Finite Group Databasebeta

← #15617346

Subgroups — #15617346

Order 2816.

4810 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×2−1+4C211yesmaximal, characteristic
2C2×#10623281C211yesmaximal, characteristic, complemented
3#13081816C211yesmaximal, characteristic, complemented
4#13077150C211yesmaximal, characteristic, complemented
5#13077149C211yesmaximal, characteristic, complemented
6#13077148C213yesmaximal, complemented
7#13077147C213yesmaximal, complemented
8#13077146C211yesmaximal, characteristic, complemented
9#13077145C213yesmaximal, complemented
10#13077144C213yesmaximal, complemented
11#13077132C213yesmaximal, complemented
12#13077131C213yesmaximal, complemented
13C2×#10622415C213yesmaximal, complemented
14D11×#419C213yesmaximal, complemented
15C11×#2898C211yesmaximal, characteristic, complemented
16C2×C11×2−1+4C2211yescharacteristic
17D11×2−1+4—28no—
18D11×2−1+4C4116yescomplemented
19C2×#67043—23no—
20C2×#67043C2213yes—
21C2×#67043C2211yescharacteristic
22C2×#41×D11—23no—
23C2×#41×D11C2213yes—
24C2×#41×D11C2211yescharacteristic
25C2×#67040—21no—
26C2×#67040C2213yes—
27C22×Q8×D11—21no—
28C22×Q8×D11C2213yes—
29C2×C11×#131C2211yescharacteristic, complemented
30C11×#520C2211yescharacteristic, complemented
31#10623358C2211yescharacteristic, complemented
32C2×#67001C2211yescharacteristic, complemented
33#10623281—28no—
34C2×#66960C2213yescomplemented
35C2×M16×D11C2213yes—
36C2×#66954C2213yescomplemented
37C22×#4313C2213yes—
38C4×#4343—21no—
39#10623103—21no—
40#10623076—23no—
41C4×#4341—23no—
42#10623054C2213yescomplemented
43D11×#117C2213yes—
44#10623035C2213yescomplemented
45C2×#66945C2213yes—
46C11×#419C2213yescomplemented
47C11×#417C2213yescomplemented
48C11×#416C2213yescomplemented
49C2×C11×#103C2213yescomplemented
50#10622846C2213yescomplemented
51#10622845C2213yescomplemented
52#10622838C2213yescomplemented
53C2×#66899C2213yescomplemented
54#10622746C2213yescomplemented
55#10622733C2213yescomplemented
56#10622726C2213yescomplemented
57C2×#66880C2213yescomplemented
58#10622617C2213yescomplemented
59#10622615C2213yescomplemented
60C2×#66874C2213yescomplemented
61#10622579C2213yescomplemented
62#10622417C2216yescomplemented
63#10622416C2213yescomplemented
64#10622416C2213yescomplemented
65#10622415C2213yes—
66#10622415C2216yes—
67#10622415C2213yes—
68#10622415C2216yescomplemented
69#10622415C2216yescomplemented
70D11×#103C2216yescomplemented
71D11×#103C2216yescomplemented
72#10622385C2216yescomplemented
73#10622384C2213yescomplemented
74#10622384C2213yescomplemented
75#10622383C2211yescharacteristic
76#10622383C2213yes—
77C11×2−1+4—24no—
78C11×2−1+4C2×C418yescomplemented
79C2×C11×#41—23no—
80C2×C11×#41C2313yes—
81C2×C11×#41C2311yescharacteristic
