Finite Group Databasebeta

← #15622529

Subgroups — #15622529

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082368C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13078869C214yesmaximal, complemented
4#13078802C214yesmaximal, complemented
5#13078756C212yesmaximal, complemented
6#13078716C212yesmaximal, complemented
7#13078665C212yesmaximal, complemented
8#13078625C212yesmaximal, complemented
9#13078565C211yesmaximal, characteristic, complemented
10#13078531C211yesmaximal, characteristic, complemented
11#13078448C212yesmaximal, complemented
12#13078129C212yesmaximal, complemented
13#13077846C211yesmaximal, characteristic
14C2×#10622344C211yesmaximal, characteristic, complemented
15#13077477C212yesmaximal, complemented
16#13077450C212yesmaximal, complemented
17C11×#2924C211yesmaximal, characteristic, complemented
18C23×D44C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20#10623322C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66961C2212yes—
24C22×#4314C2212yes—
25#10623065C2212yescomplemented
26#10623064—21no—
27#10623062—22no—
28#10623060—21no—
29#10623057C2211yescharacteristic, complemented
30#10623054C2211yescharacteristic, complemented
31#10623052—21no—
32#10623052—22no—
33#10623052—21no—
34#10623052C2214yes—
35#10623052C2212yes—
36#10623052C2212yes—
37#10623050C2211yescharacteristic, complemented
38#10623049C2212yescomplemented
39#10623047C2211yescharacteristic, complemented
40#10623044—21no—
41#10623042—21no—
42C2×#66946—21no—
43C2×#66946—21no—
44#10623026—22no—
45C2×C22⋊C4×D11—22no—
46#10623010C2212yescomplemented
47C2×C4×D44C2212yes—
48C2×C4×D44C2212yes—
49#10623001C2212yescomplemented
50C11×#433C2214yescomplemented
51C11×#432C2212yescomplemented
52C11×#431C2212yescomplemented
53C11×#424C2212yescomplemented
54C11×#407C2211yescharacteristic
55C2×C11×C22⋊C8C2211yescharacteristic
56C11×#405C2212yescomplemented
57#10622744C2212yes—
58#10622734C2212yescomplemented
59#10622733C2212yescomplemented
60#10622726C2212yescomplemented
61C2×#66885C2212yes—
62#10622719C2212yescomplemented
63#10622460C2214yescomplemented
64#10622460C2214yescomplemented
65#10622459C2214yescomplemented
66#10622457C2214yescomplemented
67#10622457C2214yescomplemented
68#10622455C2214yescomplemented
69#10622454C2214yescomplemented
70#10622454C2214yescomplemented
71#10622350C2212yescomplemented
72#10622349C2211yescharacteristic, complemented
73#10622348C2211yescharacteristic, complemented
74#10622345C2212yes—
75#10622345C2212yes—
76#10622344C2214yes—
77#10622344C2212yes—
78#10622344C2212yes—
79#10622344C2212yes—
80#10622344C2212yes—
81#10622336C2212yescomplemented
82#10622336C2214yescomplemented
83#10622335C2211yescharacteristic, complemented
84#10622335C2212yescomplemented
85#10622334C2211yescharacteristic, complemented
86#10622334C2212yescomplemented
87#10622324C2214yescomplemented
88#10622323C2214yescomplemented
89#10622323C2214yescomplemented
90#10622323C2214yescomplemented
91C4×D88C2214yescomplemented
92C4×#4314C2214yescomplemented
93C4×#4314C2214yescomplemented
94C4×#4314C2214yescomplemented
95C24×D11—21no—
96C23×C4×C11C2311yescharacteristic
97C2×#4339C2311yescharacteristic
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44—28no—
102C22×D44C2312yes—
103C22×D44C2312yes—
104C22×D44C2312yes—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×Dic22C2311yescharacteristic
108C2×C11×M16C2312yes—
109C22×C8×C11C2312yes—
110C11×#117D411yescharacteristic
