Finite Group Databasebeta

← #15624557

Subgroups — #15624557

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#13081945C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079486C214yesmaximal, complemented
4#13079479C214yesmaximal, complemented
5#13079467C214yesmaximal, complemented
6#13079465C214yesmaximal, complemented
7#13078557C211yesmaximal, characteristic, complemented
8#13078552C211yesmaximal, characteristic, complemented
9#13078546C212yesmaximal, complemented
10#13078238C212yesmaximal, complemented
11#13078229C212yesmaximal, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077841C212yesmaximal, complemented
14#13077059C211yesmaximal, characteristic, complemented
15C11×#3006C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic, complemented
17C22×D4×D11C2211yescharacteristic, complemented
18C22×#4339C2211yescharacteristic
19C2×C11×AGL(1,ℤ/8)C2212yes—
20C2×C11×#121C2211yescharacteristic
21#10623364C2212yescomplemented
22#10623364C2212yescomplemented
23#10623363—22no—
24#10623361—21no—
25#10623359C2212yes—
26#10623359C2212yescomplemented
27#10623356—21no—
28C2×#67002C2212yes—
29#10623347C2212yescomplemented
30#10623336C2212yescomplemented
31#10623335—21no—
32#10623335—21no—
33C2×#66993—21no—
34C2×#66991C2211yescharacteristic, complemented
35C2×#66990—21no—
36#10623322—22no—
37C2×#66983C2211yescharacteristic
38C2×#66979C2211yescharacteristic, complemented
39C2×M16×D11C2212yescomplemented
40#10623138—22no—
41#10623138—22no—
42#10623138C2214yes—
43#10623138C2214yescomplemented
44C2×#66948C2211yescharacteristic, complemented
45C2×#66945C2211yescharacteristic, complemented
46C2×#66938—21no—
47C2×#66935—21no—
48C11×#449C2214yescomplemented
49C11×#448C2212yescomplemented
50C11×#447C2212yescomplemented
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622851C2214yescomplemented
54#10622845C2212yescomplemented
55#10622840C2212yescomplemented
56#10622830C2212yescomplemented
57#10622828C2212yescomplemented
58#10622820C2211yescharacteristic, complemented
59#10622787C2214yescomplemented
60#10622784C2214yescomplemented
61#10622782C2214yescomplemented
62#10622782C2214yescomplemented
63#10622772C2214yescomplemented
64#10622770C2214yescomplemented
65#10622769C2214yescomplemented
66#10622769C2214yescomplemented
67#10622744C2212yescomplemented
68#10622739C2212yescomplemented
69#10622734C2212yescomplemented
70#10622648C2214yescomplemented
71#10622647C2212yescomplemented
72#10622646C2212yescomplemented
73#10622577C2212yescomplemented
74#10622428C2214yescomplemented
75#10622427C2214yescomplemented
76#10622425C2214yescomplemented
77#10622420C2214yescomplemented
78#10622397C2214yescomplemented
79#10622395C2214yescomplemented
80#10622392C2214yescomplemented
81#10622388C2214yescomplemented
82#10622350C2214yescomplemented
83#10622349C2212yescomplemented
84#10622348C2212yescomplemented
85#10622340C2214yescomplemented
86#10622340C2214yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41—44no—
91C2×C11×#41C2312yes—
92C2×C11×#41C2312yescomplemented
93C22×Q8×C11C2311yescharacteristic, complemented
94C22×D4×C11—21no—
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic, complemented
98C23×C4×C11—21no—
99C23×C4×C11C2311yescharacteristic
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—21no—
103C22×C22⋊D11D411yescharacteristic
104C22×C22⋊D11D411yescharacteristic
105C2×D4×D11—22no—
106C2×D4×D11—44no—
107C2×D4×D11C2314yes—
