Finite Group Databasebeta

← #27404395

Subgroups — #27404395

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×#16810766C211yesmaximal, characteristic
2C2×#16810723C211yesmaximal, characteristic, complemented
3C2×#16810617C211yesmaximal, characteristic, complemented
4#20277555C211yesmaximal, characteristic, complemented
5#20275590C211yesmaximal, characteristic, complemented
6#20275411C211yesmaximal, characteristic, complemented
7#20275335C211yesmaximal, characteristic, complemented
8#20275144C211yesmaximal, characteristic, complemented
9#20275073C211yesmaximal, characteristic, complemented
10#20275063C211yesmaximal, characteristic, complemented
11#20274982C211yesmaximal, characteristic, complemented
12#20274914C211yesmaximal, characteristic, complemented
13#20274548C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15C53×#2363C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20C2×C4×Dic106C2211yescharacteristic
21C2×C4×Dic106C2211yescharacteristic
22#16810766C418yescomplemented
23#16810723—24no—
24C2×#13133150C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26#16810617—24no—
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×#13133128C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810525C2211yescharacteristic
40#16810523—21no—
41#16810523—21no—
42#16810483C2211yescharacteristic
43#16810482—21no—
44#16810470—21no—
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C2×#121×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C2×#117×C53C2211yescharacteristic
54C53×#390—21no—
55C53×#390C2211yescharacteristic
56C53×#389C2211yescharacteristic
57C53×#388—21no—
58C53×#386—21no—
59C4×C4⋊C4×C53C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
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—
72C2×#11719923—22no—
73C2×#11719923—22no—
74C2×#11719923C2×C414yes—
75C2×#11719922—41no—
76C2×#11719922—41no—
77C2×#11719922C2×C414yes—
78C22×#88322—22no—
79C22×#88322—22no—
80C22×#88322—41no—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C4×Dic106—22no—
86C4×Dic106—22no—
87C4×Dic106—41no—
88C4×Dic106—41no—
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×#11719919—21no—
92C2×#11719919—21no—
93C2×C22⋊Dic53—21no—
94C2×#11719921—21no—
95C2×#11719921—21no—
96C2×#11719921—21no—
97C2×#11719921—21no—
98C2×C4×Dic53—21no—
99C2×C4×Dic53—21no—
100#13133150—22no—
101#13133148—41no—
102#13133140—22no—
103#13133140C2×C414yescomplemented
104#13133140D414yescomplemented
105#13133138—22no—
106#13133138—41no—
107#13133137—22no—
108#13133137—22no—
109#13133137C2×C414yescomplemented
110C22⋊#88322C2×C414yescomplemented
111#13133128—22no—
112#13133128—41no—
113#13133124—21no—
114C22×D4×C53—21no—
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53C2311yescharacteristic
118#121×C53—22no—
119#121×C53C2×C414yes—
120C4×D4×C53—22no—
121C4×D4×C53—41no—
122#117×C53—22no—
123#117×C53—41no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C42×C53—21no—
136C2×C42×C53—21no—
137C2×C42×C53C2311yescharacteristic
138C2×C42×C53C2311yescharacteristic
139#95×C53—21no—
140#95×C53—21no—
141#95×C53D411yescharacteristic
142#95×C53D411yescharacteristic
143C24×C53—21no—
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C2×D4×C53—24no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—21no—
152C2×D4×C53—81no—
153C2×D4×C53—81no—
154C2×D4×C53C22×C412yes—
155C22×C4×C53—21no—
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—42no—
163C22×C4×C53—42no—
164C22×C4×C53—81no—
165C22×C4×C53C22×C412yes—
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53#4112yes—
172C22×C4×C53C2411yescharacteristic
173C2×C22⋊D53—24no—
174C2×C22⋊D53—42no—
175C2×C22⋊D53—42no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179#11719945—28no—
180#11719945—44no—
181#11719945—44no—
182#11719945—44no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212—21no—
186C2×D212—21no—
187C2×D212—21no—
188C2×D212C22×C412yes—
189C2×C4×D53—24no—
190C2×C4×D53—42no—
191C2×C4×D53—42no—
192C2×Dic106—21no—
193C2×Dic106—21no—
194C2×Dic106—21no—
