Finite Group Databasebeta

← #27536837

Subgroups — #27536837

Order 13568.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288044C211yesmaximal, characteristic
2C2×#16810597C211yesmaximal, characteristic, complemented
3#20276370C212yesmaximal, complemented
4#20276366C212yesmaximal, complemented
5#20276362C214yesmaximal, complemented
6#20276357C214yesmaximal, complemented
7C2×C53×#413C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811201—21no—
10#16811201—21no—
11#16811197—21no—
12#16811194C411yescharacteristic, complemented
13#16811194C2211yescharacteristic
14#16811190—21no—
15#16811187C411yescharacteristic, complemented
16#16811187C2211yescharacteristic
17#16811182C412yescomplemented
18#16811182C2212yes—
19#16811169—21no—
20#16811169—21no—
21#16811134—21no—
22#16811134—21no—
23#16811130C412yescomplemented
24#16811130C2212yes—
25C2×#13133176—21no—
26C2×#13133176C411yescharacteristic, complemented
27#16810597—21no—
28#16810597—21no—
29#16810597C2212yes—
30#16810597C2212yes—
31C2×#13133132—21no—
32C2×#13133132C2212yes—
33#16810414C2218yescomplemented
34#16810411C2218yescomplemented
35C22×#41×C53C2211yescharacteristic
36C22×M16×C53—21no—
37C53×#413—21no—
38C53×#413—21no—
39C53×#413C2212yes—
40C53×#413C2212yes—
41C2×#101×C53—21no—
42C2×#100×C53C2212yes—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—41no—
48C2×#11719945—41no—
49C2×#11719945—41no—
50C2×#11719945—41no—
51C22×Dic106C2×C411yescharacteristic, complemented
52C22×D212C2×C411yescharacteristic, complemented
53C22×C22⋊D53C2×C412yes—
54C22×C4×D53C2×C412yescomplemented
55#13133215—21no—
56#13133215—21no—
57#13133213—21no—
58#13133213—21no—
59#13133206—21no—
60#13133206—21no—
61#13133204—21no—
62#13133204—21no—
63#13133200—22no—
64#13133200—22no—
65#13133198C2×C412yes—
66#13133198C2×C412yescomplemented
67#13133198C2×C412yescomplemented
68#13133198C2312yes—
69#13133196—21no—
70#13133196—21no—
71#13133196—21no—
72#13133196—21no—
73#13133193—22no—
74#13133193—22no—
75#13133191—21no—
76#13133191—21no—
77#13133191—21no—
78#13133191—21no—
79#13133189—22no—
80#13133189—22no—
81#13133189—22no—
82#13133189—22no—
83#13133188—22no—
84#13133188—22no—
85#13133186—22no—
86#13133186—22no—
87#13133185C2×C412yes—
88#13133185C2×C412yescomplemented
89#13133185C2×C412yescomplemented
90#13133185C2312yes—
91C4×C22⋊D53—22no—
92C4×C22⋊D53—22no—
93C4×C22⋊D53—22no—
94C4×C22⋊D53—22no—
95#13133176—21no—
96#13133176—21no—
97#13133176—22no—
98#13133176—22no—
99#13133176—41no—
100#13133176—41no—
101#13133176C2×C412yescomplemented
102#13133176C2×C411yescharacteristic, complemented
103#13133176C2×C411yescharacteristic, complemented
104C2×C4⋊Dic53—21no—
105C2×C4⋊Dic53—41no—
106C2×C22⋊Dic53—22no—
107C2×C22⋊Dic53C2×C412yes—
108C2×C4×Dic53—21no—
109C2×C4×Dic53—41no—
110#13133132—22no—
111#13133132—22no—
112#13133132—22no—
113#13133132C2314yes—
114C2×#41×C53—41no—
115C2×#41×C53—41no—
116C2×#41×C53—41no—
117C2×#41×C53—41no—
118C2×#41×C53C2×C411yescharacteristic
119C2×#41×C53C2×C411yescharacteristic
120C2×#41×C53D411yescharacteristic
121C2×#41×C53D411yescharacteristic
122C2×#41×C53D411yescharacteristic
123C2×#41×C53D411yescharacteristic
124C2×#41×C53C2311yescharacteristic
125C2×#41×C53C2311yescharacteristic
126C22×Q8×C53D411yescharacteristic
127C22×D4×C53C2×C411yescharacteristic
128C22×D4×C53D411yescharacteristic
129C22×D4×C53C2311yescharacteristic
130C23×C4×C53C2×C411yescharacteristic
