Finite Group Databasebeta

← #27400375

Subgroups — #27400375

Order 13568.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811307C211yesmaximal, characteristic
2C2×#16810692C211yesmaximal, characteristic
3#20277611C211yesmaximal, characteristic
4#20275682C211yesmaximal, characteristic, complemented
5#20275669C211yesmaximal, characteristic, complemented
6#20275135C211yesmaximal, characteristic, complemented
7#20275023C211yesmaximal, characteristic, complemented
8#20275019C211yesmaximal, characteristic, complemented
9#20274807C211yesmaximal, characteristic, complemented
10#20274800C211yesmaximal, characteristic, complemented
11#20274718C211yesmaximal, characteristic, complemented
12#20274547C211yesmaximal, characteristic, complemented
13#20274435C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1894C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17#16811307—24no—
18#16811307C418yescomplemented
19C2×#13133210—21no—
20C2×#13133208C2211yescharacteristic
21C2×#13133207—21no—
22C2×#13133199—21no—
23C2×#13133193C2211yescharacteristic
24C2×Q8×Dic53C2211yescharacteristic
25C2×C4×C22⋊D53C2211yescharacteristic
26C2×#13133177—21no—
27C2×#13133176C2211yescharacteristic
28C2×#13133175—21no—
29C22×C4⋊Dic53C2211yescharacteristic
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32#16810692—24no—
33C2×#13133146C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133127C2211yescharacteristic
39#16810520—21no—
40#16810497—21no—
41#16810495—21no—
42#16810492C2211yescharacteristic
43#16810480C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C22×M16×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×C22⋊D53D411yescharacteristic
63C23×Dic53—21no—
64C22×C4×D53—21no—
65C22×C4×D53—21no—
66C22×C4×D53C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C2×C8×D53—22no—
70C2×C8×D53—22no—
71C2×C8×D53—41no—
72#13133210—28no—
73#13133208—22no—
74#13133208C2×C414yescomplemented
75#13133207—28no—
76#13133199—28no—
77#13133193—22no—
78#13133193C2×C414yescomplemented
79Q8×Dic53—22no—
80Q8×Dic53C2×C414yescomplemented
81C4×C22⋊D53C2×C414yes—
82C4×C22⋊D53D414yes—
83#13133177—44no—
84#13133176—22no—
85#13133176C2×C414yescomplemented
86#13133175—28no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—41no—
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919—21no—
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919D411yescharacteristic
103C4⋊C4×D53—22no—
104C4⋊C4×D53—22no—
105C4⋊C4×D53—41no—
106C4⋊C4×D53C2×C414yescomplemented
107C2×C22⋊Dic53—21no—
108C2×C22⋊Dic53D411yescharacteristic
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921D411yescharacteristic
112C2×C4×Dic53—21no—
113C2×C4×Dic53—21no—
114C2×C4×Dic53—21no—
115C2×C4×Dic53C2311yescharacteristic
116#13133146—22no—
117#13133141—22no—
118#13133141—41no—
119C22⋊#88322—22no—
120#13133129—22no—
121#13133127—22no—
122#13133124—21no—
123#13133124—21no—
124C22×Q8×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C2×M16×C53—22no—
127C2×M16×C53—22no—
128C2×M16×C53—41no—
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53C2×C414yescomplemented
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53—21no—
139#103×C53—22no—
140#103×C53—41no—
141#95×C53—21no—
142C24×C53C2×D411yescharacteristic
143C23×D53C2×D411yescharacteristic
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53C22×C412yes—
150C22×C4×C53—21no—