195C2×Dic106C22×C412yes—
196C2×Dic106C2×D412yes—
197C2×Dic106#4112yes—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—81no—
203C4⋊C4×C53C22×C412yes—
204C4⋊C4×C53C2×D412yes—
205C22⋊C4×C53—24no—
206C22⋊C4×C53—41no—
207C22⋊C4×C53—41no—
208C22⋊C4×C53—42no—
209C22⋊C4×C53—42no—
210C22⋊C4×C53—42no—
211C22⋊C4×C53—81no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—42no—
217C42×C53—81no—
218C22⋊Dic53—81no—
219#11719923—28no—
220#11719922—44no—
221#11719921—42no—
222#11719921—42no—
223#11719921—81no—
224#11719921—81no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229#11719919—42no—
230#11719919—42no—
231C4×Dic53—42no—
232C4×Dic53—42no—
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—44no—
243C2×#88322C22×C412yes—
244C2×#88322C22×C412yes—
245C2×#88322C2×D412yes—
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—
268D4×C53—22no—
269D4×C53—22no—
270D4×C53—41no—
271D4×C53—41no—
272D4×C53—84no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
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—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
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—21no—
292C2×C4×C53—21no—
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×C53C4×D412yes—
302C2×C4×C53C23×C411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C22⋊D53—48no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318D212—22no—
319D212—22no—
320D212—41no—
321D212—41no—
322C4×D53—48no—
323Dic106—22no—
324Dic106—22no—
325Dic106—22no—
326Dic106C4×D414yes—
327#88322—22no—
328#88322—22no—
329#88322—22no—
330#88322—41no—
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—42no—
362C4×C53—41no—
363C4×C53—42no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—81no—
368C4×C53C2×C4×D411yescharacteristic
369C4×C53#51811yescharacteristic
370C4×C53#54611yescharacteristic
371C4×C53#55111yescharacteristic
372Dic53—24no—
373Dic53—81no—
374Dic53—81no—
375C2×#449—531no—
376C2×#440—531no—
377C2×#416—531no—
378#2363D5311yescharacteristic, complemented
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×#41—531no—
401C22×SD16—531no—
402C22×D8—531no—
403C23×C8—531no—
404C2×#121C2×D5311yescharacteristic
405C2×C4×Q8—531no—
406C2×C4×Q8—531no—
407C2×C4×D4C2×D5311yescharacteristic
408C2×#117C2×D5311yescharacteristic
409#449—538no—
410#440—1064no—
411C2×#107—531no—
412C2×#106—531no—
413#416—1064no—
414C2×#103—531no—
415C2×#103—531no—
416C2×#103—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×C22⋊C8—531no—
423C2×#97—531no—
424C2×#97—531no—
425#390—21no—
426#390—531no—
427#390—531no—
428#390—1061no—
429#390—1061no—
430#390C2×D5311yescharacteristic
431#389C2×D5311yescharacteristic
432#388—21no—
433#386—21no—
434#380—531no—
435#380—1061no—
436C4×C4⋊C4C2×D5311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—1061no—
439C4×C22⋊C4C2×D5311yescharacteristic
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#336—531no—
445#336—531no—
446C53#2285711yescharacteristic, complemented, Sylow
447C2×#41—534no—
448C2×#41—1062no—
449C2×#41—1062no—
450C2×#41—1062no—
451C2×#41—2121no—
452C2×#41—2121no—
453C22×Q8—531no—
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—531no—
468C22×C8—531no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8—1062no—
472C22×C8—1062no—
473C22×C8—2121no—
474#121—22no—
475#121C4×D5314yes—
476C4×Q8—1062no—
477C4×Q8—1062no—
478C4×Q8—2121no—
479C4×Q8—2121no—
480C4×D4—22no—
481C4×D4—41no—
482#117—22no—
483#117—41no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C4⋊C4C22×D5311yescharacteristic
491C2×C4⋊C4C22×D5311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C22⋊C4C22⋊D5311yescharacteristic
503C2×C22⋊C4C22⋊D5311yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—1061no—
507C2×C42—1061no—
508C2×C42C22×D5311yescharacteristic
509C2×C42C22×D5311yescharacteristic
510#107—1062no—
511#106—2121no—
512#103—534no—
513#103—534no—
514#103—1062no—
515#102—534no—
516#102—1062no—
517#102—1062no—
518#102—1062no—
519#102—2121no—
520C22⋊C8—534no—
521#97—1062no—
522#97—2121no—
523#95—21no—
