Finite Group Databasebeta

← #15622590

Subgroups — #15622590

Order 2816.

2058 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#13082351C211yesmaximal, characteristic
2#13078907C214yesmaximal, complemented
3#13078845C214yesmaximal, complemented
4#13078787C212yesmaximal, complemented
5#13078738C212yesmaximal, complemented
6#13078696C212yesmaximal, complemented
7#13078647C212yesmaximal, complemented
8#13078556C211yesmaximal, characteristic, complemented
9#13078529C211yesmaximal, characteristic, complemented
10#13078458C212yesmaximal, complemented
11#13078137C212yesmaximal, complemented
12#13077850C211yesmaximal, characteristic, complemented
13C2×#10622840C211yesmaximal, characteristic, complemented
14#13077475C212yesmaximal, complemented
15#13077459C212yesmaximal, complemented
16#13077274C211yesmaximal, characteristic, complemented
17C2×C11×#519C211yesmaximal, characteristic, complemented
18C23×Q8×C11C2211yescharacteristic
19C11×#519—22no—
20C11×#519—21no—
21C11×#519—21no—
22C11×#519C2212yes—
23C11×#519C2212yes—
24C11×#519C2214yescomplemented
25C2×C4×Q8×C11—21no—
26C2×C4×Q8×C11—21no—
27C2×C4×Q8×C11C2212yescomplemented
28C2×C4×Q8×C11C2212yescomplemented
29C2×C11×#117—22no—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C2×#66995C2212yes—
33C22×#4325C2212yes—
34#10623322C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36#10623066C2212yes—
37#10623065C2212yes—
38#10623063—21no—
39#10623061—21no—
40#10623058—22no—
41#10623056C2211yescharacteristic
42#10623054C2211yescharacteristic
43#10623052C2211yescharacteristic
44#10623050C2211yescharacteristic
45#10623045—21no—
46#10623038—21no—
47#10623021—22no—
48#10623010C2212yes—
49#10623008C2212yes—
50#10622841C2212yescomplemented
51#10622841C2212yescomplemented
52#10622840C2212yes—
53#10622840C2214yes—
54#10622840C2212yes—
55#10622840C2212yescomplemented
56#10622840C2212yescomplemented
57#10622838C2212yes—
58C2×#66899C2212yes—
59#10622820C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61#10622643C2214yescomplemented
62C4×#4326C2214yescomplemented
63#10622641C2214yescomplemented
64#10622641C2214yescomplemented
65#10622640C2214yescomplemented
66#10622640C2214yescomplemented
67#10622639C2214yescomplemented
68#10622639C2214yescomplemented
69#10622639C2214yescomplemented
70C4×#4325C2214yescomplemented
71C4×#4325C2214yescomplemented
72C4×#4325C2214yescomplemented
73#10622635C2214yescomplemented
74#10622635C2214yescomplemented
75#10622634C2214yescomplemented
76#10622633C2214yescomplemented
77#10622616C2214yes—
78#10622616C2212yescomplemented
79#10622615C2212yes—
80#10622614C2212yes—
81#10622613C2214yescomplemented
82#10622612C2212yes—
83#10622611C2212yes—
84#10622610C2212yes—
85#10622609C2212yescomplemented
86#10622608C2212yes—
87#10622584C2211yescharacteristic, complemented
88#10622583C2211yescharacteristic, complemented
89#10622581C2212yes—
90#10622581C2211yescharacteristic, complemented
91#10622580C2212yes—
92#10622580C2211yescharacteristic, complemented
93#10622539C2212yescomplemented
94#10622538C2212yescomplemented
95C22×Q8×C11—28no—
96C22×Q8×C11—21no—
97C22×Q8×C11—21no—
98C22×Q8×C11—21no—
99C22×Q8×C11C2312yes—
