Finite Group Databasebeta

← #15634361

Subgroups — #15634361

Order 2816.

1826 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic, complemented
2C2×#10623261C211yesmaximal, characteristic, complemented
3#13081569C214yesmaximal, complemented
4#13081568C214yesmaximal, complemented
5#13081525C212yesmaximal, complemented
6#13081514C212yesmaximal, complemented
7#13081490C212yesmaximal, complemented
8#13081482C212yesmaximal, complemented
9#13079166C212yesmaximal, complemented
10#13079158C211yesmaximal, characteristic, complemented
11#13078436C212yesmaximal, complemented
12#13078415C211yesmaximal, characteristic, complemented
13#13078412C212yesmaximal, complemented
14#13077567C211yesmaximal, characteristic, complemented
15#13077429C212yesmaximal
16C4×#67002C211yesmaximal, characteristic
17C11×#3079C211yesmaximal, characteristic, complemented
18C2×C11×C4⋊Q8C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20#41×Dic11C2212yes—
21C2×#67002C2211yescharacteristic
22C2×#66999—22no—
23#10623261—21no—
24#10623261—21no—
25#10623261—22no—
26#10623261C2212yes—
27#10623261C2212yes—
28#10623261C2214yes—
29#10623101C2211yescharacteristic, complemented
30#10623100C2212yescomplemented
31Q8×Dic22C2211yescharacteristic, complemented
32#10623074—21no—
33#10623074C2211yescharacteristic, complemented
34#10623070—22no—
35#10623070C2212yescomplemented
36D4×Dic22—21no—
37D4×Dic22C2211yescharacteristic, complemented
38#10623048—22no—
39#10623048C2212yes—
40C2×#66950—21no—
41C2×#66946C2212yes—
42C2×C4⋊C4×D11—21no—
43C2×#66943C2212yes—
44C2×C4×D44C2211yescharacteristic
45#10623001—21no—
46#10623001C2211yescharacteristic
47C2×C4×Dic22—21no—
48C2×C4×Dic22C2211yescharacteristic
49C11×#477C2212yescomplemented
50C11×#476C2212yescomplemented
51C11×#475C2212yescomplemented
52C11×#474C2212yescomplemented
53C11×#428C2212yes—
54C11×#423C2211yescharacteristic
55C11×#417C2212yes—
56#10622845C2211yescharacteristic
57#10622744C2212yes—
58#10622734C2212yes—
59#10622731C2212yes—
60M16×Dic11C2212yes—
61#10622693C2214yescomplemented
62#10622692C2212yescomplemented
63#10622691C2212yescomplemented
64#10622639C2212yes—
65C4×#4325C2212yes—
66#10622627C2212yes—
67C4×#4323C2212yes—
68#10622614C2211yescharacteristic
69#10622608C2211yescharacteristic
70#10622577C2212yes—
71#10622577C2212yes—
72C4×#4318C2211yescharacteristic
73#10622504C2214yes—
74#10622503C2214yes—
75#10622491C2214yescomplemented
76#10622489C2214yescomplemented
77#10622484C2214yes—
78#10622483C2214yes—
79#10622471C2214yescomplemented
80#10622469C2214yescomplemented
81#10622460C2214yes—
82#10622459C2212yes—
83#10622455C2212yes—
84#10622444C2212yescomplemented
85#10622443C2212yescomplemented
86#10622441C2214yescomplemented
87#10622430C2214yes—
88#10622412C2214yescomplemented
89#10622409C2214yescomplemented
90#10622401C2214yes—
91#10622398C2214yes—
92#10622379C2214yescomplemented
93#10622376C2214yescomplemented
94#10622369C2214yes—
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11—21no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×C4×D11—22no—
100C22×Dic22—21no—
101C22×Dic22D411yescharacteristic
