Finite Group Databasebeta

← #15622593

Subgroups — #15622593

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#13082353C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3#13078903C214yesmaximal, complemented
4#13078848C214yesmaximal, complemented
5#13078790C212yesmaximal, complemented
6#13078735C212yesmaximal, complemented
7#13078699C212yesmaximal, complemented
8#13078644C212yesmaximal, complemented
9#13078556C211yesmaximal, characteristic, complemented
10#13078461C212yesmaximal, complemented
11#13078140C212yesmaximal, complemented
12#13077849C211yesmaximal, characteristic, complemented
13C2×#10622351C211yesmaximal, characteristic, complemented
14#13077474C212yesmaximal, complemented
15#13077462C212yesmaximal, complemented
16#13077270C211yesmaximal, characteristic, complemented
17C11×#3091C211yesmaximal, characteristic, complemented
18C23×Dic22C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21#10623361C2211yescharacteristic
22#10623358C2211yescharacteristic
23C2×#67004C2212yes—
24C2×#66983C2211yescharacteristic
25C2×#66979C2211yescharacteristic
26C22×#4314C2212yes—
27#10623189—22no—
28#10623174C2212yes—
29#10623155C2212yes—
30#10623150C2212yes—
31#10623127C2212yes—
32#10623122—22no—
33#10623096—21no—
34#10623096—21no—
35#10623094—21no—
36#10623086—21no—
37#10623052C2211yescharacteristic
38#10623050C2211yescharacteristic
39#10623047—21no—
40#10623047—21no—
41#10623047—22no—
42#10623047C2212yes—
43#10623047C2212yes—
44#10623047C2214yescomplemented
45C2×#66940C2212yescomplemented
46C2×#66940C2212yescomplemented
47C2×#66930—22no—
48C2×C4×Dic22—21no—
49C2×C4×Dic22—21no—
50C11×#485C2212yescomplemented
51C11×#484C2211yescharacteristic, complemented
52C11×#483C2211yescharacteristic, complemented
53C11×#482C2212yescomplemented
54C11×#481C2211yescharacteristic, complemented
55C11×#480C2211yescharacteristic, complemented
56C11×#427C2212yes—
57C11×#416C2212yes—
58C2×C11×C22⋊C8C2211yescharacteristic
59#10622820C2211yescharacteristic
60C2×#66880C2212yes—
61#10622715C2212yes—
62#10622714C2212yes—
63#10622663C2212yescomplemented
64#10622663C2212yescomplemented
65#10622653C2212yescomplemented
66#10622653C2212yescomplemented
67#10622617C2212yes—
68#10622616C2214yes—
69#10622614C2212yes—
70#10622608C2212yes—
71#10622581C2212yes—
72#10622580C2212yes—
73#10622502C2214yescomplemented
74#10622502C2214yescomplemented
75#10622490C2214yescomplemented
76#10622488C2214yescomplemented
77#10622470C2214yescomplemented
78#10622467C2214yescomplemented
79#10622465C2214yescomplemented
80#10622465C2214yescomplemented
81#10622411C2214yescomplemented
82#10622411C2214yescomplemented
83#10622403C2214yescomplemented
84#10622402C2214yescomplemented
85#10622375C2214yescomplemented
86#10622375C2214yescomplemented
87#10622371C2214yescomplemented
88#10622370C2214yescomplemented
89#10622351C2212yes—
90#10622351C2214yes—
91#10622351C2212yes—
92#10622333C2214yescomplemented
93#10622332C2212yescomplemented
94#10622331C2212yescomplemented
95C2×C11×#41C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C23×Dic11—21no—
99C2×#4341—22no—
100C22×D44C2311yescharacteristic
101C22×Dic22—21no—
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22—28no—
105C22×Dic22C2312yes—
106C22×Dic22C2312yes—
107C22×Dic22C2312yes—
108C22×C8×C11C2312yes—
109C11×#123—21no—
110C11×C22⋊Q8C2311yescharacteristic
111C11×C22⋊Q8C2311yescharacteristic
112C11×#121C2311yescharacteristic
113C11×#121C2311yescharacteristic
114C11×#120—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C11×#117—21no—
118C11×#117—21no—
119C11×#117C2312yes—
120C11×#117C2312yes—