108C2×#4339—44no—
109C2×#4339D412yes—
110C2×#4339D412yes—
111C2×#4339C2312yes—
112C2×#4339C2312yes—
113C22×D44—21no—
114C22×D44D411yescharacteristic
115C22×D44C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2311yescharacteristic
118C22×Dic22D411yescharacteristic
119C11×AGL(1,ℤ/8)—44no—
120C2×C11×SD16C2314yes—
121C2×C11×D8C2314yes—
122C2×C11×M16C2312yes—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121C2312yes—
126C11×#121C2312yes—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4—21no—
129#67006—22no—
130#67006—22no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133#67002—44no—
134#67000—22no—
135#66999C2312yes—
136#66999C2312yes—
137#66999C2312yescomplemented
138#66999C2312yescomplemented
139#66997—22no—
140C2×#4325C2314yes—
141#66993—24no—
142#66993—24no—
143#66993—22no—
144#66992—22no—
145#66992—22no—
146#66992—22no—
147#66992—22no—
148#66991—22no—
149#66991C2312yes—
150#66991C2312yes—
151#66991C2314yes—
152#66991C2312yescomplemented
153#66991C2312yescomplemented
154#66990—22no—
155#66990—22no—
156#66990—24no—
157#66990—24no—
158#66989—22no—
159#66988—22no—
160#66988—22no—
161C2×#4323C2314yes—
162#66983—21no—
163#66983—21no—
164#66983—22no—
165#66983—22no—
166#66983C2312yes—
167#66983C2312yes—
168#66982—22no—
169#66982—22no—
170C4×C22⋊D11—22no—
171C4×C22⋊D11—22no—
172C4×C22⋊D11—22no—
173C4×C22⋊D11—22no—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4—21no—
176C2×(C2×D11)⋊C4—21no—
177#66979—21no—
178#66979—21no—
179#66979C2312yes—
180#66979C2312yescomplemented
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2311yescharacteristic, complemented
183C2×C4⋊Dic11C2311yescharacteristic, complemented
184#66977—22no—
185#66977—22no—
186C2×C4×Dic11—21no—
187C2×C4×Dic11—21no—
188C2×#4318C2312yes—
189M16×D11—44no—
190C2×#4313C2314yescomplemented
191C2×C8×D11C2314yescomplemented
192#66948—22no—
193#66948C2314yes—
194#66945—22no—
195#66945C2314yes—
196#66938—24no—
197#66938—24no—
198#66935—24no—
199#66935—24no—
200C11×#103C2314yescomplemented
201C11×#102C2314yescomplemented
202C11×C22⋊C8C2312yescomplemented
203C11×C22⋊C8C2312yescomplemented
204#66899C2314yescomplemented
205#66896C2314yes—
206#66896C2314yes—
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yescomplemented
209C22⋊(C11⋊C8)C2312yescomplemented
210#66885C2314yes—
211#66885C2314yes—
212(C2×D11)⋊C8C2314yes—
213(C2×D11)⋊C8C2314yes—
214#66882C2314yescomplemented
215#66881C2314yescomplemented
216#66872C2314yescomplemented
217#66871C2314yescomplemented
218#60753—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—24no—
224C23×D11—44no—
225C23×D11—82no—
226C23×D11—82no—
227C23×D11C2×D411yescharacteristic
228C23×D11C2×D411yescharacteristic
229C11×#41—24no—
230C11×#41—24no—
231C11×#41—42no—
232C11×#41—42no—
233C11×#41—44no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2412yes—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—21no—
244C2×D4×C11—24no—
245C2×D4×C11—42no—
246C2×D4×C11—44no—
247C2×D4×C11—82no—
248C2×D4×C11C2412yes—
249C2×D4×C11C2412yes—
250C22×C4×C11—24no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—22no—
254C22×C4×C11—22no—
255C22×C4×C11—44no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C2×C22⋊D11—24no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—22no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—42no—
271C2×C22⋊D11—42no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—82no—