102C2×C11×M16C2312yes—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C4×Q8×C11C2311yescharacteristic
108C4×Q8×C11C2311yescharacteristic
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11C2311yescharacteristic
112C4×D4×C11C2311yescharacteristic
113C11×#117—21no—
114C11×#117C2311yescharacteristic
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4C2312yes—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119#67002Q818yescomplemented
120#66999—24no—
121#66999—24no—
122#66999—24no—
123#66999—24no—
124Q8×Dic11C2312yes—
125Q8×Dic11C2312yes—
126C2×#4325C2312yes—
127D4×Dic11—22no—
128D4×Dic11—22no—
129D4×Dic11C2312yes—
130D4×Dic11C2312yes—
131C2×#4323C2312yes—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—22no—
134#66979—22no—
135#66979C2312yes—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140#66977—21no—
141#66977—21no—
142#66977—21no—
143#66977—21no—
144#66977—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4D412yes—
148C2×C4×Dic11—22no—
149C2×C4×Dic11C2312yes—
150C2×#4318C2311yescharacteristic
151C2×#4318C2311yescharacteristic
152#66950—22no—
153#66950—22no—
154#66950—24no—
155#66946—22no—
156#66946—22no—
157#66946C2314yes—
158#66946C2314yes—
159C4⋊C4×D11—22no—
160C4⋊C4×D11—22no—
161C4⋊C4×D11—24no—
162#66943—22no—
163#66943—22no—
164#66943—22no—
165#66943—22no—
166#66943C2314yes—
167#66943C2312yes—
168#66943C2314yes—
169#66943C2312yes—
170#66941—22no—
171#66941—22no—
172#66941C2312yes—
173#66941C2312yes—
174#66931—22no—
175#66931—22no—
176#66931—22no—
177#66931—22no—
178#66931—22no—
179#66931—22no—
180C4×D44—21no—
181C4×D44—21no—
182C4×D44C2312yes—
183C4×D44C2312yes—
184#66923—22no—
185#66923C2312yes—
186#66922—21no—
187#66922—21no—
188#66922C2311yescharacteristic
189#66922C2311yescharacteristic
190C4×Dic22—21no—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22D411yescharacteristic
198C4×Dic22D411yescharacteristic
199C4×Dic22D412yes—
200C4×Dic22C2311yescharacteristic
201C4×Dic22C2312yes—
202C4×Dic22C2311yescharacteristic
203C11×#107C2314yes—
204C11×#106C2314yes—
205C11×C4⋊C8C2312yes—
206C11×C4⋊C8C2312yes—
207C11×#103C2314yes—
208C11×#102C2314yes—
209#66899C2312yes—
210#66896C2312yes—
211#66885C2314yes—
212#66885C2314yes—
213#66882C2314yes—
214#66881C2314yes—
215#66879C2314yes—
216Dic11⋊C8C2314yes—
217Dic11⋊C8C2314yes—
218C8×Dic11C2314yes—
219#66873C2312yes—
220#66873C2312yes—
221#66872C2314yes—
222#66872C2314yes—
223#66872C2312yes—
224#66871C2312yes—
225#66871C2314yes—
226#66871C2314yes—
227#66867C2312yes—
228C4×C11⋊C8C2312yes—
229#61367—111nomaximal, Sylow
230C23×D11—21no—
231C11×#41—22no—
232C11×#41C2×Q814yes—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—82no—
236C2×Q8×C11C2411yescharacteristic
237C2×D4×C11—21no—
238C2×D4×C11C2411yescharacteristic
239C22×C4×C11—21no—
240C22×C4×C11—22no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2411yescharacteristic
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—21no—
249C22×Dic11C2×D412yes—
250C22×Dic11C2×D412yes—
251C2×D44—21no—
252C2×D44—22no—
253C2×D44C2×Q814yescomplemented
254C2×D44C2412yes—
255C2×C4×D11—24no—
256C2×C4×D11—24no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—44no—