131C23×C4×C53D411yescharacteristic
132C23×C4×C53D411yescharacteristic
133C2×M16×C53—22no—
134C2×M16×C53—22no—
135C2×M16×C53—22no—
136C2×M16×C53—41no—
137C2×M16×C53—41no—
138C2×M16×C53—41no—
139C22×C8×C53—41no—
140#101×C53—22no—
141#101×C53—22no—
142#100×C53—22no—
143#100×C53C2314yes—
144C24×C53C22⋊C411yescharacteristic
145C24×C53C22×C411yescharacteristic
146C24×C53C2×D411yescharacteristic
147C23×D53C22×C412yes—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161#41×C53—41no—
162#41×C53—41no—
163#41×C53—41no—
164C2×Q8×C53—41no—
165C2×Q8×C53—41no—
166C2×Q8×C53C22⋊C411yescharacteristic
167C2×Q8×C53C22⋊C411yescharacteristic
168C2×Q8×C53C2×D411yescharacteristic
169C2×Q8×C53C2×D411yescharacteristic
170C2×D4×C53—41no—
171C2×D4×C53—41no—
172C2×D4×C53—41no—
173C2×D4×C53—41no—
174C2×D4×C53—41no—
175C2×D4×C53—41no—
176C2×D4×C53C22⋊C411yescharacteristic
177C2×D4×C53C22⋊C411yescharacteristic
178C2×D4×C53C22⋊C411yescharacteristic
179C2×D4×C53C22⋊C411yescharacteristic
180C2×D4×C53C22×C411yescharacteristic
181C2×D4×C53C22×C411yescharacteristic
182C2×D4×C53C22×C411yescharacteristic
183C2×D4×C53C2×D411yescharacteristic
184C2×D4×C53C2×D411yescharacteristic
185C2×D4×C53C2×D411yescharacteristic
186C2×D4×C53C2×D411yescharacteristic
187C2×D4×C53C2411yescharacteristic
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53C22⋊C411yescharacteristic
201C22×C4×C53C22⋊C411yescharacteristic
202C22×C4×C53C22⋊C411yescharacteristic
203C22×C4×C53C22⋊C411yescharacteristic
204C22×C4×C53C22⋊C411yescharacteristic
205C22×C4×C53C22⋊C411yescharacteristic
206C22×C4×C53C22⋊C411yescharacteristic
207C22×C4×C53C22⋊C411yescharacteristic
208C22×C4×C53C22⋊C411yescharacteristic
209C22×C4×C53C22×C411yescharacteristic
210C22×C4×C53C22×C411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C2×C22⋊D53—22no—
217C2×C22⋊D53—22no—
218C2×C22⋊D53—22no—
219C2×C22⋊D53—22no—
220C2×C22⋊D53—22no—
221C2×C22⋊D53—22no—
222C2×C22⋊D53—42no—
223C2×C22⋊D53—42no—
224C22×Dic53—22no—
225C22×Dic53—42no—
226C22×Dic53C22×C412yes—
227#11719945—42no—
228#11719945—42no—
229#11719945—42no—
230#11719945—42no—
231#11719945—42no—
232#11719945—42no—
233#11719945—41no—
234#11719945—41no—
235#11719945—41no—
236#11719945—41no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—41no—
240C2×D212—41no—
241C2×C4×D53—22no—
242C2×C4×D53—22no—
243C2×C4×D53—42no—
244C2×C4×D53—42no—
245C2×Dic106—21no—
246C2×Dic106—21no—
247C2×Dic106—41no—
248C2×Dic106—41no—
249M16×C53—24no—
250M16×C53—42no—
251M16×C53—42no—
252M16×C53—42no—
253C2×C8×C53—42no—
254C2×C8×C53—42no—
255C2×C8×C53—42no—
256C22⋊Dic53—22no—
257C22⋊Dic53—22no—
258C22⋊Dic53—22no—
259C22⋊Dic53—22no—
260C22⋊Dic53—22no—
261C22⋊Dic53—24no—
262C22⋊Dic53—42no—
263C22⋊Dic53C22×C412yes—
264C22⋊Dic53C22×C412yes—
265#11719921—22no—
266#11719921—22no—
267#11719921—22no—
268#11719921—22no—
269C4⋊Dic53—22no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—42no—
273C4⋊Dic53—42no—
274#11719919—22no—
275#11719919—22no—
276#11719919—22no—
277#11719919—22no—
278C4×Dic53—22no—
279C4×Dic53—21no—
280C4×Dic53—21no—
281C4×Dic53—42no—
282C4×Dic53—42no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—81no—
290C23×C53—81no—
291C23×C53—81no—
292C23×C53C2×C22⋊C411yescharacteristic
293C23×C53C2×C22⋊C411yescharacteristic
294C23×C53C2×C22⋊C411yescharacteristic
295C23×C53C2×C22⋊C411yescharacteristic
296C23×C53C2×C22⋊C411yescharacteristic
297C23×C53C23×C411yescharacteristic
