Finite Group Databasebeta

← #15638788

Subgroups — #15638788

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#13082450C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080833C214yesmaximal, complemented
4#13080810C214yesmaximal, complemented
5#13080245C214yesmaximal, complemented
6#13080221C214yesmaximal, complemented
7#13079580C212yesmaximal, complemented
8#13079443C212yesmaximal, complemented
9#13079423C211yesmaximal, characteristic, complemented
10#13079413C211yesmaximal, characteristic, complemented
11#13078658C212yesmaximal, complemented
12#13077876C211yesmaximal, characteristic, complemented
13#13077840C212yesmaximal, complemented
14#13077655C211yesmaximal, characteristic, complemented
15C11×#3006C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic, complemented
18C2×C11×AGL(1,ℤ/8)C2212yescomplemented
19C2×C11×#121C2211yescharacteristic, complemented
20#10623360—22no—
21#10623360—22no—
22#10623360C2214yes—
23#10623360C2214yescomplemented
24C2×#67004C2212yescomplemented
25C2×#67000C2211yescharacteristic, complemented
26C2×#66999C2211yescharacteristic, complemented
27#10623337C2212yescomplemented
28#10623335—21no—
29C2×#66992—21no—
30C2×#66990—21no—
31#10623329—21no—
32C2×D4×Dic11C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic
34C2×#66982—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C22×(C2×D11)⋊C4—21no—
37C2×#66977C2211yescharacteristic, complemented
38C2×#66964C2214yescomplemented
39#10623149C2212yescomplemented
40#10623148—21no—
41#10623137C2212yes—
42#10623133—21no—
43#10623132—22no—
44#10623131C2212yescomplemented
45#10623129C2212yescomplemented
46#10623044C2212yescomplemented
47#10623026—22no—
48C11×#449C2214yescomplemented
49C11×#448C2212yescomplemented
50C11×#447C2212yes—
51C11×#417C2212yescomplemented
52C11×#407C2211yescharacteristic, complemented
53#10622852C2214yescomplemented
54#10622845C2212yescomplemented
55#10622841C2212yescomplemented
56#10622831C2212yescomplemented
57#10622830C2212yescomplemented
58#10622820C2211yescharacteristic, complemented
59#10622787C2214yescomplemented
60#10622786C2214yescomplemented
61#10622781C2214yescomplemented
62#10622778C2214yescomplemented
63#10622769C2214yescomplemented
64#10622766C2214yescomplemented
65D8×Dic11C2214yescomplemented
66#10622747C2214yescomplemented
67#10622741C2214yescomplemented
68#10622652C2214yescomplemented
69#10622649C2212yes—
70#10622647C2212yescomplemented
71#10622581C2212yescomplemented
72#10622429C2214yescomplemented
73#10622427C2214yescomplemented
74#10622413C2214yescomplemented
75#10622411C2214yescomplemented
76#10622389C2214yescomplemented
77#10622383C2214yescomplemented
78#10622379C2214yescomplemented
79#10622371C2214yescomplemented
80#10622351C2212yescomplemented
81#10622349C2212yescomplemented
82#10622344C2212yescomplemented
83#10622342C2214yescomplemented
84#10622339C2212yescomplemented
85#10622335C2212yescomplemented
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×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⋊D11D411yescharacteristic
103C23×Dic11—21no—
104C2×#4341C2312yes—
105C2×D4×D11—22no—
106C2×D4×D11—44no—
107C2×D4×D11C2314yes—
108C22×D44C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22C2311yescharacteristic, complemented
111C11×AGL(1,ℤ/8)—44no—
112C2×C11×SD16C2314yescomplemented
113C2×C11×D8C2314yes—
114C2×C11×M16C2312yescomplemented
115C11×#121—21no—
116C11×#121—21no—
117C11×#121C2312yes—
118C11×#121C2312yescomplemented
119C2×C11×C4⋊C4C2311yescharacteristic, complemented
120C2×C11×C22⋊C4—21no—
