Finite Group Databasebeta

← #15622208

Subgroups — #15622208

Order 2816.

2428 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3#13078768C214yesmaximal, complemented
4#13078739C212yesmaximal, complemented
5#13078708C212yesmaximal, complemented
6#13078677C214yesmaximal, complemented
7#13078648C212yesmaximal, complemented
8#13078617C212yesmaximal, complemented
9#13078557C212yesmaximal, complemented
10#13078432C212yesmaximal, complemented
11#13078097C212yesmaximal, complemented
12#13077870C212yesmaximal, complemented
13C4×#66961C214yesmaximal, complemented
14C11×#2920C211yesmaximal, characteristic, complemented
15C22×#4339—21no—
16C22×#4339C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C2×#66983—21no—
19C2×#66983C2212yes—
20C2×C4×C22⋊D11—21no—
21C2×C4×C22⋊D11—21no—
22C2×#66979C2211yescharacteristic
23C2×#66961C2214yes—
24#10623008—21no—
25#10623008—21no—
26#10623008—21no—
27#10623008—21no—
28#10623008C2212yes—
29#10623008C2212yes—
30#10623008C2212yescomplemented
31#10623008C2212yescomplemented
32C2×#66928—21no—
33C2×#66927C2211yescharacteristic, complemented
34C4×#4339—21no—
35C4×#4339—21no—
36C4×#4339—21no—
37C4×#4339—21no—
38C4×#4339C2212yes—
39C4×#4339C2212yes—
40C4×#4339C2212yescomplemented
41C4×#4339C2212yescomplemented
42C2×C4×D44—21no—
43C2×C4×D44C2212yescomplemented
44C2×C4×D44C2211yescharacteristic, complemented
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66925—21no—
47C2×C42×D11—21no—
48C2×#66922C2211yescharacteristic, complemented
49C2×C4×Dic22C2211yescharacteristic, complemented
50C2×C4×Dic22C2211yescharacteristic, complemented
51C11×#432C2212yescomplemented
52C11×#432C2212yescomplemented
53C11×#431C2212yescomplemented
54C11×#431C2212yescomplemented
55C11×#423C2212yescomplemented
56C11×#407C2212yes—
57C4×C11×M16C2212yescomplemented
58#10622746C2214yes—
59#10622744C2214yescomplemented
60#10622734C2214yescomplemented
61#10622464C2214yescomplemented
62#10622463C2214yescomplemented
63#10622461C2214yescomplemented
64#10622461C2214yescomplemented
65#10622459C2214yescomplemented
66#10622456C2214yescomplemented
67#10622456C2214yescomplemented
68#10622455C2214yescomplemented
69#10622351C2214yescomplemented
70#10622350C2218yescomplemented
71#10622349C2214yescomplemented
72#10622348C2214yescomplemented
73#10622347C2218yescomplemented
74#10622345C2214yescomplemented
75#10622324C2218yescomplemented
76#10622323C2218yescomplemented
77C4×D88C2218yescomplemented
78C4×#4314C2218yescomplemented
79C23×C4×C11D411yescharacteristic
80C23×C4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—22no—
84C2×#4339—21no—
85C2×#4339—21no—
86C2×#4339—28no—
87C2×#4339—22no—
88C2×#4339—22no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—48no—
92C2×#4339C2312yes—
93C2×#4339C2312yes—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44C2312yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—22no—
102C22×Dic22—21no—
103C22×Dic22C2311yescharacteristic
104C2×C11×M16C2314yes—
105C2×C42×C11D411yescharacteristic
106C2×C42×C11D411yescharacteristic
107C2×C42×C11D411yescharacteristic
108C2×C42×C11D411yescharacteristic
109C2×C42×C11D411yescharacteristic
110C2×C42×C11D411yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11—21no—
118#66983—22no—
119#66983—22no—
120#66983—22no—
121#66983—22no—
122#66983—22no—
123#66983—22no—
124#66983C2314yes—
125#66983C2314yes—
126C4×C22⋊D11—22no—
127C4×C22⋊D11—22no—
128C4×C22⋊D11—22no—
129C4×C22⋊D11—22no—
130C4×C22⋊D11—22no—
131C4×C22⋊D11—22no—
132C4×C22⋊D11—22no—
133C4×C22⋊D11—22no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138#66979—21no—
139#66979—21no—
140#66979C2312yes—
141#66979C2312yes—
142C2×C4⋊Dic11—21no—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151#66961—216no—