100C22×Q8×C11C2312yes—
101C22×Q8×C11C2312yes—
102C23×C4×C11—21no—
103C23×C4×C11C2311yescharacteristic
104C22×C22⋊D11—21no—
105C2×#4339—22no—
106C2×#4339C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C4×Q8×C11—22no—
109C4×Q8×C11—22no—
110C4×Q8×C11—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—24no—
113C4×Q8×C11—24no—
114C4×Q8×C11—22no—
115C4×Q8×C11—22no—
116C4×Q8×C11—22no—
117C4×Q8×C11—22no—
118C4×Q8×C11C2314yes—
119C4×Q8×C11C2314yes—
120C4×Q8×C11C2314yes—
121C4×Q8×C11C2314yes—
122C11×#117—21no—
123C11×#117—21no—
124C11×#117—24no—
125C11×#117—24no—
126C11×#117—24no—
127C11×#117—24no—
128C11×#117D412yes—
129C11×#117D411yescharacteristic
130C11×#117D411yescharacteristic
131C11×#117C2312yes—
132C11×#117C2312yes—
133C11×#117C2311yescharacteristic
134C11×#117C2311yescharacteristic
135C11×#117C2312yes—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4—22no—
138C2×C11×C4⋊C4D411yescharacteristic
139C2×C11×C4⋊C4D411yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4—21no—
143C2×C11×C22⋊C4D412yes—
144C2×C42×C11—22no—
145C2×C42×C11—22no—
146C2×C42×C11—21no—
147C2×C42×C11C2312yes—
148#67006—21no—
149C2×#4326C2314yes—
150#66995—28no—
151C2×#4325—28no—
152C2×#4325C2314yes—
153C2×#4325C2314yes—
154C2×#4325C2314yes—
155#66983—22no—
156#66983—21no—
157#66983—21no—
158#66983C2311yescharacteristic
159#66983C2312yes—
160#66983C2312yes—
161#66983C2311yescharacteristic
162#66982—22no—
163#66982—21no—
164C4×C22⋊D11—22no—
165C4×C22⋊D11—21no—
166C4×C22⋊D11—21no—
167C2×(C2×D11)⋊C4—21no—
168#66979C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977C2311yescharacteristic
171#66977C2311yescharacteristic
172C2×#4318C2312yes—
173C22×C11⋊C8C2312yes—
174#66951—22no—
175#66949—22no—
176#66948—21no—
177#66948—21no—
178#66947—22no—
179#66947—22no—
180#66946—21no—
181#66946—21no—
182#66945—21no—
183C4⋊C4×D11—21no—
184#66943—21no—
185#66941—21no—
186#66938—22no—
187#66937—22no—
188#66937—22no—
189#66936—22no—
190#66935—22no—
191(C22⋊D11)⋊C4—22no—
192C22⋊C4×D11—22no—
193#66931—22no—
194#66929—22no—
195#66928—22no—
196#66928C2312yes—
197#66927C2312yes—
198C4×D44—22no—
199C4×D44C2312yes—
200C4×D44C2312yes—
201C4×D44C2312yes—
202#66925—22no—
203#66923C2312yes—
204#66922C2312yes—
205C4×Dic22C2312yes—
206#66899C2314yes—
207#66899C2314yes—
208#66899C2314yes—
209#66899C2314yes—
210C22⋊(C11⋊C8)C2311yescharacteristic
211C22⋊(C11⋊C8)C2312yes—
212C22⋊(C11⋊C8)C2311yescharacteristic
213C22⋊(C11⋊C8)C2312yes—
214C22⋊(C11⋊C8)C2312yes—
215#66874C2312yes—
216#66874C2312yes—
217#66873C2314yes—
218#66873C2312yes—
219#66873C2314yes—
220#66873C2312yes—
221#66872C2314yes—
222#66872C2312yes—
223#66872C2312yes—
224#66871C2314yes—
225#66871C2312yes—
226#66871C2312yes—
227C4⋊(C11⋊C8)C2314yes—
228C4⋊(C11⋊C8)C2314yes—
229#66867C2314yes—
230C4×C11⋊C8C2314yes—
231#60582—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—21no—
234C2×Q8×C11—28no—
235C2×Q8×C11—28no—
236C2×Q8×C11—28no—
237C2×Q8×C11—28no—
238C2×Q8×C11—28no—
239C2×Q8×C11—22no—
240C2×Q8×C11—22no—
241C2×Q8×C11—22no—
242C2×Q8×C11—24no—
243C2×Q8×C11#4118yescomplemented
244C2×Q8×C11C2414yes—