121#67006—22no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11D411yescharacteristic
126#67004—44no—
127#67000—22no—
128#67000C2314yes—
129#66999—22no—
130#66999C2314yes—
131C2×#4326C2314yescomplemented
132#66992—22no—
133#66992—22no—
134#66992—24no—
135#66992—24no—
136#66992—22no—
137#66991C2312yes—
138#66990—22no—
139#66990—24no—
140#66990—24no—
141#66989C2312yescomplemented
142#66988—22no—
143#66988—22no—
144D4×Dic11—22no—
145D4×Dic11—22no—
146D4×Dic11—22no—
147D4×Dic11—22no—
148D4×Dic11—22no—
149D4×Dic11C2314yes—
150D4×Dic11C2312yescomplemented
151C2×#4324C2314yes—
152C2×#4323C2314yes—
153#66983—21no—
154#66983—21no—
155#66983C2312yes—
156#66983C2312yes—
157#66982—22no—
158#66982—24no—
159#66982—24no—
160C4×C22⋊D11D412yes—
161C4×C22⋊D11D412yes—
162C4×C22⋊D11C2312yes—
163C4×C22⋊D11C2312yes—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4—21no—
168C2×(C2×D11)⋊C4—24no—
169C2×(C2×D11)⋊C4—24no—
170C2×(C2×D11)⋊C4D411yescharacteristic
171#66979—22no—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic, complemented
174#66977—21no—
175#66977—21no—
176#66977C2312yes—
177#66977C2312yescomplemented
178C2×Dic11⋊C4—21no—
179C2×Dic11⋊C4—21no—
180C2×Dic11⋊C4D411yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×#4318C2312yescomplemented
183#66964—48no—
184C2×#4314C2314yes—
185C2×#4313C2314yes—
186#66951—22no—
187#66950C2312yes—
188#66945C2312yes—
189#66943C2312yescomplemented
190#66942—22no—
191#66940C2312yescomplemented
192#66939—22no—
193#66938—22no—
194#66936—22no—
195(C22⋊D11)⋊C4—22no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C11×#103C2314yescomplemented
201C11×#102C2314yes—
202C11×C22⋊C8C2312yes—
203C11×C22⋊C8C2312yescomplemented
204#66899C2314yescomplemented
205#66896C2314yes—
206#66896C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210(C2×D11)⋊C8C2314yes—
211#66882C2314yescomplemented
212#66880C2314yescomplemented
213Dic11⋊C8C2314yescomplemented
214C8×Dic11C2314yescomplemented
215#66873C2314yes—
216#66872C2314yescomplemented
217#61581—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
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—42no—
235C2×Q8×C11C2412yes—
236C2×D4×C11—24no—
237C2×D4×C11—22no—
238C2×D4×C11—22no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—21no—
242C2×D4×C11—21no—
243C2×D4×C11—42no—
244C2×D4×C11—44no—
245C2×D4×C11—44no—
246C2×D4×C11C2412yes—
247C2×D4×C11C2412yes—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—42no—
253C22×C4×C11—44no—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—24no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—42no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—82no—
268C2×C22⋊D11C2×D412yes—
269C2×C22⋊D11C2×D412yes—
270C22×Dic11—22no—
271C22×Dic11—22no—
272C22×Dic11—24no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—82no—
277C22×Dic11C2×D411yescharacteristic
278C22×Dic11C2×D411yescharacteristic
279C22×Dic11C2×D411yescharacteristic
280#4341—44no—
281D4×D11—28no—
282D4×D11—44no—
283D4×D11—48no—
284C2×D44—21no—
285C2×D44—42no—
286C2×D44C2412yes—
287C2×C4×D11—42no—
288C2×C4×D11C2×D412yes—
289C2×C4×D11C2412yes—
290C2×Dic22—21no—
291C2×Dic22—42no—
292C2×Dic22C2412yes—
293C11×SD16—44no—
294C11×D8—28no—
295C11×M16—42no—
296C2×C8×C11C2414yes—
297C11×C4⋊C4—21no—
298C11×C4⋊C4C2412yes—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—24no—
306C22⋊Dic11—22no—
307C22⋊Dic11—22no—
308C22⋊Dic11C2×D412yes—
309C22⋊Dic11C2×D412yes—
310#4326—44no—
311#4324—28no—
312#4323—44no—
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)⋊C4C2×D412yes—
