Finite Group Databasebeta

← #15636695

Subgroups — #15636695

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082650C211yesmaximal, characteristic, complemented
2#13081636C211yesmaximal, characteristic, complemented
3#13081511C211yesmaximal, characteristic, complemented
4#13081261C211yesmaximal, characteristic, complemented
5#13081251C211yesmaximal, characteristic, complemented
6#13081211C211yesmaximal, characteristic, complemented
7#13081095C212yesmaximal, complemented
8#13080544C211yesmaximal, characteristic, complemented
9#13080466C212yesmaximal, complemented
10#13080434C212yesmaximal, complemented
11#13080423C211yesmaximal, characteristic, complemented
12#13080216C211yesmaximal, characteristic, complemented
13#13080097C212yesmaximal, complemented
14#13079293C212yesmaximal, complemented
15#13079176C211yesmaximal, characteristic, complemented
16#13078815C212yesmaximal, complemented
17#13078794C212yesmaximal, complemented
18#13078711C211yesmaximal, characteristic, complemented
19#13078707C211yesmaximal, characteristic, complemented
20#13077592C211yesmaximal, characteristic, complemented
21#13077444C212yesmaximal, complemented
22C2×C4×#4323C211yesmaximal, characteristic, complemented
23C11×#3520C211yesmaximal, characteristic, complemented
24C11×#556C2211yescharacteristic, complemented
25C11×#554C2212yescomplemented
26C11×#552—21no—
27C11×#551—22no—
28D4×Q8×C11C2211yescharacteristic, complemented
29C11×#548—21no—
30C11×#547C2211yescharacteristic, complemented
31C11×#547C2211yescharacteristic, complemented
32C11×#546C2212yescomplemented
33C11×#542C2212yescomplemented
34C11×#539—22no—
35C11×#533C2211yescharacteristic, complemented
36C11×#529C2211yescharacteristic
37C11×#525—21no—
38C2×C11×C22⋊Q8—21no—
39C11×#520C2212yescomplemented
40C2×C4×D4×C11C2211yescharacteristic, complemented
41C2×#67002C2212yes—
42C22×#4323C2211yescharacteristic
43#10623235—22no—
44#10623226—21no—
45#10623207—21no—
46#10623185—22no—
47#10623158—21no—
48D11×#121—21no—
49#10623110C2211yescharacteristic, complemented
50#10623108C2211yescharacteristic, complemented
51#10623096C2212yes—
52#10623094C2211yescharacteristic, complemented
53D4×D44C2212yes—
54D4×D44C2211yescharacteristic, complemented
55#10623066C2212yescomplemented
56#10623052C2212yescomplemented
57#10623008C2211yescharacteristic
58C2×C4×D44C2211yescharacteristic
59#10622851C2212yescomplemented
60#10622851C2212yescomplemented
61#10622846C2212yescomplemented
62#10622830C2212yescomplemented
63C2×#66896C2211yescharacteristic, complemented
64#10622701C2211yescharacteristic, complemented
65#10622701C2212yescomplemented
66#10622700C2212yescomplemented
67#10622700C2211yescharacteristic, complemented
68#10622700C2211yescharacteristic, complemented
69#10622698C2211yescharacteristic, complemented
70#10622697C2212yescomplemented
71#10622696C2211yescharacteristic, complemented
72#10622696C2211yescharacteristic, complemented
73#10622694C2211yescharacteristic, complemented
74#10622693C2212yescomplemented
75#10622692C2211yescharacteristic, complemented
76#10622671C2212yescomplemented
77#10622670C2212yes—
78#10622670C2212yescomplemented
79#10622669C2212yescomplemented
80#10622662C2212yescomplemented
81#10622661C2212yescomplemented
82#10622661C2212yescomplemented
83#10622661C2212yescomplemented
84#10622659C2212yes—
85#10622659C2212yescomplemented
86#10622658C2212yescomplemented
87#10622657C2212yescomplemented
88#10622652C2212yescomplemented
89#10622651C2212yescomplemented
90#10622649C2212yes—
91#10622648C2212yescomplemented
92#10622640C2212yescomplemented
93#10622639C2212yescomplemented
94#10622639C2212yescomplemented
95#10622639C2212yescomplemented
