Finite Group Databasebeta

← #15622178

Subgroups — #15622178

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2C2×C4×#4339C211yesmaximal, characteristic, complemented
3#13078779C212yesmaximal, complemented
4#13078768C212yesmaximal, complemented
5#13078727C214yesmaximal, complemented
6#13078688C212yesmaximal, complemented
7#13078677C212yesmaximal, complemented
8#13078636C214yesmaximal, complemented
9#13078549C212yesmaximal, complemented
10#13078423C211yesmaximal, characteristic, complemented
11#13078415C211yesmaximal, characteristic, complemented
12#13078090C211yesmaximal, characteristic, complemented
13#13078082C211yesmaximal, characteristic, complemented
14#13077861C212yesmaximal, complemented
15C4×#66962C212yesmaximal, complemented
16C4×#66961C212yesmaximal, complemented
17C11×#2920C211yesmaximal, characteristic, complemented
18C22×#4339C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20#10623322—21no—
21#10623322—21no—
22#10623322C2212yes—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11—21no—
25C2×#66979C2211yescharacteristic
26C2×#66962C2212yes—
27C2×#66961C2212yes—
28#10623010—21no—
29#10623010—21no—
30#10623010—21no—
31#10623010—21no—
32#10623010C2212yescomplemented
33#10623010C2212yescomplemented
34#10623008C2211yescharacteristic
35#10623008C2211yescharacteristic, complemented
36#10623008C2211yescharacteristic, complemented
37C4×#4339—21no—
38C4×#4339—21no—
39C4×#4339—21no—
40C4×#4339—21no—
41C4×#4339—21no—
42C4×#4339—21no—
43C4×#4339C2212yes—
44C4×#4339C2212yes—
45C4×#4339C2212yes—
46C4×#4339C2212yes—
47C4×#4339C2212yes—
48C2×C4×D44C2211yescharacteristic
49C2×C4×D44C2211yescharacteristic
50C2×#66925—21no—
51C2×C42×D11—21no—
52#10623001C2211yescharacteristic
53#10623001C2211yescharacteristic, complemented
54#10623001C2211yescharacteristic, complemented
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57C11×#432C2212yescomplemented
58C11×#432C2212yescomplemented
59C11×#431C2212yescomplemented
60C11×#431C2212yescomplemented
61C11×#423C2211yescharacteristic
62C11×#423C2211yescharacteristic
63C11×#407C2212yes—
64C4×C11×M16C2212yes—
65#10622746C2212yes—
66#10622746C2212yes—
67#10622744C2212yes—
68#10622734C2212yes—
69#10622734C2212yes—
70#10622733C2212yes—
71#10622464C2212yescomplemented
72#10622463C2212yescomplemented
73#10622462C2212yescomplemented
74#10622461C2212yescomplemented
75#10622460C2214yescomplemented
76#10622459C2212yescomplemented
77#10622458C2214yescomplemented
78#10622457C2214yescomplemented
79#10622456C2212yescomplemented
80#10622455C2212yescomplemented
81#10622454C2212yescomplemented
82#10622442C2214yescomplemented
83#10622350C2214yescomplemented
84#10622350C2214yescomplemented
85#10622347C2214yes—
86#10622347C2214yes—
87#10622346C2214yes—
88#10622346C2214yes—
89#10622336C2214yescomplemented
