Finite Group Databasebeta

← #15624562

Subgroups — #15624562

Order 2816.

2322 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079490C214yesmaximal, complemented
4#13079480C214yesmaximal, complemented
5#13079475C214yesmaximal, complemented
6#13079473C214yesmaximal, complemented
7#13078556C211yesmaximal, characteristic, complemented
8#13078550C212yesmaximal, complemented
9#13078236C212yesmaximal, complemented
10#13078233C212yesmaximal, complemented
11#13077870C211yesmaximal, characteristic, complemented
12#13077866C211yesmaximal, characteristic, complemented
13#13077845C212yesmaximal, complemented
14#13077059C211yesmaximal, characteristic, complemented
15C11×#3094C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic, complemented
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic, complemented
21C2×#66993—21no—
22C2×#66991C2211yescharacteristic, complemented
23C2×#66990—21no—
24C2×#66985C2212yes—
25C2×#66983C2211yescharacteristic
26C2×#66961C2212yes—
27C2×M16×D11C2212yescomplemented
28#10623138—22no—
29#10623138—22no—
30#10623138C2214yes—
31#10623138C2214yescomplemented
32#10623057—21no—
33#10623057C2212yescomplemented
34#10623056—21no—
35#10623056C2212yescomplemented
36#10623055—22no—
37#10623055C2212yes—
38#10623055C2212yescomplemented
39#10623041C2212yescomplemented
40#10623041C2212yescomplemented
41C2×#66948C2211yescharacteristic, complemented
42C2×#66945C2211yescharacteristic, complemented
43#10623024—21no—
44#10623024—21no—
45C2×#66938—21no—
46C2×#66935—21no—
47#10623008—22no—
48C11×#482C2214yescomplemented
49C11×#481C2212yescomplemented
50C11×#480C2212yescomplemented
51C11×#428C2212yescomplemented
52C11×#418C2212yescomplemented
53C11×#407C2211yescharacteristic, complemented
54#10622820C2211yescharacteristic, complemented
55#10622746C2212yescomplemented
56#10622739C2212yescomplemented
57#10622653C2212yescomplemented
58#10622650C2214yescomplemented
59#10622649C2212yescomplemented
60#10622616C2214yescomplemented
61#10622614C2212yescomplemented
62#10622608C2212yescomplemented
63#10622581C2212yescomplemented
64#10622580C2212yescomplemented
65#10622579C2212yescomplemented
66#10622501C2214yescomplemented
67#10622499C2214yescomplemented
68#10622498C2214yescomplemented
69#10622496C2214yescomplemented
70#10622480C2214yescomplemented
71#10622479C2214yescomplemented
72#10622478C2214yescomplemented
73#10622477C2214yescomplemented
74#10622395C2214yescomplemented
75#10622393C2214yescomplemented
76#10622391C2214yescomplemented
77#10622389C2214yescomplemented
78#10622389C2214yescomplemented
79#10622388C2214yescomplemented
80#10622386C2214yescomplemented
81#10622386C2214yescomplemented
82#10622351C2212yescomplemented
83#10622347C2214yescomplemented
84#10622345C2212yescomplemented
85#10622340C2214yescomplemented
86#10622340C2214yescomplemented
87C24×D11—21no—
88C22×D4×C11—21no—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11D411yescharacteristic
96C22×C22⋊D11D411yescharacteristic
97C2×D4×D11—22no—
98C2×D4×D11—44no—
99C2×D4×D11C2314yes—
100C2×#4339—21no—
101C2×#4339—21no—
102C2×#4339—44no—
103C2×#4339—44no—
104C2×#4339D412yes—
105C2×#4339D412yes—
106C2×#4339C2312yes—
107C2×#4339C2312yes—
108C2×#4339C2312yes—
109C2×#4339C2312yescomplemented
110C22×D44—21no—
111C22×D44D411yescharacteristic
112C22×D44C2311yescharacteristic
113C22×D44C2311yescharacteristic, complemented
114C22×C4×D11—21no—
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×Dic22D411yescharacteristic
118C22×Dic22C2311yescharacteristic, complemented