260C2×C4×D11—84no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—21no—
264C2×Dic22—21no—
265C2×Dic22—42no—
266C2×Dic22—44no—
267C2×Dic22C2×D411yescharacteristic
268C2×Dic22C2×D411yescharacteristic
269C2×Dic22C2×D412yes—
270C11×M16—24no—
271C2×C8×C11C2414yes—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4—22no—
277C11×C4⋊C4C2414yes—
278C11×C4⋊C4C2411yescharacteristic
279C11×C4⋊C4C2411yescharacteristic
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C42×C11—21no—
284C42×C11—21no—
285C42×C11—21no—
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2411yescharacteristic
289C42×C11C2411yescharacteristic
290C22⋊Dic11—22no—
291C22⋊Dic11—22no—
292C22⋊Dic11—22no—
293#4325C2×Q818yescomplemented
294#4323C2×Q818yescomplemented
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—22no—
298(C2×D11)⋊C4—22no—
299C4⋊Dic11—22no—
300C4⋊Dic11—22no—
301C4⋊Dic11—22no—
302C4⋊Dic11—22no—
303C4⋊Dic11—24no—
304C4⋊Dic11—24no—
305C4⋊Dic11—21no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2×D411yescharacteristic
309C4⋊Dic11C2×D411yescharacteristic
310C4⋊Dic11C2×D412yes—
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2412yes—
313C4⋊Dic11C2412yes—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—24no—
319Dic11⋊C4—24no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4C2×D412yes—
323Dic11⋊C4C2×D412yes—
324Dic11⋊C4C2×D412yes—
325Dic11⋊C4C2×D412yes—
326C4×Dic11—22no—
327C4×Dic11—22no—
328C4×Dic11—22no—
329C4×Dic11C2×D412yes—
330C4×Dic11C2×D412yes—
331C4×Dic11C2412yes—
332C4×Dic11C2412yes—
333#4318—22no—
334#4318C2×Q814yescomplemented
335C2×C11⋊C8C2412yes—
336C2×C11⋊C8C2412yes—
337Q8×#41—111no—
338C2×#554—111no—
339#3389—114no—
340#3388—114no—
341#3385—112no—
342#3384—112no—
343#3381—112no—
344#3380—112no—
345#3166—112no—
346#3165—111no—
347#3080—112no—
348#3079D1111yescharacteristic, complemented
349#3077—112no—
350#3077—111no—
351Q8×M16—111no—
352C4×AGL(1,ℤ/8)—112no—
353C4×AGL(1,ℤ/8)—111no—
354C23×C11—21no—
355C23×C11C22×D411yescharacteristic
356C22×D11—24no—
357C22×D11—22no—
358C22×D11—42no—
359C22×D11—42no—
360Q8×C11—21no—
361Q8×C11—82no—
362Q8×C11—82no—
363Q8×C11C22×Q812yes—
364D4×C11—24no—
365D4×C11—21no—
366D4×C11C22×Q812yes—
367C2×C4×C11—21no—
368C2×C4×C11—24no—
369C2×C4×C11—22no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—24no—
373C2×C4×C11—41no—
374C2×C4×C11—44no—
375C2×C4×C11—42no—
376C2×C4×C11—81no—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×Q812yes—
383C2×C4×C112−1+412yes—
384C2×C4×C11C2511yescharacteristic
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—44no—
391C2×Dic11—42no—
392C2×Dic11—82no—
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396C2×Dic11C22×D412yes—
397D44—24no—
398D44—22no—
399D44C22×Q814yes—
400C4×D11—44no—
401C4×D11—44no—
402C4×D11—84no—
403C4×D11—84no—
404Dic22—22no—
405Dic22—22no—
406Dic22—42no—
407Dic22—44no—
408Dic22—42no—
409Dic22—82no—
410Dic22—81no—
411C8×C11—24no—
412C11⋊C8—22no—
413C11⋊C8C22×Q814yes—
414C2×AGL(1,ℤ/8)—111no—
415Q82—111no—
416#557—111no—
417#557—112no—
418#554—112no—
419#554—112no—
420#554—114no—
421#554—111no—
422#554—112no—
423#554—222no—
424#554—221no—
425#554—221no—
