Finite Group Databasebeta

← #27404394

Subgroups — #27404394

Order 13568.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810768C211yesmaximal, characteristic
2C2×#16810726C211yesmaximal, characteristic, complemented
3#20277753C211yesmaximal, characteristic, complemented
4#20277556C211yesmaximal, characteristic, complemented
5#20275588C211yesmaximal, characteristic, complemented
6#20275409C211yesmaximal, characteristic, complemented
7#20275338C211yesmaximal, characteristic, complemented
8#20275143C211yesmaximal, characteristic, complemented
9#20275068C211yesmaximal, characteristic, complemented
10#20275060C211yesmaximal, characteristic, complemented
11#20274981C211yesmaximal, characteristic, complemented
12#20274914C211yesmaximal, characteristic, complemented
13#20274547C211yesmaximal, characteristic, complemented
14#20274491C211yesmaximal, characteristic, complemented
15C2×C53×#416C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×Q8×Dic53C2211yescharacteristic
20C2×Q8×Dic53C2211yescharacteristic
21C2×#13133179C2211yescharacteristic
22#16810768C418yescomplemented
23#16810726—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133139C2211yescharacteristic
28C2×#13133139C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33#16810526—21no—
34#16810526—21no—
35#16810526C2211yescharacteristic
36#16810526C2211yescharacteristic
37#16810524C2211yescharacteristic
38#16810523—21no—
39#16810519C2211yescharacteristic
40#16810514—21no—
41#16810499—21no—
42#16810483—21no—
43#16810483C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45C4×#11719921—21no—
46C4×C22⋊Dic53—21no—
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×#41×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×#117×C53C2211yescharacteristic
57C53×#416—24no—
58C2×#103×C53C2211yescharacteristic
59C2×#103×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×#102×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C22×C4×D53—21no—
65C2×#11719924—22no—
66C2×#11719924—22no—
67C2×#11719924C2×C414yes—
68C2×#11719922—41no—
69C2×#11719922—41no—
70C2×#11719922C2×C414yes—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133191—22no—
74#13133191C2×C414yes—
75Q8×Dic53—22no—
76Q8×Dic53—22no—
77Q8×Dic53—41no—
78Q8×Dic53—41no—
79#13133179—22no—
80#13133179—41no—
81C2×C4⋊Dic53—21no—
82C2×C4⋊Dic53—21no—
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×#11719919—21no—
87C2×C22⋊Dic53—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53D411yescharacteristic
93C2×C22⋊Dic53D411yescharacteristic
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100C2×C4×Dic53—21no—
101C2×C4×Dic53C2311yescharacteristic
102C2×C4×Dic53C2311yescharacteristic
103#13133150—22no—
104#13133148—41no—
105#13133141C2×C414yescomplemented
106#13133139—22no—
107#13133139—41no—
108#13133138C2×C414yescomplemented
109C22⋊#88322C2×C414yescomplemented
110#13133127—22no—
111#13133127—41no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115#13133124D411yescharacteristic
116#13133124D411yescharacteristic
117C2×#41×C53—22no—
118C2×#41×C53—22no—
119C2×#41×C53—22no—
120C2×#41×C53—41no—
121C2×#41×C53—41no—
122C2×#41×C53C2×C414yescomplemented
123C22×Q8×C53C2311yescharacteristic
124C22×D4×C53—21no—
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128C22×C8×C53—22no—
129C22×C8×C53—22no—
130C22×C8×C53—41no—
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133#117×C53—22no—
134#117×C53—41no—
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C22⋊C4×C53—21no—
138C2×C42×C53—21no—
139#103×C53—22no—
140#103×C53D414yescomplemented
141#102×C53—22no—
142#102×C53—22no—
