Finite Group Databasebeta

← #15622160

Subgroups — #15622160

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13078754C214yesmaximal, complemented
3#13078715C212yesmaximal, complemented
4#13078707C212yesmaximal, complemented
5#13078663C214yesmaximal, complemented
6#13078624C212yesmaximal, complemented
7#13078616C212yesmaximal, complemented
8#13078539C212yesmaximal, complemented
9#13078413C212yesmaximal, complemented
10#13078080C212yesmaximal, complemented
11#13077843C212yesmaximal, complemented
12C4×#66985C214yesmaximal, complemented
13#13077249C211yesmaximal, characteristic, complemented
14C22×C4×D4×C11C211yesmaximal, characteristic, complemented
15C23×D4×C11C2211yescharacteristic
16C24×C4×C11—21no—
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2212yes—
25C2×C4×D4×C11C2212yes—
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C2×C4×D4×C11C2212yes—
29C22×C11×C4⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4—21no—
31C22×C42×C11C2211yescharacteristic
32C2×#66985C2214yes—
33#10623322—21no—
34#10623322—21no—
35#10623322C2212yes—
36#10623010—21no—
37#10623010—21no—
38#10623010—21no—
39#10623010—21no—
40#10623010C2212yescomplemented
41#10623010C2212yescomplemented
42#10623008C2211yescharacteristic, complemented
43#10623008C2211yescharacteristic, complemented
44#10623008C2211yescharacteristic, complemented
45C4×#4339—21no—
46C4×#4339—21no—
47C4×#4339C2212yescomplemented
48#10623001C2211yescharacteristic, complemented
49#10623001C2211yescharacteristic, complemented
50#10623001C2211yescharacteristic, complemented
51#10622831C2214yes—
52#10622831C2214yes—
53#10622830C2214yes—
54#10622830C2214yes—
55#10622828C2214yes—
56#10622820C2212yes—
57#10622632C2214yescomplemented
58#10622631C2218yescomplemented
59C4×#4324C2218yescomplemented
60#10622629C2218yescomplemented
61#10622628C2214yescomplemented
62#10622627C2218yescomplemented
63C4×#4323C2218yescomplemented
64#10622622C2218yescomplemented
65#10622621C2214yescomplemented
66#10622620C2214yescomplemented
67#10622584C2214yescomplemented
68#10622583C2214yescomplemented
69#10622581C2214yescomplemented
70#10622580C2214yescomplemented
71#10622579C2214yescomplemented
72#10622577C2214yescomplemented
73#10622539C2212yescomplemented
74#10622539C2212yescomplemented
75#10622538C2212yescomplemented
76#10622538C2212yescomplemented
77#10622537C2212yescomplemented
78C4×#4318C2212yescomplemented
79C25×C11—21no—
80C22×D4×C11—28no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11C2312yes—
85C22×D4×C11C2312yes—
86C22×D4×C11C2312yes—
87C23×C4×C11—21no—
88C23×C4×C11—22no—
89C23×C4×C11—22no—
90C23×C4×C11—22no—
91C23×C4×C11—22no—
92C23×C4×C11—22no—
93C23×C4×C11—22no—
94C23×C4×C11—48no—
95C23×C4×C11D411yescharacteristic
96C23×C4×C11D411yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C2×#4339—21no—
99C2×#4339—21no—
100C2×#4339C2312yes—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—22no—
109C4×D4×C11—22no—
110C4×D4×C11—22no—
111C4×D4×C11—22no—
112C4×D4×C11—22no—
113C4×D4×C11C2314yes—
114C4×D4×C11C2314yes—
115C4×D4×C11C2314yes—
116C4×D4×C11C2314yes—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—22no—
126C2×C11×C22⋊C4—22no—
127C2×C11×C22⋊C4—22no—
128C2×C11×C22⋊C4—22no—
129C2×C42×C11D411yescharacteristic
130C2×C42×C11D411yescharacteristic
131C2×C42×C11D411yescharacteristic
132C2×C42×C11D411yescharacteristic
133C2×C42×C11D411yescharacteristic
134C2×C42×C11D411yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2311yescharacteristic
137C2×C42×C11C2311yescharacteristic
138C2×C42×C11C2311yescharacteristic
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2311yescharacteristic
