Finite Group Databasebeta

← #15638798

Subgroups — #15638798

Order 2816.

2258 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082457C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080825C214yesmaximal, complemented
4#13080818C214yesmaximal, complemented
5#13080241C214yesmaximal, complemented
6#13080220C214yesmaximal, complemented
7#13079586C212yesmaximal, complemented
8#13079449C212yesmaximal, complemented
9#13079418C211yesmaximal, characteristic, complemented
10#13079416C211yesmaximal, characteristic, complemented
11#13078664C212yesmaximal, complemented
12#13077868C211yesmaximal, characteristic, complemented
13#13077844C212yesmaximal, complemented
14#13077655C211yesmaximal, characteristic, complemented
15C11×#3007C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic, complemented
18C2×C11×#137C2212yescomplemented
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20#10623360—22no—
21#10623360—22no—
22#10623360C2214yes—
23#10623360C2214yescomplemented
24C2×#67002C2212yescomplemented
25#10623348C2212yescomplemented
26C2×#67000C2211yescharacteristic, complemented
27C2×#66999C2211yescharacteristic, complemented
28C2×#66992—21no—
29C2×#66990—21no—
30C2×D4×Dic11C2211yescharacteristic, complemented
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic, complemented
33C2×#66982—21no—
34C2×C4×C22⋊D11C2211yescharacteristic
35C22×(C2×D11)⋊C4—21no—
36C2×#66967C2214yescomplemented
37#10623176—21no—
38#10623175—21no—
39#10623173C2212yescomplemented
40#10623168—22no—
41#10623161C2212yescomplemented
42#10623158C2212yes—
43#10623155C2212yescomplemented
44#10623045—22no—
45#10623045C2212yescomplemented
46#10623024—21no—
47#10623017—21no—
48C11×#452C2214yescomplemented
49C11×#451C2212yescomplemented
50C11×#450C2212yescomplemented
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622851C2214yescomplemented
54#10622845C2212yescomplemented
55#10622840C2212yescomplemented
56#10622840C2212yescomplemented
57#10622830C2212yes—
58#10622820C2211yescharacteristic, complemented
59#10622804C2214yescomplemented
60#10622802C2214yescomplemented
61#10622800C2214yescomplemented
62#10622798C2214yescomplemented
63#10622782C2214yescomplemented
64#10622778C2214yescomplemented
65SD16×Dic11C2214yescomplemented
66#10622748C2214yescomplemented
67#10622741C2214yescomplemented
68#10622662C2214yescomplemented
69#10622659C2212yescomplemented
70#10622657C2212yescomplemented
71#10622580C2212yescomplemented
72#10622432C2214yescomplemented
73#10622428C2214yescomplemented
74#10622425C2214yescomplemented
75#10622413C2214yescomplemented
76#10622386C2214yescomplemented
77#10622383C2214yescomplemented
78#10622376C2214yescomplemented
79#10622369C2214yescomplemented
80#10622348C2212yescomplemented
81#10622348C2212yescomplemented
82#10622345C2212yes—
83#10622345C2212yescomplemented
84#10622342C2214yescomplemented
85#10622339C2212yescomplemented
86#10622331C2212yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41—44no—
91C2×C11×#41C2312yes—
92C2×C11×#41C2312yes—
93C22×Q8×C11C2311yescharacteristic
94C22×Q8×C11C2311yescharacteristic, complemented
95C22×D4×C11—21no—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11D411yescharacteristic
103C23×Dic11—21no—
104C2×#4343C2312yes—
105C2×D4×D11—22no—
106C2×D4×D11—44no—
107C2×D4×D11C2314yes—
108C22×D44C2311yescharacteristic
109C22×D44C2311yescharacteristic, complemented
110C22×C4×D11C2311yescharacteristic
111C11×#137—44no—
112C2×C11×Q16C2314yescomplemented
113C2×C11×SD16C2314yes—