121C11×#117C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C42×C11—21no—
126C2×C22⋊Dic11D412yes—
127#67004—28no—
128#67000C2312yes—
129Q8×Dic11C2312yes—
130C2×#4326C2314yes—
131#66993C2312yes—
132#66992—22no—
133#66992—22no—
134#66991—22no—
135#66990—22no—
136D4×Dic11—22no—
137D4×Dic11C2312yes—
138C2×#4324C2314yes—
139#66983—21no—
140#66983—21no—
141#66983—21no—
142#66983—21no—
143#66983C2312yes—
144#66983C2312yes—
145C2×(C2×D11)⋊C4—21no—
146#66979—21no—
147#66979D411yescharacteristic
148#66979D411yescharacteristic
149#66979D412yes—
150#66979C2311yescharacteristic
151#66979C2311yescharacteristic
152#66979C2312yes—
153C2×C4⋊Dic11—21no—
154C2×C4⋊Dic11D411yescharacteristic
155C2×C4⋊Dic11D411yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×C4×Dic11—22no—
160C2×C4×Dic11—22no—
161C2×C4×Dic11C2312yes—
162C2×#4318C2312yes—
163C2×#4314—28no—
164C2×#4314C2314yes—
165C2×#4314C2314yes—
166#66951—22no—
167#66951—22no—
168#66950—22no—
169#66946C2312yes—
170#66946C2312yes—
171#66945—22no—
172#66943C2312yes—
173#66941C2312yes—
174#66940—22no—
175#66940—22no—
176#66940—22no—
177#66940—22no—
178#66940C2314yes—
179#66940C2314yes—
180#66940C2314yes—
181#66940C2314yes—
182#66939—22no—
183#66939—22no—
184#66938—22no—
185#66938—22no—
186#66936—22no—
187#66936—22no—
188(C22⋊D11)⋊C4—22no—
189(C22⋊D11)⋊C4—22no—
190C22⋊C4×D11—22no—
191#66931—22no—
192#66930—24no—
193#66930—24no—
194#66930—24no—
195#66930—24no—
196C4×D44—21no—
197C4×D44—21no—
198#66923—21no—
199#66922—21no—
200C4×Dic22—22no—
201C4×Dic22—22no—
202C4×Dic22—22no—
203C4×Dic22—22no—
204C4×Dic22—24no—
205C4×Dic22—24no—
206C11×#107C2312yes—
207C11×#107C2312yes—
208C11×#106C2312yes—
209C11×#106C2312yes—
210C11×#103C2312yes—
211C11×#103C2312yes—
212C11×#102C2312yes—
213C11×#102C2312yes—
214C11×C22⋊C8C2311yescharacteristic
215C11×C22⋊C8C2311yescharacteristic
216C11×C22⋊C8C2312yes—
217C22⋊(C11⋊C8)C2312yes—
218C22⋊(C11⋊C8)C2312yes—
219#66880C2314yes—
220#66880C2314yes—
221#66879C2314yes—
222Dic11⋊C8C2314yes—
223Dic11⋊C8C2314yes—
224C8×Dic11C2314yes—
225#66874C2314yes—
226#66874C2314yes—
227#66873C2314yes—
228#66873C2314yes—
229#66872C2314yes—
230#66871C2314yes—
231#60582—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—21no—
234C11×#41—24no—
235C2×Q8×C11C2411yescharacteristic
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11C2411yescharacteristic
240C22×C4×C11—24no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—22no—
251C2×C22⋊D11—22no—
252C2×C22⋊D11—22no—
253C2×C22⋊D11—22no—
254C2×C22⋊D11—82no—
255C22×Dic11—28no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—21no—
261C22×Dic11C2×D412yes—
262C22×Dic11C2×D412yes—
263#4341—84no—
264C2×D44—21no—
265C2×D44—24no—
266C2×D44C2412yes—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×Dic22—28no—
270C2×Dic22—28no—
271C2×Dic22—28no—
272C2×Dic22—28no—
273C2×Dic22—28no—
274C2×Dic22—22no—
275C2×Dic22—22no—
276C2×Dic22—22no—
277C2×Dic22—22no—
278C2×Dic22—24no—
279C2×Dic22#4118yescomplemented
280C2×Dic22C2414yes—
281C2×C8×C11—24no—
282C2×C8×C11C2412yes—
283C2×C8×C11C2412yes—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2412yes—
290C11×C4⋊C4C2411yescharacteristic
291C11×C4⋊C4C2411yescharacteristic
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C42×C11—22no—
300C42×C11—22no—
301C42×C11—21no—
302C22⋊Dic11—22no—
303C22⋊Dic11C2×D412yes—
304C22⋊Dic11C2×D412yes—
305C22⋊Dic11C2×D412yes—
306C22⋊Dic11C2×D412yes—
307#4326—28no—
308#4324—28no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—21no—
318C4⋊Dic11C2×D411yescharacteristic
319C4⋊Dic11C2×D411yescharacteristic
320C4⋊Dic11C2×D411yescharacteristic
