Finite Group Databasebeta

← #27422607

Subgroups — #27422607

Order 13568.

1022 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810934C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3#20277590C211yesmaximal, characteristic, complemented
4#20276110C211yesmaximal, characteristic, complemented
5#20276103C211yesmaximal, characteristic, complemented
6#20275951C211yesmaximal, characteristic, complemented
7#20275946C211yesmaximal, characteristic, complemented
8#20275648C211yesmaximal, characteristic, complemented
9#20275643C211yesmaximal, characteristic, complemented
10#20275353C211yesmaximal, characteristic, complemented
11#20275332C211yesmaximal, characteristic, complemented
12#20275154C211yesmaximal, characteristic, complemented
13#20274900C211yesmaximal, characteristic, complemented
14#20274655C211yesmaximal, characteristic, complemented
15C53×#2431C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18#16810934—24no—
19C2×#13133150C2211yescharacteristic
20C2×#13133150C2211yescharacteristic
21C2×C4⋊#88322C2211yescharacteristic
22C2×C4⋊#88322C2211yescharacteristic
23#16810624—24no—
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37#16810521C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810506—21no—
40#16810506—21no—
41#16810483C2211yescharacteristic
42#16810481—21no—
43C4×C4⋊Dic53C2211yescharacteristic
44C4×C4⋊Dic53C2211yescharacteristic
45C22⋊C4×Dic53—21no—
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C22×#41×C53C2211yescharacteristic
51C2×#127×C53C2211yescharacteristic
52C2×#124×C53C2211yescharacteristic
53C2×#121×C53C2211yescharacteristic
54C53×#392—21no—
55C53×#392—21no—
56C53×#391C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#386—21no—
59C53×#386—21no—
60C4×C22⋊C4×C53C2211yescharacteristic
61C23×Dic53—21no—
62C2×#11719917—22no—
63C2×#11719917—41no—
64C2×#11719917—41no—
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—22no—
71C2×C4⋊Dic53D414yescomplemented
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C4×Dic53—21no—
80C2×C4×Dic53—21no—
81#13133150—22no—
82#13133150—22no—
83C4⋊#88322—41no—
84C4⋊#88322—41no—
85#13133141—22no—
86#13133141—22no—
87#13133141—22no—
88#13133141—41no—
89#13133138—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—22no—
93#13133138—22no—
94#13133138—41no—
95#13133138—41no—
96#13133138—41no—
97C22⋊#88322—22no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103C2×#41×C53—22no—
104C2×#41×C53—22no—
105C2×#41×C53—22no—
106C2×#41×C53—22no—
107C2×#41×C53—41no—
108C2×#41×C53—41no—
109C22×Q8×C53C2311yescharacteristic
110C22×D4×C53—21no—
111C22×D4×C53—21no—
112C22×D4×C53—21no—
113C22×D4×C53—21no—
114C22×D4×C53C2311yescharacteristic
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53C2311yescharacteristic
118#127×C53—22no—
119#127×C53—41no—
120#124×C53—22no—
121#124×C53—41no—
122#121×C53—22no—
123#121×C53—22no—
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C42×C53C2311yescharacteristic
133C2×C42×C53C2311yescharacteristic
134#95×C53—21no—
135#95×C53—21no—
136#95×C53D411yescharacteristic
137#95×C53D411yescharacteristic
138C24×C53—21no—
139C24×C53—21no—
140C24×C53C2×D411yescharacteristic
141#41×C53—28no—
142#41×C53—44no—
143#41×C53—44no—
144#41×C53—44no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53#4112yes—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
165C2×D4×C53—42no—
166C2×D4×C53—42no—
167C2×D4×C53—42no—
168C2×D4×C53—42no—
169C2×D4×C53—42no—
170C2×D4×C53—81no—
171C2×D4×C53—81no—
172C2×D4×C53—81no—
173C2×D4×C53—81no—
174C2×D4×C53#4112yes—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—42no—
182C22×C4×C53—42no—
183C22×C4×C53—42no—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D412yes—
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53#4112yes—
191C22×C4×C53C2411yescharacteristic
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—24no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—81no—
198C22×Dic53—81no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C22⋊C4×C53—22no—
