Finite Group Databasebeta

← #27400470

Subgroups — #27400470

Order 13568.

1174 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×#16810695C211yesmaximal, characteristic
2#20277644C211yesmaximal, characteristic
3#20275689C211yesmaximal, characteristic, complemented
4#20275668C211yesmaximal, characteristic, complemented
5#20275149C211yesmaximal, characteristic, complemented
6#20275139C211yesmaximal, characteristic, complemented
7#20275028C211yesmaximal, characteristic, complemented
8#20275023C211yesmaximal, characteristic, complemented
9#20274805C211yesmaximal, characteristic, complemented
10#20274801C211yesmaximal, characteristic, complemented
11#20274730C211yesmaximal, characteristic, complemented
12#20274545C211yesmaximal, characteristic, complemented
13#20274434C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C2×C53×#554C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20#16810695—24no—
21C2×C4⋊#88322C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×C22⋊#88322C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133128C2211yescharacteristic
29#16810516—21no—
30#16810509—21no—
31#16810503—21no—
32#16810489C2211yescharacteristic
33#16810483C2211yescharacteristic
34#16810483C2211yescharacteristic
35C4×C4⋊Dic53C2211yescharacteristic
36C22⋊C4×Dic53—21no—
37#16810385C2211yescharacteristic
38#16810385C2211yescharacteristic
39#16810385C2211yescharacteristic
40#16810385C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49C53×#554—24no—
50C53×#554C418yescomplemented
51C2×C4⋊Q8×C53C2211yescharacteristic
52C2×#125×C53—21no—
53C2×C22⋊Q8×C53—21no—
54C2×C22⋊Q8×C53—21no—
55C2×C22⋊Q8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×C4×Q8×C53C2211yescharacteristic
58C2×C4×D4×C53—21no—
59C2×C4×D4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C23×Dic53—21no—
63C2×#11719917—22no—
64C2×#11719917—22no—
65C2×#11719917—41no—
66C22×#88322—22no—
67C22×#88322—22no—
68C22×#88322—41no—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133176—22no—
74#13133176—41no—
75C2×C4⋊Dic53—21no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—41no—
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C4×Dic53—21no—
86C2×C4×Dic53—21no—
87C4⋊#88322—22no—
88#13133141—22no—
89#13133141—22no—
90#13133141—41no—
91#13133141—41no—
92C22⋊#88322—22no—
93C22⋊#88322—22no—
94#13133128—22no—
95#13133124—21no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100C22×Q8×C53—21no—
101C22×Q8×C53C2311yescharacteristic
102C22×D4×C53D411yescharacteristic
103C23×C4×C53—21no—
104C23×C4×C53—21no—
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C4⋊Q8×C53—22no—
108C4⋊Q8×C53C2×C414yescomplemented
109#125×C53—28no—
110C22⋊Q8×C53—28no—
111C22⋊Q8×C53—28no—
112C22⋊Q8×C53—22no—
113C22⋊Q8×C53—22no—
114C22⋊Q8×C53C2×C414yes—
115C22⋊Q8×C53C2×C414yescomplemented
116C4×Q8×C53—22no—
117C4×Q8×C53C2×C414yescomplemented
118C4×D4×C53—28no—
119C4×D4×C53C2×C414yes—
120C4×D4×C53D414yes—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—22no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53—21no—
129C2×C4⋊C4×C53C2×C414yes—
130C2×C4⋊C4×C53C2×C414yescomplemented
131C2×C4⋊C4×C53D411yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53—21no—
137C2×C22⋊C4×C53D411yescharacteristic
138C2×C22⋊C4×C53D411yescharacteristic
139C2×C42×C53—21no—
140C2×C42×C53C2311yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C2×Q8×C53—24no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—81no—
150C2×Q8×C53—81no—
151C2×Q8×C53C22×C412yes—
152C2×D4×C53—22no—
153C2×D4×C53—22no—
154C2×D4×C53C22⋊C414yes—
155C22×C4×C53—21no—
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—24no—
168C22×C4×C53—24no—
169C22×C4×C53—81no—
170C22×C4×C53—81no—
171C22×C4×C53—81no—
172C22×C4×C53—81no—
173C22×C4×C53C22×C412yes—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2411yescharacteristic
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—42no—
187C22×Dic53—42no—
188C22×Dic53—81no—
189C4⋊C4×C53—24no—
190C4⋊C4×C53—24no—
191C4⋊C4×C53—24no—
192C4⋊C4×C53—24no—
193C4⋊C4×C53—24no—
194C4⋊C4×C53—24no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53C22⋊C414yes—
199C4⋊C4×C53C22×C412yes—
200C4⋊C4×C53C22×C412yes—
201C4⋊C4×C53C22×C412yes—
202C22⋊C4×C53—24no—
203C22⋊C4×C53—24no—
204C22⋊C4×C53C22⋊C414yes—
205C22⋊C4×C53C22⋊C414yes—
206C42×C53—24no—
207C42×C53C22×C412yes—
208C42×C53C2×D412yes—