119C2×C11×M16C2312yes—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121C2312yes—
123C11×#121C2312yes—
124C11×#117—21no—
125C11×#117—21no—
126C11×#117C2312yes—
127C11×#117C2312yescomplemented
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic, complemented
130C2×C11×C4⋊C4C2311yescharacteristic, complemented
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C42×C11—21no—
134C2×C22⋊Dic11—21no—
135#66993—24no—
136#66993—24no—
137#66991—22no—
138#66991C2314yes—
139#66990—24no—
140#66990—24no—
141C2×#4324C2314yes—
142#66985—44no—
143C2×#4323C2314yes—
144#66983—21no—
145#66983—21no—
146#66983—22no—
147#66983—22no—
148#66983—22no—
149#66983—22no—
150#66983C2312yes—
151#66983C2312yes—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4—21no—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4×Dic11—21no—
157C2×#4318C2312yes—
158#66961—44no—
159M16×D11—44no—
160C2×D88C2314yes—
161C2×#4314C2314yes—
162C2×#4313C2314yescomplemented
163C2×C8×D11C2314yescomplemented
164#66950—22no—
165#66950—22no—
166#66950C2312yes—
167#66950C2312yes—
168#66950C2312yescomplemented
169#66950C2312yescomplemented
170#66948—22no—
171#66948—22no—
172#66948—22no—
173#66948C2314yes—
174#66948C2312yes—
175#66948C2312yes—
176#66948C2312yescomplemented
177#66948C2312yescomplemented
178#66945—22no—
179#66945C2314yes—
180#66939—22no—
181#66939—22no—
182#66939—22no—
183#66939—22no—
184#66938—24no—
185#66938—24no—
186#66935—22no—
187#66935—22no—
188#66935—22no—
189#66935—22no—
190#66935—24no—
191#66935—24no—
192#66928—22no—
193#66928—22no—
194#66927—22no—
195C4×D44—22no—
196C4×D44—22no—
197C4×D44—22no—
198C4×D44—22no—
199#66922—22no—
200C11×#107C2314yescomplemented
201C11×#106C2314yescomplemented
202C11×#102C2314yes—
203C11×#102C2314yes—
204C11×C22⋊C8C2312yescomplemented
205C11×C22⋊C8C2312yescomplemented
206C22⋊(C11⋊C8)C2312yescomplemented
207C22⋊(C11⋊C8)C2312yescomplemented
208#66885C2314yescomplemented
209(C2×D11)⋊C8C2314yes—
210(C2×D11)⋊C8C2314yes—
211#66880C2314yescomplemented
212#66874C2314yescomplemented
213#66873C2314yes—
214#66873C2314yes—
215#66873C2314yescomplemented
216#66872C2314yescomplemented
217#66871C2314yescomplemented
218#60753—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—24no—
224C23×D11—44no—
225C23×D11—82no—
226C23×D11—82no—
227C23×D11C2×D411yescharacteristic
228C23×D11C2×D411yescharacteristic
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
232C2×D4×C11—24no—
233C2×D4×C11—82no—
234C2×D4×C11C2412yes—
235C22×C4×C11—24no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—22no—
249C2×C22⋊D11—22no—
250C2×C22⋊D11—24no—
251C2×C22⋊D11—42no—
252C2×C22⋊D11—42no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—82no—
256C2×C22⋊D11—82no—
257C2×C22⋊D11C2×D412yes—
258C2×C22⋊D11C2×D412yes—
259C2×C22⋊D11C2×D412yes—
260C2×C22⋊D11C2×D412yes—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11C2×D411yescharacteristic
264C22×Dic11C2×D411yescharacteristic
265D4×D11—44no—
266D4×D11—44no—
267D4×D11—48no—
268#4339—24no—
269#4339—24no—
270#4339—42no—
271#4339—42no—
272#4339—44no—
273#4339—44no—
274#4339—42no—
275#4339—42no—
276#4339—42no—
277#4339—42no—
278#4339—44no—
279#4339—44no—
280C2×D44—22no—
281C2×D44—22no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44—24no—
285C2×D44—21no—
286C2×D44—21no—
287C2×D44—24no—
288C2×D44—42no—
289C2×D44—42no—
290C2×D44—82no—
291C2×D44C2×D412yes—
292C2×D44C2×D412yes—
293C2×D44C2412yes—
294C2×D44C2412yes—
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—24no—
298C2×C4×D11—24no—
299C2×C4×D11—44no—