426#554—222no—
427#554—221no—
428D4×Q8—111no—
429D4×Q8—221no—
430#533—112no—
431#533—111no—
432#533—221no—
433#533—222no—
434C2×C4⋊Q8C2×D1111yescharacteristic
435C2×#125—112no—
436C2×C22⋊Q8—221no—
437C2×C22⋊Q8—222no—
438C4×#41—112no—
439C4×#41C2×D1111yescharacteristic
440C2×C4×Q8—111no—
441C2×C4×Q8—221no—
442C2×C4×D4—112no—
443C2×C4×D4—111no—
444C22×C4⋊C4—221no—
445#501—114no—
446#501—114no—
447#501—114no—
448#500—112no—
449#499—114no—
450#499—114no—
451#498—112no—
452#479—114no—
453#479—114no—
454#478—114no—
455#478—114no—
456#478—114no—
457#478—114no—
458#478—114no—
459#477C2×D1112yescomplemented
460#476—114no—
461#476—112no—
462#476C2×D1112yescomplemented
463#475C2×D1112yescomplemented
464#474—114no—
465#474—112no—
466#474C2×D1112yescomplemented
467#446—112no—
468#446—114no—
469C8×Q8—112no—
470#442—112no—
471#442—114no—
472#440—112no—
473#440—114no—
474C4×SD16—112no—
475C4×SD16—114no—
476C4×D8—112no—
477C4×D8—114no—
478#428—112no—
479#428—111no—
480#428—112no—
481#428—112no—
482#428C2×D1112yes—
483#423—112no—
484#423C2×D1111yescharacteristic
485#418—112no—
486#418—111no—
487#417—111no—
488#417C2×D1112yes—
489C4×M16—112no—
490C4×M16—111no—
491C22×C11—21no—
492C22×C11—21no—
493C22×C11—22no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11D4×Q812yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—24no—
499C2×D11—48no—
500C2×D11—42no—
501C2×D11—42no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—22no—
505C4×C11—21no—
506C4×C11—44no—
507C4×C11—41no—
508C4×C11—41no—
509C4×C11D4×Q812yes—
510C4×C11#57512yes—
511C4×C11C23×Q811yescharacteristic
512C4×C11C2×2−1+411yescharacteristic
513Dic11—22no—
514Dic11—22no—
515Dic11—22no—
516Dic11—22no—
517Dic11—42no—
518Dic11—42no—
519Dic11—42no—
520C2×#41C22×D1111yescharacteristic
521C22×Q8—21no—
522C22×Q8—111no—
523C22×Q8—221no—
524C22×D4—111no—
525C23×C4—222no—
526C23×C4—221no—
527AGL(1,ℤ/8)—118no—
528C2×SD16—112no—
529C2×D8—112no—
530C2×M16—111no—
531C2×M16—111no—
532C2×M16C22×D1112yes—
533C4⋊Q8—21no—
534C4⋊Q8—21no—
535C4⋊Q8—112no—
536C4⋊Q8—112no—
537C4⋊Q8—111no—
538C4⋊Q8—111no—
539C4⋊Q8—221no—
540C4⋊Q8—221no—
541C4⋊Q8—222no—
542C4⋊Q8—222no—
543C4⋊Q8C22×D1112yes—
544C4⋊Q8C22×D1112yes—
545#125—114no—
546#125—114no—
547#125—112no—
548#125—112no—
549#125—112no—
550#125—222no—
551#125—222no—
552#125—222no—
553#125—222no—
554#125—222no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8—222no—
558C22⋊Q8—222no—
559C22⋊Q8—222no—
560C22⋊Q8—222no—
561C22⋊Q8—222no—
562C22⋊Q8—222no—
563C22⋊Q8—224no—
564C22⋊Q8—221no—
565C22⋊Q8—222no—
566C22⋊Q8—224no—
567C22⋊Q8—224no—
568C22⋊Q8—224no—
569C22⋊Q8—224no—
570C22⋊Q8—221no—
571C22⋊Q8—221no—
572C22⋊Q8—221no—
573C4×Q8—111no—
574C4×Q8—112no—
575C4×Q8—111no—
576C4×Q8—111no—
577C4×Q8—111no—
578C4×Q8—112no—
579C4×Q8—112no—
580C4×Q8—112no—
581C4×Q8—222no—
582C4×Q8—222no—
583C4×Q8—222no—
584C4×Q8—221no—
585C4×Q8—221no—
586C4×Q8—221no—
587C4×Q8—221no—
588C4×Q8C22×D1111yescharacteristic
589C4×Q8C22×D1111yescharacteristic
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—112no—
593C4×D4—112no—
594C4×D4—114no—
595C4×D4—114no—
596C4×D4—112no—
597C4×D4—112no—
598C4×D4—222no—
599C4×D4—222no—
