Finite Group Databasebeta

← #15638705

Subgroups — #15638705

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082455C211yesmaximal, characteristic, complemented
2#13080742C214yesmaximal, complemented
3#13080622C214yesmaximal, complemented
4#13080197C214yesmaximal, complemented
5#13080157C214yesmaximal, complemented
6#13079634C212yesmaximal, complemented
7#13079422C211yesmaximal, characteristic, complemented
8#13079413C211yesmaximal, characteristic, complemented
9#13079381C212yesmaximal, complemented
10#13078787C212yesmaximal, complemented
11#13077876C211yesmaximal, characteristic, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077834C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C2×C11×#550C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic, complemented
18C11×#550—22no—
19C11×#550—22no—
20C11×#550C2214yes—
21C11×#550C2214yescomplemented
22C2×C11×#127—21no—
23C2×C11×#127C2211yescharacteristic, complemented
24C2×C11×#121—21no—
25C2×C11×#121—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic, complemented
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×#67004C2212yescomplemented
32C2×#67003C2214yescomplemented
33C2×#67002C2212yescomplemented
34#10623335—21no—
35#10623322C2212yes—
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38#10623096C2212yescomplemented
39#10623087—22no—
40#10623083C2212yescomplemented
41#10623081C2212yescomplemented
42#10623072C2212yescomplemented
43#10623071—22no—
44#10623046—21no—
45#10623025—21no—
46#10623017—21no—
47#10623010C2212yes—
48#10622852C2214yescomplemented
49#10622852C2214yescomplemented
50#10622851C2214yescomplemented
51#10622851C2214yescomplemented
52#10622846C2214yescomplemented
53#10622845C2212yescomplemented
54#10622845C2212yescomplemented
55#10622841C2212yescomplemented
56#10622840C2212yes—
57#10622831C2212yescomplemented
58#10622831C2212yescomplemented
59#10622830C2212yes—
60#10622830C2212yes—
61#10622820C2211yescharacteristic
62#10622820C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2212yescomplemented
64#10622688C2214yescomplemented
65#10622687C2214yescomplemented
66#10622685C2214yescomplemented
67#10622684C2214yescomplemented
68#10622655C2214yescomplemented
69#10622654C2214yescomplemented
70#10622653C2212yescomplemented
71#10622652C2214yescomplemented
72#10622651C2214yescomplemented
73#10622650C2214yescomplemented
74#10622649C2212yescomplemented
75#10622648C2214yescomplemented
76#10622647C2212yescomplemented
77#10622646C2212yescomplemented
78#10622643C2214yescomplemented
79#10622641C2214yescomplemented
80#10622639C2214yescomplemented
81#10622635C2214yescomplemented
82#10622624C2214yescomplemented
83#10622624C2214yescomplemented
84#10622583C2212yescomplemented
85#10622581C2212yes—
86#10622539C2212yescomplemented
87C2×C11×#41—21no—
88C2×C11×#41—21no—
89C2×C11×#41—22no—
90C2×C11×#41—44no—
91C2×C11×#41—44no—
92C2×C11×#41C2312yes—
93C2×C11×#41C2314yes—
94C2×C11×#41C2312yes—
95C22×Q8×C11C2311yescharacteristic
96C22×D4×C11—21no—
97C22×D4×C11—21no—
98C22×D4×C11—21no—
99C22×D4×C11—21no—
100C22×D4×C11—21no—
101C22×D4×C11—21no—
102C22×D4×C11D411yescharacteristic
103C22×D4×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11—21no—
106C23×C4×C11—21no—
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C22×C22⋊D11—21no—
110C2×#4339C2312yes—
111C22×D44C2311yescharacteristic
112C22×Dic22C2311yescharacteristic
113C11×#127—24no—
114C11×#127—24no—
115C11×#127—22no—
116C11×#127C2314yes—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—22no—
120C11×#121—24no—
121C11×#121—24no—
122C11×#121—24no—
123C11×#121—24no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C11×#121C2314yes—
127C4×Q8×C11—22no—
128C4×Q8×C11C2314yes—
129C4×D4×C11—24no—
130C4×D4×C11—24no—
131C4×D4×C11D412yes—
132C4×D4×C11D412yes—
133C4×D4×C11C2312yes—