300C2×C4×D11C2×D412yes—
301C2×C4×D11C2×D412yes—
302C2×C4×D11C2412yes—
303C2×C4×D11C2412yes—
304C2×Dic22—21no—
305C2×Dic22—42no—
306C2×Dic22—42no—
307C2×Dic22C2×D412yes—
308C2×Dic22C2×D412yes—
309C2×Dic22C2412yes—
310C11×M16—24no—
311C2×C8×C11C2414yes—
312C11×C4⋊C4—21no—
313C11×C4⋊C4—21no—
314C11×C4⋊C4—21no—
315C11×C4⋊C4C2412yes—
316C11×C4⋊C4C2412yes—
317C11×C4⋊C4C2412yes—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C42×C11—22no—
323C42×C11—22no—
324C22⋊Dic11—24no—
325#4324—44no—
326#4323—44no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—22no—
338(C2×D11)⋊C4—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—21no—
344C4⋊Dic11C2412yes—
345C4×Dic11—24no—
346#4318—24no—
347C2×C11⋊C8C2414yes—
348D88—44no—
349#4314—44no—
350#4313—44no—
351C8×D11—44no—
352#3449—111no—
353C2×#535—111no—
354#3200—114no—
355#3199—114no—
356#3198—114no—
357#3198—114no—
358#3094—111no—
359#3094D1111yescharacteristic, complemented
360#3093—112no—
361#3055—112no—
362#3055—112no—
363#3006—111no—
364#3006—111no—
365#3003—112no—
366#2879—111no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—42no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11C22×D411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—48no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—84no—
391C22×D11—84no—
392C22×D11—81no—
393C22×D11—81no—
394C22×D11—816no—
395C22×D11C22×D412yes—
396C22×D11C22×D412yes—
397D4×C11—24no—
398D4×C11—42no—
399D4×C11—82no—
400D4×C11—82no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—42no—
410C2×C4×C11—81no—
411C2×C4×C11—81no—
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11H(5,𝔽2)14yes—
416C2×C4×C11C2511yescharacteristic
417C22⋊D11—42no—
418C22⋊D11—42no—
419C22⋊D11—42no—
420C22⋊D11—42no—
421C22⋊D11—48no—
422C22⋊D11—44no—
423C22⋊D11—44no—
424C22⋊D11—84no—
425C22⋊D11—82no—
426C22⋊D11—82no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—42no—
432C2×Dic11—42no—
433C2×Dic11C22×D412yes—
434C2×Dic11C22×D412yes—
435D44—24no—
436D44—22no—
437D44—22no—
438D44—42no—
439D44—42no—
440D44—42no—
441D44—42no—
442D44—82no—
443D44—82no—
444D44—82no—
445D44—82no—
446D44—84no—
447C4×D11—24no—
448C4×D11—24no—
449C4×D11—22no—
450C4×D11—22no—
451C4×D11—22no—
452C4×D11—22no—
453C4×D11—44no—
454C4×D11—44no—
455Dic22—22no—
456Dic22—22no—
457Dic22—42no—
458Dic22—42no—
459Dic22—42no—
460C8×C11—24no—
461C11⋊C8—24no—
462C22×#41—111no—
463C22×#41—111no—
464C23×D4—111no—
465C2×AGL(1,ℤ/8)—112no—
466C2×AGL(1,ℤ/8)—112no—
467C22×M16—112no—
468#537—112no—
469#537—112no—
470#536—112no—
471#536—221no—
472#535—114no—
473#535—114no—
474#535—112no—
475#535—221no—
476#535—222no—
477#535—222no—
478#534—221no—
479#534—221no—
480#532—222no—
481C2×#127—221no—
482C2×#124—221no—
483#525—112no—
484#525—112no—
485#525—222no—
486C2×#121—111no—
487C2×#121—111no—
488C2×#121—111no—
489C2×#121C2×D1111yescharacteristic
490C2×#120—221no—
491C2×#120—221no—
492C2×#117—111no—
493C2×#117C2×D1111yescharacteristic, complemented
494#485—114no—
495#485—114no—
496#482—114no—
497#482—114no—
498#482—114no—
499#482C2×D1114yescomplemented
500#481—112no—
501#481C2×D1112yescomplemented
502#480—112no—
503#480C2×D1112yescomplemented
504#469—114no—
505#469—114no—
506#468—114no—
507#468—114no—
508#466—114no—
509#466—114no—
510#465—114no—
511#465—114no—
512#450—114no—
513#450—114no—
514#449—114no—
515#449—114no—
516#448—112no—
517#448—112no—
518#447—112no—
519#447—114no—
520#447—114no—
521#447—112no—
522#428—112no—
523#428C2×D1112yescomplemented
524#418—112no—
525#418C2×D1112yescomplemented
