Finite Group Databasebeta

← #28323674

Subgroups — #28323674

Order 13568.

918 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20290838C211yesmaximal, characteristic, complemented
2#20290837C211yesmaximal, characteristic, complemented
3#20290786C211yesmaximal, characteristic, complemented
4#20290784C211yesmaximal, characteristic, complemented
5#20290770C211yesmaximal, characteristic, complemented
6#20290769C211yesmaximal, characteristic, complemented
7#20290691C211yesmaximal, characteristic, complemented
8#20290690C211yesmaximal, characteristic, complemented
9#20290690C211yesmaximal, characteristic, complemented
10#20290689C211yesmaximal, characteristic, complemented
11#20290607C211yesmaximal, characteristic, complemented
12#20290449C211yesmaximal, characteristic, complemented
13C22⋊C4×#88324C211yesmaximal, characteristic, complemented
14C4×#13133274C211yesmaximal, characteristic, complemented
15#20277227C211yesmaximal, characteristic
16C22×D53⋊C8C2211yescharacteristic
17C23×#88324C2211yescharacteristic
18C2×#13133284C2211yescharacteristic
19C2×C4⋊#88324C2211yescharacteristic
20C2×#13133274C2211yescharacteristic
21C2×#13133274C2211yescharacteristic
22C2×#13133274C2211yescharacteristic
23C2×#13133274C2211yescharacteristic
24C2×#13133274C2211yescharacteristic
25C2×#13133274C2211yescharacteristic
26C2×#13133274C2211yescharacteristic
27C2×C22⋊#88324C2211yescharacteristic
28C2×C22⋊#88324C2211yescharacteristic
29C2×C22⋊#88324C2211yescharacteristic
30C2×C4×#88324C2211yescharacteristic
31C2×C4×#88324C2211yescharacteristic
32C2×C4×#88324C2211yescharacteristic
33C2×C4×#88324C2211yescharacteristic
34#16811489C2211yescharacteristic
35#16811489C2211yescharacteristic
36#16811489C2211yescharacteristic
37#16811489C2211yescharacteristic
38#16811489C2211yescharacteristic
39#16811489C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44C2×#13133190C411yescharacteristic
45C2×#13133179C2211yescharacteristic
46C2×#13133177C2211yescharacteristic
47C2×#13133177C2211yescharacteristic
48C2×C42×D53C2211yescharacteristic
49#16810523C411yescharacteristic
50#16810518C411yescharacteristic
51#16810514C411yescharacteristic
52#16810501C411yescharacteristic
53#16810499C411yescharacteristic
54#16810482C411yescharacteristic
55#16810474C2211yescharacteristic
56C22⋊C4×Dic53C2211yescharacteristic
57#16810470C2211yescharacteristic
58C53×#388C411yescharacteristic
59C2×D53⋊C8—22no—
60C2×D53⋊C8—41no—
61C2×D53⋊C8—41no—
62C22×#88324—22no—
63C22×#88324—41no—
64C22×#88324—41no—
65C22×#88324C2311yescharacteristic
66C22×#88324C2311yescharacteristic
67C22×#88324C2311yescharacteristic
68C22×#88324C2311yescharacteristic
69C22×#88324C2311yescharacteristic
70C22×#88324C2311yescharacteristic
71C22×#88324C2311yescharacteristic
72C22×#88324C2311yescharacteristic
73#13133284—41no—
74C4⋊#88324—41no—
75#13133274—22no—
76#13133274—22no—
77#13133274—22no—
78#13133274—41no—
79#13133274—41no—
80#13133274—41no—
81#13133274—41no—
82C22⋊#88324—22no—
83C22⋊#88324—41no—
84C22⋊#88324—41no—
85C4×#88324—41no—
86C4×#88324—41no—
87C4×#88324—41no—
88C4×#88324—41no—
89C22×D212C2×C411yescharacteristic
90C22×C22⋊D53C2×C411yescharacteristic