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×C53C22×C412yes—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2411yescharacteristic
162C2×C22⋊D53—22no—
163C2×C22⋊D53—22no—
164C2×C22⋊D53C22⋊C414yes—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—42no—
170C22×Dic53—42no—
171C22×Dic53—81no—
172C22×Dic53C2×D411yescharacteristic
173C22×Dic53C2×D411yescharacteristic
174C22×Dic53C2×D411yescharacteristic
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—24no—
180C2×C4×D53—42no—
181C2×C4×D53—42no—
182C2×C4×D53—42no—
183C2×C4×D53—42no—
184C2×C4×D53—81no—
185C2×C4×D53C22×C412yes—
186C2×C4×D53C2×D412yes—
187M16×C53—44no—
188C2×C8×C53—21no—
189C2×C8×C53—21no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53#4112yes—
194C4⋊C4×C53—24no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53C22×C412yes—
201C22⋊C4×C53—24no—
202C22⋊C4×C53—42no—
203C22⋊Dic53—24no—
204C22⋊Dic53C22⋊C414yes—
205#11719921—24no—
206#11719921—42no—
207#11719921C22⋊C414yes—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—24no—
212C4⋊Dic53—24no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—42no—
216C4⋊Dic53C22×C412yes—
217C4⋊Dic53C22×C412yes—
218C4⋊Dic53#4112yes—
219#11719919—24no—
220#11719919—24no—
221#11719919—24no—
222#11719919—42no—
223#11719919—42no—
224#11719919—81no—
225#11719919C22⋊C414yes—
226C4×Dic53—24no—
227C4×Dic53—24no—
228C4×Dic53—42no—
229C4×Dic53C22×C412yes—
230C4×Dic53C2×D412yes—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C8×D53—44no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53C2×C22⋊C412yes—
245C23×C53C22×D411yescharacteristic
246C22×D53—21no—
247C22×D53—21no—
248C22×D53—21no—
249C22×D53—21no—
250C22×D53C2×C22⋊C412yes—
251C22×D53AGL(1,ℤ/8)12yes—
252C22×D53#13712yes—
253Q8×C53—22no—
254Q8×C53—22no—
255Q8×C53—41no—
256Q8×C53—41no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53C2×C22⋊C412yes—
276C2×C4×C53C23×C411yescharacteristic
277C2×C4×C53C22×D411yescharacteristic
278C2×C4×C53C2×#4111yescharacteristic
279C2×C4×C53C2×#4111yescharacteristic
280C2×C4×C53H(5,𝔽2)11yescharacteristic
281C2×C4×C532−1+411yescharacteristic
282C22⋊D53—28no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—84no—
302C2×Dic53C2×C22⋊C412yes—
303C2×Dic53C2×C22⋊C412yes—
304C2×Dic53C2×C22⋊C412yes—
305C4×D53—22no—
306C4×D53—22no—
307C4×D53—22no—
308C4×D53—22no—
309C4×D53—48no—
310C4×D53—84no—
311C8×C53—22no—
312C8×C53—41no—
313#88322—41no—
314#88322—41no—
315#22491—531nomaximal, Sylow
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53C22×C22⋊C411yescharacteristic
324C22×C53#54611yescharacteristic
325C22×C53#54711yescharacteristic
326C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C53C2×#13711yescharacteristic
328C22×C53#57711yescharacteristic
329C22×C53#57811yescharacteristic
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—22no—
334C2×D53—22no—
335C2×D53—22no—
336C2×D53#41714yes—
337C4×C53—22no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53—81no—
341C4×C53—81no—
342C4×C53C4×#4111yescharacteristic
343C4×C53#52011yescharacteristic
344C4×C53#54611yescharacteristic
345C4×C53#54711yescharacteristic
346Dic53—22no—
347Dic53—22no—
348Dic53—22no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—81no—
353C2×#552—531no—
354C2×#435—531no—
355D4×C4⋊C4—531no—
356#1992—531no—
357#1989—531no—
358#1894D5311yescharacteristic, complemented
359#1892—531no—
360#1872—531no—
361#1872—531no—
362#1825—531no—
363#1823—531no—
364#1803—531no—
365#1763—531no—
