Finite Group Databasebeta

← #28323103

Subgroups — #28323103

Order 13568.

1046 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×#16811651C211yesmaximal, characteristic, complemented
2C2×#16811650C211yesmaximal, characteristic, complemented
3#20290787C211yesmaximal, characteristic, complemented
4#20290784C211yesmaximal, characteristic, complemented
5#20290770C211yesmaximal, characteristic, complemented
6#20290769C211yesmaximal, characteristic, complemented
7#20290691C211yesmaximal, characteristic, complemented
8#20290690C211yesmaximal, characteristic, complemented
9#20290689C211yesmaximal, characteristic, complemented
10#20290689C211yesmaximal, characteristic, complemented
11#20290660C211yesmaximal, characteristic, complemented
12#20290658C211yesmaximal, characteristic, complemented
13#20290570C211yesmaximal, characteristic, complemented
14#20290376C211yesmaximal, characteristic, complemented
15#20277227C211yesmaximal, characteristic
16C22×D53⋊C8C2211yescharacteristic
17C22×D53⋊C8C2211yescharacteristic
18C22×D53⋊C8C2211yescharacteristic
19C23×#88324C2211yescharacteristic
20#16811651—24no—
21#16811650—24no—
22C2×#13133284C2211yescharacteristic
23C2×C4⋊#88324C2211yescharacteristic
24C2×C4⋊#88324C2211yescharacteristic
25C2×C4⋊#88324C2211yescharacteristic
26C2×#13133274C2211yescharacteristic
27C2×#13133274C2211yescharacteristic
28C2×#13133274C2211yescharacteristic
29C2×#13133274C2211yescharacteristic
30C2×#13133274C2211yescharacteristic
31C2×C22⋊#88324C2211yescharacteristic
32C2×C22⋊#88324C2211yescharacteristic
33C2×C22⋊#88324C2211yescharacteristic
34C2×C4×#88324C2211yescharacteristic
35C2×C4×#88324C2211yescharacteristic
36#16811489C2211yescharacteristic
37#16811489C2211yescharacteristic
38#16811489C2211yescharacteristic
39#16811489C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44#16811489C2211yescharacteristic
45#16811489C2211yescharacteristic
46C2×#13133190C411yescharacteristic
47C2×#13133179C2211yescharacteristic
48C2×#13133177C2211yescharacteristic
49C2×#13133177C2211yescharacteristic
50C2×C42×D53C2211yescharacteristic
51#16810523C411yescharacteristic
52#16810518C411yescharacteristic
53#16810514C411yescharacteristic
54#16810501C411yescharacteristic
55#16810499C411yescharacteristic
56#16810482C411yescharacteristic
57#16810474C2211yescharacteristic
58C22⋊C4×Dic53C2211yescharacteristic
59#16810470C2211yescharacteristic
60C53×#388C411yescharacteristic
61C2×D53⋊C8—22no—
62C2×D53⋊C8—22no—
63C2×D53⋊C8—41no—
64C2×D53⋊C8—41no—
65C2×D53⋊C8—41no—
66C2×D53⋊C8—41no—
67C2×D53⋊C8—41no—
68C2×D53⋊C8—41no—
69C2×D53⋊C8D414yescomplemented
70C22×#88324—22no—
71C22×#88324—41no—
72C22×#88324—41no—
73C22×#88324C2311yescharacteristic
74C22×#88324C2311yescharacteristic
75C22×#88324C2311yescharacteristic
76C22×#88324C2311yescharacteristic
77C22×#88324C2311yescharacteristic
78C22×#88324C2311yescharacteristic
79C22×#88324C2311yescharacteristic
80C22×#88324C2311yescharacteristic
81#13133284—22no—
82C4⋊#88324—22no—
83C4⋊#88324—41no—
84C4⋊#88324—41no—
85#13133274—22no—
86#13133274—22no—
87#13133274—22no—
88#13133274—41no—
89#13133274—41no—
90C22⋊#88324—22no—
91C22⋊#88324—41no—
92C22⋊#88324—41no—
93C4×#88324—22no—
94C4×#88324—22no—
95C22×D212C2×C411yescharacteristic
96C22×C22⋊D53C2×C411yescharacteristic
97C22×C22⋊D53C2×C411yescharacteristic
98C23×Dic53C2311yescharacteristic
99C22×C4×D53C2×C411yescharacteristic
100C22×C4×D53C2×C411yescharacteristic
101C22×C4×D53C2311yescharacteristic
102C22×C4×D53C2311yescharacteristic
103#13133190C818yescomplemented
104#13133179—22no—
105#13133179—22no—
106#13133177—22no—
107#13133177—22no—
108#13133177—41no—
109#13133177—41no—
110C2×#11719919C2×C411yescharacteristic
111C2×#11719919C2×C411yescharacteristic
112C2×#11719919C2×C411yescharacteristic
113C2×#11719919C2×C411yescharacteristic
114C2×C22⋊Dic53C2×C411yescharacteristic
115C2×#11719921C2×C411yescharacteristic