526#417—112no—
527#417—112no—
528#408—114no—
529#408—114no—
530#407—111no—
531#407—112no—
532#407C2×D1111yescharacteristic, complemented
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—21no—
538C22×C11—21no—
539C22×C11—21no—
540C22×C11—21no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—82no—
545C22×C11—84no—
546C22×C11#53412yes—
547C22×C11C23×D411yescharacteristic
548C2×D11—22no—
549C2×D11—22no—
550C2×D11—22no—
551C2×D11—22no—
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—44no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—82no—
562C2×D11—816no—
563C2×D11—84no—
564C2×D11—84no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—42no—
568C4×C11—42no—
569C4×C11—42no—
570C4×C11#53412yes—
571C4×C11C2×H(5,𝔽2)12yes—
572Dic11—22no—
573Dic11—22no—
574Dic11—42no—
575Dic11—42no—
576C25—221no—
577C2×#41—112no—
578C2×#41—112no—
579C2×#41—112no—
580C2×#41—112no—
581C2×#41—112no—
582C2×#41—112no—
583C2×#41—221no—
584C2×#41—221no—
585C2×#41—444no—
586C2×#41—444no—
587C22×Q8—111no—
588C22×Q8—111no—
589C22×D4—21no—
590C22×D4—111no—
591C22×D4—111no—
592C22×D4—114no—
593C22×D4—111no—
594C22×D4—111no—
595C22×D4—111no—
596C22×D4—221no—
597C22×D4—222no—
598C22×D4—221no—
599C22×D4—221no—
600C22×D4—221no—
601C22×D4—221no—
602C22×D4—444no—
603C22×D4C22×D1111yescharacteristic
604C23×C4—111no—
605C23×C4—111no—
606C23×C4—221no—
607C23×C4C22×D1111yescharacteristic
608AGL(1,ℤ/8)—444no—
609AGL(1,ℤ/8)—444no—
610C2×SD16—114no—
611C2×SD16—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×M16—112no—
615C2×M16—114no—
616C2×M16—444no—
617C2×M16C22×D1112yes—
618C22×C8—114no—
619C4⋊Q8—222no—
620#127—222no—
621#127—224no—
622#127—224no—
623#124—222no—
624#124—222no—
625#124—224no—
626#124—224no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631C22⋊Q8—112no—
632C22⋊Q8—112no—
633C22⋊Q8—112no—
634C22⋊Q8—112no—
635C22⋊Q8—222no—
636C22⋊Q8—222no—
637#121—21no—
638#121—21no—
639#121—114no—
640#121—112no—
641#121—112no—
642#121—114no—
643#121—112no—
644#121—112no—
645#121—112no—
646#121—112no—
647#121—222no—
648#121—222no—
649#121—222no—
650#121—222no—
651#121—222no—
652#121—222no—
653#121—222no—
654#121—222no—
655#121—221no—
656#121—221no—
657#121C22×D1112yes—
658#121C22×D1112yes—
659#120—224no—
660#120—224no—
661#120—222no—
662#120—222no—
663#120—222no—
664#120—222no—
665#120—224no—
666#120—224no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—222no—
671#117—21no—
672#117—21no—
673#117—114no—
674#117—222no—
675#117C22×D1112yes—
676#117C22×D1112yescomplemented
677C2×C4⋊C4—111no—
678C2×C4⋊C4C22×D1111yescharacteristic
679C2×C4⋊C4C22×D1111yescharacteristic, complemented
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—221no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C42—21no—
688C2×C42—221no—
689#107—114no—
690#107C22×D1114yescomplemented
691#106—114no—
692#106C22×D1114yescomplemented
693#103—114no—
694#103—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102C22×D1114yes—
700#102C22×D1114yes—
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—114no—
704C22⋊C8—114no—
705C22⋊C8C22×D1112yescomplemented
706C22⋊C8C22×D1112yescomplemented
707C2×C11—22no—
708C2×C11—41no—
709C2×C11—41no—
710C2×C11—82no—
711C2×C11C2×#53411yescharacteristic
712C2×C11#358511yescharacteristic
713C2×C11#358511yescharacteristic
714D11—42no—
715D11—42no—
716D11—82no—
717D11—82no—
718C24—21no—
719C24—111no—
720C24—111no—
721C24—224no—
722C24—221no—
723C24—221no—
724C24—444no—
725C24—882no—
726C24—882no—
727C24D4×D1111yescharacteristic
728#41—224no—