209C22⋊Dic53—42no—
210C22⋊Dic53—42no—
211C22⋊Dic53—81no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—42no—
220C4⋊Dic53#4112yes—
221C4×Dic53—42no—
222C4×Dic53—81no—
223#11719917—44no—
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—21no—
234C2×#88322—21no—
235C2×#88322—44no—
236C2×#88322#4112yes—
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—21no—
246C23×C53—21no—
247C23×C53C2×C22⋊C412yes—
248C23×C53C2×C22⋊C412yes—
249C23×C53#13712yes—
250C23×C53#13712yes—
251C23×C53C22×D411yescharacteristic
252Q8×C53—22no—
253Q8×C53—22no—
254Q8×C53—41no—
255Q8×C53—41no—
256Q8×C53—84no—
257D4×C53—28no—
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—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
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—84no—
287C2×C4×C53—84no—
288C2×C4×C53C2×C22⋊C412yes—
289C2×C4×C53C2×C22⋊C412yes—
290C2×C4×C53C2×C22⋊C412yes—
291C2×C4×C53C2×C22⋊C412yes—
292C2×C4×C53C23×C411yescharacteristic
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C2×#4111yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53H(5,𝔽2)11yescharacteristic
297C2×C4×C532−1+411yescharacteristic
298C2×Dic53—22no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
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—84no—
311#88322—22no—
312#88322—41no—
313#88322—41no—
314#88322—41no—
315#22497—531nomaximal, Sylow
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53#41914yes—
330C22×C53C22×C22⋊C411yescharacteristic
331C22×C53#54611yescharacteristic
332C22×C53#54711yescharacteristic
333C22×C53C2×#13711yescharacteristic
334C22×C53C2×#13711yescharacteristic
335C22×C53#57611yescharacteristic
336C22×C53#57711yescharacteristic
337C4×C53—22no—
338C4×C53—22no—
339C4×C53—22no—
340C4×C53—22no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53—42no—
345C4×C53C4×#4111yescharacteristic
346C4×C53#52011yescharacteristic
347C4×C53#54611yescharacteristic
348C4×C53#54711yescharacteristic
349Dic53—42no—
350Dic53—81no—
351Dic53—81no—
352Dic53—81no—
353C2×#554D5311yescharacteristic
354C2×#435—531no—
355#2352—531no—
356#1993—531no—
357#1988—531no—
358#1894—531no—
359#1892—531no—
360#1873—531no—
361#1872—531no—
362#1824—531no—
363#1823—531no—
364#1805—531no—
365#1763—531no—
366#1736—531no—
367C2×#340—531no—
368C2×C53—24no—
369C2×C53—42no—
370C2×C53#233911yescharacteristic
371C2×C53C2×#41911yescharacteristic
372C2×C53#289711yescharacteristic
373C2×C53#331411yescharacteristic
374C2×C53#331611yescharacteristic
375C2×C53#334411yescharacteristic
376C2×C53#334611yescharacteristic
377C22×M16—531no—
378C23×C8—531no—
379#554—24no—
380#554Dic5318yescomplemented
381C2×C4⋊Q8C2×D5311yescharacteristic
382C2×#125—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8C2×D5311yescharacteristic
386C2×C22⋊Q8C2×D5311yescharacteristic
387C2×C4×Q8C2×D5311yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C2×D5311yescharacteristic
390C2×#117—531no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4C2×D5311yescharacteristic
393C22×C4⋊C4C2×D5311yescharacteristic
394#435—1064no—
395C2×C4⋊C8—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103—531no—
400C2×C22⋊C8—531no—
401C2×C22⋊C8—531no—
402C2×#97—531no—
403#388—1061no—
404#387—1061no—
405#386—1061no—
406#382—531no—
407#380—531no—
408#380—531no—
409C4×C4⋊C4—531no—
410C4×C22⋊C4—1061no—
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#340—531no—
422#340—531no—
423C53#2249711yescharacteristic, complemented, Sylow
424C22×Q8—21no—
425C22×Q8C22×D5311yescharacteristic
426C22×D4C22⋊D5311yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—1061no—
430C23×C4C22×D5311yescharacteristic
431C23×C4C22×D5311yescharacteristic
432C2×M16—1062no—
433C2×M16—1062no—
434C2×M16—2121no—
435C22×C8—531no—
436C22×C8—531no—
437C22×C8—531no—
438C22×C8—531no—
439C22×C8—1062no—
440C22×C8—1062no—
441C22×C8—2121no—
442C4⋊Q8—22no—
443C4⋊Q8C2×Dic5314yescomplemented
444#125—28no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8C2×Dic5314yes—
450C22⋊Q8C2×Dic5314yescomplemented
451C4×Q8—22no—
452C4×Q8C2×Dic5314yescomplemented
453C4×D4—28no—
454C4×D4C2×Dic5314yes—
455C4×D4C22⋊D5314yes—
456#117—1062no—
457#117—2121no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—531no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—1062no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—2121no—
473C2×C4⋊C4C2×Dic5314yes—