321(C2×D11)⋊C4C2×D412yes—
322C4⋊Dic11—22no—
323C4⋊Dic11—22no—
324C4⋊Dic11—21no—
325C4⋊Dic11—21no—
326C4⋊Dic11C2412yes—
327C4⋊Dic11C2412yes—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—24no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4C2×D412yes—
334Dic11⋊C4C2×D412yes—
335C4×Dic11—22no—
336C4×Dic11—22no—
337C4×Dic11C2×D412yes—
338C4×Dic11C2412yes—
339#4318—42no—
340C2×C11⋊C8C2414yes—
341#4314—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#3007—111no—
355#3006D1111yescharacteristic, complemented
356#3003—112no—
357#2975—111no—
358C23×C11—24no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—42no—
365C23×C11—42no—
366C23×C11—42no—
367C23×C11—81no—
368C23×C11—81no—
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—48no—
377C22×D11—48no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—42no—
381C22×D11—84no—
382C22×D11—816no—
383C22×D11C22×D412yes—
384Q8×C11—22no—
385Q8×C11—22no—
386Q8×C11—42no—
387D4×C11—24no—
388D4×C11—22no—
389D4×C11—24no—
390D4×C11—44no—
391D4×C11—44no—
392D4×C11—44no—
393D4×C11—44no—
394D4×C11—81no—
395D4×C11H(5,𝔽2)14yes—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—44no—
405C2×C4×C11—44no—
406C2×C4×C11—42no—
407C2×C4×C11—42no—
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—82no—
416C22⋊D11—82no—
417C22⋊D11—82no—
418C22⋊D11—82no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—42no—
426C2×Dic11—82no—
427C2×Dic11—82no—
428C2×Dic11—84no—
429C2×Dic11—81no—
430C2×Dic11—81no—
431C2×Dic11C22×D412yes—
432C2×Dic11C22×D412yes—
433C2×Dic11C22×D412yes—
434D44—24no—
435D44—42no—
436C4×D11—24no—
437C4×D11—42no—
438Dic22—24no—
439Dic22—81no—
440C8×C11—24no—
441C11⋊C8—24no—
442C22×#41C2×D1111yescharacteristic
443C23×D4—111no—
444C2×#137—112no—
445C2×AGL(1,ℤ/8)—114no—
446C2×AGL(1,ℤ/8)C2×D1112yescomplemented
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⋊Q8—111no—
466C2×#121—111no—
467C2×#121—221no—
468C2×#121C2×D1111yescharacteristic, complemented
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#452—114no—
491#451—112no—
492#450—112no—
493#450—114no—
494#450—112no—
495#449C2×D1114yescomplemented
496#448—112no—
497#448C2×D1112yescomplemented
498#447—112no—
499#447—114no—
500#447—112no—
501#447C2×D1112yes—
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—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—82no—
529C22×C11—162no—
530C22×C11#57512yes—
531C22×C11C23×D411yescharacteristic
532C2×D11—22no—
533C2×D11—22no—
534C2×D11—22no—
535C2×D11—44no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—816no—
540C2×D11—84no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—21no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11C2×H(5,𝔽2)12yes—
547Dic11—22no—
548Dic11—22no—
549Dic11—22no—
550Dic11—42no—
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×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—111no—
565C22×D4—114no—
566C22×D4—111no—
567C22×D4—222no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—444no—
571C22×D4C22×D1111yescharacteristic
572C22×D4C22×D1111yescharacteristic, complemented
573C23×C4—21no—
574C23×C4—111no—
575C23×C4—221no—
576C23×C4C22×D1111yescharacteristic
577#137—444no—
578AGL(1,ℤ/8)—44no—
579AGL(1,ℤ/8)—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16C22×D1114yescomplemented
584C2×D8—114no—
585C2×D8C22×D1114yes—
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—224no—
601#123—224no—
602#123—222no—
603#123—222no—
604#123—222no—
605C22⋊Q8—114no—
606C22⋊Q8—112no—
607C22⋊Q8—112no—
608C22⋊Q8—112no—
