Finite Group Databasebeta

← #15622162

Subgroups — #15622162

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
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13078756C214yesmaximal, complemented
4#13078716C212yesmaximal, complemented
5#13078708C212yesmaximal, complemented
6#13078665C214yesmaximal, complemented
7#13078625C212yesmaximal, complemented
8#13078617C212yesmaximal, complemented
9#13078541C212yesmaximal, complemented
10#13078415C212yesmaximal, complemented
11#13078082C212yesmaximal, complemented
12#13077846C212yesmaximal, complemented
13C4×#66961C214yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C23×D44C2211yescharacteristic
16C23×C4×D11—21no—
17C22×C42×C11C2211yescharacteristic
18#10623322—21no—
19#10623322—21no—
20#10623322C2212yes—
21C22×(C2×D11)⋊C4—21no—
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66961C2214yes—
24#10623010—21no—
25#10623010—21no—
26#10623010—21no—
27#10623010—21no—
28#10623010C2212yescomplemented
29#10623010C2212yescomplemented
30#10623008C2211yescharacteristic, complemented
31#10623008C2211yescharacteristic, complemented
32#10623008C2211yescharacteristic, complemented
33C4×#4339—21no—
34C4×#4339—21no—
35C4×#4339C2212yescomplemented
36C2×C4×D44—21no—
37C2×C4×D44—21no—
38C2×C4×D44—21no—
39C2×C4×D44—21no—
40C2×C4×D44—21no—
41C2×C4×D44—21no—
42C2×C4×D44C2212yes—
43C2×C4×D44C2212yes—
44C2×C4×D44C2212yes—
45C2×C4×D44C2212yes—
46C2×C4×D44C2212yes—
47C2×C4×D44C2212yes—
48#10623001C2211yescharacteristic, complemented
49#10623001C2211yescharacteristic, complemented
50#10623001C2211yescharacteristic, complemented
51C11×#432C2212yescomplemented
52C11×#432C2212yescomplemented
53C11×#431C2212yescomplemented
54C11×#431C2212yescomplemented
55C11×#423C2212yescomplemented
56C11×#407C2212yes—
57C4×C11×M16C2212yescomplemented
58#10622746C2214yescomplemented
59#10622744C2214yes—
60#10622734C2214yescomplemented
61#10622460C2218yescomplemented
62#10622459C2214yescomplemented
63#10622457C2218yescomplemented
64#10622456C2214yescomplemented
65#10622455C2214yescomplemented
66#10622454C2214yescomplemented
67#10622349C2214yescomplemented
68#10622348C2214yescomplemented
69#10622345C2214yes—
70#10622345C2214yes—
71#10622344C2214yes—
72#10622344C2214yes—
73#10622335C2214yescomplemented
74#10622334C2214yescomplemented
75#10622324C2218yescomplemented
76#10622323C2218yescomplemented
77C4×D88C2218yescomplemented
78C4×#4314C2218yescomplemented
79C24×D11—21no—
80C23×C4×C11D411yescharacteristic
81C23×C4×C11D411yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×Dic11—21no—
84C2×#4339—21no—
85C2×#4339—21no—
86C2×#4339C2312yes—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44—21no—
90C22×D44—28no—
91C22×D44C2312yes—
92C22×D44C2312yes—
93C22×D44C2312yes—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—48no—
101C2×C11×M16C2314yes—
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D411yescharacteristic
105C2×C42×C11D411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114#67006—22no—
115#66983—21no—
116#66983—21no—
117#66983—21no—
118#66983—21no—
119#66983C2312yes—
120#66983C2312yes—
121#66982—22no—
122#66982—22no—
123#66982—22no—
124C4×C22⋊D11—22no—
125C4×C22⋊D11—22no—
126C4×C22⋊D11—22no—
127C4×C22⋊D11—22no—
128C4×C22⋊D11—22no—
129C4×C22⋊D11—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136#66979—21no—
137#66979—21no—
138#66979C2312yes—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145#66977—21no—
146#66977—21no—
147#66977—21no—
148#66977—21no—
149#66977C2312yes—
150#66977C2312yes—
151#66961—216no—
152C2×D88C2318yes—
153C2×#4314C2318yes—
154#66929—22no—
155#66929—22no—
156#66928—21no—
157#66928—21no—
158#66928C2312yescomplemented
159#66927C2311yescharacteristic, complemented
160C4×D44—22no—
161C4×D44—22no—
162C4×D44—22no—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44—22no—
166C4×D44—22no—
167C4×D44—22no—
168C4×D44—22no—
169C4×D44—22no—
170C4×D44—22no—
171C4×D44—22no—
172C4×D44—21no—
173C4×D44—21no—
174C4×D44—21no—
175C4×D44—21no—
176C4×D44C2314yes—
177C4×D44C2314yes—
178C4×D44C2314yes—
179C4×D44C2314yes—
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
198C11×C4⋊C8C2314yescomplemented
