Finite Group Databasebeta

← #15638633

Subgroups — #15638633

Order 2816.

2374 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082373C211yesmaximal, characteristic, complemented
2C2×#10623348C211yesmaximal, characteristic, complemented
3#13080611C214yesmaximal, complemented
4#13080603C214yesmaximal, complemented
5#13080111C214yesmaximal, complemented
6#13080104C214yesmaximal, complemented
7#13079602C212yesmaximal, complemented
8#13079420C212yesmaximal, complemented
9#13079367C211yesmaximal, characteristic, complemented
10#13079364C211yesmaximal, characteristic, complemented
11#13078733C212yesmaximal, complemented
12#13077867C212yesmaximal, complemented
13C2×#10622840C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C2×C11×#448C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic, complemented
17C22×#4343C2211yescharacteristic, complemented
18C2×#67037—21no—
19C22×C11×SD16C2212yescomplemented
20C2×C11×#121C2211yescharacteristic
21#10623348—22no—
22#10623348—22no—
23#10623348C2214yescomplemented
24#10623348C2214yescomplemented
25C2×#67000—21no—
26C2×#67000C2211yescharacteristic, complemented
27C2×#66999—21no—
28C2×#66999C2211yescharacteristic, complemented
29C2×Q8×Dic11C2211yescharacteristic, complemented
30C22×#4325C2212yescomplemented
31#10623335—21no—
32D4×C22⋊D11C2212yescomplemented
33C2×#66983—21no—
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic, complemented
36C2×C4×C22⋊D11—21no—
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×#66967C2214yescomplemented
39#10623142C2212yescomplemented
40#10623141—22no—
41#10623140C2212yescomplemented
42#10623136—21no—
43D11×#121C2212yes—
44#10623128—21no—
45#10623127C2212yes—
46#10623038C2212yescomplemented
47#10623021—22no—
48C11×#448C2214yescomplemented
49C11×#448C2212yescomplemented
50C11×#448C2212yescomplemented
51C2×C11×#103C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622840C2214yescomplemented
54#10622840C2212yescomplemented
55#10622840C2212yescomplemented
56C2×#66899C2212yescomplemented
57#10622830C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622789C2214yescomplemented
60#10622787C2214yescomplemented
61#10622785C2214yescomplemented
62#10622782C2214yescomplemented
63#10622778C2214yescomplemented
64#10622777C2214yescomplemented
65#10622776C2214yescomplemented
66#10622728C2214yescomplemented
67#10622724C2214yescomplemented
68#10622651C2214yescomplemented
69#10622649C2212yescomplemented
70#10622646C2212yescomplemented
71#10622580C2212yescomplemented
72#10622432C2214yescomplemented
73#10622430C2214yescomplemented
74#10622425C2214yescomplemented
75#10622424C2214yescomplemented
76#10622422C2214yescomplemented
77#10622416C2214yescomplemented
78#10622408C2214yescomplemented
79#10622407C2214yescomplemented
80#10622349C2212yescomplemented
81#10622349C2212yescomplemented
82#10622345C2212yescomplemented
83#10622345C2212yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C22×Q8×C11—21no—
88C22×Q8×C11—21no—
89C22×Q8×C11—21no—
90C22×Q8×C11—44no—
91C22×Q8×C11C2311yescharacteristic
92C22×Q8×C11C2312yes—
93C22×Q8×C11C2312yes—
94C22×Q8×C11C2311yescharacteristic
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—22no—
102C22×C22⋊D11D411yescharacteristic
103C2×#4343—22no—
104C2×#4343—44no—
105C2×#4343C2314yes—
106#67037—48no—
107C2×#4341—22no—
108C2×#4341—22no—
109C2×D4×D11—22no—
110C2×D4×D11—22no—
111C2×D4×D11C2312yes—
112C2×#4339—22no—
113C22×D44—21no—
