes—
219#66872C2314yes—
220#66871C2312yes—
221#66871C2314yes—
222C4⋊(C11⋊C8)C2314yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2312yes—
225C4⋊(C11⋊C8)C2312yes—
226#66867C2314yes—
227#66867C2312yes—
228C4×C11⋊C8C2314yes—
229C4×C11⋊C8C2312yes—
230#61324—111nomaximal, Sylow
231C24×C11—22no—
232C2×Q8×C11—21no—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—42no—
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D412yes—
239C2×Q8×C11C2412yes—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—24no—
246C2×D4×C11—24no—
247C2×D4×C11—44no—
248C2×D4×C11—82no—
249C2×D4×C11C2414yes—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—24no—
253C22×C4×C11—24no—
254C22×C4×C11—84no—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—21no—
261Q8×D11—44no—
262#4339—22no—
263#4339#4114yes—
264C2×D44C2411yescharacteristic
265C2×C4×D11—21no—
266C2×C4×D11—22no—
267C2×C4×D11—21no—
268C2×C4×D11—22no—
269C2×C4×D11—21no—
270C2×Dic22—22no—
271C2×Dic22—21no—
272C2×Dic22—22no—
273C2×Dic22—21no—
274C2×Dic22C2411yescharacteristic
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4C2×D411yescharacteristic
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D411yescharacteristic
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C42×C11—22no—
293C42×C11—22no—
294C42×C11C2×D412yes—
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D412yes—
297C42×C11C2×D411yescharacteristic
298C42×C11C2411yescharacteristic
299C42×C11C2412yes—
300C42×C11C2412yes—
301C42×C11C2411yescharacteristic
302C22⋊Dic11—21no—
303C22⋊Dic11—22no—
304#4326—24no—
305#4325—24no—
306#4324—28no—
307#4323—28no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—22no—
312C4⋊Dic11—22no—
313C4⋊Dic11—21no—
314C4⋊Dic11—22no—
315C4⋊Dic11—21no—
316C4⋊Dic11C2411yescharacteristic
317C4⋊Dic11C2412yes—
318C4⋊Dic11C2411yescharacteristic
319C4⋊Dic11C2412yes—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—21no—
328Dic11⋊C4—21no—
329Dic11⋊C4—22no—
330C4×Dic11—21no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333C4×Dic11—21no—
334C4×Dic11—22no—
335C4×Dic11—21no—
336#4318—24no—
337#4318—22no—
338#4318—22no—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2412yes—
341C2×C11⋊C8C2414yes—
342C2×#559D1111yescharacteristic, complemented
343Q8×#41—111no—
344#3375—112no—
345#3373—112no—
346#3371—114no—
347#3370—114no—
348#3365—112no—
349#3361—112no—
350#3140—112no—
351#3138—111no—
352#3078—111no—
353#3077—112no—
354#3040—112no—
355#3038—111no—
356Q8×M16—111no—
357C4×#137—111no—
358C4×AGL(1,ℤ/8)—112no—
359C23×C11—24no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11C22×D411yescharacteristic
364C22×D11—21no—
365Q8×C11—22no—
366Q8×C11—22no—
367Q8×C11—22no—
368Q8×C11—22no—
369Q8×C11—42no—
370Q8×C11—42no—
371D4×C11—24no—
372D4×C11—24no—
373D4×C11—44no—
374D4×C11—44no—
375D4×C11—44no—
376D4×C11—82no—
377D4×C11—82no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—42no—
382C2×C4×C11—41no—
383C2×C4×C11—42no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—84no—
387C2×C4×C11—84no—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4112yes—
398C2×C4×C112−1+412yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—24no—
401C2×Dic11—21no—
402C2×Dic11—22no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—22no—
406D44—21no—
407D44C2×#4112yes—
408C4×D11—24no—