141#67006—22no—
142C2×#4324C2318yes—
143#66985—216no—
144C2×#4323C2318yes—
145#66983—21no—
146#66983—21no—
147#66983—21no—
148#66983—21no—
149#66983C2312yes—
150#66983C2312yes—
151#66982—22no—
152#66982—22no—
153#66982—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C4×C22⋊D11—22no—
157C4×C22⋊D11—22no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—22no—
160#66979—21no—
161#66979—21no—
162#66979C2312yes—
163#66977—21no—
164#66977—21no—
165#66977—21no—
166#66977—21no—
167#66977C2312yes—
168#66977C2312yes—
169C2×#4318C2314yes—
170#66929—22no—
171#66929—22no—
172#66928—21no—
173#66928—21no—
174#66928C2312yescomplemented
175#66927C2311yescharacteristic, complemented
176C4×D44—21no—
177C4×D44—21no—
178C4×D44—21no—
179C4×D44—21no—
180C4×D44C2312yescomplemented
181C4×D44C2312yescomplemented
182#66925—22no—
183#66925—22no—
184#66925—22no—
185C42×D11—22no—
186#66923—21no—
187#66923—21no—
188#66923C2312yescomplemented
189#66922C2311yescharacteristic, complemented
190#66922C2311yescharacteristic, complemented
191#66922C2311yescharacteristic, complemented
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22—21no—
196C4×Dic22C2312yescomplemented
197C4×Dic22C2312yescomplemented
198#66896C2318yes—
199#66896C2318yes—
200C22⋊(C11⋊C8)C2314yes—
201C22⋊(C11⋊C8)C2314yes—
202#66874C2318yescomplemented
203#66873C2318yescomplemented
204#66872C2318yescomplemented
205#66871C2318yescomplemented
206C4⋊(C11⋊C8)C2314yescomplemented
207C4⋊(C11⋊C8)C2314yescomplemented
208#66867C2314yescomplemented
209C4×C11⋊C8C2314yescomplemented
210#60558—111nomaximal, Sylow
211C24×C11—28no—
212C24×C11—22no—
213C24×C11—22no—
214C24×C11—22no—
215C24×C11—44no—
216C24×C11—44no—
217C24×C11C2×D411yescharacteristic
218C2×D4×C11—28no—
219C2×D4×C11—28no—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—24no—
227C2×D4×C11#4118yescomplemented
228C2×D4×C11C2414yes—
229C22×C4×C11—24no—
230C22×C4×C11—24no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—24no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—42no—
239C22×C4×C11—48no—
240C22×C4×C11—48no—
241C22×C4×C11—48no—
242C22×C4×C11—48no—
243C22×C4×C11—48no—
244C22×C4×C11—44no—
245C22×C4×C11—48no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
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×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C22×C4×C11C2411yescharacteristic
264C2×C22⋊D11—22no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267#4339—28no—
268#4339—44no—
269#4339—44no—
270C2×D44—21no—
271C2×D44—21no—
272C2×D44C2412yes—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×Dic22—21no—
277C2×Dic22—21no—
278C2×Dic22C2412yes—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4C2414yes—
283C11×C22⋊C4—24no—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D411yescharacteristic
297C42×C11C2×D411yescharacteristic
298C42×C11C2×D411yescharacteristic
299C42×C11C2411yescharacteristic
300C42×C11C2411yescharacteristic
301C42×C11C2411yescharacteristic
302C42×C11C2411yescharacteristic
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306#4324—216no—
307#4323—216no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—22no—
310(C2×D11)⋊C4—22no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—22no—
314C4⋊Dic11—21no—
315C4⋊Dic11—21no—
316C4⋊Dic11—21no—
317C4⋊Dic11—21no—
318C4⋊Dic11C2412yes—
319C4⋊Dic11C2412yes—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325Dic11⋊C4—22no—
326C4×Dic11—22no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329#4318—28no—
330C2×C11⋊C8C2418yes—
331#3444—111no—
332C22×C4×D4D1111yescharacteristic, complemented
333#3114—114no—
334#3110—112no—
335#3109—112no—
336#3105—114no—
