Finite Group Databasebeta

← #27400317

Subgroups — #27400317

Order 13568.

1162 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#88322C211yesmaximal, characteristic
2#20277644C211yesmaximal, characteristic
3#20275681C211yesmaximal, characteristic, complemented
4#20275673C211yesmaximal, characteristic, complemented
5#20275139C211yesmaximal, characteristic, complemented
6#20275139C211yesmaximal, characteristic, complemented
7#20275028C211yesmaximal, characteristic, complemented
8#20275023C211yesmaximal, characteristic, complemented
9#20274810C211yesmaximal, characteristic, complemented
10#20274801C211yesmaximal, characteristic, complemented
11#20274730C211yesmaximal, characteristic, complemented
12C4×#13133141C211yesmaximal, characteristic, complemented
13#20274431C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C2×C53×#552C211yesmaximal, characteristic
16C23×#88322C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20D4×#88322—24no—
21C2×C4⋊#88322C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×C22⋊#88322C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×C4×#88322C2211yescharacteristic
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×#552—24no—
50C53×#552C418yescomplemented
51C2×#126×C53—21no—
52C2×#125×C53—21no—
53C2×#125×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×C22⋊Q8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×C4×Q8×C53C2211yescharacteristic
58C2×C4×D4×C53C2211yescharacteristic
59C2×#117×C53—21no—
60C2×#117×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C23×Dic53—21no—
63C22×#88322—22no—
64C22×#88322—22no—
65C22×#88322—22no—
66C22×#88322—22no—
67C22×#88322—41no—
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—
94C4×#88322—22no—
95#13133124—21no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100C22×Q8×C53C2311yescharacteristic
101C22×D4×C53D411yescharacteristic
102C23×C4×C53—21no—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105#126×C53—28no—
106#125×C53—28no—
107#125×C53—22no—
108#125×C53C2×C414yescomplemented
109#123×C53—28no—
110C22⋊Q8×C53—22no—
111C22⋊Q8×C53—22no—
112C22⋊Q8×C53C2×C414yes—
113C22⋊Q8×C53C2×C414yescomplemented
114C4×Q8×C53—22no—
115C4×Q8×C53C2×C414yescomplemented
116C4×D4×C53C2×C414yes—
117C4×D4×C53D414yes—
118#117×C53—28no—
119#117×C53—22no—
120#117×C53C2×C414yescomplemented
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53C2×C414yes—
129C2×C4⋊C4×C53D411yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
131C2×C4⋊C4×C53C2311yescharacteristic
132C2×C4⋊C4×C53C2311yescharacteristic
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—21no—
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C22⋊C4×C53D411yescharacteristic
138C2×C42×C53—21no—
139C2×C42×C53—21no—
140C2×C42×C53C2311yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C2×Q8×C53—21no—
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53C22×C412yes—
149C2×D4×C53—22no—
150C2×D4×C53—22no—
151C2×D4×C53C22⋊C414yes—
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×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—24no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—42no—
166C22×C4×C53—42no—
167C22×C4×C53C22×C412yes—
168C22×C4×C53C22×C412yes—
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2×D412yes—
175C22×C4×C53C2411yescharacteristic
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—42no—
181C22×Dic53—42no—
182C22×Dic53—81no—
183C4⋊C4×C53—24no—
184C4⋊C4×C53—24no—
185C4⋊C4×C53—24no—
186C4⋊C4×C53—24no—
187C4⋊C4×C53—24no—
188C4⋊C4×C53—24no—
189C4⋊C4×C53—21no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53C22⋊C414yes—
193C4⋊C4×C53C22×C412yes—
194C4⋊C4×C53C22×C412yes—
195C4⋊C4×C53C22×C412yes—
196C22⋊C4×C53—24no—
197C22⋊C4×C53—24no—
198C22⋊C4×C53—24no—
199C22⋊C4×C53C22⋊C414yes—
200C22⋊C4×C53C22⋊C414yes—
201C42×C53—24no—
202C42×C53—24no—
203C42×C53C22×C412yes—
204C42×C53C2×D412yes—
205C22⋊Dic53—42no—
206C22⋊Dic53—42no—
207C22⋊Dic53—81no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—42no—
216C4⋊Dic53#4112yes—
217C4×Dic53—42no—
218C4×Dic53—81no—
219C2×#88322—21no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—44no—
231C2×#88322—44no—
232C2×#88322#4112yes—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53C2×C22⋊C412yes—
244C23×C53C2×C22⋊C412yes—
245C23×C53#13512yes—
246C23×C53#13512yes—