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—82no—
302Q8×C53—41no—
303Q8×C53—41no—
304Q8×C53—41no—
305Q8×C53—41no—
306D4×C53—41no—
307D4×C53—41no—
308D4×C53—41no—
309D4×C53—41no—
310D4×C53—41no—
311D4×C53—41no—
312D4×C53—41no—
313D4×C53—41no—
314D4×C53—41no—
315D4×C53—41no—
316D4×C53—41no—
317D4×C53—41no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—21no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53#9911yescharacteristic
349C2×C4×C53#9911yescharacteristic
350C2×C4×C53#9911yescharacteristic
351C2×C4×C53#9911yescharacteristic
352C2×C4×C53C2×C22⋊C411yescharacteristic
353C2×C4×C53C2×C22⋊C411yescharacteristic
354C2×C4×C53C2×C22⋊C411yescharacteristic
355C2×C4×C53C2×C22⋊C411yescharacteristic
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53C2×C22⋊C411yescharacteristic
358C2×C4×C53C2×C22⋊C411yescharacteristic
359C2×C4×C53C22×D411yescharacteristic
360C22⋊D53—44no—
361C22⋊D53—42no—
362C22⋊D53—42no—
363C22⋊D53—82no—
364C22⋊D53—82no—
365C22⋊D53—82no—
366C22⋊D53—82no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—42no—
371C2×Dic53—44no—
372C2×Dic53—82no—
373C2×Dic53—84no—
374D212—42no—
375D212—41no—
376D212—41no—
377C4×D53—44no—
378C4×D53—42no—
379C4×D53—42no—
380Dic106—42no—
381Dic106—41no—
382Dic106—41no—
383C8×C53—44no—
384#33347—531nomaximal, Sylow
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—42no—
399C22×C53—42no—
400C22×C53—81no—
401C22×C53—81no—
402C22×C53—81no—
403C22×C53—81no—
404C22×C53C2×#9911yescharacteristic
405C22×C53C2×#9911yescharacteristic
406C22×C53C22×C22⋊C411yescharacteristic
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—84no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—21no—
414C4×C53—21no—
415C4×C53—21no—
416C4×C53—21no—
417C4×C53C2×#9911yescharacteristic
418C4×C53C2×#9911yescharacteristic
419C4×C53C2×#9911yescharacteristic
420C4×C53C2×#9911yescharacteristic
421Dic53—42no—
422Dic53—42no—
423Dic53—42no—
424Dic53—84no—
425#3449—531no—
426C2×#413D5311yescharacteristic, complemented
427C2×#410—531no—
428#2123—532no—
429#2122—532no—
430#2121—534no—
431#2120—534no—
432C2×C53—21no—
433C2×C53—21no—
434C2×C53—21no—
435C2×C53—41no—
436C2×C53—41no—
437C2×C53—41no—
438C2×C53—41no—
439C2×C53—41no—
440C2×C53—41no—
441C2×C53C22×#9911yescharacteristic
442D53—82no—
443C22×#41—531no—
444C22×#41C2×D5311yescharacteristic
445C22×M16—21no—
446#537—1061no—
447#537—1061no—
448#536—531no—
449#536—531no—
450#536—1061no—
451#535—531no—
452#535—531no—
453#535—1061no—
454#534—532no—
455#534—532no—
456#532—1061no—
457#532—1061no—
458#525—532no—
459#525—532no—
460#525—1061no—
461#525—1061no—
462C2×#117—531no—
463C2×#117—1061no—
464#413—21no—
465#413—21no—
466#413C2×D5312yes—
467#413C2×D5312yes—
468C2×#101—21no—
469C2×#100C2×D5312yes—
470#410—532no—
471#410—532no—
472#410—1061no—
473#410—1061no—
474C2×#99—532no—
475C2×#99—1061no—
476#352—538no—
477AΣL(1,𝔽16)—538no—
478C53#3334711yescharacteristic, complemented, Sylow
479C2×#41—41no—
480C2×#41—41no—
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—1061no—
484C2×#41—1061no—
485C2×#41—1061no—
486C2×#41—1061no—
487C2×#41—2121no—
488C2×#41—2121no—
489C2×#41—2121no—
490C2×#41—2121no—
491C2×#41C4×D5311yescharacteristic
492C2×#41C4×D5311yescharacteristic
493C2×#41D21211yescharacteristic
494C2×#41D21211yescharacteristic
495C2×#41C22⋊D5311yescharacteristic
496C2×#41C22⋊D5311yescharacteristic
497C2×#41C22×D5311yescharacteristic
