Finite Group Databasebeta

← #15638610

Subgroups — #15638610

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic
3#13080704C214yesmaximal, complemented
4#13080696C214yesmaximal, complemented
5#13080125C214yesmaximal, complemented
6#13080121C214yesmaximal, complemented
7#13079619C211yesmaximal, characteristic, complemented
8#13079419C212yesmaximal, complemented
9#13079389C212yesmaximal, complemented
10#13078716C211yesmaximal, characteristic, complemented
11#13078711C211yesmaximal, characteristic, complemented
12#13077875C212yesmaximal, complemented
13D11×#450C212yesmaximal, complemented
14#13077644C211yesmaximal, characteristic, complemented
15C11×#3215C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C11×#533C2211yescharacteristic, complemented
19C2×C11×#124C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×#66971C2214yescomplemented
23C2×SD16×D11C2214yescomplemented
24#10623261C2212yescomplemented
25#10623258C2212yescomplemented
26#10623221—22no—
27#10623207—22no—
28#10623207—22no—
29#10623207C2214yes—
30#10623207C2214yes—
31#10623165—21no—
32#10623165—21no—
33D11×C22⋊Q8C2212yes—
34D11×C22⋊Q8C2212yescomplemented
35#10623110—22no—
36#10623110C2212yescomplemented
37Q8×D44C2212yescomplemented
38#10623052—21no—
39#10623050—21no—
40C2×#66937—21no—
41C2×#66936—21no—
42C2×#66935—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46#10623001C2211yescharacteristic, complemented
47C11×#497C2212yescomplemented
48C11×#489C2212yescomplemented
49C11×#464C2214yescomplemented
50C11×#451C2212yescomplemented
51C11×#450C2212yes—
52C11×#432C2211yescharacteristic, complemented
53#10622841C2212yescomplemented
54#10622831C2212yes—
55#10622801C2214yescomplemented
56#10622800C2214yescomplemented
57#10622799C2214yescomplemented
58#10622787C2214yescomplemented
59#10622783C2214yescomplemented
60#10622782C2214yescomplemented
61#10622700C2212yescomplemented
62#10622696C2212yescomplemented
63#10622673C2212yescomplemented
64#10622668C2212yescomplemented
65#10622667C2214yescomplemented
66#10622659C2212yes—
67#10622657C2212yescomplemented
68#10622639C2214yescomplemented
69#10622539C2211yescharacteristic, complemented
70#10622459C2212yescomplemented
71#10622454C2212yescomplemented
72#10622449C2214yescomplemented
73#10622426C2214yescomplemented
74#10622423C2214yescomplemented
75#10622422C2214yescomplemented
76#10622416C2214yescomplemented
77#10622393C2214yescomplemented
78#10622389C2214yescomplemented
79#10622387C2214yescomplemented
80D11×#102C2214yescomplemented
81#10622344C2212yes—
82#10622339C2212yescomplemented
83D11×C22⋊C8C2212yes—
84#10622335C2212yescomplemented
85#10622323C2214yescomplemented
86#10622319C2214yescomplemented
87C24×D11—21no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C2×#4343—22no—
93C2×#4343—44no—
94C2×#4343C2314yes—
95C2×Q8×D11C2312yes—
96C2×Q8×D11C2312yescomplemented
97C2×D4×D11—22no—
98C2×D4×D11—44no—
99C2×D4×D11C2314yes—
100C22×D44—21no—
101C22×D44D411yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×C4×D11C2311yescharacteristic
107C2×C11×Q16C2314yescomplemented
108C2×C11×SD16C2314yes—
109C11×C4⋊Q8C2311yescharacteristic, complemented
110C11×C4⋊Q8C2311yescharacteristic, complemented
111C11×#125—21no—
112C11×#124—21no—
113C11×#124—21no—
114C11×#124C2312yes—
115C11×#124C2312yes—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8C2312yes—
118C4×Q8×C11—21no—