152C2×D88C2318yes—
153C2×#4314C2318yes—
154#66928—22no—
155#66928—22no—
156#66928—22no—
157#66928—22no—
158#66927—21no—
159#66927—21no—
160#66927C2312yes—
161#66927C2312yes—
162C4×D44—22no—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44—22no—
166C4×D44—21no—
167C4×D44—21no—
168C4×D44—21no—
169C4×D44—21no—
170C4×D44—22no—
171C4×D44—22no—
172C4×D44C2312yes—
173C4×D44C2312yes—
174C4×D44C2312yes—
175C4×D44C2312yes—
176C4×D44C2314yes—
177C4×D44C2314yes—
178#66925—22no—
179#66925—22no—
180#66925—22no—
181#66925—22no—
182C42×D11—22no—
183C42×D11—22no—
184C42×D11—22no—
185C42×D11—22no—
186#66922—21no—
187#66922—21no—
188#66922C2312yes—
189#66922C2312yes—
190C4×Dic22—21no—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22C2312yes—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197C4×Dic22C2312yes—
198C11×C4⋊C8C2314yes—
199C11×C4⋊C8C2314yes—
200C11×C22⋊C8C2314yes—
201C11×C22⋊C8C2314yes—
202C11×#97C2314yes—
203C4×C8×C11C2314yes—
204#66885C2318yes—
205#66885C2318yes—
206#66885C2318yes—
207#66882C2318yes—
208#66881C2318yes—
209#66880C2318yes—
210#60561—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—21no—
213C23×D11—22no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—42no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—28no—
236C2×C22⋊D11—22no—
237C2×C22⋊D11—22no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—48no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—22no—
245#4339—28no—
246#4339—28no—
247#4339—24no—
248#4339—24no—
249#4339—24no—
250#4339—48no—
251#4339—48no—
252#4339—48no—
253#4339—48no—
254#4339#4118yescomplemented
255C2×D44—24no—
256C2×D44—21no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—28no—
263C2×D44—44no—
264C2×D44—44no—
265C2×D44C2414yes—
266C2×D44C2412yes—
267C2×C4×D11—28no—
268C2×C4×D11—22no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—24no—
275C2×C4×D11—24no—
276C2×C4×D11—44no—
277C2×C4×D11—48no—
278C2×C4×D11—44no—
279C2×Dic22—24no—
280C2×Dic22—21no—
281C2×Dic22—22no—
282C2×Dic22—22no—
283C2×Dic22—44no—
284C2×Dic22C2412yes—
285C11×M16—28no—
286C2×C8×C11C2418yes—
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—
305(C2×D11)⋊C4—22no—
306(C2×D11)⋊C4—22no—
307(C2×D11)⋊C4—22no—
308(C2×D11)⋊C4—22no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2412yes—
320C4⋊Dic11C2412yes—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324Dic11⋊C4—22no—
325C4×Dic11—22no—
326C4×Dic11—22no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11—22no—
331D88—216no—
332#4314—216no—
333C2×#532—111no—
334C2×C4×#41—111no—
335#3115—114no—
336#3112—112no—
337#3109—112no—
338#3106—114no—
339#3103—112no—
340#3100—112no—
341#3094—112no—
342#3079—112no—
343#3038—112no—
344#3006—112no—
345C4×AGL(1,ℤ/8)—114no—
346#2920D1111yescharacteristic, complemented
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—41no—
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C22×D11—24no—
354C22×D11—22no—
355C22×D11—24no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—44no—
359C22×D11—44no—
360C22×D11—44no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
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—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11AGL(1,ℤ/8)14yescomplemented
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
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×C11C2×#4114yes—
390C2×C4×C11C2511yescharacteristic
391C22⋊D11—28no—
392C22⋊D11—28no—
393C22⋊D11—48no—
394C22⋊D11—48no—
395C2×Dic11—24no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—44no—
401C2×Dic11—42no—
402C2×Dic11—42no—
403D44—24no—
404D44—22no—
405D44—28no—
406D44—44no—
407D44—44no—
408D44—44no—
409D44—44no—
410D44—44no—