114C2×C11×M16C2312yescomplemented
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8C2312yes—
118C11×C22⋊Q8C2312yescomplemented
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic, complemented
121C2×C11×C22⋊C4—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11D411yescharacteristic
124#67002—44no—
125#67000—22no—
126#67000—22no—
127#67000C2314yes—
128#67000C2312yescomplemented
129#66999—22no—
130#66999—22no—
131#66999C2312yes—
132#66999C2314yes—
133Q8×Dic11C2312yescomplemented
134C2×#4325C2314yes—
135C2×#4325C2314yescomplemented
136#66992—24no—
137#66992—24no—
138#66990—24no—
139#66990—24no—
140D4×Dic11—22no—
141D4×Dic11C2314yes—
142C2×#4323C2314yes—
143#66983—21no—
144#66983—21no—
145#66983—21no—
146#66983—21no—
147#66983—22no—
148#66983—22no—
149#66983C2312yes—
150#66983C2312yes—
151#66983C2312yes—
152#66983C2312yescomplemented
153#66982—24no—
154#66982—24no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11D412yes—
158C4×C22⋊D11D412yes—
159C4×C22⋊D11C2312yes—
160C4×C22⋊D11C2312yes—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—24no—
167C2×(C2×D11)⋊C4—24no—
168C2×(C2×D11)⋊C4D411yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic, complemented
171C2×Dic11⋊C4—21no—
172C2×Dic11⋊C4D411yescharacteristic
173C2×C4×Dic11C2311yescharacteristic
174C2×#4318C2312yescomplemented
175#66967—48no—
176C2×D88C2314yes—
177C2×#4313C2314yes—
178#66951—22no—
179#66951—22no—
180#66951—22no—
181#66948—22no—
182#66948C2312yes—
183#66947—22no—
184#66947—22no—
185#66947—22no—
186#66946—22no—
187#66946C2312yescomplemented
188#66945—22no—
189#66945C2312yes—
190#66943—22no—
191#66943C2312yescomplemented
192#66939—22no—
193#66939—22no—
194#66935—22no—
195#66935—22no—
196(C22⋊D11)⋊C4—22no—
197(C22⋊D11)⋊C4—22no—
198C22⋊C4×D11—22no—
199#66930—22no—
200C11×#103C2314yescomplemented
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yescomplemented
204#66899C2314yescomplemented
205#66899C2314yescomplemented
206#66896C2314yes—
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yes—
212#66881C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214C8×Dic11C2314yescomplemented
215#66873C2314yes—
216#66871C2314yescomplemented
217#61581—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—24no—
223C23×D11—44no—
224C23×D11—44no—
225C23×D11—82no—
226C23×D11C2×D411yescharacteristic
227C11×#41—24no—
228C11×#41—24no—
229C11×#41—42no—
230C11×#41—42no—
231C11×#41—44no—
232C11×#41—44no—
233C2×Q8×C11—21no—
234C2×Q8×C11—21no—
235C2×Q8×C11—42no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2412yes—
238C2×Q8×C11C2412yes—
239C2×D4×C11—24no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—44no—
244C2×D4×C11C2412yes—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—42no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—24no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—42no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—82no—
267C2×C22⋊D11C2×D412yes—
268C2×C22⋊D11C2×D412yes—
269C22×Dic11—24no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—82no—
273C22×Dic11C2×D411yescharacteristic
274C22×Dic11C2×D411yescharacteristic
275C22×Dic11C2×D411yescharacteristic
276#4343—44no—
277D4×D11—28no—
278D4×D11—44no—
279D4×D11—48no—
280C2×D44—22no—
281C2×D44—22no—
282C2×D44—21no—
283C2×D44—21no—
284C2×D44—42no—
285C2×D44—42no—
286C2×D44C2412yes—
287C2×D44C2412yes—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—42no—
291C2×C4×D11C2×D412yes—
292C2×C4×D11C2412yes—
293C11×Q16—44no—