111C11×#117D412yes—
112C11×#117D411yescharacteristic
113C11×#117C2311yescharacteristic
114C11×#117C2312yes—
115C11×#117C2311yescharacteristic
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D412yes—
119C2×C42×C11C2312yes—
120#67006—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#66983C2311yescharacteristic
124#66983C2311yescharacteristic
125#66982—22no—
126#66982—21no—
127C4×C22⋊D11—22no—
128C4×C22⋊D11—21no—
129C4×C22⋊D11—21no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132#66979—22no—
133#66979—21no—
134#66979—21no—
135#66979C2312yes—
136#66979C2311yescharacteristic
137#66979C2312yes—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977—21no—
143#66977—21no—
144#66977C2311yescharacteristic
145#66977C2312yes—
146#66977C2311yescharacteristic
147#66977C2312yes—
148C2×Dic11⋊C4—21no—
149C2×C4×Dic11—21no—
150#66961—28no—
151C2×D88C2314yes—
152C2×#4314—28no—
153C2×#4314C2314yes—
154C2×#4314C2314yes—
155C2×#4314C2314yes—
156#66951—22no—
157#66950—21no—
158#66950—21no—
159#66949—22no—
160#66946—22no—
161#66946—22no—
162#66946—22no—
163#66946—24no—
164#66946—24no—
165#66946—22no—
166#66945—21no—
167C4⋊C4×D11—21no—
168#66943—21no—
169#66942—22no—
170#66942—22no—
171#66941—21no—
172#66940—21no—
173#66940—21no—
174#66939—22no—
175#66938—22no—
176#66936—22no—
177(C22⋊D11)⋊C4—22no—
178C22⋊C4×D11—24no—
179C22⋊C4×D11—24no—
180C22⋊C4×D11—24no—
181C22⋊C4×D11—24no—
182#66932—22no—
183#66932—22no—
184#66931—22no—
185#66930—22no—
186#66929—22no—
187#66928C2312yescomplemented
188C4×D44—22no—
189C4×D44—22no—
190C4×D44—22no—
191C4×D44—22no—
192C4×D44C2314yes—
193C4×D44C2314yes—
194C4×D44C2314yes—
195C4×D44C2314yes—
196C4×D44C2312yescomplemented
197#66925—22no—
198#66923—22no—
199#66923C2312yescomplemented
200#66922C2312yescomplemented
201#66922C2312yescomplemented
202C4×Dic22—22no—
203C4×Dic22C2312yescomplemented
204C4×Dic22C2312yescomplemented
205C4×Dic22C2312yescomplemented
206C11×C4⋊C8C2314yescomplemented
207C11×C4⋊C8C2314yescomplemented
208C11×C22⋊C8C2312yes—
209C11×C22⋊C8C2311yescharacteristic
210C11×C22⋊C8C2311yescharacteristic
211C11×C22⋊C8C2312yes—
212C11×C22⋊C8C2312yes—
213C11×#97C2314yescomplemented
214C4×C8×C11C2314yescomplemented
215#66885C2314yes—
216#66885C2314yes—
217#66885C2314yes—
218#66885C2314yes—
219#66885C2312yescomplemented
220#66885C2312yescomplemented
221#66882C2314yescomplemented
222#66882C2312yescomplemented
223#66882C2312yescomplemented
224#66881C2314yescomplemented
225#66881C2312yescomplemented
226#66881C2312yescomplemented
227#66880C2312yescomplemented
228#66880C2312yescomplemented
229#66880C2314yescomplemented
230#66880C2314yescomplemented
231#60579—111nomaximal, Sylow
232C24×C11C2×D411yescharacteristic
233C23×D11—22no—
234C23×D11—28no—
235C23×D11—22no—
236C23×D11—22no—
237C23×D11—82no—
238C23×D11—82no—
239C22×C4×C11—24no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C2×C22⋊D11—21no—
249C2×C22⋊D11—21no—
250C2×C22⋊D11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255#4339—24no—
256C2×D44—28no—
257C2×D44—28no—
258C2×D44—28no—
259C2×D44—28no—
260C2×D44—28no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—24no—
265C2×D44#4118yes—
266C2×D44C2411yescharacteristic
267C2×D44C2414yes—
268C2×C4×D11—21no—
269C2×C4×D11—22no—
270C2×C4×D11—24no—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—24no—
274C2×C4×D11—84no—
275C2×C4×D11—84no—
276C2×Dic22—21no—
277C2×Dic22—22no—
278C2×Dic22—24no—
279C2×Dic22C2411yescharacteristic
