Finite Group Databasebeta

← #15638683

Subgroups — #15638683

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic, complemented
2#13080766C214yesmaximal, complemented
3#13080646C214yesmaximal, complemented
4#13080157C214yesmaximal, complemented
5#13080142C214yesmaximal, complemented
6#13079615C211yesmaximal, characteristic, complemented
7#13079599C211yesmaximal, characteristic, complemented
8#13079442C212yesmaximal, complemented
9#13079377C212yesmaximal, complemented
10#13078711C211yesmaximal, characteristic, complemented
11#13078703C211yesmaximal, characteristic, complemented
12#13077842C212yesmaximal, complemented
13#13077832C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3506C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C11×#559—22no—
19C11×#556C2212yescomplemented
20C11×#555C2212yescomplemented
21C11×#553—22no—
22C11×#550C2212yescomplemented
23C11×#547C2212yescomplemented
24C11×#538—21no—
25C11×#538—21no—
26C11×#535—21no—
27C11×#533C2211yescharacteristic, complemented
28C11×#532C2211yescharacteristic, complemented
29C11×#525C2212yes—
30C11×#525C2212yescomplemented
31C11×#520—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67003C2214yescomplemented
34C2×#67002C2214yescomplemented
35C2×#66990—21no—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623081—22no—
39#10623081—22no—
40#10623081C2214yes—
41#10623081C2214yes—
42C2×#66947—21no—
43C2×#66937—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47#10622852C2214yescomplemented
48#10622851C2214yescomplemented
49#10622820C2212yes—
50C2×C22⋊(C11⋊C8)C2212yescomplemented
51#10622702C2212yescomplemented
52#10622702C2212yescomplemented
53#10622700C2212yescomplemented
54#10622699C2212yescomplemented
55#10622697C2212yescomplemented
56#10622696C2212yescomplemented
57#10622687C2212yescomplemented
58#10622685C2212yescomplemented
59#10622665C2214yescomplemented
60#10622663C2212yescomplemented
61#10622661C2214yescomplemented
62#10622660C2214yescomplemented
63#10622659C2212yes—
64#10622659C2212yes—
65#10622659C2214yescomplemented
66#10622657C2212yescomplemented
67#10622655C2214yescomplemented
68#10622653C2212yescomplemented
69#10622651C2214yescomplemented
70#10622650C2214yescomplemented
71#10622649C2212yes—
72#10622649C2212yes—
73#10622649C2214yescomplemented
74#10622647C2212yescomplemented
75#10622641C2214yescomplemented
76#10622639C2214yescomplemented
77#10622629C2214yescomplemented
78#10622627C2214yescomplemented
79#10622624C2214yescomplemented
80#10622624C2214yescomplemented
81#10622616C2214yescomplemented
82#10622615C2214yescomplemented
83#10622614C2214yescomplemented
84#10622609C2214yescomplemented
85#10622539C2211yescharacteristic, complemented
86#10622539C2211yescharacteristic, complemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C2×C11×#41C2312yes—
90C2×C11×#41C2312yescomplemented
91C22×D4×C11D411yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C2×#4339—22no—
97C2×#4339—44no—
98C2×#4339C2314yes—
99C22×D44—21no—
100C22×D44—22no—
101C22×D44—44no—
102C22×D44C2311yescharacteristic
103C22×D44C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×Dic22C2311yescharacteristic
108C11×C4⋊Q8C2311yescharacteristic, complemented
109C11×C4⋊Q8C2311yescharacteristic, complemented
110C11×C4⋊Q8C2311yescharacteristic, complemented
111C11×#127—22no—
112C11×#127C2311yescharacteristic, complemented
