Finite Group Databasebeta

← #27404480

Subgroups — #27404480

Order 13568.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C2×#16810624C211yesmaximal, characteristic, complemented
4#20277729C211yesmaximal, characteristic, complemented
5#20275580C211yesmaximal, characteristic, complemented
6#20275415C211yesmaximal, characteristic, complemented
7#20275332C211yesmaximal, characteristic, complemented
8#20275151C211yesmaximal, characteristic, complemented
9#20275070C211yesmaximal, characteristic, complemented
10#20275066C211yesmaximal, characteristic, complemented
11#20274969C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13C4×#13133141C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2341C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×#13133177—21no—
22C22×C4⋊Dic53C2211yescharacteristic
23#16810768C418yescomplemented
24#16810721—24no—
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27#16810624—24no—
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38C2×C4×#88322C2211yescharacteristic
39#16810525C2211yescharacteristic
40#16810521C2211yescharacteristic
41#16810515—21no—
42#16810500—21no—
43#16810497—21no—
44C4×C4⋊Dic53C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C2×C4×Q8×C53C2211yescharacteristic
54C53×#390—21no—
55C53×#390—21no—
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#380—21no—
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C4×C22⋊C4×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C22×C4×D53—21no—
66C2×#11719924—22no—
67C2×#11719924—22no—
68C2×#11719924C2×C414yescomplemented
69C2×#11719922—41no—
70C2×#11719922—41no—
71C2×#11719922C2×C414yescomplemented
72C2×#11719917—22no—
73C2×#11719917—22no—
74C2×#11719917—41no—
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79#13133191—22no—
80#13133191C2×C414yes—
81C4×D212—22no—
82C4×D212—41no—
83#13133177—44no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—22no—
86C2×C4⋊Dic53—41no—
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×#11719919—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×C4×Dic53—21no—
96#13133150—22no—
97#13133150—41no—
98#13133141—22no—
99#13133141C2×C414yescomplemented
100#13133141D414yescomplemented
101#13133138—22no—
102#13133138—22no—
103#13133138C2×C414yescomplemented
104#13133137—22no—
105#13133137—41no—
106C22⋊#88322C2×C414yescomplemented
107#13133128—22no—
108C4×#88322—41no—
109#13133124—21no—
110#13133124—21no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—22no—
114C2×#41×C53—41no—
115C2×#41×C53—41no—
116C2×#41×C53C2×C414yescomplemented
117C22×Q8×C53C2311yescharacteristic
118C22×D4×C53—21no—
119C22×D4×C53C2311yescharacteristic
120C23×C4×C53—21no—
121C23×C4×C53C2311yescharacteristic
122C4×Q8×C53—22no—
123C4×Q8×C53—22no—
124C4×Q8×C53—41no—
125C4×Q8×C53—41no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C22⋊C4×C53D411yescharacteristic
137C2×C42×C53—21no—
138C2×C42×C53—21no—
139C2×C42×C53C2311yescharacteristic
140C2×C42×C53C2311yescharacteristic
141#95×C53—21no—
142#95×C53D411yescharacteristic
143#95×C53D411yescharacteristic
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146C23×D53—21no—
147#41×C53—28no—
148#41×C53—44no—
149#41×C53—44no—
150#41×C53—44no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53C22×C412yes—
155C2×Q8×C53C2×D412yes—
156C2×Q8×C53#4112yes—
157C2×D4×C53—24no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—42no—
164C2×D4×C53—42no—
165C2×D4×C53C22×C412yes—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—24no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53C22×C412yes—
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53#4112yes—
183C22×C4×C53C2411yescharacteristic
184C2×C22⋊D53—24no—
185C2×C22⋊D53—42no—
186C2×C22⋊D53—42no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—42no—
191C22×Dic53—42no—
192C22×Dic53—81no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212—21no—
196C2×D212—21no—
197C2×D212—21no—
198C2×D212C22×C412yes—
199C2×C4×D53—42no—
200C2×C4×D53—42no—
201C2×C4×D53—81no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53—42no—
208C22⋊C4×C53—22no—
209C22⋊C4×C53—41no—
210C22⋊C4×C53—42no—
211C22⋊C4×C53—42no—
212C22⋊C4×C53—81no—
213C22⋊C4×C53—81no—
214C22⋊C4×C53—81no—
215C42×C53—21no—
216C42×C53—21no—
217C42×C53—21no—
218C42×C53—21no—
219C42×C53—42no—
220C42×C53—42no—
221#11719924—28no—
222#11719922—44no—
223#11719921—24no—
224#11719921—42no—
225#11719921—42no—
226#11719921—81no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—42no—
232C4⋊Dic53C22×C412yes—
233C4⋊Dic53C2×D412yes—
234#11719919—42no—