366#1736—531no—
367C2×#340—531no—
368C2×C53—42no—
369C2×C53#233911yescharacteristic
370C2×C53C2×#41711yescharacteristic
371C2×C53#289811yescharacteristic
372C2×C53#331011yescharacteristic
373C2×C53#331211yescharacteristic
374C2×C53#334311yescharacteristic
375C2×C53#334411yescharacteristic
376D53—24no—
377C22×M16C2×D5311yescharacteristic
378C23×C8—531no—
379#552—538no—
380#552—1064no—
381C2×#126—1061no—
382C2×#125—531no—
383C2×#125—1061no—
384C2×#123—1061no—
385C2×C22⋊Q8—531no—
386C2×C22⋊Q8C2×D5311yescharacteristic
387C2×C4×Q8—531no—
388C2×C4×D4—531no—
389C2×C4×D4—1061no—
390C2×#117—531no—
391C2×#117—1061no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394C22×C4⋊C4—531no—
395#435—1064no—
396C2×C4⋊C8—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103C2×D5311yescharacteristic
400C2×#103C2×D5311yescharacteristic
401C2×C22⋊C8—531no—
402C2×C22⋊C8—531no—
403C2×#97—531no—
404#389—1061no—
405#385—1061no—
406#385—1061no—
407#384—531no—
408#380—531no—
409#380C2×D5311yescharacteristic
410C4×C4⋊C4—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340C2×D5311yescharacteristic
422#340C2×D5311yescharacteristic
423C53#2249111yescharacteristic, complemented, Sylow
424C22×Q8C22×D5311yescharacteristic
425C22×D4—531no—
426C23×C4—531no—
427C23×C4—1061no—
428C23×C4—1061no—
429C23×C4—1061no—
430C23×C4C22×D5311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—531no—
435C22×C8—531no—
436C22×C8—1062no—
437C22×C8—1062no—
438C22×C8—2121no—
439C22×C8C22×D5311yescharacteristic
440C22×C8C22×D5311yescharacteristic
441#126—1068no—
442#125—534no—
443#125—1062no—
444#125—1068no—
445#123—1068no—
446C22⋊Q8—22no—
447C22⋊Q8—534no—
448C22⋊Q8—1062no—
449C22⋊Q8C4×D5314yescomplemented
450C4×Q8—534no—
451C4×Q8—1062no—
452C4×D4—534no—
453C4×D4—534no—
454C4×D4—2124no—
455#117—534no—
456#117—1068no—
457#117—1062no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—534no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—1062no—
466C2×C4⋊C4—1062no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4—1061no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1061no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—2121no—
478C2×C4⋊C4—2121no—
479C2×C4⋊C4C22×D5311yescharacteristic
480C2×C4⋊C4C22×D5311yescharacteristic
481C2×C4⋊C4C22×D5311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—531no—
485C2×C22⋊C4—531no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C42—531no—
490C2×C42—1061no—
491C2×C42—1061no—
492C2×C42—1061no—
493C4⋊C8—1062no—
494#103—22no—
495#103—41no—
496#103—1062no—
497#103—2121no—
498C22⋊C8—1062no—
499C22⋊C8—1062no—
500#97—1062no—
501#95—21no—
502#95—1061no—
503#95—1061no—
504C24—531no—
505C24D4×D5311yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×C4×D5312yes—
512C2×D4—534no—
513C2×D4—1062no—
514C2×D4—1062no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—531no—
524C22×C4—531no—
525C22×C4—531no—
526C22×C4—532no—
527C22×C4—532no—
528C22×C4—1064no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—4241no—
538C22×C4—4241no—
539C22×C4—2122no—
540C22×C4—2122no—
541C22×C4—2122no—
542C22×C4—2122no—
543C22×C4—2122no—
544C22×C4—2122no—
545C22×C4C2×C4×D5312yes—
546C22×C4D4×D5311yescharacteristic
547C22×C4D4×D5312yes—
548C22×C4C23×D5311yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—1061no—
556C2×C8—1061no—
557C2×C8—1061no—
558C2×C8—1061no—
559C2×C8—1061no—
560C2×C8—1061no—
561C2×C8—2124no—
