Finite Group Databasebeta

← #27436958

Subgroups — #27436958

Order 13568.

1158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810958C211yesmaximal, characteristic, complemented
2C2×#16810862C211yesmaximal, characteristic, complemented
3#20278166C211yesmaximal, characteristic
4#20276040C211yesmaximal, characteristic, complemented
5#20275915C211yesmaximal, characteristic, complemented
6#20275853C211yesmaximal, characteristic, complemented
7#20275723C211yesmaximal, characteristic, complemented
8#20275056C211yesmaximal, characteristic, complemented
9#20275023C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20275008C211yesmaximal, characteristic
12#20274969C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C2×C53×#554C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×#13133196C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21#16810958—24no—
22#16810862—24no—
23C2×#13133150C2211yescharacteristic
24C2×#13133150C2211yescharacteristic
25C2×#13133150C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133140C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35#16810556—21no—
36#16810546—21no—
37#16810529C2211yescharacteristic
38#16810521C2211yescharacteristic
39#16810503—21no—
40#16810483C2211yescharacteristic
41#16810481—21no—
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C53×#554—24no—
51C53×#554—24no—
52C2×C4⋊Q8×C53C2211yescharacteristic
53C2×#125×C53—21no—
54C2×C22⋊Q8×C53—21no—
55C2×C22⋊Q8×C53—21no—
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×C22⋊Q8×C53C2211yescharacteristic
58C2×C4×Q8×C53C2211yescharacteristic
59C2×C4×D4×C53—21no—
60C2×C4×D4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719925—22no—
66C2×#11719925—22no—
67C2×#11719925—41no—
68C22×#88322—22no—
69C22×#88322—22no—
70C22×#88322—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133196—22no—
76#13133196—22no—
77#13133196—22no—
78#13133196—41no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—41no—
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×#11719919—21no—
86C2×#11719919—21no—
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91#13133150—22no—
92#13133150—22no—
93#13133150—22no—
94#13133141—22no—
95#13133141—22no—
96#13133141—41no—
97#13133140—22no—
98#13133140—22no—
99#13133140—22no—
100C22⋊#88322—22no—
101C22⋊#88322—22no—
102C22⋊#88322—41no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107C22×Q8×C53—21no—
108C22×Q8×C53C2311yescharacteristic
109C22×D4×C53D411yescharacteristic
110C23×C4×C53—21no—
111C23×C4×C53—21no—
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114C4⋊Q8×C53—22no—
115C4⋊Q8×C53—22no—
116#125×C53—28no—
117C22⋊Q8×C53—28no—
118C22⋊Q8×C53—28no—
119C22⋊Q8×C53—22no—
120C22⋊Q8×C53—22no—
121C22⋊Q8×C53—22no—
122C22⋊Q8×C53D414yes—
123C4×Q8×C53—22no—
124C4×Q8×C53—22no—
125C4×D4×C53—28no—
126C4×D4×C53—22no—
127C4×D4×C53—22no—
128C2×C4⋊C4×C53—22no—
129C2×C4⋊C4×C53—22no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—22no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53D414yes—
138C2×C4⋊C4×C53D411yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53D411yescharacteristic
145C2×C22⋊C4×C53D411yescharacteristic
146C2×C42×C53—21no—
147C2×C42×C53C2311yescharacteristic
148C24×C53C2×D411yescharacteristic
149C24×C53C2×D411yescharacteristic
150C2×Q8×C53—24no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—81no—
157C2×Q8×C53—81no—
158C2×Q8×C53C2×D412yes—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53Q1614yescomplemented
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—24no—
171C22×C4×C53—24no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—81no—
179C22×C4×C53—81no—
180C22×C4×C53—81no—
181C22×C4×C53—81no—
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D412yes—
186C22×C4×C53C2×D412yes—
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2411yescharacteristic
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—42no—
194C22×Dic53—42no—
195C22×Dic53—81no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106—21no—
201C2×Dic106—21no—
202C4⋊C4×C53—24no—
203C4⋊C4×C53—24no—
204C4⋊C4×C53—24no—
205C4⋊C4×C53—24no—
206C4⋊C4×C53—24no—
207C4⋊C4×C53—24no—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53C2×D412yes—
