Finite Group Databasebeta

← #27536889

Subgroups — #27536889

Order 13568.

1252 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288044C211yesmaximal, characteristic
2C2×#16810597C211yesmaximal, characteristic, complemented
3#20276389C212yesmaximal, complemented
4#20276386C212yesmaximal, complemented
5#20276382C214yesmaximal, complemented
6#20276378C214yesmaximal, complemented
7C2×C53×#410C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811201—21no—
10#16811201—21no—
11#16811197C412yescomplemented
12#16811194C411yescharacteristic, complemented
13#16811194C2211yescharacteristic
14#16811190C2212yes—
15#16811187C411yescharacteristic, complemented
16#16811187C2211yescharacteristic
17#16811182—21no—
18#16811182—21no—
19#16811169C412yescomplemented
20#16811169C2212yes—
21#16811134—21no—
22#16811134—21no—
23#16811130—21no—
24#16811130—21no—
25C2×#13133176—21no—
26C2×#13133176C411yescharacteristic, complemented
27#16810597—21no—
28#16810597—21no—
29#16810597C2212yes—
30#16810597C2212yescomplemented
31C2×#13133132—21no—
32C2×#13133132C2212yescomplemented
33#16810417C2218yescomplemented
34#16810415C2218yescomplemented
35C22×#41×C53C2211yescharacteristic
36C2×#117×C53—21no—
37C53×#410—21no—
38C53×#410—21no—
39C53×#410C2212yes—
40C53×#410C2212yescomplemented
41C2×#99×C53—21no—
42C2×#99×C53C2212yescomplemented
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—41no—
46C2×#11719945—41no—
47C2×#11719945—41no—
48C2×#11719945—41no—
49C2×#11719945C2×C412yes—
50C2×#11719945C2×C412yescomplemented
51C22×Dic106C2×C411yescharacteristic, complemented
52C22×D212C2×C411yescharacteristic, complemented
53C22×C22⋊D53—21no—
54C22×C4×D53—21no—
55#13133215C2×C412yescomplemented
56#13133215C2×C412yescomplemented
57#13133213C2×C412yes—
58#13133213C2312yes—
59#13133206C2×C412yescomplemented
60#13133206C2×C412yescomplemented
61#13133204C2×C412yes—
62#13133204C2312yes—
63#13133200—22no—
64#13133200—22no—
65#13133198—21no—
66#13133198—21no—
67#13133198—21no—
68#13133198—21no—
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#13133185—21no—
88#13133185—21no—
89#13133185—21no—
90#13133185—21no—
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×C412yes—
102#13133176C2×C411yescharacteristic, complemented
103#13133176C2×C411yescharacteristic, complemented
104C2×C4⋊Dic53—21no—
105C2×C4⋊Dic53—41no—
106C2×C22⋊Dic53—21no—
107C2×C22⋊Dic53—22no—
108C2×C4×Dic53—41no—
109C2×C4×Dic53C2×C412yescomplemented
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×C53C2×C411yescharacteristic
127C22×D4×C53D411yescharacteristic
128C22×D4×C53D411yescharacteristic
129C22×D4×C53C2311yescharacteristic
130C23×C4×C53C2×C411yescharacteristic
131C23×C4×C53D411yescharacteristic
132C23×C4×C53D411yescharacteristic
133#117×C53—22no—
134#117×C53—22no—
135#117×C53—41no—
136#117×C53—41no—
137C2×C4⋊C4×C53—41no—
138C2×C22⋊C4×C53—22no—
139C2×C42×C53—41no—
140#99×C53—22no—
141#99×C53—22no—
142#99×C53—22no—
143#99×C53C2314yes—
144C24×C53C22⋊C411yescharacteristic
145C24×C53C2×D411yescharacteristic
146C24×C53C2×D411yescharacteristic
147C23×D53—21no—
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×C53C22×C411yescharacteristic
169C2×Q8×C53C22×C411yescharacteristic
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×C53C2×D411yescharacteristic
182C2×D4×C53C2×D411yescharacteristic
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×C53—42no—
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×C53C22×C411yescharacteristic
212C22×C4×C53C22×C411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C2×C22⋊D53—22no—
218C2×C22⋊D53—22no—
219C2×C22⋊D53—22no—
220C2×C22⋊D53—22no—
221C2×C22⋊D53—22no—
222C2×C22⋊D53—22no—
223C2×C22⋊D53—42no—
224C2×C22⋊D53—42no—
225C22×Dic53—21no—
226C22×Dic53—22no—