202C22⋊C4×C53—41no—
203C22⋊C4×C53—42no—
204C22⋊C4×C53—42no—
205C22⋊C4×C53—42no—
206C22⋊C4×C53—81no—
207C22⋊C4×C53—81no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53—21no—
212C22⋊Dic53—42no—
213C4⋊Dic53—24no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53C2×D412yes—
221C4⋊Dic53C2×D412yes—
222#11719919—81no—
223#11719919—81no—
224C4×Dic53—81no—
225C4×Dic53—81no—
226#11719917—44no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
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—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—22no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53#12112yes—
260C23×C53C22×D411yescharacteristic
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—41no—
264Q8×C53—41no—
265D4×C53—22no—
266D4×C53—22no—
267D4×C53—48no—
268D4×C53—41no—
269D4×C53—41no—
270D4×C53—41no—
271D4×C53—41no—
272D4×C53—41no—
273D4×C53—41no—
274D4×C53—84no—
275D4×C53—84no—
276D4×C53—84no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—48no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53#12112yes—
302C2×C4×C53#13712yes—
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—84no—
322#88322—41no—
323#88322—41no—
324#88322—41no—
325#88322—41no—
326#24490—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53—81no—
341C22×C53—81no—
342C22×C53—81no—
343C22×C53—81no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53—81no—
347C22×C53—81no—
348C22×C53C2×#12111yescharacteristic
349C22×C53#54611yescharacteristic
350C22×C53#54611yescharacteristic
351C22×C53C2×#13711yescharacteristic
352C22×C53#57511yescharacteristic
353C22×C53#57611yescharacteristic
354C22×C53#57611yescharacteristic
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—41no—
358C4×C53—42no—
359C4×C53—41no—
360C4×C53—41no—
361C4×C53—81no—
362C4×C53#52511yescharacteristic
363C4×C53#53511yescharacteristic
364C4×C53#55111yescharacteristic
365C4×C53#55111yescharacteristic
366Dic53—42no—
367Dic53—42no—
368Dic53—81no—
369Dic53—81no—
370C2×#480—531no—
371C2×#417—531no—
372#2431D5311yescharacteristic
373#2345—531no—
374#2068—531no—
375#2067—531no—
376#2042—531no—
377#2041—531no—
378#1983—531no—
379#1982—531no—
380#1928—531no—
381#1925—531no—
382#1895—531no—
383#1851—531no—
384#1788—531no—
385C2×C53—42no—
386C2×C53—82no—
387C2×C53—161no—
388C2×C53#241111yescharacteristic
389C2×C53#303711yescharacteristic
390C2×C53#304111yescharacteristic
391C2×C53#330911yescharacteristic
392C2×C53#331411yescharacteristic
393C2×C53#332211yescharacteristic
394C2×C53#333311yescharacteristic
395C22×#41C2×D5311yescharacteristic
396C22×M16—531no—
397C2×#127C2×D5311yescharacteristic
398C2×#124C2×D5311yescharacteristic
399C2×#121C2×D5311yescharacteristic
400C22×C4⋊C4—531no—
401#480—1064no—
402C2×#107—531no—
403C2×#107—531no—
404C2×C4⋊C8—531no—
405C2×C4⋊C8—531no—
406#417—1064no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×#102—531no—
416C2×#102—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×C22⋊C8—531no—
420#392—21no—
421#392—21no—
422#391C2×D5311yescharacteristic
423#390C2×D5311yescharacteristic
424#389—531no—
425#389—531no—
426#387—1061no—
427#387—1061no—
428#386—21no—
429#386—21no—
430#380—531no—
431#380—1061no—
432C4×C4⋊C4—531no—
433C4×C4⋊C4—531no—
434C4×C22⋊C4—1061no—
435C4×C22⋊C4C2×D5311yescharacteristic
436#340—531no—
437#340—531no—
438#336—531no—
439#336—531no—
440C53#2449011yescharacteristic, complemented, Sylow
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—41no—
446C2×#41—41no—
447C22×Q8C22×D5311yescharacteristic
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C22×D5311yescharacteristic
453C22×D4C22×D5311yescharacteristic
454C23×C4—21no—
455C23×C4—1061no—
456C23×C4C22×D5311yescharacteristic
457C2×M16—1062no—
458C2×M16—2121no—
459C2×M16—2121no—
460C22×C8—531no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464#127—22no—
465#127—41no—
466#124—22no—
467#124—41no—
468#121—22no—
