Finite Group Databasebeta

← #15622289

Subgroups — #15622289

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13081817C211yesmaximal, characteristic, complemented
3#13078895C214yesmaximal, complemented
4#13078880C214yesmaximal, complemented
5#13078847C214yesmaximal, complemented
6#13078802C214yesmaximal, complemented
7#13078565C211yesmaximal, characteristic, complemented
8#13078557C211yesmaximal, characteristic, complemented
9#13078432C212yesmaximal, complemented
10#13078111C212yesmaximal, complemented
11#13077878C211yesmaximal, characteristic, complemented
12#13077870C211yesmaximal, characteristic
13C4×#66962C212yesmaximal, complemented
14C4×#66961C212yesmaximal, complemented
15C11×#2921C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66962C2212yes—
22C2×#66961C2212yes—
23#10623065—22no—
24#10623065—22no—
25#10623065C2214yes—
26#10623065C2214yescomplemented
27#10623054C2212yescomplemented
28#10623054C2212yescomplemented
29#10623053—22no—
30#10623052C2212yescomplemented
31D11×#117—22no—
32#10623047C2212yescomplemented
33C2×#66951—21no—
34C2×#66949—21no—
35#10623035—21no—
36#10623035—21no—
37C2×#66938—21no—
38C2×#66936—21no—
39#10623017—21no—
40#10623017—21no—
41C2×#66928C2211yescharacteristic, complemented
42C4×#4339C2212yes—
43C4×#4339C2212yes—
44C2×C4×D44C2211yescharacteristic, complemented
45C2×#66922C2211yescharacteristic, complemented
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#433C2214yescomplemented
48C11×#433C2214yescomplemented
49C11×#423C2212yescomplemented
50C11×#407C2211yescharacteristic
51C11×#407C2211yescharacteristic
52C4×C11×M16C2212yescomplemented
53#10622746C2212yes—
54#10622746C2212yes—
55#10622744C2212yescomplemented
56#10622734C2212yescomplemented
57#10622734C2212yescomplemented
58#10622733C2212yescomplemented
59#10622464C2214yescomplemented
60#10622463C2214yescomplemented
61#10622459C2214yescomplemented
62#10622458C2214yescomplemented
63#10622458C2214yescomplemented
64#10622457C2214yescomplemented
65#10622457C2214yescomplemented
66#10622455C2214yescomplemented
67#10622352C2212yescomplemented
68#10622351C2212yes—
69#10622350C2214yes—
70#10622349C2212yescomplemented
71#10622348C2212yescomplemented
72#10622347C2214yes—
73#10622346C2214yescomplemented
74#10622345C2212yes—
75#10622344C2212yescomplemented
76#10622336C2214yescomplemented
77#10622335C2212yescomplemented
78#10622334C2212yescomplemented
79#10622329C2214yescomplemented
80#10622324C2214yescomplemented
81#10622323C2214yescomplemented
82#10622323C2214yescomplemented
83C4×Dic44C2214yescomplemented
84C4×D88C2214yescomplemented
85C4×#4314C2214yescomplemented
86C4×#4314C2214yescomplemented
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C2×#4339—21no—
91C2×#4339—21no—
92C2×#4339—28no—
93C2×#4339C2312yes—
94C2×#4339C2312yes—
95C22×D44C2311yescharacteristic
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C2×C11×M16C2312yes—
103C2×C11×M16C2312yes—
104C11×#117D412yes—
105C11×#117D412yes—
106C11×#117C2312yes—
107C11×#117C2312yes—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66983—21no—
117#66983—21no—
118#66983C2312yes—
119#66983C2312yes—
120C4×C22⋊D11—22no—
121C4×C22⋊D11—22no—
122C4×C22⋊D11—22no—
123C4×C22⋊D11—22no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128#66979—21no—
129#66979—21no—
130#66979C2312yes—
131#66979C2312yes—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137#66977—21no—
138#66977—21no—
139#66977C2312yes—