729#41—224no—
730#41—444no—
731#41—444no—
732#41—442no—
733#41—442no—
734#41—442no—
735#41—442no—
736#41—442no—
737#41—442no—
738#41—444no—
739#41—444no—
740C2×Q8—112no—
741C2×Q8—112no—
742C2×Q8—112no—
743C2×Q8—221no—
744C2×Q8—442no—
745C2×Q8—442no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—21no—
749C2×D4—24no—
750C2×D4—82no—
751C2×D4—112no—
752C2×D4—112no—
753C2×D4—112no—
754C2×D4—112no—
755C2×D4—112no—
756C2×D4—112no—
757C2×D4—112no—
758C2×D4—112no—
759C2×D4—222no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—224no—
764C2×D4—224no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—224no—
768C2×D4—222no—
769C2×D4—222no—
770C2×D4—221no—
771C2×D4—221no—
772C2×D4—224no—
773C2×D4—442no—
774C2×D4—442no—
775C2×D4—444no—
776C2×D4—444no—
777C2×D4—448no—
778C2×D4—442no—
779C2×D4—442no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—882no—
783C2×D4—882no—
784C2×D4—882no—
785C2×D4C23×D1112yes—
786C22×C4—24no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—111no—
791C22×C4—111no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—224no—
797C22×C4—224no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—444no—
803C22×C4D4×D1111yescharacteristic
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809SD16—444no—
810SD16—444no—
811D8—444no—
812D8—444no—
813M16—24no—
814M16—224no—
815M16—444no—
816C2×C8—114no—
817C2×C8—444no—
818C2×C8C23×D1114yes—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—112no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—221no—
828C4⋊C4C23×D1112yes—
829C4⋊C4C23×D1112yes—
830C4⋊C4C23×D1112yes—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—224no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—224no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—224no—
846C22⋊C4—222no—
847C22⋊C4—222no—
848C42—22no—
849C42—22no—
850C42—224no—
851C11#6075311yescharacteristic, complemented, Sylow
852C23—22no—
853C23—22no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—112no—
860C23—112no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—442no—
870C23—442no—
871C23—442no—
872C23—448no—
873C23—442no—
874C23—881no—
875C23—881no—
876C23—884no—
877C23—884no—
878C23—8816no—
879C23C2×D4×D1111yescharacteristic
880C23C2×D4×D1111yescharacteristic
881C23C2×D4×D1111yescharacteristic
882Q8—222no—
883Q8—222no—
884Q8—442no—
885Q8—442no—
886Q8—442no—
887D4—24no—
888D4—42no—
889D4—82no—
890D4—82no—
891D4—222no—
892D4—222no—
893D4—224no—
894D4—442no—
895D4—442no—
896D4—442no—
897D4—442no—
898D4—442no—
899D4—442no—
900D4—442no—
901D4—448no—
902D4—444no—
903D4—444no—
904D4—442no—
905D4—884no—
906D4—882no—
907D4—882no—
908D4—882no—
909D4—882no—
910D4—882no—
911D4—882no—
912D4—884no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—42no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—224no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—444no—
937C2×C4—442no—
938C2×C4—442no—
939C2×C4—444no—
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C2×D4×D1111yescharacteristic
943C2×C4#6704214yes—
944C2×C4C24×D1111yescharacteristic
945C8—24no—
946C8—224no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—82no—
959C22—84no—
960C22—222no—
961C22—222no—
962C22—222no—
963C22—222no—
964C22—222no—
965C22—222no—
966C22—444no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—442no—
973C22—882no—
974C22—884no—
975C22—884no—
976C22—8816no—
977C22#1062318412yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—222no—
985C4—222no—
986C4—442no—
987C4—442no—
988C4#1062318412yes—