294C11×SD16—28no—
295C11×M16—42no—
296C2×C8×C11C2414yes—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—21no—
300C11×C4⋊C4C2412yes—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C22⋊Dic11—24no—
304C22⋊Dic11C2×D412yes—
305C22⋊Dic11C2×D412yes—
306#4325—44no—
307#4325—44no—
308#4323—28no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—22no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4C2×D412yes—
323(C2×D11)⋊C4C2×D412yes—
324C4⋊Dic11—22no—
325C4⋊Dic11—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11C2412yes—
329C4⋊Dic11C2412yes—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—24no—
333Dic11⋊C4C2×D412yes—
334Dic11⋊C4C2×D412yes—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11C2×D412yes—
338C4×Dic11C2412yes—
339#4318—42no—
340C2×C11⋊C8C2414yes—
341D88—44no—
342#4313—44no—
343#3505—111no—
344C2×#546—111no—
345#3323—114no—
346#3322—114no—
347#3275—114no—
348#3273—114no—
349#3211—112no—
350#3196—112no—
351#3193—111no—
352#3192—111no—
353#3105—112no—
354#3007D1111yescharacteristic, complemented
355#3006—111no—
356#3003—112no—
357#2975—111no—
358C23×C11—24no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—42no—
364C23×C11—42no—
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—48no—
374C22×D11—48no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—84no—
380C22×D11—81no—
381C22×D11—81no—
382C22×D11—816no—
383C22×D11C22×D412yes—
384Q8×C11—22no—
385Q8×C11—24no—
386Q8×C11—22no—
387Q8×C11—42no—
388Q8×C11—81no—
389D4×C11—24no—
390D4×C11—22no—
391D4×C11—44no—
392D4×C11—44no—
393D4×C11H(5,𝔽2)14yes—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11—42no—
406C2×C4×C11—81no—
407C2×C4×C11—81no—
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C2511yescharacteristic
412C22⋊D11—42no—
413C22⋊D11—42no—
414C22⋊D11—48no—
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—82no—
418C22⋊D11—82no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—42no—
425C2×Dic11—42no—
426C2×Dic11—84no—
427C2×Dic11C22×D412yes—
428C2×Dic11C22×D412yes—
429C2×Dic11C22×D412yes—
430D44—24no—
431D44—24no—
432D44—42no—
433D44—81no—
434D44—82no—
435D44—82no—
436C4×D11—24no—
437C4×D11—42no—
438C4×D11—82no—
439C4×D11—82no—
440C8×C11—24no—
441C11⋊C8—24no—
442C22×#41C2×D1111yescharacteristic
443C23×D4—111no—
444C2×#137C2×D1112yescomplemented
445C2×AGL(1,ℤ/8)—112no—
446C2×AGL(1,ℤ/8)—114no—
447#553—112no—
448#553—222no—
449#552—112no—
450#551—222no—
451#548—112no—
452#546—114no—
453#546—114no—
454#546—112no—
455#546—222no—
456#546—222no—
457#539—221no—
458#538—221no—
459#534—221no—
460#529—112no—
461C2×#124—111no—
462#525—112no—
463C2×#123—221no—
464C2×C22⋊Q8—111no—
465C2×C22⋊Q8C2×D1111yescharacteristic, complemented
466C2×#121—111no—
467C2×#121—111no—
468C2×#121—221no—
469C2×#120—221no—
470#518—221no—
471C2×C4×D4—111no—
472C2×C4×D4—111no—
473C22×C22⋊C4—221no—
474#495—114no—
475#488—114no—
476#485—114no—
477#484—112no—
478#481—112no—
479#481—112no—
480#480—112no—
481#478—114no—
482#470—114no—
483#469—114no—
484#468—114no—
485#468—114no—
486#464—114no—
487#463—114no—
488#463—114no—
489#452—114no—
490#452C2×D1114yescomplemented
491#451C2×D1112yescomplemented
492#450—114no—
493#450—112no—
494#450C2×D1112yescomplemented
495#449—114no—
496#448—112no—
497#448—112no—
498#447—112no—
499#447—114no—
500#447—112no—
501#447—112no—
502C4×SD16—114no—
503C4×D8—114no—
504#436—114no—
505#436—114no—
506#431—112no—
507#418—114no—
508#417—112no—
509#417C2×D1112yescomplemented
510#407—111no—
511#407—112no—