90#10622336C2214yescomplemented
91#10622329C2214yescomplemented
92#10622324C2214yescomplemented
93#10622323C2214yescomplemented
94#10622323C2214yescomplemented
95C4×Dic44C2214yescomplemented
96C4×D88C2214yescomplemented
97C4×#4314C2214yescomplemented
98C4×#4314C2214yescomplemented
99C23×C4×C11D411yescharacteristic
100C23×C4×C11D411yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C2×#4339—21no—
104C2×#4339—21no—
105C2×#4339—21no—
106C2×#4339—21no—
107C2×#4339—24no—
108C2×#4339—24no—
109C2×#4339C2312yes—
110C2×#4339C2312yes—
111C2×#4339C2312yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic
117C2×C11×M16C2312yes—
118C2×C11×M16C2312yes—
119C2×C42×C11D411yescharacteristic
120C2×C42×C11D411yescharacteristic
121C2×C42×C11D411yescharacteristic
122C2×C42×C11D411yescharacteristic
123C2×C42×C11D411yescharacteristic
124C2×C42×C11D411yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131#67006—22no—
132C2×C22⋊Dic11—21no—
133#66983—21no—
134#66983—21no—
135#66983—21no—
136#66983—21no—
137#66983C2312yes—
138#66983C2312yes—
139#66982—22no—
140#66982—22no—
141#66982—22no—
142C4×C22⋊D11—22no—
143C4×C22⋊D11—22no—
144C4×C22⋊D11—22no—
145C4×C22⋊D11—22no—
146C4×C22⋊D11—22no—
147C4×C22⋊D11—22no—
148C4×C22⋊D11—22no—
149C4×C22⋊D11—22no—
150C4×C22⋊D11—22no—
151C4×C22⋊D11—22no—
152C4×C22⋊D11—22no—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—22no—
155C4×C22⋊D11—22no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158#66979—21no—
159#66979—21no—
160#66979—21no—
161#66979—21no—
162#66979C2312yes—
163#66979C2312yes—
164#66979C2312yes—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167#66977—21no—
168#66977—21no—
169#66977—21no—
170#66977—21no—
171#66977C2312yes—
172#66977C2312yes—
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×C4×Dic11—21no—
176C2×C4×Dic11—21no—
177C2×C4×Dic11—21no—
178#66962—28no—
179#66961—28no—
180C2×Dic44C2314yes—
181C2×D88C2314yes—
182C2×#4314C2314yes—
183C2×#4314C2314yes—
184#66929—22no—
185#66929—22no—
186#66928—21no—
187#66928—21no—
188#66928C2312yes—
189#66927C2311yescharacteristic
190C4×D44—21no—
191C4×D44—21no—
192C4×D44—21no—
193C4×D44—21no—
194C4×D44—21no—
195C4×D44—21no—
196C4×D44—21no—
197C4×D44—21no—
198C4×D44C2312yes—
199C4×D44C2312yes—
200C4×D44C2312yes—
201C4×D44C2312yes—
202C4×D44C2312yes—
203C4×D44C2312yes—
204#66925—22no—
205#66925—22no—
206#66925—22no—
207#66925—22no—
208#66925—22no—
209#66925—22no—
210#66925—22no—
211C42×D11—22no—
212C42×D11—22no—
213C42×D11—22no—
214C42×D11—22no—
215C42×D11—22no—
216#66923—21no—
217#66923—21no—
218#66923C2312yes—
219#66922C2311yescharacteristic
220#66922C2311yescharacteristic
221#66922C2311yescharacteristic
222C4×Dic22—21no—
223C4×Dic22—21no—
224C4×Dic22—21no—
225C4×Dic22—21no—
226C4×Dic22—21no—
227C4×Dic22—21no—
228C4×Dic22—21no—
229C4×Dic22—21no—