199C11×C4⋊C8C2314yescomplemented
200C11×C22⋊C8C2314yes—
201C11×C22⋊C8C2314yes—
202C11×#97C2314yescomplemented
203C4×C8×C11C2314yescomplemented
204#66885C2318yes—
205#66885C2318yes—
206#66885C2318yescomplemented
207#66882C2318yescomplemented
208#66881C2318yescomplemented
209#66880C2318yescomplemented
210#60558—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—28no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—44no—
217C23×D11—44no—
218C22×C4×C11—24no—
219C22×C4×C11—24no—
220C22×C4×C11—42no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2411yescharacteristic
237C22×C4×C11C2411yescharacteristic
238C22×C4×C11C2411yescharacteristic
239C2×C22⋊D11—22no—
240C2×C22⋊D11—22no—
241C2×C22⋊D11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—44no—
246#4339—28no—
247#4339—44no—
248#4339—44no—
249C2×D44—28no—
250C2×D44—28no—
251C2×D44—28no—
252C2×D44—28no—
253C2×D44—28no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—21no—
258C2×D44—21no—
259C2×D44—24no—
260C2×D44#4118yescomplemented
261C2×D44C2412yes—
262C2×D44C2414yes—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—24no—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×C4×D11—24no—
270C2×C4×D11—48no—
271C2×C4×D11—48no—
272C2×C4×D11—48no—
273C2×C4×D11—48no—
274C2×C4×D11—48no—
275C2×C4×D11—48no—
276C2×Dic22—21no—
277C2×Dic22—21no—
278C2×Dic22C2412yes—
279C11×M16—28no—
280C2×C8×C11C2418yes—
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D411yescharacteristic
292C42×C11C2×D411yescharacteristic
293C42×C11C2411yescharacteristic
294C42×C11C2411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C22⋊Dic11—22no—
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—21no—
313C4⋊Dic11—21no—
314C4⋊Dic11—22no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11C2414yes—
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—
329D88—216no—
330#4314—216no—
331#3444—111no—
332C22×C4×D4—111no—
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#2920D1111yescharacteristic, complemented
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11C22×D411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C22×D11—28no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—24no—
355C22×D11—22no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—432no—
359C22×D11—44no—
360C22×D11—44no—
361C22×D11—44no—
362C22×D11—44no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
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—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11AGL(1,ℤ/8)14yescomplemented
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C2×#4114yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—44no—
394C22⋊D11—44no—
395C22⋊D11—44no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—44no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403D44—28no—
404D44—28no—
405D44—28no—
406D44—24no—
407D44—24no—
408D44—42no—
409D44—42no—
410D44C2×#4118yes—
411C4×D11—48no—
412C4×D11—48no—
413C4×D11—44no—
414C4×D11—44no—
415C4×D11—48no—
416C4×D11—48no—
417C4×D11—44no—
418Dic22—24no—
419Dic22—42no—
420Dic22—42no—
421C8×C11—28no—
422C23×D4—111no—
423C24×C4—221no—
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—112no—
444C2×C4×D4—112no—
445C2×C4×D4—112no—
446C2×C4×D4—112no—
447C2×C4×D4—112no—
448C2×C4×D4—112no—
449C2×C4×D4—221no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4—221no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455C22×C4⋊C4—111no—
456C22×C22⋊C4—221no—
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#432C2×D1112yescomplemented
477#432C2×D1112yescomplemented
478#431C2×D1112yescomplemented
479#431C2×D1112yescomplemented
480#428—114no—
481#423C2×D1112yescomplemented
482#418—114no—
483#417—114no—
484#407C2×D1112yes—
485C4×M16C2×D1112yescomplemented
486C22×C11—28no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11#52512yes—
494C22×C11C2×AGL(1,ℤ/8)12yes—
495C22×C11#57512yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—28no—
498C2×D11—416no—
499C2×D11—416no—
500C2×D11—416no—
501C2×D11—44no—
502C2×D11—44no—
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#52512yes—
515C4×C11C2×AGL(1,ℤ/8)12yes—
516C4×C11C2×AGL(1,ℤ/8)12yes—
517C4×C11C22×#4112yes—
518Dic11—42no—