411D44C2×#4114yescomplemented
412C4×D11—28no—
413C4×D11—28no—
414C4×D11—44no—
415C4×D11—48no—
416C4×D11—44no—
417C4×D11—44no—
418C4×D11—48no—
419C4×D11—44no—
420Dic22—24no—
421Dic22—22no—
422Dic22—44no—
423Dic22—44no—
424Dic22C2×#4114yescomplemented
425C8×C11—28no—
426C22×#41—111no—
427C22×#41—221no—
428C2×AGL(1,ℤ/8)—114no—
429#532—112no—
430#532—112no—
431#532—112no—
432#532—112no—
433#532—221no—
434#532—221no—
435#532—221no—
436#532—221no—
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439C2×#124—221no—
440C2×#121—112no—
441C2×#121—221no—
442C4×#41—112no—
443C4×#41—112no—
444C4×#41—112no—
445C4×#41—112no—
446C4×#41—221no—
447C4×#41—221no—
448C4×#41—221no—
449C4×#41—221no—
450C2×C4×Q8—111no—
451C2×C4×Q8—111no—
452C2×C4×D4—111no—
453C2×C4×D4—111no—
454C2×C4×D4—112no—
455C2×C4×D4—221no—
456C2×C4×D4—221no—
457C2×C4×D4—221no—
458C2×#117—111no—
459C2×#117—221no—
460C22×C42—221no—
461C22×C42C2×D1111yescharacteristic
462#482—118no—
463#481—114no—
464#480—114no—
465#477—114no—
466#476—114no—
467#475—114no—
468#474—114no—
469#460—114no—
470#460—114no—
471#459—114no—
472#459—114no—
473#449—118no—
474#448—114no—
475#447—114no—
476#442—118no—
477#440—118no—
478C4×SD16—118no—
479C4×D8—118no—
480#432C2×D1112yescomplemented
481#432C2×D1112yescomplemented
482#431C2×D1112yescomplemented
483#431C2×D1112yescomplemented
484#428—114no—
485#423C2×D1112yescomplemented
486#418—114no—
487#417—114no—
488#407C2×D1112yes—
489C4×M16C2×D1112yescomplemented
490C22×C11—21no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—21no—
494C22×C11—21no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—44no—
498C22×C11#52512yes—
499C22×C11C2×AGL(1,ℤ/8)12yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—24no—
502C2×D11—48no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—44no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—88no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—21no—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—21no—
516C4×C11#52512yes—
517C4×C11C2×AGL(1,ℤ/8)12yes—
518C4×C11C2×AGL(1,ℤ/8)12yes—
519C4×C11#57512yes—
520C4×C11C22×#4112yes—
521Dic11—24no—
522Dic11—44no—
523Dic11—42no—
524Dic11—42no—
525C2×#41—112no—
526C2×#41—112no—
527C2×#41—228no—
528C2×#41—221no—
529C2×#41—221no—
530C2×#41—222no—
531C2×#41—222no—
532C2×#41—222no—
533C2×#41—222no—
534C2×#41—448no—
535C22×Q8—111no—
536C22×Q8—221no—
537C22×D4—111no—
538C22×D4—112no—
539C22×D4—221no—
540C22×D4—222no—
541C22×D4—221no—
542C22×D4—221no—
543C23×C4—221no—
544C23×C4—222no—
545C23×C4—221no—
546C23×C4—221no—
547C23×C4D4411yescharacteristic
548C23×C4D4411yescharacteristic
549C23×C4C22×D1111yescharacteristic
550AGL(1,ℤ/8)—2216no—
551C2×SD16—118no—
552C2×D8—118no—
553C2×M16C22×D1114yes—
554C4⋊Q8—112no—
555C4⋊Q8—112no—
556C4⋊Q8—221no—
557C4⋊Q8—221no—
558#127—112no—
559#127—112no—
560#127—221no—
561#127—221no—
562#124—222no—
563#124—222no—
564#124—222no—
565#124—222no—
566#121—114no—
567#121—114no—
568#121—222no—
569#121—222no—
570#121—222no—
571#121—222no—
572#121—222no—
573#121—222no—
574C4×Q8—112no—
575C4×Q8—112no—
576C4×Q8—112no—
577C4×Q8—112no—
578C4×Q8—221no—
579C4×Q8—221no—
580C4×Q8—221no—
581C4×Q8—221no—
582C4×D4—112no—
583C4×D4—112no—
584C4×D4—112no—
585C4×D4—112no—
586C4×D4—114no—
587C4×D4—114no—
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—221no—
597C4×D4—221no—
598C4×D4—221no—
599C4×D4—221no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606#117—112no—
607#117—112no—
608#117—221no—
609#117—221no—
610#117—222no—
611#117—222no—
612#117—222no—
613#117—222no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—111no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—221no—
618C2×C4⋊C4—221no—
619C2×C4⋊C4—221no—