134C4×D4×C11C2312yes—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—21no—
140C2×C11×C22⋊C4D411yescharacteristic
141C2×C11×C22⋊C4D411yescharacteristic
142C2×C42×C11—21no—
143C2×C42×C11C2311yescharacteristic
144#67006—22no—
145C2×C22⋊Dic11—21no—
146#67004—44no—
147#67003—48no—
148#67002—44no—
149C2×#4326C2314yes—
150C2×#4325C2314yes—
151#66992—22no—
152#66992—22no—
153#66990—22no—
154#66988—22no—
155C2×#4324C2314yes—
156C2×#4324C2314yes—
157C2×#4323C2314yes—
158C2×#4323C2314yes—
159#66983—21no—
160#66983—21no—
161#66983C2312yes—
162#66983C2312yes—
163#66983C2312yes—
164#66982—22no—
165#66982—22no—
166C4×C22⋊D11—22no—
167C4×C22⋊D11—22no—
168C4×C22⋊D11—22no—
169C2×(C2×D11)⋊C4—21no—
170#66979C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—21no—
174#66977—21no—
175#66977C2312yes—
176#66977C2312yes—
177#66977C2312yes—
178C2×Dic11⋊C4—21no—
179C2×#4318C2312yes—
180C2×#4318C2312yes—
181C22×C11⋊C8C2314yes—
182#66951—22no—
183#66949—22no—
184#66947—22no—
185#66942—22no—
186#66938—22no—
187#66937—22no—
188#66936—22no—
189(C22⋊D11)⋊C4—22no—
190(C22⋊D11)⋊C4—22no—
191C22⋊C4×D11—22no—
192#66932—22no—
193#66930—22no—
194#66929—22no—
195#66928C2312yes—
196C4×D44C2312yes—
197#66925—22no—
198#66923C2312yes—
199C4×Dic22C2312yes—
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203#66896C2314yes—
204#66896C2314yes—
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2314yes—
209C22⋊(C11⋊C8)C2312yes—
210C22⋊(C11⋊C8)C2312yes—
211#66874C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216#66867C2314yes—
217#61577—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C11×#41—24no—
224C11×#41—28no—
225C11×#41—24no—
226C11×#41—44no—
227C11×#41—42no—
228C11×#41—42no—
229C11×#41—44no—
230C11×#41—44no—
231C11×#41—48no—
232C2×Q8×C11—24no—
233C2×Q8×C11—21no—
234C2×Q8×C11C2412yes—
235C2×D4×C11—22no—
236C2×D4×C11—24no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—24no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—24no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—42no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11—44no—
251C2×D4×C11—82no—
252C2×D4×C11—82no—
253C2×D4×C11—82no—
254C2×D4×C11C2×D412yes—
255C2×D4×C11C2×D412yes—
256C2×D4×C11C2412yes—
257C2×D4×C11C2412yes—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—24no—
261C22×C4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—42no—
264C22×C4×C11—42no—
265C22×C4×C11—44no—
266C22×C4×C11—44no—
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C2×C22⋊D11—22no—
279C2×C22⋊D11—22no—
280C2×C22⋊D11—22no—
281C2×C22⋊D11—22no—
282C2×C22⋊D11—44no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286#4339—44no—
287C2×D44—21no—
288C2×D44—42no—
289C2×D44C2412yes—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×Dic22—21no—
293C2×Dic22—42no—
294C2×Dic22C2412yes—
295C11×C4⋊C4—24no—
296C11×C4⋊C4—21no—
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D412yes—
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C11×C22⋊C4C2×D412yes—
306C11×C22⋊C4C2×D412yes—
307C42×C11—24no—
308C42×C11C2×D412yes—
309C42×C11C2412yes—
310C22⋊Dic11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314#4326—28no—
315#4325—28no—
316#4324—44no—
317#4324—44no—
318#4323—44no—
319#4323—44no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11C2412yes—
329C4⋊Dic11C2412yes—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338#4318—42no—
339#4318—42no—
340C2×C11⋊C8—44no—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2414yes—
343#3505—111no—
344C2×#550D1111yescharacteristic, complemented
345#3317—114no—
346#3309—114no—
347#3271—114no—
348#3268—114no—
349#3217—112no—
350#3193—111no—
351#3192—111no—
352#3188—112no—
353#3117—112no—
354#3007—111no—
355#3006—111no—
356#3002—112no—