140#66977C2312yes—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145#66962—28no—
146#66961—28no—
147C2×Dic44C2314yes—
148C2×D88C2314yes—
149C2×#4314C2314yes—
150C2×#4314C2314yes—
151#66951—24no—
152#66951—24no—
153#66949—24no—
154#66949—24no—
155#66946—22no—
156#66946—22no—
157#66945—22no—
158#66945—22no—
159C4⋊C4×D11—22no—
160C4⋊C4×D11—22no—
161#66940—22no—
162#66940—22no—
163#66938—24no—
164#66938—24no—
165#66936—24no—
166#66936—24no—
167(C22⋊D11)⋊C4—22no—
168(C22⋊D11)⋊C4—22no—
169(C22⋊D11)⋊C4—22no—
170(C22⋊D11)⋊C4—22no—
171C22⋊C4×D11—22no—
172C22⋊C4×D11—22no—
173#66930—22no—
174#66930—22no—
175#66928—22no—
176#66928C2314yes—
177C4×D44—22no—
178C4×D44C2314yes—
179C4×D44C2312yes—
180C4×D44C2312yes—
181C4×D44C2312yes—
182C4×D44C2312yes—
183#66925—22no—
184#66925—22no—
185C42×D11—22no—
186C42×D11—22no—
187#66922—22no—
188#66922C2314yes—
189C4×Dic22—22no—
190C4×Dic22C2312yes—
191C4×Dic22C2314yes—
192C4×Dic22C2312yes—
193C4×Dic22C2312yes—
194C4×Dic22C2312yes—
195C11×C4⋊C8C2314yes—
196C11×C4⋊C8C2314yes—
197C11×C22⋊C8C2312yes—
198C11×C22⋊C8C2312yes—
199C11×C22⋊C8C2312yes—
200C11×C22⋊C8C2312yes—
201C11×#97C2314yes—
202C4×C8×C11C2314yes—
203#66885C2314yes—
204#66885C2314yes—
205#66885C2314yes—
206#66885C2314yes—
207#66882C2314yes—
208#66882C2314yes—
209#66881C2314yes—
210#66881C2314yes—
211#66880C2314yes—
212#66880C2314yes—
213#66880C2314yes—
214#66880C2314yes—
215#60567—111nomaximal, Sylow
216C24×C11C2×D411yescharacteristic
217C23×D11—21no—
218C23×D11—21no—
219C22×C4×C11—24no—
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×C11C2411yescharacteristic
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C2×C22⋊D11—28no—
231C2×C22⋊D11—22no—
232C2×C22⋊D11—22no—
233C2×C22⋊D11—22no—
234C2×C22⋊D11—22no—
235C2×C22⋊D11—82no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242#4339—28no—
243#4339—28no—
244#4339—24no—
245#4339—24no—
246#4339—24no—
247#4339#4118yes—
248C2×D44—24no—
249C2×D44—21no—
250C2×D44—21no—
251C2×D44—24no—
252C2×D44C2412yes—
253C2×D44C2412yes—
254C2×C4×D11—28no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—24no—
262C2×C4×D11—82no—
263C2×Dic22—24no—
264C2×Dic22—21no—
265C2×Dic22—21no—
266C2×Dic22—24no—
267C2×Dic22—24no—
268C2×Dic22—82no—
269C2×Dic22C2412yes—
270C2×Dic22C2412yes—
271C11×M16—24no—
272C11×M16—24no—
273C2×C8×C11C2414yes—
274C2×C8×C11C2414yes—
275C11×C4⋊C4C2×D412yes—
276C11×C4⋊C4C2×D412yes—
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D412yes—
279C11×C22⋊C4C2×D412yes—
280C11×C22⋊C4C2×D412yes—
281C11×C22⋊C4C2×D412yes—
282C11×C22⋊C4C2×D412yes—
283C42×C11C2×D412yes—
284C42×C11C2×D412yes—
285C42×C11C2412yes—
286C42×C11C2412yes—
287C22⋊Dic11—22no—
288C22⋊Dic11—22no—
289C22⋊Dic11—22no—
290C22⋊Dic11—22no—
291(C2×D11)⋊C4—22no—
292(C2×D11)⋊C4—22no—
293(C2×D11)⋊C4—22no—
294(C2×D11)⋊C4—22no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300C4⋊Dic11—21no—
301C4⋊Dic11—21no—
302C4⋊Dic11—24no—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11C2412yes—
306C4⋊Dic11C2412yes—
307C4⋊Dic11C2412yes—
308C4⋊Dic11C2412yes—
309Dic11⋊C4—24no—
310Dic11⋊C4—22no—
311Dic11⋊C4—22no—
312Dic11⋊C4—22no—
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316C4×Dic11—24no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319C4×Dic11—22no—
320C4×Dic11—22no—
321C4×Dic11—22no—
322C4×Dic11—22no—
323Dic44—28no—
324D88—28no—
325#4314—28no—
326#4314—28no—
327C2×#542—111no—
328#3428—111no—
329#3125—114no—
330#3124—114no—
331#3121—114no—
332#3118—114no—
333#3095—111no—
334#3094—111no—
335#3079—112no—
336#3040—112no—