337#3101—112no—
338#3100—112no—
339#3092—112no—
340#3077—112no—
341#3036—112no—
342#3003—112no—
343C4×AGL(1,ℤ/8)—114no—
344#2920—111no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—28no—
349C23×C11—28no—
350C23×C11—28no—
351C23×C11—24no—
352C23×C11—44no—
353C23×C11—44no—
354C23×C11—432no—
355C23×C11—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11C22×D411yescharacteristic
360C23×C11C22×D411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C22×D11—22no—
363D4×C11—28no—
364D4×C11—28no—
365D4×C11—28no—
366D4×C11—24no—
367D4×C11C2×#4118yes—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—48no—
386C2×C4×C11—48no—
387C2×C4×C11—44no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—48no—
391C2×C4×C11—48no—
392C2×C4×C11AGL(1,ℤ/8)14yescomplemented
393C2×C4×C11C22×D411yescharacteristic
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C22×D411yescharacteristic
404C2×C4×C11C2×#4114yes—
405C2×C4×C11C2511yescharacteristic
406C22⋊D11—44no—
407C22⋊D11—44no—
408C22⋊D11—44no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412D44—24no—
413D44—42no—
414D44—42no—
415C4×D11—44no—
416C4×D11—44no—
417C4×D11—44no—
418Dic22—24no—
419Dic22—42no—
420Dic22—42no—
421C11⋊C8—28no—
422C23×D4C2×D1111yescharacteristic
423C24×C4—21no—
424C2×AGL(1,ℤ/8)—114no—
425#533—111no—
426#533—111no—
427#533—111no—
428#532—111no—
429#532—111no—
430#532—111no—
431#529—112no—
432#529—112no—
433#529—221no—
434#529—221no—
435#529—221no—
436#529—221no—
437#525—112no—
438#525—221no—
439#525—221no—
440C4×#41—112no—
441C4×#41—221no—
442C4×#41—221no—
443C2×C4×D4—21no—
444C2×C4×D4—21no—
445C2×C4×D4—21no—
446C2×C4×D4—21no—
447C2×C4×D4—21no—
448C2×C4×D4—21no—
449C2×C4×D4C2×D1112yes—
450C2×C4×D4C2×D1112yes—
451C2×C4×D4C2×D1112yes—
452C2×C4×D4C2×D1112yes—
453C2×C4×D4C2×D1112yes—
454C2×C4×D4C2×D1112yes—
455C22×C4⋊C4C2×D1111yescharacteristic
456C22×C22⋊C4—21no—
457C22×C42C2×D1111yescharacteristic
458#484—114no—
459#483—114no—
460#481—114no—
461#480—114no—
462#478—118no—
463#476—114no—
464#474—114no—
465#463—118no—
466#461—114no—
467#459—114no—
468#450—114no—
469#450—114no—
470#447—114no—
471#447—114no—
472#442—118no—
473#440—118no—
474C4×SD16—118no—
475C4×D8—118no—
476#432—112no—
477#432—112no—
478#431—112no—
479#431—112no—
480#428—114no—
481#423—112no—
482#418—114no—
483#417—114no—
484#407—112no—
485C4×M16—112no—
486C22×C11—28no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—28no—
494C22×C11—416no—
495C22×C11—416no—
496C22×C11—416no—
497C22×C11—44no—
498C22×C11—44no—
499C22×C11#52512yes—
500C22×C11C2×AGL(1,ℤ/8)12yes—
501C22×C11#57512yes—
502C22×C11C23×D411yescharacteristic
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—44no—
515C4×C11#52512yes—
516C4×C11C2×AGL(1,ℤ/8)12yes—
517C4×C11C2×AGL(1,ℤ/8)12yes—
518C4×C11C22×#4112yes—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522C25—21no—
523C2×#41—112no—
524C2×#41—221no—
525C2×#41—221no—
526C22×D4—28no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4C22×D1112yes—
531C22×D4C22×D1112yes—
532C22×D4C22×D1112yes—
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—22no—
537C23×C4—22no—
538C23×C4—22no—
539C23×C4—22no—
540C23×C4—48no—
541C23×C4C22⋊D1111yescharacteristic
542C23×C4C22⋊D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544AGL(1,ℤ/8)—2216no—
545C2×SD16—118no—
546C2×D8—118no—
547C2×M16—114no—
548C4⋊Q8—111no—
549C4⋊Q8—111no—
550C4⋊Q8—111no—
551#127—111no—
552#126—222no—
553#126—222no—
554#125—112no—
555#125—221no—
556#125—221no—
557#124—112no—
558#124—221no—
559#124—221no—
560#123—222no—
561#123—222no—
562#123—222no—
563C22⋊Q8—112no—
564C22⋊Q8—112no—
565C22⋊Q8—221no—
566C22⋊Q8—221no—
567C22⋊Q8—221no—
