Finite Group Databasebeta

← #15618119

Subgroups — #15618119

Order 2816.

2604 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083385C211yesmaximal, characteristic
2#13083329C212yesmaximal, complemented
3#13077534C211yesmaximal, characteristic, complemented
4#13077530C214yesmaximal, complemented
5#13077523C212yesmaximal, complemented
6#13077521C214yesmaximal, complemented
7#13077515C212yesmaximal, complemented
8#13077514C214yesmaximal, complemented
9C2×#10622810C211yesmaximal, characteristic, complemented
10C2×#10622507C211yesmaximal, characteristic, complemented
11D11×#444C214yesmaximal, complemented
12#13077224C211yesmaximal, characteristic, complemented
13#13077162C212yesmaximal, complemented
14#13077043C211yesmaximal, characteristic, complemented
15C11×#2957C211yesmaximal, characteristic, complemented
16#10623453C2212yes—
17C2×C11×#135C2211yescharacteristic
18C11×#568C2212yescomplemented
19#10623353C2212yes—
20C2×#67001C2212yescomplemented
21#10623302C412yescomplemented
22#10623301C414yescomplemented
23#10623300C412yescomplemented
24#10623299C2214yes—
25D11×#135C2214yes—
26#10623297C412yescomplemented
27#10623293C414yescomplemented
28#10623288C412yescomplemented
29#10623281—24no—
30#10623281C2218yescomplemented
31D11×#131—24no—
32D11×#131C2218yescomplemented
33#10623276—24no—
34#10623276C2212yes—
35#10623276C2212yescomplemented
36C2×#66960—24no—
37C2×#66960C2211yescharacteristic
38C2×#66960C2212yescomplemented
39C2×#66957C2211yescharacteristic
40C2×#66954C2211yescharacteristic
41#10623053C2211yescharacteristic
42C11×#444C2214yescomplemented
43C11×#443C2214yescomplemented
44C2×C11×#108C2211yescharacteristic, complemented
45C11×#421C2212yescomplemented
46C11×#405C2211yescharacteristic, complemented
47C2×#66901C2212yescomplemented
48#10622810C2212yescomplemented
49#10622810C2212yescomplemented
50#10622810C2212yescomplemented
51#10622810C2212yescomplemented
52#10622758C2218yescomplemented
53#10622757C2218yescomplemented
54C2×#66889C2212yescomplemented
55#10622737C2212yescomplemented
56M16×Dic11C2211yescharacteristic, complemented
57C2×#66883C2211yescharacteristic, complemented
58C2×#66879C2211yescharacteristic, complemented
59#10622618C2212yescomplemented
60#10622610C2211yescharacteristic, complemented
61#10622507C2212yescomplemented
62#10622507C2212yescomplemented
63#10622507C2212yescomplemented
64#10622507C2212yescomplemented
65#10622506C2214yescomplemented
66D11×#108C2214yescomplemented
67#10622437C2218yescomplemented
68#10622436C2218yescomplemented
69#10622434C2218yescomplemented
70D11×#104C2218yescomplemented
71#10622330C2214yescomplemented
72#10622321C2212yescomplemented
73D11×#97C2212yescomplemented
74#10622313C2214yescomplemented
75#10622302C2212yescomplemented
76C4×#4313C2212yescomplemented
77C2×C11×#41C2312yes—
78#67043—22no—
79#67043C2×C414yes—
80#67042—22no—
81#67042C2×C414yes—
82#41×D11—24no—
