Finite Group Databasebeta

← #27472192

Subgroups — #27472192

Order 13568.

956 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810723C211yesmaximal, characteristic, complemented
2C2×#16810695C211yesmaximal, characteristic, complemented
3#20279637C211yesmaximal, characteristic, complemented
4#20276146C211yesmaximal, characteristic, complemented
5#20276141C211yesmaximal, characteristic, complemented
6#20275718C211yesmaximal, characteristic, complemented
7#20275718C211yesmaximal, characteristic, complemented
8#20275154C211yesmaximal, characteristic, complemented
9#20275146C211yesmaximal, characteristic, complemented
10#20275144C211yesmaximal, characteristic, complemented
11#20275136C211yesmaximal, characteristic, complemented
12#20274848C211yesmaximal, characteristic, complemented
13#20274727C211yesmaximal, characteristic, complemented
14#20274715C211yesmaximal, characteristic, complemented
15C53×#2535C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C2×#13133196C2211yescharacteristic
21C2×C4×Dic106C2211yescharacteristic
22#16810723—24no—
23#16810695—24no—
24C2×#13133150C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133140C2211yescharacteristic
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35#16810546—21no—
36#16810546—21no—
37#16810526—21no—
38#16810519—21no—
39#16810493C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C2×#121×C53C2211yescharacteristic
51C2×#121×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C2×C4×D4×C53C2211yescharacteristic
54C53×#397—21no—
55C53×#392—21no—
56C53×#386—21no—
57C53×#386—21no—
58C53×#382C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C22×Dic106C2311yescharacteristic
62C2×#11719923—22no—
63C2×#11719923—22no—
64C2×#11719923—22no—
65C2×#11719917—22no—
66C2×#11719917—41no—
67C2×#11719917—41no—
68C22×#88322—22no—
69C22×#88322—41no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133196—22no—
76#13133196—22no—
77#13133196—41no—
78#13133196—41no—
79C4×Dic106—22no—
80C4×Dic106—22no—
81C2×C4⋊Dic53—21no—
82C2×C4⋊Dic53—21no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×#11719919—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C4×Dic53—21no—
94#13133150—22no—
95C4⋊#88322—22no—
96#13133140—22no—
97#13133140—41no—
98#13133140—41no—
99#13133138—22no—
100#13133138—41no—
101#13133138—41no—
102C22⋊#88322—22no—
103C22⋊#88322—22no—
104#13133128D414yescomplemented
105#13133124—21no—
106#13133124—21no—
107C22×D4×C53—21no—
108C22×D4×C53—21no—
109C22×D4×C53D411yescharacteristic
110C22×D4×C53C2311yescharacteristic
111C23×C4×C53—21no—
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114#121×C53—22no—
115#121×C53—22no—
116#121×C53—41no—
117#121×C53—41no—
118C4×D4×C53—22no—
119C4×D4×C53—22no—
120C4×D4×C53—22no—
121C4×D4×C53—22no—
122C2×C4⋊C4×C53D411yescharacteristic
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C42×C53C2311yescharacteristic
134#95×C53—21no—
135#95×C53—21no—
136#95×C53—21no—
137#95×C53—21no—
138C24×C53—21no—
139C24×C53C2×D411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C2×D4×C53—22no—
142C2×D4×C53—22no—
143C2×D4×C53—21no—
144C2×D4×C53—21no—
145C2×D4×C53—21no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—41no—
149C2×D4×C53—42no—
150C2×D4×C53—42no—
151C2×D4×C53—42no—
152C2×D4×C53—42no—
153C2×D4×C53—81no—
154C2×D4×C53—81no—
155C2×D4×C53#4112yes—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—42no—
172C22×C4×C53—81no—
173C22×C4×C53—81no—
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2411yescharacteristic
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C2×Dic106—21no—
184C2×Dic106—21no—
185C2×Dic106—21no—
186C2×Dic106—21no—
187C2×Dic106—21no—
188C2×Dic106#4112yes—
189C4⋊C4×C53—22no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C22⋊C4×C53—22no—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—42no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53—42no—
201C22⋊C4×C53—81no—
202C22⋊C4×C53—81no—
203C42×C53C2×D412yes—
204C42×C53#4112yes—
205C22⋊Dic53—42no—
