Finite Group Databasebeta

← #15622288

Subgroups — #15622288

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×#10623174C211yesmaximal, characteristic, complemented
2#13081819C211yesmaximal, characteristic, complemented
3#13078886C214yesmaximal, complemented
4#13078879C214yesmaximal, complemented
5#13078846C214yesmaximal, complemented
6#13078801C214yesmaximal, complemented
7#13078560C211yesmaximal, characteristic, complemented
8#13078557C211yesmaximal, characteristic, complemented
9#13078427C212yesmaximal, complemented
10#13078112C212yesmaximal, complemented
11#13077868C211yesmaximal, characteristic
12#137×Dic11C212yesmaximal, complemented
13#13077429C212yesmaximal, complemented
14#13077251C211yesmaximal, characteristic, complemented
15C11×#3007C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×#137C2212yes—
18C2×C11×C22⋊Q8C2211yescharacteristic
19#10623358—21no—
20#10623358—21no—
21#10623358C2212yescomplemented
22#10623358C2212yescomplemented
23#41×Dic11—22no—
24#41×Dic11C2212yes—
25#41×Dic11C2212yes—
26C2×#67002C2212yes—
27C2×#67000C2211yescharacteristic, complemented
28#10623343C2212yescomplemented
29C2×Q8×Dic11C2211yescharacteristic, complemented
30#10623329—21no—
31#10623329—21no—
32#10623329C2212yescomplemented
33C2×#66983C2211yescharacteristic
34C2×#66979—22no—
35C2×#66979C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37#10623174—22no—
38#10623174—22no—
39#10623174C2214yes—
40#10623174C2214yescomplemented
41C2×#66951—21no—
42C2×#66950—21no—
43C2×#66946C2211yescharacteristic, complemented
44C2×#66941C2211yescharacteristic, complemented
45C2×#66938—21no—
46C2×#66936—21no—
47C11×#452C2214yescomplemented
48C11×#451C2212yescomplemented
49C11×#450C2212yescomplemented
50C11×#417C2212yes—
51C11×#407C2211yescharacteristic
52#10622851C2214yes—
53#10622845C2212yes—
54#10622840C2212yes—
55#10622838C2212yescomplemented
56#10622830C2212yes—
57#10622820C2211yescharacteristic
58#10622798C2214yescomplemented
59#10622798C2214yescomplemented
60#10622797C2214yescomplemented
61Q16×Dic11C2214yescomplemented
62#10622778C2214yescomplemented
63#10622778C2214yescomplemented
64#10622777C2214yescomplemented
65SD16×Dic11C2214yescomplemented
66#10622744C2212yescomplemented
67#10622734C2212yescomplemented
68#10622731C2212yescomplemented
69M16×Dic11C2212yescomplemented
70#10622658C2214yescomplemented
71#10622657C2212yescomplemented
72#10622656C2212yescomplemented
73#10622577C2212yescomplemented
74#10622430C2214yescomplemented
75#10622407C2214yescomplemented
76#10622404C2214yescomplemented
77#10622401C2214yescomplemented
78#10622398C2214yescomplemented
79#10622374C2214yescomplemented
80#10622372C2214yescomplemented
81#10622369C2214yescomplemented
82#10622350C2214yes—
83#10622349C2212yescomplemented
84#10622348C2212yescomplemented
85#10622333C2214yescomplemented
86#10622333C2214yescomplemented
87C2×C11×#41—28no—
88C2×C11×#41—21no—
89C2×C11×#41—21no—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C22×Q8×C11C2311yescharacteristic
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11—21no—
95C22×D4×C11C2311yescharacteristic
96C23×C4×C11—21no—
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—21no—
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×Dic22—21no—
102C11×#137—28no—
103C2×C11×Q16C2314yes—
104C2×C11×SD16C2314yes—
105C2×C11×M16C2312yes—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8C2312yes—