113C11×#126—22no—
114C11×#126—22no—
115C11×#125—21no—
116C11×#124—22no—
117C11×#124—22no—
118C11×#124—22no—
119C11×#124—21no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8C2312yes—
126C11×C22⋊Q8C2312yes—
127C11×C22⋊Q8C2312yescomplemented
128C11×#121—22no—
129C11×#121—22no—
130C11×#121—21no—
131C11×#121—22no—
132C11×#121—22no—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C11×#121C2312yescomplemented
136C11×#120—22no—
137C11×#120—22no—
138C4×Q8×C11—22no—
139C4×Q8×C11—21no—
140C4×Q8×C11C2312yescomplemented
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—21no—
147C4×D4×C11D412yes—
148C4×D4×C11D412yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2312yes—
151C4×D4×C11C2312yescomplemented
152C11×#117—21no—
153C11×#117—22no—
154C11×#117C2312yes—
155C11×#117C2312yescomplemented
156C2×C11×C4⋊C4—22no—
157C2×C11×C4⋊C4D411yescharacteristic
158C2×C11×C22⋊C4D411yescharacteristic
159C2×C11×C22⋊C4D411yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C22⋊Dic11—21no—
162#67003—48no—
163#67002—48no—
164C2×#4326C2314yescomplemented
165C2×#4325C2314yes—
166C2×#4325C2314yes—
167#66990—24no—
168#66990—24no—
169C2×#4324C2314yescomplemented
170C2×#4323C2314yes—
171C2×#4323C2314yes—
172#66983—22no—
173#66983C2314yes—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4—21no—
176C2×(C2×D11)⋊C4—21no—
177C2×(C2×D11)⋊C4—21no—
178C2×C4⋊Dic11C2311yescharacteristic
179#66977—22no—
180#66977C2314yes—
181C2×Dic11⋊C4—21no—
182C2×#4318C2314yes—
183C22×C11⋊C8C2314yescomplemented
184#66947—24no—
185#66947—24no—
186#66937—24no—
187#66937—24no—
188C22⋊C4×D11—24no—
189C22⋊C4×D11—24no—
190#66928—21no—
191#66928—21no—
192#66928C2312yes—
193#66928C2312yes—
194C4×D44—21no—
195C4×D44—21no—
196C4×D44C2312yes—
197C4×D44C2312yes—
198#66899C2314yescomplemented
199#66896C2314yescomplemented
200C22⋊(C11⋊C8)C2312yes—
201C22⋊(C11⋊C8)C2312yes—
202C22⋊(C11⋊C8)C2314yes—
203C22⋊(C11⋊C8)C2314yescomplemented
204#66874C2314yescomplemented
205#66874C2314yescomplemented
206#66873C2314yes—
207#66873C2314yes—
208#66873C2314yes—
209#66873C2314yes—
210#66872C2314yescomplemented
211#66871C2314yescomplemented
212C4⋊(C11⋊C8)C2312yescomplemented
213C4⋊(C11⋊C8)C2312yescomplemented
214#66867C2312yescomplemented
215#66867C2312yescomplemented
216#61576—111nomaximal, Sylow
217C24×C11C2×D411yescharacteristic
218C24×C11C2×D411yescharacteristic
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—24no—
222C23×D11—44no—
223C23×D11—44no—
224C23×D11—82no—
225C11×#41—44no—
226C11×#41—44no—
227C11×#41—44no—
228C2×Q8×C11—21no—
229C2×Q8×C11—21no—
230C2×Q8×C11C2412yes—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—42no—
239C2×D4×C11C2×D412yes—
240C2×D4×C11C2×D412yes—
241C2×D4×C11C2412yes—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—82no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262#4339—28no—
263#4339—44no—
264#4339—48no—
265C2×D44—24no—
266C2×D44—28no—
267C2×D44—21no—
268C2×D44—21no—
269C2×D44—24no—
270C2×D44—44no—
271C2×D44—42no—
272C2×D44—44no—
273C2×D44—48no—
274C2×D44C2412yes—
275C2×D44C2412yes—
276C2×C4×D11—24no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—44no—
280C2×C4×D11—82no—
281C2×Dic22—21no—
282C2×Dic22—42no—
283C2×Dic22C2412yes—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—21no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—21no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4C2×D412yes—