83#41×D11C2318yes—
84#67040C2×C414yes—
85#67037—24no—
86#67037C2×C414yes—
87C2×#4339—24no—
88C2×#4339C2312yes—
89C2×#4339C2311yescharacteristic
90C11×#135C2×C412yescomplemented
91C11×#135C2×C412yescomplemented
92C11×#135C2312yes—
93C11×#135C2312yes—
94C2×C11×Q16C2×C411yescharacteristic, complemented
95C2×C11×SD16C2×C412yescomplemented
96C2×C11×D8C2×C411yescharacteristic, complemented
97C11×#131—24no—
98C11×#131C2318yes—
99C2×C11×M16—24no—
100C2×C11×M16C2312yes—
101C2×C11×M16C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#117C2311yescharacteristic
104#67004C2×C414yescomplemented
105#67003C2318yes—
106#67002C2×C414yescomplemented
107#67001—22no—
108#67001—22no—
109#67001C2314yes—
110#67001C2314yes—
111#66995C2×C414yescomplemented
112#66985C2×C414yescomplemented
113C2×C4×Dic11C2311yescharacteristic
114C2×#4318—22no—
115C2×#4318C2312yes—
116C2×#4318C2311yescharacteristic
117C22×C11⋊C8—22no—
118C22×C11⋊C8C2311yescharacteristic
119#66972C2×C414yescomplemented
120#66971C2×C418yescomplemented
121Q16×D11C2×C414yescomplemented
122#66969C2×C418yescomplemented
123#66968C2×C418yescomplemented
124#66967C2×C418yescomplemented
125SD16×D11C2×C418yescomplemented
126#66965C2×C414yescomplemented
127#66964C2×C418yescomplemented
128D8×D11C2×C414yescomplemented
129#66960—24no—
130#66960—24no—
131#66960—22no—
132#66960—22no—
133#66960—28no—
134#66960—28no—
135#66960D414yes—
136#66960D414yes—
137#66960C2314yes—
138#66960C2314yes—
139M16×D11—24no—
140M16×D11—28no—
141M16×D11—28no—
142M16×D11C2318yes—
143C2×Dic44C2×C411yescharacteristic, complemented
144#66957C2×C412yescomplemented
145#66957C2×C412yescomplemented
146#66957C2312yes—
147#66957C2312yes—
148C2×D88C2×C411yescharacteristic, complemented
149C2×#4314C2×C412yescomplemented
150#66954—24no—
151#66954—28no—
152#66954—28no—
153#66954C2×C412yes—
154#66954C2×C412yes—
155#66954C2×C412yes—
156#66954C2×C412yes—
157#66954C2318yes—
158C2×#4313—22no—
159C2×#4313—28no—
160C2×#4313C2312yes—
161C2×#4313C2312yes—
162C2×C8×D11—22no—
163C2×C8×D11—28no—
164C2×C8×D11C2312yes—
165C2×C8×D11C2312yes—
166#66946—21no—
167#66940—21no—
168(C22⋊D11)⋊C4—22no—
169#66925C2312yes—
170C42×D11C2312yes—
171C11×#108C2312yes—
172C11×#108C2312yes—
173C11×#104C2318yes—
174C11×#97C2312yes—
175C4×C8×C11C2312yes—
176#66901C2314yes—
177#66901C2314yes—
178#66889C2314yes—
179#66889C2314yes—
180#66886C2318yes—
181#66883C2312yes—
182#66883C2312yes—
183#66879C2312yes—
184#66879C2311yescharacteristic
185#66879C2311yescharacteristic
186#66879C2311yescharacteristic
187#66879C2311yescharacteristic
188C8×Dic11C2312yes—
189#66869C2318yes—
190#66867C2312yes—
191C4×C11⋊C8C2312yes—
192#60184—111nomaximal, Sylow
193C11×#41—22no—
194C11×#41—22no—
195C11×#41C22×C414yes—
196C11×#41C2414yes—
197C2×Q8×C11C22×C412yes—
198C2×D4×C11—22no—
199C2×D4×C11C22×C412yes—
200C22×C4×C11—22no—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—22no—