235C4×Dic53—42no—
236#11719917—44no—
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×#88322C22×C412yes—
247C2×#88322C22×C412yes—
248C2×#88322C2×D412yes—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53C4×D412yes—
263C23×C53C22×D411yescharacteristic
264C22×D53—22no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271Q8×C53—22no—
272Q8×C53—22no—
273Q8×C53—22no—
274Q8×C53C4×D414yescomplemented
275D4×C53—22no—
276D4×C53—22no—
277D4×C53—48no—
278D4×C53—41no—
279D4×C53—41no—
280C2×C4×C53—22no—
281C2×C4×C53—21no—
282C2×C4×C53—22no—
283C2×C4×C53—21no—
284C2×C4×C53—22no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—48no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53C4×D412yes—
308C2×C4×C53AGL(1,ℤ/8)12yes—
309C2×C4×C53C23×C411yescharacteristic
310C2×C4×C53C22×D411yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×C4×C53C2×#4111yescharacteristic
313C2×C4×C53H(5,𝔽2)11yescharacteristic
314C2×C4×C53H(5,𝔽2)11yescharacteristic
315C22⋊D53—48no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—84no—
326D212—22no—
327D212—22no—
328D212—41no—
329D212—41no—
330C4×D53—84no—
331#88322—22no—
332#88322—22no—
333#88322—22no—
334#88322—41no—
335#22863—531nomaximal, Sylow
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—22no—
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×C4×D411yescharacteristic
351C22×C53D4211yescharacteristic
352C22×C53#54611yescharacteristic
353C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C53#57511yescharacteristic
355C22×C53#57611yescharacteristic
356C22×C53#57811yescharacteristic
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—81no—
361C2×D53—81no—
362C2×D53—81no—
363C2×D53—81no—
364C4×C53—22no—
365C4×C53—24no—
366C4×C53—22no—
367C4×C53—41no—
368C4×C53—41no—
369C4×C53—41no—
370C4×C53—81no—
371C4×C53—81no—
372C4×C53C2×C4×D411yescharacteristic
373C4×C53#51811yescharacteristic
374C4×C53#54611yescharacteristic
375C4×C53#55111yescharacteristic
376Dic53—42no—
377Dic53—42no—
378Dic53—81no—
379C2×#449—531no—
380C2×#440—531no—
381C2×#417—531no—
382#2361—531no—
383#2341D5311yescharacteristic, complemented
384#1970—531no—
385#1936—531no—
386#1925—531no—
387#1895—531no—
388#1880—531no—
389#1879—531no—
390#1863—531no—
391#1852—531no—
392C4×#103—531no—
393#1753—531no—
394C2×C53—42no—
395C2×C53—82no—
396C2×C53#235811yescharacteristic
397C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C53#295111yescharacteristic
399C2×C53#327411yescharacteristic
400C2×C53#327711yescharacteristic
401C2×C53#330811yescharacteristic
402C2×C53#330911yescharacteristic
403D53—82no—
404C22×#41C2×D5311yescharacteristic
405C22×SD16—531no—
406C22×D8—531no—
407C22×M16—531no—
408C2×#121—531no—
409C2×C4×Q8C2×D5311yescharacteristic
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×D4—531no—
412C2×C4×D4—1061no—
413C22×C4⋊C4—531no—
414#449—538no—
415#440—1064no—
416C2×#107—531no—
417C2×#107—531no—
418#417—1064no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×#102—531no—
425C2×#102—531no—
426C2×#102—531no—
427C2×C22⋊C8—531no—
428C2×#97—531no—
429C2×C4×C8—531no—
430#390—21no—
431#390—21no—
432#390—531no—
433#390C2×D5311yescharacteristic
434#390C2×D5311yescharacteristic
435#389—531no—
436#388—1061no—
437#386—1061no—
438#385—1061no—
439#380—21no—
440#380C2×D5311yescharacteristic
441C4×C4⋊C4—531no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2×D5311yescharacteristic
444#340—531no—
445#340—531no—
446#340—531no—
447#340—531no—
448#336—531no—
449#336—531no—
450C53#2286311yescharacteristic, complemented, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C4×D5314yescomplemented
457C22×Q8C22×D5311yescharacteristic
458C22×D4—21no—
459C22×D4—531no—
460C22×D4—1061no—
461C22×D4C22×D5311yescharacteristic
462C23×C4—21no—
463C23×C4—1061no—
464C23×C4—1061no—
465C23×C4C22×D5311yescharacteristic
466C2×SD16—534no—
467C2×SD16—1062no—
468C2×SD16—1062no—
469C2×D8—534no—
470C2×D8—2121no—
471C2×D8—2121no—
472C2×M16—1062no—
473C2×M16—1062no—
474C2×M16—2121no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479#121—534no—
480#121—1062no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—41no—
484C4×Q8—41no—
485C4×D4—1062no—
486C4×D4—2121no—
487C4×D4—2124no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—1062no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—2121no—
497C2×C4⋊C4C22×D5311yescharacteristic
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1061no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4C22⋊D5311yescharacteristic