109C11×C22⋊Q8C2312yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11D411yescharacteristic
117C2×C22⋊Dic11D411yescharacteristic
118#67002—28no—
119#67000—22no—
120#67000C2314yes—
121Q8×Dic11—22no—
122Q8×Dic11—22no—
123Q8×Dic11—22no—
124Q8×Dic11C2314yes—
125Q8×Dic11C2312yes—
126Q8×Dic11C2312yes—
127Q8×Dic11C2312yes—
128Q8×Dic11C2312yes—
129C2×#4325C2314yes—
130D4×Dic11—22no—
131D4×Dic11—22no—
132D4×Dic11—22no—
133D4×Dic11—22no—
134D4×Dic11—22no—
135D4×Dic11—22no—
136D4×Dic11—22no—
137D4×Dic11—22no—
138D4×Dic11—22no—
139D4×Dic11—22no—
140D4×Dic11C2312yes—
141D4×Dic11C2312yes—
142D4×Dic11C2312yes—
143D4×Dic11C2312yes—
144C2×#4323C2314yes—
145#66983—21no—
146#66983—21no—
147#66983C2312yes—
148#66983C2312yes—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153#66979—21no—
154#66979—21no—
155#66979—22no—
156#66979—22no—
157#66979—22no—
158#66979—22no—
159#66979—22no—
160#66979—22no—
161#66979D412yes—
162#66979D412yes—
163#66979C2312yes—
164#66979C2312yes—
165#66979C2312yes—
166#66979C2312yes—
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11—22no—
169C2×C4⋊Dic11—22no—
170C2×C4⋊Dic11D411yescharacteristic
171C2×C4⋊Dic11D411yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×Dic11⋊C4—21no—
176C2×C4×Dic11—21no—
177C2×C4×Dic11—21no—
178C2×C4×Dic11—22no—
179C2×C4×Dic11—22no—
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×#4318C2312yes—
183#66951—24no—
184#66951—24no—
185#66950—24no—
186#66950—24no—
187#66946—22no—
188#66946C2314yes—
189#66941—22no—
190#66941C2314yes—
191#66938—24no—
192#66938—24no—
193#66936—24no—
194#66936—24no—
195C11×#103C2314yes—
196C11×#102C2314yes—
197C11×C22⋊C8C2312yes—
198C11×C22⋊C8C2312yes—
199#66899C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66896C2314yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205#66885C2314yes—
206#66885C2314yes—
207#66882C2314yes—
208#66881C2314yes—
209#66879C2314yes—
210Dic11⋊C8C2314yes—
211Dic11⋊C8C2314yes—
212C8×Dic11C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215#60567—111nomaximal, Sylow
216C24×C11—21no—
217C24×C11C2×D411yescharacteristic
218C23×D11—21no—
219C11×#41—28no—
220C11×#41—28no—
221C11×#41—24no—
222C11×#41—24no—
223C11×#41—24no—
224C11×#41#4118yes—
225C2×Q8×C11—24no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—24no—
229C2×Q8×C11C2412yes—
230C2×Q8×C11C2412yes—
231C2×D4×C11—28no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—24no—
235C2×D4×C11—21no—
236C2×D4×C11C2412yes—
237C22×C4×C11—28no—
238C22×C4×C11—21no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—24no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—22no—
251C2×C22⋊D11—22no—
252C2×C22⋊D11—82no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262C22×Dic11C2×D411yescharacteristic
263C22×Dic11C2×D411yescharacteristic
264C2×D44—21no—
265C2×D44—24no—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—82no—
269C2×Dic22—24no—
270C2×Dic22—82no—
271C11×Q16—28no—
272C11×SD16—28no—
273C11×M16—24no—
274C2×C8×C11C2414yes—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4C2412yes—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C22⋊Dic11—22no—
282C22⋊Dic11—22no—
283C22⋊Dic11—22no—
284C22⋊Dic11—22no—
285C22⋊Dic11—22no—
286C22⋊Dic11—22no—
287C22⋊Dic11C2×D412yes—
288C22⋊Dic11C2×D412yes—
289C22⋊Dic11C2×D412yes—
290C22⋊Dic11C2×D412yes—
291#4325—28no—
292#4323—28no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—22no—