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146#41×C53—28no—
147#41×C53—44no—
148#41×C53—44no—
149#41×C53—44no—
150C2×Q8×C53—21no—
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53C22×C412yes—
154C2×Q8×C53C2×D412yes—
155C2×Q8×C53#4112yes—
156C2×D4×C53—24no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—42no—
163C2×D4×C53—42no—
164C2×D4×C53C22×C412yes—
165C22×C4×C53—21no—
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—42no—
174C22×C4×C53—42no—
175C22×C4×C53C22×C412yes—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53#4112yes—
178C22×C4×C53C2411yescharacteristic
179C2×C22⋊D53—24no—
180C2×C22⋊D53—81no—
181C2×C22⋊D53—81no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53C2×D411yescharacteristic
186C22×Dic53C2×D411yescharacteristic
187C22×Dic53C2×D411yescharacteristic
188C22×Dic53C2×D411yescharacteristic
189C2×D212—21no—
190C2×D212—21no—
191C2×D212—21no—
192C2×D212—21no—
193C2×D212—21no—
194C2×D212C22×C412yes—
195C2×C4×D53—42no—
196C2×C4×D53—42no—
197C2×C4×D53—81no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—44no—
204C2×C8×C53C2×D412yes—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53C2×D412yes—
209C22⋊C4×C53—42no—
210C42×C53—42no—
211C22⋊Dic53—41no—
212C22⋊Dic53—41no—
213C22⋊Dic53—42no—
214C22⋊Dic53—42no—
215C22⋊Dic53—81no—
216C22⋊Dic53—81no—
217C22⋊Dic53—81no—
218#11719924—28no—
219#11719922—44no—
220#11719921—24no—
221#11719921—42no—
222#11719921—42no—
223#11719921—81no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—42no—
230C4⋊Dic53—42no—
231C4⋊Dic53C22×C412yes—
232#11719919—81no—
233C4×Dic53—21no—
234C4×Dic53—21no—
235C4×Dic53—21no—
236C4×Dic53—21no—
237C4×Dic53—42no—
238C4×Dic53—42no—
239C4×Dic53—81no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322C22×C412yes—
245C2×#88322C22×C412yes—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—22no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53C4×D412yes—
260C23×C53C22×D411yescharacteristic
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268Q8×C53—22no—
269Q8×C53—22no—
270Q8×C53—22no—
271Q8×C53C4×D414yes—
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—48no—
275D4×C53—41no—
276D4×C53—41no—
277C2×C4×C53—22no—
278C2×C4×C53—21no—
279C2×C4×C53—22no—
280C2×C4×C53—21no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—48no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53C4×D412yes—
294C2×C4×C53C23×C411yescharacteristic
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C22⋊D53—84no—
301C2×Dic53—22no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
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—41no—
325D212—41no—
326C4×D53—84no—
327C8×C53—22no—
328C8×C53—41no—
329#88322—22no—
330#88322—22no—
331#22857—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—81no—
343C22×C53—81no—
344C22×C53—81no—
345C22×C53—81no—
346C22×C53C2×C4×D411yescharacteristic
347C22×C53D4211yescharacteristic
348C22×C53#54611yescharacteristic
349C22×C53#57511yescharacteristic
350C22×C53#57511yescharacteristic
351C22×C53#57611yescharacteristic
352C22×C53#57711yescharacteristic
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—81no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C4×C53—22no—
361C4×C53—24no—
362C4×C53—42no—
363C4×C53—81no—
364C4×C53C2×C4×D411yescharacteristic
365C4×C53#51811yescharacteristic
366C4×C53#54611yescharacteristic
367C4×C53#55111yescharacteristic
368Dic53—42no—
369Dic53—41no—
370Dic53—41no—
371Dic53—41no—
372Dic53—41no—
373Dic53—81no—
374Dic53—81no—
375C2×#449—531no—
376C2×#440—531no—
377C2×#416D5311yescharacteristic, complemented
378#2363—531no—
379#2341—531no—