337#3007—111no—
338#3006—111no—
339C4×#137—112no—
340C4×AGL(1,ℤ/8)—112no—
341#2921D1111yescharacteristic, complemented
342C23×C11—22no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11C22×D411yescharacteristic
346C23×C11C22×D411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C22×D11—22no—
349C22×D11—24no—
350C22×D11—22no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—81no—
355C22×D11—81no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4114yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—28no—
375C22⋊D11—28no—
376C22⋊D11—82no—
377C22⋊D11—82no—
378C2×Dic11—24no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—81no—
389C2×Dic11—81no—
390D44—24no—
391D44—22no—
392D44—24no—
393D44—42no—
394D44C2×#4114yes—
395C4×D11—28no—
396C4×D11—28no—
397C4×D11—82no—
398C4×D11—82no—
399C4×D11—82no—
400C4×D11—82no—
401C4×D11—84no—
402Dic22—24no—
403Dic22—22no—
404Dic22—24no—
405Dic22—42no—
406Dic22—84no—
407Dic22C2×#4114yes—
408C8×C11—24no—
409C8×C11—24no—
410C22×#41—111no—
411C2×#137—112no—
412C2×AGL(1,ℤ/8)—112no—
413#542—114no—
414#542—114no—
415#542—222no—
416#542—222no—
417C2×C4⋊Q8—111no—
418C2×#126—221no—
419C2×#124—111no—
420C2×#124—221no—
421C2×#123—221no—
422C2×C22⋊Q8—111no—
423C2×C22⋊Q8—221no—
424C2×#121—111no—
425#520—112no—
426#520—112no—
427#520—221no—
428#520—221no—
429#519—112no—
430#518—112no—
431#518—221no—
432#518—221no—
433C4×#41—112no—
434C4×#41—112no—
435C4×#41—222no—
436C2×C4×Q8—111no—
437C2×C4×D4—111no—
438C2×#117—111no—
439C2×#117—222no—
440C2×#117C2×D1111yescharacteristic
441#485—114no—
442#484—112no—
443#483—112no—
444#482—114no—
445#481—112no—
446#480—112no—
447#477—114no—
448#476—114no—
449#475—114no—
450#474—114no—
451#464—114no—
452#464—114no—
453#463—114no—
454#463—114no—
455#452—114no—
456#451—112no—
457#450—112no—
458#449—114no—
459#448—112no—
460#447—112no—
461#442—114no—
462#441—114no—
463#440—114no—
464#440—114no—
465C4×Q16—114no—
466C4×SD16—114no—
467C4×SD16—114no—
468C4×D8—114no—
469#433C2×D1114yescomplemented
470#433C2×D1114yescomplemented
471#428—112no—
472#428—112no—
473#423C2×D1112yescomplemented
474#419—112no—
475#418—112no—
476#417—112no—
477#417—112no—
478#407C2×D1111yescharacteristic
479#407C2×D1111yescharacteristic
480C4×M16C2×D1112yescomplemented
481C22×C11—21no—
482C22×C11—21no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—82no—
490C22×C11#52512yes—
491C22×C11C23×D411yescharacteristic
492C2×D11—24no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—84no—
499C2×D11—84no—
500C4×C11—22no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11#52512yes—
507C4×C11C22×#4112yes—
508Dic11—24no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—112no—
515C2×#41—112no—
516C2×#41—228no—
517C2×#41—221no—
518C2×#41—221no—
519C22×Q8—111no—
520C22×Q8—111no—
521C22×Q8—221no—
522C22×D4—111no—
523C22×D4—111no—
524C22×D4—221no—
525C22×D4—221no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529#137—228no—
530AGL(1,ℤ/8)—228no—
531C2×Q16—114no—
532C2×SD16—114no—
533C2×SD16—114no—
534C2×D8—114no—
535C2×M16C22×D1112yes—
536C2×M16C22×D1112yes—
537C4⋊Q8—114no—
538C4⋊Q8—222no—
539#126—224no—
540#126—224no—
541#124—114no—
542#124—224no—
543#124—224no—
544#124—222no—
545#123—224no—
546#123—224no—
547C22⋊Q8—112no—
548C22⋊Q8—112no—
549C22⋊Q8—221no—
550C22⋊Q8—221no—
551C22⋊Q8—224no—
552C22⋊Q8—224no—
553#121—112no—
554#121—112no—
555#121—221no—
556#121—221no—
557C4×Q8—114no—
558C4×Q8—112no—
559C4×Q8—112no—
560C4×Q8—112no—
561C4×Q8—112no—