96C4×#4325C2212yescomplemented
97C4×#4325C2212yescomplemented
98C4×#4325C2212yescomplemented
99#10622637C2211yescharacteristic, complemented
100Q8×C11⋊C8C2211yescharacteristic, complemented
101#10622635C2212yescomplemented
102#10622628C2212yescomplemented
103#10622628C2211yescharacteristic, complemented
104#10622628C2211yescharacteristic, complemented
105#10622627C2212yes—
106#10622627C2212yescomplemented
107#10622627C2212yescomplemented
108C4×#4323C2211yescharacteristic
109C4×#4323C2211yescharacteristic
110C4×#4323C2211yescharacteristic
111C4×#4323C2211yescharacteristic
112C4×#4323C2211yescharacteristic, complemented
113C4×#4323C2211yescharacteristic, complemented
114C4×#4323C2211yescharacteristic, complemented
115C4×#4323C2211yescharacteristic, complemented
116C4×#4323C2212yescomplemented
117#10622625C2211yescharacteristic, complemented
118#10622624C2212yescomplemented
119D4×C11⋊C8C2211yescharacteristic, complemented
120D4×C11⋊C8C2212yescomplemented
121#10622622C2212yescomplemented
122#10622621C2211yescharacteristic, complemented
123#10622621C2211yescharacteristic, complemented
124#10622613C2212yescomplemented
125#10622610C2212yescomplemented
126#10622581C2212yescomplemented
127#10622581C2212yescomplemented
128#10622580C2212yescomplemented
129C2×#66873C2211yescharacteristic
130C2×#66873C2212yescomplemented
131#10622577C2212yescomplemented
132C2×#66871C2211yescharacteristic, complemented
133#10622539C2211yescharacteristic, complemented
134C2×C4×C11⋊C8C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41C2312yes—
137C22×Q8×C11—21no—
138C22×D4×C11C2311yescharacteristic
139C23×C4×C11—21no—
140C2×#4343—21no—
141C2×D4×D11—22no—
142C2×D4×D11—21no—
143C2×#4339—21no—
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×C4×D11—21no—
147C11×C4⋊Q8C2311yescharacteristic
148C11×C4⋊Q8C2311yescharacteristic
149C11×C4⋊Q8C2312yes—
150C11×#126—22no—
151C11×#126—22no—
152C11×#126D412yes—
153C11×#125—22no—
154C11×#125—21no—
155C11×#125D411yescharacteristic
156C11×#124—22no—
157C11×#124D411yescharacteristic
158C11×#124C2312yes—
159C11×#123—22no—
160C11×#123—22no—
161C11×#123—22no—
162C11×#123—22no—
163C11×#123D412yes—
164C11×C22⋊Q8—21no—
165C11×C22⋊Q8—21no—
166C11×C22⋊Q8—22no—
167C11×C22⋊Q8—21no—
168C11×C22⋊Q8—21no—
169C11×C22⋊Q8—22no—
170C11×C22⋊Q8—22no—
171C11×C22⋊Q8—22no—
172C11×C22⋊Q8D411yescharacteristic
173C11×C22⋊Q8C2312yes—
174C11×C22⋊Q8C2312yes—
175C11×#121—21no—
176C11×#121—22no—
177C11×#121D411yescharacteristic
178C11×#121C2312yes—
179C11×#120—22no—
180C4×Q8×C11—21no—
181C4×Q8×C11C2312yes—
182C4×Q8×C11C2312yes—
183C4×Q8×C11C2311yescharacteristic
184C4×D4×C11—22no—
185C4×D4×C11—22no—
186C4×D4×C11—22no—
187C4×D4×C11—21no—
188C4×D4×C11—21no—
189C4×D4×C11C2311yescharacteristic
190C4×D4×C11C2311yescharacteristic
191C4×D4×C11C2311yescharacteristic
192C4×D4×C11C2311yescharacteristic
193C4×D4×C11C2312yes—
194C4×D4×C11C2312yes—
195C4×D4×C11C2311yescharacteristic
196C11×#117—21no—
197C11×#117—22no—
198C11×#117—21no—
199C11×#117C2312yes—
200C2×C11×C4⋊C4—22no—
201C2×C11×C4⋊C4—21no—
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2312yes—
204C2×C11×C22⋊C4—21no—
205C2×C11×C22⋊C4—22no—
206C2×C42×C11C2311yescharacteristic
207#67002—28no—
208#66999—21no—
209C2×#4325C2312yes—
210C2×#4325C2312yes—
211C2×#4325C2312yes—
212C2×#4325C2312yes—
213#66992—22no—
214#66991—21no—
215C2×#4323—24no—
216C2×#4323C2311yescharacteristic
217C2×#4323C2311yescharacteristic
218C2×#4323C2311yescharacteristic
219C2×#4323C2312yes—
220C2×#4323C2312yes—
221C2×#4323C2311yescharacteristic
222#66983—21no—
223#66983C2312yes—
224#66983C2312yes—
225#66983C2312yes—
226C2×(C2×D11)⋊C4—21no—
227#66979C2312yes—
228C2×C4⋊Dic11C2311yescharacteristic