227C22×Dic53—42no—
228#11719945—42no—
229#11719945—42no—
230#11719945—41no—
231#11719945—41no—
232#11719945—41no—
233#11719945—41no—
234#11719945—42no—
235#11719945—42no—
236#11719945—42no—
237#11719945—42no—
238C2×D212—21no—
239C2×D212—41no—
240C2×D212—41no—
241C2×D212C22×C412yes—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—42no—
245C2×C4×D53—42no—
246C2×Dic106—21no—
247C2×Dic106—41no—
248C2×Dic106—41no—
249C2×Dic106C22×C412yes—
250C4⋊C4×C53—42no—
251C4⋊C4×C53—42no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53—42no—
254C42×C53—42no—
255C42×C53—42no—
256C22⋊Dic53—22no—
257C22⋊Dic53—21no—
258C22⋊Dic53—21no—
259C22⋊Dic53—22no—
260C22⋊Dic53—22no—
261C22⋊Dic53—22no—
262C22⋊Dic53—22no—
263C22⋊Dic53—24no—
264C22⋊Dic53—42no—
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—42no—
280C4×Dic53—42no—
281C4×Dic53C22×C412yes—
282C4×Dic53C22×C412yes—
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×C53C22×D411yescharacteristic
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—44no—
349C2×C4×C53—84no—
350C2×C4×C53#9911yescharacteristic
351C2×C4×C53#9911yescharacteristic
352C2×C4×C53#9911yescharacteristic
353C2×C4×C53#9911yescharacteristic
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×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C2×C22⋊C411yescharacteristic
361C2×C4×C53C23×C411yescharacteristic
362C22⋊D53—44no—
363C22⋊D53—42no—
364C22⋊D53—42no—
365C22⋊D53—82no—
366C22⋊D53—82no—
367C22⋊D53—82no—
368C22⋊D53—82no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—42no—
373C2×Dic53—44no—
374C2×Dic53—82no—
375C2×Dic53—84no—
376D212—42no—
377D212—41no—
378D212—41no—
379C4×D53—44no—
380C4×D53—42no—
381C4×D53—42no—
382Dic106—41no—
383Dic106—41no—
384Dic106—42no—
385#33358—531nomaximal, Sylow
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—42no—
400C22×C53—42no—
401C22×C53—81no—
402C22×C53—81no—
403C22×C53—81no—
404C22×C53—81no—
405C22×C53C2×#9911yescharacteristic
406C22×C53C2×#9911yescharacteristic
407C22×C53C22×C22⋊C411yescharacteristic
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—84no—
412C4×C53—21no—
413C4×C53—21no—
414C4×C53—21no—
415C4×C53—21no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—84no—
419C4×C53C2×#9911yescharacteristic
420C4×C53C2×#9911yescharacteristic
421C4×C53C2×#9911yescharacteristic
422C4×C53C2×#9911yescharacteristic
423Dic53—42no—
424Dic53—42no—
425Dic53—42no—
426Dic53—84no—
427#3449—531no—
428C2×#410—531no—
429C2×#410D5311yescharacteristic, complemented
430#2129—532no—
431#2128—532no—
432#2127—534no—
433#2126—534no—
434C2×C53—21no—
435C2×C53—21no—
436C2×C53—21no—
437C2×C53—41no—
438C2×C53—41no—
439C2×C53—41no—
440C2×C53—41no—
441C2×C53—41no—
442C2×C53—41no—
443C2×C53C22×#9911yescharacteristic
444D53—82no—
445C22×#41—531no—
446C22×#41C2×D5311yescharacteristic
447#537—1061no—
448#537—1061no—
449#536—531no—
450#536—531no—
451#536—532no—
452#535—531no—
453#535—531no—
454#535—532no—
455#534—1061no—
456#534—1061no—
457#532—532no—
458#532—532no—
459#525—1061no—
460#525—1061no—
461#525—1061no—
462#525—1061no—
463C2×#117—21no—
464C2×#117—531no—
465C2×#117—1061no—
466#410—21no—
467#410—21no—
468#410—532no—
469#410—532no—
470#410—1061no—
471#410—1061no—
472#410C2×D5312yes—
473#410C2×D5312yescomplemented
474C2×#99—21no—
475C2×#99—532no—
476C2×#99—1061no—
477C2×#99C2×D5312yescomplemented
478#354—538no—
479#353—538no—
480C53#3335811yescharacteristic, complemented, Sylow
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—532no—
486C2×#41—532no—
487C2×#41—1061no—
488C2×#41—1061no—
489C2×#41—2121no—
490C2×#41—2121no—
491C2×#41—2121no—
492C2×#41—2121no—
493C2×#41C4×D5311yescharacteristic
494C2×#41C4×D5311yescharacteristic
495C2×#41D21211yescharacteristic
496C2×#41D21211yescharacteristic
