Finite Group Databasebeta

← #15638474

Subgroups — #15638474

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic, complemented
2#13080460C214yesmaximal, complemented
3#13080445C214yesmaximal, complemented
4#13080324C214yesmaximal, complemented
5#13080297C214yesmaximal, complemented
6#13079577C212yesmaximal, complemented
7#13079388C211yesmaximal, characteristic, complemented
8#13079377C212yesmaximal, complemented
9#13079373C211yesmaximal, characteristic, complemented
10#13078659C212yesmaximal, complemented
11#13077832C212yesmaximal, complemented
12C2×#10622659C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077640C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic, complemented
17C23×D44C2211yescharacteristic
18C11×#553—22no—
19C11×#553C2212yescomplemented
20C11×#552C2212yescomplemented
21C11×#551—22no—
22C11×#548C2212yescomplemented
23C11×#546C2212yescomplemented
24C11×#539—21no—
25C11×#538—21no—
26C11×#534—21no—
27C11×#529C2212yescomplemented
28C11×#525C2212yescomplemented
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67003C2214yescomplemented
34C22×#4325C2212yescomplemented
35C2×#66990—21no—
36C22×#4323C2212yescomplemented
37C2×#66983C2211yescharacteristic, complemented
38C2×#66977C2211yescharacteristic
39#10623081—22no—
40#10623081—22no—
41#10623081C2214yes—
42#10623081C2214yescomplemented
43C2×#66947—21no—
44C2×#66937—21no—
45C2×C22⋊C4×D11—21no—
46C2×#66928C2211yescharacteristic, complemented
47C2×C4×D44C2211yescharacteristic, complemented
48#10622851C2214yescomplemented
49#10622841C2212yescomplemented
50#10622831C2212yescomplemented
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2212yescomplemented
54#10622681C2214yescomplemented
55#10622679C2214yescomplemented
56#10622672C2214yescomplemented
57#10622670C2214yescomplemented
58#10622664C2214yescomplemented
59#10622663C2212yescomplemented
60#10622661C2214yescomplemented
61#10622660C2214yescomplemented
62#10622659C2212yescomplemented
63#10622659C2212yescomplemented
64#10622659C2214yescomplemented
65#10622657C2212yescomplemented
66#10622654C2214yescomplemented
67#10622653C2212yescomplemented
68#10622651C2214yescomplemented
69#10622650C2214yescomplemented
70#10622649C2212yes—
71#10622649C2212yes—
72#10622649C2214yescomplemented
73#10622647C2212yescomplemented
74#10622641C2214yescomplemented
75C4×#4325C2214yescomplemented
76#10622629C2214yescomplemented
77C4×#4323C2214yescomplemented
78D4×C11⋊C8C2214yescomplemented
79D4×C11⋊C8C2214yescomplemented
80#10622616C2214yescomplemented
81#10622615C2214yescomplemented
82#10622584C2212yescomplemented
83#10622583C2212yescomplemented
84C2×#66873C2212yescomplemented
85C2×#66873C2212yescomplemented
86#10622538C2212yescomplemented
87C24×D11—21no—
88C2×C11×#41C2312yescomplemented
89C22×Q8×C11C2311yescharacteristic
90C22×D4×C11—21no—
91C22×D4×C11D411yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C2×#4339—22no—
98C2×#4339—44no—
99C2×#4339C2314yes—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—44no—
104C22×D44C2311yescharacteristic
105C22×D44C2312yes—
106C22×D44C2312yes—
107C22×D44C2311yescharacteristic
108C22×C4×D11—21no—
109C22×C4×D11—21no—
110C22×Dic22C2311yescharacteristic
111C11×#126—22no—
112C11×#126—22no—
113C11×#126—22no—
114C11×#125—22no—
115C11×#125C2312yescomplemented