357#2973—111no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—42no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D412yes—
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C22×D11—22no—
377C22×D11—42no—
378C22×D11—81no—
379C22×D11—81no—
380Q8×C11—24no—
381Q8×C11—22no—
382Q8×C11H(5,𝔽2)14yes—
383D4×C11—22no—
384D4×C11—24no—
385D4×C11—22no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11—44no—
389D4×C11—44no—
390D4×C11—48no—
391D4×C11—48no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—84no—
395D4×C11—82no—
396D4×C11—82no—
397D4×C11—84no—
398C2×C4×C11—24no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—24no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—42no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—44no—
413C2×C4×C11—48no—
414C2×C4×C11—44no—
415C2×C4×C11—42no—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C2511yescharacteristic
423C22⋊D11—44no—
424C22⋊D11—44no—
425C22⋊D11—82no—
426C22⋊D11—82no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—42no—
431C2×Dic11—81no—
432C2×Dic11—81no—
433D44—24no—
434D44—81no—
435C4×D11—82no—
436C4×D11—82no—
437Dic22—24no—
438Dic22—81no—
439C11⋊C8—24no—
440C11⋊C8—24no—
441C22×#41C2×D1111yescharacteristic
442C22×#41C2×D1111yescharacteristic, complemented
443C2×#137—112no—
444C2×AGL(1,ℤ/8)—112no—
445C2×#135—114no—
446#553—112no—
447#553—222no—
448#552—112no—
449#551—222no—
450#550—22no—
451#550—22no—
452#550C2×D1114yes—
453#550C2×D1114yescomplemented
454#548—112no—
455#546—112no—
456#539—221no—
457#538—221no—
458#534—221no—
459C2×#127—21no—
460C2×#127C2×D1111yescharacteristic, complemented
461#529—112no—
462#525—112no—
463C2×C22⋊Q8—111no—
464C2×#121—21no—
465C2×#121—21no—
466C2×#121—111no—
467C2×#121C2×D1111yescharacteristic
468C2×#121C2×D1111yescharacteristic, complemented
469#518—221no—
470C2×C4×Q8C2×D1111yescharacteristic, complemented
471C2×C4×D4—21no—
472C2×C4×D4C2×D1111yescharacteristic
473#496—114no—
474#490—114no—
475#484—112no—
476#482—114no—
477#481—112no—
478#481—112no—
479#480—112no—
480#479—114no—
481#469—114no—
482#468—114no—
483#466—114no—
484#465—114no—
485#464—114no—
486#460—114no—
487#459—114no—
488#452—114no—
489#452—114no—
490#451—112no—
491#450—112no—
492#450—112no—
493#449—114no—
494#449—114no—
495#449—114no—
496#448—112no—
497#448—112no—
498#447—112no—
499#447—112no—
500#447—112no—
501#441—114no—
502#440—114no—
503#435—114no—
504#435—114no—
505#432—112no—
506#417—112no—
507#417—112no—
508#416—114no—
509#407—111no—
510#407—111no—
511C2×C22⋊C8—112no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—22no—
520C22×C11—21no—
521C22×C11—22no—
522C22×C11—21no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—82no—
530C22×C11—82no—
531C22×C11—84no—
532C22×C11—84no—
533C22×C11#57512yes—
534C22×C11C23×D411yescharacteristic
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—162no—
539C4×C11—22no—
540C4×C11—24no—
541C4×C11—21no—
542C4×C11—22no—
543C4×C11—21no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—42no—
547C4×C11C2×H(5,𝔽2)12yes—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—22no—
554C2×#41—44no—
555C2×#41—44no—
556C2×#41—112no—
557C2×#41C22×D1112yes—
558C2×#41C22×D1114yes—
559C2×#41C22×D1112yes—
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—111no—
569C22×D4—221no—
570C22×D4C22⋊D1111yescharacteristic
571C22×D4C22×D1111yescharacteristic
572C22×D4C22×D1111yescharacteristic
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577#137—444no—
578AGL(1,ℤ/8)—444no—
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×D8—114no—
585C2×D8—114no—
586C2×M16—112no—
587C2×M16—112no—
588C22×C8—114no—
589#127—24no—
590#127—24no—
591#127—22no—
592#127C22×D1114yes—
593#126—222no—
594#126—222no—
595#126—222no—
596#125—112no—
597#125—222no—
598#124—112no—
599#124—222no—
600#123—222no—
601#123—222no—
602#123—222no—
603#123—222no—
