Finite Group Databasebeta

← D53×#3231 #28256154

Subgroups — D53×#3231 #28256154

Order 13568.

1778 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D53C211yesmaximal, characteristic
2#533×D53C211yesmaximal, characteristic
3#20285877C211yesmaximal, characteristic, complemented
4#20285876C211yesmaximal, characteristic, complemented
5#20285875C211yesmaximal, characteristic, complemented
6#20285874C211yesmaximal, characteristic, complemented
7#20285873C214yesmaximal, complemented
8#20285872C214yesmaximal, complemented
9#20285871C211yesmaximal, characteristic, complemented
10#20285870C211yesmaximal, characteristic, complemented
11#20285869C211yesmaximal, characteristic, complemented
12#500×D53C211yesmaximal, characteristic, complemented
13#498×D53C211yesmaximal, characteristic, complemented
14#487×D53C211yesmaximal, characteristic, complemented
15#487×D53C211yesmaximal, characteristic, complemented
16#485×D53C214yesmaximal
17#479×D53C214yesmaximal, complemented
18#431×D53C211yesmaximal, characteristic
19C53×#3231C211yesmaximal, characteristic, complemented
20#16811180C2211yescharacteristic
21#16811180C2211yescharacteristic
22#16811179—21no—
23#16811179C2212yes—
24#16811178C2211yescharacteristic
25#16811178C2211yescharacteristic
26#16811178C2211yescharacteristic
27#16811178C2211yescharacteristic
28#16811177—21no—
29#16811177—21no—
30#16811177—21no—
31#16811177C2212yes—
32#16811176—21no—
33#16811176C2212yes—
34#16811175—21no—
35#16811175—21no—
36#16811175—21no—
37#16811175C2212yes—
38C4⋊Q8×D53C2211yescharacteristic
39C4⋊Q8×D53C2211yescharacteristic
40C4⋊Q8×D53C2211yescharacteristic
41C4⋊Q8×D53C2211yescharacteristic
42#125×D53—21no—
43#125×D53C2212yes—
44C22⋊Q8×D53—21no—
45C22⋊Q8×D53—21no—
46C22⋊Q8×D53—21no—
47C22⋊Q8×D53C2212yes—
48C4×Q8×D53—21no—
49C4×Q8×D53—21no—
50C4×Q8×D53—21no—
51C4×Q8×D53C2212yes—
52#117×D53—21no—
53#117×D53C2212yes—
54C2×C42×D53C2211yescharacteristic
55#16811028C2211yescharacteristic, complemented
56#16811027C2214yescomplemented
57#16811026C2211yescharacteristic, complemented
58#16811026C2211yescharacteristic, complemented
59#16811021C2211yescharacteristic, complemented
60#16811020C2214yescomplemented
61#16811019C2211yescharacteristic, complemented
62#16811019C2211yescharacteristic, complemented
63#16810975C2211yescharacteristic, complemented
64#16810975C2211yescharacteristic, complemented
65#16810974C2211yescharacteristic, complemented
66#16810974C2211yescharacteristic, complemented
67#16810973C2211yescharacteristic, complemented
68#16810973C2211yescharacteristic, complemented
69#16810972C2214yescomplemented
70#16810972C2214yescomplemented
71#16810967C2214yes—
72#16810966C2214yes—
73#16810965C2214yes—
74#16810964C2214yes—
75#16810963C2214yes—
76#16810962C2214yes—
77#16810961C2214yes—
78#16810933C2214yescomplemented
