Finite Group Databasebeta

← #27404530

Subgroups — #27404530

Order 13568.

1218 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810766C211yesmaximal, characteristic
2C2×#16810733C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic, complemented
4#20277546C211yesmaximal, characteristic, complemented
5#20275568C211yesmaximal, characteristic, complemented
6#20275404C211yesmaximal, characteristic, complemented
7#20275349C211yesmaximal, characteristic, complemented
8#20275154C211yesmaximal, characteristic, complemented
9#20275066C211yesmaximal, characteristic, complemented
10#20275049C211yesmaximal, characteristic, complemented
11#20274975C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13C4×#13133137C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#2361C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×D212C2211yescharacteristic
22#16810766C418yescomplemented
23#16810733—24no—
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26#16810622—24no—
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810529C2211yescharacteristic
39#16810529C2211yescharacteristic
40#16810499—21no—
41#16810499—21no—
42#16810485—21no—
43#16810483C2211yescharacteristic
44#95×D53—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C2×#121×C53C2211yescharacteristic
52C2×C4×D4×C53—21no—
53C2×C4×D4×C53C2211yescharacteristic
54C22×C4⋊C4×C53C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#389C2211yescharacteristic
57C53×#388—21no—
58C53×#386—21no—
59C53×#385—21no—
60C4×C4⋊C4×C53C2211yescharacteristic
61C4×C22⋊C4×C53C2211yescharacteristic
62C2×#11719945—22no—
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C2×#11719945C2×C414yescomplemented
68C22×Dic106C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C22×C22⋊D53—21no—
71C22×C4×D53—21no—
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C2×#11719923—41no—
75C2×#11719923—41no—
76C2×#11719923C2×C414yescomplemented
77C2×#11719922—22no—
78C2×#11719922—22no—
79C2×#11719922C2×C414yescomplemented
80C2×#11719917—22no—
81C2×#11719917—22no—
82C2×#11719917—41no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C4×D212—22no—
88C4×D212—22no—
89C4×D212—41no—
90C4×D212—41no—
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C22⋊Dic53—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96#13133148—22no—
97#13133148—41no—
98#13133140—22no—
99#13133140—22no—
100#13133140C2×C414yescomplemented
101#13133138—22no—
102#13133138—41no—
103#13133137—22no—
104#13133137C2×C414yescomplemented
105#13133137D414yescomplemented
106C22⋊#88322C2×C414yescomplemented
107#13133128—22no—
108C4×#88322—41no—
109#13133124—21no—
110#13133124—21no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114C22×D4×C53—21no—
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119#121×C53—22no—
120#121×C53C2×C414yescomplemented
121C4×D4×C53—22no—
122C4×D4×C53—41no—
123C4×D4×C53—44no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—21no—
126C2×C4⋊C4×C53—22no—
127C2×C4⋊C4×C53—41no—
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53C2311yescharacteristic
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×C53C2311yescharacteristic
139C2×C42×C53C2311yescharacteristic
140#95×C53—21no—
141#95×C53—21no—
142#95×C53D411yescharacteristic
143#95×C53D411yescharacteristic
144C24×C53—21no—
145C24×C53C2×D411yescharacteristic
146C23×D53—21no—
147C2×D4×C53—24no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—21no—
153C2×D4×C53—42no—
154C2×D4×C53—42no—
155C2×D4×C53C22×C412yes—
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—42no—
164C22×C4×C53—42no—
165C22×C4×C53—42no—
166C22×C4×C53—42no—