82C22×Q8×C11—21no—
83C22×Q8×C11C2313yes—
84#67043—24no—
85#67043—248no—
86#67043—212no—
87#67043C2×C4124yescomplemented
88#67043C2×C418yescomplemented
89#41×D11—248no—
90#41×D11—212no—
91#41×D11C2×C418yes—
92#41×D11C2×C4124yescomplemented
93#41×D11D418yes—
94#67040—216no—
95#67040—212no—
96#67040C2×C4124yescomplemented
97C2×#4343—23no—
98C2×#4343D411yescharacteristic
99C2×#4343C2313yes—
100C2×Q8×D11—21no—
101C2×Q8×D11—216no—
102C2×Q8×D11—23no—
103C2×Q8×D11—23no—
104C2×Q8×D11—212no—
105C2×Q8×D11—23no—
106C2×Q8×D11C2×C4124yescomplemented
107C2×Q8×D11D411yescharacteristic
108C2×Q8×D11C2316yes—
109C2×Q8×D11C2313yes—
110C2×#4341—23no—
111C2×#4341—26no—
112C2×#4341—23no—
113C2×#4341D413yes—
114C2×#4341C2313yes—
115C2×D4×D11—23no—
116C2×D4×D11D413yes—
117C2×D4×D11C2311yescharacteristic
118C2×#4339—26no—
119C2×#4339—23no—
120C2×#4339—23no—
121C2×#4339C2313yes—
122C2×#4339C2313yes—
123C22×C4×D11—23no—
124C22×C4×D11—23no—
125C22×C4×D11C2313yes—
126C22×Dic22—23no—
127C22×Dic22—23no—
128C22×Dic22C2313yes—
129C11×#131—24no—
130C2×C11×M16C2313yes—
131C22×C8×C11C2313yes—
132C4×Q8×C11—21no—
133C4×D4×C11—23no—
134C11×#117C2313yes—
135C2×C11×C4⋊C4C2313yes—
136#67001—24no—
137Q8×Dic11—21no—
138D4×Dic11—23no—
139C4×C22⋊D11—26no—
140C2×(C2×D11)⋊C4—23no—
141#66979C2313yes—
142C2×C4⋊Dic11C2313yes—
143C2×C4×Dic11—23no—
144C2×#4318C2313yes—
145C22×C11⋊C8C2313yes—
146#66960—212no—
147M16×D11—212no—
148#66954—212no—
149C2×#4313—212no—
150C2×#4313C2311yescharacteristic
151C2×#4313C2313yes—
152C2×#4313C2313yes—
153C2×#4313C2313yes—
154C2×C8×D11C2316yes—
155#66946—23no—
156#66945—23no—
157#66945—23no—
158#66945C2313yes—
159#66945C2316yes—
160#66945C2311yescharacteristic
161C4⋊C4×D11C2313yes—
162C4⋊C4×D11C2313yes—
163#66940—23no—
164(C22⋊D11)⋊C4—26no—
165C22⋊C4×D11—23no—
166#66930—23no—
167C4×D44—23no—
168#66925—23no—
169C42×D11—23no—
170C4×Dic22—23no—
171C11×#103C2313yes—
172C11×#103C2316yes—
173C11×#103C2313yes—
174C11×#102C2311yescharacteristic
175C11×#102C2313yes—
176#66899C2313yes—
177#66899C2316yes—
178#66899C2313yes—
179#66896C2313yes—
180#66896C2311yescharacteristic
181#66885C2311yescharacteristic
182#66885C2313yes—
183#66880C2313yes—
184#66880C2313yes—
185#66880C2316yes—
186#66874C2316yes—
187#66874C2313yes—
188#66874C2313yes—
189#66873C2313yes—
190#66873C2311yescharacteristic
191#60088—111nomaximal, Sylow
192C23×D11—21no—
193C23×D11C2×D413yes—
194C11×#41—224no—
195C11×#41—26no—
196C11×#41C22×C4112yes—
197C11×#41C22×C414yes—
198C11×#41C2×D414yes—
199C2×Q8×C11—28no—
200C2×Q8×C11—23no—
201C2×Q8×C11—26no—
202C2×Q8×C11C22×C4112yes—
203C2×Q8×C11C2×D411yescharacteristic
204C2×Q8×C11C2413yes—
205C2×D4×C11—23no—
206C2×D4×C11C2×D413yes—
207C2×D4×C11C2411yescharacteristic