229C2×#4318C2312yes—
230C22×C11⋊C8C2311yescharacteristic
231C22×C11⋊C8C2311yescharacteristic
232C22×C11⋊C8C2312yes—
233#66951—22no—
234#66949—22no—
235#66948—22no—
236#66948—22no—
237#66948—21no—
238#66948—21no—
239#66947—22no—
240#66947—22no—
241#66946—22no—
242#66946—22no—
243#66945—21no—
244C4⋊C4×D11—21no—
245#66938—22no—
246#66937—22no—
247#66937—22no—
248#66936—22no—
249#66935—22no—
250#66935—22no—
251#66935—22no—
252(C22⋊D11)⋊C4—22no—
253C22⋊C4×D11—22no—
254C22⋊C4×D11—22no—
255#66928—21no—
256#66927C2311yescharacteristic
257#66927C2312yes—
258C4×D44—21no—
259C4×D44—21no—
260C4×D44—21no—
261C4×D44C2311yescharacteristic
262C4×D44C2311yescharacteristic
263C4×D44C2311yescharacteristic
264C4×D44C2311yescharacteristic
265C4×D44C2312yes—
266C4×D44C2312yes—
267C4×D44C2312yes—
268#66923C2312yes—
269#66922C2311yescharacteristic
270#66899C2312yes—
271#66899C2312yes—
272#66899C2312yes—
273#66899C2312yes—
274#66896C2311yescharacteristic
275#66896C2311yescharacteristic
276#66896C2311yescharacteristic
277#66896C2311yescharacteristic
278#66896C2312yes—
279#66896C2312yes—
280C22⋊(C11⋊C8)C2312yes—
281C22⋊(C11⋊C8)C2312yes—
282C22⋊(C11⋊C8)C2312yes—
283#66873C2311yescharacteristic
284#66873C2311yescharacteristic
285#66873C2311yescharacteristic
286#66873C2311yescharacteristic
287#66873C2312yes—
288#66873C2312yes—
289#66873C2312yes—
290#66873C2312yes—
291#66873C2312yes—
292#66873C2312yes—
293#66872C2312yes—
294#66872C2312yes—
295#66872C2312yes—
296#66872C2312yes—
297#66871C2311yescharacteristic
298#66871C2311yescharacteristic
299#66871C2311yescharacteristic
300#66871C2311yescharacteristic
301#66871C2312yes—
302#66871C2312yes—
303C4⋊(C11⋊C8)C2311yescharacteristic
304C4⋊(C11⋊C8)C2311yescharacteristic
305C4⋊(C11⋊C8)C2312yes—
306C4⋊(C11⋊C8)C2312yes—
307#66867C2312yes—
308#66867C2312yes—
309C4×C11⋊C8C2311yescharacteristic
310C4×C11⋊C8C2311yescharacteristic
311C4×C11⋊C8C2311yescharacteristic
312C4×C11⋊C8C2311yescharacteristic
313C4×C11⋊C8C2312yes—
314#61496—111nomaximal, Sylow
315C24×C11—21no—
316C23×D11—21no—
317C23×D11—22no—
318C11×#41—24no—
319C11×#41—42no—
320C11×#41—82no—
321C2×Q8×C11—21no—
322C2×Q8×C11—22no—
323C2×Q8×C11—82no—
324C2×Q8×C11C2×D411yescharacteristic
325C2×Q8×C11C2412yes—
326C2×D4×C11—22no—
327C2×D4×C11—22no—
328C2×D4×C11—22no—
329C2×D4×C11—21no—
330C2×D4×C11—41no—
331C2×D4×C11C2×D411yescharacteristic
332C2×D4×C11C2×D412yes—
333C2×D4×C11C2411yescharacteristic
334C2×D4×C11C2411yescharacteristic
335C22×C4×C11—21no—
336C22×C4×C11—22no—
337C22×C4×C11—22no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—22no—
341C22×C4×C11—21no—
342C22×C4×C11—21no—
343C22×C4×C11—82no—
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2×D411yescharacteristic
346C22×C4×C11C2411yescharacteristic
347C22×C4×C11C2412yes—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C22×Dic11—21no—
352#4343—82no—
353D4×D11—84no—
354D4×D11—82no—
355#4339—82no—
356C2×D44—22no—
357C2×D44—24no—
358C2×D44—21no—
359C2×D44—21no—
360C2×D44—22no—
361C2×D44—21no—
362C2×D44—22no—
363C2×D44—22no—
364C2×D44—41no—
365C2×D44—42no—
366C2×D44C2411yescharacteristic
367C2×D44C2412yes—
368C2×D44C2411yescharacteristic
369C2×C4×D11—21no—
370C2×C4×D11—21no—
371C2×C4×D11—21no—
372C2×C4×D11—22no—
373C2×C4×D11—21no—
374C2×C4×D11—22no—
375C2×C4×D11—22no—
376C2×C4×D11—82no—
377C2×Dic22—21no—
378C11×C4⋊C4—22no—
379C11×C4⋊C4—21no—
380C11×C4⋊C4—22no—
381C11×C4⋊C4—22no—
382C11×C4⋊C4—22no—
383C11×C4⋊C4—21no—
384C11×C4⋊C4—21no—
385C11×C4⋊C4—21no—
386C11×C4⋊C4—22no—
387C11×C4⋊C4—22no—
388C11×C4⋊C4C2×D411yescharacteristic
389C11×C4⋊C4C2×D411yescharacteristic
390C11×C4⋊C4C2×D412yes—
391C11×C4⋊C4C2×D412yes—
392C11×C4⋊C4C2×D412yes—