230C4×Dic22C2312yes—
231C4×Dic22C2312yes—
232C4×Dic22C2312yes—
233C4×Dic22C2312yes—
234C4×Dic22C2312yes—
235C4×Dic22C2312yes—
236C11×C4⋊C8C2312yes—
237C11×C4⋊C8C2312yes—
238C11×C4⋊C8C2312yes—
239C11×C4⋊C8C2312yes—
240C11×C22⋊C8C2314yes—
241C11×C22⋊C8C2314yes—
242C11×#97C2314yes—
243C4×C8×C11C2314yes—
244#66885C2314yes—
245#66885C2314yes—
246#66885C2314yes—
247#66885C2314yes—
248#66882C2314yes—
249#66882C2314yes—
250#66881C2314yes—
251#66881C2314yes—
252#66880C2314yes—
253#66880C2314yes—
254#66880C2314yes—
255#66880C2314yes—
256#60559—111nomaximal, Sylow
257C24×C11C2×D411yescharacteristic
258C23×D11—21no—
259C22×C4×C11—22no—
260C22×C4×C11—22no—
261C22×C4×C11—42no—
262C22×C4×C11—42no—
263C22×C4×C11C2×D411yescharacteristic
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D411yescharacteristic
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2×D411yescharacteristic
270C22×C4×C11C2×D411yescharacteristic
271C22×C4×C11C2×D411yescharacteristic
272C22×C4×C11C2×D411yescharacteristic
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—28no—
282C2×C22⋊D11—22no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—22no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290#4339—28no—
291#4339—28no—
292#4339—24no—
293#4339—24no—
294#4339—24no—
295#4339—24no—
296#4339—24no—
297#4339—24no—
298#4339—44no—
299#4339—44no—
300C2×D44—21no—
301C2×D44—21no—
302C2×D44—21no—
303C2×D44—22no—
304C2×D44#4114yescomplemented
305C2×D44C2412yes—
306C2×D44C2412yes—
307C2×C4×D11—28no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×C4×D11—22no—
311C2×C4×D11—22no—
312C2×C4×D11—22no—
313C2×C4×D11—22no—
314C2×C4×D11—22no—
315C2×C4×D11—22no—
316C2×C4×D11—22no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×Dic22—21no—
320C2×Dic22—21no—
321C2×Dic22—21no—
322C2×Dic22—22no—
323C2×Dic22#4114yescomplemented
324C2×Dic22C2412yes—
325C2×Dic22C2412yes—
326C11×M16—24no—
327C11×M16—24no—
328C2×C8×C11C2414yes—
329C2×C8×C11C2414yes—
330C42×C11C2×D411yescharacteristic
331C42×C11C2×D411yescharacteristic
332C42×C11C2×D411yescharacteristic
333C42×C11C2×D411yescharacteristic
334C42×C11C2×D411yescharacteristic
335C42×C11C2×D411yescharacteristic
336C42×C11C2×D411yescharacteristic
337C42×C11C2×D411yescharacteristic
338C42×C11C2×D411yescharacteristic
339C42×C11C2×D411yescharacteristic
340C42×C11C2×D411yescharacteristic
341C42×C11C2×D411yescharacteristic
342C42×C11C2411yescharacteristic
343C42×C11C2411yescharacteristic
344C42×C11C2411yescharacteristic
345C42×C11C2411yescharacteristic
346C22⋊Dic11—22no—
347C22⋊Dic11—22no—
348C22⋊Dic11—22no—
349C22⋊Dic11—22no—
350C22⋊Dic11—22no—
351(C2×D11)⋊C4—22no—
352(C2×D11)⋊C4—22no—
353(C2×D11)⋊C4—22no—
354(C2×D11)⋊C4—22no—
355(C2×D11)⋊C4—22no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—22no—
358(C2×D11)⋊C4—22no—
359(C2×D11)⋊C4—22no—
