Finite Group Databasebeta

← #27417799

Subgroups — #27417799

Order 13568.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810944C211yesmaximal, characteristic, complemented
2C2×#16810663C211yesmaximal, characteristic, complemented
3#20279012C211yesmaximal, characteristic, complemented
4#20276045C211yesmaximal, characteristic, complemented
5#20276040C211yesmaximal, characteristic, complemented
6#20275901C211yesmaximal, characteristic, complemented
7#20275894C211yesmaximal, characteristic, complemented
8#20275154C211yesmaximal, characteristic, complemented
9#20275013C211yesmaximal, characteristic, complemented
10#20274976C211yesmaximal, characteristic, complemented
11#20274962C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274903C211yesmaximal, characteristic, complemented
14#20274805C211yesmaximal, characteristic, complemented
15C2×C53×#547C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18#16810944—24no—
19#16810663—24no—
20C2×#13133150C2211yescharacteristic
21C2×#13133150C2211yescharacteristic
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×C22⋊#88322C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33#16810551—21no—
34#16810537—21no—
35#16810521C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810511—21no—
38#16810504—21no—
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C22×#41×C53—21no—
51C53×#547—24no—
52C53×#547—24no—
53C2×C4⋊Q8×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#123×C53—21no—
56C2×C22⋊Q8×C53—21no—
57C2×#121×C53C2211yescharacteristic
58C2×#121×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C2×#11719917—22no—
64C2×#11719917—22no—
65C2×#11719917—22no—
66C22×#88322C2311yescharacteristic
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70#13133176—22no—
71#13133176—22no—
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C4⋊Dic53C2311yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C22⋊Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133150—22no—
85#13133150—22no—
86#13133148—22no—
87#13133148—22no—
88#13133148—22no—
89#13133138—22no—
90#13133138—22no—
91#13133138—22no—
92#13133138—22no—
93C22⋊#88322—22no—
94C22⋊#88322—22no—
95C22⋊#88322—22no—
96#13133124—21no—
97#13133124—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101C2×#41×C53—28no—
102C2×#41×C53—44no—
103C2×#41×C53—44no—
104C22×Q8×C53—21no—
105C22×D4×C53—21no—
106C22×D4×C53—21no—
107C22×D4×C53D411yescharacteristic
108C22×D4×C53C2311yescharacteristic
109C23×C4×C53—21no—
110C23×C4×C53—21no—
111C23×C4×C53—21no—
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
114C4⋊Q8×C53—22no—
115C4⋊Q8×C53—22no—
116#123×C53—28no—
117#123×C53—28no—
118C22⋊Q8×C53—28no—
119#121×C53—22no—
120#121×C53—22no—
121#121×C53—22no—
122#121×C53D414yes—
123C4×D4×C53—22no—
124C4×D4×C53—22no—
125C4×D4×C53—22no—
126C4×D4×C53—22no—
127C2×C4⋊C4×C53—22no—
128C2×C4⋊C4×C53—22no—
129C2×C4⋊C4×C53—21no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53D414yes—
134C2×C4⋊C4×C53D411yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C22⋊C4×C53—21no—
139C2×C22⋊C4×C53—21no—
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53D411yescharacteristic
142C2×C22⋊C4×C53D411yescharacteristic
143C2×C42×C53C2311yescharacteristic
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146C24×C53C2×D411yescharacteristic
147#41×C53—432no—
148C2×Q8×C53—24no—
149C2×Q8×C53—42no—
150C2×Q8×C53—42no—
151C2×D4×C53—22no—
152C2×D4×C53—22no—
153C2×D4×C53—24no—
154C2×D4×C53—24no—
155C2×D4×C53—22no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
165C2×D4×C53C2×D412yes—
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—24no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—42no—
183C22×C4×C53—42no—
184C22×C4×C53—42no—
185C22×C4×C53—42no—
186C22×C4×C53—42no—
187C22×C4×C53—42no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C4⋊C4×C53—24no—
200C4⋊C4×C53—24no—
201C4⋊C4×C53—24no—
202C4⋊C4×C53—22no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53C2×D412yes—
207C4⋊C4×C53C2×D412yes—