116C2×#11719921C2×C411yescharacteristic
117C2×#11719921C2×C411yescharacteristic
118C2×#11719921C2×C411yescharacteristic
119C2×#11719921C2×C411yescharacteristic
120C2×#11719921C2×C411yescharacteristic
121C2×C4×Dic53C2×C411yescharacteristic
122C2×C4×Dic53C2311yescharacteristic
123C2×C4×Dic53C2311yescharacteristic
124C2×C4×Dic53C2311yescharacteristic
125C2×C4×Dic53C2311yescharacteristic
126C42×D53—41no—
127C42×D53—41no—
128#13133124C2×C411yescharacteristic
129#13133124C2×C411yescharacteristic
130#13133124C2×C411yescharacteristic
131#13133124C2×C411yescharacteristic
132C2×C4⋊C4×C53C2×C411yescharacteristic
133C2×C22⋊C4×C53C2×C411yescharacteristic
134C2×C22⋊C4×C53C2×C411yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C42×C53C2×C411yescharacteristic
137#95×C53C2×C411yescharacteristic
138#95×C53C2×C411yescharacteristic
139C24×C53C22×C411yescharacteristic
140C23×D53C22×C411yescharacteristic
141C23×D53C22×C411yescharacteristic
142C22×C4×C53C22×C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C22×C4×C53C22×C411yescharacteristic
145C22×C4×C53C22×C411yescharacteristic
146C22×C4×C53C22×C411yescharacteristic
147C22×C4×C53C22×C411yescharacteristic
148C2×C22⋊D53—22no—
149C2×C22⋊D53—22no—
150C2×C22⋊D53—41no—
151C2×C22⋊D53—41no—
152C2×C22⋊D53C2×C814yescomplemented
153C2×C22⋊D53C2×C814yescomplemented
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53C22×C411yescharacteristic
161C22×Dic53C22×C411yescharacteristic
162C22×Dic53C22×C411yescharacteristic
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165C22×Dic53C2411yescharacteristic
166C2×D212—22no—
167C2×D212—22no—
168C2×D212C2×C814yescomplemented
169C2×C4×D53—21no—
170C2×C4×D53—21no—
171C2×C4×D53—21no—
172C2×C4×D53—21no—
173C2×C4×D53—22no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—41no—
181C2×C4×D53—41no—
182C2×C4×D53—41no—
183C2×C4×D53—41no—
184C2×C4×D53C2×C814yescomplemented
185C2×C4×D53C2×D412yes—
186C2×C4×D53#4112yes—
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—21no—
204C2×#88324—21no—
205C2×#88324—21no—
206C2×#88324—21no—
207C2×#88324—21no—
208C2×#88324—21no—
209C2×#88324—44no—
210C2×#88324C2×D412yes—
211C2×#88324C2×D412yes—
212D53⋊C8—44no—
213D53⋊C8—44no—
214D53⋊C8—44no—
215C4⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—41no—
218C22⋊C4×C53C2×C814yescomplemented
219C42×C53—41no—
220C22⋊Dic53—41no—
221#11719921—22no—
222#11719921—22no—
223#11719921—22no—
224#11719921—41no—
225#11719921—41no—
226#11719921C2×C814yescomplemented
227#11719919—22no—
228#11719919—41no—
229#11719919—41no—
230#11719919C2×C814yescomplemented
231C4×Dic53—21no—
232C4×Dic53—21no—
233C4×Dic53—21no—
234C4×Dic53—21no—
235C4×Dic53—21no—
236C4×Dic53—21no—
237C4×Dic53—21no—
238C4×Dic53—21no—
239C4×Dic53—41no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53C22×C812yes—
247C23×C53C23×C411yescharacteristic
248C22×D53—21no—
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53C4×D412yes—
259C22×D53C22×C812yes—
260C22×D53C22×C812yes—
261C22×D53#13112yes—
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×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53C4×D412yes—
278C2×C4×C53C22×C812yes—
279C2×C4×C53C22×C812yes—
280C22⋊D53—28no—
281C22⋊D53—44no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53C22×C812yes—
300C2×Dic53C22×C812yes—
301C2×Dic53C22×D411yescharacteristic
302C2×Dic53C2×#4111yescharacteristic
303C2×Dic53H(5,𝔽2)11yescharacteristic
304C2×Dic53H(5,𝔽2)11yescharacteristic
305C2×Dic53H(5,𝔽2)11yescharacteristic
306C2×Dic532−1+411yescharacteristic
307D212—28no—
308C4×D53—22no—
309C4×D53—22no—
310C4×D53—22no—
311C4×D53—22no—
312C4×D53—44no—
313C4×D53—44no—
314C4×D53—41no—
315C4×D53—41no—
316C4×D53—41no—
317C4×D53—41no—
318#88324—22no—
319#88324—22no—
320#88324—41no—
321#88324—41no—
322#88324—41no—
323#88324—41no—
324#88324—41no—
325#88324—41no—