208C22×C4×C11—23no—
209C22×C4×C11—23no—
210C22×C4×C11—23no—
211C22×C4×C11C2413yes—
212C2×C22⋊D11—21no—
213C2×C22⋊D11—23no—
214C2×C22⋊D11—23no—
215C2×C22⋊D11C2×D416yes—
216C22×Dic11—23no—
217C22×Dic11—23no—
218C22×Dic11—23no—
219C22×Dic11C2×D413yes—
220#4343—224no—
221#4343—26no—
222#4343C22⋊C418yes—
223#4343C22×C4112yes—
224Q8×D11—224no—
225Q8×D11—224no—
226Q8×D11—26no—
227Q8×D11—212no—
228Q8×D11—224no—
229Q8×D11—28no—
230Q8×D11C22⋊C418yes—
231Q8×D11C22×C4112yes—
232Q8×D11C22×C4124yes—
233#4341—248no—
234#4341—224no—
235#4341—26no—
236#4341—224no—
237#4341C22⋊C4124yes—
238#4341C22×C4112yes—
239D4×D11—22no—
240D4×D11—224no—
241D4×D11C22⋊C4124yes—
242D4×D11C22×C414yes—
243#4339—248no—
244#4339—224no—
245#4339—224no—
246#4339—26no—
247#4339C22×C4112yes—
248#4339C22×C4112yes—
249#4339C2×D4112yes—
250C2×D44—23no—
251C2×D44C2×D413yes—
252C2×D44C2411yescharacteristic
253C2×C4×D11—23no—
254C2×C4×D11—224no—
255C2×C4×D11—224no—
256C2×C4×D11—23no—
257C2×C4×D11—26no—
258C2×C4×D11—23no—
259C2×C4×D11—23no—
260C2×C4×D11—23no—
261C2×C4×D11C22×C4112yes—
262C2×C4×D11C2×D4112yes—
263C2×C4×D11C2×D413yes—
264C2×C4×D11C2×D413yes—
265C2×C4×D11C2413yes—
266C2×C4×D11C2411yescharacteristic
267C2×Dic22—224no—
268C2×Dic22—23no—
269C2×Dic22—26no—
270C2×Dic22—224no—
271C2×Dic22—23no—
272C2×Dic22—26no—
273C2×Dic22C22×C4112yes—
274C2×Dic22C2×D413yes—
275C2×Dic22C2413yes—
276C11×M16—26no—
277C2×C8×C11—26no—
278C2×C8×C11C2413yes—
279C2×C8×C11C2411yescharacteristic
280C11×C4⋊C4—23no—
281C11×C4⋊C4C2411yescharacteristic
282C11×C4⋊C4C2413yes—
283C11×C22⋊C4—23no—
284C42×C11—23no—
285C22⋊Dic11—23no—
286(C2×D11)⋊C4—21no—
287(C2×D11)⋊C4—23no—
288(C2×D11)⋊C4—26no—
289C4⋊Dic11—23no—
290C4⋊Dic11C2411yescharacteristic
291C4⋊Dic11C2413yes—
292Dic11⋊C4—23no—
293Dic11⋊C4—23no—
294C4×Dic11—26no—
295C4×Dic11—21no—
296C4×Dic11—23no—
297C4×Dic11—23no—
298#4318—26no—
299C2×C11⋊C8—26no—
300C2×C11⋊C8C2413yes—
301C2×C11⋊C8C2411yescharacteristic
302#4313—22no—
303#4313—26no—
304#4313—26no—
305#4313—26no—
306C8×D11—212no—
307C22×2−1+4—111no—
308C2×#568—111no—
309#3428—111no—
310#2898—113no—
311#2898—113no—
312#2898—113no—
313#2898—113no—
314#2898—111no—
315#2898—111no—
316#2898—111no—
317#2898D1111yescharacteristic, complemented
318#2896—113no—
319#2896—113no—
320C2×#419—113no—
321C2×#419—113no—
322C23×C11—21no—
323C23×C11C22×D413yes—
324C22×D11—21no—
325C22×D11—24no—
326C22×D11—43no—
327C22×D11—43no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11C2×C22⋊C4112yes—
331C22×D11C22×D411yescharacteristic
332C22×D11C22×D413yes—
333Q8×C11—212no—
334Q8×C11—23no—
335Q8×C11C2×C22⋊C414yes—
336Q8×C11C23×C416yes—
337D4×C11—212no—
338D4×C11—21no—
339D4×C11C2×C22⋊C4112yes—
340D4×C11C23×C412yes—
341C2×C4×C11—212no—