280C2×Dic22C2412yes—
281C11×M16—24no—
282C2×C8×C11—24no—
283C2×C8×C11C2414yes—
284C2×C8×C11C2412yes—
285C2×C8×C11C2412yes—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2×D412yes—
291C11×C4⋊C4C2×D411yescharacteristic
292C11×C22⋊C4C2×D412yes—
293C11×C22⋊C4C2×D412yes—
294C11×C22⋊C4C2×D412yes—
295C11×C22⋊C4C2×D412yes—
296C42×C11C2×D412yes—
297C42×C11C2×D412yes—
298C42×C11C2412yes—
299C42×C11C2412yes—
300C22⋊Dic11—21no—
301C22⋊Dic11—21no—
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—21no—
306C22⋊Dic11—22no—
307(C2×D11)⋊C4—21no—
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—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—21no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11—22no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321C4⋊Dic11—21no—
322C4⋊Dic11C2412yes—
323C4⋊Dic11C2412yes—
324C4⋊Dic11C2411yescharacteristic
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2412yes—
327Dic11⋊C4—21no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—21no—
335Dic11⋊C4—22no—
336C4×Dic11—22no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—21no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342D88—28no—
343#4314—28no—
344#4314—28no—
345#4314—28no—
346#3495—111no—
347C2×#518—111no—
348#3123—114no—
349#3118—114no—
350#3114—112no—
351#3110—112no—
352#3105—112no—
353#3101—112no—
354#3095—111no—
355#3091—111no—
356#3081—112no—
357#3042—112no—
358#3003—111no—
359C2×#450—111no—
360#2949—112no—
361#2946—112no—
362#2924D1111yescharacteristic, complemented
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—41no—
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—28no—
370C22×D11—24no—
371C22×D11—28no—
372C22×D11—28no—
373C22×D11—21no—
374C22×D11—44no—
375C22×D11—44no—
376C22×D11—82no—
377C22×D11—82no—
378C22×D11—82no—
379C22×D11—82no—
380C22×D11—816no—
381C2×C4×C11—22no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—42no—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D412yes—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D412yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C2×#4114yes—
396C2×C4×C11C2511yescharacteristic
397C22⋊D11—42no—
398C22⋊D11—42no—
399C22⋊D11—81no—
400C2×Dic11—21no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11—42no—
410C2×Dic11—81no—
411D44—28no—
412D44—28no—
413D44—28no—
414D44—24no—
415D44—22no—
416D44C2×#4118yes—
417C4×D11—42no—
418C4×D11—82no—
419C4×D11—84no—
420C4×D11—84no—
421C4×D11—84no—
422C4×D11—84no—
423Dic22—24no—
424Dic22—22no—
425Dic22—42no—
426Dic22—82no—
427C8×C11—22no—
428C8×C11—22no—
429C8×C11—24no—
430C23×D4—111no—
431C2×AGL(1,ℤ/8)—112no—
432C22×SD16—112no—
433#556—221no—
434#554—221no—
435#552—221no—
436#552—222no—
437#552—221no—
438#551—222no—
439#544—111no—
440#542—112no—
441#541—112no—
442#536—111no—
443#533—112no—
444#529—112no—
445#525—111no—
446C2×C22⋊Q8—111no—
447#520—111no—
448#519—111no—
449#518—112no—
450#518—114no—
451#518—112no—
452#518—222no—
453#518—221no—
454#518—221no—
455C2×C4×D4—112no—
456C2×C4×D4—112no—
457C2×C4×D4—221no—
458C2×C4×D4—221no—
459C2×#117—111no—
460C2×#117C2×D1111yescharacteristic
461C22×C22⋊C4—222no—
462#485—112no—
463#485—114no—
464#484—111no—
465#484—112no—
466#483—111no—
467#483—112no—
468#482—112no—
469#481—111no—
470#480—111no—
471#478—114no—
472#478—114no—
473#476—114no—
474#474—114no—
475#463—114no—
476#463—114no—
477#461—114no—
478#461—114no—
479#450—112no—
480#450—112no—
481#450—112no—
482#450—114no—
483#450—112no—
