Finite Group Databasebeta

← #27404470

Subgroups — #27404470

Order 13568.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810783C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic
4#20277546C211yesmaximal, characteristic
5#20275575C211yesmaximal, characteristic, complemented
6#20275404C211yesmaximal, characteristic, complemented
7#20275356C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275056C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274961C211yesmaximal, characteristic, complemented
12#20274903C211yesmaximal, characteristic, complemented
13C4×#13133137C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2360C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×D212C2211yescharacteristic
22#16810783C418yescomplemented
23#16810721—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26#16810622—24no—
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810529C2211yescharacteristic
39#16810529C2211yescharacteristic
40#16810499—21no—
41#16810499—21no—
42#16810485—21no—
43#16810483C2211yescharacteristic
44#95×D53—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C2×C22⋊Q8×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C53×#391C2211yescharacteristic
55C53×#389—21no—
56C53×#389C2211yescharacteristic
57C53×#387—21no—
58C53×#385—21no—
59C4×C4⋊C4×C53C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C4×C22⋊C4×C53C2211yescharacteristic
62C2×#11719945—22no—
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C2×#11719945C2×C414yes—
68C22×Dic106C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C22×C22⋊D53—21no—
71C22×C4×D53—21no—
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C2×#11719925—41no—
75C2×#11719925—41no—
76C2×#11719925C2×C414yescomplemented
77C2×#11719924—22no—
78C2×#11719924—22no—
79C2×#11719924C2×C414yescomplemented
80C2×#11719917—22no—
81C2×#11719917—22no—
82C2×#11719917—41no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C4×D212—22no—
88C4×D212—22no—
89C4×D212—41no—
90C4×D212—41no—
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C22⋊Dic53—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96#13133150—22no—
97#13133150—41no—
98#13133141—22no—
99#13133141—41no—
100#13133140—22no—
101#13133140—22no—
102#13133140C2×C414yescomplemented
103#13133137—22no—
104#13133137C2×C414yescomplemented
105#13133137D414yes—
106C22⋊#88322C2×C414yescomplemented
107#13133128—22no—
108C4×#88322—41no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114C22×Q8×C53C2311yescharacteristic
115C23×C4×C53—21no—
116C23×C4×C53C2311yescharacteristic
117C22⋊Q8×C53—22no—
118C22⋊Q8×C53C2×C414yescomplemented
119C4×Q8×C53—22no—
120C4×Q8×C53—41no—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—22no—
126C2×C4⋊C4×C53—41no—
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C42×C53—21no—
134C2×C42×C53—21no—
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53D411yescharacteristic
142#95×C53D411yescharacteristic
143C24×C53C2×D411yescharacteristic
144C23×D53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53C22×C412yes—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—42no—
160C22×C4×C53—42no—
161C22×C4×C53—81no—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53#4112yes—
169C22×C4×C53C2411yescharacteristic
170C2×C22⋊D53—24no—
171C2×C22⋊D53—42no—
172C2×C22⋊D53—42no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176#11719945—28no—
177#11719945—44no—
178#11719945—44no—
179#11719945—44no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—21no—
183C2×D212C22×C412yes—
184C2×D212C2×D412yes—
185C2×D212#4112yes—
186C2×C4×D53—24no—
187C2×C4×D53—42no—
188C2×C4×D53—42no—
189C2×C4×D53—42no—
190C2×C4×D53—42no—
191C2×C4×D53—42no—
192C2×C4×D53—42no—
193C2×C4×D53—81no—
194C2×C4×D53—81no—
195C2×Dic106—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106C22×C412yes—
201C4⋊C4×C53—24no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53—42no—
208C4⋊C4×C53—81no—
209C4⋊C4×C53C22×C412yes—
210C4⋊C4×C53C2×D412yes—
211C22⋊C4×C53—24no—
212C22⋊C4×C53—22no—
213C22⋊C4×C53—41no—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—21no—
217C42×C53—21no—
218C42×C53—42no—
219C42×C53—81no—
220C22⋊Dic53—81no—
221#11719925—44no—
222#11719924—28no—
223#11719921—42no—
224#11719921—42no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229#11719917—44no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322C22×C412yes—