297(C2×D11)⋊C4—22no—
298C4⋊Dic11—24no—
299C4⋊Dic11—22no—
300C4⋊Dic11—22no—
301C4⋊Dic11—22no—
302C4⋊Dic11—22no—
303C4⋊Dic11—21no—
304C4⋊Dic11—21no—
305C4⋊Dic11—21no—
306C4⋊Dic11C2×D412yes—
307C4⋊Dic11C2×D412yes—
308C4⋊Dic11C2×D412yes—
309C4⋊Dic11C2×D412yes—
310C4⋊Dic11C2412yes—
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—24no—
314C4×Dic11—24no—
315C4×Dic11—22no—
316C4×Dic11—22no—
317C4×Dic11—22no—
318C4×Dic11—22no—
319C4×Dic11—22no—
320C4×Dic11—22no—
321C4×Dic11C2×D412yes—
322C4×Dic11C2×D412yes—
323C4×Dic11C2412yes—
324C4×Dic11C2412yes—
325#4318—24no—
326C2×C11⋊C8C2414yes—
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#3007D1111yescharacteristic, complemented
338#3006—111no—
339C4×#137—112no—
340C4×AGL(1,ℤ/8)—112no—
341#2921—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—81no—
348C23×C11—81no—
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C22×D11—22no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356Q8×C11—24no—
357Q8×C11—22no—
358Q8×C11—24no—
359Q8×C11—42no—
360Q8×C11C2×#4114yes—
361D4×C11—28no—
362D4×C11—24no—
363D4×C11—28no—
364D4×C11—22no—
365D4×C11C2×#4114yes—
366C2×C4×C11—24no—
367C2×C4×C11—28no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—28no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C2×#4114yes—
383C2×C4×C11C2511yescharacteristic
384C22⋊D11—82no—
385C22⋊D11—82no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—42no—
394C2×Dic11—82no—
395C2×Dic11—82no—
396C2×Dic11—82no—
397C2×Dic11—82no—
398C2×Dic11—81no—
399C2×Dic11—81no—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402C2×Dic11C22×D412yes—
403C2×Dic11C22×D412yes—
404D44—24no—
405D44—42no—
406C4×D11—84no—
407Dic22—84no—
408C8×C11—24no—
409C11⋊C8—24no—
410C22×#41C2×D1111yescharacteristic
411C2×#137C2×D1112yes—
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—221no—
423C2×C22⋊Q8C2×D1111yescharacteristic
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—111no—
440C2×#117—222no—
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#452C2×D1114yescomplemented
456#451C2×D1112yescomplemented
457#450C2×D1112yescomplemented
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#433—114no—
470#433—114no—
471#428—112no—
472#428—112no—
473#423—112no—
474#419—112no—
475#418—112no—
476#417—112no—
477#417C2×D1112yes—
478#407—111no—
479#407C2×D1111yescharacteristic
480C4×M16—112no—
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—24no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—82no—
493C22×C11—84no—
494C22×C11#52512yes—
495C22×C11C23×D411yescharacteristic
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—84no—
500C4×C11—21no—
501C4×C11—24no—
502C4×C11—21no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11#52512yes—
506C4×C11C22×#4112yes—
507Dic11—22no—
508Dic11—22no—
509Dic11—22no—
510Dic11—22no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—28no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41C22×D1112yes—
518C2×#41C22×D1112yes—
519C22×Q8—221no—
520C22×Q8C22×D1111yescharacteristic
521C22×Q8C22×D1111yescharacteristic
522C22×D4—21no—
523C22×D4—111no—
524C22×D4—221no—
525C22×D4C22×D1111yescharacteristic
526C23×C4—21no—
527C23×C4—221no—
528C23×C4C22×D1111yescharacteristic
529#137—28no—
530AGL(1,ℤ/8)—228no—
531C2×Q16C22×D1114yes—
532C2×SD16—114no—
533C2×SD16C22×D1114yes—
534C2×D8—114no—
535C2×M16—112no—
536C2×M16C22×D1112yes—
537C4⋊Q8—114no—
538C4⋊Q8—222no—