213C4⋊C4×C53C2×D412yes—
214C4⋊C4×C53C2×D412yes—
215C22⋊C4×C53—24no—
216C22⋊C4×C53—24no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C42×C53—24no—
220C42×C53—21no—
221C42×C53—21no—
222C22⋊Dic53—42no—
223C22⋊Dic53—42no—
224C22⋊Dic53—81no—
225#11719925—44no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—42no—
232C4⋊Dic53#4112yes—
233#11719919—42no—
234#11719919—42no—
235#11719919—81no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—44no—
248C2×#88322#4112yes—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53#12012yes—
260C23×C53C2×Q1612yes—
261C23×C53C2×Q1612yes—
262C23×C53#13712yes—
263C23×C53C22×D411yescharacteristic
264Q8×C53—22no—
265Q8×C53—22no—
266Q8×C53—41no—
267Q8×C53—41no—
268Q8×C53—84no—
269D4×C53—28no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—21no—
282C2×C4×C53—22no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—84no—
301C2×C4×C53—84no—
302C2×C4×C53#12012yes—
303C2×C4×C53C2×Q1612yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53C2×#4111yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×C4×C532−1+411yescharacteristic
310C2×Dic53—22no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—84no—
323Dic106—41no—
324Dic106—41no—
325Dic106—41no—
326Dic106—41no—
327#88322—22no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#25545—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53#45114yes—
346C22×C53C2×#12011yescharacteristic
347C22×C53#54611yescharacteristic
348C22×C53#54711yescharacteristic
349C22×C53C22×Q1611yescharacteristic
350C22×C53C2×#13711yescharacteristic
351C22×C53#57611yescharacteristic
352C22×C53#57711yescharacteristic
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—41no—
356C4×C53—42no—
357C4×C53—41no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53#53211yescharacteristic
362C4×C53#53711yescharacteristic
363C4×C53#54611yescharacteristic
364C4×C53#54711yescharacteristic
365Dic53—42no—
366Dic53—81no—
367Dic53—81no—
368Dic53—81no—
369C2×#554D5311yescharacteristic
370C2×#484—531no—
371C2×#467—531no—
372#2417—531no—
373#2057—531no—
374#2036—531no—
375#2024—531no—
376#2001—531no—
377#1878—531no—
378#1872—531no—
379#1872—531no—
380#1869—531no—
381#1863—531no—
382#1852—531no—
383C2×#340—531no—
384C2×C53—24no—
385C2×C53—42no—
386C2×C53#243011yescharacteristic
387C2×C53C2×#45111yescharacteristic
388C2×C53#301211yescharacteristic
389C2×C53#329911yescharacteristic
390C2×C53#331411yescharacteristic
391C2×C53#333811yescharacteristic
392C2×C53#334411yescharacteristic
393C22×Q16—531no—
394C23×C8—531no—
395#554—24no—
396#554—24no—
397C2×C4⋊Q8C2×D5311yescharacteristic
398C2×#125—21no—
399C2×C22⋊Q8—21no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8—531no—
402C2×C22⋊Q8—531no—
403C2×C22⋊Q8C2×D5311yescharacteristic
404C2×C22⋊Q8C2×D5311yescharacteristic
405C2×C4×Q8C2×D5311yescharacteristic
406C2×C4×D4—21no—
407C2×C4×D4C2×D5311yescharacteristic
408C22×C4⋊C4—531no—
409C22×C4⋊C4C2×D5311yescharacteristic
410C22×C4⋊C4C2×D5311yescharacteristic
411#484—1064no—
412#467—1064no—
413C2×#107—531no—
414C2×#107—531no—
415C2×#107—531no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×C22⋊C8—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425#398—1061no—
426#396—1061no—
427#391—531no—
428#389—531no—
429#386—1061no—
430#380—531no—
431#380—1061no—
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#340—531no—
437#340—531no—
438#336—531no—
439#336—531no—
440C53#2554511yescharacteristic, complemented, Sylow
441C22×Q8—21no—
442C22×Q8—531no—
443C22×Q8C22×D5311yescharacteristic
444C22×D4C22⋊D5311yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—1061no—
448C23×C4C22×D5311yescharacteristic
449C23×C4C22×D5311yescharacteristic
450C2×Q16—1062no—
451C2×Q16—1062no—
452C2×Q16—2121no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—1062no—
458C22×C8—1062no—
459C22×C8—2121no—
460C4⋊Q8—22no—
461C4⋊Q8—22no—
462#125—28no—
463C22⋊Q8—28no—
464C22⋊Q8—28no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—1062no—
469C22⋊Q8—1062no—
470C22⋊Q8—1062no—
471C22⋊Q8—2121no—
472C22⋊Q8C22⋊D5314yes—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×D4—28no—
476C4×D4—22no—
477C4×D4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1061no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—2121no—