247C23×C53C22×D411yescharacteristic
248Q8×C53—22no—
249Q8×C53—22no—
250Q8×C53—41no—
251Q8×C53—41no—
252D4×C53—28no—
253C2×C4×C53—21no—
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—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
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—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—48no—
282C2×C4×C53C2×C22⋊C412yes—
283C2×C4×C53C2×C22⋊C412yes—
284C2×C4×C53C2×C22⋊C412yes—
285C2×C4×C53C2×C22⋊C412yes—
286C2×C4×C53C23×C411yescharacteristic
287C2×C4×C53C22×D411yescharacteristic
288C2×C4×C53C2×#4111yescharacteristic
289C2×C4×C53C2×#4111yescharacteristic
290C2×C4×C53H(5,𝔽2)11yescharacteristic
291C2×C4×C532−1+411yescharacteristic
292C2×Dic53—22no—
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—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—84no—
305#88322—22no—
306#88322—41no—
307#88322—41no—
308#88322—41no—
309#22486—531nomaximal, Sylow
310C22×C53—22no—
311C22×C53—22no—
312C22×C53—22no—
313C22×C53—22no—
314C22×C53—22no—
315C22×C53—22no—
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53#41614yes—
324C22×C53C22×C22⋊C411yescharacteristic
325C22×C53#54611yescharacteristic
326C22×C53#54711yescharacteristic
327C22×C53C2×#13511yescharacteristic
328C22×C53C2×#13511yescharacteristic
329C22×C53#57711yescharacteristic
330C22×C53#57811yescharacteristic
331C4×C53—22no—
332C4×C53—22no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—42no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53C4×#4111yescharacteristic
340C4×C53#52011yescharacteristic
341C4×C53#54611yescharacteristic
342C4×C53#54711yescharacteristic
343Dic53—42no—
344Dic53—81no—
345Dic53—81no—
346Dic53—81no—
347C2×#552D5311yescharacteristic
348C2×C8×D4—531no—
349#2352—531no—
350#1991—531no—
351#1989—531no—
352#1892—531no—
353#1892—531no—
354#1873—531no—
355#1872—531no—
356#1825—531no—
357#1823—531no—
358#1805—531no—
359C4×#103—531no—
360#1735—531no—
361C2×#340—531no—
362C2×C53—24no—
363C2×C53—42no—
364C2×C53#233911yescharacteristic
365C2×C53C2×#41611yescharacteristic
366C2×C53#289811yescharacteristic
367C2×C53#329611yescharacteristic
368C2×C53#330011yescharacteristic
369C2×C53#333611yescharacteristic
370C2×C53#333711yescharacteristic
371C23×C8—531no—
372C23×C8—531no—
373#552—24no—
374#552Dic5318yescomplemented
375C2×#126—21no—
376C2×#125—21no—
377C2×#125C2×D5311yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8C2×D5311yescharacteristic
380C2×C22⋊Q8C2×D5311yescharacteristic
381C2×C4×Q8C2×D5311yescharacteristic
382C2×C4×D4C2×D5311yescharacteristic
383C2×#117—21no—
384C2×#117—531no—
385C2×#117C2×D5311yescharacteristic
386C22×C4⋊C4—531no—
387C22×C4⋊C4C2×D5311yescharacteristic
388C8×D4—1064no—
389C2×C4⋊C8—531no—
390C2×#103—531no—
391C2×#103—531no—
392C2×#103—531no—
393C2×#103—531no—
394C2×C22⋊C8—531no—
395C2×C22⋊C8—531no—
396C2×C4×C8—531no—
397#388—1061no—
398#387—1061no—
399#386—1061no—
400#382—531no—
401#380—531no—
402#380—531no—
403C4×C4⋊C4—531no—
404C4×C22⋊C4—1061no—
405#340—531no—
406#340—531no—
407#340—531no—
408#340—531no—
409#340—531no—
410#340—531no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417C53#2248611yescharacteristic, complemented, Sylow
418C22×Q8C22×D5311yescharacteristic
419C22×D4C22⋊D5311yescharacteristic
420C23×C4—21no—
421C23×C4—1061no—
422C23×C4C22×D5311yescharacteristic
423C23×C4C22×D5311yescharacteristic
424C22×C8—531no—
425C22×C8—531no—
426C22×C8—531no—
427C22×C8—531no—
428C22×C8—1062no—
429C22×C8—1062no—
430C22×C8—1062no—
431C22×C8—1062no—
432C22×C8—2121no—
433C22×C8—2121no—
434#126—28no—
435#125—28no—
436#125—22no—
437#125C2×Dic5314yescomplemented
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic5314yes—
442C22⋊Q8C2×Dic5314yescomplemented
443C4×Q8—22no—
444C4×Q8C2×Dic5314yescomplemented
445C4×D4C2×Dic5314yes—
446C4×D4C22⋊D5314yes—
447#117—22no—
448#117—28no—
449#117—1062no—
450#117—2121no—
451#117C2×Dic5314yescomplemented
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—1062no—
464C2×C4⋊C4—1061no—
465C2×C4⋊C4—2121no—
466C2×C4⋊C4C2×Dic5314yes—
467C2×C4⋊C4C22⋊D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C4⋊C4C22×D5311yescharacteristic
470C2×C4⋊C4C22×D5311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1061no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4C22⋊D5311yescharacteristic