326#22168—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53C2×C4×D411yescharacteristic
335C22×C53#51811yescharacteristic
336C22×C53#52011yescharacteristic
337C22×C53C23×C811yescharacteristic
338C22×C53C2×#13111yescharacteristic
339C22×C53#56811yescharacteristic
340C22×C53#56811yescharacteristic
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C2×D53C8×D414yes—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—22no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53—41no—
361Dic53—22no—
362Dic53—22no—
363Dic53—41no—
364Dic53—41no—
365Dic53—41no—
366Dic53#53411yescharacteristic
367Dic53#53711yescharacteristic
368Dic53#53811yescharacteristic
369Dic53#53911yescharacteristic
370C2×C8×D4—531no—
371C2×C8×D4—531no—
372C4×#121—531no—
373#1923—531no—
374#1923—531no—
375#1916—531no—
376#1916—531no—
377#1869—531no—
378#1869—531no—
379#1869—531no—
380#1869—531no—
381#1850—531no—
382#1850—531no—
383#1797—531no—
384C2×#336—531no—
385C2×C53—42no—
386C2×C53#232511yescharacteristic
387C2×C53C2×C8×D411yescharacteristic
388C2×C53#293211yescharacteristic
389C2×C53#297211yescharacteristic
390C2×C53#297611yescharacteristic
391C2×C53#298811yescharacteristic
392C2×C53#299211yescharacteristic
393D53—24no—
394D53—42no—
395C23×C8—531no—
396C23×C8—531no—
397C23×C8—531no—
398C23×C8—531no—
399C2×#121—531no—
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C22×C42—531no—
404C8×D4—1064no—
405C8×D4—1064no—
406C2×C4⋊C8—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×C4⋊C8—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8—531no—
417C2×C22⋊C8—531no—
418C2×C4×C8—531no—
419C2×C4×C8—531no—
420#390—531no—
421#389—531no—
422#388—531no—
423#388#615711yescharacteristic
424#386—531no—
425#386—531no—
426#380—531no—
427C4×C4⋊C4—531no—
428C4×C22⋊C4—531no—
429C4×C22⋊C4—531no—
430#336—531no—
431#336—531no—
432#336—531no—
433#336—531no—
434#336—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336—531no—
440C53#2216811yescharacteristic, complemented, Sylow
441C22×D4—531no—
442C22×D4—531no—
443C22×D4—531no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—534no—
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—1062no—
459C22×C8—1062no—
460C22×C8—1062no—
461C22×C8—2121no—
462C22×C8—2121no—
463C22×C8—2121no—
464C22×C8—2121no—
465C22×C8—2121no—
466C22×C8—2121no—
467C22×C8—2121no—
468C22×C8—2121no—
469#121—538no—
470C4×D4—1062no—
471C4×D4—1062no—
472C4×D4—1062no—
473C4×D4—1062no—
474C4×D4—2121no—
475C4×D4—2121no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4C2×#615711yescharacteristic
481C2×C22⋊C4—531no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C22⋊C4—531no—
487C2×C22⋊C4—531no—
488C2×C22⋊C4C2×#615711yescharacteristic
489C2×C22⋊C4C2×#615711yescharacteristic
490C2×C22⋊C4C2×#615711yescharacteristic
491C2×C42—531no—
492C2×C42—531no—
493C2×C42—531no—
494C2×C42—531no—
495C2×C42—531no—
496C2×C42—2121no—
497C2×C42—2121no—
498C2×C42C2×#615711yescharacteristic
499C4⋊C8—1062no—
500C4⋊C8—1062no—
501C4⋊C8—2121no—
502C4⋊C8—2121no—
503C22⋊C8—1062no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—2121no—
508C22⋊C8—2121no—
509C22⋊C8—2121no—
510C22⋊C8—2121no—
511C4×C8—1062no—
512C4×C8—1062no—
513#95—531no—
514#95—531no—
515#95—531no—
516#95—531no—
517#95C2×#615711yescharacteristic
518#95C2×#615711yescharacteristic
519C24—531no—
520C24—531no—
521C24C22×#615711yescharacteristic
522C2×D4—534no—
523C2×D4—534no—
524C2×D4—534no—
525C2×D4—1062no—
526C2×D4—1062no—
527C2×D4—1062no—
528C2×D4—1062no—
529C2×D4—2121no—
530C2×D4—2121no—
531C22×C4—531no—
532C22×C4—531no—
533C22×C4—531no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—534no—
537C22×C4—531no—
538C22×C4—531no—
539C22×C4—531no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1061no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1062no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—2121no—
558C22×C4—2121no—
559C22×C4—2121no—
560C22×C4—2121no—