245C22×C4×C11—28no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—24no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—21no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—21no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—21no—
265C2×C22⋊D11—82no—
266C22×Dic11—21no—
267#4339—24no—
268#4339—84no—
269C2×D44—21no—
270C2×D44—22no—
271C2×D44—22no—
272C2×D44—24no—
273C2×D44C2411yescharacteristic
274C2×D44C2412yes—
275C2×C4×D11—21no—
276C2×C4×D11—22no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×Dic22—22no—
280C2×Dic22C2411yescharacteristic
281C11×C4⋊C4—24no—
282C11×C4⋊C4—24no—
283C11×C4⋊C4—24no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D411yescharacteristic
290C11×C4⋊C4C2×D411yescharacteristic
291C11×C4⋊C4C2×D412yes—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2412yes—
294C11×C4⋊C4C2412yes—
295C11×C22⋊C4—22no—
296C11×C22⋊C4—22no—
297C11×C22⋊C4C2×D412yes—
298C11×C22⋊C4C2×D412yes—
299C11×C22⋊C4C2×D412yes—
300C11×C22⋊C4C2×D412yes—
301C42×C11—24no—
302C42×C11—24no—
303C42×C11—24no—
304C42×C11—24no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11C2×D412yes—
308C42×C11C2×D412yes—
309C42×C11C2412yes—
310C42×C11C2412yes—
311C22⋊Dic11—21no—
312C22⋊Dic11—21no—
313C22⋊Dic11—21no—
314#4326—28no—
315#4325—28no—
316#4325—28no—
317#4325—28no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—21no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—21no—
326(C2×D11)⋊C4—22no—
327C4⋊Dic11—22no—
328C4⋊Dic11—21no—
329C4⋊Dic11C2412yes—
330C4⋊Dic11C2411yescharacteristic
331C4⋊Dic11C2411yescharacteristic
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—21no—
336Dic11⋊C4—21no—
337C4×Dic11—22no—
338C4×Dic11—21no—
339#4318—24no—
340C2×C11⋊C8—24no—
341C2×C11⋊C8C2412yes—
342C2×C11⋊C8C2414yes—
343C2×C11⋊C8C2412yes—
344#3494—111no—
345C2×#519D1111yescharacteristic, complemented
346#3126—114no—
347#3121—114no—
348#3117—112no—
349#3112—112no—
350#3108—112no—
351#3103—112no—
352#3094—111no—
353#3091—111no—
354#3082—112no—
355#3043—112no—
356#3004—111no—
357C2×#448—111no—
358#2949—112no—
359#2947—112no—
360#2924—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—41no—
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C22×D11—22no—
368C22×D11—21no—
369C22×D11—42no—
370C22×D11—81no—
371C22×D11—81no—
372Q8×C11—28no—
373Q8×C11—28no—
374Q8×C11—28no—
375Q8×C11—24no—
376Q8×C11C2×#4118yes—
377C2×C4×C11—28no—
378C2×C4×C11—28no—
379C2×C4×C11—28no—
380C2×C4×C11—22no—
381C2×C4×C11—24no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D412yes—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C2×#4114yes—
400C2×C4×C11C2511yescharacteristic
401C22⋊D11—42no—
402C22⋊D11—42no—
403C22⋊D11—44no—
404C22⋊D11—81no—
405C22⋊D11—82no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—22no—
409C2×Dic11—21no—
410C2×Dic11—81no—
411D44—24no—
412D44—22no—
413D44—42no—
414D44—82no—
415D44—82no—
416C4×D11—42no—
417C4×D11—82no—
418C4×D11—82no—
419C4×D11—82no—
420Dic22—22no—
421Dic22—82no—
422C11⋊C8—22no—
423C11⋊C8—22no—
424C11⋊C8—24no—
425C23×Q8C2×D1111yescharacteristic
426C2×#137—112no—
427C22×SD16—112no—
428#555—221no—
429#553—221no—
430#553—221no—
431#551—222no—
432#547—221no—
433#546—222no—
434#544—111no—
435#542—112no—
436#540—112no—
437#535—111no—