114C22×D44C2311yescharacteristic
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C22×C4×D11C2311yescharacteristic
118C2×C11×SD16—44no—
119C2×C11×SD16C2314yes—
120C2×C11×SD16C2314yes—
121C22×C8×C11C2312yes—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128#67006—22no—
129C2×C22⋊Dic11D411yescharacteristic
130#67000—24no—
131#67000—24no—
132#67000—22no—
133#67000C2314yes—
134#66999—22no—
135#66999—24no—
136#66999—24no—
137#66999C2314yes—
138Q8×Dic11—22no—
139Q8×Dic11C2314yes—
140C2×#4325—44no—
141C2×#4325C2314yes—
142C2×#4325C2314yes—
143#66993C2312yes—
144#66992—22no—
145#66992—22no—
146#66992—22no—
147#66991C2312yes—
148#66990—22no—
149#66990—22no—
150#66988—22no—
151D4×Dic11C2312yes—
152C2×#4323C2314yes—
153#66983—21no—
154#66983—21no—
155#66983—21no—
156#66983—21no—
157#66983—24no—
158#66983—24no—
159#66983C2312yes—
160#66983C2312yes—
161#66983C2312yes—
162#66983C2312yes—
163#66982—22no—
164C4×C22⋊D11—24no—
165C4×C22⋊D11—24no—
166C4×C22⋊D11D412yes—
167C4×C22⋊D11D412yes—
168C4×C22⋊D11C2312yes—
169C4×C22⋊D11C2312yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—21no—
172C2×(C2×D11)⋊C4—21no—
173C2×(C2×D11)⋊C4—21no—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4D411yescharacteristic
176C2×C4⋊Dic11—21no—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×Dic11⋊C4—21no—
180C2×Dic11⋊C4D411yescharacteristic
181C2×C4×Dic11—21no—
182C2×C4×Dic11C2311yescharacteristic
183C22×C11⋊C8C2312yes—
184#66967—48no—
185C2×D88C2314yes—
186C2×#4313C2314yes—
187#66949—22no—
188#66948C2312yes—
189#66947—22no—
190#66946C2312yes—
191C4⋊C4×D11C2312yes—
192#66941C2312yes—
193#66938—22no—
194#66937—22no—
195#66937—22no—
196#66936—22no—
197#66935—22no—
198(C22⋊D11)⋊C4—22no—
199C22⋊C4×D11—22no—
200#66931—22no—
201C11×#103C2314yes—
202C11×#103C2314yes—
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yes—
205#66899C2314yes—
206#66899C2314yes—
207#66896C2314yes—
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yes—
210#66885C2314yes—
211#66885C2314yes—
212(C2×D11)⋊C8C2314yes—
213#66882C2314yes—
214#66879C2314yes—
215Dic11⋊C8C2314yes—
216#66873C2314yes—
217#66871C2314yes—
218#61572—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—22no—
224C23×D11C2×D411yescharacteristic
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11—22no—
228C2×Q8×C11—22no—
229C2×Q8×C11—21no—
230C2×Q8×C11—24no—
231C2×Q8×C11—24no—
232C2×Q8×C11—42no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11—44no—
236C2×Q8×C11—44no—
237C2×Q8×C11—44no—
238C2×Q8×C11C2412yes—
239C2×Q8×C11C2412yes—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—42no—
244C2×D4×C11—44no—
245C2×D4×C11C2412yes—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—21no—
251C22×C4×C11—42no—
252C22×C4×C11—44no—
253C22×C4×C11C2×D411yescharacteristic
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—22no—
260C2×C22⋊D11—22no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—22no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—48no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11C2×D412yes—
272C2×C22⋊D11C2×D412yes—
273C22×Dic11—22no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11C2×D411yescharacteristic
277C22×Dic11C2×D411yescharacteristic
278C22×Dic11C2×D411yescharacteristic
279#4343—28no—
280#4343—44no—
281#4343—48no—
282#4341—48no—
283#4341—48no—
284D4×D11—44no—
285D4×D11—48no—
286D4×D11—48no—
287#4339—48no—
288C2×D44—22no—
289C2×D44—24no—
290C2×D44—21no—
291C2×D44—21no—