498C2×#41C22×D5311yescharacteristic
499C22×Q8—531no—
500C22×Q8C22⋊D5311yescharacteristic
501C22×D4—532no—
502C22×D4—531no—
503C22×D4C4×D5311yescharacteristic
504C22×D4D21211yescharacteristic
505C22×D4C22×D5311yescharacteristic
506C23×C4—532no—
507C23×C4C4×D5311yescharacteristic
508C23×C4D21211yescharacteristic
509C23×C4C22⋊D5311yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—1061no—
518C4⋊Q8—1061no—
519#127—1061no—
520#127—1061no—
521#124—1061no—
522#124—1061no—
523#124—1061no—
524#124—1061no—
525#123—532no—
526#123—532no—
527#123—532no—
528#123—532no—
529#123—1062no—
530#123—1062no—
531C22⋊Q8—1062no—
532C22⋊Q8—1062no—
533C22⋊Q8—1061no—
534C22⋊Q8—1061no—
535C22⋊Q8—1061no—
536C22⋊Q8—1061no—
537#121—1062no—
538#121—1062no—
539#121—1062no—
540#121—1062no—
541#121—1062no—
542#121—1062no—
543#121—1061no—
544#121—1061no—
545#121—1061no—
546#121—1061no—
547#120—532no—
548#120—532no—
549#120—532no—
550#120—532no—
551#120—1062no—
552#120—1062no—
553C4×D4—1062no—
554C4×D4—1062no—
555C4×D4—1062no—
556C4×D4—1062no—
557#117—532no—
558#117—531no—
559#117—531no—
560#117—1061no—
561#117—1061no—
562#117—1062no—
563#117—1062no—
564#117—2121no—
565#117—2121no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—2121no—
568C2×C22⋊C4—532no—
569C2×C22⋊C4—1062no—
570C2×C42—1061no—
571C2×C42—2121no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C22×D5314yes—
576#99—534no—
577#99—1062no—
578#99—1062no—
579#99—1062no—
580C24—532no—
581C24#1171992111yescharacteristic
582C24C2×C4×D5311yescharacteristic
583C24C2×D21211yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—2122no—
601#41—2122no—
602#41—2122no—
603#41—2122no—
604#41—2122no—
605#41—2122no—
606#41—2121no—
607#41—2121no—
608#41—2121no—
609#41—2121no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8—1061no—
613C2×Q8—1061no—
614C2×Q8—2121no—
615C2×Q8—2121no—
616C2×Q8#1171992111yescharacteristic
617C2×Q8#1171992111yescharacteristic
618C2×Q8C2×C22⋊D5311yescharacteristic
619C2×Q8C2×C22⋊D5311yescharacteristic
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—1062no—
627C2×D4—1062no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—1061no—
633C2×D4—1061no—
634C2×D4—2121no—
635C2×D4—2121no—
636C2×D4—2122no—
637C2×D4—2122no—
638C2×D4#1171992111yescharacteristic
639C2×D4#1171992111yescharacteristic
640C2×D4#1171992111yescharacteristic
641C2×D4#1171992111yescharacteristic
642C2×D4C2×C4×D5311yescharacteristic
643C2×D4C2×C4×D5311yescharacteristic
644C2×D4C2×C4×D5311yescharacteristic
645C2×D4C2×D21211yescharacteristic
646C2×D4C2×D21211yescharacteristic
647C2×D4C2×D21211yescharacteristic
648C2×D4C2×C22⋊D5311yescharacteristic
649C2×D4C23×D5311yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—532no—
663C22×C4—1062no—
664C22×C4—1062no—
665C22×C4—1062no—
666C22×C4—2122no—
667C22×C4—2122no—
668C22×C4—2122no—
669C22×C4#1171992111yescharacteristic
670C22×C4#1171992111yescharacteristic
671C22×C4#1171992111yescharacteristic
672C22×C4#1171992111yescharacteristic
673C22×C4#1171992111yescharacteristic
674C22×C4#1171992111yescharacteristic
675C22×C4#1171992111yescharacteristic
676C22×C4#1171992111yescharacteristic
677C22×C4#1171992111yescharacteristic
678C22×C4C2×C4×D5311yescharacteristic
679C22×C4C2×C4×D5311yescharacteristic
680C22×C4C2×D21211yescharacteristic
681C22×C4C2×D21211yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684C22×C4C2×C22⋊D5311yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—1062no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1062no—