562C4×Q8—222no—
563C4×Q8—222no—
564C4×Q8—222no—
565C4×D4—114no—
566C4×D4—112no—
567C4×D4—112no—
568C4×D4—112no—
569C4×D4—112no—
570C4×D4—222no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4—222no—
574C4×D4—222no—
575C4×D4—222no—
576C4×D4—222no—
577C4×D4—222no—
578C4×D4—222no—
579C4×D4—222no—
580C4×D4—222no—
581#117—112no—
582#117—112no—
583#117—221no—
584#117—221no—
585#117—222no—
586#117—222no—
587#117—222no—
588#117—222no—
589#117—222no—
590#117—222no—
591#117D4412yes—
592#117D4412yes—
593#117C22×D1112yes—
594#117C22×D1112yes—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—222no—
604C2×C4⋊C4D4411yescharacteristic
605C2×C4⋊C4D4411yescharacteristic
606C2×C22⋊C4—221no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—222no—
614C2×C22⋊C4D4411yescharacteristic
615C2×C22⋊C4D4411yescharacteristic
616C2×C42—221no—
617C2×C42—221no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42C22×D1111yescharacteristic
621C2×C42C22×D1111yescharacteristic
622#107—114no—
623#107—114no—
624#106—114no—
625#106—114no—
626C4⋊C8C22×D1114yes—
627C4⋊C8C22×D1114yes—
628#103—114no—
629#103—114no—
630#103—114no—
631#103—114no—
632#102—114no—
633#102—114no—
634#102—114no—
635#102—114no—
636C22⋊C8C22×D1112yes—
637C22⋊C8C22×D1112yes—
638C22⋊C8C22×D1112yes—
639C22⋊C8C22×D1112yes—
640#97C22×D1114yes—
641C4×C8C22×D1114yes—
642C2×C11—22no—
643C2×C11—41no—
644C2×C11—41no—
645C2×C11C2×#52511yescharacteristic
646C2×C11#358511yescharacteristic
647C2×C11#358611yescharacteristic
648D11—44no—
649D11—82no—
650C24—221no—
651C24—221no—
652C24C2×D4411yescharacteristic
653#41—118no—
654#41—224no—
655#41—224no—
656#41—228no—
657#41—228no—
658#41—224no—
659C2×Q8—112no—
660C2×Q8—112no—
661C2×Q8—224no—
662C2×Q8—221no—
663C2×Q8—221no—
664C2×Q8—224no—
665C2×Q8—224no—
666C2×Q8—882no—
667C2×D4—112no—
668C2×D4—112no—
669C2×D4—224no—
670C2×D4—228no—
671C2×D4—222no—
672C2×D4—222no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—221no—
676C2×D4—221no—
677C2×D4—224no—
678C2×D4—882no—
679C22×C4—24no—
680C22×C4—228no—
681C22×C4—221no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—224no—
694C22×C4—882no—
695C22×C4C2×D4411yescharacteristic
696C22×C4C2×D4411yescharacteristic
697C22×C4C2×D4411yescharacteristic
698C22×C4C2×D4411yescharacteristic
699C22×C4C2×D4411yescharacteristic
700C22×C4C2×D4411yescharacteristic
701C22×C4C2×D4411yescharacteristic
702C22×C4C23×D1111yescharacteristic
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705Q16—228no—
706SD16—228no—
707SD16—228no—
708D8—228no—
709M16—24no—
710M16—24no—
711C2×C8C23×D1114yes—
712C2×C8C23×D1114yes—
713C4⋊C4—112no—
714C4⋊C4—112no—
715C4⋊C4—112no—
716C4⋊C4—112no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—222no—
725C4⋊C4—224no—
726C4⋊C4—222no—
727C4⋊C4—222no—
728C4⋊C4—224no—
729C4⋊C4C2×D4412yes—
730C4⋊C4C2×D4412yes—
731C4⋊C4C2×D4412yes—
732C4⋊C4C2×D4412yes—
733C22⋊C4—222no—
734C22⋊C4—222no—
735C22⋊C4—222no—
736C22⋊C4—222no—
737C22⋊C4—222no—
738C22⋊C4—222no—
739C22⋊C4—222no—
740C22⋊C4—222no—
741C22⋊C4—224no—
742C22⋊C4—222no—
743C22⋊C4—222no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4C2×D4412yes—
747C22⋊C4C2×D4412yes—
748C22⋊C4C2×D4412yes—
749C22⋊C4C2×D4412yes—
750C42—222no—
751C42—222no—
752C42—222no—
753C42—222no—
754C42—222no—
755C42—222no—
756C42—224no—
757C42C2×D4412yes—
758C42C2×D4412yes—
759C42C23×D1112yes—
760C42C23×D1112yes—
761C11#6056711yescharacteristic, complemented, Sylow
762C23—22no—
763C23—41no—
764C23—41no—
765C23—224no—