274C2×C22⋊D11—82no—
275C2×C22⋊D11C2×D412yes—
276C2×C22⋊D11C2×D412yes—
277C2×C22⋊D11C2×D412yes—
278C2×C22⋊D11C2×D412yes—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11C2×D411yescharacteristic
283C22×Dic11C2×D411yescharacteristic
284D4×D11—44no—
285D4×D11—44no—
286D4×D11—48no—
287#4339—44no—
288#4339—44no—
289#4339—42no—
290#4339—42no—
291#4339—42no—
292#4339—42no—
293C2×D44—24no—
294C2×D44—21no—
295C2×D44—24no—
296C2×D44—42no—
297C2×D44—82no—
298C2×D44C2×D412yes—
299C2×D44C2×D412yes—
300C2×D44C2412yes—
301C2×C4×D11—24no—
302C2×C4×D11—24no—
303C2×C4×D11C2×D412yes—
304C2×C4×D11C2×D412yes—
305C2×C4×D11C2412yes—
306C2×C4×D11C2412yes—
307C2×Dic22—42no—
308C2×Dic22C2×D412yes—
309C2×Dic22C2×D412yes—
310C11×SD16—44no—
311C11×D8—44no—
312C11×M16—24no—
313C2×C8×C11C2414yes—
314C11×C4⋊C4—21no—
315C11×C4⋊C4C2412yes—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C22⋊Dic11—24no—
319C22⋊Dic11—22no—
320C22⋊Dic11—22no—
321C22⋊Dic11—22no—
322C22⋊Dic11—22no—
323C22⋊Dic11—22no—
324C22⋊Dic11—22no—
325#4325—44no—
326#4323—44no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334(C2×D11)⋊C4—22no—
335C4⋊Dic11—21no—
336C4⋊Dic11—21no—
337C4⋊Dic11—21no—
338C4⋊Dic11C2412yes—
339C4⋊Dic11C2412yes—
340C4⋊Dic11C2412yes—
341Dic11⋊C4—22no—
342Dic11⋊C4—22no—
343Dic11⋊C4—22no—
344Dic11⋊C4—22no—
345C4×Dic11—24no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348#4318—24no—
349C2×C11⋊C8C2414yes—
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#3094—111no—
360#3093—112no—
361#3055—112no—
362#3055—112no—
363#3006—111no—
364#3006D1111yescharacteristic, complemented
365#3003—112no—
366#2879—111no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—42no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—81no—
377C23×C11—81no—
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C23×C11C22×D411yescharacteristic
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—48no—
389C22×D11—42no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—84no—
393C22×D11—84no—
394C22×D11—816no—
395C22×D11C22×D412yes—
396C22×D11C22×D412yes—
397Q8×C11—22no—
398Q8×C11—22no—
399Q8×C11—42no—
400D4×C11—22no—
401D4×C11—22no—
402D4×C11—24no—
403D4×C11—42no—
404D4×C11—44no—
405D4×C11—44no—
406D4×C11—42no—
407D4×C11—82no—
408D4×C11—82no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—44no—
417C2×C4×C11—42no—
418C2×C4×C11—42no—
419C2×C4×C11—44no—
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C22×D411yescharacteristic
423C2×C4×C11H(5,𝔽2)14yes—
424C2×C4×C11C2511yescharacteristic
425C22⋊D11—42no—
426C22⋊D11—42no—
427C22⋊D11—42no—
428C22⋊D11—42no—
429C22⋊D11—48no—
430C22⋊D11—82no—
431C22⋊D11—82no—
432C22⋊D11—82no—
433C22⋊D11—82no—
434C22⋊D11—84no—
435C22⋊D11—82no—
436C22⋊D11—82no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—42no—
443C2×Dic11—81no—
444C2×Dic11—81no—
445C2×Dic11C22×D412yes—
446C2×Dic11C22×D412yes—
447D44—24no—
448D44—42no—
449D44—42no—
450D44—42no—
451D44—84no—
452C4×D11—24no—
453C4×D11—24no—
454C4×D11—22no—
455C4×D11—22no—
456C4×D11—22no—
457C4×D11—22no—
458Dic22—42no—
459Dic22—42no—
460C8×C11—24no—
461C11⋊C8—24no—
462C22×#41—111no—
463C22×#41C2×D1111yescharacteristic, complemented
464C23×D4—111no—
465C2×AGL(1,ℤ/8)—112no—
466C2×AGL(1,ℤ/8)C2×D1112yes—
467C22×M16—112no—
468#537—112no—
469#537—112no—
470#536—112no—
471#536—221no—
472#535—112no—
473#535—114no—
474#535—114no—
475#535—222no—
476#535—222no—
477#535—221no—