119C4×Q8×C11C2312yescomplemented
120C11×#117—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125#66999—22no—
126#66999—22no—
127#66999—22no—
128#66999C2312yes—
129#66999C2314yes—
130#66999C2312yescomplemented
131C2×#4326C2314yescomplemented
132C2×#4325C2314yes—
133#66991—22no—
134#66991C2314yes—
135C2×#4324C2314yes—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4D411yescharacteristic
139C2×(C2×D11)⋊C4D411yescharacteristic
140#66979—21no—
141C2×C4⋊Dic11D411yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143#66977—21no—
144#66977C2312yes—
145C2×Dic11⋊C4—21no—
146#66971—48no—
147SD16×D11—48no—
148C2×#4314C2314yes—
149C2×#4313C2314yescomplemented
150C2×C8×D11C2314yes—
151#66950—22no—
152#66950—22no—
153#66950C2312yes—
154#66950C2312yescomplemented
155#66949—22no—
156#66949—22no—
157#66949—22no—
158#66949—22no—
159#66949—22no—
160#66949—22no—
161#66946—22no—
162#66946—22no—
163C4⋊C4×D11—22no—
164C4⋊C4×D11—22no—
165C4⋊C4×D11C2312yes—
166C4⋊C4×D11C2312yescomplemented
167#66943—22no—
168#66941—22no—
169#66937—24no—
170#66937—24no—
171#66936—24no—
172#66936—24no—
173#66935—24no—
174#66935—24no—
175C22⋊C4×D11—22no—
176C22⋊C4×D11—22no—
177C22⋊C4×D11—24no—
178C22⋊C4×D11—24no—
179#66931—22no—
180#66931—22no—
181C4×D44—22no—
182C4×D44—22no—
183C4×D44—21no—
184C4×D44—21no—
185C4×D44D412yes—
186C4×D44D412yes—
187C4×D44C2312yes—
188C4×D44C2312yes—
189C4×D44C2312yes—
190C4×D44C2312yes—
191#66923—21no—
192#66923—22no—
193#66922—22no—
194#66922C2311yescharacteristic, complemented
195#66922C2311yescharacteristic, complemented
196C4×Dic22—21no—
197C4×Dic22C2312yescomplemented
198C11×C4⋊C8C2312yescomplemented
199C11×#103C2314yescomplemented
200C11×#102C2314yes—
201C11×C22⋊C8C2312yes—
202C11×#97C2312yescomplemented
203#66899C2314yescomplemented
204#66899C2314yescomplemented
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207#66885C2314yes—
208(C2×D11)⋊C8C2314yes—
209(C2×D11)⋊C8C2314yescomplemented
210#66882C2314yescomplemented
211#66880C2314yescomplemented
212#66873C2314yes—
213#66871C2314yescomplemented
214C4⋊(C11⋊C8)C2312yescomplemented
215#66867C2312yescomplemented
216#61570—111nomaximal, Sylow
217C24×C11—21no—
218C23×D11—21no—
219C23×D11—24no—
220C23×D11—44no—
221C23×D11—44no—
222C23×D11—82no—
223C23×D11C2×D411yescharacteristic
224C23×D11C2×D411yescharacteristic
225C2×Q8×C11—21no—
226C2×Q8×C11—21no—
227C2×Q8×C11—42no—
228C2×Q8×C11C2412yes—
229C2×Q8×C11C2412yes—
230C2×D4×C11—21no—
231C2×D4×C11—42no—
232C2×D4×C11C2412yes—
233C22×C4×C11—21no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—82no—
241C22×Dic11—21no—
242C22×Dic11C2×D411yescharacteristic
243C22×Dic11C2×D411yescharacteristic
244#4343—28no—
245#4343—44no—
246#4343—48no—
247Q8×D11—44no—
248Q8×D11—44no—
249D4×D11—28no—
250D4×D11—44no—
251D4×D11—48no—
252C2×D44—24no—
253C2×D44—24no—
254C2×D44—24no—
255C2×D44—21no—
256C2×D44—44no—
257C2×D44C2×D412yes—
258C2×D44C2×D412yes—
259C2×D44C2412yes—
260C2×C4×D11—24no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—22no—
267C2×C4×D11—42no—
268C2×C4×D11—42no—
269C2×C4×D11—44no—
270C2×C4×D11—82no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2×D412yes—
273C2×C4×D11C2412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—22no—
276C2×Dic22—22no—
277C2×Dic22—21no—
278C2×Dic22C2412yes—
279C11×Q16—44no—
280C11×SD16—44no—