568C22⋊Q8—221no—
569#121—112no—
570#121—112no—
571#121—221no—
572#121—221no—
573#121—221no—
574#121—221no—
575#120—222no—
576C4×Q8—112no—
577C4×Q8—112no—
578C4×Q8—221no—
579C4×Q8—221no—
580C4×Q8—221no—
581C4×Q8—221no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—112no—
595C4×D4—112no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—221no—
603C4×D4—221no—
604C4×D4—221no—
605C4×D4—221no—
606C4×D4C22×D1114yes—
607C4×D4C22×D1114yes—
608C4×D4C22×D1114yes—
609C4×D4C22×D1114yes—
610#117—112no—
611#117—221no—
612#117—221no—
613#117—222no—
614#117—222no—
615#117—222no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C22×D1112yes—
620C2×C4⋊C4C22×D1112yes—
621C2×C4⋊C4C22×D1112yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C42—222no—
629C2×C42C22⋊D1111yescharacteristic
630C2×C42C22⋊D1111yescharacteristic
631C2×C42C22⋊D1111yescharacteristic
632C2×C42C22⋊D1111yescharacteristic
633C2×C42C22⋊D1111yescharacteristic
634C2×C42C22⋊D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641#107—118no—
642#106—118no—
643C4⋊C8—114no—
644C4⋊C8—114no—
645#103—118no—
646#102—118no—
647#102—118no—
648#102—118no—
649C22⋊C8—114no—
650C22⋊C8—114no—
651#97—114no—
652C4×C8—114no—
653C2×C11—22no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11—48no—
657C2×C11C2×#52511yescharacteristic
658C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C11C2×#57511yescharacteristic
660D11—82no—
661C24—28no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—44no—
666C24—44no—
667C24C2×C22⋊D1111yescharacteristic
668#41—228no—
669#41—444no—
670#41—444no—
671C2×Q8—112no—
672C2×Q8—221no—
673C2×Q8—221no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—24no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—112no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4#433918yescomplemented
690C2×D4C23×D1114yes—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—42no—
701C22×C4—48no—
702C22×C4—48no—
703C22×C4—48no—
704C22×C4—48no—
705C22×C4—48no—
706C22×C4—44no—
707C22×C4—48no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C2×C22⋊D1111yescharacteristic
713C22×C4C2×C22⋊D1111yescharacteristic
714C22×C4C2×C22⋊D1111yescharacteristic
715C22×C4C2×C22⋊D1111yescharacteristic
716C22×C4C2×C22⋊D1111yescharacteristic
717C22×C4C2×C22⋊D1111yescharacteristic
718C22×C4C2×C22⋊D1111yescharacteristic
719C22×C4C2×C22⋊D1111yescharacteristic
720C22×C4C2×C22⋊D1111yescharacteristic
721C22×C4C2×C22⋊D1111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1111yescharacteristic
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729SD16—2216no—
730D8—2216no—
731M16—228no—
732C2×C8—118no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—22no—
736C4⋊C4—112no—
737C4⋊C4—112no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—221no—
741C4⋊C4—221no—
742C4⋊C4—221no—
743C4⋊C4—221no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4C23×D1114yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—222no—
762C42—222no—
763C42—222no—
764C42—222no—
765C42C2×C22⋊D1111yescharacteristic
766C42C2×C22⋊D1111yescharacteristic
767C42C2×C22⋊D1111yescharacteristic
768C42C2×C22⋊D1111yescharacteristic
769C42C2×C22⋊D1111yescharacteristic
770C42C2×C22⋊D1111yescharacteristic
771C42C2×C22⋊D1111yescharacteristic
772C42C2×C22⋊D1111yescharacteristic
773C42C2×C22⋊D1111yescharacteristic
774C42C2×C22⋊D1111yescharacteristic
775C42C2×C22⋊D1111yescharacteristic
776C42C2×C22⋊D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C42C23×D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C11#6055811yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—24no—
789C23—44no—
790C23—44no—