91C22×C22⋊D53C2×C411yescharacteristic
92C23×Dic53C2311yescharacteristic
93C22×C4×D53C2×C411yescharacteristic
94C22×C4×D53C2×C411yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C22×C4×D53C2311yescharacteristic
97#13133190C818yescomplemented
98#13133179—41no—
99#13133179—41no—
100#13133177—41no—
101#13133177—41no—
102#13133177—41no—
103#13133177—41no—
104C2×#11719919C2×C411yescharacteristic
105C2×#11719919C2×C411yescharacteristic
106C2×#11719919C2×C411yescharacteristic
107C2×#11719919C2×C411yescharacteristic
108C2×C22⋊Dic53C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×#11719921C2×C411yescharacteristic
111C2×#11719921C2×C411yescharacteristic
112C2×#11719921C2×C411yescharacteristic
113C2×#11719921C2×C411yescharacteristic
114C2×#11719921C2×C411yescharacteristic
115C2×C4×Dic53C2×C411yescharacteristic
116C2×C4×Dic53C2311yescharacteristic
117C2×C4×Dic53C2311yescharacteristic
118C2×C4×Dic53C2311yescharacteristic
119C2×C4×Dic53C2311yescharacteristic
120C42×D53—41no—
121C42×D53—41no—
122#13133124C2×C411yescharacteristic
123#13133124C2×C411yescharacteristic
124#13133124C2×C411yescharacteristic
125#13133124C2×C411yescharacteristic
126C2×C4⋊C4×C53C2×C411yescharacteristic
127C2×C22⋊C4×C53C2×C411yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C42×C53C2×C411yescharacteristic
131#95×C53C2×C411yescharacteristic
132#95×C53C2×C411yescharacteristic
133C24×C53C22×C411yescharacteristic
134C23×D53C22×C411yescharacteristic
135C23×D53C22×C411yescharacteristic
136C22×C4×C53C22×C411yescharacteristic
137C22×C4×C53C22×C411yescharacteristic
138C22×C4×C53C22×C411yescharacteristic
139C22×C4×C53C22×C411yescharacteristic
140C22×C4×C53C22×C411yescharacteristic
141C22×C4×C53C22×C411yescharacteristic
142C2×C22⋊D53—41no—
143C2×C22⋊D53—41no—
144C2×C22⋊D53—41no—
145C2×C22⋊D53—41no—
146C2×C22⋊D53C2×C814yes—
147C2×C22⋊D53C2×C814yescomplemented
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53C22×C411yescharacteristic
155C22×Dic53C22×C411yescharacteristic
156C22×Dic53C22×C411yescharacteristic
157C22×Dic53C22×C411yescharacteristic
158C22×Dic53C22×C411yescharacteristic
159C22×Dic53C2411yescharacteristic
160C2×D212—41no—
161C2×D212—41no—
162C2×D212C2×C814yescomplemented
163C2×C4×D53—22no—
164C2×C4×D53—21no—
165C2×C4×D53—21no—
166C2×C4×D53—21no—
167C2×C4×D53—21no—
168C2×C4×D53—21no—
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—41no—
177C2×C4×D53—41no—
178C2×C4×D53—41no—
179C2×C4×D53—41no—
180C2×C4×D53C2×C814yescomplemented
181C2×#88324—21no—
182C2×#88324—21no—
183C2×#88324—21no—
184C2×#88324—21no—
185C2×#88324—21no—
186C2×#88324—21no—
187C2×#88324—21no—
188C2×#88324—21no—
189C2×#88324—21no—
190C2×#88324—21no—
191C2×#88324—21no—
192C2×#88324—21no—
193C2×#88324—21no—
194C2×#88324—21no—
195C2×#88324—21no—
196C2×#88324—21no—
197C2×#88324—21no—
198C2×#88324—21no—
199C2×#88324—21no—
200C2×#88324—21no—
201C2×#88324—21no—
202C2×#88324—21no—
203C2×#88324—44no—
204C2×#88324#4112yes—
205C2×#88324#4112yes—
206D53⋊C8—44no—
207C4⋊C4×C53—41no—
208C22⋊C4×C53—41no—
209C22⋊C4×C53—41no—
210C22⋊C4×C53C2×C814yescomplemented
211C42×C53—41no—
212C22⋊Dic53—22no—
213#11719921—22no—
214#11719921—41no—