512#407C2×D1111yescharacteristic, complemented
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—24no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—48no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—82no—
526C22×C11#57512yes—
527C22×C11C23×D411yescharacteristic
528C2×D11—22no—
529C2×D11—22no—
530C2×D11—22no—
531C2×D11—44no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—816no—
539C2×D11—84no—
540C2×D11—162no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—21no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11C2×H(5,𝔽2)12yes—
548Dic11—22no—
549Dic11—22no—
550Dic11—22no—
551Dic11—42no—
552Dic11—42no—
553C25—221no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—44no—
557C2×#41—112no—
558C2×#41C22×D1112yes—
559C2×#41C22×D1112yes—
560C22×Q8C22×D1111yescharacteristic
561C22×Q8C22×D1111yescharacteristic, complemented
562C22×D4—21no—
563C22×D4—111no—
564C22×D4—114no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—222no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—444no—
572C22×D4C22×D1111yescharacteristic
573C23×C4—21no—
574C23×C4—111no—
575C23×C4—221no—
576C23×C4C22×D1111yescharacteristic
577#137—44no—
578AGL(1,ℤ/8)—444no—
579AGL(1,ℤ/8)—448no—
580C2×Q16C22×D1114yescomplemented
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16C22×D1114yes—
584C2×D8—114no—
585C2×D8—114no—
586C2×M16—112no—
587C2×M16—114no—
588C2×M16C22×D1112yescomplemented
589#126—222no—
590#126—222no—
591#126—222no—
592#125—112no—
593#125—222no—
594#124—114no—
595#124—112no—
596#124—222no—
597#124—222no—
598#123—222no—
599#123—222no—
600#123—222no—
601#123—222no—
602#123—222no—
603#123—224no—
604#123—224no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—114no—
608C22⋊Q8—112no—
609C22⋊Q8—222no—
610C22⋊Q8—222no—
611C22⋊Q8C22×D1112yes—
612C22⋊Q8C22×D1112yescomplemented
613#121—112no—
614#121—112no—
615#121—112no—
616#121—112no—
617#121—112no—
618#121—222no—
619#121—224no—
620#121—224no—
621#121—222no—
622#121—222no—
623#121—221no—
624#121—221no—
625#121—221no—
626#121—221no—
627#120—222no—
628#120—222no—
629#120—224no—
630#120—224no—
631C4×Q8—112no—
632C4×D4—112no—
633C4×D4—112no—
634C4×D4—112no—
635C4×D4—112no—
636C4×D4—114no—
637C4×D4—112no—
638C4×D4—222no—
639C4×D4—222no—
640C4×D4—222no—
641C4×D4—222no—
642C4×D4—222no—
643C4×D4—222no—
644#117—112no—
645#117—222no—
646#117—222no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22×D1111yescharacteristic, complemented
653C2×C22⋊C4—21no—
654C2×C22⋊C4—111no—
655C2×C22⋊C4—111no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—224no—
659C2×C22⋊C4—221no—
660C2×C22⋊C4—221no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C42—111no—
666#107—114no—
667#106—114no—
668C4⋊C8—114no—
669#103—114no—
670#103—114no—
671#103C22×D1114yescomplemented
672#102—114no—
673#102—114no—
674#102—114no—
675#102—114no—
676#102C22×D1114yes—
677C22⋊C8—112no—
678C22⋊C8—112no—
679C22⋊C8—114no—
680C22⋊C8C22×D1112yes—
681C22⋊C8C22×D1112yescomplemented
682C4×C8—114no—
683C2×C11—22no—
684C2×C11—44no—
685C2×C11—41no—
686C2×C11—41no—
687C2×C11#348411yescharacteristic
688C2×C11C2×#57511yescharacteristic
689C2×C11#358511yescharacteristic
690D11—42no—
691D11—82no—
692D11—82no—
693C24—21no—
694C24—111no—
695C24—224no—
696C24—221no—
697C24—221no—
698C24—444no—
699C24—444no—
700C24—882no—
701C24D4×D1111yescharacteristic
702#41—24no—
703#41—24no—
704#41—42no—
705#41—42no—
706#41—44no—
707#41—44no—
708#41—444no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—42no—