292C2×D44—42no—
293C2×D44—44no—
294C2×D44—42no—
295C2×D44C2412yes—
296C2×D44C2412yes—
297C2×C4×D11—22no—
298C2×C4×D11—24no—
299C2×C4×D11—22no—
300C2×C4×D11—42no—
301C2×C4×D11—44no—
302C2×C4×D11C2×D412yes—
303C2×C4×D11C2412yes—
304C2×Dic22—22no—
305C11×SD16—28no—
306C11×SD16—44no—
307C2×C8×C11—42no—
308C2×C8×C11C2414yes—
309C11×C4⋊C4—21no—
310C11×C4⋊C4C2412yes—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11C2×D412yes—
316C22⋊Dic11C2×D412yes—
317#4325—28no—
318#4325—44no—
319#4323—44no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4C2×D412yes—
330(C2×D11)⋊C4C2×D412yes—
331C4⋊Dic11—24no—
332C4⋊Dic11—21no—
333C4⋊Dic11—21no—
334C4⋊Dic11C2412yes—
335C4⋊Dic11C2412yes—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—24no—
339Dic11⋊C4C2×D412yes—
340Dic11⋊C4C2×D412yes—
341C4×Dic11—24no—
342C4×Dic11C2×D412yes—
343C4×Dic11C2412yes—
344C2×C11⋊C8—42no—
345C2×C11⋊C8C2414yes—
346D88—44no—
347#4313—44no—
348#3496—111no—
349C2×#548—111no—
350#3308—114no—
351#3308—114no—
352#3265—114no—
353#3265—114no—
354#3213—112no—
355#3193—112no—
356#3186—111no—
357#3186—111no—
358#3112—112no—
359#3006—112no—
360C2×#448—111no—
361C2×#448D1111yescharacteristic, complemented
362#2973—111no—
363C23×C11—22no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—42no—
367C23×C11—81no—
368C23×C11—81no—
369C23×C11AGL(1,ℤ/8)14yescomplemented
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—44no—
379C22×D11—42no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—42no—
383C22×D11—82no—
384C22×D11—82no—
385C22×D11—81no—
386C22×D11—81no—
387C22×D11C22×D412yes—
388Q8×C11—24no—
389Q8×C11—22no—
390Q8×C11—22no—
391Q8×C11—22no—
392Q8×C11—44no—
393Q8×C11—44no—
394Q8×C11—42no—
395Q8×C11H(5,𝔽2)14yescomplemented
396D4×C11—24no—
397D4×C11—44no—
398D4×C11—44no—
399D4×C11—81no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—44no—
411C2×C4×C11—44no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C22×D411yescharacteristic
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C2511yescharacteristic
418C22⋊D11—24no—
419C22⋊D11—24no—
420C22⋊D11—44no—
421C22⋊D11—44no—
422C22⋊D11—44no—
423C22⋊D11—44no—
424C22⋊D11—44no—
425C22⋊D11—44no—
426C22⋊D11—82no—
427C22⋊D11—82no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—44no—
434C2×Dic11—42no—
435C2×Dic11—42no—
436C2×Dic11C22×D412yes—
437C2×Dic11C22×D412yes—
438C2×Dic11C22×D412yes—
439D44—24no—
440D44—24no—
441D44—48no—
442D44—42no—
443D44—44no—
444D44—81no—
445C4×D11—24no—
446C4×D11—42no—
447C4×D11—48no—
448C4×D11—44no—
449C4×D11—44no—
450Dic22—44no—
451C8×C11—24no—
452C11⋊C8—24no—
453C2×H(5,𝔽2)—221no—
454C22×#41—111no—
455C23×Q8C2×D1111yescharacteristic, complemented
456C2×AGL(1,ℤ/8)—114no—
457C22×SD16—112no—
458C22×SD16C2×D1112yescomplemented
459#548—114no—
460#548—114no—
461#548—222no—
462#548—222no—
463#547—112no—
464#547—112no—
465#546—222no—
466#546—222no—
467D42—112no—
468D42—112no—
469#537—221no—
470#534—221no—
471#534—221no—
472#532—112no—
473C2×#124—111no—
474C2×#124—221no—
475C2×C22⋊Q8—111no—
476C2×C22⋊Q8—221no—
477C2×#121—111no—
478C2×#121—111no—
479C2×#121—112no—
480C2×#121—221no—
481C2×#121C2×D1111yescharacteristic
482C2×C4×Q8—111no—
483C2×C4×D4—111no—
484C2×C4×D4—221no—
485#496—114no—
486#489—114no—
487#484—114no—
488#480—112no—
489#480—112no—
490#480—112no—
491#480—112no—
492#477—114no—
493#468—114no—
494#468—114no—
495#466—114no—
496#466—114no—
497#463—114no—
498#463—114no—
499#460—114no—
500#450—114no—