204C2×C22⋊D11#4112yes—
205C22×Dic11—21no—
206#4343—24no—
207#4343C22×C418yes—
208Q8×D11—24no—
209Q8×D11C22×C418yes—
210#4341—28no—
211#4341—28no—
212#4341—24no—
213#4341C22×C418yes—
214D4×D11—28no—
215D4×D11—24no—
216D4×D11—28no—
217D4×D11C22×C418yes—
218#4339—28no—
219#4339—24no—
220#4339—28no—
221#4339—24no—
222#4339—22no—
223#4339—22no—
224#4339C22×C412yes—
225#4339C22×C412yes—
226#4339C22×C414yes—
227#4339C2×D412yes—
228#4339C2×D412yes—
229#4339C2414yes—
230C2×D44—24no—
231C2×D44C22×C412yes—
232C2×D44#4111yescharacteristic
233C2×C4×D11—28no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11C2412yes—
237C2×Dic22—24no—
238C2×Dic22C22×C412yes—
239C2×Dic22#4111yescharacteristic
240C11×Q16C22×C412yes—
241C11×Q16C22×C412yes—
242C11×SD16C22×C414yes—
243C11×SD16C22×C414yes—
244C11×D8C22×C412yes—
245C11×D8C22×C412yes—
246C11×M16—28no—
247C11×M16—22no—
248C11×M16C2×D412yes—
249C11×M16C2×D412yes—
250C11×M16C2414yes—
251C2×C8×C11—28no—
252C2×C8×C11—22no—
253C2×C8×C11C22×C411yescharacteristic
254C2×C8×C11C22×C411yescharacteristic
255C2×C8×C11C22×C411yescharacteristic
256C2×C8×C11C22×C411yescharacteristic
257C2×C8×C11C2411yescharacteristic
258C2×C8×C11C2411yescharacteristic
259C2×C8×C11C2412yes—
260C11×C4⋊C4—21no—
261C11×C22⋊C4—21no—
262C42×C11C2412yes—
263#4326C22×C418yes—
264#4325C22×C418yes—
265#4324C22×C418yes—
266#4323C22×C418yes—
267(C2×D11)⋊C4—22no—
268Dic11⋊C4—22no—
269C4×Dic11—22no—
270C4×Dic11—21no—
271C4×Dic11C2411yescharacteristic
272C4×Dic11C2411yescharacteristic
273#4318—24no—
274#4318—24no—
275#4318—22no—
276#4318C22×C412yes—
277#4318C22×C412yes—
278#4318C2414yes—
279C2×C11⋊C8—24no—
280C2×C11⋊C8—24no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2×D412yes—
283C2×C11⋊C8C2×D412yes—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2411yescharacteristic
286C2×C11⋊C8C2411yescharacteristic
287Dic44C22×C412yes—
288Dic44C22×C412yes—
289D88C22×C412yes—
290D88C22×C412yes—
291#4314C22×C414yes—
292#4314C22×C414yes—
293#4313—28no—
294#4313—28no—
295#4313—24no—
296#4313—24no—
297#4313C22×C414yes—
298#4313C22×C414yes—
299#4313C2×D418yes—
300C8×D11—28no—
301C8×D11—28no—
302C8×D11—24no—
303C8×D11—24no—
304C8×D11C22×C414yes—
305C8×D11C22×C414yes—
306C8×D11C2×D418yes—
307#3584—111no—
308#3573—112no—
309#2957—114no—
310#2957—111no—
311#2957D1111yescharacteristic, complemented
312#2956—114no—
313#2956—112no—
314#2955—114no—
315#2955—112no—
316C2×#444—114no—
317C2×#444—111no—
318C2×#444—111no—
319#2916—111no—
320#2901—112no—
321#2875—111no—
322C23×C11—22no—
323C23×C11C2×#4111yescharacteristic
324C22×D11—22no—
325C22×D11—28no—
326C22×D11C2×#4112yes—
327Q8×C11—22no—
328Q8×C11C23×C414yes—
329D4×C11—24no—
330D4×C11—24no—
331D4×C11—22no—
332D4×C11C23×C414yes—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11C23×C411yescharacteristic
338C2×C4×C11C23×C411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11C2511yescharacteristic