79#16810932C2214yescomplemented
80#16810931C2214yescomplemented
81#16810930C2214yescomplemented
82#16810929C2214yescomplemented
83#16810928C2214yescomplemented
84#16810927C2214yescomplemented
85#16810676C2211yescharacteristic
86#16810675C2212yes—
87#16810674C2211yescharacteristic
88#16810674C2211yescharacteristic
89#16810673C2212yes—
90#107×D53C2214yes—
91#106×D53C2214yes—
92C4⋊C8×D53C2212yes—
93#103×D53C2214yes—
94#103×D53C2214yes—
95C22⋊C8×D53C2212yes—
96C4×C8×D53C2211yescharacteristic
97C4×C8×D53C2211yescharacteristic
98C53×#533C2211yescharacteristic
99C53×#533C2211yescharacteristic
100C53×#500C2211yescharacteristic, complemented
101C53×#498C2211yescharacteristic, complemented
102C53×#487C2211yescharacteristic, complemented
103C53×#487C2211yescharacteristic, complemented
104C53×#485C2214yes—
105C53×#479C2214yescomplemented
106C53×#431C2211yescharacteristic
107C2×Q8×D53—21no—
108C2×Q8×D53—21no—
109C2×Q8×D53—21no—
110C2×Q8×D53C2312yes—
111C22×C4×D53D411yescharacteristic
112C22×C4×D53D411yescharacteristic
113C22×C4×D53C2311yescharacteristic
114C2×C8×D53C2312yes—
115C2×C8×D53C2312yes—
116#13133217C2311yescharacteristic
117#13133217C2311yescharacteristic
118#13133217C2311yescharacteristic
119#13133217C2311yescharacteristic
120#13133216—21no—
121#13133216—21no—
122#13133216—21no—
123#13133216—21no—
124#13133216—21no—
125#13133216C2312yes—
126#13133216C2312yes—
127#13133216C2312yes—
128#13133215—21no—
129#13133215—21no—
130#13133215—21no—
131#13133215C2312yes—
132#13133209—21no—
133#13133209C2312yes—
134#13133208—21no—
135#13133208—21no—
136#13133208C2312yes—
137#13133208C2312yes—
138#13133207—22no—
139#13133207—22no—
140#13133207—22no—
141#13133207—22no—
142#13133197—21no—
143#13133197—21no—
144#13133197—21no—
145#13133197C2312yes—
146#13133196—21no—
147#13133196—21no—
148#13133196—21no—
149#13133196C2312yes—
150#13133195—22no—
151#13133195—22no—
152#13133195—22no—
153#13133195—22no—
154#13133194—22no—
155#13133194—22no—
156#13133194—22no—
157#13133194—22no—
158#13133193—21no—
159#13133193—21no—
160#13133193—21no—
161#13133193C2312yes—
162Q8×Dic53—21no—
163Q8×Dic53—21no—
164Q8×Dic53—21no—
165Q8×Dic53C2312yes—
166C4×Dic106—21no—
167C4×Dic106—21no—
168C4×Dic106—21no—
169C4×Dic106—22no—
170C4×Dic106—22no—
171C4×Dic106—22no—
172C4×Dic106—22no—
173C4×Dic106C2312yes—
174#13133182—21no—
175#13133182—21no—
176#13133182—21no—
177#13133182—22no—
178#13133182—22no—
179#13133182—22no—
180#13133182—22no—
181#13133182C2312yes—
182#13133176—21no—
183#13133176C2312yes—
184#13133175—21no—
185#13133175—21no—
186#13133175C2312yes—
187#13133175C2312yes—
188#13133174—22no—
189#13133174—22no—
190#13133173—22no—
191#13133173—22no—
192C4⋊C4×D53—21no—
193C4⋊C4×D53—21no—
194C4⋊C4×D53—22no—
195C4⋊C4×D53—22no—
196C4⋊C4×D53—21no—
197C4⋊C4×D53—21no—
198C4⋊C4×D53—21no—
199C4⋊C4×D53—22no—