561C22×C4C22×#615711yescharacteristic
562C22×C4C22×#615711yescharacteristic
563C22×C4C22×#615711yescharacteristic
564C22×C4C22×#615711yescharacteristic
565C22×C4C22×#615711yescharacteristic
566C22×C4C22×#615711yescharacteristic
567C2×C8—532no—
568C2×C8—532no—
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—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—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—2124no—
592C2×C8—2124no—
593C2×C8—2124no—
594C2×C8—2124no—
595C4⋊C4—22no—
596C4⋊C4—534no—
597C4⋊C4—1062no—
598C4⋊C4—2121no—
599C4⋊C4—2121no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—534no—
603C22⋊C4—1062no—
604C22⋊C4—1062no—
605C22⋊C4—1062no—
606C22⋊C4—2121no—
607C22⋊C4—2121no—
608C22⋊C4—2121no—
609C22⋊C4D53⋊C814yescomplemented
610C42—41no—
611C42—1061no—
612C42—1061no—
613C42—1061no—
614C42—1061no—
615C42—1061no—
616C42—1061no—
617C42—1061no—
618C42—1061no—
619C42—2121no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—532no—
627C23—532no—
628C23—532no—
629C23—532no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23C2×D53⋊C812yes—
641C23C23×#615711yescharacteristic
642D4—1068no—
643D4—1068no—
644D4—2124no—
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—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—531no—
661C2×C4—531no—
662C2×C4—531no—
663C2×C4—531no—
664C2×C4—531no—
665C2×C4—531no—
666C2×C4—532no—
667C2×C4—532no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—1061no—
680C2×C4—1061no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—2124no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2124no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4D4×#615712yes—
696C2×C4C2×D53⋊C812yes—
697C2×C4C2×D53⋊C812yes—
698C8—1062no—
699C8—1062no—
700C8—2121no—
701C8—2121no—
702C8—2121no—
703C8—2121no—
704C8—2121no—
705C8—2121no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—534no—
714C22—1062no—
715C22—1062no—
716C22—1062no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—1062no—
721C22—1062no—
722C22—1062no—
723C22—2121no—
724C22—2121no—
725C22—2121no—
726C22—2121no—
727C22C2×D4×#615711yescharacteristic
728C22#1681169011yescharacteristic
729C22#1681169211yescharacteristic
730C22C22×D53⋊C811yescharacteristic
731C22D53⋊#13111yescharacteristic
732C22#1681170211yescharacteristic
733C22#1681170211yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—531no—
741C4—531no—
742C4—531no—
743C4—531no—
744C4—1062no—
745C4—1062no—
746C4—2121no—
747C4—2121no—
748C4—2121no—
749C2—42no—
750C2—1064no—
751C2—2122no—
752C2#2029120411yescharacteristic
753C2D4×D53⋊C811yescharacteristic
754C2#2029144111yescharacteristic
755C2#2029156311yescharacteristic
756C2#2029158311yescharacteristic
757C2#2029163211yescharacteristic
758C2#2029165311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C23×C8
FittingC53×#388C4
socleC23×C53C23×C4
prime radicalC2×#13133190C4
cosocleC22×Dic53C24
hypercenter#388#6157
hypocenterC53#22168
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16811651C2semidirect
2. C2×#16811650C2semidirect
3. #20290787C2semidirect
4. #20290784C2semidirect
5. #20290770C2semidirect
6. #20290769C2semidirect
7. #20290691C2semidirect
8. #20290690C2semidirect
9. #20290689C2semidirect
10. #20290689C2semidirect
11. #20290660C2semidirect
12. #20290658C2semidirect
13. #20290570C2semidirect
14. #20290376C2semidirect
69. C2×D53⋊C8D4semidirect
103. #13133190C8semidirect
152. C2×C22⋊D53C2×C8semidirect
153. C2×C22⋊D53C2×C8semidirect
168. C2×D212C2×C8semidirect
184. C2×C4×D53C2×C8semidirect
218. C22⋊C4×C53C2×C8semidirect
226. #11719921C2×C8semidirect
230. #11719919C2×C8semidirect
440. C53#22168semidirect
609. C22⋊C4D53⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×#168116512
C2×#168116502
#202907872
#202907842
#202907702
#202907692
#202906912
#202906902
#202906892
#202906602
#202906582
#202905702
#202903762
#202772272
#2216853