208C4⋊C4×C53C2×D412yes—
209C22⋊C4×C53—24no—
210C22⋊C4×C53—24no—
211C22⋊C4×C53—22no—
212C22⋊C4×C53—24no—
213C22⋊C4×C53—22no—
214C42×C53—21no—
215C42×C53—21no—
216C22⋊Dic53—42no—
217C22⋊Dic53—42no—
218C22⋊Dic53—81no—
219C22⋊Dic53—81no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228#11719919—42no—
229#11719919—81no—
230C4×Dic53—42no—
231#11719917—28no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322#4112yescomplemented
243C2×#88322#4112yescomplemented
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—21no—
256C23×C53—22no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53#12012yes—
264C23×C53AGL(1,ℤ/8)12yes—
265C23×C53C22×D411yescharacteristic
266Q8×C53—48no—
267D4×C53—28no—
268D4×C53—22no—
269D4×C53—22no—
270D4×C53—48no—
271D4×C53—48no—
272D4×C53—41no—
273D4×C53—41no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—48no—
292C2×C4×C53—48no—
293C2×C4×C53—48no—
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—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53#12012yes—
305C2×C4×C53AGL(1,ℤ/8)12yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4111yescharacteristic
309C2×C4×C53C2×#4111yescharacteristic
310C2×C4×C532−1+411yescharacteristic
311C2×C4×C532−1+411yescharacteristic
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—41no—
323C2×Dic53—41no—
324#88322—22no—
325#88322—22no—
326#88322—41no—
327#88322—41no—
328#24100—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—42no—
346C22×C53—81no—
347C22×C53—81no—
348C22×C53—81no—
349C22×C53—81no—
350C22×C53C2×#12011yescharacteristic
351C22×C53#54711yescharacteristic
352C22×C53#54711yescharacteristic
353C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C53#57711yescharacteristic
356C22×C53#57811yescharacteristic
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—41no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53—42no—
363C4×C53—41no—
364C4×C53#52511yescharacteristic
365C4×C53#53611yescharacteristic
366C4×C53#54711yescharacteristic
367C4×C53#54711yescharacteristic
368Dic53—81no—
369Dic53—81no—
370Dic53—81no—
371Dic53—81no—
372C2×#547D5311yescharacteristic
373C2×#482—531no—
374C2×#428—531no—
375#2485—531no—
376#2058—531no—
377#2057—531no—
378#2034—531no—
379#2033—531no—
380#1895—531no—
381#1870—531no—
382#1864—531no—
383#1862—531no—
384#1853—531no—
385#1852—531no—
386#1824—531no—
387C2×C53—42no—
388C2×C53—42no—
389C2×C53—82no—
390C2×C53#240611yescharacteristic
391C2×C53#300311yescharacteristic
392C2×C53#301311yescharacteristic
393C2×C53#334311yescharacteristic
394C2×C53#334511yescharacteristic
395C2×C53#335311yescharacteristic
396C2×C53#335411yescharacteristic
397C22×#41—21no—
398C22×M16—531no—
399#547—24no—
400#547—24no—
401C2×C4⋊Q8C2×D5311yescharacteristic
402C2×#123—21no—
403C2×#123—21no—
404C2×C22⋊Q8—21no—
405C2×#121C2×D5311yescharacteristic
406C2×#121C2×D5311yescharacteristic
407C2×C4×D4C2×D5311yescharacteristic
408C2×C4×D4C2×D5311yescharacteristic
409C2×#117—531no—
410C22×C4⋊C4C2×D5311yescharacteristic
411C22×C4⋊C4C2×D5311yescharacteristic
412#482—1064no—
413#428—1064no—
414C2×#107—531no—
415C2×#107—531no—
416C2×#107—531no—
417C2×#106—531no—
418C2×#106—531no—
419C2×#106—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×C22⋊C8—531no—
425C2×C22⋊C8—531no—
426C2×C22⋊C8—531no—
427#397—1061no—
428#394—1061no—
429#389—531no—
430#389—531no—
431#388—1061no—
432#387—1061no—
433#380—531no—
434#380—531no—
435#380—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#340—531no—
441#340—531no—
442#336—531no—
443#336—531no—
444C53#2410011yescharacteristic, complemented, Sylow
445C2×#41—28no—
446C2×#41—44no—
447C2×#41—44no—
448C22×Q8—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C22⋊D5311yescharacteristic
452C22×D4C22×D5311yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4C22×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C2×M16—1062no—
459C2×M16—1062no—
460C2×M16—1062no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C4⋊Q8—22no—
466C4⋊Q8—22no—
467#123—28no—
468#123—28no—