393C11×C4⋊C4C2×D412yes—
394C11×C4⋊C4C2411yescharacteristic
395C11×C4⋊C4C2411yescharacteristic
396C11×C4⋊C4C2412yes—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—21no—
400C11×C22⋊C4—21no—
401C11×C22⋊C4—21no—
402C11×C22⋊C4—21no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4—22no—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4C2×D412yes—
408C11×C22⋊C4C2×D412yes—
409C11×C22⋊C4C2×D412yes—
410C11×C22⋊C4C2×D412yes—
411C11×C22⋊C4C2×D412yes—
412C42×C11—22no—
413C42×C11—22no—
414C42×C11C2×D411yescharacteristic
415C42×C11C2×D411yescharacteristic
416C42×C11C2411yescharacteristic
417C42×C11C2411yescharacteristic
418C42×C11C2412yes—
419C22⋊Dic11—22no—
420#4325—24no—
421#4325—24no—
422#4325—42no—
423#4325—42no—
424#4323—22no—
425#4323—22no—
426#4323—22no—
427#4323—24no—
428#4323—42no—
429#4323#4114yescomplemented
430(C2×D11)⋊C4—21no—
431(C2×D11)⋊C4—21no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—21no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440C4⋊Dic11—21no—
441C4⋊Dic11—21no—
442C4⋊Dic11C2411yescharacteristic
443C4⋊Dic11C2411yescharacteristic
444C4⋊Dic11C2412yes—
445Dic11⋊C4—22no—
446Dic11⋊C4—22no—
447C4×Dic11—22no—
448#4318—24no—
449C2×C11⋊C8—22no—
450C2×C11⋊C8—41no—
451C2×C11⋊C8—42no—
452C2×C11⋊C8C2411yescharacteristic
453C2×C11⋊C8C2411yescharacteristic
454C2×C11⋊C8C2411yescharacteristic
455C2×C11⋊C8C2412yes—
456C2×C11⋊C8C2412yes—
457C2×C11⋊C8C2411yescharacteristic
458#3520D1111yescharacteristic, complemented
459#3519—111no—
460#3397—111no—
461#3384—111no—
462#3360—111no—
463#3358—111no—
464#3354—111no—
465#3346—112no—
466#3303—111no—
467#3297—112no—
468#3295—112no—
469#3294—111no—
470#3272—111no—
471#3264—112no—
472#3179—112no—
473#3167—111no—
474#3119—112no—
475#3118—112no—
476#3110—111no—
477#3109—111no—
478#2966—111no—
479#2946—112no—
480C2×C4×D8—111no—
481C23×C11—21no—
482C23×C11—21no—
483C23×C11—42no—
484C23×C11—42no—
485C23×C11—81no—
486C23×C11C22×D412yes—
487C23×C11C22×D411yescharacteristic
488C22×D11—21no—
489C22×D11—21no—
490C22×D11—22no—
491C22×D11—42no—
492C22×D11—44no—
493C22×D11—42no—
494C22×D11—81no—
495C22×D11—82no—
496C22×D11—82no—
497Q8×C11—22no—
498Q8×C11—22no—
499Q8×C11—22no—
500Q8×C11—42no—
501Q8×C11—82no—
502D4×C11—24no—
503D4×C11—22no—
504D4×C11—21no—
505D4×C11—21no—
506D4×C11—21no—
507D4×C11—42no—
508D4×C11—44no—
509D4×C11—82no—
510D4×C11C2×#4112yes—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—21no—
514C2×C4×C11—22no—
515C2×C4×C11—21no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—21no—
521C2×C4×C11—44no—
522C2×C4×C11—42no—
523C2×C4×C11—42no—
524C2×C4×C11—81no—
525C2×C4×C11—81no—
526C2×C4×C11—82no—
527C2×C4×C11—81no—
528C2×C4×C11—82no—
529C2×C4×C11C22×D412yes—
530C2×C4×C11C22×D412yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C22×D411yescharacteristic
534C2×C4×C11C22×D411yescharacteristic
535C2×C4×C11C22×D411yescharacteristic
536C2×C4×C11C22×D411yescharacteristic
537C2×C4×C11C2511yescharacteristic
538C22⋊D11—44no—
539C22⋊D11—82no—
540C22⋊D11—82no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—21no—
544C2×Dic11—81no—
545D44—21no—
546D44—22no—
547D44—21no—
548D44—22no—
549D44—21no—
550D44—44no—
551D44—42no—
552D44—42no—
553D44—81no—
554D44—82no—
555D44—82no—
556D44C2×#4112yes—
557C4×D11—42no—
558C4×D11—42no—
559C4×D11—81no—
560C4×D11—81no—
561C4×D11—82no—
562C4×D11—82no—
563C4×D11—82no—
564Dic22—81no—
565C11⋊C8—21no—
566C11⋊C8—22no—
567C11⋊C8—21no—
568C11⋊C8—22no—
569C11⋊C8—21no—
570C11⋊C8C2×#4112yes—
571C2×AGL(1,ℤ/8)—112no—
572C22×D8—111no—
573#556C2×D1111yescharacteristic, complemented
574#555—111no—
575#554—111no—
576#554C2×D1112yescomplemented
577#553—112no—
578#553—221no—
579#552—21no—