360(C2×D11)⋊C4—22no—
361C4⋊Dic11—21no—
362C4⋊Dic11—21no—
363C4⋊Dic11—21no—
364C4⋊Dic11—21no—
365C4⋊Dic11—21no—
366C4⋊Dic11—21no—
367C4⋊Dic11C2412yes—
368C4⋊Dic11C2412yes—
369C4⋊Dic11C2412yes—
370C4⋊Dic11C2412yes—
371Dic11⋊C4—22no—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—22no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378Dic11⋊C4—22no—
379Dic11⋊C4—22no—
380Dic11⋊C4—22no—
381C4×Dic11—22no—
382C4×Dic11—22no—
383C4×Dic11—22no—
384C4×Dic11—22no—
385C4×Dic11—22no—
386C4×Dic11—22no—
387C4×Dic11—22no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390Dic44—28no—
391D88—28no—
392#4314—28no—
393#4314—28no—
394#3444—111no—
395C2×C4×#41—111no—
396#3116—112no—
397#3115—112no—
398#3111—114no—
399#3107—112no—
400#3106—112no—
401#3102—114no—
402#3093—112no—
403#3078—111no—
404#3077—111no—
405#3037—111no—
406#3036—111no—
407#3005—112no—
408C4×#137—112no—
409C4×AGL(1,ℤ/8)—112no—
410#2920D1111yescharacteristic, complemented
411C23×C11—22no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C22×D411yescharacteristic
417C22×D11—24no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—42no—
421C22×D11—42no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11C22×D411yescharacteristic
442C2×C4×C11C22×D411yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C22×D411yescharacteristic
446C2×C4×C11C22×D411yescharacteristic
447C2×C4×C11C22×D411yescharacteristic
448C2×C4×C11C22×D411yescharacteristic
449C2×C4×C11C22×D411yescharacteristic
450C2×C4×C11C22×D411yescharacteristic
451C2×C4×C11C22×D411yescharacteristic
452C2×C4×C11C2×#4112yes—
453C2×C4×C11C2×#4112yes—
454C2×C4×C11C2511yescharacteristic
455C22⋊D11—28no—
456C22⋊D11—28no—
457C22⋊D11—44no—
458C22⋊D11—44no—
459C22⋊D11—44no—
460C2×Dic11—24no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—42no—
468C2×Dic11—42no—
469D44—24no—
470D44—22no—
471D44—22no—
472D44—22no—
473D44—42no—
474D44—42no—
475D44C2×#4114yes—
476C4×D11—28no—
477C4×D11—28no—
478C4×D11—44no—
479C4×D11—44no—
480C4×D11—44no—
481C4×D11—44no—
482C4×D11—44no—
483C4×D11—44no—
484C4×D11—44no—
485Dic22—24no—
486Dic22—22no—
487Dic22—22no—
488Dic22—22no—
489Dic22—42no—
490Dic22—42no—
491Dic22C2×#4114yes—
492C8×C11—24no—
493C8×C11—24no—
494C22×#41—111no—
495C2×#137—112no—
496C2×AGL(1,ℤ/8)—112no—
497#533—111no—
498#533—111no—
499#533—111no—
500#532—111no—
501#532—111no—
502#532—111no—
503#529—112no—
504#529—112no—
505#529—221no—
506#529—221no—
507#529—221no—
508#529—221no—
509#525—112no—
510#525—221no—
511#525—221no—
512C4×#41—112no—
513C4×#41—112no—
514C4×#41—112no—
515C4×#41—112no—
516C4×#41—112no—
517C4×#41—221no—
518C4×#41—221no—
519C4×#41—221no—
520C4×#41—221no—
521C4×#41—221no—
522C4×#41—221no—
523C2×C4×Q8—111no—
524C2×C4×Q8—111no—
525C2×C4×D4—111no—
526C2×C4×D4—111no—
527C2×C4×D4—221no—
528C2×C4×D4—221no—
529C2×#117—111no—