469C22⋊Q8—28no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121C22⋊D5314yes—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478#117—1062no—
479#117—1062no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4C22⋊D5311yescharacteristic
493C2×C4⋊C4C22⋊D5314yes—
494C2×C4⋊C4C22×D5311yescharacteristic
495C2×C4⋊C4C22×D5311yescharacteristic
496C2×C4⋊C4C22×D5311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C22⋊C4C22⋊D5311yescharacteristic
505C2×C22⋊C4C22⋊D5311yescharacteristic
506C2×C42—1061no—
507C2×C42C22×D5311yescharacteristic
508#107—1062no—
509#107—1062no—
510#107—1062no—
511#106—1062no—
512#106—1062no—
513#106—1062no—
514#102—1062no—
515#102—1062no—
516#102—1062no—
517#102—1062no—
518C22⋊C8—1062no—
519C22⋊C8—1062no—
520C22⋊C8—1062no—
521#95—1061no—
522#95—1061no—
523#95—1061no—
524#95—1061no—
525#95—1061no—
526C24—21no—
527C24C2×C22⋊D5311yescharacteristic
528C24C2×C22⋊D5311yescharacteristic
529#41—432no—
530C2×Q8—24no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C2×C22⋊D5312yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5312yes—
578C22×C4C2×C22⋊D5312yes—
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C23×D5311yescharacteristic
581M16—1068no—
582C2×C8—532no—
583C2×C8—532no—
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—1061no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—4241no—
610C4⋊C4—2122no—
611C4⋊C4C2×C22⋊D5312yes—
612C4⋊C4C2×C22⋊D5312yes—
613C4⋊C4C2×C22⋊D5312yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—4241no—
620C22⋊C4—4241no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C42—21no—
624C42—21no—
625C42—2122no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#1313318612yes—
646C23#1313324312yes—
647C23C22×C22⋊D5311yescharacteristic
648Q8—48no—
649D4—28no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—48no—
654D4—41no—
655D4—41no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
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—2121no—
698C2×C4#1313318612yes—
699C2×C4#1313324312yes—
700C2×C4C22×C22⋊D5311yescharacteristic
701C2×C4C22×C22⋊D5311yescharacteristic
702C2×C4#41×D5311yescharacteristic
703C2×C4#41×D5311yescharacteristic
704C2×C4#1313326411yescharacteristic
705C2×C4#1313326411yescharacteristic
706C8—1062no—
707C8—1062no—
708C8—2121no—
709C8—2121no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#1313318611yescharacteristic
732C22#1681127211yescharacteristic
733C22#1681127211yescharacteristic
734C22C2×#1313324311yescharacteristic
735C22C2×#1313324311yescharacteristic
736C22#1681143111yescharacteristic
737C22#1681143811yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—41no—
745C4—4241no—
746C4—4241no—
747C4—4241no—
748C4—4241no—
749C4#1681113011yescharacteristic
750C4#1681119411yescharacteristic
751C4#1681127211yescharacteristic
752C4#1681127211yescharacteristic
753C2—42no—
754C2—42no—
755C2—82no—
756C2#2027804611yescharacteristic
757C2#2028394211yescharacteristic
758C2#2028403011yescharacteristic
759C2#2028714911yescharacteristic
760C2#2028718511yescharacteristic
761C2#2028729911yescharacteristic
762C2#2028731011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#547C2
socleC23×C53C22×D4
hypercenterC2×#547D53
hypocenterC53#24100
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16810944C2semidirect
2. C2×#16810663C2semidirect
3. #20279012C2semidirect
4. #20276045C2semidirect
5. #20276040C2semidirect
6. #20275901C2semidirect
7. #20275894C2semidirect
8. #20275154C2semidirect
9. #20275013C2semidirect
10. #20274976C2semidirect
11. #20274962C2semidirect
12. #20274908C2semidirect
13. #20274903C2semidirect
14. #20274805C2semidirect
242. C2×#88322#41semidirect
243. C2×#88322#41semidirect
444. C53#24100semidirect

Maximal subgroups

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

subgroupindex
C2×#168109442
C2×#168106632
#202790122
#202760452
#202760402
#202759012
#202758942
#202751542
#202750132
#202749762
#202749622
#202749082
#202749032
#202748052
C2×C53×#5472
#2410053