293C11×C4⋊C4C2×D412yes—
294C11×C4⋊C4C2412yes—
295C11×C4⋊C4C2412yes—
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C11×C22⋊C4C2×D412yes—
308C11×C22⋊C4C2×D412yes—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11C2×D411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2411yescharacteristic
315C42×C11C2411yescharacteristic
316C22⋊Dic11—24no—
317#4326—44no—
318#4325—28no—
319#4325—44no—
320#4324—44no—
321#4323—28no—
322#4323—44no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—24no—
330C4⋊Dic11—21no—
331C4⋊Dic11C2412yes—
332Dic11⋊C4—24no—
333#4318—44no—
334C2×C11⋊C8—44no—
335C2×C11⋊C8C2414yes—
336C2×C11⋊C8C2414yes—
337#3506D1111yescharacteristic, complemented
338C2×#546—111no—
339#3319—114no—
340#3311—114no—
341#3268—114no—
342#3267—114no—
343#3215—111no—
344#3213—111no—
345#3196—112no—
346#3188—112no—
347#3110—111no—
348#3109—111no—
349#3003—112no—
350#3002—112no—
351#2973—111no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11C22×D412yes—
360C23×C11C22×D412yes—
361C23×C11C22×D411yescharacteristic
362C22×D11—24no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—48no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—48no—
371C22×D11—42no—
372C22×D11—84no—
373C22×D11—816no—
374Q8×C11—24no—
375Q8×C11—42no—
376Q8×C11—81no—
377D4×C11—24no—
378D4×C11—42no—
379D4×C11—42no—
380D4×C11—42no—
381D4×C11—44no—
382D4×C11—81no—
383D4×C11—82no—
384D4×C11—82no—
385D4×C11—82no—
386D4×C11—82no—
387C2×C4×C11—22no—
388C2×C4×C11—24no—
389C2×C4×C11—24no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—42no—
397C2×C4×C11—41no—
398C2×C4×C11—42no—
399C2×C4×C11—44no—
400C2×C4×C11—82no—
401C2×C4×C11—82no—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C22×D411yescharacteristic
405C2×C4×C11C22×D411yescharacteristic
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—48no—
411C22⋊D11—84no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416D44—24no—
417D44—22no—
418D44—24no—
419D44—48no—
420D44—42no—
421D44H(5,𝔽2)14yes—
422C4×D11—48no—
423C4×D11—82no—
424C4×D11—82no—
425Dic22—24no—
426Dic22—42no—
427C11⋊C8—24no—
428C11⋊C8—24no—
429C22×#41—111no—
430C23×D4—111no—
431C2×AGL(1,ℤ/8)—114no—
432C2×#135—114no—
433#559—22no—
434#556C2×D1112yescomplemented
435#555C2×D1112yescomplemented
436#553—22no—
437#550C2×D1112yescomplemented
438#547C2×D1112yescomplemented
439#546—114no—
440#546—114no—
441#546—222no—
442#546—222no—
443#538—21no—
444#538—21no—
445#535—21no—
446#533C2×D1111yescharacteristic, complemented
447#532C2×D1111yescharacteristic, complemented
448C2×#124—111no—
449#525C2×D1112yes—
450#525C2×D1112yescomplemented
451C2×#123—221no—
452C2×C22⋊Q8—111no—
453C2×#121—111no—
454C2×#121—221no—
455C2×#120—221no—
456#520—21no—
457C2×C4×D4—111no—
458C2×C4×D4C2×D1111yescharacteristic
459C22×C22⋊C4—221no—
460#497—112no—
461#496—112no—
462#489—112no—
463#489—112no—
464#485—114no—
465#484—112no—
466#482—114no—
467#481—112no—
468#476—112no—
469#474—112no—
470#470—114no—
471#468—114no—
472#466—114no—
473#465—114no—
474#464—114no—
475#463—114no—
476#461—112no—
477#459—112no—
478#452—114no—
479#452—114no—
480#451—112no—
481#450—112no—
482#450—112no—
483#450—114no—
484#449—114no—
485#449—114no—
486#448—112no—
487#447—112no—
488#447—112no—
489#447—114no—
490#442—114no—
491#440—114no—
492#435—114no—
493#435—114no—
494#432—111no—