580#551—22no—
581#550—111no—
582D4×Q8C2×D1111yescharacteristic, complemented
583#548—21no—
584#547C2×D1111yescharacteristic, complemented
585#547C2×D1111yescharacteristic, complemented
586#546—221no—
587#546—222no—
588#546C2×D1112yescomplemented
589D42—112no—
590D42—111no—
591#542C2×D1112yescomplemented
592#540—112no—
593#539—22no—
594#538—222no—
595#533C2×D1111yescharacteristic, complemented
596#532—111no—
597#529C2×D1111yescharacteristic
598#525—21no—
599#525—221no—
600C2×C22⋊Q8—21no—
601C2×#121—221no—
602#520C2×D1112yescomplemented
603#518—112no—
604C2×C4×D4—111no—
605C2×C4×D4C2×D1111yescharacteristic, complemented
606#501—112no—
607#498—111no—
608#496—112no—
609#492—111no—
610#488—112no—
611#487—111no—
612#486—111no—
613#486—112no—
614#485—112no—
615#484—112no—
616#482—112no—
617#481—112no—
618#481—112no—
619#480—112no—
620#479—112no—
621#478—112no—
622#476—112no—
623#476—111no—
624#476—111no—
625#474—112no—
626#474—111no—
627#474—111no—
628#469—112no—
629#468—112no—
630#466—112no—
631#465—112no—
632#465—112no—
633#465—112no—
634#463—112no—
635#463—112no—
636#461—111no—
637#461—111no—
638#460—112no—
639#459—111no—
640#459—112no—
641#459—111no—
642#450—112no—
643#450—112no—
644#449—112no—
645#449—112no—
646#447—112no—
647#447—112no—
648#446—111no—
649C8×Q8—111no—
650#442—112no—
651#442—112no—
652#442—112no—
653#440—112no—
654#440—112no—
655#440—112no—
656C4×SD16—112no—
657C4×SD16—112no—
658C4×SD16—112no—
659C4×D8—111no—
660C4×D8—111no—
661C4×D8—112no—
662C4×D8—111no—
663C4×D8—111no—
664C4×D8—111no—
665C4×D8—111no—
666C4×D8—111no—
667C4×D8—111no—
668#436—111no—
669#435—112no—
670C8×D4—111no—
671C8×D4—112no—
672#433—112no—
673#432—111no—
674#428—112no—
675C2×#107—111no—
676#416—112no—
677C2×#102—111no—
678C2×#102—111no—
679C2×#102—112no—
680#405—112no—
681C2×C4×C8—111no—
682C22×C11—21no—
683C22×C11—21no—
684C22×C11—22no—
685C22×C11—22no—
686C22×C11—22no—
687C22×C11—22no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—41no—
692C22×C11—41no—
693C22×C11—84no—
694C22×C11#57712yes—
695C22×C11C23×D411yescharacteristic
696C2×D11—22no—
697C2×D11—41no—
698C2×D11—41no—
699C2×D11—41no—
700C2×D11—42no—
701C2×D11—41no—
702C2×D11—42no—
703C2×D11—41no—
704C2×D11—42no—
705C2×D11—84no—
706C2×D11—164no—
707C4×C11—22no—
708C4×C11—21no—
709C4×C11—21no—
710C4×C11—22no—
711C4×C11—21no—
712C4×C11—21no—
713C4×C11—22no—
714C4×C11—42no—
715C4×C11—41no—
716C4×C11—41no—
717C4×C11—42no—
718C4×C11#57612yes—
719C4×C11C22×#4111yescharacteristic
720C4×C11#58511yescharacteristic
721Dic11—41no—
722Dic11—41no—
723Dic11—42no—
724C2×#41—21no—
725C2×#41—221no—
726C2×#41—221no—
727C2×#41C22×D1112yes—
728C22×Q8—21no—
729C22×D4—111no—
730C22×D4—112no—
731C22×D4—221no—
732C22×D4—222no—
733C22×D4C22×D1111yescharacteristic
734C23×C4—21no—
735C23×C4—221no—
736AGL(1,ℤ/8)—228no—
737C2×SD16—112no—
738C2×SD16—112no—
739C2×SD16—112no—
740C2×SD16—112no—
741C2×D8—111no—
742C2×D8—111no—
743C2×D8—111no—
744C2×D8—111no—
745C2×D8—112no—
746C2×D8—112no—
747C2×D8—224no—
748C2×M16—112no—
749C22×C8—111no—
750C22×C8—111no—
751C22×C8—112no—
752C4⋊Q8—111no—
753C4⋊Q8C22×D1111yescharacteristic
754C4⋊Q8C22×D1111yescharacteristic
755C4⋊Q8C22×D1112yes—
756#127—111no—
757#127—112no—
758#126—22no—
759#126—22no—
760#126—222no—
761#126C22⋊D1112yes—
762#125—22no—
763#125—21no—
764#125—112no—
765#125C22⋊D1111yescharacteristic
766#124—22no—
767#124—222no—
768#124—221no—
769#124C22⋊D1111yescharacteristic
770#124C22×D1112yes—
771#123—22no—
772#123—22no—
773#123—22no—
774#123—22no—
775#123—222no—
776#123—222no—
777#123—222no—
778#123C22⋊D1112yes—
779C22⋊Q8—21no—
780C22⋊Q8—21no—
781C22⋊Q8—22no—
782C22⋊Q8—21no—
783C22⋊Q8—21no—
784C22⋊Q8—22no—