409C4×D11—44no—
410C4×D11—42no—
411C4×D11—82no—
412C4×D11—81no—
413Dic22—21no—
414Dic22—44no—
415Dic22—42no—
416Dic22—82no—
417Dic22—81no—
418Dic22C2×#4112yes—
419C11⋊C8—24no—
420C11⋊C8—22no—
421C11⋊C8—22no—
422C2×#137—111no—
423C2×AGL(1,ℤ/8)—112no—
424#559—21no—
425#559—22no—
426#559—21no—
427#559C2×D1112yes—
428#559C2×D1114yes—
429#559C2×D1112yes—
430Q82—111no—
431#557—111no—
432#557—112no—
433#554—111no—
434#554—112no—
435#554—221no—
436#554—222no—
437D4×Q8—111no—
438D4×Q8—221no—
439#533—112no—
440#533—111no—
441#533—222no—
442#533—221no—
443C2×#127C2×D1111yescharacteristic
444C2×#124—21no—
445C2×#124C2×D1112yes—
446C2×#123—22no—
447C4×#41—112no—
448C4×#41—111no—
449C2×C4×Q8—221no—
450C2×C4×Q8C2×D1111yescharacteristic
451C2×C4×Q8C2×D1111yescharacteristic
452C2×C4×D4—21no—
453C2×C4×D4C2×D1112yes—
454#490—114no—
455#489—114no—
456#489—114no—
457#488—114no—
458#488—114no—
459#486—112no—
460#486—112no—
461#479—114no—
462#478—114no—
463#478—114no—
464#477—112no—
465#476—114no—
466#475—112no—
467#474—114no—
468#464—114no—
469#464—114no—
470#463—114no—
471#463—114no—
472#460—112no—
473#460—112no—
474#459—112no—
475#459—112no—
476#446—114no—
477#446—112no—
478C8×Q8—112no—
479#442—114no—
480#441—112no—
481#440—112no—
482#440—114no—
483C4×Q16—112no—
484C4×SD16—112no—
485C4×SD16—114no—
486C4×D8—114no—
487#428—111no—
488#428—112no—
489#423—112no—
490#423—111no—
491#419—112no—
492#419—111no—
493#418—112no—
494#418—112no—
495#418—112no—
496#417—111no—
497C4×M16—111no—
498C4×M16—112no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—44no—
502C22×C11—44no—
503C22×C11—44no—
504C22×C11—88no—
505C22×C11#54812yes—
506C22×C11C23×D411yescharacteristic
507C2×D11—22no—
508C2×D11—41no—
509C2×D11—41no—
510C4×C11—22no—
511C4×C11—22no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11#54812yes—
520C4×C11#57512yes—
521C4×C11C22×#4111yescharacteristic
522C4×C11C2×2−1+411yescharacteristic
523Dic11—22no—
524Dic11—41no—
525Dic11—42no—
526Dic11—41no—
527Dic11—42no—
528C2×#41—111no—
529C22×Q8—221no—
530C22×Q8C22⋊D1111yescharacteristic
531C22×Q8C22×D1111yescharacteristic
532C22×D4—21no—
533C22×D4—21no—
534C22×D4C22×D1112yes—
535C23×C4—22no—
536#137—224no—
537AGL(1,ℤ/8)—228no—
538C2×Q16—112no—
539C2×SD16—112no—
540C2×SD16—114no—
541C2×D8—114no—
542C2×M16—112no—
543C2×M16—111no—
544C2×M16—111no—
545C4⋊Q8—111no—
546C4⋊Q8—112no—
547C4⋊Q8—112no—
548C4⋊Q8—111no—
549C4⋊Q8—221no—
550C4⋊Q8—222no—
551C4⋊Q8—221no—
552C4⋊Q8—222no—
553#127—21no—
554#127—21no—
555#127C22×D1112yes—
556#127C22×D1112yes—
557#125—112no—
558#125—112no—
559#125—112no—
560#125—222no—
561#125—222no—
562#125—222no—
563#124—22no—
564#124—22no—
565#124—24no—
566#124—22no—
567#124—22no—
568#124C22×D1114yes—
569#124C22×D1114yes—
570#123—24no—
571#123—24no—
572#123—24no—
573#123—24no—
574C22⋊Q8—221no—
575C22⋊Q8—222no—
576C22⋊Q8—221no—
577C22⋊Q8—222no—
578C22⋊Q8—222no—
579C22⋊Q8—221no—
580C22⋊Q8—221no—
581C22⋊Q8—222no—
582C22⋊Q8—222no—
583C22⋊Q8—222no—
584C22⋊Q8—222no—
585C4×Q8—21no—
586C4×Q8—21no—
587C4×Q8—112no—
588C4×Q8—111no—
589C4×Q8—111no—
590C4×Q8—112no—
591C4×Q8—221no—
592C4×Q8—221no—
593C4×Q8—222no—
594C4×Q8—222no—
595C4×Q8—221no—
596C4×Q8—222no—
597C4×Q8—221no—
598C4×Q8C22⋊D1111yescharacteristic
599C4×Q8C22⋊D1112yes—
600C4×Q8C22⋊D1111yescharacteristic
601C4×Q8C22×D1112yes—