600C4×D4—222no—
601C4×D4—222no—
602C4×D4—221no—
603C4×D4—221no—
604C4×D4C22×D1111yescharacteristic
605C4×D4C22×D1111yescharacteristic
606#117—21no—
607#117—112no—
608#117—222no—
609#117C22×D1111yescharacteristic
610C2×C4⋊C4—21no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—224no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—221no—
619C2×C4⋊C4—222no—
620C2×C4⋊C4—222no—
621C2×C4⋊C4C22×D1112yes—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—221no—
624C2×C42—21no—
625C2×C42—112no—
626C2×C42—222no—
627C2×C42C22×D1111yescharacteristic
628#107—114no—
629#107—112no—
630#107—114no—
631#107—114no—
632#107C22×D1114yes—
633#106—114no—
634#106—114no—
635#106—112no—
636#106—114no—
637#106C22×D1114yes—
638C4⋊C8—114no—
639C4⋊C8—114no—
640C4⋊C8C22×D1112yes—
641C4⋊C8C22×D1112yes—
642#103—112no—
643#103C22×D1114yes—
644#102—112no—
645#102—114no—
646#102—114no—
647#102—112no—
648#102—112no—
649#102C22×D1114yes—
650#97—114no—
651#97—112no—
652C4×C8—114no—
653C4×C8—112no—
654C2×C11—22no—
655C2×C11—42no—
656C2×C11C2×D4×Q811yescharacteristic
657C2×C11C2×#57511yescharacteristic
658C2×C11#358511yescharacteristic
659D11—44no—
660C24—221no—
661#41—22no—
662#41Q8×D1114yes—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—82no—
666C2×Q8—111no—
667C2×Q8—111no—
668C2×Q8—112no—
669C2×Q8—222no—
670C2×Q8—222no—
671C2×Q8—221no—
672C2×Q8—221no—
673C2×Q8—442no—
674C2×Q8—444no—
675C2×Q8C23×D1111yescharacteristic
676C2×D4—21no—
677C2×D4—114no—
678C2×D4—112no—
679C2×D4—221no—
680C2×D4—222no—
681C2×D4C23×D1111yescharacteristic
682C22×C4—21no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—224no—
689C22×C4—224no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—221no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—444no—
696C22×C4—884no—
697C22×C4D4×D1111yescharacteristic
698C22×C4D4×D1111yescharacteristic
699C22×C4C23×D1111yescharacteristic
700SD16—118no—
701D8—118no—
702M16—24no—
703M16—114no—
704M16—222no—
705C2×C8—112no—
706C2×C8—112no—
707C2×C8C23×D1114yes—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—111no—
714C4⋊C4—112no—
715C4⋊C4—111no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—112no—
722C4⋊C4—112no—
723C4⋊C4—224no—
724C4⋊C4—224no—
725C4⋊C4—222no—
726C4⋊C4—222no—
727C4⋊C4—222no—
728C4⋊C4—224no—
729C4⋊C4—224no—
730C4⋊C4—222no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4—222no—
735C4⋊C4—221no—
736C4⋊C4—222no—
737C4⋊C4—221no—
738C4⋊C4—222no—
739C4⋊C4—221no—
740C4⋊C4C23×D1111yescharacteristic
741C4⋊C4C23×D1111yescharacteristic
742C4⋊C4C23×D1114yes—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—222no—
749C22⋊C4—222no—
750C22⋊C4—222no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—112no—
757C42—112no—
758C42—112no—
759C42—112no—
760C42—222no—
761C42—222no—
762C42—222no—
763C42D4×D1111yescharacteristic
764C42D4×D1111yescharacteristic
765C42C23×D1111yescharacteristic
766C42C23×D1111yescharacteristic
767C11#6136711yescharacteristic, complemented, Sylow
768C23—21no—
769C23—224no—
770C23—222no—
771C23—442no—
772C23—442no—
773C23C2×D4×D1111yescharacteristic
774Q8—21no—
775Q8—82no—
776Q8—82no—
777Q8—222no—
778Q8—222no—
779Q8—442no—