604#123—222no—
605C22⋊Q8—112no—
606C22⋊Q8—112no—
607C22⋊Q8—112no—
608C22⋊Q8—221no—
609C22⋊Q8—221no—
610C22⋊Q8—222no—
611#121—21no—
612#121—21no—
613#121—22no—
614#121—24no—
615#121—24no—
616#121—24no—
617#121—24no—
618#121—112no—
619#121—112no—
620#121—112no—
621#121—222no—
622#121—222no—
623#121—221no—
624#121—221no—
625#121—222no—
626#121C22×D1112yes—
627#121C22×D1112yes—
628#121C22×D1114yes—
629#120—222no—
630#120—222no—
631C4×Q8—22no—
632C4×Q8—112no—
633C4×Q8C22×D1114yes—
634C4×D4—24no—
635C4×D4—24no—
636C4×D4—112no—
637C4×D4—222no—
638C4×D4—222no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4—222no—
642C4×D4C22⋊D1112yes—
643C4×D4C22⋊D1112yes—
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yes—
646#117—112no—
647#117—222no—
648#117—222no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—221no—
653C2×C4⋊C4C22⋊D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—221no—
658C2×C22⋊C4—221no—
659C2×C22⋊C4—222no—
660C2×C22⋊C4C22⋊D1111yescharacteristic
661C2×C22⋊C4C22⋊D1111yescharacteristic
662C2×C42—21no—
663C2×C42C22×D1111yescharacteristic
664#107—114no—
665#106—114no—
666C4⋊C8—114no—
667#103—114no—
668#103—114no—
669#103—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102—114no—
674#102—114no—
675C22⋊C8—112no—
676C22⋊C8—112no—
677C22⋊C8—114no—
678C22⋊C8—112no—
679C22⋊C8—112no—
680#97—114no—
681C2×C11—22no—
682C2×C11—41no—
683C2×C11—41no—
684C2×C11—42no—
685C2×C11—82no—
686C2×C11—82no—
687C2×C11#348411yescharacteristic
688C2×C11C2×#57511yescharacteristic
689C2×C11#358511yescharacteristic
690D11—82no—
691C24—21no—
692C24—21no—
693C24—221no—
694C24C2×C22⋊D1111yescharacteristic
695C24C2×C22⋊D1111yescharacteristic
696#41—28no—
697#41—24no—
698#41—24no—
699#41—44no—
700#41—42no—
701#41—42no—
702#41—44no—
703#41—44no—
704#41—48no—
705#41—444no—
706C2×Q8—24no—
707C2×Q8—21no—
708C2×Q8—112no—
709C2×Q8—221no—
710C2×Q8—442no—
711C2×Q8C23×D1112yes—
712C2×D4—22no—
713C2×D4—24no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—22no—
718C2×D4—24no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—24no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—82no—
729C2×D4—82no—
730C2×D4—82no—
731C2×D4—112no—
732C2×D4—222no—
733C2×D4—222no—
734C2×D4—222no—
735C2×D4—222no—
736C2×D4—221no—
737C2×D4—442no—
738C2×D4—444no—
739C2×D4C2×C22⋊D1112yes—
740C2×D4C2×C22⋊D1112yes—
741C2×D4C23×D1112yes—
742C2×D4C23×D1112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—24no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4C2×C22⋊D1111yescharacteristic
758C22×C4C2×C22⋊D1111yescharacteristic
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1111yescharacteristic
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1112yes—
764C22×C4C23×D1111yescharacteristic
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1112yes—
768Q16—228no—
769SD16—228no—
770SD16—444no—
771SD16—444no—
772D8—444no—
773D8—444no—
774M16—442no—
775M16—442no—
776C2×C8—114no—
777C2×C8—114no—
778C2×C8—444no—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—112no—
782C4⋊C4—112no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—222no—
786C4⋊C4—222no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4C2×C22⋊D1112yes—
792C4⋊C4C2×C22⋊D1112yes—
793C4⋊C4C23×D1112yes—
794C22⋊C4—24no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—222no—
798C22⋊C4—222no—
799C22⋊C4—222no—
800C22⋊C4—222no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4C2×C22⋊D1112yes—
808C22⋊C4C2×C22⋊D1112yes—
809C22⋊C4C2×C22⋊D1112yes—
810C22⋊C4C2×C22⋊D1112yes—
811C42—24no—
812C42—222no—
813C42—222no—
814C42C2×C22⋊D1112yes—
815C42C23×D1112yes—
816C11#6157711yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—222no—
832C23—442no—
833C23—881no—
834C23—881no—
835C23C22×C22⋊D1111yescharacteristic
836C23C22×C22⋊D1112yes—
837C23C22×C22⋊D1111yescharacteristic