240C2×#88322C22×C412yes—
241C2×#88322C2×D412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53C4×D412yes—
249C23×C53C22×D411yescharacteristic
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—41no—
260Q8×C53—41no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—21no—
272C2×C4×C53—22no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—84no—
291C2×C4×C53C4×D412yes—
292C2×C4×C53#13712yes—
293C2×C4×C53C23×C411yescharacteristic
294C2×C4×C53C22×D411yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C22⋊D53—48no—
300C2×Dic53—22no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309D212—22no—
310D212—22no—
311D212—22no—
312D212C4×D414yes—
313C4×D53—48no—
314C4×D53—84no—
315C4×D53—84no—
316Dic106—22no—
317Dic106—22no—
318Dic106—41no—
319Dic106—41no—
320#88322—22no—
321#88322—22no—
322#88322—22no—
323#88322—41no—
324#22862—531nomaximal, Sylow
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53C2×C4×D411yescharacteristic
333C22×C53D4211yescharacteristic
334C22×C53#54611yescharacteristic
335C22×C53C2×#13711yescharacteristic
336C22×C53#57511yescharacteristic
337C22×C53#57611yescharacteristic
338C22×C53#57811yescharacteristic
339C2×D53—24no—
340C2×D53—42no—
341C2×D53—42no—
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—42no—
349C4×C53—42no—
350C4×C53—41no—
351C4×C53—42no—
352C4×C53—41no—
353C4×C53—41no—
354C4×C53—81no—
355C4×C53C2×C4×D411yescharacteristic
356C4×C53#51811yescharacteristic
357C4×C53#54611yescharacteristic
358C4×C53#55111yescharacteristic
359Dic53—42no—
360Dic53—81no—
361Dic53—81no—
362C2×#452—531no—
363C2×#440—531no—
364C2×#417—531no—
365#2360D5311yescharacteristic, complemented
366#2339—531no—
367#1969—531no—
368#1935—531no—
369#1928—531no—
370#1894—531no—
371#1878—531no—
372#1877—531no—
373#1862—531no—
374#1852—531no—
375C4×#102—531no—
376#1753—531no—
377C2×C53—42no—
378C2×C53#235811yescharacteristic
379C2×C53C4×#13711yescharacteristic
380C2×C53#295111yescharacteristic
381C2×C53#327311yescharacteristic
382C2×C53#327611yescharacteristic
383C2×C53#331411yescharacteristic
384C2×C53#331511yescharacteristic
385D53—44no—
386C22×#41—531no—
387C22×Q16—531no—
388C22×SD16—531no—
389C22×M16—531no—
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×D4—531no—
393C2×C4×D4—531no—
394C22×C4⋊C4C2×D5311yescharacteristic
395#452—538no—
396#440—1064no—
397C2×#107—531no—
398C2×#107—531no—
399#417—1064no—
400C2×#103—531no—
401C2×#103—531no—
402C2×#103—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#102—531no—
406C2×#102—531no—
407C2×#102—531no—
408C2×C22⋊C8—531no—
409C2×#97—531no—
410C2×C4×C8—531no—
411#391—531no—
412#391—531no—
413#391C2×D5311yescharacteristic
414#389—21no—
415#389C2×D5311yescharacteristic
416#387—21no—
417#386—1061no—
418#386—1061no—
419#385—21no—
420#381—1061no—
421#380—531no—
422C4×C4⋊C4C2×D5311yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4C2×D5311yescharacteristic
425C2×#95—1061no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#336—531no—
431#336—531no—
432C53#2286211yescharacteristic, complemented, Sylow
433C2×#41—534no—
434C2×#41—1062no—
435C2×#41—1062no—
436C2×#41—1062no—
437C2×#41—2121no—
438C2×#41—2121no—
439C22×Q8—531no—
440C22×Q8C22×D5311yescharacteristic
441C22×D4—531no—
442C22×D4—1061no—
443C23×C4—21no—
444C23×C4—1061no—
445C23×C4—1061no—
446C23×C4—1061no—
447C23×C4C22×D5311yescharacteristic
448C2×Q16—534no—
449C2×Q16—2121no—
450C2×Q16—2121no—
451C2×SD16—534no—
452C2×SD16—1062no—
453C2×SD16—1062no—
454C2×M16—1062no—
455C2×M16—1062no—
456C2×M16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22⋊Q8—22no—
462C22⋊Q8C4×D5314yescomplemented
463C4×Q8—22no—
464C4×Q8—41no—
465C4×D4—1062no—
466C4×D4—1062no—
467C4×D4—2121no—
468C4×D4—2121no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4C22⋊D5311yescharacteristic
485C2×C22⋊C4C22⋊D5311yescharacteristic
486C2×C42—21no—
487C2×C42—21no—
488C2×C42C22×D5311yescharacteristic
489C2×C42C22×D5311yescharacteristic
490#107—1062no—
491#107—2121no—
492#103—534no—
493#103—1062no—
494#103—1062no—
495#103—1062no—
496#103—2121no—
497#102—534no—
498#102—534no—
499#102—1062no—
500C22⋊C8—534no—
501#97—1062no—
502C4×C8—2121no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—1061no—
508#95—1061no—