530C2×#117—221no—
531C22×C42—221no—
532C22×C42C2×D1111yescharacteristic
533#485—114no—
534#485—114no—
535#482—114no—
536#482—114no—
537#479—114no—
538#478—114no—
539#477—112no—
540#476—112no—
541#475—112no—
542#474—112no—
543#464—114no—
544#463—114no—
545#462—112no—
546#461—112no—
547#460—112no—
548#459—112no—
549#452—114no—
550#452—114no—
551#449—114no—
552#449—114no—
553#442—114no—
554#441—114no—
555#440—114no—
556#440—114no—
557C4×Q16—114no—
558C4×SD16—114no—
559C4×SD16—114no—
560C4×D8—114no—
561#432C2×D1112yescomplemented
562#432C2×D1112yescomplemented
563#431C2×D1112yescomplemented
564#431C2×D1112yescomplemented
565#428—112no—
566#428—112no—
567#423C2×D1111yescharacteristic
568#423C2×D1111yescharacteristic
569#419—112no—
570#418—112no—
571#417—112no—
572#417—112no—
573#407C2×D1112yes—
574C4×M16C2×D1112yes—
575C22×C11—21no—
576C22×C11—21no—
577C22×C11—21no—
578C22×C11—21no—
579C22×C11—21no—
580C22×C11—21no—
581C22×C11—21no—
582C22×C11—21no—
583C22×C11—44no—
584C22×C11#52512yes—
585C22×C11C23×D411yescharacteristic
586C2×D11—24no—
587C2×D11—48no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C4×C11—21no—
594C4×C11—21no—
595C4×C11—21no—
596C4×C11—21no—
597C4×C11—21no—
598C4×C11—21no—
599C4×C11—21no—
600C4×C11—21no—
601C4×C11#52512yes—
602C4×C11#57512yes—
603C4×C11#57512yes—
604C4×C11C22×#4111yescharacteristic
605C4×C11C22×#4111yescharacteristic
606Dic11—24no—
607Dic11—42no—
608Dic11—42no—
609Dic11—42no—
610Dic11—42no—
611Dic11—42no—
612C2×#41—112no—
613C2×#41—112no—
614C2×#41—112no—
615C2×#41—224no—
616C2×#41—224no—
617C2×#41—221no—
618C2×#41—221no—
619C2×#41—221no—
620C2×#41—221no—
621C22×Q8—111no—
622C22×D4—111no—
623C22×D4—221no—
624C23×C4—221no—
625C23×C4—221no—
626C23×C4—221no—
627C23×C4D4411yescharacteristic
628C23×C4D4411yescharacteristic
629C23×C4C22×D1111yescharacteristic
630#137—228no—
631AGL(1,ℤ/8)—228no—
632C2×Q16—114no—
633C2×SD16—114no—
634C2×SD16—114no—
635C2×D8—114no—
636C2×M16C22×D1112yes—
637C2×M16C22×D1112yes—
638C4⋊Q8—111no—
639C4⋊Q8—111no—
640C4⋊Q8—111no—
641#127—111no—
642#126—222no—
643#126—222no—
644#125—112no—
645#125—221no—
646#125—221no—
647#124—112no—
648#124—221no—
649#124—221no—
650#123—222no—
651#123—222no—
652#123—222no—
653C22⋊Q8—112no—
654C22⋊Q8—112no—
655C22⋊Q8—221no—
656C22⋊Q8—221no—
657C22⋊Q8—221no—
658C22⋊Q8—221no—
659#121—112no—
660#121—112no—
661#121—221no—
662#121—221no—
663#121—221no—
664#121—221no—
665#120—222no—
666C4×Q8—112no—
667C4×Q8—112no—
668C4×Q8—112no—
669C4×Q8—112no—
670C4×Q8—112no—
671C4×Q8—112no—
672C4×Q8—221no—
673C4×Q8—221no—
674C4×Q8—221no—
675C4×Q8—221no—
676C4×Q8—221no—
677C4×Q8—221no—
678C4×Q8—221no—
679C4×Q8—221no—
680C4×D4—112no—
681C4×D4—112no—
682C4×D4—112no—
683C4×D4—112no—
684C4×D4—112no—
685C4×D4—112no—
686C4×D4—222no—
687C4×D4—222no—
688C4×D4—222no—
689C4×D4—222no—