495#432—111no—
496#418—114no—
497#416—114no—
498#407—112no—
499C2×C22⋊C8—112no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—44no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—82no—
513C22×C11#57512yes—
514C22×C11C23×D411yescharacteristic
515C2×D11—24no—
516C2×D11—48no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—816no—
523C2×D11—84no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—21no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11C2×H(5,𝔽2)12yes—
535Dic11—42no—
536Dic11—42no—
537C25—221no—
538C2×#41—21no—
539C2×#41—114no—
540C2×#41—222no—
541C2×#41—444no—
542C2×#41C22×D1112yes—
543C2×#41C22×D1112yescomplemented
544C22×Q8—111no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—222no—
552C22×D4—444no—
553C22×D4C22⋊D1111yescharacteristic
554C23×C4—221no—
555C23×C4—221no—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558AGL(1,ℤ/8)—448no—
559#135—448no—
560C2×Q16—114no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—114no—
564C2×D8—114no—
565C2×D8—114no—
566C2×M16—114no—
567C22×C8—114no—
568C4⋊Q8C22×D1111yescharacteristic, complemented
569C4⋊Q8C22×D1111yescharacteristic, complemented
570C4⋊Q8C22×D1111yescharacteristic, complemented
571#127—22no—
572#127C22×D1111yescharacteristic, complemented
573#126—22no—
574#126—22no—
575#125—21no—
576#124—22no—
577#124—22no—
578#124—22no—
579#124—21no—
580#124—112no—
581#124—112no—
582#124—221no—
583#124—221no—
584#123—22no—
585#123—22no—
586#123—22no—
587#123—22no—
588#123—224no—
589#123—224no—
590C22⋊Q8—21no—
591C22⋊Q8—114no—
592C22⋊Q8—222no—
593C22⋊Q8C22×D1112yes—
594C22⋊Q8C22×D1112yes—
595C22⋊Q8C22×D1112yescomplemented
596#121—22no—
597#121—22no—
598#121—21no—
599#121—22no—
600#121—22no—
601#121—114no—
602#121—222no—
603#121—224no—
604#121—224no—
605#121C22×D1112yes—
606#121C22×D1112yes—
607#121C22×D1112yescomplemented
608#120—22no—
609#120—22no—
610#120—224no—
611#120—224no—
612C4×Q8—22no—
613C4×Q8—21no—
614C4×Q8C22×D1112yescomplemented
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—21no—
621C4×D4—112no—
622C4×D4—112no—
623C4×D4—221no—
624C4×D4—221no—
625C4×D4C22⋊D1112yes—
626C4×D4C22⋊D1112yes—
627C4×D4C22×D1112yes—
628C4×D4C22×D1112yes—
629C4×D4C22×D1112yescomplemented
630#117—21no—
631#117—22no—
632#117C22×D1112yes—
633#117C22×D1112yescomplemented
634C2×C4⋊C4—22no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4C22⋊D1111yescharacteristic
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—221no—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4C22⋊D1111yescharacteristic
646C2×C22⋊C4C22⋊D1111yescharacteristic
647C2×C42C22×D1111yescharacteristic
648#107—114no—
649#106—114no—
650C4⋊C8—112no—
651C4⋊C8—112no—
652#103—114no—
653#103—114no—
654#103—114no—
655#102—114no—
656#102—114no—
657#102—114no—
658#102—114no—
659#102—114no—
660C22⋊C8—112no—
661C22⋊C8—112no—
662C22⋊C8—114no—
663C22⋊C8—114no—
664#97—112no—
665#97—112no—
666C2×C11—22no—
667C2×C11—42no—
668C2×C11—42no—
669C2×C11—82no—
670C2×C11#348411yescharacteristic
671C2×C11C2×#57511yescharacteristic
672C2×C11#358511yescharacteristic
673D11—44no—
674D11—82no—
675C24—221no—
676C24—221no—
677C24—224no—
678C24—444no—
679C24—444no—
680C24—882no—
681C24C2×C22⋊D1111yescharacteristic
682C24C2×C22⋊D1111yescharacteristic
683#41—44no—
684#41—44no—
685#41—44no—
686#41—228no—
687#41—444no—