484#447—112no—
485#447—112no—
486#442—114no—
487#440—114no—
488#440—114no—
489#440—114no—
490C4×SD16—114no—
491C4×SD16—114no—
492C4×SD16—114no—
493C4×D8—114no—
494#433C2×D1114yescomplemented
495#432C2×D1112yescomplemented
496#431C2×D1112yescomplemented
497#428—112no—
498#427—112no—
499#424C2×D1112yescomplemented
500#419—112no—
501#418—112no—
502#416—112no—
503C2×#102—112no—
504#407C2×D1111yescharacteristic
505C2×C22⋊C8C2×D1111yescharacteristic
506#405C2×D1112yescomplemented
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—44no—
515C22×C11#52512yes—
516C22×C11#57712yes—
517C22×C11C23×D411yescharacteristic
518C2×D11—28no—
519C2×D11—416no—
520C2×D11—44no—
521C2×D11—44no—
522C2×D11—41no—
523C2×D11—41no—
524C2×D11—41no—
525C2×D11—88no—
526C2×D11—88no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11#52512yes—
534C4×C11C22×#4112yes—
535Dic11—41no—
536Dic11—42no—
537Dic11—42no—
538Dic11—42no—
539Dic11—41no—
540Dic11—42no—
541Dic11—41no—
542C25—221no—
543C2×#41—111no—
544C22×Q8—111no—
545C22×D4—112no—
546C22×D4—112no—
547C22×D4—112no—
548C22×D4—228no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4C22×D1111yescharacteristic
555AGL(1,ℤ/8)—228no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—228no—
560C2×D8—114no—
561C2×M16C22×D1112yes—
562C22×C8C22×D1112yes—
563C4⋊Q8—112no—
564C4⋊Q8—112no—
565C4⋊Q8—221no—
566#126—222no—
567#126—222no—
568#126—222no—
569#126—222no—
570#125—112no—
571#125—222no—
572#125—222no—
573#125—221no—
574#125—222no—
575#124—112no—
576#124—222no—
577#123—221no—
578#123—222no—
579#123—222no—
580#123—222no—
581C22⋊Q8—112no—
582C22⋊Q8—112no—
583C22⋊Q8—111no—
584C22⋊Q8—111no—
585C22⋊Q8—221no—
586C22⋊Q8—221no—
587C22⋊Q8—222no—
588C22⋊Q8—221no—
589C22⋊Q8—221no—
590C22⋊Q8—222no—
591C22⋊Q8—222no—
592#121—111no—
593#121—111no—
594#120—221no—
595C4×Q8—112no—
596C4×Q8—112no—
597C4×Q8—112no—
598C4×Q8—221no—
599C4×Q8—221no—
600C4×Q8—222no—
601C4×D4—114no—
602C4×D4—114no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—112no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—224no—
613C4×D4—222no—
614C4×D4—224no—
615C4×D4—222no—
616C4×D4—222no—
617C4×D4—222no—
618C4×D4—222no—
619C4×D4—222no—
620#117—112no—
621#117—112no—
622#117—111no—
623#117—221no—
624#117—221no—
625#117—222no—
626#117—221no—
627#117—222no—
628#117—222no—
629#117D4411yescharacteristic
630#117D4412yes—
631#117D4411yescharacteristic
632#117C22×D1111yescharacteristic
633#117C22×D1111yescharacteristic
634#117C22×D1112yes—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4—221no—
640C2×C4⋊C4D4411yescharacteristic
641C2×C4⋊C4D4411yescharacteristic
642C2×C22⋊C4—221no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—222no—
645C2×C22⋊C4—222no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—224no—
648C2×C22⋊C4—224no—
649C2×C22⋊C4—224no—
650C2×C22⋊C4D4412yes—
651C2×C42—221no—
652C2×C42C22×D1112yes—
653#107—112no—
654#107—112no—
655#107—114no—
656#106—112no—
657#106—112no—
658#106—114no—
659C4⋊C8C22×D1114yescomplemented
660C4⋊C8C22×D1114yescomplemented
661#103—112no—
662#103—112no—
663#103—114no—
664#103—114no—
665#102—114no—
666#102—114no—
667#102—114no—
668#102—114no—
669#102—112no—
670#102—112no—
671C22⋊C8C22×D1111yescharacteristic
672C22⋊C8C22×D1111yescharacteristic
673C22⋊C8C22×D1112yes—
674C22⋊C8C22×D1112yes—
675C22⋊C8C22×D1112yes—
676#97C22×D1114yescomplemented
677C4×C8C22×D1114yescomplemented
678C2×C11—22no—
679C2×C11—22no—
680C2×C11—41no—
681C2×C11C2×#52511yescharacteristic