690C4×D4—222no—
691C4×D4—222no—
692C4×D4—222no—
693C4×D4—222no—
694C4×D4—222no—
695C4×D4—222no—
696C4×D4—222no—
697C4×D4—222no—
698C4×D4—222no—
699C4×D4—222no—
700C4×D4—221no—
701C4×D4—221no—
702C4×D4—221no—
703C4×D4—221no—
704C4×D4—221no—
705C4×D4—221no—
706C4×D4—221no—
707C4×D4—221no—
708#117—112no—
709#117—112no—
710#117—112no—
711#117—221no—
712#117—221no—
713#117—221no—
714#117—221no—
715#117—222no—
716#117—222no—
717#117—222no—
718#117—222no—
719#117—222no—
720#117—222no—
721#117—222no—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—111no—
724C2×C4⋊C4—221no—
725C2×C4⋊C4—221no—
726C2×C22⋊C4—221no—
727C2×C22⋊C4—221no—
728C2×C22⋊C4—221no—
729C2×C42—221no—
730C2×C42—221no—
731C2×C42—221no—
732C2×C42—222no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737C2×C42D4411yescharacteristic
738C2×C42D4411yescharacteristic
739C2×C42D4411yescharacteristic
740C2×C42D4411yescharacteristic
741C2×C42D4411yescharacteristic
742C2×C42D4411yescharacteristic
743C2×C42C22×D1111yescharacteristic
744C2×C42C22×D1111yescharacteristic
745C2×C42C22×D1111yescharacteristic
746C2×C42C22×D1111yescharacteristic
747C2×C42C22×D1111yescharacteristic
748C2×C42C22×D1111yescharacteristic
749#107—114no—
750#107—114no—
751#106—114no—
752#106—114no—
753C4⋊C8C22×D1112yes—
754C4⋊C8C22×D1112yes—
755C4⋊C8C22×D1112yes—
756C4⋊C8C22×D1112yes—
757#103—114no—
758#103—114no—
759#103—114no—
760#103—114no—
761#102—114no—
762#102—114no—
763#102—114no—
764#102—114no—
765C22⋊C8C22×D1114yes—
766C22⋊C8C22×D1114yes—
767#97C22×D1114yes—
768C4×C8C22×D1114yes—
769C2×C11—22no—
770C2×C11—41no—
771C2×C11—41no—
772C2×C11C2×#52511yescharacteristic
773C2×C11C2×#57511yescharacteristic
774C2×C11C2×#57511yescharacteristic
775D11—44no—
776D11—82no—
777C24—221no—
778C24C2×D4411yescharacteristic
779#41—224no—
780#41—224no—
781#41—224no—
782#41—224no—
783#41—228no—
784#41—228no—
785#41—224no—
786#41—224no—
787#41—444no—
788#41—444no—
789C2×Q8—114no—
790C2×Q8—112no—
791C2×Q8—112no—
792C2×Q8—221no—
793C2×Q8—221no—
794C2×Q8—221no—
795C2×Q8—222no—
796C2×D4—114no—
797C2×D4—112no—
798C2×D4—112no—
799C2×D4—228no—
800C2×D4—222no—
801C2×D4—222no—
802C2×D4—222no—
803C2×D4—222no—
804C2×D4—222no—
805C2×D4—221no—
806C2×D4—221no—
807C2×D4—221no—
808C2×D4—222no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—228no—
814C22×C4—221no—
815C22×C4—222no—
816C22×C4—222no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—222no—
820C22×C4—222no—
821C22×C4—222no—
822C22×C4—222no—
823C22×C4—222no—
824C22×C4—222no—
825C22×C4—222no—
826C22×C4—444no—
827C22×C4—444no—
828C22×C4C2×D4411yescharacteristic
829C22×C4C2×D4411yescharacteristic
830C22×C4C2×D4411yescharacteristic
831C22×C4C2×D4411yescharacteristic
832C22×C4C2×D4411yescharacteristic
833C22×C4C2×D4411yescharacteristic
834C22×C4C2×D4411yescharacteristic