688#41—448no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—112no—
692C2×Q8—221no—
693C2×Q8—442no—
694C2×Q8C23×D1112yes—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—22no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—112no—
704C2×D4—112no—
705C2×D4—224no—
706C2×D4—228no—
707C2×D4—224no—
708C2×D4—224no—
709C2×D4—221no—
710C2×D4—224no—
711C2×D4—221no—
712C2×D4—444no—
713C2×D4—442no—
714C2×D4—448no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4—882no—
718C2×D4C2×C22⋊D1112yes—
719C2×D4C2×C22⋊D1112yes—
720C2×D4C23×D1112yes—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—224no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—444no—
732C22×C4—882no—
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1111yescharacteristic
735C22×C4C2×C22⋊D1111yescharacteristic
736C22×C4C2×C22⋊D1111yescharacteristic
737C22×C4C2×C22⋊D1112yes—
738C22×C4C2×C22⋊D1112yes—
739C22×C4C23×D1111yescharacteristic
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742Q16—444no—
743SD16—228no—
744SD16—444no—
745SD16—444no—
746D8—228no—
747D8—444no—
748M16—444no—
749C2×C8—114no—
750C2×C8—114no—
751C2×C8—444no—
752C4⋊C4—21no—
753C4⋊C4—22no—
754C4⋊C4—22no—
755C4⋊C4—21no—
756C4⋊C4—22no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—22no—
760C4⋊C4—112no—
761C4⋊C4—221no—
762C4⋊C4—224no—
763C4⋊C4C2×C22⋊D1112yes—
764C4⋊C4C2×C22⋊D1112yes—
765C4⋊C4C23×D1112yes—
766C4⋊C4C23×D1112yes—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4—222no—
781C22⋊C4—222no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4C2×C22⋊D1112yes—
785C22⋊C4C2×C22⋊D1112yes—
786C22⋊C4C2×C22⋊D1112yes—
787C22⋊C4C2×C22⋊D1112yes—
788C42—22no—
789C42—22no—
790C42—22no—
791C42C2×C22⋊D1111yescharacteristic
792C42C2×C22⋊D1111yescharacteristic
793C42C23×D1111yescharacteristic
794C42C23×D1111yescharacteristic
795C11#6157611yescharacteristic, complemented, Sylow
796C23—22no—
797C23—22no—
798C23—22no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—224no—
804C23—222no—
805C23—222no—
806C23—448no—
807C23—442no—
808C23—442no—
809C23—442no—
810C23—448no—
811C23—442no—
812C23—442no—
813C23—884no—
814C23—8816no—
815C23C22×C22⋊D1112yes—
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818Q8—24no—
819Q8—42no—
820Q8—81no—
821Q8—224no—
822Q8—442no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—44no—
828D4—81no—
829D4—82no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—114no—
834D4—224no—
835D4—222no—
836D4—224no—
837D4—448no—
838D4—442no—
839D4—448no—
840D4—884no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—44no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—448no—
859C2×C4—442no—
860C2×C4—442no—
861C2×C4—882no—
862C2×C4—882no—
863C2×C4C22×C22⋊D1111yescharacteristic
864C2×C4C22×C22⋊D1112yes—
865C2×C4C22×C22⋊D1112yes—
866C2×C4C22×C22⋊D1111yescharacteristic
867C2×C4C22×C22⋊D1111yescharacteristic
868C2×C4C22×C22⋊D1111yescharacteristic
869C2×C4C22×C22⋊D1111yescharacteristic
870C2×C4C24×D1111yescharacteristic
871C8—224no—
872C8—224no—
873C22—21no—
874C22—21no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—44no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—82no—
886C22—224no—
887C22—448no—
888C22—442no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—884no—
894C22—8816no—
895C22#1062335312yes—
896C22C23×C22⋊D1111yescharacteristic
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—22no—