780Q8—444no—
781Q8—442no—
782Q8—881no—
783Q8—882no—
784Q8C2×Q8×D1112yes—
785D4—24no—
786D4—21no—
787D4—114no—
788D4—224no—
789D4—222no—
790D4C2×Q8×D1112yes—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—24no—
797C2×C4—41no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—81no—
801C2×C4—112no—
802C2×C4—112no—
803C2×C4—112no—
804C2×C4—112no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—444no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—444no—
812C2×C4—442no—
813C2×C4—444no—
814C2×C4—884no—
815C2×C4—884no—
816C2×C4—882no—
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4C2×D4×D1111yescharacteristic
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×Q8×D1112yes—
823C2×C4#6704312yes—
824C2×C4C24×D1111yescharacteristic
825C8—24no—
826C8—114no—
827C8—222no—
828C22—21no—
829C22—21no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—224no—
834C22—448no—
835C22—442no—
836C22—442no—
837C22#1062316312yes—
838C22C22×D4×D1111yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—22no—
843C4—44no—
844C4—41no—
845C4—41no—
846C4—222no—
847C4—222no—
848C4—222no—
849C4—222no—
850C4—442no—
851C4—442no—
852C4—442no—
853C4#1062316312yes—
854C4#1062330812yes—
855C4C22×Q8×D1111yescharacteristic
856C4C2×#6704311yescharacteristic
857C2—22no—
858C2—42no—
859C2—444no—
860C2C2×#1062316311yescharacteristic
861C2C2×#1062330811yescharacteristic
862C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3079C2
socleC22×C11C23×D4
prime radicalC2×#67002C22
hypercenter#3079D11
hypocenterC11#61367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #41×Dic22C2semidirect
2. C2×#10623261C2semidirect
3. #13081569C2semidirect
4. #13081568C2semidirect
5. #13081525C2semidirect
6. #13081514C2semidirect
7. #13081490C2semidirect
8. #13081482C2semidirect
9. #13079166C2semidirect
10. #13079158C2semidirect
11. #13078436C2semidirect
12. #13078415C2semidirect
13. #13078412C2semidirect
14. #13077567C2semidirect
17. C11×#3079C2semidirect
29. #10623101C22semidirect
30. #10623100C22semidirect
31. Q8×Dic22C22semidirect
33. #10623074C22semidirect
35. #10623070C22semidirect
37. D4×Dic22C22semidirect
49. C11×#477C22semidirect
50. C11×#476C22semidirect
51. C11×#475C22semidirect
52. C11×#474C22semidirect
61. #10622693C22semidirect
62. #10622692C22semidirect
63. #10622691C22semidirect
75. #10622491C22semidirect
76. #10622489C22semidirect
79. #10622471C22semidirect
80. #10622469C22semidirect
84. #10622444C22semidirect
85. #10622443C22semidirect
86. #10622441C22semidirect
88. #10622412C22semidirect
89. #10622409C22semidirect
92. #10622379C22semidirect
93. #10622376C22semidirect
119. #67002Q8semidirect
253. C2×D44C2×Q8semidirect
293. #4325C2×Q8semidirect
294. #4323C2×Q8semidirect
334. #4318C2×Q8semidirect
348. #3079D11semidirect
459. #477C2×D11semidirect
462. #476C2×D11semidirect
463. #475C2×D11semidirect
466. #474C2×D11semidirect
767. C11#61367semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
C2×#106232612
#130815692
#130815682
#130815252
#130815142
#130814902
#130814822
#130791662
#130791582
#130784362
#130784152
#130784122
#130775672
#130774292
C4×#670022
C11×#30792
#6136711