602C4×Q8C22×D1112yes—
603C4×Q8C22×D1111yescharacteristic
604C4×Q8C22×D1111yescharacteristic
605C4×Q8C22×D1112yes—
606C4×D4—22no—
607C4×D4—24no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—111no—
612C4×D4—112no—
613C4×D4—112no—
614C4×D4—111no—
615C4×D4—221no—
616C4×D4—222no—
617C4×D4—222no—
618C4×D4—221no—
619C4×D4C22×D1114yes—
620C4×D4C22×D1114yes—
621#117—112no—
622#117—111no—
623#117—222no—
624#117—221no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—221no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4C22⋊D1111yescharacteristic
629C2×C4⋊C4C22⋊D1112yes—
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C42—21no—
635C2×C42—222no—
636C2×C42—221no—
637C2×C42C22×D1112yes—
638C2×C42C22×D1111yescharacteristic
639#107—114no—
640#107—112no—
641#106—112no—
642#106—114no—
643C4⋊C8—112no—
644C4⋊C8—114no—
645C4⋊C8—112no—
646C4⋊C8—114no—
647#103—112no—
648#103—112no—
649#103—114no—
650#103—114no—
651#103—112no—
652#102—114no—
653#102—114no—
654#102—114no—
655#102—114no—
656#102—114no—
657#102—114no—
658#102—112no—
659#97—112no—
660#97—114no—
661C4×C8—114no—
662C4×C8—112no—
663C2×C11—22no—
664C2×C11—84no—
665C2×C11C2×#54811yescharacteristic
666C2×C11C2×#57511yescharacteristic
667C2×C11#358511yescharacteristic
668D11—42no—
669C24—22no—
670#41—114no—
671#41—222no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—42no—
676C2×Q8—111no—
677C2×Q8—222no—
678C2×Q8—221no—
679C2×Q8—222no—
680C2×Q8—221no—
681C2×Q8—444no—
682C2×Q8C2×C22⋊D1111yescharacteristic
683C2×Q8C2×C22⋊D1111yescharacteristic
684C2×Q8C2×C22⋊D1112yes—
685C2×Q8C23×D1112yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—44no—
694C2×D4—82no—
695C2×D4—111no—
696C2×D4—221no—
697C2×D4C23×D1114yes—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—84no—
703C22×C4—221no—
704C22×C4—222no—
705C22×C4—221no—
706C22×C4—222no—
707C22×C4—221no—
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1112yes—
710C22×C4C2×C22⋊D1112yes—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C23×D1111yescharacteristic
713Q16—224no—
714SD16—228no—
715SD16—224no—
716D8—228no—
717M16—224no—
718M16—222no—
719M16—222no—
720C2×C8—112no—
721C2×C8—112no—
722C2×C8—114no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—112no—
727C4⋊C4—111no—
728C4⋊C4—112no—
729C4⋊C4—111no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4—221no—
735C4⋊C4—221no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—221no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—221no—
744C4⋊C4C2×C22⋊D1111yescharacteristic
745C4⋊C4C2×C22⋊D1112yes—
746C4⋊C4C2×C22⋊D1112yes—
747C4⋊C4C2×C22⋊D1111yescharacteristic
748C4⋊C4C2×C22⋊D1112yes—
749C4⋊C4C2×C22⋊D1112yes—
750C4⋊C4C2×C22⋊D1112yes—
751C4⋊C4C23×D1112yes—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—222no—
759C22⋊C4—221no—
760C22⋊C4—221no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4—221no—
764C42—22no—
765C42—22no—
766C42—222no—
767C42—221no—
768C42—222no—
769C42—221no—
770C42—222no—
771C42—221no—
772C42C2×C22⋊D1112yes—
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1112yes—
775C42C2×C22⋊D1111yescharacteristic
776C42C23×D1112yes—
777C42C23×D1111yescharacteristic
778C42C23×D1112yes—
779C42C23×D1111yescharacteristic
780C11#6132411yescharacteristic, complemented, Sylow
781C23—24no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—221no—