342C2×C4×C11—23no—
343C2×C4×C11—212no—
344C2×C4×C11—23no—
345C2×C4×C11—21no—
346C2×C4×C11—83no—
347C2×C4×C11C23×C416yes—
348C2×C4×C11C22×D413yes—
349C2×C4×C11C22×D416yes—
350C2×C4×C11C2511yescharacteristic
351C22⋊D11—212no—
352C22⋊D11—212no—
353C22⋊D11—24no—
354C22⋊D11C2×C22⋊C4124yes—
355C2×Dic11—212no—
356C2×Dic11—23no—
357C2×Dic11—212no—
358C2×Dic11—21no—
359C2×Dic11—23no—
360C2×Dic11—83no—
361C2×Dic11C2×C22⋊C4112yes—
362C2×Dic11C22×D411yescharacteristic
363C2×Dic11C22×D413yes—
364D44—212no—
365D44—21no—
366D44C2×C22⋊C4112yes—
367D44C23×C412yes—
368C4×D11—212no—
369C4×D11—224no—
370C4×D11—212no—
371C4×D11—212no—
372C4×D11—83no—
373C4×D11—83no—
374C4×D11C2×C22⋊C4112yes—
375C4×D11C2×C22⋊C4112yes—
376C4×D11C23×C412yes—
377C4×D11C23×C416yes—
378C4×D11C22×D416yes—
379C4×D11C22×D412yes—
380Dic22—212no—
381Dic22—23no—
382Dic22—212no—
383Dic22—224no—
384Dic22C2×C22⋊C4112yes—
385Dic22C23×C416yes—
386C8×C11—23no—
387C8×C11—21no—
388C11⋊C8—23no—
389C11⋊C8—21no—
390C2×2−1+4—1116no—
391C2×2−1+4—113no—
392C2×2−1+4—111no—
393C2×2−1+4—113no—
394C2×2−1+4—221no—
395C2×2−1+4—223no—
396C2×2−1+4—228no—
397C2×2−1+4C2×D1111yescharacteristic
398C22×#41—111no—
399C22×#41—113no—
400C22×#41—223no—
401C23×Q8—113no—
402C23×Q8—221no—
403#568—228no—
404C2×#131—111no—
405C2×#131—113no—
406C2×#131—113no—
407C2×#131C2×D1111yescharacteristic, complemented
408C22×M16—113no—
409C22×M16—113no—
410#520—111no—
411#520—113no—
412#520—113no—
413#520C2×D1111yescharacteristic, complemented
414#519—221no—
415#518—223no—
416C4×#41—223no—
417C4×#41—221no—
418C2×#117—113no—
419C2×#117—113no—
420#419—113no—
421#419—113no—
422#419—113no—
423#419—113no—
424#419—116no—
425#419—113no—
426#419—116no—
427#419—116no—
428#419C2×D1113yescomplemented
429#418—113no—
430#418—111no—
431#417—113no—
432#417—113no—
433#417—113no—
434#417—113no—
435#417—113no—
436#417—113no—
437#417—113no—
438#417C2×D1113yescomplemented
439#416—113no—
440#416—113no—
441#416—113no—
442#416—116no—
443#416—116no—
444#416C2×D1113yescomplemented
445C2×#103—113no—
446C2×#103—113no—
447C2×#103—113no—
448C2×#103—116no—
449C2×#103—116no—
450C2×#103C2×D1113yescomplemented
451C22×C11—23no—
452C22×C11—23no—
453C22×C11—22no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11C22×C22⋊C416yes—
457C22×C11C23×D411yescharacteristic
458C2×D11—21no—
459C2×D11—21no—
460C2×D11—23no—
461C2×D11—23no—
462C2×D11—22no—
463C2×D11—412no—
464C2×D11—48no—
465C2×D11—41no—
466C2×D11—41no—
467C2×D11C22×C22⋊C412yes—
468C2×D11C22×C22⋊C416yes—
469C4×C11—26no—
470C4×C11—43no—
471C4×C11—41no—
472C4×C11C22×C22⋊C416yes—
473C4×C11C24×C411yescharacteristic
474C4×C11C23×D411yescharacteristic
475Dic11—26no—
476Dic11—41no—
477Dic11—43no—
478Dic11C22×C22⋊C412yes—