200C4⋊C4×D53—22no—
201C4⋊C4×D53C2312yes—
202C4⋊C4×D53C2312yes—
203C4⋊C4×D53C2312yes—
204C22⋊C4×D53—22no—
205C22⋊C4×D53—22no—
206C2×C4×Dic53D411yescharacteristic
207C2×C4×Dic53D411yescharacteristic
208C2×C4×Dic53C2311yescharacteristic
209C42×D53—22no—
210C42×D53—22no—
211C42×D53D411yescharacteristic
212C42×D53D411yescharacteristic
213C42×D53D411yescharacteristic
214C42×D53D411yescharacteristic
215C42×D53C2311yescharacteristic
216C42×D53C2311yescharacteristic
217C42×D53C2311yescharacteristic
218C42×D53C2311yescharacteristic
219#13133151C2314yes—
220#13133150C2314yes—
221#13133150C2314yes—
222#13133149C2314yes—
223#13133148C2314yes—
224#13133148C2314yes—
225C4⋊#88322C2312yes—
226#13133146C2312yes—
227#13133146C2312yes—
228#13133142C2314yes—
229#13133142C2314yes—
230#13133141C2314yes—
231#13133141C2314yes—
232#13133140C2314yes—
233#13133140C2314yes—
234C22⋊#88322C2312yes—
235#13133129C2312yes—
236#13133129C2312yes—
237C4×#88322C2311yescharacteristic
238C4×#88322C2311yescharacteristic
239C8×Dic53C2312yes—
240C8×Dic53C2312yes—
241C4⋊Q8×C53C2311yescharacteristic
242C4⋊Q8×C53C2311yescharacteristic
243C4⋊Q8×C53C2311yescharacteristic
244C4⋊Q8×C53C2311yescharacteristic
245#125×C53—21no—
246#125×C53C2312yes—
247C22⋊Q8×C53—21no—
248C22⋊Q8×C53—21no—
249C22⋊Q8×C53—21no—
250C22⋊Q8×C53C2312yes—
251C4×Q8×C53—21no—
252C4×Q8×C53—21no—
253C4×Q8×C53—21no—
254C4×Q8×C53C2312yes—
255#117×C53—21no—
256#117×C53C2312yes—
257C2×C42×C53C2311yescharacteristic
258#107×C53C2314yes—
259#106×C53C2314yes—
260C4⋊C8×C53C2312yes—
261#103×C53C2314yes—
262#103×C53C2314yes—
263C22⋊C8×C53C2312yes—
264C4×C8×C53C2311yescharacteristic
265C4×C8×C53C2311yescharacteristic
266C23×D53C2×D411yescharacteristic
267C2×Q8×C53—21no—
268C2×Q8×C53—21no—
269C2×Q8×C53—21no—
270C2×Q8×C53C2412yes—
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2411yescharacteristic
274C22×Dic53C2×D411yescharacteristic
275C22×Dic53C2×D411yescharacteristic
276C22×Dic53C2×D411yescharacteristic
277Q8×D53—28no—
278Q8×D53—44no—
279Q8×D53—44no—
280Q8×D53—44no—
281C2×C4×D53—24no—
282C2×C4×D53—24no—
283C2×C4×D53—24no—
284C2×C4×D53—22no—
285C2×C4×D53—22no—
286C2×C4×D53—22no—
287C2×C4×D53—22no—
288C2×C4×D53C2×D411yescharacteristic
289C2×C4×D53C2×D411yescharacteristic
290C2×C4×D53C2×D411yescharacteristic
291C2×C4×D53C2×D411yescharacteristic
292C2×C4×D53C2×D411yescharacteristic
293C2×C4×D53C2×D411yescharacteristic
294C2×C4×D53C2×D411yescharacteristic
295C2×C4×D53C2×D411yescharacteristic
296C2×C4×D53C2×D411yescharacteristic
297C2×C4×D53C2×D411yescharacteristic
298C2×C4×D53C2411yescharacteristic
299C2×C4×D53C2411yescharacteristic
300C2×Dic106—21no—
301C2×Dic106—21no—
302C2×Dic106—21no—
303C2×Dic106—22no—
304C2×Dic106—22no—
305C2×Dic106—22no—
306C2×Dic106—22no—
307C2×Dic106C2412yes—
308C2×C8×C53C2412yes—
309C2×C8×C53C2412yes—