206C22⋊Dic53—42no—
207C22⋊Dic53—81no—
208C22⋊Dic53—81no—
209#11719923—28no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—42no—
217C4⋊Dic53—81no—
218#11719919—42no—
219#11719919—42no—
220#11719919—42no—
221C4×Dic53—42no—
222#11719917—44no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—44no—
234C2×#88322C2×D412yes—
235C2×#88322C2×D412yes—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—22no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53#13712yes—
257C23×C53C22×D411yescharacteristic
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—44no—
261D4×C53—41no—
262D4×C53—41no—
263D4×C53—84no—
264D4×C53—84no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
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—41no—
291C2×C4×C53—41no—
292C2×C4×C53—84no—
293C2×C4×C53#12112yes—
294C2×C4×C53#12112yes—
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53C2×#4111yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×Dic53—22no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313Dic106—22no—
314Dic106—22no—
315Dic106—41no—
316Dic106—41no—
317#88322—22no—
318#88322—22no—
319#88322—41no—
320#88322—41no—
321#28155—531nomaximal, Sylow
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—42no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—42no—
334C22×C53—41no—
335C22×C53—42no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53—81no—
342C22×C53—81no—
343C22×C53C2×#12111yescharacteristic
344C22×C53#54611yescharacteristic
345C22×C53#54611yescharacteristic
346C22×C53C2×#13711yescharacteristic
347C22×C53#57511yescharacteristic
348C22×C53#57611yescharacteristic
349C22×C53#57711yescharacteristic
350C4×C53—22no—
351C4×C53—22no—
352C4×C53—41no—
353C4×C53—41no—
354C4×C53—81no—
355C4×C53—81no—
356C4×C53—81no—
357C4×C53#52511yescharacteristic
358C4×C53#53511yescharacteristic
359C4×C53#55311yescharacteristic
360C4×C53#55311yescharacteristic
361Dic53—42no—
362Dic53—81no—
363Dic53—81no—
364Dic53—81no—
365C2×#440—531no—
366C2×#435—531no—
367#2538—531no—
368#2535D5311yescharacteristic
369#2076—531no—
370#2075—531no—
371#2000—531no—
372#2000—531no—
373#1895—531no—
374#1894—531no—
375#1893—531no—
376#1892—531no—
377#1836—531no—
378#1805—531no—
379#1802—531no—
380C2×C53—42no—
381C2×C53—81no—
382C2×C53—82no—
383C2×C53#253511yescharacteristic
384C2×C53#305611yescharacteristic
385C2×C53#306211yescharacteristic
386C2×C53#330911yescharacteristic
387C2×C53#331111yescharacteristic
388C2×C53#331411yescharacteristic
389C2×C53#332011yescharacteristic
390C22×SD16—531no—
391C22×M16—531no—
392C23×C8—531no—
393C2×C22⋊Q8—531no—
394C2×C22⋊Q8—531no—
395C2×#121C2×D5311yescharacteristic
396C2×#121C2×D5311yescharacteristic
397C2×C4×Q8—531no—
398C2×C4×D4C2×D5311yescharacteristic
399C2×C4×D4C2×D5311yescharacteristic
400#440—1064no—
401#435—1064no—
402C2×#107—531no—
403C2×C4⋊C8—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#102—531no—
408C2×#102—531no—
409C2×#102—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×#97—531no—
413#397—21no—
414#396—1061no—
415#396—1061no—
416#392—21no—
417#390—1061no—
418#389—1061no—
419#386—21no—
420#386—21no—
421#384—531no—
422#382C2×D5311yescharacteristic
423#380—531no—
424#380—531no—
425#380C2×D5311yescharacteristic
426#380C2×D5311yescharacteristic
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340—531no—
434#340—531no—
435C53#2815511yescharacteristic, complemented, Sylow
436C22×Q8—531no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C22⋊D5311yescharacteristic
440C22×D4C22×D5311yescharacteristic
441C23×C4—21no—
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C2×SD16—1062no—
445C2×SD16—1062no—
446C2×SD16—1062no—
447C2×M16—1062no—
448C2×M16—2121no—
449C2×M16—2121no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—1062no—
455C22×C8—2121no—
456C22×C8—2121no—
457C22⋊Q8—1062no—
458C22⋊Q8—1062no—
459C22⋊Q8—2121no—
460C22⋊Q8—2121no—
461#121—22no—
462#121—22no—
463#121—41no—
464#121—41no—
465C4×Q8—1062no—