479Dic11C22×C22⋊C416yes—
4802−1+4—24no—
4812−1+4—1124no—
4822−1+4—118no—
4832−1+4—1124no—
4842−1+4—2216no—
4852−1+4—2212no—
4862−1+4—2248no—
4872−1+4—2212no—
4882−1+4—224no—
4892−1+4C4×D1118yescomplemented
490C2×#41—23no—
491C2×#41—118no—
492C2×#41—118no—
493C2×#41—111no—
494C2×#41—113no—
495C2×#41—113no—
496C2×#41—1124no—
497C2×#41—113no—
498C2×#41—113no—
499C2×#41—113no—
500C2×#41—223no—
501C2×#41—226no—
502C2×#41—223no—
503C2×#41—223no—
504C2×#41—2212no—
505C2×#41—226no—
506C2×#41—223no—
507C2×#41—2248no—
508C2×#41—223no—
509C2×#41C22×D1113yes—
510C2×#41C22×D1111yescharacteristic
511C22×Q8—21no—
512C22×Q8—111no—
513C22×Q8—1124no—
514C22×Q8—113no—
515C22×Q8—116no—
516C22×Q8—113no—
517C22×Q8—223no—
518C22×Q8—223no—
519C22×Q8—223no—
520C22×Q8—223no—
521C22×Q8—2212no—
522C22×Q8—2216no—
523C22×Q8—223no—
524C22×Q8—221no—
525C22×Q8C22×D1113yes—
526C22×D4—113no—
527C22×D4—111no—
528C22×D4—223no—
529C23×C4—113no—
530C23×C4—223no—
531C23×C4—223no—
532#131—24no—
533#131—2212no—
534#131—2212no—
535#131—224no—
536C2×M16—113no—
537C2×M16—113no—
538C2×M16—111no—
539C2×M16—113no—
540C2×M16—113no—
541C2×M16—2212no—
542C2×M16—2212no—
543C2×M16C22×D1113yes—
544C22×C8—113no—
545C22×C8—116no—
546C22×C8C22×D1113yes—
547C4×Q8—21no—
548C4×Q8—223no—
549C4×Q8—223no—
550C4×Q8—221no—
551C4×D4—23no—
552C4×D4—223no—
553C4×D4—226no—
554C4×D4—223no—
555C4×D4—226no—
556C4×D4—223no—
557#117—113no—
558#117—111no—
559#117—113no—
560#117—116no—
561#117—223no—
562#117—223no—
563#117—223no—
564#117—223no—
565#117C22×D1113yes—
566C2×C4⋊C4—113no—
567C2×C4⋊C4—113no—
568C2×C4⋊C4—113no—
569C2×C4⋊C4C22×D1113yes—
570C2×C22⋊C4—223no—
571C2×C22⋊C4—223no—
572C2×C42—223no—
573C2×C42—223no—
574#103—113no—
575#103—116no—
576#103—113no—
577#103—113no—
578#103—116no—
579#103—113no—
580#103—113no—
581#103—116no—
582#103—113no—
583#103C22×D1113yes—
584#103C22×D1116yes—
585#103C22×D1113yes—
586#102—113no—
587#102—111no—
588#102—113no—
589#102—111no—
590#102—111no—
591#102—113no—
592#102C22×D1113yes—
593#102C22×D1111yescharacteristic
594C2×C11—26no—
595C2×C11—42no—
596C2×C11C23×C22⋊C411yescharacteristic
597C2×C11#358611yescharacteristic
598C2×C11#358611yescharacteristic
599D11—22no—
600D11—26no—
601D11—42no—
602C24—113no—
603C24—221no—
604#41—224no—
605#41—26no—
606#41—118no—
607#41—1124no—
608#41—1112no—
609#41—1112no—
610#41—1112no—
611#41—1112no—
612#41—1112no—
613#41—2224no—
614#41—2248no—
615#41—2224no—
616#41—2224no—
617#41—226no—
618#41—226no—
619#41—2248no—
620#41—2224no—
621#41—2224no—
622#41—226no—
623#41C2×C4×D11112yes—
624#41C2×C4×D1114yes—
625#41D4×D1114yes—
626C2×Q8—28no—
627C2×Q8—23no—
628C2×Q8—26no—
629C2×Q8—118no—
630C2×Q8—113no—
631C2×Q8—1112no—
632C2×Q8—1124no—
633C2×Q8—1112no—
634C2×Q8—113no—