682C2×C11C2×#57711yescharacteristic
683C2×C11#358511yescharacteristic
684D11—48no—
685D11—81no—
686C24—228no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—882no—
691C24—882no—
692C24C2×D4411yescharacteristic
693#41—224no—
694C2×Q8—112no—
695C2×Q8—111no—
696C2×Q8—221no—
697C2×Q8—222no—
698C2×Q8—224no—
699C2×D4—118no—
700C2×D4—114no—
701C2×D4—111no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—228no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—221no—
708C2×D4—221no—
709C2×D4—221no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—224no—
714C22×C4—24no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—224no—
721C22×C4—224no—
722C22×C4—224no—
723C22×C4—224no—
724C22×C4—222no—
725C22×C4—884no—
726C22×C4—884no—
727C22×C4C2×D4411yescharacteristic
728C22×C4C2×D4412yes—
729C22×C4C2×D4411yescharacteristic
730C22×C4C2×D4411yescharacteristic
731C22×C4C2×D4412yes—
732C22×C4C23×D1111yescharacteristic
733C22×C4C23×D1111yescharacteristic
734C22×C4C23×D1111yescharacteristic
735SD16—228no—
736SD16—228no—
737SD16—228no—
738D8—228no—
739M16—24no—
740C2×C8—24no—
741C2×C8C23×D1112yes—
742C2×C8C23×D1114yes—
743C2×C8C23×D1112yes—
744C4⋊C4—112no—
745C4⋊C4—111no—
746C4⋊C4—111no—
747C4⋊C4—112no—
748C4⋊C4—112no—
749C4⋊C4—221no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4—222no—
755C4⋊C4—222no—
756C4⋊C4—222no—
757C4⋊C4—222no—
758C4⋊C4—222no—
759C4⋊C4—222no—
760C4⋊C4—221no—
761C4⋊C4—221no—
762C4⋊C4—222no—
763C4⋊C4—222no—
764C4⋊C4C2×D4411yescharacteristic
765C4⋊C4C2×D4411yescharacteristic
766C4⋊C4C2×D4412yes—
767C4⋊C4C2×D4411yescharacteristic
768C4⋊C4C2×D4411yescharacteristic
769C4⋊C4C2×D4412yes—
770C22⋊C4—222no—
771C22⋊C4—222no—
772C22⋊C4—222no—
773C22⋊C4—222no—
774C22⋊C4—221no—
775C22⋊C4—221no—
776C22⋊C4—221no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C22⋊C4—224no—
781C22⋊C4—221no—
782C22⋊C4—222no—
783C22⋊C4—222no—
784C22⋊C4—221no—
785C22⋊C4—222no—
786C22⋊C4C2×D4412yes—
787C22⋊C4C2×D4412yes—
788C22⋊C4C2×D4412yes—
789C22⋊C4C2×D4412yes—
790C42—222no—
791C42—222no—
792C42—221no—
793C42—222no—
794C42—222no—
795C42—222no—
796C42C2×D4412yes—
797C42C2×D4412yes—
798C42C23×D1112yes—
799C42C23×D1112yes—
800C11#6057911yescharacteristic, complemented, Sylow
801C23—22no—
802C23—22no—
803C23—41no—
804C23—228no—
805C23—228no—
806C23—224no—
807C23—228no—
808C23—221no—
809C23—444no—
810C23—444no—
811C23—882no—
812C23—882no—
813C23—882no—
814C23—882no—
815C23—8816no—
816C23C22×D4411yescharacteristic
817C23C22×D4411yescharacteristic
818C23C22×D4411yescharacteristic
819Q8—224no—
820Q8—222no—
821Q8—442no—
822Q8—882no—
823D4—118no—
824D4—228no—
825D4—228no—
826D4—228no—
827D4—224no—
828D4—222no—
829D4—442no—
830D4—442no—
831D4—881no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—42no—
839C2×C4—221no—
840C2×C4—221no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—221no—
845C2×C4—222no—
846C2×C4—442no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—884no—
851C2×C4—884no—
852C2×C4—884no—
853C2×C4—884no—
854C2×C4—882no—
855C2×C4—881no—
856C2×C4C22×D4412yes—
857C2×C4C22×D4411yescharacteristic
858C2×C4C22×D4412yes—
859C2×C4C22×D4411yescharacteristic
860C2×C4C22×D4412yes—
861C2×C4C22×D4412yes—
862C2×C4C22×D4411yescharacteristic
863C2×C4#41×D1114yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—22no—
867C8—24no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—228no—
877C22—4416no—
878C22—444no—
879C22—444no—
880C22—441no—
881C22—441no—