116C11×#124—22no—
117C11×#124C2312yescomplemented
118C11×#123—22no—
119C11×#123—22no—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×C22⋊Q8—21no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8C2312yes—
127C11×C22⋊Q8C2312yes—
128C11×C22⋊Q8C2312yescomplemented
129C11×#121—22no—
130C11×#121—22no—
131C11×#121—21no—
132C11×#121—21no—
133C11×#121—22no—
134C11×#121C2312yes—
135C11×#121C2312yes—
136C11×#121C2312yescomplemented
137C11×#120—22no—
138C11×#120—22no—
139C4×Q8×C11C2312yescomplemented
140C4×D4×C11—22no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11D412yes—
146C4×D4×C11D412yes—
147C4×D4×C11C2312yes—
148C4×D4×C11C2312yes—
149C4×D4×C11C2312yescomplemented
150C11×#117—22no—
151C11×#117—22no—
152C11×#117C2312yescomplemented
153C2×C11×C4⋊C4—21no—
154C2×C11×C4⋊C4D411yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—22no—
160C2×C11×C22⋊C4D411yescharacteristic
161C2×C11×C22⋊C4D411yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C22⋊Dic11—21no—
164#67003—48no—
165C2×#4326C2314yescomplemented
166C2×#4325—44no—
167C2×#4325C2314yes—
168C2×#4325C2314yes—
169#66990—24no—
170#66990—24no—
171C2×#4324C2314yescomplemented
172C2×#4323—44no—
173C2×#4323C2314yes—
174C2×#4323C2314yes—
175#66983—22no—
176#66983C2314yes—
177C2×(C2×D11)⋊C4—21no—
178C2×(C2×D11)⋊C4—21no—
179C2×(C2×D11)⋊C4—21no—
180C2×(C2×D11)⋊C4—21no—
181C2×C4⋊Dic11C2311yescharacteristic
182#66977—21no—
183#66977—21no—
184#66977C2312yes—
185#66977C2312yes—
186C2×Dic11⋊C4—21no—
187C22×C11⋊C8C2312yes—
188C22×C11⋊C8C2312yes—
189C22×C11⋊C8C2314yescomplemented
190#66947—24no—
191#66947—24no—
192#66937—24no—
193#66937—24no—
194C22⋊C4×D11—24no—
195C22⋊C4×D11—24no—
196#66928—22no—
197#66928C2314yes—
198C4×D44—22no—
199C4×D44C2314yes—
200#66899C2314yescomplemented
201#66896C2314yescomplemented
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2314yescomplemented
207#66874C2314yescomplemented
208#66874C2314yescomplemented
209#66873C2314yes—
210#66873C2314yes—
211#66873C2314yes—
212#66873C2314yes—
213#66872C2314yescomplemented
214#66871C2314yescomplemented
215C4⋊(C11⋊C8)C2314yescomplemented
216C4×C11⋊C8C2314yescomplemented
217#61561—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—44no—
226C23×D11—44no—
227C23×D11—82no—
228C11×#41—44no—
229C2×Q8×C11—21no—
230C2×Q8×C11—42no—
231C2×Q8×C11C2412yes—
232C2×D4×C11—24no—
233C2×D4×C11—22no—
234C2×D4×C11—22no—
235C2×D4×C11—22no—
236C2×D4×C11—22no—
237C2×D4×C11—21no—
238C2×D4×C11—42no—
239C2×D4×C11—44no—
240C2×D4×C11C2×D412yes—
241C2×D4×C11C2×D412yes—
242C2×D4×C11C2412yes—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D411yescharacteristic
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—82no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267#4339—28no—
268#4339—44no—
269#4339—48no—
270C2×D44—24no—
271C2×D44—24no—
272C2×D44—24no—
273C2×D44—21no—
274C2×D44—21no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—42no—
278C2×D44—42no—
279C2×D44—42no—
280C2×D44—44no—
281C2×D44—44no—
282C2×D44—44no—
283C2×D44C2412yes—
284C2×D44C2412yes—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11—44no—
288C2×C4×D11—82no—
289C2×Dic22—21no—
290C2×Dic22—42no—
291C2×Dic22C2412yes—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4C2×D412yes—
301C11×C4⋊C4C2×D412yes—
302C11×C4⋊C4C2412yes—