838C23C22×C22⋊D1111yescharacteristic
839Q8—24no—
840Q8—22no—
841Q8—224no—
842Q8—881no—
843Q8#6703714yes—
844D4—22no—
845D4—24no—
846D4—22no—
847D4—42no—
848D4—42no—
849D4—44no—
850D4—48no—
851D4—44no—
852D4—48no—
853D4—42no—
854D4—42no—
855D4—84no—
856D4—82no—
857D4—84no—
858D4—82no—
859D4—224no—
860D4—444no—
861D4—444no—
862D4—881no—
863D4—882no—
864D4—882no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—48no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—442no—
887C2×C4—882no—
888C2×C4—882no—
889C2×C4—881no—
890C2×C4—881no—
891C2×C4C22×C22⋊D1112yes—
892C2×C4C22×C22⋊D1112yes—
893C2×C4C22×C22⋊D1112yes—
894C2×C4C22×C22⋊D1111yescharacteristic
895C2×C4C22×C22⋊D1111yescharacteristic
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C24×D1111yescharacteristic
898C8—224no—
899C8—224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—22no—
904C22—21no—
905C22—21no—
906C22—22no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—22no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—82no—
918C22—82no—
919C22—84no—
920C22—84no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—1762no—
925C22#1062335312yes—
926C22C23×C22⋊D1111yescharacteristic
927C4—22no—
928C4—24no—
929C4—22no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—22no—
934C4—42no—
935C4—442no—
936C4—442no—
937C4—442no—
938C4C2×#6703712yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—42no—
943C2—82no—
944C2—82no—
945C2—882no—
946C2#1308225111yescharacteristic
947C2C2×#1062335311yescharacteristic
948C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC22×C11C23×D4
hypercenterC2×#550D11
hypocenterC11#61577
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13082455C2semidirect
2. #13080742C2semidirect
3. #13080622C2semidirect
4. #13080197C2semidirect
5. #13080157C2semidirect
6. #13079634C2semidirect
7. #13079422C2semidirect
8. #13079413C2semidirect
9. #13079381C2semidirect
10. #13078787C2semidirect
11. #13077876C2semidirect
12. #13077868C2semidirect
13. #13077834C2semidirect
14. #13077645C2semidirect
15. C2×C11×#550C2semidirect
17. C22×C11×#41C22semidirect
21. C11×#550C22semidirect
23. C2×C11×#127C22semidirect
27. C2×C11×#121C22semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×#67004C22semidirect
32. C2×#67003C22semidirect
33. C2×#67002C22semidirect
38. #10623096C22semidirect
40. #10623083C22semidirect
41. #10623081C22semidirect
42. #10623072C22semidirect
48. #10622852C22semidirect
49. #10622852C22semidirect
50. #10622851C22semidirect
51. #10622851C22semidirect
52. #10622846C22semidirect
53. #10622845C22semidirect
54. #10622845C22semidirect
55. #10622841C22semidirect
57. #10622831C22semidirect
58. #10622831C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622688C22semidirect
65. #10622687C22semidirect
66. #10622685C22semidirect
67. #10622684C22semidirect
68. #10622655C22semidirect
69. #10622654C22semidirect
70. #10622653C22semidirect
71. #10622652C22semidirect
72. #10622651C22semidirect
73. #10622650C22semidirect
74. #10622649C22semidirect
75. #10622648C22semidirect
76. #10622647C22semidirect
77. #10622646C22semidirect
78. #10622643C22semidirect
79. #10622641C22semidirect
80. #10622639C22semidirect
81. #10622635C22semidirect
82. #10622624C22semidirect
83. #10622624C22semidirect
84. #10622583C22semidirect
86. #10622539C22semidirect
344. C2×#550D11semidirect
442. C22×#41C2×D11semidirect
453. #550C2×D11semidirect
460. C2×#127C2×D11semidirect
468. C2×#121C2×D11semidirect
470. C2×C4×Q8C2×D11semidirect
816. C11#61577semidirect

Maximal subgroups

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

subgroupindex
#130824552
#130807422
#130806222
#130801972
#130801572
#130796342
#130794222
#130794132
#130793812
#130787872
#130778762
#130778682
#130778342
#130776452
C2×C11×#5502
#6157711