167C22×C4×C53—81no—
168C22×C4×C53—81no—
169C22×C4×C53C22×C412yes—
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53#4112yes—
176C22×C4×C53C2411yescharacteristic
177C2×C22⋊D53—24no—
178C2×C22⋊D53—42no—
179C2×C22⋊D53—42no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183#11719945—28no—
184#11719945—44no—
185#11719945—44no—
186#11719945—44no—
187C2×D212—21no—
188C2×D212—21no—
189C2×D212—21no—
190C2×D212C22×C412yes—
191C2×D212C2×D412yes—
192C2×D212#4112yes—
193C2×C4×D53—24no—
194C2×C4×D53—42no—
195C2×C4×D53—42no—
196C2×C4×D53—42no—
197C2×C4×D53—42no—
198C2×C4×D53—42no—
199C2×C4×D53—42no—
200C2×C4×D53—81no—
201C2×C4×D53—81no—
202C2×Dic106—21no—
203C2×Dic106—21no—
204C2×Dic106—21no—
205C2×Dic106—21no—
206C2×Dic106—21no—
207C2×Dic106C22×C412yes—
208C4⋊C4×C53—21no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53—42no—
213C4⋊C4×C53—42no—
214C4⋊C4×C53C22×C412yes—
215C4⋊C4×C53C2×D412yes—
216C22⋊C4×C53—24no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—41no—
219C22⋊C4×C53—42no—
220C22⋊C4×C53—42no—
221C22⋊C4×C53—81no—
222C42×C53—21no—
223C42×C53—21no—
224C42×C53—21no—
225C42×C53—21no—
226C42×C53—42no—
227C22⋊Dic53—81no—
228#11719923—44no—
229#11719922—28no—
230#11719921—42no—
231#11719921—42no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—21no—
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—22no—
266C22×D53—22no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271D4×C53—22no—
272D4×C53—22no—
273D4×C53—48no—
274D4×C53—41no—
275D4×C53—41no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
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—22no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
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—84no—
303C2×C4×C53—84no—
304C2×C4×C53C4×D412yes—
305C2×C4×C53AGL(1,ℤ/8)12yes—
306C2×C4×C53C23×C411yescharacteristic
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C2×#4111yescharacteristic
309C2×C4×C53C2×#4111yescharacteristic
310C2×C4×C53H(5,𝔽2)11yescharacteristic
311C2×C4×C53H(5,𝔽2)11yescharacteristic
312C22⋊D53—48no—
313C2×Dic53—22no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322D212—22no—
323D212—22no—
324D212—22no—
325D212C4×D414yescomplemented
326C4×D53—48no—
327C4×D53—84no—
328C4×D53—84no—
329Dic106—22no—
330Dic106—22no—
331Dic106—41no—
332Dic106—41no—
333#88322—22no—
334#88322—22no—
335#88322—22no—
336#88322—41no—
337#22866—531nomaximal, Sylow
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—42no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—81no—
349C22×C53—81no—
350C22×C53—81no—
351C22×C53—81no—
352C22×C53C2×C4×D411yescharacteristic
353C22×C53D4211yescharacteristic
354C22×C53#54611yescharacteristic
355C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C53#57511yescharacteristic
357C22×C53#57711yescharacteristic
358C22×C53#57711yescharacteristic
359C2×D53—24no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C4×C53—22no—
367C4×C53—22no—
368C4×C53—42no—
369C4×C53—41no—
370C4×C53—42no—
371C4×C53—41no—
372C4×C53—41no—
373C4×C53—81no—
374C4×C53C2×C4×D411yescharacteristic
375C4×C53#51811yescharacteristic
376C4×C53#54611yescharacteristic
377C4×C53#55111yescharacteristic
378Dic53—42no—
379Dic53—81no—
380Dic53—81no—
381C2×#449—531no—
382C2×#442—531no—
383C2×#417—531no—
384#2361D5311yescharacteristic, complemented
385#2339—531no—
386#1968—531no—
387#1935—531no—
388#1927—531no—
389#1895—531no—
390#1879—531no—
391#1877—531no—
392#1864—531no—
393#1853—531no—
394C4×#102—531no—
395#1753—531no—
396C2×C53—42no—
397C2×C53—82no—
398C2×C53#235811yescharacteristic
399C2×C53C4×AGL(1,ℤ/8)11yescharacteristic