785C22⋊Q8—22no—
786C22⋊Q8—22no—
787C22⋊Q8—221no—
788C22⋊Q8—222no—
789C22⋊Q8C22⋊D1111yescharacteristic
790C22⋊Q8C22×D1112yes—
791C22⋊Q8C22×D1112yes—
792#121—21no—
793#121—22no—
794#121—112no—
795#121—112no—
796#121—112no—
797#121—222no—
798#121—221no—
799#121—221no—
800#121—221no—
801#121—221no—
802#121—222no—
803#121—222no—
804#121—222no—
805#121—222no—
806#121C22⋊D1111yescharacteristic
807#121C22×D1112yes—
808#120—22no—
809#120—222no—
810#120—222no—
811#120—222no—
812C4×Q8—21no—
813C4×Q8C22×D1112yes—
814C4×Q8C22×D1112yes—
815C4×Q8C22×D1111yescharacteristic
816C4×D4—22no—
817C4×D4—22no—
818C4×D4—22no—
819C4×D4—21no—
820C4×D4—21no—
821C4×D4—111no—
822C4×D4—111no—
823C4×D4—111no—
824C4×D4—111no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—222no—
829C4×D4—222no—
830C4×D4—222no—
831C4×D4—221no—
832C4×D4—221no—
833C4×D4—221no—
834C4×D4C22×D1111yescharacteristic
835C4×D4C22×D1111yescharacteristic
836C4×D4C22×D1111yescharacteristic
837C4×D4C22×D1111yescharacteristic
838C4×D4C22×D1112yes—
839C4×D4C22×D1112yes—
840C4×D4C22×D1111yescharacteristic
841#117—21no—
842#117—22no—
843#117—21no—
844#117—112no—
845#117—221no—
846#117C22×D1112yes—
847C2×C4⋊C4—22no—
848C2×C4⋊C4—21no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—221no—
851C2×C4⋊C4C22×D1111yescharacteristic
852C2×C4⋊C4C22×D1112yes—
853C2×C22⋊C4—21no—
854C2×C22⋊C4—22no—
855C2×C22⋊C4—221no—
856C2×C22⋊C4—222no—
857C2×C22⋊C4—222no—
858C2×C42C22×D1111yescharacteristic
859#107—111no—
860#107—111no—
861#107—111no—
862#107—111no—
863#107—112no—
864#107—112no—
865#106—112no—
866#106—112no—
867#106—112no—
868#106—112no—
869C4⋊C8—111no—
870C4⋊C8—111no—
871C4⋊C8—112no—
872C4⋊C8—112no—
873#103—112no—
874#103—112no—
875#103—112no—
876#103—112no—
877#102—111no—
878#102—111no—
879#102—111no—
880#102—111no—
881#102—112no—
882#102—112no—
883#102—111no—
884#102—111no—
885#102—111no—
886#102—111no—
887#102—112no—
888#102—112no—
889#102—112no—
890#102—112no—
891#102—112no—
892#102—112no—
893C22⋊C8—112no—
894C22⋊C8—112no—
895C22⋊C8—112no—
896#97—112no—
897#97—112no—
898C4×C8—111no—
899C4×C8—111no—
900C4×C8—111no—
901C4×C8—111no—
902C4×C8—112no—
903C2×C11—22no—
904C2×C11—42no—
905C2×C11—42no—
906C2×C11—81no—
907C2×C11D4×#4111yescharacteristic
908C2×C11C2×#57611yescharacteristic
909C2×C11C2×#57711yescharacteristic
910D11—42no—
911D11—81no—
912D11—82no—
913C24—21no—
914C24—221no—
915C24—222no—
916#41—24no—
917#41—42no—
918#41—82no—
919#41—882no—
920#41—882no—
921C2×Q8—21no—
922C2×Q8—22no—
923C2×Q8—82no—
924C2×Q8—221no—
925C2×Q8C2×C22⋊D1111yescharacteristic
926C2×Q8C23×D1112yes—
927C2×D4—22no—
928C2×D4—22no—
929C2×D4—22no—
930C2×D4—21no—
931C2×D4—41no—
932C2×D4—111no—
933C2×D4—111no—
934C2×D4—112no—
935C2×D4—222no—
936C2×D4—224no—
937C2×D4—222no—
938C2×D4—222no—
939C2×D4—222no—
940C2×D4—222no—
941C2×D4—221no—
942C2×D4—221no—
943C2×D4—222no—
944C2×D4—221no—
945C2×D4—222no—
946C2×D4—441no—
947C2×D4—442no—
948C2×D4—882no—
949C2×D4—884no—
950C2×D4C2×C22⋊D1112yes—
951C2×D4C2×C22⋊D1111yescharacteristic
952C2×D4C23×D1111yescharacteristic
953C2×D4C23×D1111yescharacteristic
954C22×C4—21no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—22no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—82no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—222no—
968C22×C4—222no—
969C22×C4—222no—
970C22×C4—221no—
971C22×C4—882no—
972C22×C4C2×C22⋊D1111yescharacteristic
973C22×C4C2×C22⋊D1111yescharacteristic
974C22×C4C23×D1111yescharacteristic
975C22×C4C23×D1112yes—
976SD16—224no—
977SD16—224no—
978SD16—442no—
979SD16—442no—
980D8—114no—
981D8—222no—
982D8—222no—
983D8—222no—
984D8—224no—
985D8—442no—
986M16—224no—
987C2×C8—111no—
988C2×C8—111no—
989C2×C8—111no—