524#95—21no—
525#95—1061no—
526#95C22⋊D5311yescharacteristic
527#95C22⋊D5311yescharacteristic
528C24—21no—
529C24—1061no—
530C24C2×C22⋊D5311yescharacteristic
531#41—1068no—
532#41—2124no—
533#41—2124no—
534#41—2124no—
535C2×Q8—532no—
536C2×Q8—532no—
537C2×Q8—532no—
538C2×Q8—1061no—
539C2×Q8—1061no—
540C2×Q8—1061no—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—532no—
550C2×D4—1064no—
551C2×D4—1061no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1061no—
555C2×D4—1061no—
556C2×D4—2122no—
557C2×D4—2122no—
558C2×D4C2×C4×D5312yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—81no—
569C22×C4—1061no—
570C22×C4—1064no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4C2×C4×D5312yes—
576C22×C4#1171994512yes—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C23×D5311yescharacteristic
583SD16—1068no—
584D8—2124no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—1061no—
591C2×C8—1061no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—2124no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—81no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—2122no—
608C4⋊C4—2122no—
609C4⋊C4C2×C4×D5312yes—
610C4⋊C4D4×D5312yes—
611C22⋊C4—24no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—81no—
618C22⋊C4—4241no—
619C22⋊C4—4241no—
620C22⋊C4—4241no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—42no—
628C42—81no—
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—
651C23C4×C22⋊D5312yes—
652C23C22×C22⋊D5311yescharacteristic
653Q8—534no—
654Q8—1062no—
655Q8—1062no—
656Q8—1062no—
657D4—22no—
658D4—22no—
659D4—41no—
660D4—41no—
661D4—84no—
662D4—1062no—
663D4—1062no—
664D4—2128no—
665D4—2121no—
666D4—2121no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—84no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—2128no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4C4×C22⋊D5312yes—
706C2×C4C22×C4×D5311yescharacteristic
707C2×C4C2×D4×D5311yescharacteristic
708C2×C4#41×D5311yescharacteristic
709C2×C4C2×#1171994511yescharacteristic
710C2×C4#1313326211yescharacteristic
711C2×C4#1313326311yescharacteristic
712C8—1062no—
713C8—1062no—
714C8—1062no—
715C8—2121no—
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×C4×C22⋊D5311yescharacteristic
738C22D4×C22⋊D5311yescharacteristic
739C22#1681126111yescharacteristic
740C22#1681142111yescharacteristic
741C22#1681142111yescharacteristic
742C22#1681142611yescharacteristic
743C22#1681143411yescharacteristic
744C4—22no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—42no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—1064no—
753C4—4241no—
754C4—4241no—
755C4C4×D4×D5311yescharacteristic
756C4#1681109511yescharacteristic
757C4#1681126911yescharacteristic
758C4#1681130211yescharacteristic
759C2—42no—
760C2—82no—
761C2—4242no—
762C2#2027769211yescharacteristic
763C2#2028351311yescharacteristic
764C2#2028354711yescharacteristic
765C2#2028625111yescharacteristic
766C2#2028629611yescharacteristic
767C2#2028671511yescharacteristic
768C2#2028689511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2363C2
socleC23×C53C22×D4
prime radicalC2×#16810766C2
cosocleC22×C4×C53C24
hypercenter#2363D53
hypocenterC53#22857
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#16810723C2semidirect
3. C2×#16810617C2semidirect
4. #20277555C2semidirect
5. #20275590C2semidirect
6. #20275411C2semidirect
7. #20275335C2semidirect
8. #20275144C2semidirect
9. #20275073C2semidirect
10. #20275063C2semidirect
11. #20274982C2semidirect
12. #20274914C2semidirect
13. #20274548C2semidirect
14. #20274493C2semidirect
15. C53×#2363C2semidirect
22. #16810766C4semidirect
67. C2×#11719945C2×C4semidirect
103. #13133140C2×C4semidirect
104. #13133140D4semidirect
109. #13133137C2×C4semidirect
110. C22⋊#88322C2×C4semidirect
378. #2363D53semidirect
446. C53#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#168107662
C2×#168107232
C2×#168106172
#202775552
#202755902
#202754112
#202753352
#202751442
#202750732
#202750632
#202749822
#202749142
#202745482
#202744932
C53×#23632
#2285753