609C22⋊Q8—222no—
610C22⋊Q8—222no—
611C22⋊Q8—221no—
612C22⋊Q8—221no—
613#121—21no—
614#121—21no—
615#121—112no—
616#121—112no—
617#121—112no—
618#121—224no—
619#121—224no—
620#121—222no—
621#121—222no—
622#121—222no—
623#121—221no—
624#121—221no—
625#121C22×D1112yes—
626#121C22×D1112yescomplemented
627#120—224no—
628#120—224no—
629#120—222no—
630#120—222no—
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—111no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—221no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22×D1111yescharacteristic, complemented
653C2×C22⋊C4—21no—
654C2×C22⋊C4—111no—
655C2×C22⋊C4—111no—
656C2×C22⋊C4—224no—
657C2×C22⋊C4—224no—
658C2×C22⋊C4—222no—
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—82no—
688C2×C11#348411yescharacteristic
689C2×C11C2×#57511yescharacteristic
690C2×C11#358511yescharacteristic
691D11—42no—
692D11—82no—
693C24—21no—
694C24—21no—
695C24—111no—
696C24—224no—
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—42no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—442no—
714C2×Q8C23×D1112yes—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—112no—
726C2×D4—112no—
727C2×D4—112no—
728C2×D4—224no—
729C2×D4—228no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—222no—
734C2×D4—221no—
735C2×D4—442no—
736C2×D4—444no—
737C2×D4—442no—
738C2×D4—448no—
739C2×D4—444no—
740C2×D4—882no—
741C2×D4C23×D1112yes—
742C2×D4C23×D1112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—42no—
748C22×C4—44no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—112no—
753C22×C4—112no—
754C22×C4—224no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—221no—
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—444no—
769SD16—44no—
770SD16—228no—
771SD16—444no—
772D8—28no—
773D8—444no—
774M16—42no—
775M16—444no—
776M16—442no—
777C2×C8—114no—
778C2×C8C23×D1114yes—
779C4⋊C4—21no—
780C4⋊C4—112no—
781C4⋊C4—112no—
782C4⋊C4—112no—
783C4⋊C4—112no—
784C4⋊C4—224no—
785C4⋊C4—222no—
786C4⋊C4—222no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—221no—
790C4⋊C4—221no—
791C4⋊C4—222no—
792C4⋊C4—222no—
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—224no—
802C22⋊C4—224no—
803C22⋊C4—222no—
804C22⋊C4—222no—
805C22⋊C4—224no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—222no—
809C22⋊C4—222no—
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—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—81no—
829C23—81no—
830C23—112no—
831C23—222no—
832C23—222no—
833C23—441no—
834C23—441no—
835C23—448no—
836C23—442no—
837C23—442no—
838C23—448no—
839C23—442no—
840C23—884no—
841C23—8816no—
842C23C2×D4×D1111yescharacteristic
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845Q8—22no—
846Q8—22no—
847Q8—42no—
848Q8—224no—
849Q8—881no—
850D4—24no—
851D4—22no—
852D4—24no—
853D4—44no—
854D4—44no—
855D4—44no—
856D4—44no—
857D4—81no—
858D4—224no—
859D4—442no—
860D4—442no—
861D4—442no—
862D4—448no—
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—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—112no—
881C2×C4—112no—
882C2×C4—112no—
883C2×C4—222no—
884C2×C4—224no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—442no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—442no—
892C2×C4—884no—
893C2×C4—882no—
894C2×C4—882no—
895C2×C4—881no—
896C2×C4—881no—
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—42no—
916C22—42no—
917C22—42no—
918C22—82no—
919C22—162no—
920C22—222no—
921C22—222no—
922C22—222no—
923C22—444no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—884no—