882C22—441no—
883C22—888no—
884C22—888no—
885C22#1062305512yes—
886C22#1062328212yes—
887C22C23×D4411yescharacteristic
888C4—21no—
889C4—21no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—22no—
894C4—441no—
895C4—442no—
896C4—442no—
897C4—442no—
898C4—441no—
899C4—442no—
900C4—441no—
901C4#1062305512yes—
902C4C2×#41×D1112yes—
903C2—22no—
904C2—22no—
905C2—41no—
906C2—448no—
907C2—881no—
908C2C2×#1062305511yescharacteristic
909C2C2×#1062328211yescharacteristic
910C2#1308339711yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2924C2
socleC22×C11C23×D4
prime radical#13077846C2
hypercenter#2924D11
hypocenterC11#60579
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
1. #13082368C2semidirect
2. C2×#10623052C2semidirect
3. #13078869C2semidirect
4. #13078802C2semidirect
5. #13078756C2semidirect
6. #13078716C2semidirect
7. #13078665C2semidirect
8. #13078625C2semidirect
9. #13078565C2semidirect
10. #13078531C2semidirect
11. #13078448C2semidirect
12. #13078129C2semidirect
14. C2×#10622344C2semidirect
15. #13077477C2semidirect
16. #13077450C2semidirect
17. C11×#2924C2semidirect
25. #10623065C22semidirect
29. #10623057C22semidirect
30. #10623054C22semidirect
37. #10623050C22semidirect
38. #10623049C22semidirect
39. #10623047C22semidirect
46. #10623010C22semidirect
49. #10623001C22semidirect
50. C11×#433C22semidirect
51. C11×#432C22semidirect
52. C11×#431C22semidirect
53. C11×#424C22semidirect
56. C11×#405C22semidirect
58. #10622734C22semidirect
59. #10622733C22semidirect
60. #10622726C22semidirect
62. #10622719C22semidirect
63. #10622460C22semidirect
64. #10622460C22semidirect
65. #10622459C22semidirect
66. #10622457C22semidirect
67. #10622457C22semidirect
68. #10622455C22semidirect
69. #10622454C22semidirect
70. #10622454C22semidirect
71. #10622350C22semidirect
72. #10622349C22semidirect
73. #10622348C22semidirect
81. #10622336C22semidirect
82. #10622336C22semidirect
83. #10622335C22semidirect
84. #10622335C22semidirect
85. #10622334C22semidirect
86. #10622334C22semidirect
87. #10622324C22semidirect
88. #10622323C22semidirect
89. #10622323C22semidirect
90. #10622323C22semidirect
91. C4×D88C22semidirect
92. C4×#4314C22semidirect
93. C4×#4314C22semidirect
94. C4×#4314C22semidirect
187. #66928C23semidirect
196. C4×D44C23semidirect
199. #66923C23semidirect
200. #66922C23semidirect
201. #66922C23semidirect
203. C4×Dic22C23semidirect
204. C4×Dic22C23semidirect
205. C4×Dic22C23semidirect
206. C11×C4⋊C8C23semidirect
207. C11×C4⋊C8C23semidirect
213. C11×#97C23semidirect
214. C4×C8×C11C23semidirect
219. #66885C23semidirect
220. #66885C23semidirect
221. #66882C23semidirect
222. #66882C23semidirect
223. #66882C23semidirect
224. #66881C23semidirect
225. #66881C23semidirect
226. #66881C23semidirect
227. #66880C23semidirect
228. #66880C23semidirect
229. #66880C23semidirect
230. #66880C23semidirect
362. #2924D11semidirect
494. #433C2×D11semidirect
495. #432C2×D11semidirect
496. #431C2×D11semidirect
499. #424C2×D11semidirect
506. #405C2×D11semidirect
659. C4⋊C8C22×D11semidirect
660. C4⋊C8C22×D11semidirect
676. #97C22×D11semidirect
677. C4×C8C22×D11semidirect
800. C11#60579semidirect

Maximal subgroups

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

subgroupindex
#130823682
C2×#106230522
#130788692
#130788022
#130787562
#130787162
#130786652
#130786252
#130785652
#130785312
#130784482
#130781292
#130778462
C2×#106223442
#130774772
#130774502
C11×#29242
#6057911