281C2×C8×C11C2414yes—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4C2412yes—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C42×C11—22no—
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C22⋊Dic11—24no—
299C22⋊Dic11—22no—
300#4326—44no—
301#4325—28no—
302#4324—44no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4C2×D412yes—
311(C2×D11)⋊C4C2×D412yes—
312(C2×D11)⋊C4C2×D412yes—
313(C2×D11)⋊C4C2×D412yes—
314C4⋊Dic11—22no—
315C4⋊Dic11—22no—
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11C2×D412yes—
321C4⋊Dic11C2×D412yes—
322C4⋊Dic11C2412yes—
323C4⋊Dic11C2412yes—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327Dic11⋊C4—22no—
328Dic11⋊C4—24no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331C4×Dic11—22no—
332C2×C11⋊C8C2414yes—
333#4314—28no—
334#4313—44no—
335C8×D11—44no—
336#3501—111no—
337C2×#546—111no—
338#3314—114no—
339#3314—114no—
340#3266—114no—
341#3266—114no—
342#3215—111no—
343#3215D1111yescharacteristic, complemented
344#3193—112no—
345#3189—112no—
346#3110—111no—
347#3110—111no—
348#3007—112no—
349C2×#450—112no—
350#2973—111no—
351C23×C11—22no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11C22×D411yescharacteristic
356C22×D11—24no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—41no—
360C22×D11—41no—
361C22×D11—41no—
362C22×D11—41no—
363C22×D11—48no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—48no—
367C22×D11—84no—
368C22×D11—816no—
369C22×D11#13714yescomplemented
370C22×D11C22×D412yes—
371C22×D11C22×D412yes—
372Q8×C11—24no—
373Q8×C11—24no—
374Q8×C11—42no—
375Q8×C11—81no—
376D4×C11—24no—
377D4×C11—42no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—41no—
384C2×C4×C11—42no—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C2511yescharacteristic
391C22⋊D11—48no—
392C22⋊D11—84no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—42no—
399C2×Dic11C22×D412yes—
400C2×Dic11C22×D412yes—
401D44—24no—
402D44—24no—
403D44—24no—
404D44—22no—
405D44—48no—
406D44H(5,𝔽2)14yes—
407C4×D11—24no—
408C4×D11—24no—
409C4×D11—42no—
410C4×D11—42no—
411C4×D11—48no—
412C4×D11—82no—
413C4×D11—82no—
414C4×D11—82no—
415C4×D11—82no—
416C4×D11—82no—
417C4×D11—82no—
418Dic22—24no—
419Dic22—82no—
420Dic22—82no—
421Dic22—81no—
422C8×C11—24no—
423C11⋊C8—24no—
424C22×#41—111no—
425C23×D4—111no—
426C2×#137—114no—
427C22×SD16—114no—
428#554—112no—
429#554—112no—
430#554—222no—
431#554—222no—
432D4×Q8—112no—
433D4×Q8—112no—
434#546—114no—
435#546—114no—
436#546—222no—
437#546—222no—
438#544—221no—
439#543—221no—
440#543—221no—
441#533—111no—
442#533C2×D1111yescharacteristic, complemented
443C2×#124C2×D1111yescharacteristic
444C2×#123—221no—
445C2×C22⋊Q8—111no—
446C2×C22⋊Q8—112no—
447C2×C22⋊Q8—112no—
448C2×#121—111no—
449C2×#121—221no—
450C2×#120—221no—
451#518—221no—
452C2×C4×D4—111no—
453C2×C4×D4—111no—
454C22×C22⋊C4—221no—
455#497—112no—
456#497C2×D1112yescomplemented
457#489—112no—
458#489C2×D1112yescomplemented
459#484—112no—
460#484—114no—
461#484—112no—
462#480—114no—
463#474—112no—
464#474—112no—
465#468—114no—
466#468—114no—
467#467—114no—
468#467—114no—
469#464—114no—
470#464C2×D1114yescomplemented
471#461—112no—
472#461—112no—
473#452—114no—
474#452—114no—
475#451—112no—
476#451—114no—
477#451C2×D1112yescomplemented
478#450—112no—
479#450—114no—
480#450—112no—
481#450—114no—
482#450—112no—
483#450C2×D1112yes—
484#448—114no—
485#440—114no—
486#440—114no—
487#435—114no—
488#435—114no—