620C2×C22⋊C4—221no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C42—221no—
626C2×C42—221no—
627C2×C42—221no—
628C2×C42—222no—
629C2×C42—222no—
630C2×C42—222no—
631C2×C42—222no—
632C2×C42D4411yescharacteristic
633C2×C42D4411yescharacteristic
634C2×C42D4411yescharacteristic
635C2×C42D4411yescharacteristic
636C2×C42D4411yescharacteristic
637C2×C42D4411yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640C2×C42C22×D1111yescharacteristic
641C2×C42C22×D1111yescharacteristic
642C2×C42C22×D1111yescharacteristic
643C2×C42C22×D1111yescharacteristic
644#107—118no—
645#106—118no—
646C4⋊C8C22×D1114yes—
647C4⋊C8C22×D1114yes—
648#103—118no—
649#102—118no—
650#102—118no—
651#102—118no—
652C22⋊C8C22×D1114yes—
653C22⋊C8C22×D1114yes—
654#97C22×D1114yes—
655C4×C8C22×D1114yes—
656C2×C11—22no—
657C2×C11—22no—
658C2×C11—41no—
659C2×C11C2×#52511yescharacteristic
660C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
661C2×C11C2×#57511yescharacteristic
662D11—44no—
663D11—84no—
664C24—221no—
665C24—222no—
666C24C2×D4411yescharacteristic
667#41—118no—
668#41—224no—
669#41—224no—
670#41—228no—
671#41—228no—
672#41—224no—
673#41—448no—
674#41—448no—
675#41—448no—
676#41—448no—
677C2×Q8—112no—
678C2×Q8—224no—
679C2×Q8—221no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8—444no—
683C2×D4—112no—
684C2×D4—114no—
685C2×D4—224no—
686C2×D4—228no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—224no—
690C2×D4—224no—
691C2×D4—221no—
692C2×D4—222no—
693C2×D4—222no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—222no—
697C2×D4—228no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—448no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—42no—
704C22×C4—228no—
705C22×C4—221no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—224no—
715C22×C4—222no—
716C22×C4—224no—
717C22×C4—448no—
718C22×C4—444no—
719C22×C4—444no—
720C22×C4C2×D4411yescharacteristic
721C22×C4C2×D4411yescharacteristic
722C22×C4C2×D4411yescharacteristic
723C22×C4C2×D4411yescharacteristic
724C22×C4C2×D4411yescharacteristic
725C22×C4C2×D4411yescharacteristic
726C22×C4C2×D4411yescharacteristic
727C22×C4C2×D4411yescharacteristic
728C22×C4C2×D4411yescharacteristic
729C22×C4C2×D4411yescharacteristic
730C22×C4C2×D4411yescharacteristic
731C22×C4C2×D4411yescharacteristic
732C22×C4C2×D4411yescharacteristic
733C22×C4C2×D4411yescharacteristic
734C22×C4C2×D4411yescharacteristic
735C22×C4C23×D1111yescharacteristic
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738SD16—2216no—
739D8—2216no—
740M16—28no—
741C2×C8C23×D1118yes—
742C4⋊C4—112no—
743C4⋊C4—112no—
744C4⋊C4—114no—
745C4⋊C4—221no—
746C4⋊C4—221no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—222no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C22⋊C4—222no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C42—222no—
765C42—222no—
766C42—222no—
767C42—222no—
768C42—222no—
769C42—222no—
770C42C2×D4411yescharacteristic
771C42C2×D4411yescharacteristic
772C42C2×D4411yescharacteristic
773C42C2×D4411yescharacteristic
774C42C2×D4411yescharacteristic
775C42C2×D4411yescharacteristic
776C42C2×D4411yescharacteristic
777C42C2×D4411yescharacteristic
778C42C2×D4411yescharacteristic
779C42C2×D4411yescharacteristic
780C42C2×D4411yescharacteristic
781C42C2×D4411yescharacteristic
782C42C23×D1111yescharacteristic
783C42C23×D1111yescharacteristic
784C42C23×D1111yescharacteristic
785C42C23×D1111yescharacteristic
786C11#6056111yescharacteristic, complemented, Sylow
787C23—22no—
788C23—22no—
789C23—41no—
790C23—224no—
791C23—222no—
792C23—224no—
793C23—442no—
794C23—444no—
795C23—444no—
796C23—442no—
797C23—444no—
798C23C22×D4411yescharacteristic
799C23C22×D4411yescharacteristic
800C23C22×D4411yescharacteristic