519Dic11—42no—
520Dic11—44no—
521Dic11—42no—
522C25—221no—
523C2×#41—112no—
524C2×#41—221no—
525C2×#41—221no—
526C22×D4—112no—
527C22×D4—112no—
528C22×D4—112no—
529C22×D4—228no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—221no—
533C23×C4—221no—
534C23×C4—222no—
535C23×C4—222no—
536C23×C4—222no—
537C23×C4—222no—
538C23×C4—222no—
539C23×C4—222no—
540C23×C4—448no—
541C23×C4D4411yescharacteristic
542C23×C4D4411yescharacteristic
543C23×C4C22×D1111yescharacteristic
544AGL(1,ℤ/8)—2216no—
545C2×SD16—118no—
546C2×D8—118no—
547C2×M16C22×D1114yes—
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—114no—
583C4×D4—114no—
584C4×D4—114no—
585C4×D4—114no—
586C4×D4—112no—
587C4×D4—112no—
588C4×D4—222no—
589C4×D4—222no—
590C4×D4—222no—
591C4×D4—222no—
592C4×D4—222no—
593C4×D4—222no—
594C4×D4—222no—
595C4×D4—222no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—221no—
609C4×D4—221no—
610#117—112no—
611#117—221no—
612#117—221no—
613#117—222no—
614#117—222no—
615#117—222no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C42—222no—
629C2×C42D4411yescharacteristic
630C2×C42D4411yescharacteristic
631C2×C42D4411yescharacteristic
632C2×C42D4411yescharacteristic
633C2×C42D4411yescharacteristic
634C2×C42D4411yescharacteristic
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⋊C8C22×D1114yescomplemented
644C4⋊C8C22×D1114yescomplemented
645#103—118no—
646#102—118no—
647#102—118no—
648#102—118no—
649C22⋊C8C22×D1114yes—
650C22⋊C8C22×D1114yes—
651#97C22×D1114yescomplemented
652C4×C8C22×D1114yescomplemented
653C2×C11—22no—
654C2×C11—22no—
655C2×C11—22no—
656C2×C11C2×#52511yescharacteristic
657C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
658C2×C11C2×#57511yescharacteristic
659D11—48no—
660D11—82no—
661C24—228no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—444no—
666C24—444no—
667C24C2×D4411yescharacteristic
668#41—228no—
669#41—444no—
670#41—444no—
671C2×Q8—112no—
672C2×Q8—221no—
673C2×Q8—221no—
674C2×D4—118no—
675C2×D4—114no—
676C2×D4—112no—
677C2×D4—228no—
678C2×D4—228no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—228no—
682C2×D4—222no—
683C2×D4—222no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—221no—
689C2×D4—221no—
690C2×D4—224no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—224no—
700C22×C4—224no—
701C22×C4—224no—
702C22×C4—222no—
703C22×C4—224no—
704C22×C4—448no—
705C22×C4—448no—
706C22×C4—448no—
707C22×C4—448no—
708C22×C4—448no—
709C22×C4—444no—
710C22×C4—448no—
711C22×C4C2×D4411yescharacteristic
712C22×C4C2×D4411yescharacteristic
713C22×C4C2×D4411yescharacteristic
714C22×C4C2×D4411yescharacteristic
715C22×C4C2×D4411yescharacteristic
716C22×C4C2×D4411yescharacteristic
717C22×C4C2×D4411yescharacteristic
718C22×C4C2×D4411yescharacteristic
719C22×C4C2×D4411yescharacteristic
720C22×C4C2×D4411yescharacteristic
721C22×C4C2×D4411yescharacteristic
722C22×C4C2×D4411yescharacteristic
723C22×C4C2×D4411yescharacteristic
724C22×C4C2×D4411yescharacteristic
725C22×C4C2×D4411yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729SD16—2216no—
730D8—2216no—
731M16—28no—
732C2×C8C23×D1118yes—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—114no—
736C4⋊C4—222no—
737C4⋊C4—222no—
738C4⋊C4—222no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—221no—
742C4⋊C4—221no—
743C4⋊C4—221no—
744C4⋊C4—221no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—224no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
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×D4411yescharacteristic
766C42C2×D4411yescharacteristic
767C42C2×D4411yescharacteristic
768C42C2×D4411yescharacteristic
769C42C2×D4411yescharacteristic
770C42C2×D4411yescharacteristic
771C42C2×D4411yescharacteristic
772C42C2×D4411yescharacteristic
773C42C2×D4411yescharacteristic
774C42C2×D4411yescharacteristic
775C42C2×D4411yescharacteristic
776C42C2×D4411yescharacteristic
777C42C23×D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C42C23×D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C11#6055811yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—228no—
786C23—228no—
787C23—228no—
788C23—224no—
789C23—222no—
790C23—444no—
791C23—444no—