400C2×C53#295211yescharacteristic
401C2×C53#327211yescharacteristic
402C2×C53#327511yescharacteristic
403C2×C53#330611yescharacteristic
404C2×C53#330711yescharacteristic
405D53—44no—
406C22×#41—531no—
407C22×SD16—531no—
408C22×D8—531no—
409C22×M16—531no—
410C2×#121C2×D5311yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4—531no—
413C2×C4×D4—531no—
414C2×C4×D4C2×D5311yescharacteristic
415C22×C4⋊C4C2×D5311yescharacteristic
416#449—538no—
417#442—1064no—
418C2×#106—531no—
419C2×#106—531no—
420#417—1064no—
421C2×#103—531no—
422C2×#103—531no—
423C2×#103—531no—
424C2×#102—531no—
425C2×#102—531no—
426C2×#102—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×C22⋊C8—531no—
430C2×#97—531no—
431C2×C4×C8—531no—
432#391—531no—
433#391—531no—
434#390C2×D5311yescharacteristic
435#389C2×D5311yescharacteristic
436#388—21no—
437#386—21no—
438#386—1061no—
439#386—1061no—
440#385—21no—
441#381—1061no—
442#380—531no—
443C4×C4⋊C4C2×D5311yescharacteristic
444C4×C22⋊C4C2×D5311yescharacteristic
445C2×#95—1061no—
446#340—531no—
447#340—531no—
448#340—531no—
449#340—531no—
450#336—531no—
451#336—531no—
452C53#2286611yescharacteristic, complemented, Sylow
453C2×#41—534no—
454C2×#41—1062no—
455C2×#41—1062no—
456C2×#41—1062no—
457C2×#41—2121no—
458C2×#41—2121no—
459C22×Q8—531no—
460C22×D4—21no—
461C22×D4—531no—
462C22×D4—1061no—
463C22×D4C22×D5311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—1061no—
467C23×C4—1061no—
468C23×C4—1061no—
469C23×C4C22×D5311yescharacteristic
470C2×SD16—534no—
471C2×SD16—2121no—
472C2×SD16—2121no—
473C2×D8—534no—
474C2×D8—1062no—
475C2×D8—1062no—
476C2×M16—1062no—
477C2×M16—1062no—
478C2×M16—2121no—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8—531no—
483#121—22no—
484#121C4×D5314yescomplemented
485C4×D4—22no—
486C4×D4—41no—
487C4×D4—44no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—2121no—
491C4×D4—2121no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4C22×D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—1061no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4C22⋊D5311yescharacteristic
509C2×C22⋊C4C22⋊D5311yescharacteristic
510C2×C42—21no—
511C2×C42C22×D5311yescharacteristic
512C2×C42C22×D5311yescharacteristic
513#106—1062no—
514#106—2121no—
515#103—534no—
516#103—1062no—
517#103—1062no—
518#102—534no—
519#102—534no—
520#102—1062no—
521#102—1062no—
522#102—2121no—
523C22⋊C8—534no—
524#97—1062no—
525C4×C8—2121no—
526#95—21no—
527#95—21no—
528#95—1061no—
529#95—1061no—
530#95—1061no—
531#95—1061no—
532#95—1061no—
533#95C22⋊D5311yescharacteristic
534#95C22⋊D5311yescharacteristic
535C24—21no—
536C24—1061no—
537C24C2×C22⋊D5311yescharacteristic
538#41—1068no—
539#41—2124no—
540#41—2124no—
541#41—2124no—
542C2×Q8—532no—
543C2×Q8—1061no—
544C2×Q8—1061no—
545C2×Q8—1061no—
546C2×Q8—1061no—
547C2×Q8—1061no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—532no—
557C2×D4—532no—
558C2×D4—532no—
559C2×D4—1064no—
560C2×D4—1061no—
561C2×D4—1061no—
562C2×D4—1061no—
563C2×D4—2122no—
564C2×D4—2122no—
565C2×D4C2×C4×D5312yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4—1061no—
580C22×C4—1064no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—4241no—
584C22×C4—4241no—
585C22×C4—2122no—
586C22×C4—2122no—
587C22×C4—2122no—
588C22×C4—2122no—
589C22×C4—2122no—
590C22×C4—2122no—
591C22×C4C2×C4×D5312yes—
592C22×C4#1171994512yes—
593C22×C4C2×C22⋊D5311yescharacteristic
594C22×C4C2×C22⋊D5311yescharacteristic
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C23×D5311yescharacteristic
599SD16—2124no—
600D8—1068no—
601M16—2124no—
602C2×C8—532no—
603C2×C8—532no—
604C2×C8—532no—
605C2×C8—1061no—