438#532—112no—
439#529—112no—
440#525—111no—
441C2×#121—111no—
442#520—111no—
443#519—22no—
444#519—21no—
445#519—21no—
446#519C2×D1112yes—
447#519C2×D1112yes—
448#519C2×D1114yescomplemented
449#518—111no—
450C2×C4×Q8—21no—
451C2×C4×Q8—21no—
452C2×C4×Q8C2×D1112yescomplemented
453C2×C4×Q8C2×D1112yescomplemented
454C2×#117—22no—
455C2×#117C2×D1111yescharacteristic
456C2×#117C2×D1111yescharacteristic
457#485—112no—
458#484—111no—
459#483—111no—
460#482—112no—
461#482—114no—
462#481—111no—
463#481—112no—
464#480—111no—
465#480—112no—
466#479—114no—
467#479—114no—
468#477—114no—
469#475—114no—
470#464—114no—
471#464—114no—
472#460—114no—
473#460—114no—
474#451—112no—
475#451—112no—
476#448—112no—
477#448—112no—
478#448—112no—
479#448—114no—
480#448—112no—
481#441—114no—
482#440—114no—
483#440—114no—
484#440—114no—
485C4×Q16—114no—
486C4×SD16—114no—
487C4×SD16—114no—
488C4×SD16—114no—
489#433—114no—
490#432—112no—
491#431—112no—
492#428—112no—
493#427—112no—
494#424—112no—
495#419—112no—
496#418—112no—
497#416—112no—
498C2×#103—112no—
499#407—111no—
500C2×C22⋊C8—111no—
501#405—112no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—44no—
510C22×C11#52512yes—
511C22×C11#57712yes—
512C22×C11C23×D411yescharacteristic
513C2×D11—42no—
514C2×D11—41no—
515C2×D11—42no—
516C2×D11—41no—
517C2×D11—42no—
518C2×D11—41no—
519C2×D11—162no—
520C4×C11—22no—
521C4×C11—22no—
522C4×C11—28no—
523C4×C11—21no—
524C4×C11—21no—
525C4×C11—22no—
526C4×C11—22no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11#52512yes—
530C4×C11C22×#4112yes—
531Dic11—41no—
532Dic11—41no—
533Dic11—41no—
534Dic11—42no—
535C2×#41—111no—
536C2×#41—222no—
537C22×Q8—28no—
538C22×Q8—21no—
539C22×Q8—21no—
540C22×Q8—21no—
541C22×Q8C22×D1112yes—
542C22×Q8C22×D1112yes—
543C22×Q8C22×D1112yes—
544C22×D4—111no—
545C22×D4—221no—
546C23×C4—21no—
547C23×C4C22×D1111yescharacteristic
548#137—228no—
549C2×Q16—114no—
550C2×SD16—114no—
551C2×SD16—114no—
552C2×SD16—114no—
553C2×SD16—228no—
554C2×M16—112no—
555C22×C8—112no—
556C4⋊Q8—112no—
557C4⋊Q8—221no—
558#127—112no—
559#126—222no—
560#126—222no—
561#125—112no—
562#125—221no—
563#124—112no—
564#124—222no—
565#124—222no—
566#123—221no—
567#123—222no—
568#123—222no—
569#123—222no—
570#123—222no—
571C22⋊Q8—111no—
572C22⋊Q8—111no—
573C22⋊Q8—222no—
574C22⋊Q8—222no—
575#121—112no—
576#121—112no—
577#121—111no—
578#121—111no—
579#121—221no—
580#121—221no—
581#121—222no—
582#121—221no—
583#121—221no—
584#121—222no—
585#121—222no—
586#120—221no—
587#120—222no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—24no—
593C4×Q8—24no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—112no—
599C4×Q8C22×D1114yes—
600C4×Q8C22×D1114yes—
601C4×Q8C22×D1114yes—
602C4×Q8C22×D1114yes—
603C4×D4—112no—
604C4×D4—112no—
605C4×D4—112no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—222no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4—222no—
612C4×D4—222no—
613#117—21no—
614#117—21no—
615#117—24no—
616#117—24no—
617#117—24no—
618#117—24no—
619#117—111no—
620#117—221no—
621#117—222no—
622#117C22⋊D1112yes—
623#117C22⋊D1111yescharacteristic
624#117C22⋊D1111yescharacteristic
625#117C22×D1112yes—