215#11719921—41no—
216#11719921—41no—
217#11719921—41no—
218#11719921C2×C814yescomplemented
219#11719919—41no—
220#11719919—41no—
221#11719919—41no—
222#11719919C2×C814yescomplemented
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C4×Dic53—21no—
228C4×Dic53—21no—
229C4×Dic53—21no—
230C4×Dic53—21no—
231C4×Dic53—41no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53C22×C812yes—
239C23×C53C23×C411yescharacteristic
240C22×D53—21no—
241C22×D53—21no—
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53C22×C812yes—
253C22×D53C22×C812yes—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53C22×C812yes—
271C2×C4×C53C22×C812yes—
272C22⋊D53—44no—
273C22⋊D53—44no—
274C2×Dic53—21no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53—21no—
278C2×Dic53—21no—
279C2×Dic53—21no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53C22×C812yes—
291C2×Dic53C22×C812yes—
292C2×Dic53#13112yes—
293C2×Dic53C2×#4111yescharacteristic
294C2×Dic53C2×#4111yescharacteristic
295C2×Dic53H(5,𝔽2)11yescharacteristic
296C2×Dic53H(5,𝔽2)11yescharacteristic
297C2×Dic53H(5,𝔽2)11yescharacteristic
298C2×Dic53H(5,𝔽2)11yescharacteristic
299D212—44no—
300C4×D53—44no—
301C4×D53—44no—
302C4×D53—41no—
303C4×D53—41no—
304C4×D53—41no—
305C4×D53—41no—
306C4×D53—41no—
307C4×D53—41no—
308C4×D53—41no—
309C4×D53—41no—
310#88324—22no—
311#88324—22no—
312#88324—41no—
313#88324—41no—
314#88324—41no—
315#88324—41no—
316#88324—41no—
317#88324—41no—
318#22329—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53—41no—
326C22×C53C4×#4111yescharacteristic
327C22×C53#51811yescharacteristic
328C22×C53#51811yescharacteristic
329C22×C53C23×C811yescharacteristic
330C22×C53C2×#13111yescharacteristic
331C22×C53#56811yescharacteristic
332C22×C53#56811yescharacteristic
333C2×D53—22no—
334C2×D53—22no—
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—22no—
339C2×D53—41no—
340C2×D53—41no—
341C2×D53—41no—
342C2×D53—41no—
343C2×D53—41no—
344C2×D53—41no—
345C2×D53—41no—
346C2×D53—41no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—41no—
350C4×C53—41no—
351C4×C53—41no—
352C4×C53—41no—
353Dic53—22no—
354Dic53—22no—
355Dic53—22no—
356Dic53—41no—
357Dic53—41no—
358Dic53#53811yescharacteristic
359Dic53#53811yescharacteristic
360Dic53#54011yescharacteristic
361Dic53#54011yescharacteristic
362C4×#121—531no—
363#1954—531no—
364#1954—531no—
365#1923—531no—
366#1923—531no—
367#1916—531no—
368#1916—531no—
369#1869—531no—
370#1869—531no—
371#1869—531no—
372#1869—531no—
373#1817—531no—
374C8×C22⋊C4—531no—
375C8×C22⋊C4—531no—
376C4×C22⋊C8—531no—
377C2×C53—42no—
378C2×C53#233311yescharacteristic
379C2×C53C8×#4111yescharacteristic
380C2×C53#296711yescharacteristic
381C2×C53#297211yescharacteristic
382C2×C53#297211yescharacteristic
383C2×C53#297611yescharacteristic
384C2×C53#298111yescharacteristic
385D53—42no—
386D53—42no—
387C23×C8—531no—
388C23×C8—531no—
389C2×#121—531no—
390C2×C4×D4—531no—
391C2×C4×D4—531no—
392C2×C4×D4—531no—
393C22×C42—531no—
394C2×C4⋊C8—531no—
395C2×C4⋊C8—531no—
396C2×C22⋊C8—531no—
397C2×C22⋊C8—531no—
398C2×C22⋊C8—531no—
399C2×C22⋊C8—531no—
400C2×C22⋊C8—531no—
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8—531no—