489#432—111no—
490#432C2×D1111yescharacteristic, complemented
491#417—114no—
492C2×#102—114no—
493#407—112no—
494C2×C22⋊C8—112no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—84no—
501C22×C11C2×#13712yes—
502C22×C11C23×D411yescharacteristic
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—24no—
507C2×D11—22no—
508C2×D11—22no—
509C2×D11—44no—
510C2×D11—48no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—816no—
514C2×D11—82no—
515C2×D11C2×#13714yes—
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—21no—
521C4×C11—42no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11C2×H(5,𝔽2)12yes—
525Dic11—22no—
526Dic11—22no—
527Dic11—42no—
528Dic11—42no—
529Dic11—42no—
530C25—221no—
531C2×#41—114no—
532C2×#41—222no—
533C2×#41—444no—
534C22×Q8—112no—
535C22×Q8—112no—
536C22×Q8C22×D1111yescharacteristic
537C22×D4—114no—
538C22×D4—111no—
539C22×D4—111no—
540C22×D4—221no—
541C22×D4—222no—
542C22×D4—221no—
543C22×D4—221no—
544C22×D4—444no—
545C22×D4C22×D1111yescharacteristic
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—221no—
549C23×C4—221no—
550#137—448no—
551C2×Q16—114no—
552C2×Q16C22×D1114yescomplemented
553C2×SD16—114no—
554C2×SD16—114no—
555C2×SD16—114no—
556C2×SD16—448no—
557C2×SD16C22×D1114yes—
558C2×M16—114no—
559C22×C8—114no—
560C4⋊Q8—111no—
561C4⋊Q8—111no—
562C4⋊Q8—222no—
563C4⋊Q8—222no—
564C4⋊Q8C22×D1111yescharacteristic, complemented
565C4⋊Q8C22×D1111yescharacteristic, complemented
566#125—21no—
567#125—222no—
568#125—222no—
569#125—221no—
570#124—21no—
571#124—21no—
572#124C22×D1112yes—
573#124C22×D1112yes—
574#123—224no—
575#123—224no—
576C22⋊Q8—21no—
577C22⋊Q8—114no—
578C22⋊Q8—112no—
579C22⋊Q8—112no—
580C22⋊Q8—112no—
581C22⋊Q8—112no—
582C22⋊Q8—112no—
583C22⋊Q8—222no—
584C22⋊Q8—222no—
585C22⋊Q8—222no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8—222no—
589C22⋊Q8—222no—
590C22⋊Q8—222no—
591C22⋊Q8—222no—
592C22⋊Q8—222no—
593C22⋊Q8—222no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8—221no—
597C22⋊Q8C22×D1112yes—
598#121—114no—
599#121—224no—
600#121—224no—
601#121—222no—
602#120—224no—
603#120—224no—
604C4×Q8—21no—
605C4×Q8—112no—
606C4×Q8—221no—
607C4×Q8C22×D1112yescomplemented
608C4×D4—112no—
609C4×D4—112no—
610C4×D4—112no—
611C4×D4—112no—
612C4×D4—112no—
613C4×D4—112no—
614C4×D4—222no—
615C4×D4—222no—
616C4×D4—222no—
617C4×D4—222no—
618C4×D4—221no—
619C4×D4—221no—
620#117—21no—
621#117—221no—
622C2×C4⋊C4—111no—
623C2×C4⋊C4—111no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—222no—
628C2×C4⋊C4—221no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—111no—
632C2×C22⋊C4—111no—
633C2×C22⋊C4—224no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4—222no—
637C2×C22⋊C4—221no—
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C42C22×D1111yescharacteristic
641#107—114no—
642#107—114no—
643C4⋊C8—112no—
644C4⋊C8C22×D1112yescomplemented
645#103—114no—
646#103—114no—
647#103—114no—
648#103C22×D1114yescomplemented
649#102—114no—
650#102—114no—
651#102—114no—
652#102C22×D1114yes—
653C22⋊C8—112no—
654C22⋊C8—114no—
655C22⋊C8—114no—
656C22⋊C8C22×D1112yes—
657#97—112no—
658#97C22×D1112yescomplemented
659C2×C11—22no—
660C2×C11—82no—
661C2×C11#348411yescharacteristic
662C2×C11C22×#13711yescharacteristic
663C2×C11#358511yescharacteristic
664D11—24no—
665D11—42no—
666D11—44no—
667C24—21no—
668C24—111no—
669C24—111no—
670C24—224no—