902C4—21no—
903C4—21no—
904C4—42no—
905C4—42no—
906C4—42no—
907C4—442no—
908C4—442no—
909C4D11×H(5,𝔽2)12yes—
910C2—22no—
911C2—42no—
912C2—42no—
913C2—82no—
914C2—444no—
915C2—882no—
916C2#1308224711yescharacteristic
917C2C2×#1062335311yescharacteristic
918C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61576
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C2×#10623081C2semidirect
2. #13080766C2semidirect
3. #13080646C2semidirect
4. #13080157C2semidirect
5. #13080142C2semidirect
6. #13079615C2semidirect
7. #13079599C2semidirect
8. #13079442C2semidirect
9. #13079377C2semidirect
10. #13078711C2semidirect
11. #13078703C2semidirect
12. #13077842C2semidirect
13. #13077832C2semidirect
14. #13077645C2semidirect
15. C11×#3506C2semidirect
19. C11×#556C22semidirect
20. C11×#555C22semidirect
22. C11×#550C22semidirect
23. C11×#547C22semidirect
27. C11×#533C22semidirect
28. C11×#532C22semidirect
30. C11×#525C22semidirect
33. C2×#67003C22semidirect
34. C2×#67002C22semidirect
47. #10622852C22semidirect
48. #10622851C22semidirect
50. C2×C22⋊(C11⋊C8)C22semidirect
51. #10622702C22semidirect
52. #10622702C22semidirect
53. #10622700C22semidirect
54. #10622699C22semidirect
55. #10622697C22semidirect
56. #10622696C22semidirect
57. #10622687C22semidirect
58. #10622685C22semidirect
59. #10622665C22semidirect
60. #10622663C22semidirect
61. #10622661C22semidirect
62. #10622660C22semidirect
65. #10622659C22semidirect
66. #10622657C22semidirect
67. #10622655C22semidirect
68. #10622653C22semidirect
69. #10622651C22semidirect
70. #10622650C22semidirect
73. #10622649C22semidirect
74. #10622647C22semidirect
75. #10622641C22semidirect
76. #10622639C22semidirect
77. #10622629C22semidirect
78. #10622627C22semidirect
79. #10622624C22semidirect
80. #10622624C22semidirect
81. #10622616C22semidirect
82. #10622615C22semidirect
83. #10622614C22semidirect
84. #10622609C22semidirect
85. #10622539C22semidirect
86. #10622539C22semidirect
90. C2×C11×#41C23semidirect
108. C11×C4⋊Q8C23semidirect
109. C11×C4⋊Q8C23semidirect
110. C11×C4⋊Q8C23semidirect
112. C11×#127C23semidirect
127. C11×C22⋊Q8C23semidirect
135. C11×#121C23semidirect
140. C4×Q8×C11C23semidirect
151. C4×D4×C11C23semidirect
155. C11×#117C23semidirect
164. C2×#4326C23semidirect
169. C2×#4324C23semidirect
183. C22×C11⋊C8C23semidirect
198. #66899C23semidirect
199. #66896C23semidirect
203. C22⋊(C11⋊C8)C23semidirect
204. #66874C23semidirect
205. #66874C23semidirect
210. #66872C23semidirect
211. #66871C23semidirect
212. C4⋊(C11⋊C8)C23semidirect
213. C4⋊(C11⋊C8)C23semidirect
214. #66867C23semidirect
215. #66867C23semidirect
337. #3506D11semidirect
434. #556C2×D11semidirect
435. #555C2×D11semidirect
437. #550C2×D11semidirect
438. #547C2×D11semidirect
446. #533C2×D11semidirect
447. #532C2×D11semidirect
450. #525C2×D11semidirect
543. C2×#41C22×D11semidirect
568. C4⋊Q8C22×D11semidirect
569. C4⋊Q8C22×D11semidirect
570. C4⋊Q8C22×D11semidirect
572. #127C22×D11semidirect
595. C22⋊Q8C22×D11semidirect
607. #121C22×D11semidirect
614. C4×Q8C22×D11semidirect
629. C4×D4C22×D11semidirect
633. #117C22×D11semidirect
795. C11#61576semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
#130807662
#130806462
#130801572
#130801422
#130796152
#130795992
#130794422
#130793772
#130787112
#130787032
#130778422
#130778322
#130776452
C11×#35062
#6157611