539#126—224no—
540#126—224no—
541#124—114no—
542#124—222no—
543#124—224no—
544#124—224no—
545#123—224no—
546#123—224no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—224no—
550C22⋊Q8—224no—
551C22⋊Q8C22×D1112yes—
552C22⋊Q8C22×D1112yes—
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—112no—
566C4×D4—112no—
567C4×D4—112no—
568C4×D4—112no—
569C4×D4—114no—
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—112no—
584#117—112no—
585#117—112no—
586#117—112no—
587#117—222no—
588#117—222no—
589#117—222no—
590#117—222no—
591#117—222no—
592#117—222no—
593#117—221no—
594#117—221no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—111no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—222no—
602C2×C4⋊C4—222no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4C22×D1111yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—111no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C42—111no—
617C2×C42—111no—
618C2×C42—222no—
619C2×C42—222no—
620C2×C42—221no—
621C2×C42—221no—
622#107—114no—
623#107—114no—
624#106—114no—
625#106—114no—
626C4⋊C8—114no—
627C4⋊C8—114no—
628#103—114no—
629#103—114no—
630#103—114no—
631#103C22×D1114yes—
632#102—114no—
633#102—114no—
634#102—114no—
635#102C22×D1114yes—
636C22⋊C8—112no—
637C22⋊C8—112no—
638C22⋊C8C22×D1112yes—
639C22⋊C8C22×D1112yes—
640#97—114no—
641C4×C8—114no—
642C2×C11—22no—
643C2×C11—41no—
644C2×C11—41no—
645C2×C11—44no—
646C2×C11C2×#52511yescharacteristic
647C2×C11#358511yescharacteristic
648C2×C11#358611yescharacteristic
649D11—82no—
650C24—21no—
651C24—221no—
652C24D4×D1111yescharacteristic
653#41—28no—
654#41—28no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41#434118yes—
659C2×Q8—24no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—224no—
664C2×Q8—882no—
665C2×Q8C23×D1112yes—
666C2×Q8C23×D1112yes—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—21no—
672C2×D4—112no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—221no—
676C2×D4—224no—
677C2×D4—882no—
678C2×D4C23×D1112yes—
679C22×C4—28no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—111no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—111no—
690C22×C4—224no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—882no—
699C22×C4D4×D1111yescharacteristic
700C22×C4D4×D1111yescharacteristic
701C22×C4D4×D1111yescharacteristic
702C22×C4C23×D1111yescharacteristic
703C22×C4C23×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705Q16—28no—
706SD16—28no—
707SD16—228no—
708D8—228no—
709M16—24no—
710M16—224no—
711C2×C8—114no—
712C2×C8C23×D1114yes—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—21no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—112no—
722C4⋊C4—112no—
723C4⋊C4—222no—
724C4⋊C4—222no—
725C4⋊C4—222no—
726C4⋊C4—222no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—221no—
730C4⋊C4—221no—
731C4⋊C4—221no—
732C4⋊C4C23×D1112yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—112no—
736C22⋊C4—112no—
737C22⋊C4—112no—
738C22⋊C4—112no—
739C22⋊C4—224no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—222no—
743C22⋊C4—222no—
744C22⋊C4—222no—
745C22⋊C4—222no—
746C22⋊C4—222no—
747C22⋊C4—222no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C42—112no—
751C42—112no—
752C42—112no—
753C42—112no—
754C42—222no—
755C42—222no—
756C42—222no—
757C42—222no—
758C42—224no—
759C42—222no—
760C42—222no—
761C11#6056711yescharacteristic, complemented, Sylow