497C2×#41C22⋊D5311yescharacteristic
498C2×#41C22⋊D5311yescharacteristic
499C2×#41C22×D5311yescharacteristic
500C2×#41C22×D5311yescharacteristic
501C22×Q8—531no—
502C22×Q8C4×D5311yescharacteristic
503C22×D4—531no—
504C22×D4—1061no—
505C22×D4D21211yescharacteristic
506C22×D4C22⋊D5311yescharacteristic
507C22×D4C22×D5311yescharacteristic
508C23×C4—1061no—
509C23×C4C4×D5311yescharacteristic
510C23×C4D21211yescharacteristic
511C23×C4C22⋊D5311yescharacteristic
512C4⋊Q8—532no—
513C4⋊Q8—532no—
514#127—532no—
515#127—532no—
516#124—532no—
517#124—532no—
518#124—532no—
519#124—532no—
520#123—1061no—
521#123—1061no—
522#123—1061no—
523#123—1061no—
524#123—1062no—
525#123—1062no—
526C22⋊Q8—1062no—
527C22⋊Q8—1062no—
528C22⋊Q8—1061no—
529C22⋊Q8—1061no—
530C22⋊Q8—1061no—
531C22⋊Q8—1061no—
532#121—1062no—
533#121—1062no—
534#121—1062no—
535#121—1062no—
536#121—1062no—
537#121—1062no—
538#121—1061no—
539#121—1061no—
540#121—1061no—
541#121—1061no—
542#120—1062no—
543#120—1062no—
544#120—1061no—
545#120—1061no—
546#120—1061no—
547#120—1061no—
548C4×D4—1062no—
549C4×D4—1062no—
550C4×D4—1062no—
551C4×D4—1062no—
552#117—22no—
553#117—22no—
554#117—41no—
555#117—41no—
556#117—532no—
557#117—531no—
558#117—531no—
559#117—1061no—
560#117—1061no—
561#117—1062no—
562#117—1062no—
563#117—2121no—
564#117—2121no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—2121no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1062no—
571C2×C42—41no—
572C2×C42—532no—
573C2×C42—2121no—
574#99—22no—
575#99—22no—
576#99—22no—
577#99—534no—
578#99—1062no—
579#99—1062no—
580#99—1062no—
581#99C22×D5314yes—
582C24—1061no—
583C24#1171992111yescharacteristic
584C24C2×D21211yescharacteristic
585C24C2×C22⋊D5311yescharacteristic
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—41no—
601#41—41no—
602#41—2122no—
603#41—2122no—
604#41—2122no—
605#41—2122no—
606#41—2122no—
607#41—2122no—
608#41—2121no—
609#41—2121no—
610#41—2121no—
611#41—2121no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—532no—
615C2×Q8—1061no—
616C2×Q8—2121no—
617C2×Q8—2121no—
618C2×Q8#1171992111yescharacteristic
619C2×Q8#1171992111yescharacteristic
620C2×Q8C2×C4×D5311yescharacteristic
621C2×Q8C2×C4×D5311yescharacteristic
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—532no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—1061no—
636C2×D4—2121no—
637C2×D4—2121no—
638C2×D4—2122no—
639C2×D4—2122no—
640C2×D4#1171992111yescharacteristic
641C2×D4#1171992111yescharacteristic
642C2×D4#1171992111yescharacteristic
643C2×D4#1171992111yescharacteristic
644C2×D4C2×C4×D5311yescharacteristic
645C2×D4C2×D21211yescharacteristic
646C2×D4C2×D21211yescharacteristic
647C2×D4C2×D21211yescharacteristic
648C2×D4C2×C22⋊D5311yescharacteristic
649C2×D4C2×C22⋊D5311yescharacteristic
650C2×D4C2×C22⋊D5311yescharacteristic
651C2×D4C23×D5311yescharacteristic
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—21no—
663C22×C4—21no—
664C22×C4—42no—
665C22×C4—1062no—
666C22×C4—1061no—
667C22×C4—1062no—
668C22×C4—1062no—
669C22×C4—2122no—
670C22×C4—2122no—
671C22×C4—2122no—
672C22×C4#1171992111yescharacteristic
673C22×C4#1171992111yescharacteristic
674C22×C4#1171992111yescharacteristic
675C22×C4#1171992111yescharacteristic
676C22×C4#1171992111yescharacteristic
677C22×C4#1171992111yescharacteristic
678C22×C4#1171992111yescharacteristic
679C22×C4#1171992111yescharacteristic
680C22×C4#1171992111yescharacteristic
681C22×C4C2×C4×D5311yescharacteristic
682C22×C4C2×C4×D5311yescharacteristic
683C22×C4C2×C4×D5311yescharacteristic
684C22×C4C2×D21211yescharacteristic
685C22×C4C2×D21211yescharacteristic
686C22×C4C2×C22⋊D5311yescharacteristic
687C22×C4C2×C22⋊D5311yescharacteristic