786C23C22×C22⋊D1111yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—22no—
790Q8—22no—
791Q8—42no—
792Q8—42no—
793Q8—112no—
794Q8—221no—
795Q8—444no—
796Q8—442no—
797Q8—882no—
798Q8—881no—
799D4—24no—
800D4—24no—
801D4—44no—
802D4—44no—
803D4—44no—
804D4—82no—
805D4—82no—
806D4—112no—
807D4—224no—
808D4—221no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4—221no—
820C2×C4—224no—
821C2×C4—222no—
822C2×C4—221no—
823C2×C4—222no—
824C2×C4—221no—
825C2×C4—444no—
826C2×C4—442no—
827C2×C4—882no—
828C2×C4—881no—
829C2×C4#41×D1112yes—
830C2×C4#6704312yes—
831C2×C4C22×C22⋊D1111yescharacteristic
832C2×C4C22×C22⋊D1112yes—
833C2×C4C22×C22⋊D1112yes—
834C2×C4C22×C22⋊D1111yescharacteristic
835C2×C4C22×C22⋊D1112yes—
836C2×C4C22×C22⋊D1112yes—
837C2×C4C22×C22⋊D1111yescharacteristic
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C24×D1111yescharacteristic
841C8—224no—
842C8—222no—
843C8—222no—
844C22—21no—
845C22—21no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—88no—
850C22—222no—
851C22—441no—
852C22—441no—
853C22#1062336212yes—
854C22C23×C22⋊D1111yescharacteristic
855C4—22no—
856C4—22no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—22no—
861C4—22no—
862C4—42no—
863C4—42no—
864C4—222no—
865C4—442no—
866C4—441no—
867C4—442no—
868C4—441no—
869C4#1062335312yes—
870C4#1062336212yes—
871C4C2×#41×D1111yescharacteristic
872C4C2×#6704311yescharacteristic
873C2—22no—
874C2—84no—
875C2—442no—
876C2C2×#1062336211yescharacteristic
877C2C2×#1062335311yescharacteristic
878C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#559C2
socleC22×C11C23×D4
prime radical#13078092C2
hypercenterC2×#559D11
hypocenterC11#61324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. Q8×#4339C2semidirect
2. #13081426C2semidirect
3. #13081404C2semidirect
4. #13081378C2semidirect
5. #13081363C2semidirect
6. #13081308C2semidirect
7. #13081272C2semidirect
8. #13079002C2semidirect
9. #13078990C2semidirect
10. #13078421C2semidirect
11. #13078413C2semidirect
12. #13078106C2semidirect
14. Q8×#4318C2semidirect
15. C4×#66995C2semidirect
16. C4×#66985C2semidirect
17. C2×C11×#559C2semidirect
35. #10623110C22semidirect
36. #10623110C22semidirect
39. Q8×D44C22semidirect
41. #10623098C22semidirect
42. #10623098C22semidirect
43. Q8×Dic22C22semidirect
62. #10622670C22semidirect
63. #10622670C22semidirect
64. #10622669C22semidirect
65. #10622669C22semidirect
66. #10622668C22semidirect
67. #10622668C22semidirect
68. #10622667C22semidirect
69. #10622667C22semidirect
70. #10622643C22semidirect
71. C4×#4326C22semidirect
72. #10622639C22semidirect
73. C4×#4325C22semidirect
74. #10622637C22semidirect
75. #10622637C22semidirect
76. Q8×C11⋊C8C22semidirect
77. #10622635C22semidirect
78. #10622634C22semidirect
79. #10622633C22semidirect
80. #10622631C22semidirect
81. C4×#4324C22semidirect
82. #10622627C22semidirect
83. C4×#4323C22semidirect
84. #10622622C22semidirect
85. #10622622C22semidirect
86. #10622621C22semidirect
87. #10622620C22semidirect
342. C2×#559D11semidirect
780. C11#61324semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130814262
#130814042
#130813782
#130813632
#130813082
#130812722
#130790022
#130789902
#130784212
#130784132
#130781062
#130780922
Q8×#43182
C4×#669952
C4×#669852
C2×C11×#5592
#6132411