303C11×C4⋊C4C2412yes—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4C2×D412yes—
315C11×C22⋊C4C2×D412yes—
316C11×C22⋊C4C2×D412yes—
317C11×C22⋊C4C2×D412yes—
318C42×C11—22no—
319C42×C11—22no—
320C42×C11C2×D412yes—
321C42×C11C2412yes—
322C22⋊Dic11—22no—
323C22⋊Dic11—22no—
324#4326—44no—
325#4325—28no—
326#4325—44no—
327#4324—44no—
328#4323—28no—
329#4323—44no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338C2×C11⋊C8—42no—
339C2×C11⋊C8—42no—
340C2×C11⋊C8—44no—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2414yes—
343#3505D1111yescharacteristic, complemented
344C2×#546—111no—
345#3297—114no—
346#3296—114no—
347#3282—114no—
348#3280—114no—
349#3211—112no—
350#3189—111no—
351#3188—112no—
352#3187—111no—
353#3105—112no—
354#3002—112no—
355C2×#450—111no—
356C2×#447—111no—
357#2972—111no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—42no—
365C23×C11—81no—
366C23×C11—81no—
367C23×C11#13514yescomplemented
368C23×C11C22×D412yes—
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—24no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—42no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—42no—
384C22×D11—82no—
385C22×D11—82no—
386C22×D11—816no—
387Q8×C11—24no—
388Q8×C11—81no—
389D4×C11—24no—
390D4×C11—24no—
391D4×C11—24no—
392D4×C11—44no—
393D4×C11—44no—
394D4×C11—81no—
395D4×C11—82no—
396D4×C11—82no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—42no—
411C2×C4×C11—42no—
412C2×C4×C11—82no—
413C2×C4×C11—82no—
414C2×C4×C11—81no—
415C2×C4×C11—81no—
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C22×D412yes—
420C2×C4×C11C22×D412yes—
421C2×C4×C11C22×D412yes—
422C2×C4×C11C2511yescharacteristic
423C22⋊D11—48no—
424C22⋊D11—84no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—42no—
428C2×Dic11—42no—
429D44—24no—
430D44—22no—
431D44—22no—
432D44—22no—
433D44—44no—
434D44—44no—
435D44—42no—
436D44H(5,𝔽2)14yes—
437C4×D11—48no—
438C4×D11—84no—
439Dic22—24no—
440Dic22—42no—
441C11⋊C8—24no—
442C11⋊C8—24no—
443C22×#41—111no—
444C23×D4—111no—
445C2×#135—114no—
446C22×SD16—112no—
447C22×D8—112no—
448#553—22no—
449#553C2×D1112yescomplemented
450#552C2×D1112yescomplemented
451#551—22no—
452#548C2×D1112yescomplemented
453#546—114no—
454#546—114no—
455#546—222no—
456#546—222no—
457#546C2×D1112yescomplemented
458#539—21no—
459#538—21no—
460#534—21no—
461#529C2×D1112yescomplemented
462C2×#124—111no—
463#525C2×D1112yescomplemented
464C2×#123—221no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8C2×D1111yescharacteristic
467C2×#121—111no—
468C2×#121—221no—
469C2×#121C2×D1111yescharacteristic
470C2×#120—221no—
471#518—21no—
472C2×C4×D4—111no—
473C2×C4×D4C2×D1111yescharacteristic
474C22×C22⋊C4—221no—
475#495—114no—
476#488—114no—
477#484—112no—
478#484—112no—
479#483—112no—
480#482—114no—
481#481—112no—
482#478—114no—
483#467—114no—
484#466—114no—
485#465—114no—
486#465—114no—
487#464—114no—
488#463—114no—
489#463—114no—
490#452—114no—
491#451—112no—
492#451—112no—
493#450—112no—
494#450—112no—
495#450—112no—
496#450—114no—
497#449—114no—
498#449—114no—
499#448—112no—
500#447—112no—
501#447—112no—
502#447—114no—
503C4×SD16—114no—
504C4×D8—114no—
505C8×D4—114no—
506C8×D4—114no—
507#431—112no—
508#416—114no—
509C2×#102—112no—
510C2×#102—112no—
511C2×C22⋊C8—111no—