343C22⋊D11—24no—
344C22⋊D11—24no—
345C22⋊D11—28no—
346C22⋊D11—28no—
347C22⋊D11C4×D414yes—
348C22⋊D11C4×D414yes—
349C2×Dic11—22no—
350C2×Dic11—28no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—81no—
354C2×Dic11C2×#4112yes—
355D44—28no—
356D44—22no—
357D44C4×D412yes—
358D44C4×D412yes—
359D44C23×C414yes—
360C4×D11—28no—
361C4×D11—24no—
362C4×D11—24no—
363C4×D11—28no—
364C4×D11—82no—
365C4×D11C23×C414yes—
366C4×D11C22×D414yes—
367Dic22—22no—
368Dic22—28no—
369Dic22C4×D412yes—
370Dic22C4×D412yes—
371Dic22C23×C414yes—
372C8×C11—24no—
373C8×C11C23×C411yescharacteristic
374C8×C11C23×C411yescharacteristic
375C8×C11C23×C411yescharacteristic
376C8×C11C23×C411yescharacteristic
377C8×C11C22×D414yes—
378C11⋊C8—24no—
379C11⋊C8C23×C414yes—
380C11⋊C8C22×D412yes—
381C11⋊C8C22×D412yes—
382#585—112no—
383#578—112no—
384#578—112no—
385#577—114no—
386#577—114no—
387#576—112no—
388#576—112no—
389#575—112no—
390#575—114no—
391C2×#135—114no—
392C2×#135—111no—
393C2×#135C2×D1111yescharacteristic
394#568—112no—
395#568—118no—
396#568—112no—
397#568—224no—
398#568—224no—
399#568C2×D1112yescomplemented
400C2×#131—111no—
401C2×#131—111no—
402C2×#131—112no—
403C2×#131—118no—
404C2×#131—112no—
405C2×#131—224no—
406C2×#131—224no—
407C4×#41—111no—
408#444—112no—
409#444—112no—
410#444—112no—
411#444—112no—
412#444—118no—
413#444—112no—
414#444—112no—
415#444—112no—
416#444—112no—
417#444—118no—
418#444—114no—
419#444C2×D1114yescomplemented
420#443—118no—
421#443—118no—
422#443—114no—
423#443C2×D1114yescomplemented
424#430—112no—
425#430—114no—
426C2×#108—111no—
427C2×#108—114no—
428C2×#108C2×D1111yescharacteristic, complemented
429#421—112no—
430#421—118no—
431#421C2×D1112yescomplemented
432C2×#104—112no—
433C2×#104—112no—
434C2×#104—118no—
435#405—111no—
436#405—112no—
437#405—112no—
438#405C2×D1111yescharacteristic, complemented
439C4×M16—111no—
440C4×M16—112no—
441C2×#97—111no—
442C2×#97—112no—
443C22×C11—24no—
444C22×C11—41no—
445C22×C11—82no—
446C22×C11C2×C4×D411yescharacteristic
447C22×C11C2×C4×D411yescharacteristic
448C22×C11C22×#4111yescharacteristic
449C2×D11—24no—
450C2×D11—42no—
451C2×D11—88no—
452C2×D11—82no—
453C2×D11C2×C4×D414yes—
454C4×C11—24no—
455C4×C11—42no—
456C4×C11C2×C4×D411yescharacteristic
457C4×C11C2×C4×D411yescharacteristic
458C4×C11C24×C411yescharacteristic
459C4×C11C23×D411yescharacteristic
460Dic11—24no—
461Dic11—41no—
462Dic11—41no—
463Dic11C2×C4×D414yes—
4642−1+4—114no—
4652−1+4—114no—
4662−1+4—222no—
467H(5,𝔽2)—114no—
468H(5,𝔽2)—114no—
469H(5,𝔽2)—224no—
470H(5,𝔽2)—222no—
471C2×#41—111no—
472C2×#41—118no—
473C2×#41—112no—
474C2×#41—224no—
475C2×#41—224no—
476C2×#41C22×D1112yes—
477#137—114no—
478#137—114no—
479#137—118no—
480#137—118no—
481AGL(1,ℤ/8)—114no—
482AGL(1,ℤ/8)—114no—
483AGL(1,ℤ/8)—118no—
484AGL(1,ℤ/8)—118no—
485#135—118no—
486#135—114no—
487#135—118no—
488#135—114no—