310C4⋊C4×C53—21no—
311C4⋊C4×C53—21no—
312C4⋊C4×C53—22no—
313C4⋊C4×C53—22no—
314C4⋊C4×C53—21no—
315C4⋊C4×C53—21no—
316C4⋊C4×C53—21no—
317C4⋊C4×C53—22no—
318C4⋊C4×C53—22no—
319C4⋊C4×C53C2412yes—
320C4⋊C4×C53C2412yes—
321C4⋊C4×C53C2412yes—
322C22⋊C4×C53—22no—
323C22⋊C4×C53—22no—
324C42×C53—22no—
325C42×C53—22no—
326C42×C53C2×D411yescharacteristic
327C42×C53C2×D411yescharacteristic
328C42×C53C2411yescharacteristic
329C42×C53C2411yescharacteristic
330C22⋊Dic53—22no—
331C22⋊Dic53—22no—
332#11719921—22no—
333#11719921—22no—
334#11719921—22no—
335#11719921—22no—
336C4⋊Dic53—21no—
337C4⋊Dic53—21no—
338C4⋊Dic53—21no—
339C4⋊Dic53—21no—
340C4⋊Dic53—21no—
341C4⋊Dic53—22no—
342C4⋊Dic53—22no—
343C4⋊Dic53—22no—
344C4⋊Dic53—22no—
345C4⋊Dic53C2412yes—
346C4⋊Dic53C2412yes—
347C4⋊Dic53C2412yes—
348#11719919—22no—
349#11719919—22no—
350#11719919—22no—
351#11719919—22no—
352#11719919—22no—
353#11719919—22no—
354#11719919—22no—
355#11719919—22no—
356#11719919—22no—
357#11719919—22no—
358#11719919—22no—
359#11719919—22no—
360#11719919—22no—
361#11719919—22no—
362#11719919—22no—
363#11719919—22no—
364C4×Dic53—22no—
365C4×Dic53—22no—
366C4×Dic53—22no—
367C4×Dic53—22no—
368C4×Dic53—22no—
369C4×Dic53—22no—
370C4×Dic53C2×D411yescharacteristic
371C4×Dic53C2×D411yescharacteristic
372C4×Dic53C2×D411yescharacteristic
373C4×Dic53C2×D411yescharacteristic
374C4×Dic53C2×D411yescharacteristic
375C4×Dic53C2×D411yescharacteristic
376C4×Dic53C2×D411yescharacteristic
377C4×Dic53C2×D411yescharacteristic
378C4×Dic53C2×D411yescharacteristic
379C4×Dic53C2×D411yescharacteristic
380C4×Dic53C2411yescharacteristic
381C4×Dic53C2411yescharacteristic
382C2×#88322C2412yes—
383C2×#88322C2412yes—
384C8×D53—24no—
385C8×D53—24no—
386C23×C53C22×D411yescharacteristic
387C22×D53—22no—
388C22×D53—22no—
389C22×D53—22no—
390C22×D53C22×D411yescharacteristic
391C22×D53C22×D411yescharacteristic
392Q8×C53—24no—
393Q8×C53—42no—
394Q8×C53—42no—
395Q8×C53—42no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—22no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53C22×D411yescharacteristic
404C2×C4×C53C22×D411yescharacteristic
405C2×C4×C53C22×D411yescharacteristic
406C2×C4×C53C22×D411yescharacteristic
407C2×C4×C53C22×D411yescharacteristic
408C2×C4×C53C2511yescharacteristic
409C2×Dic53—22no—
410C2×Dic53—22no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—22no—
415C2×Dic53—22no—
416C2×Dic53C22×D411yescharacteristic
417C2×Dic53C22×D411yescharacteristic
418C2×Dic53C22×D411yescharacteristic
419C2×Dic53C22×D411yescharacteristic
420C2×Dic53C22×D411yescharacteristic
421C2×Dic53C22×D411yescharacteristic
422C4×D53—22no—
423C4×D53—22no—
424C4×D53—22no—
425C4×D53—22no—
426C4×D53—22no—
427C4×D53—22no—
428C4×D53—22no—
429C4×D53—22no—
430C4×D53—22no—
431C4×D53—44no—
432C4×D53—44no—
433C4×D53—44no—
434C4×D53—44no—