512C2×C22⋊C8—111no—
513C2×C22⋊C8—112no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—22no—
521C22×C11—22no—
522C22×C11—22no—
523C22×C11—44no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—82no—
528C22×C11—162no—
529C22×C11C2×#13512yes—
530C22×C11C2×#13512yes—
531C22×C11C2×#13512yes—
532C22×C11C23×D411yescharacteristic
533C2×D11—24no—
534C2×D11—48no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—88no—
541C2×D11—88no—
542C2×D11—84no—
543C4×C11—22no—
544C4×C11—21no—
545C4×C11—22no—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—22no—
549C4×C11—42no—
550C4×C11—42no—
551C4×C11—42no—
552C4×C11C2×H(5,𝔽2)12yes—
553Dic11—42no—
554Dic11—42no—
555C25—221no—
556C2×#41—114no—
557C2×#41—222no—
558C2×#41—444no—
559C2×#41C22×D1112yescomplemented
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—111no—
564C22×D4—112no—
565C22×D4—112no—
566C22×D4—111no—
567C22×D4—221no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4—221no—
572C22×D4—444no—
573C22×D4C22⋊D1111yescharacteristic
574C22×D4C22×D1111yescharacteristic
575C23×C4—221no—
576C23×C4—221no—
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—444no—
585C2×D8—114no—
586C2×D8—114no—
587C2×D8—444no—
588C22×C8—112no—
589C22×C8—112no—
590C22×C8—114no—
591#126—22no—
592#126—22no—
593#126—22no—
594#125—22no—
595#125C22×D1112yescomplemented
596#124—22no—
597#124—114no—
598#124—222no—
599#124C22×D1112yescomplemented
600#123—22no—
601#123—22no—
602#123—22no—
603#123—22no—
604#123—22no—
605#123—224no—
606#123—224no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—22no—
610C22⋊Q8—112no—
611C22⋊Q8—112no—
612C22⋊Q8—221no—
613C22⋊Q8—221no—
614C22⋊Q8C22×D1112yes—
615C22⋊Q8C22×D1112yes—
616C22⋊Q8C22×D1112yescomplemented
617#121—22no—
618#121—22no—
619#121—21no—
620#121—21no—
621#121—22no—
622#121—114no—
623#121—222no—
624#121—224no—
625#121—224no—
626#121C22×D1112yes—
627#121C22×D1112yes—
628#121C22×D1112yescomplemented
629#120—22no—
630#120—22no—
631#120—224no—
632#120—224no—
633C4×Q8C22×D1112yescomplemented
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—114no—
640C4×D4—222no—
641C4×D4C22⋊D1112yes—
642C4×D4C22⋊D1112yes—
643C4×D4C22×D1112yes—
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yescomplemented
646#117—22no—
647#117—22no—
648#117C22×D1112yescomplemented
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22⋊D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—221no—
659C2×C22⋊C4—221no—
660C2×C22⋊C4—221no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—224no—
665C2×C22⋊C4C22⋊D1111yescharacteristic
666C2×C22⋊C4C22⋊D1111yescharacteristic
667C2×C42C22×D1111yescharacteristic
668#107—114no—
669#106—114no—
670C4⋊C8—114no—
671#103—114no—
672#103—114no—
673#103—114no—
674#102—114no—
675#102—114no—
676#102—114no—
677#102—114no—
678#102—114no—
679C22⋊C8—112no—
680C22⋊C8—112no—
681C22⋊C8—112no—
682C22⋊C8—112no—
683C22⋊C8—114no—
684C4×C8—114no—
685C2×C11—22no—
686C2×C11—22no—
687C2×C11—22no—
688C2×C11—42no—
689C2×C11—82no—
690C2×C11#348411yescharacteristic
691C2×C11C22×#13511yescharacteristic
692C2×C11#358511yescharacteristic
693D11—44no—
694D11—82no—
695C24—21no—
696C24—221no—
697C24—221no—
698C24—222no—
699C24—222no—
700C24—444no—
701C24—444no—
702C24—882no—
703C24C2×C22⋊D1111yescharacteristic
704C24C2×C22⋊D1111yescharacteristic