489#135—112no—
490#135—112no—
491#135—112no—
492#135—112no—
493#135C4×D1112yescomplemented
494#135C4×D1112yescomplemented
495#135C22×D1112yes—
496#135C22×D1112yes—
497C2×Q16—114no—
498C2×Q16—111no—
499C2×Q16C4×D1111yescharacteristic, complemented
500C2×SD16—118no—
501C2×SD16—112no—
502C2×SD16C4×D1112yescomplemented
503C2×D8—114no—
504C2×D8—111no—
505C2×D8C4×D1111yescharacteristic, complemented
506#131—24no—
507#131—114no—
508#131—114no—
509#131—112no—
510#131—112no—
511#131—112no—
512#131—112no—
513#131—114no—
514#131—114no—
515#131—114no—
516#131—114no—
517#131—118no—
518#131—228no—
519#131—228no—
520#131—224no—
521#131—222no—
522#131—228no—
523#131—222no—
524#131—222no—
525#131—222no—
526#131—228no—
527#131—224no—
528#131—224no—
529#131C22×D1118yes—
530C2×M16—24no—
531C2×M16—111no—
532C2×M16—112no—
533C2×M16—112no—
534C2×M16—112no—
535C2×M16—118no—
536C2×M16—222no—
537C2×M16—228no—
538C2×M16—228no—
539C2×M16—222no—
540C2×M16—228no—
541C2×M16—224no—
542C2×M16C22×D1112yes—
543C2×M16C22×D1111yescharacteristic
544C22×C8—111no—
545C22×C8—112no—
546C22×C8—112no—
547C22×C8—222no—
548C22×C8—228no—
549C22×C8—222no—
550C22×C8C22×D1111yescharacteristic
551C4×Q8—221no—
552C4×D4—222no—
553C4×D4—221no—
554#117—112no—
555#117C22×D1111yescharacteristic
556C2×C42—111no—
557C2×C42—112no—
558#108—118no—
559#108—112no—
560#108—112no—
561#108C22×D1112yes—
562#108C22×D1112yes—
563#104—114no—
564#104—114no—
565#104—114no—
566#104—114no—
567#104—118no—
568#104C22×D1118yes—
569#97—111no—
570#97—112no—
571#97—111no—
572#97—111no—
573#97—111no—
574#97—112no—
575#97C22×D1112yes—
576C4×C8—112no—
577C4×C8—112no—
578C4×C8C22×D1112yes—
579C2×C11—21no—
580C2×C11—21no—
581C2×C11—21no—
582C2×C11—44no—
583C2×C11C22×C4×D411yescharacteristic
584D11—24no—
585D11—44no—
586#41—22no—
587#41—22no—
588#41—112no—
589#41—112no—
590#41—112no—
591#41—112no—
592#41—118no—
593#41—118no—
594#41—114no—
595#41—114no—
596#41—228no—
597#41—228no—
598#41—224no—
599#41—224no—
600#41—228no—
601#41—228no—
602#41—224no—
603#41—224no—
604#41—222no—
605#41—222no—
606#41C2×C4×D1114yes—
607#41C23×D1114yes—
608C2×Q8—111no—
609C2×Q8—118no—
610C2×Q8—112no—
611C2×Q8—224no—
612C2×Q8—224no—
613C2×Q8C2×C4×D1112yes—
614C2×D4—22no—
615C2×D4—112no—
616C2×D4—118no—
617C2×D4—112no—
618C2×D4—111no—
619C2×D4—224no—
620C2×D4—228no—
621C2×D4—224no—
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—222no—
625C2×D4C2×C4×D1112yes—
626C22×C4—22no—
627C22×C4—112no—
628C22×C4—228no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—221no—
632C22×C4C23×D1111yescharacteristic
633Q16—118no—
634Q16—112no—
635Q16—112no—
636Q16C2×C4×D1112yes—
637Q16C2×C4×D1112yes—
638SD16—118no—
639SD16—118no—
640SD16—114no—
641SD16—114no—
642SD16C2×C4×D1114yes—
643SD16C2×C4×D1114yes—
644D8—118no—
645D8—112no—
646D8—112no—
647D8C2×C4×D1112yes—
648D8C2×C4×D1112yes—
649M16—22no—
650M16—28no—
651M16—112no—