712C2×Q8—42no—
713C2×Q8C23×D1112yes—
714C2×Q8C23×D1112yes—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—21no—
719C2×D4—44no—
720C2×D4—112no—
721C2×D4—112no—
722C2×D4—112no—
723C2×D4—112no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—224no—
727C2×D4—228no—
728C2×D4—222no—
729C2×D4—222no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—221no—
733C2×D4—221no—
734C2×D4—442no—
735C2×D4—442no—
736C2×D4—444no—
737C2×D4—442no—
738C2×D4—448no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—882no—
742C2×D4C23×D1112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—112no—
754C22×C4—112no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—224no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—442no—
761C22×C4—882no—
762C22×C4D4×D1111yescharacteristic
763C22×C4D4×D1111yescharacteristic
764C22×C4D4×D1111yescharacteristic
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768Q16—44no—
769SD16—28no—
770SD16—444no—
771SD16—444no—
772D8—228no—
773D8—444no—
774M16—42no—
775M16—444no—
776M16—442no—
777C2×C8—114no—
778C2×C8C23×D1114yes—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—21no—
782C4⋊C4—112no—
783C4⋊C4—112no—
784C4⋊C4—112no—
785C4⋊C4—112no—
786C4⋊C4—224no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—222no—
790C4⋊C4—222no—
791C4⋊C4—221no—
792C4⋊C4—221no—
793C4⋊C4C23×D1112yes—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—112no—
797C22⋊C4—112no—
798C22⋊C4—112no—
799C22⋊C4—112no—
800C22⋊C4—224no—
801C22⋊C4—222no—
802C22⋊C4—222no—
803C22⋊C4—224no—
804C22⋊C4—222no—
805C22⋊C4—222no—
806C22⋊C4—224no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—224no—
810C22⋊C4—222no—
811C22⋊C4—222no—
812C22⋊C4—222no—
813C22⋊C4—222no—
814C42—112no—
815C42—112no—
816C42—222no—
817C42—222no—
818C11#6158111yescharacteristic, complemented, Sylow
819C23—24no—
820C23—22no—
821C23—22no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—42no—
826C23—112no—
827C23—222no—
828C23—222no—
829C23—222no—
830C23—441no—
831C23—441no—
832C23—448no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23—448no—
837C23—442no—
838C23—881no—
839C23—881no—
840C23—884no—
841C23—8816no—
842C23C2×D4×D1111yescharacteristic
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845Q8—24no—
846Q8—22no—
847Q8—22no—
848Q8—42no—
849Q8—81no—
850D4—24no—
851D4—22no—
852D4—44no—
853D4—44no—
854D4—224no—
855D4—224no—
856D4—442no—
857D4—442no—
858D4—442no—
859D4—448no—
860D4—444no—
861D4—444no—
862D4—881no—
863D4—882no—
864D4—882no—
865D4—882no—
866D4—882no—
867D4#6703714yes—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—112no—
883C2×C4—112no—
884C2×C4—112no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—442no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—442no—
893C2×C4—442no—
894C2×C4—882no—
895C2×C4—882no—
896C2×C4—884no—
897C2×C4C2×D4×D1111yescharacteristic
898C2×C4C2×D4×D1111yescharacteristic
899C2×C4C2×D4×D1111yescharacteristic
900C2×C4C24×D1111yescharacteristic
901C8—24no—
902C8—224no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—24no—
910C22—21no—
911C22—21no—
912C22—48no—
913C22—42no—
914C22—42no—
915C22—82no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—444no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—884no—
927C22—8816no—
928C22—1762no—
929C22#1062330812yes—
930C22C22×D4×D1111yescharacteristic
931C4—21no—
932C4—21no—
933C4—21no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—222no—
938C4—222no—
939C4—222no—
940C4—442no—
941C4—442no—