509#95—1061no—
510#95—1061no—
511#95—1061no—
512#95C22⋊D5311yescharacteristic
513#95C22⋊D5311yescharacteristic
514C24—1061no—
515C24C2×C22⋊D5311yescharacteristic
516#41—1068no—
517#41—2124no—
518#41—2124no—
519#41—2124no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—532no—
526C2×Q8—1061no—
527C2×Q8—1061no—
528C2×Q8—1061no—
529C2×Q8—1061no—
530C2×Q8—1061no—
531C2×Q8C2×C4×D5312yes—
532C2×D4—532no—
533C2×D4—532no—
534C2×D4—532no—
535C2×D4—1064no—
536C2×D4—1061no—
537C2×D4—1061no—
538C2×D4—1061no—
539C2×D4—2122no—
540C2×D4—2122no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—81no—
552C22×C4—1061no—
553C22×C4—1064no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—4241no—
557C22×C4—4241no—
558C22×C4—2122no—
559C22×C4—2122no—
560C22×C4—2122no—
561C22×C4—2122no—
562C22×C4—2122no—
563C22×C4—2122no—
564C22×C4C2×C4×D5312yes—
565C22×C4#1171994512yes—
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C2×C22⋊D5311yescharacteristic
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C23×D5311yescharacteristic
572Q16—2124no—
573SD16—1068no—
574M16—2124no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1061no—
579C2×C8—1061no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C4⋊C4—24no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4C2×C4×D5312yes—
600C4⋊C4D4×D5312yes—
601C22⋊C4—24no—
602C22⋊C4—22no—
603C22⋊C4—41no—
604C22⋊C4—4241no—
605C22⋊C4—2122no—
606C22⋊C4—2122no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—42no—
612C42—81no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—1062no—
620C23—1062no—
621C23—1062no—
622C23—2121no—
623C23—2121no—
624C23—2121no—
625C23—2121no—
626C23C4×C22⋊D5312yes—
627C23C22×C22⋊D5311yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—1062no—
633Q8—1062no—
634Q8—2121no—
635Q8—2121no—
636D4—534no—
637D4—1062no—
638D4—1062no—
639D4—1062no—
640D4—2128no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—84no—
671C2×C4—1062no—
672C2×C4—4244no—
673C2×C4—4244no—
674C2×C4—2128no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4C4×C22⋊D5312yes—
684C2×C4#1313324812yes—
685C2×C4C22×C4×D5311yescharacteristic
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4#41×D5311yescharacteristic
688C2×C4C2×#1171994511yescharacteristic
689C2×C4#1313326211yescharacteristic
690C2×C4#1313326311yescharacteristic
691C8—1062no—
692C8—1062no—
693C8—1062no—
694C8—2121no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—1064no—
703C22—2122no—
704C22—2122no—
705C22—2122no—
706C22—2122no—
707C22—2122no—
708C22—2122no—
709C22C2×C4×C22⋊D5311yescharacteristic
710C22D4×C22⋊D5311yescharacteristic
711C22#1681126111yescharacteristic
712C22C2×#1313324811yescharacteristic
713C22#1681142111yescharacteristic
714C22#1681142611yescharacteristic
715C22#1681143811yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—81no—
725C4—4241no—
726C4—4241no—
727C4—2122no—
728C4C4×D4×D5311yescharacteristic
729C4#1681109511yescharacteristic
730C4#1681126911yescharacteristic
731C4#1681130211yescharacteristic
732C2—42no—
733C2—2124no—
734C2#2027769211yescharacteristic
735C2C4×#1313324811yescharacteristic
736C2#2028358811yescharacteristic
737C2#2028632211yescharacteristic
738C2#2028636111yescharacteristic
739C2#2028679011yescharacteristic
740C2#2028680511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2360C2
socleC23×C53C22×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#2360D53
hypocenterC53#22862
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#16810721C2semidirect
5. #20275575C2semidirect
6. #20275404C2semidirect
7. #20275356C2semidirect
8. #20275149C2semidirect
9. #20275056C2semidirect
10. #20275052C2semidirect
11. #20274961C2semidirect
12. #20274903C2semidirect
13. C4×#13133137C2semidirect
14. #20274499C2semidirect
15. C53×#2360C2semidirect
22. #16810783C4semidirect
76. C2×#11719925C2×C4semidirect
79. C2×#11719924C2×C4semidirect
102. #13133140C2×C4semidirect
104. #13133137C2×C4semidirect
106. C22⋊#88322C2×C4semidirect
118. C22⋊Q8×C53C2×C4semidirect
365. #2360D53semidirect
432. C53#22862semidirect
462. C22⋊Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107832
C2×#168107212
C2×#168106222
#202775462
#202755752
#202754042
#202753562
#202751492
#202750562
#202750522
#202749612
#202749032
C4×#131331372
#202744992
C53×#23602
#2286253