635C2×Q8—223no—
636C2×Q8—226no—
637C2×Q8—2224no—
638C2×Q8—2224no—
639C2×Q8—2224no—
640C2×Q8—226no—
641C2×Q8—2224no—
642C2×Q8—2212no—
643C2×Q8—2224no—
644C2×Q8—228no—
645C2×Q8—223no—
646C2×Q8—226no—
647C2×Q8C2×C4×D11112yes—
648C2×Q8D4×D1111yescharacteristic
649C2×Q8C23×D1113yes—
650C2×D4—23no—
651C2×D4—116no—
652C2×D4—1124no—
653C2×D4—114no—
654C2×D4—113no—
655C2×D4—111no—
656C2×D4—223no—
657C2×D4—222no—
658C2×D4—221no—
659C2×D4—2224no—
660C2×D4—223no—
661C2×D4—223no—
662C2×D4D4×D1113yes—
663C2×D4C23×D1111yescharacteristic
664C22×C4—23no—
665C22×C4—23no—
666C22×C4—23no—
667C22×C4—113no—
668C22×C4—1112no—
669C22×C4—113no—
670C22×C4—113no—
671C22×C4—1112no—
672C22×C4—113no—
673C22×C4—111no—
674C22×C4—223no—
675C22×C4—2224no—
676C22×C4—223no—
677C22×C4—2224no—
678C22×C4—226no—
679C22×C4—223no—
680C22×C4—223no—
681C22×C4—223no—
682C22×C4—223no—
683C22×C4—223no—
684C22×C4—223no—
685C22×C4C23×D1113yes—
686M16—26no—
687M16—222no—
688M16—226no—
689M16—226no—
690M16—226no—
691M16—226no—
692C2×C8—26no—
693C2×C8—111no—
694C2×C8—113no—
695C2×C8—2212no—
696C2×C8—226no—
697C2×C8C23×D1113yes—
698C2×C8C23×D1111yescharacteristic
699C4⋊C4—23no—
700C4⋊C4—113no—
701C4⋊C4—111no—
702C4⋊C4—223no—
703C4⋊C4—223no—
704C4⋊C4—223no—
705C4⋊C4C23×D1111yescharacteristic
706C4⋊C4C23×D1113yes—
707C22⋊C4—23no—
708C22⋊C4—221no—
709C22⋊C4—223no—
710C22⋊C4—226no—
711C22⋊C4—223no—
712C42—23no—
713C42—221no—
714C42—223no—
715C42—226no—
716C42—223no—
717C11#6008811yescharacteristic, complemented, Sylow
718C23—21no—
719C23—111no—
720C23—113no—
721C23—1112no—
722C23—224no—
723C23—221no—
724C23—443no—
725C23—443no—
726C23—442no—
727C23—442no—
728C23C2×D4×D1113yes—
729Q8—212no—
730Q8—23no—
731Q8—1112no—
732Q8—116no—
733Q8—2212no—
734Q8—2224no—
735Q8—2212no—
736Q8—223no—
737Q8C22⋊C4×D1114yes—
738Q8C22×C4×D1116yes—
739D4—212no—
740D4—21no—
741D4—1124no—
742D4—1112no—
743D4—112no—
744D4—2212no—
745D4—224no—
746D4—2212no—
747D4—2212no—
748D4—221no—
749D4C22⋊C4×D11112yes—
750D4C22×C4×D1112yes—
751C2×C4—212no—
752C2×C4—23no—
753C2×C4—212no—
754C2×C4—21no—
755C2×C4—23no—
756C2×C4—83no—
757C2×C4—1112no—
758C2×C4—111no—
759C2×C4—113no—
760C2×C4—1112no—
761C2×C4—1112no—
762C2×C4—112no—
763C2×C4—116no—
764C2×C4—116no—
765C2×C4—112no—
766C2×C4—2212no—
767C2×C4—2212no—
768C2×C4—2224no—
769C2×C4—2212no—
770C2×C4—2212no—
771C2×C4—223no—
772C2×C4—2212no—
773C2×C4—221no—
774C2×C4—223no—
775C2×C4—883no—
776C2×C4—883no—
777C2×C4—883no—
778C2×C4C22×C4×D1116yes—
779C2×C4C2×D4×D1113yes—
780C2×C4C2×D4×D1116yes—
781C2×C4C24×D1111yescharacteristic
782C8—21no—
783C8—23no—
784C8—223no—
785C8—221no—
786C22—23no—
787C22—23no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—112no—
792C22—116no—
793C22—223no—