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×#117—111no—
494#485—114no—
495#485—114no—
496#482—114no—
497#482—114no—
498#482—114no—
499#482—114no—
500#481—112no—
501#481—112no—
502#480—112no—
503#480—112no—
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#449C2×D1114yescomplemented
516#448—112no—
517#448C2×D1112yescomplemented
518#447—112no—
519#447—114no—
520#447—114no—
521#447C2×D1112yescomplemented
522#428—112no—
523#428—112no—
524#418—112no—
525#418—112no—
526#417—112no—
527#417C2×D1112yescomplemented
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—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—82no—
548C22×C11—84no—
549C22×C11—84no—
550C22×C11#53412yes—
551C22×C11C23×D411yescharacteristic
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—22no—
555C2×D11—22no—
556C2×D11—22no—
557C2×D11—22no—
558C2×D11—44no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—82no—
563C2×D11—816no—
564C2×D11—84no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—42no—
568C4×C11—42no—
569C4×C11#53412yes—
570C4×C11C2×H(5,𝔽2)12yes—
571Dic11—22no—
572Dic11—22no—
573Dic11—42no—
574Dic11—42no—
575Dic11—42no—
576C25—221no—
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—44no—
580C2×#41—112no—
581C2×#41—112no—
582C2×#41—112no—
583C2×#41—112no—
584C2×#41—444no—
585C2×#41C22×D1112yes—
586C2×#41C22×D1112yescomplemented
587C22×Q8—111no—
588C22×Q8C22×D1111yescharacteristic, complemented
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—111no—
592C22×D4—111no—
593C22×D4—114no—
594C22×D4—111no—
595C22×D4—111no—
596C22×D4—221no—
597C22×D4—222no—
598C22×D4—221no—
599C22×D4—221no—
600C22×D4—221no—
601C22×D4—444no—
602C22×D4C22×D1111yescharacteristic
603C22×D4C22×D1111yescharacteristic, complemented
604C23×C4—21no—
605C23×C4—111no—
606C23×C4—111no—
607C23×C4C22×D1111yescharacteristic
608AGL(1,ℤ/8)—44no—
609AGL(1,ℤ/8)—444no—
610C2×SD16—114no—
611C2×SD16C22×D1114yes—
612C2×D8—114no—
613C2×D8C22×D1114yes—
614C2×M16—112no—
615C2×M16—114no—
616C2×M16—444no—
617C2×M16C22×D1112yes—
618C22×C8—114no—
619C4⋊Q8—222no—
620#127—224no—
621#127—224no—
622#127—222no—
623#124—224no—
624#124—224no—
625#124—222no—
626#124—222no—
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—112no—
643#121—112no—
644#121—112no—
645#121—112no—
646#121—114no—
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—224no—
662#120—224no—
663#120—222no—
664#120—222no—
665#120—222no—
666#120—222no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—222no—
671#117—112no—
672#117—112no—
673#117—114no—
674#117—222no—
675#117—221no—
676#117—221no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—111no—
680C2×C4⋊C4C22×D1111yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—221no—
683C2×C22⋊C4—221no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C42—221no—
688C2×C42—221no—
689#107—114no—
690#107—114no—
691#106—114no—
692#106—114no—
693#103—114no—
694#103C22×D1114yescomplemented
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102C22×D1114yescomplemented
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×C11—82no—
712C2×C11C2×#53411yescharacteristic
713C2×C11#358511yescharacteristic
714C2×C11#358511yescharacteristic
715D11—42no—
716D11—42no—
717D11—82no—
718C24—21no—
719C24—21no—
720C24—111no—
721C24—111no—
722C24—224no—
723C24—221no—
724C24—444no—
725C24—882no—
726C24—882no—
727C24D4×D1111yescharacteristic
728#41—24no—