696C4⋊C4—1062no—
697C4⋊C4—1062no—
698C4⋊C4—1062no—
699C4⋊C4—2122no—
700C4⋊C4—2122no—
701C22⋊C4—532no—
702C22⋊C4—532no—
703C22⋊C4—1062no—
704C22⋊C4—1062no—
705C22⋊C4—1062no—
706C22⋊C4—1062no—
707C22⋊C4—1062no—
708C22⋊C4—1062no—
709C22⋊C4—1062no—
710C22⋊C4—1062no—
711C22⋊C4—1062no—
712C22⋊C4—1064no—
713C22⋊C4—2122no—
714C42—1062no—
715C42—1061no—
716C42—1061no—
717C42—2122no—
718C42—2122no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—1062no—
729C23—4242no—
730C23—2122no—
731C23C2×#1171992111yescharacteristic
732C23C2×#1171992111yescharacteristic
733C23C2×#1171992111yescharacteristic
734C23C2×#1171992111yescharacteristic
735C23C2×#1171992111yescharacteristic
736C23C22×C4×D5311yescharacteristic
737C23C22×D21211yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—2122no—
743Q8—2121no—
744Q8—2121no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—4242no—
758D4—4242no—
759D4—4242no—
760D4—4242no—
761D4—2122no—
762D4—2124no—
763D4—2122no—
764D4—2122no—
765D4—2121no—
766D4—2121no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—4244no—
801C2×C4—4242no—
802C2×C4—2124no—
803C2×C4—2124no—
804C2×C4—2122no—
805C2×C4—2122no—
806C2×C4—2122no—
807C2×C4#1313313111yescharacteristic
808C2×C4#1313313111yescharacteristic
809C2×C4#1313313111yescharacteristic
810C2×C4#1313313111yescharacteristic
811C2×C4C2×#1171992111yescharacteristic
812C2×C4C2×#1171992111yescharacteristic
813C2×C4C2×#1171992111yescharacteristic
814C2×C4C2×#1171992111yescharacteristic
815C2×C4C2×#1171992111yescharacteristic
816C2×C4C2×#1171992111yescharacteristic
817C2×C4C2×#1171992111yescharacteristic
818C2×C4C22×C22⋊D5311yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—4244no—
840C22—2122no—
841C22—2122no—
842C22—2122no—
843C22C2×#1313313111yescharacteristic
844C22C2×#1313313111yescharacteristic
845C22C22×#1171992111yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—4244no—
853C4—2122no—
854C4—2122no—
855C4—2122no—
856C4C2×#1313313111yescharacteristic
857C4C2×#1313313111yescharacteristic
858C4C2×#1313313111yescharacteristic
859C4C2×#1313313111yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—4242no—
870C2C22×#1313313111yescharacteristic
subgroupG/H
centerC4C2×#13133131
commutatorC23×C53C23×C4
FrattiniC2×D4C23×D53
FittingC2×C53×#413C2
socleC2×C53C22×#99
prime radical#20288044C2
cosocleC2×D4×C53C24
hypercenterC2×#413D53
hypocenterC53#33347
LCSG ▷ C23×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#16810597C2semidirect
3. #20276370C2semidirect
4. #20276366C2semidirect
5. #20276362C2semidirect
6. #20276357C2semidirect
7. C2×C53×#413C2semidirect
8. C22×#11719945C4semidirect
12. #16811194C4semidirect
15. #16811187C4semidirect
17. #16811182C4semidirect
23. #16811130C4semidirect
26. C2×#13133176C4semidirect
33. #16810414C22semidirect
34. #16810411C22semidirect
51. C22×Dic106C2×C4semidirect
52. C22×D212C2×C4semidirect
54. C22×C4×D53C2×C4semidirect
66. #13133198C2×C4semidirect
67. #13133198C2×C4semidirect
88. #13133185C2×C4semidirect
89. #13133185C2×C4semidirect
101. #13133176C2×C4semidirect
102. #13133176C2×C4semidirect
103. #13133176C2×C4semidirect
426. C2×#413D53semidirect
478. C53#33347semidirect

Maximal subgroups

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

subgroupindex
#202880442
C2×#168105972
#202763702
#202763662
#202763622
#202763572
C2×C53×#4132
#3334753