791C23—432no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—222no—
797C23C22×C22⋊D1111yescharacteristic
798C23C22×C22⋊D1111yescharacteristic
799C23C22×C22⋊D1111yescharacteristic
800Q8—224no—
801Q8—442no—
802Q8—442no—
803D4—28no—
804D4—28no—
805D4—28no—
806D4—24no—
807D4—224no—
808D4—442no—
809D4—444no—
810D4—444no—
811D4—444no—
812D4—442no—
813D4C2×#433918yes—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4#6698514yescomplemented
845C2×C4C2×#433914yes—
846C2×C4C22×C22⋊D1111yescharacteristic
847C2×C4C22×C22⋊D1111yescharacteristic
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1111yescharacteristic
852C2×C4C22×C22⋊D1111yescharacteristic
853C2×C4C22×C22⋊D1111yescharacteristic
854C2×C4C22×C22⋊D1111yescharacteristic
855C2×C4C22×C22⋊D1111yescharacteristic
856C2×C4C22×C22⋊D1111yescharacteristic
857C2×C4C24×D1111yescharacteristic
858C8—228no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—28no—
867C22—416no—
868C22—416no—
869C22—416no—
870C22—44no—
871C22—44no—
872C22—442no—
873C22—442no—
874C22—442no—
875C22#1062332212yes—
876C22C2×#6698512yes—
877C22#1062335312yes—
878C22C23×C22⋊D1111yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—44no—
888C4—442no—
889C4—442no—
890C4—442no—
891C4#1062332212yes—
892C4C2×#6698512yes—
893C4C2×#6698512yes—
894C4C22×#433912yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—48no—
899C2—882no—
900C2C2×#1062332211yescharacteristic
901C2C22×#6698511yescharacteristic
902C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C4×D4×C11C2
socleC22×C11C23×D4
hypercenterC22×C4×D4D11
hypocenterC11#60558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13078754C2semidirect
3. #13078715C2semidirect
4. #13078707C2semidirect
5. #13078663C2semidirect
6. #13078624C2semidirect
7. #13078616C2semidirect
8. #13078539C2semidirect
9. #13078413C2semidirect
10. #13078080C2semidirect
11. #13077843C2semidirect
12. C4×#66985C2semidirect
13. #13077249C2semidirect
14. C22×C4×D4×C11C2semidirect
40. #10623010C22semidirect
41. #10623010C22semidirect
42. #10623008C22semidirect
43. #10623008C22semidirect
44. #10623008C22semidirect
47. C4×#4339C22semidirect
48. #10623001C22semidirect
49. #10623001C22semidirect
50. #10623001C22semidirect
57. #10622632C22semidirect
58. #10622631C22semidirect
59. C4×#4324C22semidirect
60. #10622629C22semidirect
61. #10622628C22semidirect
62. #10622627C22semidirect
63. C4×#4323C22semidirect
64. #10622622C22semidirect
65. #10622621C22semidirect
66. #10622620C22semidirect
67. #10622584C22semidirect
68. #10622583C22semidirect
69. #10622581C22semidirect
70. #10622580C22semidirect
71. #10622579C22semidirect
72. #10622577C22semidirect
73. #10622539C22semidirect
74. #10622539C22semidirect
75. #10622538C22semidirect
76. #10622538C22semidirect
77. #10622537C22semidirect
78. C4×#4318C22semidirect
174. #66928C23semidirect
175. #66927C23semidirect
180. C4×D44C23semidirect
181. C4×D44C23semidirect
188. #66923C23semidirect
189. #66922C23semidirect
190. #66922C23semidirect
191. #66922C23semidirect
196. C4×Dic22C23semidirect
197. C4×Dic22C23semidirect
202. #66874C23semidirect
203. #66873C23semidirect
204. #66872C23semidirect
205. #66871C23semidirect
206. C4⋊(C11⋊C8)C23semidirect
207. C4⋊(C11⋊C8)C23semidirect
208. #66867C23semidirect
209. C4×C11⋊C8C23semidirect
227. C2×D4×C11#41semidirect
332. C22×C4×D4D11semidirect
392. C2×C4×C11AGL(1,ℤ/8)semidirect
689. C2×D4#4339semidirect
781. C11#60558semidirect
844. C2×C4#66985semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130787542
#130787152
#130787072
#130786632
#130786242
#130786162
#130785392
#130784132
#130780802
#130778432
C4×#669852
#130772492
C22×C4×D4×C112
#6055811