729#41—24no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—44no—
734#41—444no—
735#41—444no—
736#41—442no—
737#41—442no—
738#41—442no—
739#41—442no—
740C2×Q8—21no—
741C2×Q8—42no—
742C2×Q8—112no—
743C2×Q8—112no—
744C2×Q8—442no—
745C2×Q8C23×D1112yes—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—24no—
753C2×D4—42no—
754C2×D4—44no—
755C2×D4—82no—
756C2×D4—112no—
757C2×D4—112no—
758C2×D4—112no—
759C2×D4—112no—
760C2×D4—112no—
761C2×D4—112no—
762C2×D4—112no—
763C2×D4—224no—
764C2×D4—224no—
765C2×D4—222no—
766C2×D4—222no—
767C2×D4—222no—
768C2×D4—222no—
769C2×D4—224no—
770C2×D4—222no—
771C2×D4—222no—
772C2×D4—221no—
773C2×D4—224no—
774C2×D4—442no—
775C2×D4—444no—
776C2×D4—444no—
777C2×D4—448no—
778C2×D4—442no—
779C2×D4—442no—
780C2×D4—444no—
781C2×D4—882no—
782C2×D4—882no—
783C2×D4—882no—
784C2×D4C23×D1112yes—
785C2×D4C23×D1112yes—
786C22×C4—24no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—44no—
792C22×C4—111no—
793C22×C4—111no—
794C22×C4—112no—
795C22×C4—112no—
796C22×C4—112no—
797C22×C4—112no—
798C22×C4—224no—
799C22×C4—224no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4D4×D1111yescharacteristic
804C22×C4D4×D1111yescharacteristic
805C22×C4D4×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809SD16—44no—
810SD16—444no—
811D8—44no—
812D8—444no—
813M16—24no—
814M16—224no—
815M16—444no—
816C2×C8—114no—
817C2×C8—444no—
818C2×C8C23×D1114yes—
819C4⋊C4—21no—
820C4⋊C4—112no—
821C4⋊C4—112no—
822C4⋊C4—112no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—221no—
828C4⋊C4—221no—
829C4⋊C4—221no—
830C4⋊C4C23×D1112yes—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—222no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—224no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C22⋊C4—222no—
847C22⋊C4—222no—
848C42—224no—
849C42—222no—
850C42—222no—
851C11#6075311yescharacteristic, complemented, Sylow
852C23—22no—
853C23—22no—
854C23—22no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—81no—
862C23—81no—
863C23—112no—
864C23—112no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—441no—
869C23—441no—
870C23—441no—
871C23—441no—
872C23—442no—
873C23—442no—
874C23—448no—
875C23—442no—
876C23—884no—
877C23—884no—
878C23—8816no—
879C23C2×D4×D1111yescharacteristic
880C23C2×D4×D1111yescharacteristic
881C23C2×D4×D1111yescharacteristic
882Q8—22no—
883Q8—22no—
884Q8—42no—
885Q8—442no—
886Q8—442no—
887D4—22no—
888D4—24no—
889D4—22no—
890D4—42no—
891D4—44no—
892D4—44no—
893D4—42no—
894D4—82no—
895D4—82no—
896D4—224no—
897D4—442no—
898D4—442no—
899D4—442no—
900D4—442no—
901D4—442no—
902D4—442no—
903D4—448no—
904D4—442no—
905D4—884no—
906D4—882no—
907D4—882no—
908D4—884no—
909D4—882no—
910D4—882no—
911D4—882no—
912D4—882no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—44no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
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—222no—
937C2×C4—442no—
938C2×C4—881no—
939C2×C4—881no—
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C2×D4×D1111yescharacteristic
943C2×C4#6703714yes—
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—42no—
959C22—42no—
960C22—42no—
961C22—82no—
962C22—84no—
963C22—84no—
964C22—222no—
965C22—222no—
966C22—222no—
967C22—222no—
968C22—222no—
969C22—222no—
970C22—444no—
971C22—442no—
972C22—442no—
973C22—442no—
974C22—882no—
975C22—884no—
976C22—8816no—
977C22#1062312012yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—42no—