990C2×C8—111no—
991C2×C8—112no—
992C2×C8—112no—
993C2×C8—222no—
994C2×C8—442no—
995C2×C8—441no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—112no—
1007C4⋊C4—111no—
1008C4⋊C4—111no—
1009C4⋊C4—221no—
1010C4⋊C4—221no—
1011C4⋊C4—222no—
1012C4⋊C4—222no—
1013C4⋊C4C2×C22⋊D1111yescharacteristic
1014C4⋊C4C2×C22⋊D1112yes—
1015C4⋊C4C2×C22⋊D1111yescharacteristic
1016C4⋊C4C2×C22⋊D1112yes—
1017C4⋊C4C2×C22⋊D1112yes—
1018C4⋊C4C2×C22⋊D1112yes—
1019C4⋊C4C23×D1111yescharacteristic
1020C4⋊C4C23×D1111yescharacteristic
1021C4⋊C4C23×D1112yes—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—21no—
1025C22⋊C4—21no—
1026C22⋊C4—21no—
1027C22⋊C4—21no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—222no—
1033C22⋊C4—221no—
1034C22⋊C4—222no—
1035C22⋊C4—221no—
1036C22⋊C4—222no—
1037C22⋊C4—221no—
1038C22⋊C4—222no—
1039C22⋊C4—221no—
1040C22⋊C4—222no—
1041C22⋊C4—222no—
1042C22⋊C4—222no—
1043C22⋊C4C2×C22⋊D1112yes—
1044C22⋊C4C2×C22⋊D1112yes—
1045C22⋊C4C2×C22⋊D1112yes—
1046C22⋊C4C2×C22⋊D1112yes—
1047C22⋊C4C2×C22⋊D1112yes—
1048C42—22no—
1049C42—22no—
1050C42—222no—
1051C42C2×C22⋊D1111yescharacteristic
1052C42C2×C22⋊D1111yescharacteristic
1053C42C23×D1111yescharacteristic
1054C42C23×D1111yescharacteristic
1055C42C23×D1112yes—
1056C11#6149611yescharacteristic, complemented, Sylow
1057C23—21no—
1058C23—21no—
1059C23—42no—
1060C23—42no—
1061C23—81no—
1062C23—221no—
1063C23—221no—
1064C23—222no—
1065C23—442no—
1066C23—444no—
1067C23—442no—
1068C23—881no—
1069C23—882no—
1070C23—882no—
1071C23C22×C22⋊D1112yes—
1072C23C22×C22⋊D1111yescharacteristic
1073Q8—22no—
1074Q8—22no—
1075Q8—22no—
1076Q8—42no—
1077Q8—82no—
1078Q8—881no—
1079D4—24no—
1080D4—22no—
1081D4—21no—
1082D4—21no—
1083D4—21no—
1084D4—42no—
1085D4—44no—
1086D4—82no—
1087D4—112no—
1088D4—221no—
1089D4—222no—
1090D4—221no—
1091D4—222no—
1092D4—221no—
1093D4—444no—
1094D4—442no—
1095D4—444no—
1096D4—442no—
1097D4—882no—
1098D4—882no—
1099D4—881no—
1100D4—882no—
1101D4—882no—
1102D4#41×D1112yes—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—44no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—81no—
1117C2×C4—81no—
1118C2×C4—82no—
1119C2×C4—81no—
1120C2×C4—82no—
1121C2×C4—221no—
1122C2×C4—222no—
1123C2×C4—221no—
1124C2×C4—442no—
1125C2×C4—442no—
1126C2×C4—881no—
1127C2×C4—881no—
1128C2×C4—882no—
1129C2×C4—882no—
1130C2×C4—882no—
1131C2×C4—881no—
1132C2×C4C22×C22⋊D1111yescharacteristic
1133C2×C4C22×C22⋊D1112yes—
1134C2×C4C22×C22⋊D1112yes—
1135C2×C4C22×C22⋊D1111yescharacteristic
1136C2×C4C22×C22⋊D1111yescharacteristic
1137C2×C4C22×C22⋊D1111yescharacteristic
1138C2×C4C22×C22⋊D1112yes—
1139C2×C4C22×C22⋊D1111yescharacteristic
1140C2×C4C24×D1111yescharacteristic
1141C8—112no—
1142C8—221no—
1143C8—222no—
1144C8—221no—
1145C8—222no—
1146C8—221no—
1147C22—21no—
1148C22—21no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—84no—
1159C22—222no—
1160C22—441no—
1161C22—441no—
1162C22—441no—
1163C22—442no—
1164C22—442no—
1165C22—441no—
1166C22—441no—
1167C22—442no—
1168C22—884no—
1169C22—1764no—
1170C22#1062336812yes—
1171C22C23×C22⋊D1111yescharacteristic
1172C4—21no—
1173C4—22no—
1174C4—21no—
1175C4—21no—
1176C4—22no—
1177C4—22no—
1178C4—21no—
1179C4—41no—
1180C4—41no—
1181C4—42no—
1182C4—42no—
1183C4—441no—
1184C4—441no—
1185C4—442no—
1186C4#1062336612yes—
1187C4C2×#41×D1111yescharacteristic
1188C4#1062345311yescharacteristic
1189C2—22no—
1190C2—42no—
1191C2—42no—
1192C2—81no—
1193C2—442no—
1194C2—881no—
1195C2—882no—
1196C2#41×C22⋊D1111yescharacteristic
1197C2C2×#1062336611yescharacteristic
1198C2C2×#1062336811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3520C2
socleC22×C11C23×D4
hypercenter#3520D11
hypocenterC11#61496