705#41—44no—
706#41—228no—
707#41—444no—
708#41—448no—
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—42no—
722C2×D4—44no—
723C2×D4—112no—
724C2×D4—112no—
725C2×D4—224no—
726C2×D4—224no—
727C2×D4—224no—
728C2×D4—224no—
729C2×D4—224no—
730C2×D4—221no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—221no—
734C2×D4—442no—
735C2×D4—442no—
736C2×D4—442no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—882no—
742C2×D4C2×C22⋊D1112yes—
743C2×D4C2×C22⋊D1112yes—
744C2×D4C23×D1112yes—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—224no—
755C22×C4—224no—
756C22×C4—444no—
757C22×C4—882no—
758C22×C4C2×C22⋊D1111yescharacteristic
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1111yescharacteristic
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1111yescharacteristic
764C22×C4C2×C22⋊D1112yes—
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1112yes—
769Q16—444no—
770SD16—228no—
771SD16—444no—
772SD16—444no—
773D8—228no—
774D8—444no—
775C2×C8—114no—
776C2×C8—114no—
777C2×C8—442no—
778C2×C8—442no—
779C2×C8—444no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—112no—
789C4⋊C4—221no—
790C4⋊C4—222no—
791C4⋊C4—222no—
792C4⋊C4C2×C22⋊D1112yes—
793C4⋊C4C2×C22⋊D1112yes—
794C4⋊C4C23×D1112yes—
795C4⋊C4C23×D1112yes—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—222no—
807C22⋊C4—222no—
808C22⋊C4—224no—
809C22⋊C4—224no—
810C22⋊C4—224no—
811C22⋊C4—224no—
812C22⋊C4C2×C22⋊D1112yes—
813C22⋊C4C2×C22⋊D1112yes—
814C22⋊C4C2×C22⋊D1112yes—
815C22⋊C4C2×C22⋊D1112yes—
816C42—22no—
817C42—22no—
818C42C2×C22⋊D1112yes—
819C42C23×D1112yes—
820C11#6156111yescharacteristic, complemented, Sylow
821C23—22no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—81no—
829C23—81no—
830C23—224no—
831C23—222no—
832C23—222no—
833C23—444no—
834C23—444no—
835C23—442no—
836C23—442no—
837C23—442no—
838C23—442no—
839C23—444no—
840C23—444no—
841C23—442no—
842C23—882no—
843C23—882no—
844C23—8816no—
845C23#6700314yescomplemented
846C23C22×C22⋊D1112yes—
847C23C22×C22⋊D1111yescharacteristic
848C23C22×C22⋊D1111yescharacteristic
849C23C22×C22⋊D1111yescharacteristic
850Q8—24no—
851Q8—81no—
852Q8—224no—
853Q8—442no—
854D4—24no—
855D4—24no—
856D4—24no—
857D4—44no—
858D4—44no—
859D4—81no—
860D4—82no—
861D4—82no—
862D4—114no—
863D4—224no—
864D4—222no—
865D4—222no—
866D4—222no—
867D4—444no—
868D4—444no—
869D4—442no—
870D4—448no—
871D4—884no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—82no—
888C2×C4—82no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—448no—
894C2×C4—442no—
895C2×C4—442no—
896C2×C4—884no—
897C2×C4C22×C22⋊D1112yes—
898C2×C4C22×C22⋊D1112yes—
899C2×C4C22×C22⋊D1111yescharacteristic
900C2×C4C22×C22⋊D1112yes—
901C2×C4C22×C22⋊D1111yescharacteristic
902C2×C4C22×C22⋊D1111yescharacteristic
903C2×C4C24×D1111yescharacteristic
904C8—224no—
905C8—224no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—44no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—82no—
920C22—162no—
921C22—224no—
922C22—448no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—888no—
929C22—888no—
930C22—884no—
931C22C2×#6700312yes—
932C22C2×#6700312yes—
933C22C2×#6700312yes—
934C22C23×C22⋊D1111yescharacteristic
935C4—22no—
936C4—21no—
937C4—22no—
938C4—21no—
939C4—21no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—442no—