766C23—222no—
767C23—222no—
768C23—442no—
769C23—442no—
770C23—442no—
771C23—881no—
772C23—881no—
773C23C22×D4411yescharacteristic
774C23C22×D4411yescharacteristic
775C23C22×D4411yescharacteristic
776Q8—114no—
777Q8—224no—
778Q8—222no—
779Q8—224no—
780Q8—442no—
781Q8—884no—
782D4—114no—
783D4—224no—
784D4—228no—
785D4—228no—
786D4—222no—
787D4—224no—
788D4—442no—
789D4—882no—
790D4—882no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—228no—
801C2×C4—224no—
802C2×C4—222no—
803C2×C4—228no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—884no—
813C2×C4—882no—
814C2×C4—882no—
815C2×C4—882no—
816C2×C4—882no—
817C2×C4—881no—
818C2×C4—881no—
819C2×C4C22×D4412yes—
820C2×C4C22×D4411yescharacteristic
821C2×C4C22×D4412yes—
822C2×C4C22×D4412yes—
823C2×C4C22×D4412yes—
824C2×C4C22×D4411yescharacteristic
825C2×C4C22×D4411yescharacteristic
826C2×C4#41×D1114yes—
827C2×C4C24×D1111yescharacteristic
828C8—24no—
829C8—24no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—82no—
839C22—224no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—884no—
846C22—884no—
847C22#1062305512yes—
848C22C23×D4411yescharacteristic
849C4—21no—
850C4—21no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—224no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4#1062305512yes—
862C4C2×#41×D1112yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—444no—
867C2—882no—
868C2C2×#1062305511yescharacteristic
869C2#1308339711yescharacteristic
870C2#1308340411yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2921C2
socleC22×C11C23×D4
prime radical#13077870C2
hypercenter#2921D11
hypocenterC11#60567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13081817C2semidirect
3. #13078895C2semidirect
4. #13078880C2semidirect
5. #13078847C2semidirect
6. #13078802C2semidirect
7. #13078565C2semidirect
8. #13078557C2semidirect
9. #13078432C2semidirect
10. #13078111C2semidirect
11. #13077878C2semidirect
13. C4×#66962C2semidirect
14. C4×#66961C2semidirect
15. C11×#2921C2semidirect
26. #10623065C22semidirect
27. #10623054C22semidirect
28. #10623054C22semidirect
30. #10623052C22semidirect
32. #10623047C22semidirect
41. C2×#66928C22semidirect
44. C2×C4×D44C22semidirect
45. C2×#66922C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#433C22semidirect
48. C11×#433C22semidirect
49. C11×#423C22semidirect
52. C4×C11×M16C22semidirect
55. #10622744C22semidirect
56. #10622734C22semidirect
57. #10622734C22semidirect
58. #10622733C22semidirect
59. #10622464C22semidirect
60. #10622463C22semidirect
61. #10622459C22semidirect
62. #10622458C22semidirect
63. #10622458C22semidirect
64. #10622457C22semidirect
65. #10622457C22semidirect
66. #10622455C22semidirect
67. #10622352C22semidirect
70. #10622349C22semidirect
71. #10622348C22semidirect
73. #10622346C22semidirect
75. #10622344C22semidirect
76. #10622336C22semidirect
77. #10622335C22semidirect
78. #10622334C22semidirect
79. #10622329C22semidirect
80. #10622324C22semidirect
81. #10622323C22semidirect
82. #10622323C22semidirect
83. C4×Dic44C22semidirect
84. C4×D88C22semidirect
85. C4×#4314C22semidirect
86. C4×#4314C22semidirect
341. #2921D11semidirect
469. #433C2×D11semidirect
470. #433C2×D11semidirect
473. #423C2×D11semidirect
480. C4×M16C2×D11semidirect
761. C11#60567semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130818172
#130788952
#130788802
#130788472
#130788022
#130785652
#130785572
#130784322
#130781112
#130778782
#130778702
C4×#669622
C4×#669612
C11×#29212
#6056711