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—1062no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1062no—
694C4⋊C4—1062no—
695C4⋊C4—1062no—
696C4⋊C4—1062no—
697C4⋊C4—2122no—
698C4⋊C4—2122no—
699C22⋊C4—24no—
700C22⋊C4—42no—
701C22⋊C4—1061no—
702C22⋊C4—1061no—
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—42no—
715C42—42no—
716C42—532no—
717C42—532no—
718C42—1062no—
719C42—2122no—
720C42—2122no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—1062no—
731C23—4242no—
732C23—2122no—
733C23C2×#1171992111yescharacteristic
734C23C2×#1171992111yescharacteristic
735C23C2×#1171992111yescharacteristic
736C23C2×#1171992111yescharacteristic
737C23C2×#1171992111yescharacteristic
738C23C22×C22⋊D5311yescharacteristic
739C23C22×D21211yescharacteristic
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—2122no—
745Q8—2121no—
746Q8—2121no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—4242no—
760D4—4242no—
761D4—4242no—
762D4—4242no—
763D4—2122no—
764D4—2124no—
765D4—2122no—
766D4—2122no—
767D4—2121no—
768D4—2121no—
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—21no—
798C2×C4—21no—
799C2×C4—44no—
800C2×C4—84no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4—4244no—
805C2×C4—4242no—
806C2×C4—2124no—
807C2×C4—2124no—
808C2×C4—2122no—
809C2×C4—2122no—
810C2×C4—2122no—
811C2×C4#1313313111yescharacteristic
812C2×C4#1313313111yescharacteristic
813C2×C4#1313313111yescharacteristic
814C2×C4#1313313111yescharacteristic
815C2×C4C2×#1171992111yescharacteristic
816C2×C4C2×#1171992111yescharacteristic
817C2×C4C2×#1171992111yescharacteristic
818C2×C4C2×#1171992111yescharacteristic
819C2×C4C2×#1171992111yescharacteristic
820C2×C4C2×#1171992111yescharacteristic
821C2×C4C2×#1171992111yescharacteristic
822C2×C4C22×C4×D5311yescharacteristic
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—4244no—
843C22—2122no—
844C22—2122no—
845C22—2122no—
846C22C2×#1313313111yescharacteristic
847C22C2×#1313313111yescharacteristic
848C22C22×#1171992111yescharacteristic
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—84no—
856C4—4244no—
857C4—2122no—
858C4—2122no—
859C4—2122no—
860C4C2×#1313313111yescharacteristic
861C4C2×#1313313111yescharacteristic
862C4C2×#1313313111yescharacteristic
863C4C2×#1313313111yescharacteristic
864C2—21no—
865C2—21no—
866C2—21no—
867C2—41no—
868C2—41no—
869C2—41no—
870C2—41no—
871C2—41no—
872C2—41no—
873C2—4242no—
874C2C22×#1313313111yescharacteristic
subgroupG/H
centerC4C2×#13133131
commutatorC2×C4×C53C23×C4
FrattiniC2×D4C23×D53
FittingC2×C53×#410C2
socleC2×C53C22×#99
prime radical#20288044C2
cosocleC2×D4×C53C24
hypercenterC2×#410D53
hypocenterC53#33358
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#16810597C2semidirect
3. #20276389C2semidirect
4. #20276386C2semidirect
5. #20276382C2semidirect
6. #20276378C2semidirect
7. C2×C53×#410C2semidirect
8. C22×#11719945C4semidirect
11. #16811197C4semidirect
12. #16811194C4semidirect
15. #16811187C4semidirect
19. #16811169C4semidirect
26. C2×#13133176C4semidirect
30. #16810597C22semidirect
32. C2×#13133132C22semidirect
33. #16810417C22semidirect
34. #16810415C22semidirect
40. C53×#410C22semidirect
42. C2×#99×C53C22semidirect
50. C2×#11719945C2×C4semidirect
51. C22×Dic106C2×C4semidirect
52. C22×D212C2×C4semidirect
55. #13133215C2×C4semidirect
56. #13133215C2×C4semidirect
59. #13133206C2×C4semidirect
60. #13133206C2×C4semidirect
102. #13133176C2×C4semidirect
103. #13133176C2×C4semidirect
109. C2×C4×Dic53C2×C4semidirect
429. C2×#410D53semidirect
473. #410C2×D53semidirect
477. C2×#99C2×D53semidirect
480. C53#33358semidirect

Maximal subgroups

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

subgroupindex
#202880442
C2×#168105972
#202763892
#202763862
#202763822
#202763782
C2×C53×#4102
#3335853