945C4—442no—
946C4D11×H(5,𝔽2)12yes—
947C2—22no—
948C2—22no—
949C2—22no—
950C2—42no—
951C2—82no—
952C2—444no—
953C2—882no—
954C2#1308224711yescharacteristic
955C2C22×#6700311yescharacteristic
956C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61561
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×#10623081C2semidirect
2. #13080460C2semidirect
3. #13080445C2semidirect
4. #13080324C2semidirect
5. #13080297C2semidirect
6. #13079577C2semidirect
7. #13079388C2semidirect
8. #13079377C2semidirect
9. #13079373C2semidirect
10. #13078659C2semidirect
11. #13077832C2semidirect
12. C2×#10622659C2semidirect
13. C2×#10622649C2semidirect
14. #13077640C2semidirect
15. C11×#3505C2semidirect
16. C22×#4339C22semidirect
19. C11×#553C22semidirect
20. C11×#552C22semidirect
22. C11×#548C22semidirect
23. C11×#546C22semidirect
27. C11×#529C22semidirect
28. C11×#525C22semidirect
33. C2×#67003C22semidirect
34. C22×#4325C22semidirect
36. C22×#4323C22semidirect
37. C2×#66983C22semidirect
42. #10623081C22semidirect
46. C2×#66928C22semidirect
47. C2×C4×D44C22semidirect
48. #10622851C22semidirect
49. #10622841C22semidirect
50. #10622831C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622681C22semidirect
55. #10622679C22semidirect
56. #10622672C22semidirect
57. #10622670C22semidirect
58. #10622664C22semidirect
59. #10622663C22semidirect
60. #10622661C22semidirect
61. #10622660C22semidirect
62. #10622659C22semidirect
63. #10622659C22semidirect
64. #10622659C22semidirect
65. #10622657C22semidirect
66. #10622654C22semidirect
67. #10622653C22semidirect
68. #10622651C22semidirect
69. #10622650C22semidirect
72. #10622649C22semidirect
73. #10622647C22semidirect
74. #10622641C22semidirect
75. C4×#4325C22semidirect
76. #10622629C22semidirect
77. C4×#4323C22semidirect
78. D4×C11⋊C8C22semidirect
79. D4×C11⋊C8C22semidirect
80. #10622616C22semidirect
81. #10622615C22semidirect
82. #10622584C22semidirect
83. #10622583C22semidirect
84. C2×#66873C22semidirect
85. C2×#66873C22semidirect
86. #10622538C22semidirect
88. C2×C11×#41C23semidirect
115. C11×#125C23semidirect
117. C11×#124C23semidirect
128. C11×C22⋊Q8C23semidirect
136. C11×#121C23semidirect
139. C4×Q8×C11C23semidirect
149. C4×D4×C11C23semidirect
152. C11×#117C23semidirect
165. C2×#4326C23semidirect
171. C2×#4324C23semidirect
189. C22×C11⋊C8C23semidirect
200. #66899C23semidirect
201. #66896C23semidirect
206. C22⋊(C11⋊C8)C23semidirect
207. #66874C23semidirect
208. #66874C23semidirect
213. #66872C23semidirect
214. #66871C23semidirect
215. C4⋊(C11⋊C8)C23semidirect
216. C4×C11⋊C8C23semidirect
343. #3505D11semidirect
367. C23×C11#135semidirect
449. #553C2×D11semidirect
450. #552C2×D11semidirect
452. #548C2×D11semidirect
457. #546C2×D11semidirect
461. #529C2×D11semidirect
463. #525C2×D11semidirect
559. C2×#41C22×D11semidirect
595. #125C22×D11semidirect
599. #124C22×D11semidirect
616. C22⋊Q8C22×D11semidirect
628. #121C22×D11semidirect
633. C4×Q8C22×D11semidirect
645. C4×D4C22×D11semidirect
648. #117C22×D11semidirect
820. C11#61561semidirect
845. C23#67003semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
#130804602
#130804452
#130803242
#130802972
#130795772
#130793882
#130793772
#130793732
#130786592
#130778322
C2×#106226592
C2×#106226492
#130776402
C11×#35052
#6156111