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #529 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #13082650C2semidirect
2. #13081636C2semidirect
3. #13081511C2semidirect
4. #13081261C2semidirect
5. #13081251C2semidirect
6. #13081211C2semidirect
7. #13081095C2semidirect
8. #13080544C2semidirect
9. #13080466C2semidirect
10. #13080434C2semidirect
11. #13080423C2semidirect
12. #13080216C2semidirect
13. #13080097C2semidirect
14. #13079293C2semidirect
15. #13079176C2semidirect
16. #13078815C2semidirect
17. #13078794C2semidirect
18. #13078711C2semidirect
19. #13078707C2semidirect
20. #13077592C2semidirect
21. #13077444C2semidirect
22. C2×C4×#4323C2semidirect
23. C11×#3520C2semidirect
24. C11×#556C22semidirect
25. C11×#554C22semidirect
28. D4×Q8×C11C22semidirect
30. C11×#547C22semidirect
31. C11×#547C22semidirect
32. C11×#546C22semidirect
33. C11×#542C22semidirect
35. C11×#533C22semidirect
39. C11×#520C22semidirect
40. C2×C4×D4×C11C22semidirect
49. #10623110C22semidirect
50. #10623108C22semidirect
52. #10623094C22semidirect
54. D4×D44C22semidirect
55. #10623066C22semidirect
56. #10623052C22semidirect
59. #10622851C22semidirect
60. #10622851C22semidirect
61. #10622846C22semidirect
62. #10622830C22semidirect
63. C2×#66896C22semidirect
64. #10622701C22semidirect
65. #10622701C22semidirect
66. #10622700C22semidirect
67. #10622700C22semidirect
68. #10622700C22semidirect
69. #10622698C22semidirect
70. #10622697C22semidirect
71. #10622696C22semidirect
72. #10622696C22semidirect
73. #10622694C22semidirect
74. #10622693C22semidirect
75. #10622692C22semidirect
76. #10622671C22semidirect
78. #10622670C22semidirect
79. #10622669C22semidirect
80. #10622662C22semidirect
81. #10622661C22semidirect
82. #10622661C22semidirect
83. #10622661C22semidirect
85. #10622659C22semidirect
86. #10622658C22semidirect
87. #10622657C22semidirect
88. #10622652C22semidirect
89. #10622651C22semidirect
91. #10622648C22semidirect
92. #10622640C22semidirect
93. #10622639C22semidirect
94. #10622639C22semidirect
95. #10622639C22semidirect
96. C4×#4325C22semidirect
97. C4×#4325C22semidirect
98. C4×#4325C22semidirect
99. #10622637C22semidirect
100. Q8×C11⋊C8C22semidirect
101. #10622635C22semidirect
102. #10622628C22semidirect
103. #10622628C22semidirect
104. #10622628C22semidirect
106. #10622627C22semidirect
107. #10622627C22semidirect
112. C4×#4323C22semidirect
113. C4×#4323C22semidirect
114. C4×#4323C22semidirect
115. C4×#4323C22semidirect
116. C4×#4323C22semidirect
117. #10622625C22semidirect
118. #10622624C22semidirect
119. D4×C11⋊C8C22semidirect
120. D4×C11⋊C8C22semidirect
121. #10622622C22semidirect
122. #10622621C22semidirect
123. #10622621C22semidirect
124. #10622613C22semidirect
125. #10622610C22semidirect
126. #10622581C22semidirect
127. #10622581C22semidirect
128. #10622580C22semidirect
130. C2×#66873C22semidirect
131. #10622577C22semidirect
132. C2×#66871C22semidirect
133. #10622539C22semidirect
134. C2×C4×C11⋊C8C22semidirect
429. #4323#41semidirect
458. #3520D11semidirect
573. #556C2×D11semidirect
576. #554C2×D11semidirect
582. D4×Q8C2×D11semidirect
584. #547C2×D11semidirect
585. #547C2×D11semidirect
588. #546C2×D11semidirect
591. #542C2×D11semidirect
595. #533C2×D11semidirect
602. #520C2×D11semidirect
605. C2×C4×D4C2×D11semidirect
1056. C11#61496semidirect

Maximal subgroups

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

subgroupindex
#130826502
#130816362
#130815112
#130812612
#130812512
#130812112
#130810952
#130805442
#130804662
#130804342
#130804232
#130802162
#130800972
#130792932
#130791762
#130788152
#130787942
#130787112
#130787072
#130775922
#130774442
C2×C4×#43232
C11×#35202
#6149611