794C22—221no—
795C22—223no—
796C22—221no—
797C22—222no—
798C22—4412no—
799C22—448no—
800C22—441no—
801C22—441no—
802C22C2×C22⋊C4×D1116yes—
803C22C22×D4×D1111yescharacteristic
804C4—26no—
805C4—43no—
806C4—41no—
807C4—112no—
808C4—116no—
809C4—226no—
810C4—441no—
811C4—443no—
812C4C2×C22⋊C4×D1116yes—
813C4C23×C4×D1111yescharacteristic
814C4C22×D4×D1111yescharacteristic
815C2—26no—
816C2—42no—
817C2—222no—
818C2—226no—
819C2—442no—
820C2C22×C22⋊C4×D1111yescharacteristic
821C2#1308339811yescharacteristic
822C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2898C2
socleC22×C11C23×D4
prime radicalC2×D11×2−1+4C2
cosocleC2×C4×C11C25
hypercenter#2898D11
hypocenterC11#60088
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#10623281C2semidirect
3. #13081816C2semidirect
4. #13077150C2semidirect
5. #13077149C2semidirect
6. #13077148C2semidirect
7. #13077147C2semidirect
8. #13077146C2semidirect
9. #13077145C2semidirect
10. #13077144C2semidirect
11. #13077132C2semidirect
12. #13077131C2semidirect
13. C2×#10622415C2semidirect
14. D11×#419C2semidirect
15. C11×#2898C2semidirect
18. D11×2−1+4C4semidirect
29. C2×C11×#131C22semidirect
30. C11×#520C22semidirect
31. #10623358C22semidirect
32. C2×#67001C22semidirect
34. C2×#66960C22semidirect
36. C2×#66954C22semidirect
42. #10623054C22semidirect
44. #10623035C22semidirect
46. C11×#419C22semidirect
47. C11×#417C22semidirect
48. C11×#416C22semidirect
49. C2×C11×#103C22semidirect
50. #10622846C22semidirect
51. #10622845C22semidirect
52. #10622838C22semidirect
53. C2×#66899C22semidirect
54. #10622746C22semidirect
55. #10622733C22semidirect
56. #10622726C22semidirect
57. C2×#66880C22semidirect
58. #10622617C22semidirect
59. #10622615C22semidirect
60. C2×#66874C22semidirect
61. #10622579C22semidirect
62. #10622417C22semidirect
63. #10622416C22semidirect
64. #10622416C22semidirect
68. #10622415C22semidirect
69. #10622415C22semidirect
70. D11×#103C22semidirect
71. D11×#103C22semidirect
72. #10622385C22semidirect
73. #10622384C22semidirect
74. #10622384C22semidirect
78. C11×2−1+4C2×C4semidirect
87. #67043C2×C4semidirect
88. #67043C2×C4semidirect
92. #41×D11C2×C4semidirect
96. #67040C2×C4semidirect
106. C2×Q8×D11C2×C4semidirect
317. #2898D11semidirect
407. C2×#131C2×D11semidirect
413. #520C2×D11semidirect
428. #419C2×D11semidirect
438. #417C2×D11semidirect
444. #416C2×D11semidirect
450. C2×#103C2×D11semidirect
489. 2−1+4C4×D11semidirect
717. C11#60088semidirect

Maximal subgroups

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

subgroupindex
C2×D11×2−1+42
C2×#106232812
#130818162
#130771502
#130771492
#130771482
#130771472
#130771462
#130771452
#130771442
#130771322
#130771312
C2×#106224152
D11×#4192
C11×#28982
#6008811