652M16—112no—
653M16—114no—
654M16—114no—
655M16—118no—
656M16—114no—
657M16—224no—
658M16—224no—
659M16—228no—
660M16—224no—
661M16—224no—
662M16—222no—
663M16—228no—
664M16D4×D1112yes—
665M16D4×D1112yes—
666M16C23×D1114yes—
667C2×C8—22no—
668C2×C8—28no—
669C2×C8—112no—
670C2×C8—112no—
671C2×C8—112no—
672C2×C8—111no—
673C2×C8—111no—
674C2×C8—114no—
675C2×C8—114no—
676C2×C8—118no—
677C2×C8—224no—
678C2×C8—224no—
679C2×C8—228no—
680C2×C8—224no—
681C2×C8—224no—
682C2×C8—222no—
683C2×C8—228no—
684C2×C8C2×C4×D1111yescharacteristic
685C2×C8C2×C4×D1111yescharacteristic
686C2×C8C2×C4×D1111yescharacteristic
687C2×C8C2×C4×D1111yescharacteristic
688C2×C8C23×D1111yescharacteristic
689C2×C8C23×D1111yescharacteristic
690C2×C8C23×D1112yes—
691C4⋊C4—21no—
692C4⋊C4—222no—
693C22⋊C4—21no—
694C22⋊C4—222no—
695C42—111no—
696C42—111no—
697C42—222no—
698C42—221no—
699C42C23×D1112yes—
700C11#6018411yescharacteristic, complemented, Sylow
701C23—22no—
702C23—112no—
703C23—228no—
704C23—222no—
705C23#41×D1111yescharacteristic
706Q8—22no—
707Q8—112no—
708Q8—112no—
709Q8—114no—
710Q8—228no—
711Q8—222no—
712Q8C22×C4×D1114yes—
713D4—24no—
714D4—24no—
715D4—22no—
716D4—114no—
717D4—114no—
718D4—112no—
719D4—112no—
720D4—114no—
721D4—228no—
722D4—228no—
723D4—228no—
724D4—224no—
725D4—224no—
726D4—222no—
727D4C22×C4×D1114yes—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—112no—
733C2×C4—114no—
734C2×C4—114no—
735C2×C4—228no—
736C2×C4—228no—
737C2×C4—228no—
738C2×C4—222no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—882no—
744C2×C4—881no—
745C2×C4C22×C4×D1111yescharacteristic
746C2×C4C22×C4×D1111yescharacteristic
747C2×C4C2×D4×D1111yescharacteristic
748C2×C4C2×D4×D1111yescharacteristic
749C2×C4#41×D1111yescharacteristic
750C2×C4C24×D1111yescharacteristic
751C8—24no—
752C8—114no—
753C8—112no—
754C8—112no—
755C8—224no—
756C8C22×C4×D1111yescharacteristic
757C8C22×C4×D1111yescharacteristic
758C8C22×C4×D1111yescharacteristic
759C8C22×C4×D1111yescharacteristic
760C8C2×D4×D1114yes—
761C22—24no—
762C22—41no—
763C22—82no—
764C22—114no—
765C22—224no—
766C22—442no—
767C22—882no—
768C22—888no—
769C22C4×D4×D1111yescharacteristic
770C22C4×D4×D1111yescharacteristic
771C22C2×#41×D1111yescharacteristic
772C4—24no—
773C4—42no—
774C4—114no—
775C4—224no—
776C4—441no—
777C4—441no—
778C4C4×D4×D1111yescharacteristic
779C4C4×D4×D1111yescharacteristic
780C4C23×C4×D1111yescharacteristic
781C4C22×D4×D1111yescharacteristic
782C2—21no—
783C2—21no—
784C2—21no—
785C2—44no—
786C2—224no—
787C2—444no—
788C2C2×C4×D4×D1111yescharacteristic
subgroupG/H
centerC4C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2957C2
socleC2×C11C22×C4×D4
prime radical#13083385C2
cosocleC2×C4×C11C25
hypercenter#2957D11
hypocenterC11#60184
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×M16 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #13083329C2semidirect