435C4×D53#13514yes—
436C4×D53#13714yes—
437C4×D532−1+414yes—
438Dic106—24no—
439Dic106—42no—
440Dic106—42no—
441Dic106—42no—
442Dic106—44no—
443Dic106—44no—
444Dic106—44no—
445Dic106—44no—
446C8×C53—22no—
447C8×C53—22no—
448#88322—22no—
449#88322—22no—
450C2×#3231—531nomaximal, Sylow
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53C23×D411yescharacteristic
455C2×D53—21no—
456C2×D53—21no—
457C2×D53—21no—
458C2×D53—44no—
459C2×D53#53612yes—
460C2×D53C2×#13512yes—
461C2×D53C2×#13712yes—
462C4×C53—21no—
463C4×C53—21no—
464C4×C53—21no—
465C4×C53—42no—
466C4×C53—42no—
467C4×C53—42no—
468C4×C53—42no—
469C4×C53C2×#13512yes—
470C4×C53C2×#13712yes—
471C4×C53C2×2−1+412yes—
472Dic53—21no—
473Dic53—21no—
474Dic53—21no—
475Dic53—42no—
476Dic53—42no—
477Dic53—42no—
478Dic53—42no—
479Dic53#53612yes—
480Dic53C2×#13512yes—
481Dic53C2×#13712yes—
482C2×#533—531no—
483C2×#533—531no—
484#3231—531no—
485#3231—531no—
486#3231—531no—
487#3231—531no—
488#3231—534no—
489#3231—534no—
490#3231—531no—
491#3231—531no—
492#3231—531no—
493#3231D5311yescharacteristic, direct product factor
494C2×#500—531no—
495C2×#498—531no—
496C2×#487—531no—
497C2×#487—531no—
498C2×#485—534no—
499C2×#479—534no—
500C2×#431—531no—
501C2×C53—41no—
502C2×C53C2×#53611yescharacteristic
503C2×C53C22×#13511yescharacteristic
504C2×C53C22×#13711yescharacteristic
505D53—41no—
506D53#323114yesdirect product factor
507#533—531no—
508#533—531no—
509#533—532no—
510#533—532no—
511#533—531no—
512#533—531no—
513#533—532no—
514#533—532no—
515#533—531no—
516#533—531no—
517#533—1061no—
518#533—1061no—
519#533—1061no—
520#533—1061no—
521#533—1061no—
522#533—1061no—
523#533—1061no—
524#533—1061no—
525#533C2×D5311yescharacteristic
526#533C2×D5311yescharacteristic
527C2×C4⋊Q8—531no—
528C2×C4⋊Q8—531no—
529C2×C4⋊Q8—531no—
530C2×C4⋊Q8—531no—
531C2×#125—532no—
532C2×#125—1061no—
533C2×C22⋊Q8—532no—
534C2×C22⋊Q8—1061no—
535C2×C22⋊Q8—1061no—
536C2×C22⋊Q8—1061no—
537C2×C4×Q8—532no—
538C2×C4×Q8—1061no—
539C2×C4×Q8—1061no—
540C2×C4×Q8—1061no—
541C2×#117—532no—
542C2×#117—1061no—
543C22×C42—531no—
544#500—531no—
545#500—531no—
546#500—534no—
547#500—531no—
548#500C2×D5311yescharacteristic, complemented
549#498—531no—
550#498—531no—
551#498—534no—
552#498—531no—
553#498C2×D5311yescharacteristic, complemented
554#487—531no—
555#487—531no—
556#487—531no—
557#487—531no—
558#487—534no—
559#487—534no—
560#487—531no—
561#487—531no—
562#487C2×D5311yescharacteristic, complemented
563#487C2×D5311yescharacteristic, complemented
564#485—534no—
565#485—534no—
566#485—534no—
567#485—534no—
568#485—534no—
569#485—534no—
570#485—534no—
571#485C2×D5314yes—
572#479—534no—
573#479—534no—
574#479—534no—
575#479—534no—
576#479—534no—
577#479—534no—
578#479—534no—
579#479C2×D5314yescomplemented
580#431—531no—
581#431—532no—
582#431—532no—
583#431—531no—