671C24—221no—
672C24—444no—
673C24—444no—
674C24—882no—
675#41—228no—
676#41—444no—
677#41—448no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—42no—
681C2×Q8—112no—
682C2×Q8—222no—
683C2×Q8—222no—
684C2×Q8—221no—
685C2×Q8—444no—
686C2×Q8—444no—
687C2×Q8C23×D1112yes—
688C2×Q8C23×D1112yes—
689C2×D4—21no—
690C2×D4—42no—
691C2×D4—112no—
692C2×D4—112no—
693C2×D4—112no—
694C2×D4—224no—
695C2×D4—224no—
696C2×D4—224no—
697C2×D4—224no—
698C2×D4—228no—
699C2×D4—224no—
700C2×D4—221no—
701C2×D4—444no—
702C2×D4—444no—
703C2×D4—448no—
704C2×D4—444no—
705C2×D4—882no—
706C2×D4C23×D1112yes—
707C22×C4—21no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—112no—
714C22×C4—224no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—442no—
723C22×C4—442no—
724C22×C4—444no—
725C22×C4—882no—
726C22×C4D4×D1111yescharacteristic
727C22×C4D4×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729Q16—44no—
730Q16—444no—
731SD16—44no—
732SD16—228no—
733SD16—228no—
734SD16—444no—
735M16—444no—
736C2×C8—114no—
737C2×C8—444no—
738C2×C8C23×D1114yes—
739C4⋊C4—22no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—22no—
744C4⋊C4—112no—
745C4⋊C4—112no—
746C4⋊C4—112no—
747C4⋊C4—112no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—224no—
751C4⋊C4—222no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—221no—
756C4⋊C4—222no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—222no—
760C4⋊C4—221no—
761C4⋊C4C23×D1112yes—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—112no—
768C22⋊C4—112no—
769C22⋊C4—112no—
770C22⋊C4—112no—
771C22⋊C4—224no—
772C22⋊C4—222no—
773C22⋊C4—222no—
774C22⋊C4—222no—
775C22⋊C4—222no—
776C22⋊C4—224no—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C42—22no—
781C42—222no—
782C42D4×D1111yescharacteristic
783C42D4×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C42C23×D1111yescharacteristic
786C11#6157011yescharacteristic, complemented, Sylow
787C23—22no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—112no—
792C23—114no—
793C23—112no—
794C23—224no—
795C23—222no—
796C23—222no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—442no—
802C23—448no—
803C23—448no—
804C23—442no—
805C23—884no—
806C23—8816no—
807C23C2×D4×D1111yescharacteristic
808Q8—24no—
809Q8—24no—
810Q8—42no—
811Q8—81no—
812Q8—224no—
813Q8—881no—
814Q8—882no—
815Q8—882no—
816D4—24no—
817D4—42no—
818D4—114no—
819D4—224no—
820D4—224no—
821D4—224no—
822D4—222no—
823D4—448no—
824D4—448no—
825D4—884no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—112no—
834C2×C4—112no—
835C2×C4—224no—
836C2×C4—224no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—442no—
841C2×C4—442no—
842C2×C4—448no—
843C2×C4—441no—
844C2×C4—441no—
845C2×C4—442no—
846C2×C4—882no—
847C2×C4—882no—
848C2×C4—882no—
849C2×C4—882no—
850C2×C4—882no—
851C2×C4—882no—
852C2×C4C2×D4×D1111yescharacteristic
853C2×C4C2×D4×D1111yescharacteristic
854C2×C4C2×D4×D1111yescharacteristic
855C2×C4C2×D4×D1111yescharacteristic
856C2×C4C2×D4×D1111yescharacteristic
857C2×C4C24×D1111yescharacteristic
858C8—24no—
859C8—224no—
860C22—21no—
861C22—21no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—84no—
866C22—114no—
867C22—222no—
868C22—222no—
869C22—222no—
870C22—222no—
871C22—224no—
872C22—222no—
873C22—444no—
874C22—448no—
875C22—442no—
876C22—442no—
877C22—882no—
878C22—8816no—
879C22D11×#13712yes—
880C22C22×D4×D1111yescharacteristic