501#449—114no—
502#449—114no—
503#448—112no—
504#448—112no—
505#448—114no—
506#448C2×D1112yescomplemented
507#448C2×D1112yescomplemented
508#448C2×D1114yescomplemented
509#447—112no—
510#447—112no—
511#447—112no—
512#447—112no—
513#440—114no—
514#440—114no—
515#435—114no—
516#435—114no—
517#432—112no—
518#417—114no—
519C2×#103—112no—
520C2×#103C2×D1112yescomplemented
521#407—112no—
522C2×C22⋊C8—111no—
523C2×C22⋊C8C2×D1111yescharacteristic, complemented
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—44no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—162no—
535C22×C11C2×AGL(1,ℤ/8)12yes—
536C22×C11C2×AGL(1,ℤ/8)12yes—
537C22×C11C2×AGL(1,ℤ/8)12yes—
538C22×C11C23×D411yescharacteristic
539C2×D11—22no—
540C2×D11—22no—
541C2×D11—22no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—82no—
549C2×D11—84no—
550C2×D11—164no—
551C2×D11—162no—
552C4×C11—24no—
553C4×C11—21no—
554C4×C11—21no—
555C4×C11—21no—
556C4×C11—42no—
557C4×C11—42no—
558C4×C11C2×H(5,𝔽2)12yes—
559Dic11—22no—
560Dic11—22no—
561Dic11—22no—
562Dic11—42no—
563Dic11—42no—
564H(5,𝔽2)—448no—
565C2×#41—114no—
566C2×#41—222no—
567C2×#41—222no—
568C2×#41—222no—
569C2×#41—222no—
570C2×#41—444no—
571C22×Q8—21no—
572C22×Q8—21no—
573C22×Q8—21no—
574C22×Q8—44no—
575C22×Q8C22×D1111yescharacteristic
576C22×Q8C22×D1112yes—
577C22×Q8C22×D1112yes—
578C22×Q8C22×D1111yescharacteristic
579C22×D4—21no—
580C22×D4—111no—
581C22×D4—112no—
582C22×D4—111no—
583C22×D4—111no—
584C22×D4—221no—
585C22×D4—222no—
586C22×D4—222no—
587C22×D4—222no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4C22×D1111yescharacteristic
591C23×C4—21no—
592C23×C4—111no—
593C23×C4—221no—
594C23×C4C22×D1111yescharacteristic
595AGL(1,ℤ/8)—448no—
596C2×SD16—44no—
597C2×SD16—114no—
598C2×SD16—114no—
599C2×SD16—444no—
600C2×SD16C22×D1114yes—
601C2×SD16C22×D1114yes—
602C2×D8—114no—
603C2×D8—114no—
604C2×M16—114no—
605C22×C8—112no—
606C22×C8C22×D1112yes—
607C4⋊Q8—112no—
608#127—112no—
609#124—114no—
610#124—222no—
611#124—222no—
612#124—224no—
613#124—224no—
614#123—222no—
615#123—222no—
616#123—222no—
617#123—222no—
618C22⋊Q8—114no—
619C22⋊Q8—222no—
620C22⋊Q8—222no—
621C22⋊Q8—224no—
622C22⋊Q8—224no—
623C22⋊Q8—222no—
624#121—21no—
625#121—21no—
626#121—112no—
627#121—112no—
628#121—112no—
629#121—112no—
630#121—112no—
631#121—112no—
632#121—222no—
633#121—222no—
634#121—222no—
635#121—224no—
636#121—224no—
637#121—222no—
638#121—222no—
639#121—221no—
640#121—221no—
641#121—221no—
642#121—221no—
643#121C22×D1112yes—
644#121C22×D1112yes—
645#120—222no—
646#120—222no—
647#120—222no—
648#120—222no—
649C4×Q8—114no—
650C4×Q8—222no—
651C4×D4—112no—
652C4×D4—112no—
653C4×D4—112no—
654C4×D4—112no—
655C4×D4—112no—
656C4×D4—112no—
657C4×D4—222no—
658C4×D4—224no—
659C4×D4—224no—
660C2×C4⋊C4—111no—
661C2×C4⋊C4—111no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4—221no—
665C2×C4⋊C4—221no—
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—111no—
669C2×C22⋊C4—111no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—221no—
672C2×C22⋊C4—221no—
673C2×C22⋊C4—221no—
674C2×C22⋊C4—221no—
675C2×C22⋊C4—221no—
676C2×C42—111no—
677C2×C42—221no—
678#107—114no—
679#107—114no—
680C4⋊C8—114no—
681#103—114no—
682#103—114no—
683#103C22×D1114yes—
684#103C22×D1114yes—
685#102—114no—
686#102—114no—
687#102—114no—
688#102—114no—
689C22⋊C8—112no—
690C22⋊C8—112no—
691C22⋊C8—114no—
692C22⋊C8C22×D1112yes—
693C22⋊C8C22×D1112yes—
694#97—114no—