584#431—531no—
585#431C2×D5311yescharacteristic
586C2×#107—534no—
587C2×#106—534no—
588C2×C4⋊C8—532no—
589C2×#103—534no—
590C2×#103—534no—
591C2×C22⋊C8—532no—
592C2×C4×C8—531no—
593C2×C4×C8—531no—
594C53C2×#323111yescharacteristic, complemented, Sylow
595C22×Q8—532no—
596C22×Q8—1061no—
597C22×Q8—1061no—
598C22×Q8—1061no—
599C23×C4—531no—
600C23×C4—531no—
601C23×C4—531no—
602C22×C8—532no—
603C22×C8—532no—
604C4⋊Q8—532no—
605C4⋊Q8—532no—
606C4⋊Q8—532no—
607C4⋊Q8—532no—
608C4⋊Q8—531no—
609C4⋊Q8—531no—
610C4⋊Q8—531no—
611C4⋊Q8—531no—
612C4⋊Q8—1061no—
613C4⋊Q8—1061no—
614C4⋊Q8—1061no—
615C4⋊Q8—1061no—
616C4⋊Q8—1061no—
617C4⋊Q8—1061no—
618C4⋊Q8—1061no—
619C4⋊Q8—1061no—
620C4⋊Q8C22×D5311yescharacteristic
621C4⋊Q8C22×D5311yescharacteristic
622C4⋊Q8C22×D5311yescharacteristic
623C4⋊Q8C22×D5311yescharacteristic
624#125—21no—
625#125—532no—
626#125—532no—
627#125—532no—
628#125—1062no—
629#125—1062no—
630#125—1062no—
631#125—1062no—
632#125—1061no—
633#125—1061no—
634#125—1061no—
635#125C22×D5312yes—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—532no—
640C22⋊Q8—532no—
641C22⋊Q8—532no—
642C22⋊Q8—1062no—
643C22⋊Q8—1062no—
644C22⋊Q8—1062no—
645C22⋊Q8—1062no—
646C22⋊Q8—1062no—
647C22⋊Q8—1062no—
648C22⋊Q8—1062no—
649C22⋊Q8—1062no—
650C22⋊Q8—1061no—
651C22⋊Q8—1061no—
652C22⋊Q8—1061no—
653C22⋊Q8—1061no—
654C22⋊Q8—1061no—
655C22⋊Q8—1061no—
656C22⋊Q8—1061no—
657C22⋊Q8—1061no—
658C22⋊Q8—1061no—
659C22⋊Q8C22×D5312yes—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—532no—
664C4×Q8—532no—
665C4×Q8—532no—
666C4×Q8—1062no—
667C4×Q8—1062no—
668C4×Q8—1062no—
669C4×Q8—1062no—
670C4×Q8—1062no—
671C4×Q8—1062no—
672C4×Q8—1061no—
673C4×Q8—1061no—
674C4×Q8—1062no—
675C4×Q8—1062no—
676C4×Q8—1061no—
677C4×Q8—1061no—
678C4×Q8—1061no—
679C4×Q8—1061no—
680C4×Q8—1061no—
681C4×Q8—1061no—
682C4×Q8—1061no—
683C4×Q8C22×D5312yes—
684#117—21no—
685#117—532no—
686#117—532no—
687#117—532no—
688#117—1062no—
689#117—1062no—
690#117—1062no—
691#117—1062no—
692#117—1061no—
693#117—1061no—
694#117—1061no—
695#117C22×D5312yes—
696C2×C4⋊C4—532no—
697C2×C4⋊C4—532no—
698C2×C4⋊C4—532no—
699C2×C4⋊C4—1061no—
700C2×C4⋊C4—1061no—
701C2×C4⋊C4—1062no—
702C2×C4⋊C4—1062no—
703C2×C4⋊C4—1062no—
704C2×C4⋊C4—1062no—
705C2×C4⋊C4—1061no—
706C2×C4⋊C4—1061no—
707C2×C4⋊C4—1061no—
708C2×C22⋊C4—1062no—
709C2×C22⋊C4—1062no—
710C2×C42—531no—
711C2×C42—531no—
712C2×C42—531no—
713C2×C42—531no—
714C2×C42—531no—
715C2×C42—531no—
716C2×C42—531no—
717C2×C42—531no—
718C2×C42—531no—
719C2×C42—531no—
720C2×C42—531no—
721C2×C42—1062no—
722C2×C42—1062no—
723C2×C42C22×D5311yescharacteristic
724#107—534no—
725#107—534no—
726#107—534no—
727#107C22×D5314yes—
728#106—534no—
729#106—534no—
730#106—534no—
731#106C22×D5314yes—
732C4⋊C8—532no—
733C4⋊C8—532no—
734C4⋊C8—532no—
735C4⋊C8C22×D5312yes—
736#103—534no—
737#103—534no—