406C2×C4×C8—531no—
407C2×C4×C8—531no—
408C2×C4×C8—531no—
409C2×C4×C8—531no—
410#390—531no—
411#389—531no—
412#388—531no—
413#388#615711yescharacteristic
414#386—531no—
415#386—531no—
416#380—531no—
417C4×C4⋊C4—531no—
418C4×C22⋊C4—531no—
419C4×C22⋊C4—531no—
420#336—531no—
421#336—531no—
422#336—531no—
423#336—531no—
424#336—531no—
425#336—531no—
426#336—531no—
427#336—531no—
428#336—531no—
429#336—531no—
430C53#2232911yescharacteristic, complemented, Sylow
431C22×D4—531no—
432C22×D4—531no—
433C22×D4—531no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—531no—
438C23×C4—531no—
439C22×C8—531no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—531no—
446C22×C8—531no—
447C22×C8—1062no—
448C22×C8—1062no—
449C22×C8—2121no—
450C22×C8—2121no—
451C22×C8—2121no—
452C22×C8—2121no—
453#121—538no—
454C4×D4—2121no—
455C4×D4—2121no—
456C4×D4—2121no—
457C4×D4—2121no—
458C4×D4—2121no—
459C4×D4—2121no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4C2×#615711yescharacteristic
465C2×C22⋊C4—531no—
466C2×C22⋊C4—531no—
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—531no—
470C2×C22⋊C4—531no—
471C2×C22⋊C4—531no—
472C2×C22⋊C4C2×#615711yescharacteristic
473C2×C22⋊C4C2×#615711yescharacteristic
474C2×C22⋊C4C2×#615711yescharacteristic
475C2×C42—531no—
476C2×C42—531no—
477C2×C42—531no—
478C2×C42—531no—
479C2×C42—531no—
480C2×C42—2121no—
481C2×C42—2121no—
482C2×C42C2×#615711yescharacteristic
483C4⋊C8—2121no—
484C4⋊C8—2121no—
485C22⋊C8—1062no—
486C22⋊C8—1062no—
487C22⋊C8—1062no—
488C22⋊C8—1062no—
489C22⋊C8—2121no—
490C22⋊C8—2121no—
491C22⋊C8—2121no—
492C22⋊C8—2121no—
493C22⋊C8—2121no—
494C22⋊C8—2121no—
495C4×C8—2121no—
496C4×C8—2121no—
497C4×C8—2121no—
498C4×C8—2121no—
499#95—531no—
500#95—531no—
501#95—531no—
502#95—531no—
503#95C2×#615711yescharacteristic
504#95C2×#615711yescharacteristic
505C24—531no—
506C24—531no—
507C24C22×#615711yescharacteristic
508C2×D4—534no—
509C2×D4—534no—
510C2×D4—534no—
511C2×D4—2121no—
512C2×D4—2121no—
513C2×D4—2121no—
514C2×D4—2121no—
515C2×D4—2121no—
516C2×D4—2121no—
517C22×C4—531no—
518C22×C4—531no—
519C22×C4—531no—
520C22×C4—531no—
521C22×C4—534no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1062no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—2121no—
544C22×C4—2121no—
545C22×C4—2121no—
546C22×C4—2121no—
547C22×C4C22×#615711yescharacteristic
548C22×C4C22×#615711yescharacteristic
549C22×C4C22×#615711yescharacteristic
550C22×C4C22×#615711yescharacteristic
551C22×C4C22×#615711yescharacteristic
552C22×C4C22×#615711yescharacteristic
553C2×C8—532no—
554C2×C8—532no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—1061no—
562C2×C8—1061no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
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—2124no—
578C2×C8—2124no—
579C4⋊C4—41no—
580C4⋊C4—534no—
581C4⋊C4—2121no—
582C4⋊C4—2121no—
583C4⋊C4—2121no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—534no—
587C22⋊C4—1062no—
588C22⋊C4—1062no—
589C22⋊C4—2121no—
590C22⋊C4—2121no—
591C22⋊C4—2121no—
592C22⋊C4—2121no—
593C22⋊C4D53⋊C814yescomplemented
594C42—41no—
595C42—1061no—
596C42—1061no—
597C42—1061no—
598C42—1061no—