695C2×C11—22no—
696C2×C11—22no—
697C2×C11—22no—
698C2×C11—82no—
699C2×C11#348411yescharacteristic
700C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
701C2×C11#358611yescharacteristic
702D11—42no—
703D11—82no—
704D11—82no—
705C24—21no—
706C24—111no—
707C24—222no—
708C24—221no—
709C24—221no—
710C24D4×D1111yescharacteristic
711#41—228no—
712#41—448no—
713#41—448no—
714#41—444no—
715#41—448no—
716#41—448no—
717C2×Q8—24no—
718C2×Q8—21no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—21no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—222no—
731C2×Q8C23×D1112yes—
732C2×Q8C23×D1112yes—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—21no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—112no—
739C2×D4—112no—
740C2×D4—112no—
741C2×D4—112no—
742C2×D4—222no—
743C2×D4—224no—
744C2×D4—222no—
745C2×D4—222no—
746C2×D4—222no—
747C2×D4—224no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—222no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—221no—
754C2×D4—221no—
755C2×D4—442no—
756C2×D4—442no—
757C2×D4—444no—
758C2×D4—444no—
759C2×D4—448no—
760C2×D4—448no—
761C2×D4—448no—
762C2×D4—444no—
763C2×D4—444no—
764C2×D4C23×D1112yes—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—42no—
771C22×C4—44no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—222no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—442no—
784C22×C4—444no—
785C22×C4D4×D1111yescharacteristic
786C22×C4D4×D1111yescharacteristic
787C22×C4D4×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791SD16—28no—
792SD16—44no—
793SD16—228no—
794SD16—444no—
795D8—444no—
796D8—444no—
797M16—444no—
798C2×C8—42no—
799C2×C8—114no—
800C2×C8—442no—
801C2×C8C23×D1114yes—
802C4⋊C4—21no—
803C4⋊C4—112no—
804C4⋊C4—112no—
805C4⋊C4—112no—
806C4⋊C4—112no—
807C4⋊C4—222no—
808C4⋊C4—224no—
809C4⋊C4—224no—
810C4⋊C4—222no—
811C4⋊C4—221no—
812C4⋊C4—221no—
813C4⋊C4C23×D1112yes—
814C22⋊C4—22no—
815C22⋊C4—22no—
816C22⋊C4—112no—
817C22⋊C4—112no—
818C22⋊C4—112no—
819C22⋊C4—112no—
820C22⋊C4—224no—
821C22⋊C4—222no—
822C22⋊C4—224no—
823C22⋊C4—222no—
824C22⋊C4—224no—
825C22⋊C4—222no—
826C22⋊C4—222no—
827C22⋊C4—222no—
828C22⋊C4—222no—
829C22⋊C4—222no—
830C22⋊C4—222no—
831C42—112no—
832C42—112no—
833C42—224no—
834C11#6157211yescharacteristic, complemented, Sylow
835C23—22no—
836C23—41no—
837C23—41no—
838C23—42no—
839C23—81no—
840C23—81no—
841C23—112no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—441no—
846C23—441no—
847C23—442no—
848C23—442no—
849C23—444no—
850C23—442no—
851C23—442no—
852C23—881no—
853C23—881no—
854C23—882no—
855C23—882no—
856C23#6696714yescomplemented
857C23C2×D4×D1111yescharacteristic
858C23C2×D4×D1111yescharacteristic
859C23C2×D4×D1111yescharacteristic
860Q8—24no—
861Q8—22no—
862Q8—22no—
863Q8—22no—
864Q8—44no—
865Q8—44no—
866Q8—42no—
867Q8—444no—
868Q8#6703714yescomplemented
869D4—24no—
870D4—44no—
871D4—44no—
872D4—81no—
873D4—224no—
874D4—224no—
875D4—224no—
876D4—224no—
877D4—448no—
878D4—442no—
879D4—444no—
880D4—444no—
881D4—444no—
882D4—444no—
883D4—444no—
884D4—444no—
885D4—444no—
886D4—881no—
887D4—882no—
888D4—882no—
889C2×C4—24no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—222no—
907C2×C4—224no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—442no—
911C2×C4—448no—
912C2×C4—444no—
913C2×C4—444no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—444no—
917C2×C4—442no—
918C2×C4—442no—
919C2×C4C2×D4×D1111yescharacteristic