380#1972—531no—
381#1936—531no—
382#1925—531no—
383#1893—531no—
384#1880—531no—
385#1879—531no—
386#1865—531no—
387#1854—531no—
388#1763—531no—
389#1752—531no—
390C2×C53—42no—
391C2×C53—82no—
392C2×C53#235811yescharacteristic
393C2×C53#294311yescharacteristic
394C2×C53#294611yescharacteristic
395C2×C53#326811yescharacteristic
396C2×C53#327111yescharacteristic
397C2×C53#330911yescharacteristic
398C2×C53#332111yescharacteristic
399D53—82no—
400C22×#41C2×D5311yescharacteristic
401C22×SD16—531no—
402C22×D8—531no—
403C23×C8C2×D5311yescharacteristic
404C2×#121—531no—
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×D4—531no—
408C2×#117C2×D5311yescharacteristic
409#449—538no—
410#440—1064no—
411C2×#107—531no—
412C2×#106—531no—
413#416—24no—
414C2×#103—531no—
415C2×#103C2×D5311yescharacteristic
416C2×#103C2×D5311yescharacteristic
417C2×#102—531no—
418C2×#102—531no—
419C2×#102—531no—
420C2×#102C2×D5311yescharacteristic
421C2×#102C2×D5311yescharacteristic
422C2×C22⋊C8—531no—
423C2×#97—531no—
424C2×#97—531no—
425#390—531no—
426#390—531no—
427#390—531no—
428#390—1061no—
429#390—1061no—
430#390—1061no—
431#389—531no—
432#388—1061no—
433#386—1061no—
434#380—531no—
435#380—1061no—
436C4×C4⋊C4—531no—
437C4×C22⋊C4—531no—
438C4×C22⋊C4—1061no—
439C4×C22⋊C4—1061no—
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#336—531no—
445#336—531no—
446C53#2285711yescharacteristic, complemented, Sylow
447C2×#41—22no—
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—41no—
451C2×#41—41no—
452C2×#41C4×D5314yescomplemented
453C22×Q8C22×D5311yescharacteristic
454C22×D4—21no—
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4C22×D5311yescharacteristic
458C23×C4—21no—
459C23×C4—1061no—
460C23×C4C22×D5311yescharacteristic
461C2×SD16—534no—
462C2×SD16—1062no—
463C2×SD16—1062no—
464C2×D8—534no—
465C2×D8—2121no—
466C2×D8—2121no—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—41no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8C22×D5311yescharacteristic
473C22×C8C22×D5311yescharacteristic
474#121—534no—
475#121—1062no—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×Q8—2121no—
479C4×Q8—2121no—
480C4×D4—1062no—
481C4×D4—2121no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—1061no—
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C4⋊C4C22×D5311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—531no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4—1061no—
503C2×C22⋊C4—1061no—
504C2×C42—21no—
505C2×C42—531no—
506C2×C42—531no—
507C2×C42—1061no—
508C2×C42—1061no—
509C2×C42—1061no—
510#107—1062no—
511#106—2121no—
512#103—22no—
513#103—534no—
514#103C22⋊D5314yescomplemented
515#102—22no—
516#102—22no—
517#102—534no—
518#102—1062no—
519#102—2121no—
520C22⋊C8—534no—
521#97—1062no—
522#97—2121no—
523#95—531no—
524#95—531no—
525#95—1061no—
526#95—1061no—
527#95—1061no—
528C24—21no—
529C24—1061no—
530C24D4×D5311yescharacteristic
531#41—28no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D5312yes—
539C2×Q8#1171994512yes—
540C2×Q8C2×C22⋊D5312yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—532no—
550C2×D4—1064no—
551C2×D4—1061no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1061no—
555C2×D4—1061no—
556C2×D4—4241no—
557C2×D4—4241no—
558C2×D4C2×C4×D5312yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—531no—
570C22×C4—531no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—4241no—
577C22×C4—2122no—
578C22×C4—2122no—
579C22×C4C2×C4×D5312yes—
580C22×C4D4×D5311yescharacteristic
581C22×C4#1171994712yes—
582C22×C4C23×D5311yescharacteristic
583SD16—1068no—
584D8—2124no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8—532no—