599C42—1061no—
600C42—1061no—
601C42—1061no—
602C42—1061no—
603C42—2121no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—532no—
611C23—532no—
612C23—1061no—
613C23—1061no—
614C23—1061no—
615C23—1061no—
616C23—1061no—
617C23—1061no—
618C23—1061no—
619C23—1061no—
620C23—1061no—
621C23—1061no—
622C23—1061no—
623C23—1061no—
624C23C2×D53⋊C812yes—
625C23C23×#615711yescharacteristic
626D4—2124no—
627D4—2124no—
628D4—2124no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—531no—
646C2×C4—531no—
647C2×C4—531no—
648C2×C4—531no—
649C2×C4—531no—
650C2×C4—531no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—532no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
658C2×C4—1061no—
659C2×C4—1061no—
660C2×C4—1061no—
661C2×C4—1061no—
662C2×C4—1061no—
663C2×C4—1061no—
664C2×C4—1061no—
665C2×C4—1061no—
666C2×C4—2124no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2124no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4C2×D53⋊C812yes—
681C2×C4C2×D53⋊C812yes—
682C8—1062no—
683C8—1062no—
684C8—2121no—
685C8—2121no—
686C8—2121no—
687C8—2121no—
688C8—2121no—
689C8—2121no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—1062no—
698C22—1062no—
699C22—1062no—
700C22—1062no—
701C22—1062no—
702C22—1062no—
703C22—2121no—
704C22—2121no—
705C22—2121no—
706C22—2121no—
707C22—2121no—
708C22—2121no—
709C22—2121no—
710C22—2121no—
711C22#41×#615711yescharacteristic
712C22#1681169011yescharacteristic
713C22#1681169011yescharacteristic
714C22C22×D53⋊C811yescharacteristic
715C22D53⋊#13111yescharacteristic
716C22#1681170211yescharacteristic
717C22#1681170211yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—531no—
725C4—531no—
726C4—531no—
727C4—531no—
728C4—1062no—
729C4—1062no—
730C4—1062no—
731C4—2121no—
732C4—2121no—
733C2—42no—
734C2—2122no—
735C2—2122no—
736C2#2029121211yescharacteristic
737C2#2029151911yescharacteristic
738C2#2029153811yescharacteristic
739C2#2029156311yescharacteristic
740C2#2029156311yescharacteristic
741C2#2029158311yescharacteristic
742C2#2029160611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C23×C8
FittingC53×#388C4
socleC23×C53C23×C4
prime radicalC2×#13133190C4
cosocleC22×Dic53C24
hypercenter#388#6157
hypocenterC53#22329
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #20290838C2semidirect
2. #20290837C2semidirect
3. #20290786C2semidirect
4. #20290784C2semidirect
5. #20290770C2semidirect
6. #20290769C2semidirect
7. #20290691C2semidirect
8. #20290690C2semidirect
9. #20290690C2semidirect
10. #20290689C2semidirect
11. #20290607C2semidirect
12. #20290449C2semidirect
13. C22⋊C4×#88324C2semidirect
14. C4×#13133274C2semidirect
97. #13133190C8semidirect
147. C2×C22⋊D53C2×C8semidirect
162. C2×D212C2×C8semidirect
180. C2×C4×D53C2×C8semidirect
210. C22⋊C4×C53C2×C8semidirect
218. #11719921C2×C8semidirect
222. #11719919C2×C8semidirect
430. C53#22329semidirect
593. C22⋊C4D53⋊C8semidirect

Maximal subgroups

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

subgroupindex
#202908382
#202908372
#202907862
#202907842
#202907702
#202907692
#202906912
#202906902
#202906892
#202906072
#202904492
C22⋊C4×#883242
C4×#131332742
#202772272
#2232953