478C2×C22⋊C4C22⋊D5311yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1061no—
482C2×C42—1061no—
483C2×C42C22×D5311yescharacteristic
484C4⋊C8—1062no—
485#103—1062no—
486#103—1062no—
487#103—2121no—
488#103—2121no—
489C22⋊C8—1062no—
490C22⋊C8—1062no—
491C4×C8—1062no—
492#95—1061no—
493#95—1061no—
494#95—1061no—
495#95—1061no—
496#95—1061no—
497C24C2×C22⋊D5311yescharacteristic
498C24C2×C22⋊D5311yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×Dic5312yes—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4C22⋊Dic5314yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—1061no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—4241no—
528C22×C4—2122no—
529C22×C4—2122no—
530C22×C4C22×Dic5312yes—
531C22×C4C22×Dic5312yes—
532C22×C4C2×C22⋊D5311yescharacteristic
533C22×C4C2×C22⋊D5311yescharacteristic
534C22×C4C2×C22⋊D5311yescharacteristic
535C22×C4C2×C22⋊D5311yescharacteristic
536C22×C4C2×C22⋊D5312yes—
537C22×C4C2×C22⋊D5312yes—
538C22×C4C23×D5311yescharacteristic
539C2×C8—532no—
540C2×C8—1061no—
541C2×C8—1061no—
542C2×C8—1061no—
543C2×C8—1061no—
544C2×C8—1061no—
545C2×C8—1061no—
546C2×C8—1061no—
547C2×C8—1061no—
548C2×C8—1061no—
549C2×C8—1061no—
550C2×C8—1061no—
551C2×C8—2124no—
552C2×C8—2124no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—532no—
563C4⋊C4—1061no—
564C4⋊C4—1061no—
565C4⋊C4—1061no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C4⋊C4—1061no—
569C4⋊C4—1061no—
570C4⋊C4—2122no—
571C4⋊C4C22⋊Dic5314yes—
572C4⋊C4C22×Dic5312yes—
573C4⋊C4C22×Dic5312yes—
574C4⋊C4C22×Dic5312yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—4241no—
579C22⋊C4—2122no—
580C22⋊C4—2122no—
581C22⋊C4C22⋊Dic5314yes—
582C22⋊C4C22⋊Dic5314yes—
583C42—24no—
584C42—24no—
585C42—4241no—
586C42—2122no—
587C42C22×Dic5312yes—
588C42C2×C22⋊D5312yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23C2×C22⋊Dic5312yes—
600C23C2×C22⋊Dic5312yes—
601C23#1313323712yes—
602C23#1313323712yes—
603C23C22×C22⋊D5311yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—48no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—1062no—
639C2×C4—4244no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4C2×C22⋊Dic5312yes—
652C2×C4C2×C22⋊Dic5312yes—
653C2×C4C2×C22⋊Dic5312yes—
654C2×C4C2×C22⋊Dic5312yes—
655C2×C4C23×Dic5311yescharacteristic
656C2×C4C22×C22⋊D5311yescharacteristic
657C2×C4#41×D5311yescharacteristic
658C2×C4#41×D5311yescharacteristic
659C2×C4#1313326311yescharacteristic
660C2×C4#1313326411yescharacteristic
661C8—1062no—
662C8—2121no—
663C8—2121no—
664C8—2121no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22#1681061914yes—
679C22C22×C22⋊Dic5311yescharacteristic
680C22#1681126111yescharacteristic
681C22#1681127211yescharacteristic
682C22C2×#1313323711yescharacteristic
683C22C2×#1313323711yescharacteristic
684C22#1681143111yescharacteristic
685C22#1681143811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—4241no—
695C4—4241no—
696C4—4241no—
697C4—2122no—
698C4#41×Dic5311yescharacteristic
699C4#1681110611yescharacteristic
700C4#1681126111yescharacteristic
701C4#1681127211yescharacteristic
702C2—24no—
703C2—42no—
704C2#2027754511yescharacteristic
705C2C2×#1681061911yescharacteristic
706C2#2028324811yescharacteristic
707C2#2028654411yescharacteristic
708C2#2028659611yescharacteristic
709C2#2028707711yescharacteristic
710C2#2028709411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
cosocleC22×C4×C53C24
hypercenterC2×#552D53
hypocenterC53#22486
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #20275681C2semidirect
4. #20275673C2semidirect
5. #20275139C2semidirect
6. #20275139C2semidirect
7. #20275028C2semidirect
8. #20275023C2semidirect
9. #20274810C2semidirect
10. #20274801C2semidirect
11. #20274730C2semidirect
12. C4×#13133141C2semidirect
13. #20274431C2semidirect
14. C2×#16810385C2semidirect
50. C53×#552C4semidirect
108. #125×C53C2×C4semidirect
113. C22⋊Q8×C53C2×C4semidirect
115. C4×Q8×C53C2×C4semidirect
120. #117×C53C2×C4semidirect
374. #552Dic53semidirect
417. C53#22486semidirect
437. #125C2×Dic53semidirect
442. C22⋊Q8C2×Dic53semidirect
444. C4×Q8C2×Dic53semidirect
451. #117C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#883222
#202776442
#202756812
#202756732
#202751392
#202750282
#202750232
#202748102
#202748012
#202747302
C4×#131331412
#202744312
C2×#168103852
C2×C53×#5522
#2248653