469#121—22no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4C22⋊D5311yescharacteristic
487C2×C22⋊C4C22⋊D5311yescharacteristic
488C2×C42—1061no—
489C2×C42—1061no—
490C2×C42C22×D5311yescharacteristic
491C2×C42C22×D5311yescharacteristic
492#107—1062no—
493#107—1062no—
494C4⋊C8—2121no—
495C4⋊C8—2121no—
496#103—1062no—
497#103—1062no—
498#103—1062no—
499#103—2121no—
500#102—1062no—
501#102—1062no—
502#102—1062no—
503#102—1062no—
504#102—1062no—
505#102—2121no—
506#102—2121no—
507#102—2121no—
508C22⋊C8—1062no—
509#95—21no—
510#95—21no—
511#95—1061no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95C22⋊D5311yescharacteristic
517#95C22⋊D5311yescharacteristic
518C24—21no—
519C24—21no—
520C24C2×C22⋊D5311yescharacteristic
521#41—28no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8#1171994712yes—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4#1171994712yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—1064no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—4241no—
570C22×C4—4241no—
571C22×C4D4×D5312yes—
572C22×C4#1171994712yes—
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C23×D5311yescharacteristic
579M16—2124no—
580C2×C8—1061no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—1061no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—532no—
595C4⋊C4—532no—
596C4⋊C4—1064no—
597C4⋊C4—1061no—
598C4⋊C4—1061no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—4241no—
604C4⋊C4—4241no—
605C22⋊C4—22no—
606C22⋊C4—41no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—2122no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—4241no—
618C42—4241no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23#1313318812yes—
640C23C22×C22⋊D5311yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655D4—84no—
656D4—84no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—4244no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4#1313318812yes—
695C2×C4#1313324712yes—
696C2×C4C2×D4×D5311yescharacteristic
697C2×C4C2×#1171994711yescharacteristic
698C2×C4C2×#1171994711yescharacteristic
699C2×C4C2×#1171994711yescharacteristic
700C2×C4#1313326211yescharacteristic
701C2×C4#1313326211yescharacteristic
702C8—2121no—
703C8—2121no—
704C8—2121no—
705C8—2121no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22C2×#1313318811yescharacteristic
728C22#1681126711yescharacteristic
729C22#1681126711yescharacteristic
730C22C2×#1313324711yescharacteristic
731C22#1681142111yescharacteristic
732C22#1681142611yescharacteristic
733C22#1681142611yescharacteristic
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—81no—
741C4—4241no—
742C4—4241no—
743C4—2122no—
744C4—2122no—
745C4#1681112911yescharacteristic
746C4#1681118811yescharacteristic
747C4#1681130411yescharacteristic
748C4#1681130411yescharacteristic
749C2—42no—
750C2—82no—
751C2—161no—
752C2#2027809611yescharacteristic
753C2#2028418311yescharacteristic
754C2#2028421411yescharacteristic
755C2#2028672111yescharacteristic
756C2#2028679611yescharacteristic
757C2#2028691611yescharacteristic
758C2#2028705311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#2431C2
socleC23×C53C22×D4
hypercenter#2431D53
hypocenterC53#24490
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2431

Complements

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

NH ≅ G/Ntype
1. C2×#16810934C2semidirect
2. C2×#16810624C2semidirect
3. #20277590C2semidirect
4. #20276110C2semidirect
5. #20276103C2semidirect
6. #20275951C2semidirect
7. #20275946C2semidirect
8. #20275648C2semidirect
9. #20275643C2semidirect
10. #20275353C2semidirect
11. #20275332C2semidirect
12. #20275154C2semidirect
13. #20274900C2semidirect
14. #20274655C2semidirect
71. C2×C4⋊Dic53D4semidirect
440. C53#24490semidirect

Maximal subgroups

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

subgroupindex
C2×#168109342
C2×#168106242
#202775902
#202761102
#202761032
#202759512
#202759462
#202756482
#202756432
#202753532
#202753322
#202751542
#202749002
#202746552
C53×#24312
#2449053