928C22—8816no—
929C22#1062330412yes—
930C22C22×D4×D1111yescharacteristic
931C4—21no—
932C4—21no—
933C4—21no—
934C4—42no—
935C4—42no—
936C4—222no—
937C4—222no—
938C4—222no—
939C4—442no—
940C4—442no—
941C4—442no—
942C4C2×#6703712yes—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—44no—
947C2—82no—
948C2—442no—
949C2—882no—
950C2#1308224511yescharacteristic
951C2C2×#1062330411yescharacteristic
952C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#61581
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. #13082450C2semidirect
2. C2×#10623360C2semidirect
3. #13080833C2semidirect
4. #13080810C2semidirect
5. #13080245C2semidirect
6. #13080221C2semidirect
7. #13079580C2semidirect
8. #13079443C2semidirect
9. #13079423C2semidirect
10. #13079413C2semidirect
11. #13078658C2semidirect
12. #13077876C2semidirect
13. #13077840C2semidirect
14. #13077655C2semidirect
15. C11×#3006C2semidirect
17. C22×D4×D11C22semidirect
18. C2×C11×AGL(1,ℤ/8)C22semidirect
19. C2×C11×#121C22semidirect
23. #10623360C22semidirect
24. C2×#67004C22semidirect
25. C2×#67000C22semidirect
26. C2×#66999C22semidirect
27. #10623337C22semidirect
32. C2×D4×Dic11C22semidirect
37. C2×#66977C22semidirect
38. C2×#66964C22semidirect
39. #10623149C22semidirect
44. #10623131C22semidirect
45. #10623129C22semidirect
46. #10623044C22semidirect
48. C11×#449C22semidirect
49. C11×#448C22semidirect
51. C11×#417C22semidirect
52. C11×#407C22semidirect
53. #10622852C22semidirect
54. #10622845C22semidirect
55. #10622841C22semidirect
56. #10622831C22semidirect
57. #10622830C22semidirect
58. #10622820C22semidirect
59. #10622787C22semidirect
60. #10622786C22semidirect
61. #10622781C22semidirect
62. #10622778C22semidirect
63. #10622769C22semidirect
64. #10622766C22semidirect
65. D8×Dic11C22semidirect
66. #10622747C22semidirect
67. #10622741C22semidirect
68. #10622652C22semidirect
70. #10622647C22semidirect
71. #10622581C22semidirect
72. #10622429C22semidirect
73. #10622427C22semidirect
74. #10622413C22semidirect
75. #10622411C22semidirect
76. #10622389C22semidirect
77. #10622383C22semidirect
78. #10622379C22semidirect
79. #10622371C22semidirect
80. #10622351C22semidirect
81. #10622349C22semidirect
82. #10622344C22semidirect
83. #10622342C22semidirect
84. #10622339C22semidirect
85. #10622335C22semidirect
86. #10622331C22semidirect
97. C22×D4×C11C23semidirect
110. C22×Dic22C23semidirect
112. C2×C11×SD16C23semidirect
114. C2×C11×M16C23semidirect
118. C11×#121C23semidirect
119. C2×C11×C4⋊C4C23semidirect
131. C2×#4326C23semidirect
141. #66989C23semidirect
150. D4×Dic11C23semidirect
173. C2×C4⋊Dic11C23semidirect
177. #66977C23semidirect
182. C2×#4318C23semidirect
189. #66943C23semidirect
191. #66940C23semidirect
200. C11×#103C23semidirect
203. C11×C22⋊C8C23semidirect
204. #66899C23semidirect
206. #66896C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
211. #66882C23semidirect
212. #66880C23semidirect
213. Dic11⋊C8C23semidirect
214. C8×Dic11C23semidirect
216. #66872C23semidirect
355. #3006D11semidirect
446. C2×AGL(1,ℤ/8)C2×D11semidirect
468. C2×#121C2×D11semidirect
495. #449C2×D11semidirect
497. #448C2×D11semidirect
509. #417C2×D11semidirect
512. #407C2×D11semidirect
572. C22×D4C22×D11semidirect
583. C2×SD16C22×D11semidirect
588. C2×M16C22×D11semidirect
626. #121C22×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
#130824502
C2×#106233602
#130808332
#130808102
#130802452
#130802212
#130795802
#130794432
#130794232
#130794132
#130786582
#130778762
#130778402
#130776552
C11×#30062
#6158111