982C4—42no—
983C4—222no—
984C4—222no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4#1062312012yes—
989C4C2×#6703712yes—
990C2—22no—
991C2—41no—
992C2—41no—
993C2—82no—
994C2—82no—
995C2—442no—
996C2—442no—
997C2—882no—
998C2C2×#1062312011yescharacteristic
999C2#1308339211yescharacteristic
1000C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#60753
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #13081945C2semidirect
2. C2×#10623138C2semidirect
3. #13079486C2semidirect
4. #13079479C2semidirect
5. #13079467C2semidirect
6. #13079465C2semidirect
7. #13078557C2semidirect
8. #13078552C2semidirect
9. #13078546C2semidirect
10. #13078238C2semidirect
11. #13078229C2semidirect
12. #13077868C2semidirect
13. #13077841C2semidirect
14. #13077059C2semidirect
15. C11×#3006C2semidirect
16. C22×C11×#41C22semidirect
17. C22×D4×D11C22semidirect
21. #10623364C22semidirect
22. #10623364C22semidirect
26. #10623359C22semidirect
29. #10623347C22semidirect
30. #10623336C22semidirect
34. C2×#66991C22semidirect
38. C2×#66979C22semidirect
39. C2×M16×D11C22semidirect
43. #10623138C22semidirect
44. C2×#66948C22semidirect
45. C2×#66945C22semidirect
48. C11×#449C22semidirect
49. C11×#448C22semidirect
50. C11×#447C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622851C22semidirect
54. #10622845C22semidirect
55. #10622840C22semidirect
56. #10622830C22semidirect
57. #10622828C22semidirect
58. #10622820C22semidirect
59. #10622787C22semidirect
60. #10622784C22semidirect
61. #10622782C22semidirect
62. #10622782C22semidirect
63. #10622772C22semidirect
64. #10622770C22semidirect
65. #10622769C22semidirect
66. #10622769C22semidirect
67. #10622744C22semidirect
68. #10622739C22semidirect
69. #10622734C22semidirect
70. #10622648C22semidirect
71. #10622647C22semidirect
72. #10622646C22semidirect
73. #10622577C22semidirect
74. #10622428C22semidirect
75. #10622427C22semidirect
76. #10622425C22semidirect
77. #10622420C22semidirect
78. #10622397C22semidirect
79. #10622395C22semidirect
80. #10622392C22semidirect
81. #10622388C22semidirect
82. #10622350C22semidirect
83. #10622349C22semidirect
84. #10622348C22semidirect
85. #10622340C22semidirect
86. #10622340C22semidirect
92. C2×C11×#41C23semidirect
93. C22×Q8×C11C23semidirect
97. C22×D4×C11C23semidirect
137. #66999C23semidirect
138. #66999C23semidirect
152. #66991C23semidirect
153. #66991C23semidirect
180. #66979C23semidirect
182. C2×C4⋊Dic11C23semidirect
183. C2×C4⋊Dic11C23semidirect
190. C2×#4313C23semidirect
191. C2×C8×D11C23semidirect
200. C11×#103C23semidirect
201. C11×#102C23semidirect
202. C11×C22⋊C8C23semidirect
203. C11×C22⋊C8C23semidirect
204. #66899C23semidirect
207. #66896C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
214. #66882C23semidirect
215. #66881C23semidirect
216. #66872C23semidirect
217. #66871C23semidirect
364. #3006D11semidirect
463. C22×#41C2×D11semidirect
515. #449C2×D11semidirect
517. #448C2×D11semidirect
521. #447C2×D11semidirect
527. #417C2×D11semidirect
532. #407C2×D11semidirect
586. C2×#41C22×D11semidirect
588. C22×Q8C22×D11semidirect
603. C22×D4C22×D11semidirect
694. #103C22×D11semidirect
700. #102C22×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
#130819452
C2×#106231382
#130794862
#130794792
#130794672
#130794652
#130785572
#130785522
#130785462
#130782382
#130782292
#130778682
#130778412
#130770592
C11×#30062
#6075311