801Q8—114no—
802Q8—224no—
803Q8—222no—
804Q8—444no—
805Q8—444no—
806D4—114no—
807D4—224no—
808D4—228no—
809D4—228no—
810D4—222no—
811D4—228no—
812D4—444no—
813D4—444no—
814D4—448no—
815D4—448no—
816D4—444no—
817D4—444no—
818D4—444no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—228no—
836C2×C4—224no—
837C2×C4—222no—
838C2×C4—228no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—224no—
842C2×C4—448no—
843C2×C4—444no—
844C2×C4—444no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—448no—
848C2×C4—444no—
849C2×C4—444no—
850C2×C4—444no—
851C2×C4#6696114yescomplemented
852C2×C4C22×D4411yescharacteristic
853C2×C4C22×D4411yescharacteristic
854C2×C4C22×D4411yescharacteristic
855C2×C4C22×D4411yescharacteristic
856C2×C4C22×D4411yescharacteristic
857C2×C4C22×D4411yescharacteristic
858C2×C4C22×D4411yescharacteristic
859C2×C4C22×D4411yescharacteristic
860C2×C4C22×D4411yescharacteristic
861C2×C4C22×D4411yescharacteristic
862C2×C4C22×D4411yescharacteristic
863C2×C4#41×D1114yes—
864C2×C4C24×D1111yescharacteristic
865C8—28no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—44no—
874C22—224no—
875C22—448no—
876C22—442no—
877C22—442no—
878C22—444no—
879C22—444no—
880C22—444no—
881C22—888no—
882C22#1062305512yes—
883C22C2×#6696112yes—
884C22C23×D4411yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—224no—
893C4—444no—
894C4—442no—
895C4—442no—
896C4#1062305512yes—
897C4C2×#6696112yes—
898C4C2×#6696112yes—
899C4#1062327912yes—
900C4C2×#41×D1112yes—
901C2—22no—
902C2—22no—
903C2—41no—
904C2—444no—
905C2—884no—
906C2C2×#1062305511yescharacteristic
907C2C22×#6696111yescharacteristic
908C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
hypercenter#2920D11
hypocenterC11#60561
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. C2×#10623008C2semidirect
2. C2×C4×#4339C2semidirect
3. #13078768C2semidirect
4. #13078739C2semidirect
5. #13078708C2semidirect
6. #13078677C2semidirect
7. #13078648C2semidirect
8. #13078617C2semidirect
9. #13078557C2semidirect
10. #13078432C2semidirect
11. #13078097C2semidirect
12. #13077870C2semidirect
13. C4×#66961C2semidirect
14. C11×#2920C2semidirect
30. #10623008C22semidirect
31. #10623008C22semidirect
33. C2×#66927C22semidirect
40. C4×#4339C22semidirect
41. C4×#4339C22semidirect
43. C2×C4×D44C22semidirect
44. C2×C4×D44C22semidirect
45. C2×C4×D44C22semidirect
48. C2×#66922C22semidirect
49. C2×C4×Dic22C22semidirect
50. C2×C4×Dic22C22semidirect
51. C11×#432C22semidirect
52. C11×#432C22semidirect
53. C11×#431C22semidirect
54. C11×#431C22semidirect
55. C11×#423C22semidirect
57. C4×C11×M16C22semidirect
59. #10622744C22semidirect
60. #10622734C22semidirect
61. #10622464C22semidirect
62. #10622463C22semidirect
63. #10622461C22semidirect
64. #10622461C22semidirect
65. #10622459C22semidirect
66. #10622456C22semidirect
67. #10622456C22semidirect
68. #10622455C22semidirect
69. #10622351C22semidirect
70. #10622350C22semidirect
71. #10622349C22semidirect
72. #10622348C22semidirect
73. #10622347C22semidirect
74. #10622345C22semidirect
75. #10622324C22semidirect
76. #10622323C22semidirect
77. C4×D88C22semidirect
78. C4×#4314C22semidirect
254. #4339#41semidirect
346. #2920D11semidirect
377. C2×C4×C11AGL(1,ℤ/8)semidirect
411. D44C2×#41semidirect
424. Dic22C2×#41semidirect
480. #432C2×D11semidirect
481. #432C2×D11semidirect
482. #431C2×D11semidirect
483. #431C2×D11semidirect
485. #423C2×D11semidirect
489. C4×M16C2×D11semidirect
786. C11#60561semidirect
851. C2×C4#66961semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×C4×#43392
#130787682
#130787392
#130787082
#130786772
#130786482
#130786172
#130785572
#130784322
#130780972
#130778702
C4×#669612
C11×#29202
#6056111