835C22×C4C2×D4411yescharacteristic
836C22×C4C2×D4411yescharacteristic
837C22×C4C2×D4411yescharacteristic
838C22×C4C2×D4411yescharacteristic
839C22×C4C2×D4411yescharacteristic
840C22×C4C2×D4411yescharacteristic
841C22×C4C2×D4411yescharacteristic
842C22×C4C2×D4411yescharacteristic
843C22×C4C23×D1111yescharacteristic
844C22×C4C23×D1111yescharacteristic
845C22×C4C23×D1111yescharacteristic
846Q16—228no—
847SD16—228no—
848SD16—228no—
849D8—228no—
850M16—24no—
851M16—24no—
852C2×C8C23×D1114yes—
853C2×C8C23×D1114yes—
854C4⋊C4—112no—
855C4⋊C4—112no—
856C4⋊C4—112no—
857C4⋊C4—112no—
858C4⋊C4—221no—
859C4⋊C4—221no—
860C4⋊C4—222no—
861C4⋊C4—222no—
862C4⋊C4—222no—
863C4⋊C4—222no—
864C4⋊C4—222no—
865C4⋊C4—222no—
866C4⋊C4—221no—
867C4⋊C4—221no—
868C4⋊C4—221no—
869C4⋊C4—221no—
870C4⋊C4—222no—
871C4⋊C4—222no—
872C4⋊C4—222no—
873C4⋊C4—222no—
874C22⋊C4—222no—
875C22⋊C4—222no—
876C22⋊C4—222no—
877C22⋊C4—222no—
878C22⋊C4—222no—
879C22⋊C4—222no—
880C22⋊C4—222no—
881C22⋊C4—222no—
882C22⋊C4—222no—
883C22⋊C4—222no—
884C22⋊C4—222no—
885C22⋊C4—222no—
886C22⋊C4—222no—
887C22⋊C4—222no—
888C22⋊C4—222no—
889C42—222no—
890C42—222no—
891C42—222no—
892C42—222no—
893C42—222no—
894C42—222no—
895C42—222no—
896C42—222no—
897C42—222no—
898C42C2×D4411yescharacteristic
899C42C2×D4411yescharacteristic
900C42C2×D4411yescharacteristic
901C42C2×D4411yescharacteristic
902C42C2×D4411yescharacteristic
903C42C2×D4411yescharacteristic
904C42C2×D4411yescharacteristic
905C42C2×D4411yescharacteristic
906C42C2×D4411yescharacteristic
907C42C2×D4411yescharacteristic
908C42C2×D4411yescharacteristic
909C42C2×D4411yescharacteristic
910C42C23×D1111yescharacteristic
911C42C23×D1111yescharacteristic
912C42C23×D1111yescharacteristic
913C42C23×D1111yescharacteristic
914C11#6055911yescharacteristic, complemented, Sylow
915C23—22no—
916C23—41no—
917C23—41no—
918C23—224no—
919C23—222no—
920C23—222no—
921C23—442no—
922C23—442no—
923C23C22×D4411yescharacteristic
924C23C22×D4411yescharacteristic
925C23C22×D4411yescharacteristic
926Q8—114no—
927Q8—224no—
928Q8—222no—
929Q8—222no—
930Q8—222no—
931Q8—442no—
932Q8—442no—
933D4—114no—
934D4—228no—
935D4—228no—
936D4—224no—
937D4—222no—
938D4—222no—
939D4—222no—
940D4—442no—
941D4—444no—
942D4—444no—
943D4—444no—
944D4—442no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—228no—
965C2×C4—228no—
966C2×C4—224no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—222no—
973C2×C4—444no—
974C2×C4—444no—
975C2×C4—444no—
976C2×C4—442no—
977C2×C4—442no—
978C2×C4—444no—
979C2×C4—444no—
980C2×C4—444no—
981C2×C4—444no—
982C2×C4C22×D4411yescharacteristic
983C2×C4C22×D4411yescharacteristic
984C2×C4C22×D4411yescharacteristic
985C2×C4C22×D4411yescharacteristic
986C2×C4C22×D4411yescharacteristic
987C2×C4C22×D4411yescharacteristic
988C2×C4C22×D4411yescharacteristic