626#117C22×D1112yes—
627#117C22×D1111yescharacteristic
628#117C22×D1111yescharacteristic
629#117C22×D1112yes—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—221no—
634C2×C4⋊C4C22⋊D1111yescharacteristic
635C2×C4⋊C4C22⋊D1111yescharacteristic
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4C22⋊D1112yes—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—21no—
645C2×C42C22×D1112yes—
646#107—112no—
647#107—112no—
648#107—114no—
649#106—112no—
650#106—112no—
651#106—114no—
652C4⋊C8—114no—
653C4⋊C8—114no—
654#103—114no—
655#103—114no—
656#103—114no—
657#103—114no—
658#103—112no—
659#103—112no—
660#102—112no—
661#102—112no—
662#102—114no—
663#102—114no—
664C22⋊C8—111no—
665C22⋊C8—111no—
666C22⋊C8—112no—
667C22⋊C8—112no—
668C22⋊C8—112no—
669#97—114no—
670C4×C8—114no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—41no—
674C2×C11C2×#52511yescharacteristic
675C2×C11C2×#57711yescharacteristic
676C2×C11#358611yescharacteristic
677D11—81no—
678D11—82no—
679C24—221no—
680C24C2×C22⋊D1111yescharacteristic
681#41—224no—
682#41—884no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—24no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—22no—
692C2×Q8—111no—
693C2×Q8—222no—
694C2×Q8#433918yescomplemented
695C2×Q8C23×D1114yes—
696C2×D4—112no—
697C2×D4—111no—
698C2×D4—221no—
699C2×D4—221no—
700C2×D4—222no—
701C2×D4—221no—
702C2×D4—222no—
703C2×D4—224no—
704C2×D4—221no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—882no—
708C22×C4—28no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4C2×C22⋊D1112yes—
721C22×C4C2×C22⋊D1111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1112yes—
725C22×C4C23×D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728Q16—228no—
729SD16—228no—
730SD16—228no—
731SD16—228no—
732M16—224no—
733C2×C8—112no—
734C2×C8—114no—
735C2×C8—112no—
736C2×C8—224no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—112no—
744C4⋊C4—111no—
745C4⋊C4—111no—
746C4⋊C4—221no—
747C4⋊C4—222no—
748C4⋊C4—221no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—222no—
752C4⋊C4—221no—
753C4⋊C4C2×C22⋊D1111yescharacteristic
754C4⋊C4C2×C22⋊D1111yescharacteristic
755C4⋊C4C2×C22⋊D1111yescharacteristic
756C4⋊C4C2×C22⋊D1111yescharacteristic
757C4⋊C4C2×C22⋊D1112yes—
758C4⋊C4C2×C22⋊D1112yes—
759C4⋊C4C23×D1112yes—
760C4⋊C4C23×D1112yes—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—221no—
764C22⋊C4—221no—
765C22⋊C4—221no—
766C22⋊C4—222no—
767C22⋊C4—222no—
768C22⋊C4—222no—
769C22⋊C4—222no—
770C22⋊C4—222no—
771C22⋊C4—222no—
772C22⋊C4—221no—
773C22⋊C4—222no—
774C22⋊C4—221no—
775C22⋊C4C2×C22⋊D1112yes—
776C22⋊C4C2×C22⋊D1112yes—
777C22⋊C4C2×C22⋊D1112yes—
778C22⋊C4C2×C22⋊D1112yes—
779C42—24no—
780C42—24no—
781C42—24no—
782C42—24no—
783C42—22no—
784C42—22no—
785C42—221no—
786C42—222no—
787C42C2×C22⋊D1112yes—
788C42C2×C22⋊D1112yes—
789C42C23×D1112yes—
790C42C23×D1112yes—
791C11#6058211yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—41no—
795C23—222no—
796C23—221no—
797C23—442no—
798C23—881no—
799C23—881no—
800C23C22×C22⋊D1111yescharacteristic
801C23C22×C22⋊D1111yescharacteristic
802C23C22×C22⋊D1111yescharacteristic
803Q8—28no—
804Q8—28no—
805Q8—28no—
806Q8—24no—
807Q8—222no—