3. #13077534C2semidirect
4. #13077530C2semidirect
5. #13077523C2semidirect
6. #13077521C2semidirect
7. #13077515C2semidirect
8. #13077514C2semidirect
9. C2×#10622810C2semidirect
10. C2×#10622507C2semidirect
11. D11×#444C2semidirect
12. #13077224C2semidirect
13. #13077162C2semidirect
14. #13077043C2semidirect
15. C11×#2957C2semidirect
18. C11×#568C22semidirect
20. C2×#67001C22semidirect
21. #10623302C4semidirect
22. #10623301C4semidirect
23. #10623300C4semidirect
26. #10623297C4semidirect
27. #10623293C4semidirect
28. #10623288C4semidirect
30. #10623281C22semidirect
32. D11×#131C22semidirect
35. #10623276C22semidirect
38. C2×#66960C22semidirect
42. C11×#444C22semidirect
43. C11×#443C22semidirect
44. C2×C11×#108C22semidirect
45. C11×#421C22semidirect
46. C11×#405C22semidirect
47. C2×#66901C22semidirect
48. #10622810C22semidirect
49. #10622810C22semidirect
50. #10622810C22semidirect
51. #10622810C22semidirect
52. #10622758C22semidirect
53. #10622757C22semidirect
54. C2×#66889C22semidirect
55. #10622737C22semidirect
56. M16×Dic11C22semidirect
57. C2×#66883C22semidirect
58. C2×#66879C22semidirect
59. #10622618C22semidirect
60. #10622610C22semidirect
61. #10622507C22semidirect
62. #10622507C22semidirect
63. #10622507C22semidirect
64. #10622507C22semidirect
65. #10622506C22semidirect
66. D11×#108C22semidirect
67. #10622437C22semidirect
68. #10622436C22semidirect
69. #10622434C22semidirect
70. D11×#104C22semidirect
71. #10622330C22semidirect
72. #10622321C22semidirect
73. D11×#97C22semidirect
74. #10622313C22semidirect
75. #10622302C22semidirect
76. C4×#4313C22semidirect
90. C11×#135C2×C4semidirect
91. C11×#135C2×C4semidirect
94. C2×C11×Q16C2×C4semidirect
95. C2×C11×SD16C2×C4semidirect
96. C2×C11×D8C2×C4semidirect
104. #67004C2×C4semidirect
106. #67002C2×C4semidirect
111. #66995C2×C4semidirect
112. #66985C2×C4semidirect
119. #66972C2×C4semidirect
120. #66971C2×C4semidirect
121. Q16×D11C2×C4semidirect
122. #66969C2×C4semidirect
123. #66968C2×C4semidirect
124. #66967C2×C4semidirect
125. SD16×D11C2×C4semidirect
126. #66965C2×C4semidirect
127. #66964C2×C4semidirect
128. D8×D11C2×C4semidirect
143. C2×Dic44C2×C4semidirect
144. #66957C2×C4semidirect
145. #66957C2×C4semidirect
148. C2×D88C2×C4semidirect
149. C2×#4314C2×C4semidirect
311. #2957D11semidirect
399. #568C2×D11semidirect
419. #444C2×D11semidirect
423. #443C2×D11semidirect
428. C2×#108C2×D11semidirect
431. #421C2×D11semidirect
438. #405C2×D11semidirect
493. #135C4×D11semidirect
494. #135C4×D11semidirect
499. C2×Q16C4×D11semidirect
502. C2×SD16C4×D11semidirect
505. C2×D8C4×D11semidirect
700. C11#60184semidirect

Maximal subgroups

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

subgroupindex
#130833852
#130833292
#130775342
#130775302
#130775232
#130775212
#130775152
#130775142
C2×#106228102
C2×#106225072
D11×#4442
#130772242
#130771622
#130770432
C11×#29572
#6018411