942C4C2×#6703712yes—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—44no—
947C2—442no—
948C2—882no—
949C2—882no—
950C2#1308224511yescharacteristic
951C2C2×#1062330811yescharacteristic
952C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
hypercenter#3007D11
hypocenterC11#61581
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #13082457C2semidirect
2. C2×#10623360C2semidirect
3. #13080825C2semidirect
4. #13080818C2semidirect
5. #13080241C2semidirect
6. #13080220C2semidirect
7. #13079586C2semidirect
8. #13079449C2semidirect
9. #13079418C2semidirect
10. #13079416C2semidirect
11. #13078664C2semidirect
12. #13077868C2semidirect
13. #13077844C2semidirect
14. #13077655C2semidirect
15. C11×#3007C2semidirect
17. C22×D4×D11C22semidirect
18. C2×C11×#137C22semidirect
19. C2×C11×C22⋊Q8C22semidirect
23. #10623360C22semidirect
24. C2×#67002C22semidirect
25. #10623348C22semidirect
26. C2×#67000C22semidirect
27. C2×#66999C22semidirect
30. C2×D4×Dic11C22semidirect
32. C2×#66983C22semidirect
36. C2×#66967C22semidirect
39. #10623173C22semidirect
41. #10623161C22semidirect
43. #10623155C22semidirect
45. #10623045C22semidirect
48. C11×#452C22semidirect
49. C11×#451C22semidirect
50. C11×#450C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622851C22semidirect
54. #10622845C22semidirect
55. #10622840C22semidirect
56. #10622840C22semidirect
58. #10622820C22semidirect
59. #10622804C22semidirect
60. #10622802C22semidirect
61. #10622800C22semidirect
62. #10622798C22semidirect
63. #10622782C22semidirect
64. #10622778C22semidirect
65. SD16×Dic11C22semidirect
66. #10622748C22semidirect
67. #10622741C22semidirect
68. #10622662C22semidirect
69. #10622659C22semidirect
70. #10622657C22semidirect
71. #10622580C22semidirect
72. #10622432C22semidirect
73. #10622428C22semidirect
74. #10622425C22semidirect
75. #10622413C22semidirect
76. #10622386C22semidirect
77. #10622383C22semidirect
78. #10622376C22semidirect
79. #10622369C22semidirect
80. #10622348C22semidirect
81. #10622348C22semidirect
83. #10622345C22semidirect
84. #10622342C22semidirect
85. #10622339C22semidirect
86. #10622331C22semidirect
94. C22×Q8×C11C23semidirect
109. C22×D44C23semidirect
112. C2×C11×Q16C23semidirect
114. C2×C11×M16C23semidirect
118. C11×C22⋊Q8C23semidirect
120. C2×C11×C4⋊C4C23semidirect
128. #67000C23semidirect
133. Q8×Dic11C23semidirect
135. C2×#4325C23semidirect
152. #66983C23semidirect
170. C2×C4⋊Dic11C23semidirect
174. C2×#4318C23semidirect
187. #66946C23semidirect
191. #66943C23semidirect
200. C11×#103C23semidirect
203. C11×C22⋊C8C23semidirect
204. #66899C23semidirect
205. #66899C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
212. #66881C23semidirect
213. Dic11⋊C8C23semidirect
214. C8×Dic11C23semidirect
216. #66871C23semidirect
354. #3007D11semidirect
444. C2×#137C2×D11semidirect
465. C2×C22⋊Q8C2×D11semidirect
490. #452C2×D11semidirect
491. #451C2×D11semidirect
494. #450C2×D11semidirect
509. #417C2×D11semidirect
512. #407C2×D11semidirect
561. C22×Q8C22×D11semidirect
580. C2×Q16C22×D11semidirect
588. C2×M16C22×D11semidirect
612. C22⋊Q8C22×D11semidirect
652. C2×C4⋊C4C22×D11semidirect
671. #103C22×D11semidirect
681. C22⋊C8C22×D11semidirect
818. C11#61581semidirect

Maximal subgroups

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

subgroupindex
#130824572
C2×#106233602
#130808252
#130808182
#130802412
#130802202
#130795862
#130794492
#130794182
#130794162
#130786642
#130778682
#130778442
#130776552
C11×#30072
#6158111