989C4C2×#6704212yes—
990C2—22no—
991C2—41no—
992C2—41no—
993C2—82no—
994C2—442no—
995C2—442no—
996C2—882no—
997C2—882no—
998C2C2×#1062318411yescharacteristic
999C2#1308339211yescharacteristic
1000C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3094C2
socleC22×C11C23×D4
hypercenter#3094D11
hypocenterC11#60753
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #13081949C2semidirect
2. C2×#10623138C2semidirect
3. #13079490C2semidirect
4. #13079480C2semidirect
5. #13079475C2semidirect
6. #13079473C2semidirect
7. #13078556C2semidirect
8. #13078550C2semidirect
9. #13078236C2semidirect
10. #13078233C2semidirect
11. #13077870C2semidirect
12. #13077866C2semidirect
13. #13077845C2semidirect
14. #13077059C2semidirect
15. C11×#3094C2semidirect
16. C22×D4×D11C22semidirect
18. C22×#4339C22semidirect
20. C2×C11×#117C22semidirect
22. C2×#66991C22semidirect
27. C2×M16×D11C22semidirect
31. #10623138C22semidirect
33. #10623057C22semidirect
35. #10623056C22semidirect
38. #10623055C22semidirect
39. #10623041C22semidirect
40. #10623041C22semidirect
41. C2×#66948C22semidirect
42. C2×#66945C22semidirect
48. C11×#482C22semidirect
49. C11×#481C22semidirect
50. C11×#480C22semidirect
51. C11×#428C22semidirect
52. C11×#418C22semidirect
53. C11×#407C22semidirect
54. #10622820C22semidirect
55. #10622746C22semidirect
56. #10622739C22semidirect
57. #10622653C22semidirect
58. #10622650C22semidirect
59. #10622649C22semidirect
60. #10622616C22semidirect
61. #10622614C22semidirect
62. #10622608C22semidirect
63. #10622581C22semidirect
64. #10622580C22semidirect
65. #10622579C22semidirect
66. #10622501C22semidirect
67. #10622499C22semidirect
68. #10622498C22semidirect
69. #10622496C22semidirect
70. #10622480C22semidirect
71. #10622479C22semidirect
72. #10622478C22semidirect
73. #10622477C22semidirect
74. #10622395C22semidirect
75. #10622393C22semidirect
76. #10622391C22semidirect
77. #10622389C22semidirect
78. #10622389C22semidirect
79. #10622388C22semidirect
80. #10622386C22semidirect
81. #10622386C22semidirect
82. #10622351C22semidirect
83. #10622347C22semidirect
84. #10622345C22semidirect
85. #10622340C22semidirect
86. #10622340C22semidirect
109. C2×#4339C23semidirect
113. C22×D44C23semidirect
118. C22×Dic22C23semidirect
127. C11×#117C23semidirect
129. C2×C11×C4⋊C4C23semidirect
130. C2×C11×C4⋊C4C23semidirect
162. C2×#4313C23semidirect
163. C2×C8×D11C23semidirect
168. #66950C23semidirect
169. #66950C23semidirect
176. #66948C23semidirect
177. #66948C23semidirect
200. C11×#107C23semidirect
201. C11×#106C23semidirect
204. C11×C22⋊C8C23semidirect
205. C11×C22⋊C8C23semidirect
206. C22⋊(C11⋊C8)C23semidirect
207. C22⋊(C11⋊C8)C23semidirect
208. #66885C23semidirect
211. #66880C23semidirect
212. #66874C23semidirect
215. #66873C23semidirect
216. #66872C23semidirect
217. #66871C23semidirect
359. #3094D11semidirect
493. C2×#117C2×D11semidirect
499. #482C2×D11semidirect
501. #481C2×D11semidirect
503. #480C2×D11semidirect
523. #428C2×D11semidirect
525. #418C2×D11semidirect
532. #407C2×D11semidirect
676. #117C22×D11semidirect
679. C2×C4⋊C4C22×D11semidirect
680. C2×C4⋊C4C22×D11semidirect
690. #107C22×D11semidirect
692. #106C22×D11semidirect
705. C22⋊C8C22×D11semidirect
706. C22⋊C8C22×D11semidirect
851. C11#60753semidirect

Maximal subgroups

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

subgroupindex
#130819492
C2×#106231382
#130794902
#130794802
#130794752
#130794732
#130785562
#130785502
#130782362
#130782332
#130778702
#130778662
#130778452
#130770592
C11×#30942
#6075311