496C2×C4⋊C4C22⋊D5311yescharacteristic
497C2×C4⋊C4C22⋊D5314yes—
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—1061no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4C22⋊D5311yescharacteristic
507C2×C22⋊C4C22⋊D5311yescharacteristic
508C2×C42—21no—
509C2×C42C22×D5311yescharacteristic
510#107—1062no—
511#107—1062no—
512#107—1062no—
513#103—1062no—
514#103—1062no—
515#103—1062no—
516#103—1062no—
517#103—1062no—
518#103—2121no—
519C22⋊C8—1062no—
520C22⋊C8—1062no—
521C22⋊C8—2121no—
522#95—1061no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526C24C2×C22⋊D5311yescharacteristic
527C24C2×C22⋊D5311yescharacteristic
528C2×Q8—24no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—81no—
535C2×Q8—81no—
536C2×Q8—1061no—
537C2×Q8—1061no—
538C2×Q8—1061no—
539C2×Q8—1061no—
540C2×Q8—1061no—
541C2×Q8—1061no—
542C2×Q8C2×C22⋊D5312yes—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4#1171992514yescomplemented
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1061no—
570C22×C4—4241no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5312yes—
577C22×C4C2×C22⋊D5312yes—
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C23×D5311yescharacteristic
580Q16—2124no—
581C2×C8—532no—
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—1061no—
592C2×C8—1061no—
593C2×C8—2124no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—532no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—4241no—
611C4⋊C4—2122no—
612C4⋊C4—2122no—
613C4⋊C4—2122no—
614C4⋊C4C2×C22⋊D5312yes—
615C4⋊C4C2×C22⋊D5312yes—
616C4⋊C4C2×C22⋊D5312yes—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—4241no—
622C22⋊C4—2122no—
623C22⋊C4—2122no—
624C42—24no—
625C42—21no—
626C42—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23#1313318612yes—
638C23C2×#1171992512yes—
639C23C2×#1171992512yes—
640C23#1313324812yes—
641C23C22×C22⋊D5311yescharacteristic
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8—84no—
647Q8—2121no—
648Q8—2121no—
649Q8—2121no—
650Q8—2121no—
651D4—28no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—1062no—
685C2×C4—4244no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4—2121no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4#1313318612yes—
698C2×C4C2×#1171992512yes—
699C2×C4C22×C22⋊D5311yescharacteristic
700C2×C4C22×C22⋊D5311yescharacteristic
701C2×C4#41×D5311yescharacteristic
702C2×C4#41×D5311yescharacteristic
703C2×C4#1313326311yescharacteristic
704C2×C4#1313326411yescharacteristic
705C8—1062no—
706C8—2121no—
707C8—2121no—
708C8—2121no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22#1681077914yes—
723C22C2×#1313318611yescharacteristic
724C22#1681126111yescharacteristic
725C22#1681127211yescharacteristic
726C22C22×#1171992511yescharacteristic
727C22C2×#1313324811yescharacteristic
728C22#1681142611yescharacteristic
729C22#1681143411yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—4241no—
739C4—4241no—
740C4—4241no—
741C4—2122no—
742C4#1681116911yescharacteristic
743C4#1681120111yescharacteristic
744C4#1681126111yescharacteristic
745C4#1681127211yescharacteristic
746C2—24no—
747C2—42no—
748C2#2027831911yescharacteristic
749C2C2×#1681077911yescharacteristic
750C2#2028401911yescharacteristic
751C2#2028658511yescharacteristic
752C2#2028679011yescharacteristic
753C2#2028710311yescharacteristic
754C2#2028716411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#554D53
hypocenterC53#25545
LCSG ▷ C22×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
1. C2×#16810958C2semidirect
2. C2×#16810862C2semidirect
4. #20276040C2semidirect
5. #20275915C2semidirect
6. #20275853C2semidirect
7. #20275723C2semidirect
8. #20275056C2semidirect
9. #20275023C2semidirect
10. #20275022C2semidirect
12. #20274969C2semidirect
13. #20274903C2semidirect
14. C2×#16810385C2semidirect
161. C2×D4×C53Q16semidirect
440. C53#25545semidirect
545. C2×D4#11719925semidirect

Maximal subgroups

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

subgroupindex
C2×#168109582
C2×#168108622
#202781662
#202760402
#202759152
#202758532
#202757232
#202750562
#202750232
#202750222
#202750082
#202749692
#202749032
C2×#168103852
C2×C53×#5542
#2554553