606C2×C8—1061no—
607C2×C8—1061no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—1061no—
613C2×C8—1061no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—1061no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1061no—
624C4⋊C4C2×C4×D5312yes—
625C4⋊C4D4×D5312yes—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—41no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—4241no—
633C22⋊C4—2122no—
634C22⋊C4—2122no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—42no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—1062no—
654C23—1062no—
655C23—1062no—
656C23—2121no—
657C23—2121no—
658C23—2121no—
659C23—2121no—
660C23C4×C22⋊D5312yes—
661C23C22×C22⋊D5311yescharacteristic
662Q8—1062no—
663Q8—1062no—
664Q8—2121no—
665Q8—2121no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—41no—
670D4—41no—
671D4—534no—
672D4—1062no—
673D4—1062no—
674D4—1062no—
675D4—2128no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
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—22no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—1062no—
705C2×C4—4244no—
706C2×C4—4244no—
707C2×C4—2128no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4—2121no—
713C2×C4—2121no—
714C2×C4—2121no—
715C2×C4—2121no—
716C2×C4C4×C22⋊D5312yes—
717C2×C4#1313324312yes—
718C2×C4C22×C4×D5311yescharacteristic
719C2×C4C2×D4×D5311yescharacteristic
720C2×C4#41×D5311yescharacteristic
721C2×C4C2×#1171994511yescharacteristic
722C2×C4#1313326211yescharacteristic
723C2×C4#1313326311yescharacteristic
724C8—1062no—
725C8—1062no—
726C8—1062no—
727C8—2121no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—1064no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22—2122no—
749C22C2×C4×C22⋊D5311yescharacteristic
750C22D4×C22⋊D5311yescharacteristic
751C22#1681126111yescharacteristic
752C22C2×#1313324311yescharacteristic
753C22#1681142111yescharacteristic
754C22#1681143111yescharacteristic
755C22#1681143411yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—81no—
764C4—4241no—
765C4—4241no—
766C4—2122no—
767C4C4×D4×D5311yescharacteristic
768C4#1681109511yescharacteristic
769C4#1681126911yescharacteristic
770C4#1681130211yescharacteristic
771C2—42no—
772C2—82no—
773C2—2124no—
774C2#2027769211yescharacteristic
775C2C4×#1313324311yescharacteristic
776C2#2028359611yescharacteristic
777C2#2028631111yescharacteristic
778C2#2028634711yescharacteristic
779C2#2028667011yescharacteristic
780C2#2028668511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2361C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
cosocleC22×C4×C53C24
hypercenter#2361D53
hypocenterC53#22866
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#16810733C2semidirect
3. C2×#16810622C2semidirect
4. #20277546C2semidirect
5. #20275568C2semidirect
6. #20275404C2semidirect
7. #20275349C2semidirect
8. #20275154C2semidirect
9. #20275066C2semidirect
10. #20275049C2semidirect
11. #20274975C2semidirect
12. #20274908C2semidirect
13. C4×#13133137C2semidirect
14. #20274499C2semidirect
15. C53×#2361C2semidirect
22. #16810766C4semidirect
67. C2×#11719945C2×C4semidirect
76. C2×#11719923C2×C4semidirect
79. C2×#11719922C2×C4semidirect
100. #13133140C2×C4semidirect
104. #13133137C2×C4semidirect
105. #13133137D4semidirect
106. C22⋊#88322C2×C4semidirect
120. #121×C53C2×C4semidirect
325. D212C4×D4semidirect
384. #2361D53semidirect
452. C53#22866semidirect
484. #121C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107662
C2×#168107332
C2×#168106222
#202775462
#202755682
#202754042
#202753492
#202751542
#202750662
#202750492
#202749752
#202749082
C4×#131331372
#202744992
C53×#23612
#2286653