808Q8—882no—
809Q8C2×#433918yes—
810D4—224no—
811D4—222no—
812D4—442no—
813D4—444no—
814D4—442no—
815D4—442no—
816D4—882no—
817D4—882no—
818D4—882no—
819D4—881no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—221no—
836C2×C4—221no—
837C2×C4—221no—
838C2×C4—222no—
839C2×C4—442no—
840C2×C4—882no—
841C2×C4—882no—
842C2×C4—882no—
843C2×C4—881no—
844C2×C4C2×#433914yes—
845C2×C4C22×C22⋊D1112yes—
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1112yes—
848C2×C4C22×C22⋊D1112yes—
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C24×D1111yescharacteristic
853C8—222no—
854C8—222no—
855C8—224no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—44no—
864C22—441no—
865C22—442no—
866C22—442no—
867C22—441no—
868C22—441no—
869C22—442no—
870C22—1762no—
871C22#1062332212yes—
872C22#1062336812yes—
873C22C23×C22⋊D1111yescharacteristic
874C4—28no—
875C4—21no—
876C4—21no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—42no—
883C4—441no—
884C4—441no—
885C4—442no—
886C4—441no—
887C4#1062332212yes—
888C4C22×#433912yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—882no—
893C2—881no—
894C2C2×#1062332211yescharacteristic
895C2C2×#1062336811yescharacteristic
896C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#519C2
socleC22×C11C23×D4
prime radical#13082351C2
hypercenterC2×#519D11
hypocenterC11#60582
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #13078907C2semidirect
3. #13078845C2semidirect
4. #13078787C2semidirect
5. #13078738C2semidirect
6. #13078696C2semidirect
7. #13078647C2semidirect
8. #13078556C2semidirect
9. #13078529C2semidirect
10. #13078458C2semidirect
11. #13078137C2semidirect
12. #13077850C2semidirect
13. C2×#10622840C2semidirect
14. #13077475C2semidirect
15. #13077459C2semidirect
16. #13077274C2semidirect
17. C2×C11×#519C2semidirect
24. C11×#519C22semidirect
27. C2×C4×Q8×C11C22semidirect
28. C2×C4×Q8×C11C22semidirect
50. #10622841C22semidirect
51. #10622841C22semidirect
55. #10622840C22semidirect
56. #10622840C22semidirect
61. #10622643C22semidirect
62. C4×#4326C22semidirect
63. #10622641C22semidirect
64. #10622641C22semidirect
65. #10622640C22semidirect
66. #10622640C22semidirect
67. #10622639C22semidirect
68. #10622639C22semidirect
69. #10622639C22semidirect
70. C4×#4325C22semidirect
71. C4×#4325C22semidirect
72. C4×#4325C22semidirect
73. #10622635C22semidirect
74. #10622635C22semidirect
75. #10622634C22semidirect
76. #10622633C22semidirect
78. #10622616C22semidirect
81. #10622613C22semidirect
85. #10622609C22semidirect
87. #10622584C22semidirect
88. #10622583C22semidirect
90. #10622581C22semidirect
92. #10622580C22semidirect
93. #10622539C22semidirect
94. #10622538C22semidirect
243. C2×Q8×C11#41semidirect
345. C2×#519D11semidirect
448. #519C2×D11semidirect
452. C2×C4×Q8C2×D11semidirect
453. C2×C4×Q8C2×D11semidirect
694. C2×Q8#4339semidirect
791. C11#60582semidirect

Maximal subgroups

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

subgroupindex
#130823512
#130789072
#130788452
#130787872
#130787382
#130786962
#130786472
#130785562
#130785292
#130784582
#130781372
#130778502
C2×#106228402
#130774752
#130774592
#130772742
C2×C11×#5192
#6058211