989C2×C4C22×D4411yescharacteristic
990C2×C4C22×D4411yescharacteristic
991C2×C4C22×D4411yescharacteristic
992C2×C4C22×D4411yescharacteristic
993C2×C4#41×D1112yes—
994C2×C4#41×D1112yes—
995C2×C4C24×D1111yescharacteristic
996C8—24no—
997C8—24no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—44no—
1007C22—224no—
1008C22—448no—
1009C22—442no—
1010C22—442no—
1011C22—442no—
1012C22—442no—
1013C22—442no—
1014C22#1062305512yes—
1015C22C23×D4411yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—224no—
1025C4—442no—
1026C4—442no—
1027C4—442no—
1028C4—442no—
1029C4—442no—
1030C4#1062305512yes—
1031C4#1062327912yes—
1032C4#1062327912yes—
1033C4C2×#41×D1111yescharacteristic
1034C4C2×#41×D1111yescharacteristic
1035C2—22no—
1036C2—41no—
1037C2—41no—
1038C2—444no—
1039C2—882no—
1040C2C2×#1062305511yescharacteristic
1041C2C2×#1062327911yescharacteristic
1042C2C2×#1062327911yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2920C2
socleC22×C11C23×D4
hypercenter#2920D11
hypocenterC11#60559
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. C2×C4×#4339C2semidirect
3. #13078779C2semidirect
4. #13078768C2semidirect
5. #13078727C2semidirect
6. #13078688C2semidirect
7. #13078677C2semidirect
8. #13078636C2semidirect
9. #13078549C2semidirect
10. #13078423C2semidirect
11. #13078415C2semidirect
12. #13078090C2semidirect
13. #13078082C2semidirect
14. #13077861C2semidirect
15. C4×#66962C2semidirect
16. C4×#66961C2semidirect
17. C11×#2920C2semidirect
32. #10623010C22semidirect
33. #10623010C22semidirect
35. #10623008C22semidirect
36. #10623008C22semidirect
53. #10623001C22semidirect
54. #10623001C22semidirect
57. C11×#432C22semidirect
58. C11×#432C22semidirect
59. C11×#431C22semidirect
60. C11×#431C22semidirect
71. #10622464C22semidirect
72. #10622463C22semidirect
73. #10622462C22semidirect
74. #10622461C22semidirect
75. #10622460C22semidirect
76. #10622459C22semidirect
77. #10622458C22semidirect
78. #10622457C22semidirect
79. #10622456C22semidirect
80. #10622455C22semidirect
81. #10622454C22semidirect
82. #10622442C22semidirect
83. #10622350C22semidirect
84. #10622350C22semidirect
89. #10622336C22semidirect
90. #10622336C22semidirect
91. #10622329C22semidirect
92. #10622324C22semidirect
93. #10622323C22semidirect
94. #10622323C22semidirect
95. C4×Dic44C22semidirect
96. C4×D88C22semidirect
97. C4×#4314C22semidirect
98. C4×#4314C22semidirect
304. C2×D44#41semidirect
323. C2×Dic22#41semidirect
410. #2920D11semidirect
561. #432C2×D11semidirect
562. #432C2×D11semidirect
563. #431C2×D11semidirect
564. #431C2×D11semidirect
914. C11#60559semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×C4×#43392
#130787792
#130787682
#130787272
#130786882
#130786772
#130786362
#130785492
#130784232
#130784152
#130780902
#130780822
#130778612
C4×#669622
C4×#669612
C11×#29202
#6055911