792C23—4432no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23—444no—
797C23C22×D4411yescharacteristic
798C23C22×D4411yescharacteristic
799C23C22×D4411yescharacteristic
800Q8—224no—
801Q8—442no—
802Q8—442no—
803D4—118no—
804D4—228no—
805D4—228no—
806D4—228no—
807D4—224no—
808D4—224no—
809D4—442no—
810D4—444no—
811D4—444no—
812D4—444no—
813D4—442no—
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—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—224no—
834C2×C4—448no—
835C2×C4—448no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4—444no—
839C2×C4—444no—
840C2×C4—448no—
841C2×C4—448no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4#6696114yescomplemented
845C2×C4C22×D4411yescharacteristic
846C2×C4C22×D4411yescharacteristic
847C2×C4C22×D4411yescharacteristic
848C2×C4C22×D4411yescharacteristic
849C2×C4C22×D4411yescharacteristic
850C2×C4C22×D4411yescharacteristic
851C2×C4C22×D4411yescharacteristic
852C2×C4C22×D4411yescharacteristic
853C2×C4C22×D4411yescharacteristic
854C2×C4C22×D4411yescharacteristic
855C2×C4C22×D4411yescharacteristic
856C2×C4#41×D1114yes—
857C2×C4C24×D1111yescharacteristic
858C8—28no—
859C22—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—228no—
867C22—4416no—
868C22—4416no—
869C22—4416no—
870C22—444no—
871C22—444no—
872C22—442no—
873C22—442no—
874C22—442no—
875C22#1062305512yes—
876C22C2×#6696112yes—
877C22#1062327912yes—
878C22C23×D4411yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—442no—
888C4—444no—
889C4—442no—
890C4—442no—
891C4#1062305512yes—
892C4C2×#6696112yes—
893C4C2×#6696112yes—
894C4C2×#41×D1112yes—
895C2—22no—
896C2—22no—
897C2—22no—
898C2—448no—
899C2—882no—
900C2C2×#1062305511yescharacteristic
901C2C22×#6696111yescharacteristic
902C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
hypercenter#2920D11
hypocenterC11#60558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. C22×C4×D44C2semidirect
3. #13078756C2semidirect
4. #13078716C2semidirect
5. #13078708C2semidirect
6. #13078665C2semidirect
7. #13078625C2semidirect
8. #13078617C2semidirect
9. #13078541C2semidirect
10. #13078415C2semidirect
11. #13078082C2semidirect
12. #13077846C2semidirect
13. C4×#66961C2semidirect
14. C11×#2920C2semidirect
28. #10623010C22semidirect
29. #10623010C22semidirect
30. #10623008C22semidirect
31. #10623008C22semidirect
32. #10623008C22semidirect
35. C4×#4339C22semidirect
48. #10623001C22semidirect
49. #10623001C22semidirect
50. #10623001C22semidirect
51. C11×#432C22semidirect
52. C11×#432C22semidirect
53. C11×#431C22semidirect
54. C11×#431C22semidirect
55. C11×#423C22semidirect
57. C4×C11×M16C22semidirect
58. #10622746C22semidirect
60. #10622734C22semidirect
61. #10622460C22semidirect
62. #10622459C22semidirect
63. #10622457C22semidirect
64. #10622456C22semidirect
65. #10622455C22semidirect
66. #10622454C22semidirect
67. #10622349C22semidirect
68. #10622348C22semidirect
73. #10622335C22semidirect
74. #10622334C22semidirect
75. #10622324C22semidirect
76. #10622323C22semidirect
77. C4×D88C22semidirect
78. C4×#4314C22semidirect
158. #66928C23semidirect
159. #66927C23semidirect
180. C4×D44C23semidirect
181. C4×D44C23semidirect
188. #66923C23semidirect
189. #66922C23semidirect
190. #66922C23semidirect
191. #66922C23semidirect
196. C4×Dic22C23semidirect
197. C4×Dic22C23semidirect
198. C11×C4⋊C8C23semidirect
199. C11×C4⋊C8C23semidirect
202. C11×#97C23semidirect
203. C4×C8×C11C23semidirect
206. #66885C23semidirect
207. #66882C23semidirect
208. #66881C23semidirect
209. #66880C23semidirect
260. C2×D44#41semidirect
344. #2920D11semidirect
379. C2×C4×C11AGL(1,ℤ/8)semidirect
476. #432C2×D11semidirect
477. #432C2×D11semidirect
478. #431C2×D11semidirect
479. #431C2×D11semidirect
481. #423C2×D11semidirect
485. C4×M16C2×D11semidirect
643. C4⋊C8C22×D11semidirect
644. C4⋊C8C22×D11semidirect
651. #97C22×D11semidirect
652. C4×C8C22×D11semidirect
781. C11#60558semidirect
844. C2×C4#66961semidirect

Maximal subgroups

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

subgroupindex
#130819122
C22×C4×D442
#130787562
#130787162
#130787082
#130786652
#130786252
#130786172
#130785412
#130784152
#130780822
#130778462
C4×#669612
C11×#29202
#6055811