321C4⋊Dic11C2×D411yescharacteristic
322C4⋊Dic11C2×D412yes—
323C4⋊Dic11C2×D412yes—
324C4⋊Dic11C2412yes—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—24no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331C4×Dic11—24no—
332C4×Dic11—24no—
333C4×Dic11—24no—
334C4×Dic11—24no—
335C4×Dic11—22no—
336C4×Dic11C2×D412yes—
337C4×Dic11C2×D412yes—
338C4×Dic11C2412yes—
339C4×Dic11C2412yes—
340#4318—24no—
341C2×C11⋊C8C2414yes—
342#4314—28no—
343#4314—28no—
344#3494—111no—
345C2×#519—111no—
346#3126—114no—
347#3121—114no—
348#3117—112no—
349#3112—112no—
350#3108—112no—
351#3103—112no—
352#3094—111no—
353#3091D1111yescharacteristic, complemented
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—21no—
364C23×C11—41no—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C22×D11—22no—
369C22×D11—42no—
370C22×D11—81no—
371C22×D11—81no—
372Q8×C11—22no—
373D4×C11—22no—
374D4×C11—42no—
375D4×C11—42no—
376D4×C11—81no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C2×#4114yes—
394C2×C4×C11C2511yescharacteristic
395C22⋊D11—44no—
396C22⋊D11—82no—
397C22⋊D11—82no—
398C22⋊D11—82no—
399C2×Dic11—28no—
400C2×Dic11—28no—
401C2×Dic11—28no—
402C2×Dic11—24no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—42no—
406C2×Dic11—82no—
407C2×Dic11—81no—
408C2×Dic11C22×D412yes—
409C2×Dic11C22×D412yes—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412D44—24no—
413D44—42no—
414C4×D11—82no—
415C4×D11—82no—
416Dic22—28no—
417Dic22—28no—
418Dic22—28no—
419Dic22—24no—
420Dic22—82no—
421Dic22C2×#4118yes—
422C8×C11—22no—
423C8×C11—22no—
424C11⋊C8—24no—
425C23×Q8—111no—
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#525C2×D1111yescharacteristic
441C2×#121—111no—
442#520—111no—
443#519—112no—
444#519—114no—
445#519—112no—
446#519—222no—
447#519—221no—
448#519—221no—
449#518—111no—
450C2×C4×Q8—112no—
451C2×C4×Q8—112no—
452C2×C4×Q8—221no—
453C2×C4×Q8—221no—
454C2×#117—111no—
455C2×#117—222no—
456C2×#117C2×D1111yescharacteristic
457#485C2×D1112yescomplemented
458#484C2×D1111yescharacteristic, complemented
459#483C2×D1111yescharacteristic, complemented
460#482—114no—
461#482C2×D1112yescomplemented
462#481—112no—
463#481C2×D1111yescharacteristic, complemented
464#480—112no—
465#480C2×D1111yescharacteristic, complemented
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—112no—
480#448—114no—
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#427C2×D1112yes—
494#424—112no—
495#419—112no—
496#418—112no—
497#416C2×D1112yes—
498C2×#103—112no—
499#407—111no—
500C2×C22⋊C8C2×D1111yescharacteristic
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—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11#52512yes—
514C22×C11#57712yes—
515C22×C11C23×D411yescharacteristic
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—162no—
520C4×C11—21no—
521C4×C11—21no—
522C4×C11—42no—
523C4×C11—41no—
524C4×C11—41no—
525C4×C11—42no—
526C4×C11—41no—
527C4×C11#52512yes—
528C4×C11C22×#4112yes—
529Dic11—22no—
530Dic11—22no—
531Dic11—28no—
532Dic11—22no—
533Dic11—22no—
534Dic11—42no—
535C2×#41—222no—
536C2×#41C22×D1111yescharacteristic
537C22×Q8—112no—
538C22×Q8—112no—
539C22×Q8—112no—
540C22×Q8—228no—
541C22×Q8—221no—
542C22×Q8—221no—
543C22×Q8—221no—
544C22×D4—111no—
545C22×D4—221no—
546C23×C4—221no—
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×C8C22×D1112yes—
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—21no—
567#123—222no—
568#123—222no—
569#123—222no—
570#123—222no—
571C22⋊Q8—222no—
572C22⋊Q8—222no—
573C22⋊Q8C22×D1111yescharacteristic
574C22⋊Q8C22×D1111yescharacteristic
575#121—112no—
576#121—112no—
577#121—222no—