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—222no—
890C4—222no—
891C4—442no—
892C4—442no—
893C4—442no—
894C4D11×H(5,𝔽2)12yes—
895C2—22no—
896C2—82no—
897C2—224no—
898C2—442no—
899C2—444no—
900C2#1308225011yescharacteristic
901C2C2×D11×#13711yescharacteristic
902C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3215C2
socleC22×C11C23×D4
prime radicalC2×#10623207C2
hypercenter#3215D11
hypocenterC11#61570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
1. #13082417C2semidirect
3. #13080704C2semidirect
4. #13080696C2semidirect
5. #13080125C2semidirect
6. #13080121C2semidirect
7. #13079619C2semidirect
8. #13079419C2semidirect
9. #13079389C2semidirect
10. #13078716C2semidirect
11. #13078711C2semidirect
12. #13077875C2semidirect
13. D11×#450C2semidirect
14. #13077644C2semidirect
15. C11×#3215C2semidirect
18. C11×#533C22semidirect
22. C2×#66971C22semidirect
23. C2×SD16×D11C22semidirect
24. #10623261C22semidirect
25. #10623258C22semidirect
34. D11×C22⋊Q8C22semidirect
36. #10623110C22semidirect
37. Q8×D44C22semidirect
46. #10623001C22semidirect
47. C11×#497C22semidirect
48. C11×#489C22semidirect
49. C11×#464C22semidirect
50. C11×#451C22semidirect
52. C11×#432C22semidirect
53. #10622841C22semidirect
55. #10622801C22semidirect
56. #10622800C22semidirect
57. #10622799C22semidirect
58. #10622787C22semidirect
59. #10622783C22semidirect
60. #10622782C22semidirect
61. #10622700C22semidirect
62. #10622696C22semidirect
63. #10622673C22semidirect
64. #10622668C22semidirect
65. #10622667C22semidirect
67. #10622657C22semidirect
68. #10622639C22semidirect
69. #10622539C22semidirect
70. #10622459C22semidirect
71. #10622454C22semidirect
72. #10622449C22semidirect
73. #10622426C22semidirect
74. #10622423C22semidirect
75. #10622422C22semidirect
76. #10622416C22semidirect
77. #10622393C22semidirect
78. #10622389C22semidirect
79. #10622387C22semidirect
80. D11×#102C22semidirect
82. #10622339C22semidirect
84. #10622335C22semidirect
85. #10622323C22semidirect
86. #10622319C22semidirect
96. C2×Q8×D11C23semidirect
107. C2×C11×Q16C23semidirect
109. C11×C4⋊Q8C23semidirect
110. C11×C4⋊Q8C23semidirect
119. C4×Q8×C11C23semidirect
130. #66999C23semidirect
131. C2×#4326C23semidirect
149. C2×#4313C23semidirect
154. #66950C23semidirect
166. C4⋊C4×D11C23semidirect
194. #66922C23semidirect
195. #66922C23semidirect
197. C4×Dic22C23semidirect
198. C11×C4⋊C8C23semidirect
199. C11×#103C23semidirect
202. C11×#97C23semidirect
203. #66899C23semidirect
204. #66899C23semidirect
209. (C2×D11)⋊C8C23semidirect
210. #66882C23semidirect
211. #66880C23semidirect
213. #66871C23semidirect
214. C4⋊(C11⋊C8)C23semidirect
215. #66867C23semidirect
343. #3215D11semidirect
369. C22×D11#137semidirect
442. #533C2×D11semidirect
456. #497C2×D11semidirect
458. #489C2×D11semidirect
470. #464C2×D11semidirect
477. #451C2×D11semidirect
490. #432C2×D11semidirect
552. C2×Q16C22×D11semidirect
564. C4⋊Q8C22×D11semidirect
565. C4⋊Q8C22×D11semidirect
607. C4×Q8C22×D11semidirect
644. C4⋊C8C22×D11semidirect
648. #103C22×D11semidirect
658. #97C22×D11semidirect
786. C11#61570semidirect

Maximal subgroups

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

subgroupindex
#130824172
C2×#106232072
#130807042
#130806962
#130801252
#130801212
#130796192
#130794192
#130793892
#130787162
#130787112
#130778752
D11×#4502
#130776442
C11×#32152
#6157011