474C2×C4⋊C4C2×Dic5314yescomplemented
475C2×C4⋊C4C22⋊D5311yescharacteristic
476C2×C4⋊C4C22×D5311yescharacteristic
477C2×C4⋊C4C22×D5311yescharacteristic
478C2×C4⋊C4C22×D5311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4C22⋊D5311yescharacteristic
485C2×C22⋊C4C22⋊D5311yescharacteristic
486C2×C42—21no—
487C2×C42—1061no—
488C2×C42—1061no—
489C2×C42C22×D5311yescharacteristic
490C4⋊C8—1062no—
491#103—1062no—
492#103—1062no—
493#103—2121no—
494#103—2121no—
495C22⋊C8—1062no—
496C22⋊C8—1062no—
497#97—1062no—
498#95—1061no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503C24C2×C22⋊D5311yescharacteristic
504C24C2×C22⋊D5311yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—81no—
512C2×Q8—81no—
513C2×Q8C22×Dic5312yes—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4C22⋊Dic5314yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—1061no—
536C22×C4—1061no—
537C22×C4—1061no—
538C22×C4—1061no—
539C22×C4—4241no—
540C22×C4—2122no—
541C22×C4—2122no—
542C22×C4C22×Dic5312yes—
543C22×C4C22×Dic5312yes—
544C22×C4C2×C22⋊D5311yescharacteristic
545C22×C4C2×C22⋊D5311yescharacteristic
546C22×C4C2×C22⋊D5311yescharacteristic
547C22×C4C2×C22⋊D5311yescharacteristic
548C22×C4C2×C22⋊D5312yes—
549C22×C4C2×C22⋊D5312yes—
550C22×C4C23×D5311yescharacteristic
551M16—2124no—
552C2×C8—532no—
553C2×C8—1061no—
554C2×C8—1061no—
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—2124no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—532no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—2122no—
583C4⋊C4C22⋊Dic5314yes—
584C4⋊C4C22×Dic5312yes—
585C4⋊C4C22×Dic5312yes—
586C4⋊C4C22×Dic5312yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—4241no—
590C22⋊C4—2122no—
591C22⋊C4—2122no—
592C22⋊C4C22⋊Dic5314yes—
593C22⋊C4C22⋊Dic5314yes—
594C42—24no—
595C42—4241no—
596C42—2122no—
597C42C22×Dic5312yes—
598C42C2×C22⋊D5312yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C22⋊Dic5312yes—
610C23C2×C22⋊Dic5312yes—
611C23#1313324812yes—
612C23#1313324812yes—
613C23C22×C22⋊D5311yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—1062no—
651C2×C4—4244no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4C2×C22⋊Dic5312yes—
664C2×C4C2×C22⋊Dic5312yes—
665C2×C4C2×C22⋊Dic5312yes—
666C2×C4C2×C22⋊Dic5312yes—
667C2×C4C23×Dic5311yescharacteristic
668C2×C4C22×C22⋊D5311yescharacteristic
669C2×C4#41×D5311yescharacteristic
670C2×C4#41×D5311yescharacteristic
671C2×C4#1313326311yescharacteristic
672C2×C4#1313326411yescharacteristic
673C8—1062no—
674C8—2121no—
675C8—2121no—
676C8—2121no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1681063214yes—
691C22C22×C22⋊Dic5311yescharacteristic
692C22#1681126111yescharacteristic
693C22#1681127211yescharacteristic
694C22C2×#1313324811yescharacteristic
695C22C2×#1313324811yescharacteristic
696C22#1681142611yescharacteristic
697C22#1681143411yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—4241no—
707C4—4241no—
708C4—4241no—
709C4—2122no—
710C4#41×Dic5311yescharacteristic
711C4#1681110611yescharacteristic
712C4#1681126111yescharacteristic
713C4#1681127211yescharacteristic
714C2—24no—
715C2—42no—
716C2#2027754511yescharacteristic
717C2C2×#1681063211yescharacteristic
718C2#2028324111yescharacteristic
719C2#2028679011yescharacteristic
720C2#2028682011yescharacteristic
721C2#2028716411yescharacteristic
722C2#2028719411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
cosocleC22×C4×C53C24
hypercenterC2×#554D53
hypocenterC53#22497
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #20275689C2semidirect
4. #20275668C2semidirect
5. #20275149C2semidirect
6. #20275139C2semidirect
7. #20275028C2semidirect
8. #20275023C2semidirect
9. #20274805C2semidirect
10. #20274801C2semidirect
11. #20274730C2semidirect
12. #20274545C2semidirect
13. #20274434C2semidirect
14. C2×#16810385C2semidirect
50. C53×#554C4semidirect
108. C4⋊Q8×C53C2×C4semidirect
115. C22⋊Q8×C53C2×C4semidirect
117. C4×Q8×C53C2×C4semidirect
130. C2×C4⋊C4×C53C2×C4semidirect
380. #554Dic53semidirect
423. C53#22497semidirect
443. C4⋊Q8C2×Dic53semidirect
450. C22⋊Q8C2×Dic53semidirect
452. C4×Q8C2×Dic53semidirect
474. C2×C4⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168106952
#202776442
#202756892
#202756682
#202751492
#202751392
#202750282
#202750232
#202748052
#202748012
#202747302
#202745452
#202744342
C2×#168103852
C2×C53×#5542
#2249753