562C2×C8#1171994712yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—534no—
570C4⋊C4—532no—
571C4⋊C4—532no—
572C4⋊C4—532no—
573C4⋊C4—1064no—
574C4⋊C4—1064no—
575C4⋊C4—1064no—
576C4⋊C4—1064no—
577C4⋊C4—1064no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—4241no—
584C4⋊C4—2122no—
585C4⋊C4—2122no—
586C4⋊C4—2122no—
587C4⋊C4C2×C4×D5312yes—
588C22⋊C4—24no—
589C22⋊C4—42no—
590C22⋊C4—534no—
591C22⋊C4—534no—
592C22⋊C4—1064no—
593C22⋊C4—1064no—
594C22⋊C4—2122no—
595C42—532no—
596C42—532no—
597C42—1064no—
598C42—1064no—
599C42—2122no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—532no—
607C23—532no—
608C23—532no—
609C23—1061no—
610C23—1061no—
611C23—1061no—
612C23—1061no—
613C23C22⋊C4×D5312yes—
614C23C2×D4×D5311yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—1068no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—532no—
639C2×C4—532no—
640C2×C4—532no—
641C2×C4—1061no—
642C2×C4—1061no—
643C2×C4—1061no—
644C2×C4—1061no—
645C2×C4—1061no—
646C2×C4—1061no—
647C2×C4—1062no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—4244no—
655C2×C4—4244no—
656C2×C4—2128no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4—2121no—
664C2×C4—2121no—
665C2×C4—2121no—
666C2×C4C22⋊C4×D5312yes—
667C2×C4C22×C4×D5311yescharacteristic
668C2×C4C2×D4×D5311yescharacteristic
669C2×C4#41×D5311yescharacteristic
670C2×C4C2×#1171994711yescharacteristic
671C2×C4#1313326211yescharacteristic
672C2×C4#1313326411yescharacteristic
673C8—22no—
674C8—41no—
675C8—2121no—
676C8—2121no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—534no—
685C22—1062no—
686C22—1062no—
687C22—1062no—
688C22—1062no—
689C22—1062no—
690C22—1062no—
691C22C2×C22⋊C4×D5311yescharacteristic
692C22#1681126211yescharacteristic
693C22#1681127311yescharacteristic
694C22AGL(1,ℤ/8)×D5311yescharacteristic
695C22#137×D5311yescharacteristic
696C22#1681143211yescharacteristic
697C22#1681143911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—1062no—
704C4—1062no—
705C4—1062no—
706C4—4241no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4C4×#1171994711yescharacteristic
711C4#1681110211yescharacteristic
712C4#1681126011yescharacteristic
713C4#1681127111yescharacteristic
714C2—42no—
715C2—1064no—
716C2#2027754111yescharacteristic
717C2#417×D5311yescharacteristic
718C2#2028324711yescharacteristic
719C2#2028673111yescharacteristic
720C2#2028676111yescharacteristic
721C2#2028715011yescharacteristic
722C2#2028716511yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1894C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenter#1894D53
hypocenterC53#22491
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #20275682C2semidirect
5. #20275669C2semidirect
6. #20275135C2semidirect
7. #20275023C2semidirect
8. #20275019C2semidirect
9. #20274807C2semidirect
10. #20274800C2semidirect
11. #20274718C2semidirect
12. #20274547C2semidirect
13. #20274435C2semidirect
14. #340×D53C2semidirect
15. C53×#1894C2semidirect
18. #16811307C4semidirect
74. #13133208C2×C4semidirect
78. #13133193C2×C4semidirect
80. Q8×Dic53C2×C4semidirect
85. #13133176C2×C4semidirect
106. C4⋊C4×D53C2×C4semidirect
132. C22⋊Q8×C53C2×C4semidirect
358. #1894D53semidirect
423. C53#22491semidirect
449. C22⋊Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113072
C2×#168106922
#202776112
#202756822
#202756692
#202751352
#202750232
#202750192
#202748072
#202748002
#202747182
#202745472
#202744352
#340×D532
C53×#18942
#2249153