592C2×C8—532no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8C2×C22⋊D5312yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—532no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—4241no—
608C4⋊C4—2122no—
609C4⋊C4—2122no—
610C4⋊C4C2×C22⋊D5312yes—
611C22⋊C4—42no—
612C22⋊C4—1064no—
613C22⋊C4—4241no—
614C22⋊C4—4241no—
615C22⋊C4—4241no—
616C22⋊C4—4241no—
617C22⋊C4—2122no—
618C22⋊C4—2122no—
619C22⋊C4—2121no—
620C22⋊C4—2121no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C42—42no—
624C42—1061no—
625C42—1061no—
626C42—1061no—
627C42—1061no—
628C42—4241no—
629C42—2122no—
630C42—2122no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—1062no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23#1313317712yes—
652C23C2×D4×D5311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×C22⋊D5314yes—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—1062no—
663D4—1062no—
664D4—4244no—
665D4—2121no—
666D4—2121no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—1062no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1061no—
690C2×C4—1061no—
691C2×C4—1061no—
692C2×C4—1061no—
693C2×C4—1061no—
694C2×C4—1061no—
695C2×C4—1061no—
696C2×C4—4244no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4#1313317712yes—
706C2×C4C22×C4×D5311yescharacteristic
707C2×C4C22×C22⋊D5311yescharacteristic
708C2×C4C2×#1171994711yescharacteristic
709C2×C4C2×#1171994511yescharacteristic
710C2×C4#1313326211yescharacteristic
711C2×C4#1313326211yescharacteristic
712C8—22no—
713C8—41no—
714C8—1062no—
715C8—1062no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—4241no—
731C22—4241no—
732C22—4241no—
733C22—4241no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22C2×#1313317711yescharacteristic
738C22D4×C22⋊D5311yescharacteristic
739C22#1681126311yescharacteristic
740C22#1681142011yescharacteristic
741C22#1681142011yescharacteristic
742C22#1681142511yescharacteristic
743C22#1681143011yescharacteristic
744C4—22no—
745C4—24no—
746C4—42no—
747C4—81no—
748C4—4241no—
749C4—4241no—
750C4—2121no—
751C4—2121no—
752C4—2122no—
753C4—2121no—
754C4—2121no—
755C4C2×C4×C22⋊D5311yescharacteristic
756C4#1681109611yescharacteristic
757C4#1681126711yescharacteristic
758C4#1681129911yescharacteristic
759C2—42no—
760C2—82no—
761C2—4242no—
762C2#2027769411yescharacteristic
763C2#2028351111yescharacteristic
764C2#2028355011yescharacteristic
765C2#2028625511yescharacteristic
766C2#2028630011yescharacteristic
767C2#2028671711yescharacteristic
768C2#2028689711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#416C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
cosocleC22×C4×C53C24
hypercenterC2×#416D53
hypocenterC53#22857
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#16810726C2semidirect
3. #20277753C2semidirect
4. #20277556C2semidirect
5. #20275588C2semidirect
6. #20275409C2semidirect
7. #20275338C2semidirect
8. #20275143C2semidirect
9. #20275068C2semidirect
10. #20275060C2semidirect
11. #20274981C2semidirect
12. #20274914C2semidirect
13. #20274547C2semidirect
14. #20274491C2semidirect
15. C2×C53×#416C2semidirect
22. #16810768C4semidirect
105. #13133141C2×C4semidirect
108. #13133138C2×C4semidirect
109. C22⋊#88322C2×C4semidirect
122. C2×#41×C53C2×C4semidirect
140. #103×C53D4semidirect
377. C2×#416D53semidirect
446. C53#22857semidirect
452. C2×#41C4×D53semidirect
514. #103C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107682
C2×#168107262
#202777532
#202775562
#202755882
#202754092
#202753382
#202751432
#202750682
#202750602
#202749812
#202749142
#202745472
#202744912
C2×C53×#4162
#2285753