509C2×C22⋊C4C22⋊D5311yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—1061no—
513C2×C42C22×D5311yescharacteristic
514C2×C42C22×D5311yescharacteristic
515#107—1062no—
516#107—2121no—
517#103—534no—
518#103—534no—
519#103—1062no—
520#102—534no—
521#102—1062no—
522#102—1062no—
523#102—1062no—
524#102—2121no—
525C22⋊C8—534no—
526#97—1062no—
527C4×C8—2121no—
528#95—21no—
529#95—1061no—
530#95—1061no—
531#95C22⋊D5311yescharacteristic
532#95C22⋊D5311yescharacteristic
533C24—21no—
534C24—1061no—
535C24C2×C22⋊D5311yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D5312yes—
544C2×Q8D4×D5312yes—
545C2×Q8#1171994712yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—532no—
555C2×D4—1064no—
556C2×D4—1061no—
557C2×D4—1061no—
558C2×D4—1061no—
559C2×D4—1061no—
560C2×D4—1061no—
561C2×D4—2122no—
562C2×D4—2122no—
563C2×D4C2×C4×D5312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—4241no—
578C22×C4—4241no—
579C22×C4—2122no—
580C22×C4—2122no—
581C22×C4—2122no—
582C22×C4—2122no—
583C22×C4C2×C4×D5312yes—
584C22×C4#1171994512yes—
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C2×C22⋊D5311yescharacteristic
589C22×C4C2×C22⋊D5311yescharacteristic
590C22×C4C23×D5311yescharacteristic
591SD16—1068no—
592D8—2124no—
593M16—2124no—
594C2×C8—532no—
595C2×C8—532no—
596C2×C8—532no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—532no—
613C4⋊C4—532no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—2122no—
619C4⋊C4—2122no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—1064no—
628C22⋊C4—4241no—
629C22⋊C4—2122no—
630C22⋊C4—2122no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—42no—
637C42—2122no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—1062no—
652C23—2121no—
653C23—2121no—
654C23—2121no—
655C23—2121no—
656C23—2121no—
657C23—2121no—
658C23C4×C22⋊D5312yes—
659C23C22×C22⋊D5311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8#1313317714yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—1062no—
670D4—1062no—
671D4—2128no—
672D4—2121no—
673D4—2121no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—4244no—
704C2×C4—4244no—
705C2×C4—2121no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4C4×C22⋊D5312yes—
713C2×C4#1313324212yes—
714C2×C4C22×C4×D5311yescharacteristic
715C2×C4C2×D4×D5311yescharacteristic
716C2×C4C2×#1171994711yescharacteristic
717C2×C4C2×#1171994511yescharacteristic
718C2×C4#1313326211yescharacteristic
719C2×C4#1313326211yescharacteristic
720C8—1062no—
721C8—1062no—
722C8—1062no—
723C8—2121no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—4241no—
739C22—4241no—
740C22—4241no—
741C22—4241no—
742C22—2122no—
743C22—2122no—
744C22—2122no—
745C22C2×C4×C22⋊D5311yescharacteristic
746C22D4×C22⋊D5311yescharacteristic
747C22#1681126711yescharacteristic
748C22C2×#1313324211yescharacteristic
749C22#1681142111yescharacteristic
750C22#1681142611yescharacteristic
751C22#1681143811yescharacteristic
752C4—22no—
753C4—24no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—4241no—
761C4—2122no—
762C4—2122no—
763C4C2×#1313317711yescharacteristic
764C4#1681109611yescharacteristic
765C4#1681126311yescharacteristic
766C4#1681129911yescharacteristic
767C2—42no—
768C2—82no—
769C2—4242no—
770C2#2027769411yescharacteristic
771C2C4×#1313324211yescharacteristic
772C2#2028358811yescharacteristic
773C2#2028633511yescharacteristic
774C2#2028636811yescharacteristic
775C2#2028670611yescharacteristic
776C2#2028672111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2341C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenter#2341D53
hypocenterC53#22863
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#16810721C2semidirect
3. C2×#16810624C2semidirect
4. #20277729C2semidirect
5. #20275580C2semidirect
6. #20275415C2semidirect
7. #20275332C2semidirect
8. #20275151C2semidirect
9. #20275070C2semidirect
10. #20275066C2semidirect
11. #20274969C2semidirect
12. #20274902C2semidirect
13. C4×#13133141C2semidirect
14. #20274499C2semidirect
15. C53×#2341C2semidirect
23. #16810768C4semidirect
68. C2×#11719924C2×C4semidirect
71. C2×#11719922C2×C4semidirect
99. #13133141C2×C4semidirect
100. #13133141D4semidirect
103. #13133138C2×C4semidirect
106. C22⋊#88322C2×C4semidirect
116. C2×#41×C53C2×C4semidirect
274. Q8×C53C4×D4semidirect
383. #2341D53semidirect
450. C53#22863semidirect
456. C2×#41C4×D53semidirect
663. Q8#13133177semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C2×#168107212
C2×#168106242
#202777292
#202755802
#202754152
#202753322
#202751512
#202750702
#202750662
#202749692
#202749022
C4×#131331412
#202744992
C53×#23412
#2286353