578#121—222no—
579#121—221no—
580#121—221no—
581#121—222no—
582#121—221no—
583#121—221no—
584#121C22×D1111yescharacteristic
585#121C22×D1111yescharacteristic
586#120—21no—
587#120—222no—
588C4×Q8—112no—
589C4×Q8—114no—
590C4×Q8—114no—
591C4×Q8—114no—
592C4×Q8—114no—
593C4×Q8—222no—
594C4×Q8—222no—
595C4×Q8—222no—
596C4×Q8—222no—
597C4×Q8—224no—
598C4×Q8—224no—
599C4×Q8—222no—
600C4×Q8—222no—
601C4×Q8—222no—
602C4×Q8—222no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—112no—
606C4×D4—112no—
607C4×D4—112no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613#117—21no—
614#117—21no—
615#117—112no—
616#117—111no—
617#117—111no—
618#117—111no—
619#117—111no—
620#117—112no—
621#117—222no—
622#117—224no—
623#117—224no—
624#117—224no—
625#117—224no—
626#117—221no—
627#117C22×D1112yes—
628#117C22×D1112yes—
629#117C22×D1111yescharacteristic
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—221no—
634C2×C4⋊C4—222no—
635C2×C4⋊C4—222no—
636C2×C4⋊C4C22×D1111yescharacteristic
637C2×C4⋊C4C22×D1111yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—222no—
641C2×C22⋊C4—221no—
642C2×C42—21no—
643C2×C42—112no—
644C2×C42—222no—
645C2×C42—222no—
646#107—114no—
647#107C22×D1112yes—
648#107C22×D1112yes—
649#106—114no—
650#106C22×D1112yes—
651#106C22×D1112yes—
652C4⋊C8—114no—
653C4⋊C8—114no—
654#103—114no—
655#103—114no—
656#103—114no—
657#103—114no—
658#103C22×D1112yes—
659#103C22×D1112yes—
660#102—114no—
661#102—114no—
662#102C22×D1112yes—
663#102C22×D1112yes—
664C22⋊C8—112no—
665C22⋊C8—112no—
666C22⋊C8C22×D1111yescharacteristic
667C22⋊C8C22×D1111yescharacteristic
668C22⋊C8C22×D1112yes—
669#97—114no—
670C4×C8—114no—
671C2×C11—22no—
672C2×C11—22no—
673C2×C11—41no—
674C2×C11—81no—
675C2×C11C2×#52511yescharacteristic
676C2×C11C2×#57711yescharacteristic
677C2×C11#358611yescharacteristic
678D11—82no—
679C24—221no—
680C24D4×D1111yescharacteristic
681#41—24no—
682#41—884no—
683C2×Q8—118no—
684C2×Q8—114no—
685C2×Q8—222no—
686C2×Q8—228no—
687C2×Q8—228no—
688C2×Q8—228no—
689C2×Q8—228no—
690C2×Q8—228no—
691C2×Q8—222no—
692C2×Q8—222no—
693C2×Q8—222no—
694C2×Q8—224no—
695C2×Q8C23×D1111yescharacteristic
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—112no—
700C2×D4—222no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—221no—
705C2×D4—224no—
706C2×D4—882no—
707C2×D4C23×D1111yescharacteristic
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—222no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—228no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—221no—
722C22×C4D4×D1111yescharacteristic
723C22×C4D4×D1111yescharacteristic
724C22×C4D4×D1111yescharacteristic
725C22×C4C23×D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728Q16—228no—
729SD16—228no—
730SD16—228no—
731SD16—228no—
732M16—224no—
733C2×C8—24no—
734C2×C8—114no—
735C2×C8C23×D1112yes—
736C2×C8C23×D1112yes—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—111no—
742C4⋊C4—111no—
743C4⋊C4—111no—
744C4⋊C4—111no—
745C4⋊C4—112no—
746C4⋊C4—112no—
747C4⋊C4—112no—
748C4⋊C4—224no—
749C4⋊C4—224no—
750C4⋊C4—224no—
751C4⋊C4—224no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—222no—
756C4⋊C4—221no—
757C4⋊C4C23×D1112yes—
758C4⋊C4C23×D1112yes—
759C4⋊C4C23×D1111yescharacteristic
760C4⋊C4C23×D1111yescharacteristic
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—112no—
769C22⋊C4—112no—
770C22⋊C4—112no—
771C22⋊C4—112no—
772C22⋊C4—222no—
773C22⋊C4—222no—
774C22⋊C4—222no—
775C22⋊C4—222no—
776C22⋊C4—222no—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C42—22no—
780C42—22no—
781C42—21no—
782C42—112no—
783C42—112no—
784C42—112no—
785C42—112no—