762C23—24no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—81no—
768C23—81no—
769C23—222no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23C2×D4×D1111yescharacteristic
774C23C2×D4×D1111yescharacteristic
775C23C2×D4×D1111yescharacteristic
776Q8—24no—
777Q8—22no—
778Q8—24no—
779Q8—42no—
780Q8—884no—
781Q8C2×#434114yes—
782D4—28no—
783D4—24no—
784D4—28no—
785D4—22no—
786D4—224no—
787D4—442no—
788D4—882no—
789D4—882no—
790D4C2×#434114yes—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—442no—
816C2×C4—884no—
817C2×C4—882no—
818C2×C4—882no—
819C2×C4—882no—
820C2×C4—882no—
821C2×C4—881no—
822C2×C4—881no—
823C2×C4C2×D4×D1111yescharacteristic
824C2×C4C2×D4×D1111yescharacteristic
825C2×C4C2×D4×D1111yescharacteristic
826C2×C4C2×#434114yes—
827C2×C4C24×D1111yescharacteristic
828C8—24no—
829C8—224no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—24no—
839C22—42no—
840C22—42no—
841C22—82no—
842C22—84no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—884no—
847C22#1062311712yes—
848C22C22×D4×D1111yescharacteristic
849C4—21no—
850C4—24no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—222no—
855C4—222no—
856C4—222no—
857C4—222no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4#1062311712yes—
862C4C22×#434112yes—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—44no—
867C2—882no—
868C2C2×#1062311711yescharacteristic
869C2#1308339311yescharacteristic
870C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3007C2
socleC22×C11C23×D4
prime radical#13077868C2
hypercenter#3007D11
hypocenterC11#60567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C2×#10623174C2semidirect
2. #13081819C2semidirect
3. #13078886C2semidirect
4. #13078879C2semidirect
5. #13078846C2semidirect
6. #13078801C2semidirect
7. #13078560C2semidirect
8. #13078557C2semidirect
9. #13078427C2semidirect
10. #13078112C2semidirect
12. #137×Dic11C2semidirect
13. #13077429C2semidirect
14. #13077251C2semidirect
15. C11×#3007C2semidirect
21. #10623358C22semidirect
22. #10623358C22semidirect
27. C2×#67000C22semidirect
28. #10623343C22semidirect
29. C2×Q8×Dic11C22semidirect
32. #10623329C22semidirect
40. #10623174C22semidirect
43. C2×#66946C22semidirect
44. C2×#66941C22semidirect
47. C11×#452C22semidirect
48. C11×#451C22semidirect
49. C11×#450C22semidirect
55. #10622838C22semidirect
58. #10622798C22semidirect
59. #10622798C22semidirect
60. #10622797C22semidirect
61. Q16×Dic11C22semidirect
62. #10622778C22semidirect
63. #10622778C22semidirect
64. #10622777C22semidirect
65. SD16×Dic11C22semidirect
66. #10622744C22semidirect
67. #10622734C22semidirect
68. #10622731C22semidirect
69. M16×Dic11C22semidirect
70. #10622658C22semidirect
71. #10622657C22semidirect
72. #10622656C22semidirect
73. #10622577C22semidirect
74. #10622430C22semidirect
75. #10622407C22semidirect
76. #10622404C22semidirect
77. #10622401C22semidirect
78. #10622398C22semidirect
79. #10622374C22semidirect
80. #10622372C22semidirect
81. #10622369C22semidirect
83. #10622349C22semidirect
84. #10622348C22semidirect
85. #10622333C22semidirect
86. #10622333C22semidirect
337. #3007D11semidirect
455. #452C2×D11semidirect
456. #451C2×D11semidirect
457. #450C2×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×#106231742
#130818192
#130788862
#130788792
#130788462
#130788012
#130785602
#130785572
#130784272
#130781122
#130778682
#137×Dic112
#130774292
#130772512
C11×#30072
#6056711