738#103—534no—
739#103—534no—
740#103—534no—
741#103—534no—
742#103C22×D5314yes—
743#103C22×D5314yes—
744C22⋊C8—532no—
745C22⋊C8—532no—
746C22⋊C8—532no—
747C22⋊C8C22×D5312yes—
748C4×C8—532no—
749C4×C8—532no—
750C4×C8—531no—
751C4×C8—531no—
752C4×C8C22×D5311yescharacteristic
753C4×C8C22×D5311yescharacteristic
754C24—531no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—532no—
759C2×Q8—1062no—
760C2×Q8—1062no—
761C2×Q8—1062no—
762C2×Q8—1062no—
763C2×Q8—1068no—
764C2×Q8—1061no—
765C2×Q8—1061no—
766C2×Q8—1061no—
767C2×Q8—2124no—
768C2×Q8—2124no—
769C2×Q8—2124no—
770C2×Q8C23×D5312yes—
771C22×C4—531no—
772C22×C4—531no—
773C22×C4—531no—
774C22×C4—531no—
775C22×C4—531no—
776C22×C4—531no—
777C22×C4—531no—
778C22×C4—531no—
779C22×C4—531no—
780C22×C4—531no—
781C22×C4—531no—
782C22×C4—531no—
783C22×C4—531no—
784C22×C4—531no—
785C22×C4—531no—
786C22×C4—1064no—
787C22×C4—1064no—
788C22×C4—1064no—
789C22×C4—1062no—
790C22×C4—1062no—
791C22×C4—1062no—
792C22×C4—1062no—
793C22×C4D4×D5311yescharacteristic
794C22×C4D4×D5311yescharacteristic
795C22×C4C23×D5311yescharacteristic
796C2×C8—532no—
797C2×C8—532no—
798C2×C8—1064no—
799C2×C8—1064no—
800C2×C8C23×D5312yes—
801C2×C8C23×D5312yes—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—532no—
812C4⋊C4—532no—
813C4⋊C4—532no—
814C4⋊C4—1062no—
815C4⋊C4—1062no—
816C4⋊C4—1062no—
817C4⋊C4—1062no—
818C4⋊C4—1062no—
819C4⋊C4—1062no—
820C4⋊C4—1062no—
821C4⋊C4—1062no—
822C4⋊C4—1062no—
823C4⋊C4—1062no—
824C4⋊C4—1062no—
825C4⋊C4—1062no—
826C4⋊C4—1062no—
827C4⋊C4—1062no—
828C4⋊C4—1062no—
829C4⋊C4—1062no—
830C4⋊C4—1061no—
831C4⋊C4—1061no—
832C4⋊C4—1062no—
833C4⋊C4—1062no—
834C4⋊C4—1062no—
835C4⋊C4—1062no—
836C4⋊C4—1061no—
837C4⋊C4—1061no—
838C4⋊C4—1061no—
839C4⋊C4C23×D5312yes—
840C4⋊C4C23×D5312yes—
841C4⋊C4C23×D5312yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—1062no—
845C22⋊C4—1062no—
846C22⋊C4—1062no—
847C22⋊C4—1062no—
848C22⋊C4—1062no—
849C22⋊C4—1062no—
850C42—22no—
851C42—22no—
852C42—531no—
853C42—531no—
854C42—531no—
855C42—531no—
856C42—531no—
857C42—531no—
858C42—531no—
859C42—531no—
860C42—531no—
861C42—531no—
862C42—531no—
863C42—531no—
864C42—1062no—
865C42—1062no—
866C42—1062no—
867C42—1062no—
868C42—1062no—
869C42—1062no—
870C42D4×D5311yescharacteristic
871C42D4×D5311yescharacteristic
872C42C23×D5311yescharacteristic
873C42C23×D5311yescharacteristic
874C23—531no—
875C23—531no—
876C23—1062no—
877C23—1062no—
878C23—1062no—
879C23C2×D4×D5311yescharacteristic
880Q8—24no—
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—1064no—
885Q8—2124no—
886Q8—2124no—
887Q8—2124no—
888Q8—2124no—
889Q8—2122no—
890Q8—2122no—
891Q8—2122no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—531no—
900C2×C4—531no—
901C2×C4—531no—
902C2×C4—534no—
903C2×C4—534no—
904C2×C4—534no—
905C2×C4—531no—
906C2×C4—531no—