786C42—224no—
787C42—224no—
788C42—224no—
789C42—224no—
790C42—222no—
791C11#6058211yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—21no—
795C23—41no—
796C23—222no—
797C23—442no—
798C23—881no—
799C23—881no—
800C23C2×D4×D1111yescharacteristic
801C23C2×D4×D1111yescharacteristic
802C23C2×D4×D1111yescharacteristic
803Q8—22no—
804Q8—118no—
805Q8—228no—
806Q8—228no—
807Q8—228no—
808Q8—224no—
809Q8—882no—
810D4—22no—
811D4—42no—
812D4—42no—
813D4—81no—
814D4—224no—
815D4—444no—
816D4—442no—
817D4—882no—
818D4—882no—
819D4—882no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—112no—
834C2×C4—112no—
835C2×C4—112no—
836C2×C4—112no—
837C2×C4—228no—
838C2×C4—228no—
839C2×C4—224no—
840C2×C4—228no—
841C2×C4—224no—
842C2×C4—222no—
843C2×C4—442no—
844C2×C4—882no—
845C2×C4—882no—
846C2×C4—882no—
847C2×C4—881no—
848C2×C4C2×D4×D1111yescharacteristic
849C2×C4C2×D4×D1111yescharacteristic
850C2×C4C2×D4×D1111yescharacteristic
851C2×C4#41×D1114yes—
852C2×C4C24×D1111yescharacteristic
853C8—22no—
854C8—22no—
855C8—224no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—44no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—442no—
868C22—442no—
869C22—442no—
870C22—1762no—
871C22#1062318712yes—
872C22#1062330112yes—
873C22C22×D4×D1111yescharacteristic
874C4—21no—
875C4—21no—
876C4—42no—
877C4—41no—
878C4—42no—
879C4—41no—
880C4—41no—
881C4—222no—
882C4—222no—
883C4—222no—
884C4—222no—
885C4—228no—
886C4—442no—
887C4#1062318712yes—
888C4C2×#41×D1112yes—
889C2—22no—
890C2—22no—
891C2—41no—
892C2—81no—
893C2—882no—
894C2C2×#1062318711yescharacteristic
895C2C2×#1062330111yescharacteristic
896C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3091C2
socleC22×C11C23×D4
prime radical#13082353C2
hypercenter#3091D11
hypocenterC11#60582
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
3. #13078903C2semidirect
4. #13078848C2semidirect
5. #13078790C2semidirect
6. #13078735C2semidirect
7. #13078699C2semidirect
8. #13078644C2semidirect
9. #13078556C2semidirect
10. #13078461C2semidirect
11. #13078140C2semidirect
12. #13077849C2semidirect
13. C2×#10622351C2semidirect
14. #13077474C2semidirect
15. #13077462C2semidirect
16. #13077270C2semidirect
17. C11×#3091C2semidirect
44. #10623047C22semidirect
45. C2×#66940C22semidirect
46. C2×#66940C22semidirect
50. C11×#485C22semidirect
51. C11×#484C22semidirect
52. C11×#483C22semidirect
53. C11×#482C22semidirect
54. C11×#481C22semidirect
55. C11×#480C22semidirect
63. #10622663C22semidirect
64. #10622663C22semidirect
65. #10622653C22semidirect
66. #10622653C22semidirect
73. #10622502C22semidirect
74. #10622502C22semidirect
75. #10622490C22semidirect
76. #10622488C22semidirect
77. #10622470C22semidirect
78. #10622467C22semidirect
79. #10622465C22semidirect
80. #10622465C22semidirect
81. #10622411C22semidirect
82. #10622411C22semidirect
83. #10622403C22semidirect
84. #10622402C22semidirect
85. #10622375C22semidirect
86. #10622375C22semidirect
87. #10622371C22semidirect
88. #10622370C22semidirect
92. #10622333C22semidirect
93. #10622332C22semidirect
94. #10622331C22semidirect
279. C2×Dic22#41semidirect
353. #3091D11semidirect
457. #485C2×D11semidirect
458. #484C2×D11semidirect
459. #483C2×D11semidirect
461. #482C2×D11semidirect
463. #481C2×D11semidirect
465. #480C2×D11semidirect
791. C11#60582semidirect

Maximal subgroups

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

subgroupindex
#130823532
C2×#106230472
#130789032
#130788482
#130787902
#130787352
#130786992
#130786442
#130785562
#130784612
#130781402
#130778492
C2×#106223512
#130774742
#130774622
#130772702
C11×#30912
#6058211