920C2×C4C2×D4×D1111yescharacteristic
921C2×C4C2×D4×D1111yescharacteristic
922C2×C4C24×D1111yescharacteristic
923C8—24no—
924C8—224no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—44no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—162no—
936C22—222no—
937C22—222no—
938C22—222no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—882no—
946C22—884no—
947C22—1762no—
948C22—1764no—
949C22C2×#6696712yes—
950C22C2×#6696712yes—
951C22C2×#6696712yes—
952C22C22×D4×D1111yescharacteristic
953C4—24no—
954C4—21no—
955C4—21no—
956C4—21no—
957C4—42no—
958C4—42no—
959C4—222no—
960C4—222no—
961C4—222no—
962C4—442no—
963C4—442no—
964C4C2×#6703712yes—
965C2—22no—
966C2—22no—
967C2—22no—
968C2—82no—
969C2—442no—
970C2—882no—
971C2—882no—
972C2#1308224511yescharacteristic
973C2C22×#6696711yescharacteristic
974C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#448C2
socleC22×C11C23×D4
hypercenterC2×#448D11
hypocenterC11#61572
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. #13082373C2semidirect
2. C2×#10623348C2semidirect
3. #13080611C2semidirect
4. #13080603C2semidirect
5. #13080111C2semidirect
6. #13080104C2semidirect
7. #13079602C2semidirect
8. #13079420C2semidirect
9. #13079367C2semidirect
10. #13079364C2semidirect
11. #13078733C2semidirect
12. #13077867C2semidirect
13. C2×#10622840C2semidirect
14. #13077642C2semidirect
15. C2×C11×#448C2semidirect
16. C23×Q8×C11C22semidirect
17. C22×#4343C22semidirect
19. C22×C11×SD16C22semidirect
23. #10623348C22semidirect
24. #10623348C22semidirect
26. C2×#67000C22semidirect
28. C2×#66999C22semidirect
29. C2×Q8×Dic11C22semidirect
30. C22×#4325C22semidirect
32. D4×C22⋊D11C22semidirect
35. C2×#66983C22semidirect
38. C2×#66967C22semidirect
39. #10623142C22semidirect
41. #10623140C22semidirect
46. #10623038C22semidirect
48. C11×#448C22semidirect
49. C11×#448C22semidirect
50. C11×#448C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622840C22semidirect
54. #10622840C22semidirect
55. #10622840C22semidirect
56. C2×#66899C22semidirect
57. #10622830C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622789C22semidirect
60. #10622787C22semidirect
61. #10622785C22semidirect
62. #10622782C22semidirect
63. #10622778C22semidirect
64. #10622777C22semidirect
65. #10622776C22semidirect
66. #10622728C22semidirect
67. #10622724C22semidirect
68. #10622651C22semidirect
69. #10622649C22semidirect
70. #10622646C22semidirect
71. #10622580C22semidirect
72. #10622432C22semidirect
73. #10622430C22semidirect
74. #10622425C22semidirect
75. #10622424C22semidirect
76. #10622422C22semidirect
77. #10622416C22semidirect
78. #10622408C22semidirect
79. #10622407C22semidirect
80. #10622349C22semidirect
81. #10622349C22semidirect
82. #10622345C22semidirect
83. #10622345C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
361. C2×#448D11semidirect
369. C23×C11AGL(1,ℤ/8)semidirect
395. Q8×C11H(5,𝔽2)semidirect
455. C23×Q8C2×D11semidirect
458. C22×SD16C2×D11semidirect
506. #448C2×D11semidirect
507. #448C2×D11semidirect
508. #448C2×D11semidirect
520. C2×#103C2×D11semidirect
523. C2×C22⋊C8C2×D11semidirect
834. C11#61572semidirect
856. C23#66967semidirect
868. Q8#67037semidirect

Maximal subgroups

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

subgroupindex
#130823732
C2×#106233482
#130806112
#130806032
#130801112
#130801042
#130796022
#130794202
#130793672
#130793642
#130787332
#130778672
C2×#106228402
#130776422
C2×C11×#4482
#6157211