907C2×C4—531no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1062no—
923C2×C4—1062no—
924C2×C4—2124no—
925C2×C4—2124no—
926C2×C4—2124no—
927C2×C4—2124no—
928C2×C4C2×D4×D5311yescharacteristic
929C2×C4C2×D4×D5311yescharacteristic
930C2×C4C2×D4×D5311yescharacteristic
931C2×C4C2×D4×D5311yescharacteristic
932C2×C4C2×D4×D5311yescharacteristic
933C2×C4C24×D5311yescharacteristic
934C8—22no—
935C8—22no—
936C8—1062no—
937C8—1062no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—532no—
942C22—532no—
943C22—532no—
944C22—1061no—
945C22—1061no—
946C22—1061no—
947C22—2124no—
948C22C22×D4×D5311yescharacteristic
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—532no—
957C4—532no—
958C4—532no—
959C4—1061no—
960C4—1061no—
961C4—1061no—
962C4—2122no—
963C4—2122no—
964C4—2122no—
965C4—2122no—
966C4#135×D5312yes—
967C4#137×D5312yes—
968C42−1+4×D5312yes—
969C2—41no—
970C2—534no—
971C2—2121no—
972C2#536×D5311yescharacteristic
973C2C2×#135×D5311yescharacteristic
974C2C2×#137×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3231C2
socleC22×C53C23×D4
prime radicalC23×D53C2×D4
hypercenter#3231D53
hypocenterC53C2×#3231
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #20285877C2semidirect
4. #20285876C2semidirect
5. #20285875C2semidirect
6. #20285874C2semidirect
7. #20285873C2semidirect
8. #20285872C2semidirect
9. #20285871C2semidirect
10. #20285870C2semidirect
11. #20285869C2semidirect
12. #500×D53C2semidirect
13. #498×D53C2semidirect
14. #487×D53C2semidirect
15. #487×D53C2semidirect
17. #479×D53C2semidirect
19. C53×#3231C2semidirect
55. #16811028C22semidirect
56. #16811027C22semidirect
57. #16811026C22semidirect
58. #16811026C22semidirect
59. #16811021C22semidirect
60. #16811020C22semidirect
61. #16811019C22semidirect
62. #16811019C22semidirect
63. #16810975C22semidirect
64. #16810975C22semidirect
65. #16810974C22semidirect
66. #16810974C22semidirect
67. #16810973C22semidirect
68. #16810973C22semidirect
69. #16810972C22semidirect
70. #16810972C22semidirect
78. #16810933C22semidirect
79. #16810932C22semidirect
80. #16810931C22semidirect
81. #16810930C22semidirect
82. #16810929C22semidirect
83. #16810928C22semidirect
84. #16810927C22semidirect
100. C53×#500C22semidirect
101. C53×#498C22semidirect
102. C53×#487C22semidirect
103. C53×#487C22semidirect
105. C53×#479C22semidirect
493. #3231D53direct (N × H)
506. D53#3231direct (N × H)
548. #500C2×D53semidirect
553. #498C2×D53semidirect
562. #487C2×D53semidirect
563. #487C2×D53semidirect
579. #479C2×D53semidirect
594. C53C2×#3231semidirect

Maximal subgroups

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

subgroupindex
#533×D532
#202858772
#202858762
#202858752
#202858742
#202858732
#202858722
#202858712
#202858702
#202858692
#500×D532
#498×D532
#487×D532
#485×D532
#479×D532
#431×D532
C53×#32312
C2×#323153