466C4×Q8—1062no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4C22⋊D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4C22⋊D5311yescharacteristic
493C2×C22⋊C4C22⋊D5311yescharacteristic
494C2×C42—1061no—
495C2×C42C22×D5311yescharacteristic
496#107—1062no—
497C4⋊C8—1062no—
498#103—1062no—
499#103—2121no—
500#103—2121no—
501#102—1062no—
502#102—2121no—
503#102—2121no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506#97—534no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—1061no—
512#95—1061no—
513C24—21no—
514C24C2×C22⋊D5311yescharacteristic
515C24C2×C22⋊D5311yescharacteristic
516C2×Q8—532no—
517C2×Q8—1061no—
518C2×Q8—1061no—
519C2×Q8—1061no—
520C2×Q8—1061no—
521C2×Q8—1061no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—41no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4#1171994712yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
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—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C23×D5311yescharacteristic
564SD16—1068no—
565M16—2124no—
566C2×C8—532no—
567C2×C8—532no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C2×C8—1061no—
576C2×C8—1061no—
577C2×C8—1061no—
578C2×C8—2124no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—4241no—
593C4⋊C4—2122no—
594C4⋊C4—2122no—
595C4⋊C4—2122no—
596C4⋊C4—2122no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—4241no—
605C22⋊C4—4241no—
606C22⋊C4—2122no—
607C22⋊C4—2122no—
608C42—2122no—
609C42D4×D5312yes—
610C42#1171994712yes—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23#1313324712yes—
632C23C22×C22⋊D5311yescharacteristic
633Q8—1062no—
634Q8—1062no—
635Q8—2121no—
636Q8—2121no—
637D4—22no—
638D4—22no—
639D4—44no—
640D4—41no—
641D4—41no—
642D4—84no—
643D4—84no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
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—41no—
671C2×C4—84no—
672C2×C4—1062no—
673C2×C4—2121no—
674C2×C4—2121no—
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×C4—2121no—
684C2×C4#1313318912yes—
685C2×C4#1313318912yes—
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4#41×D5311yescharacteristic
688C2×C4C2×#1171994711yescharacteristic
689C2×C4C2×#1171994711yescharacteristic
690C2×C4#1313326211yescharacteristic
691C2×C4#1313326311yescharacteristic
692C8—1062no—
693C8—1062no—
694C8—2121no—
695C8—2121no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#1313318911yescharacteristic
718C22#1681126111yescharacteristic
719C22#1681126711yescharacteristic
720C22C2×#1313324711yescharacteristic
721C22#1681142111yescharacteristic
722C22#1681142611yescharacteristic
723C22#1681143411yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—41no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—4241no—
732C4—4241no—
733C4—4241no—
734C4—2122no—
735C4#1681113311yescharacteristic
736C4#1681118911yescharacteristic
737C4#1681132011yescharacteristic
738C4#1681132511yescharacteristic
739C2—42no—
740C2—81no—
741C2—82no—
742C2#2027961411yescharacteristic
743C2#2028434711yescharacteristic
744C2#2028439111yescharacteristic
745C2#2028671511yescharacteristic
746C2#2028675111yescharacteristic
747C2#2028679611yescharacteristic
748C2#2028688011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#2535C2
socleC23×C53C22×D4
hypercenter#2535D53
hypocenterC53#28155
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#16810723C2semidirect
2. C2×#16810695C2semidirect
3. #20279637C2semidirect
4. #20276146C2semidirect
5. #20276141C2semidirect
6. #20275718C2semidirect
7. #20275718C2semidirect
8. #20275154C2semidirect
9. #20275146C2semidirect
10. #20275144C2semidirect
11. #20275136C2semidirect
12. #20274848C2semidirect
13. #20274727C2semidirect
14. #20274715C2semidirect
104. #13133128D4semidirect
435. C53#28155semidirect

Maximal subgroups

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

subgroupindex
C2×#168107232
C2×#168106952
#202796372
#202761462
#202761412
#202757182
#202751542
#202751462
#202751442
#202751362
#202748482
#202747272
#202747152
C53×#25352
#2815553