Finite Group Databasebeta

← #27416775

Subgroups — #27416775

Order 13568.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810961C211yesmaximal, characteristic, complemented
2C2×#16810944C211yesmaximal, characteristic, complemented
3#20277098C211yesmaximal, characteristic, complemented
4#20275915C211yesmaximal, characteristic, complemented
5#20275908C211yesmaximal, characteristic, complemented
6#20275901C211yesmaximal, characteristic, complemented
7#20275894C211yesmaximal, characteristic, complemented
8#20275038C211yesmaximal, characteristic, complemented
9#20275028C211yesmaximal, characteristic, complemented
10#20274914C211yesmaximal, characteristic, complemented
11#20274914C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274625C211yesmaximal, characteristic, complemented
15C2×C53×#525C211yesmaximal, characteristic
16C2×#13133176C2211yescharacteristic
17C2×#13133176C2211yescharacteristic
18#16810961—24no—
19#16810944—24no—
20C2×#13133150C2211yescharacteristic, complemented
21C2×#13133150C2211yescharacteristic, complemented
22C2×#13133148C2211yescharacteristic, complemented
23C2×#13133148C2211yescharacteristic, complemented
24C2×#13133141C2211yescharacteristic, complemented
25C2×#13133141C2211yescharacteristic, complemented
26C2×#13133141C2211yescharacteristic, complemented
27C2×#13133141C2211yescharacteristic, complemented
28C2×#13133138C2211yescharacteristic, complemented
29C2×#13133138C2211yescharacteristic, complemented
30C2×#13133138C2211yescharacteristic, complemented
31C2×#13133138C2211yescharacteristic, complemented
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38#16810486—21no—
39#16810483C2211yescharacteristic
40#16810483C2211yescharacteristic
41#16810483C2211yescharacteristic
42#16810483C2211yescharacteristic
43#16810479—21no—
44C4×C22⋊Dic53—21no—
45C4×C22⋊Dic53—21no—
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50C22×#41×C53C2211yescharacteristic
51C24×C4×C53C2211yescharacteristic
52C53×#525—24no—
53C53×#525—24no—
54C2×#123×C53—21no—
55C2×C22⋊Q8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C2×#121×C53C2211yescharacteristic
59C2×#120×C53—21no—
60C2×C4×D4×C53—21no—
61C2×C4×D4×C53—21no—
62C2×#117×C53C2211yescharacteristic
63C22×#88322C2311yescharacteristic
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67#13133176—22no—
68#13133176—22no—
69#13133176—41no—
70#13133176—41no—
71C2×C4⋊Dic53C2311yescharacteristic
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C4⋊Dic53C2311yescharacteristic
75C2×C22⋊Dic53—21no—
76C2×C22⋊Dic53—21no—
77C2×C22⋊Dic53—21no—
78C2×C22⋊Dic53—21no—
79C2×C22⋊Dic53—21no—
80C2×C22⋊Dic53—21no—
81C2×C4×Dic53—21no—
82C2×C4×Dic53—21no—
83#13133150—22no—
84#13133150—22no—
85#13133148—22no—
86#13133148—22no—
87#13133141—22no—
88#13133141—22no—
89#13133141—41no—
90#13133141—41no—
91#13133138—22no—
92#13133138—22no—
93#13133138—41no—
94#13133138—41no—
95C22⋊#88322—22no—
96C22⋊#88322—22no—
97C22⋊#88322—22no—
98C22⋊#88322—22no—
99C22⋊#88322—41no—
100C22⋊#88322—41no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C25×C53D411yescharacteristic
106C2×#41×C53—22no—
107C2×#41×C53—22no—
108C2×#41×C53—22no—
109C2×#41×C53—22no—
110C2×#41×C53—41no—
111C2×#41×C53—41no—
112C22×Q8×C53C2311yescharacteristic
113C22×D4×C53—21no—
114C22×D4×C53—21no—
115C22×D4×C53—21no—
116C22×D4×C53C2311yescharacteristic
117C23×C4×C53—21no—
118C23×C4×C53—22no—
119C23×C4×C53—22no—
120C23×C4×C53—22no—
121C23×C4×C53—22no—
122C23×C4×C53—41no—
123C23×C4×C53—41no—
124C23×C4×C53D411yescharacteristic
125C23×C4×C53D411yescharacteristic
126C23×C4×C53D411yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130#123×C53—28no—
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53—22no—
133C22⋊Q8×C53—22no—
134C22⋊Q8×C53D414yes—
135#121×C53—22no—
136#121×C53—22no—
137#121×C53—22no—
138#121×C53D414yes—
139#120×C53—28no—
140C4×D4×C53—28no—
141C4×D4×C53—28no—
142#117×C53—22no—
143#117×C53—22no—
144C2×C4⋊C4×C53—21no—
145C2×C4⋊C4×C53—21no—
146C2×C4⋊C4×C53C2311yescharacteristic
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53—21no—
150C2×C22⋊C4×C53—21no—
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C42×C53—21no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—21no—
158C24×C53—41no—
159C24×C53—41no—
160C24×C53—41no—
161C24×C53—41no—
162C24×C53C2×D411yescharacteristic
163C24×C53C2×D411yescharacteristic
164C24×C53C2×D411yescharacteristic
165#41×C53—44no—
166#41×C53—44no—
167#41×C53—44no—
168#41×C53—44no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53C2×D412yes—
175C2×D4×C53—24no—
176C2×D4×C53—24no—
177C2×D4×C53—24no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—42no—
184C2×D4×C53—42no—
185C2×D4×C53—42no—
186C2×D4×C53—42no—
187C2×D4×C53—42no—
188C2×D4×C53—42no—
189C2×D4×C53C2×D412yes—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—41no—
215C22×C4×C53—41no—
216C22×C4×C53—41no—
217C22×C4×C53—44no—
218C22×C4×C53—44no—
219C22×C4×C53—44no—
220C22×C4×C53—44no—
221C22×C4×C53—42no—
222C22×C4×C53—42no—
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53#4112yes—
229C22×C4×C53#4112yes—
230C22×C4×C53C2411yescharacteristic
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53C2×D412yes—
240C4⋊C4×C53C2×D412yes—
241C22⋊C4×C53—24no—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C42×C53—24no—
247C22⋊Dic53—42no—
248C22⋊Dic53—42no—
249C22⋊Dic53—42no—
250C22⋊Dic53—42no—
251C22⋊Dic53—42no—
252C22⋊Dic53—42no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53—21no—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4×Dic53—42no—
262C4×Dic53—42no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—22no—
294C23×C53—44no—
295C23×C53—44no—
296C23×C53—44no—
297C23×C53—44no—
298C23×C53—44no—
299C23×C53—44no—
300C23×C53—44no—
301C23×C53—41no—
302C23×C53—41no—
303C23×C53—41no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—41no—
307C23×C53#12012yes—
308C23×C53#12312yes—
309C23×C53#13512yes—
310C23×C53C22×D411yescharacteristic
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53—41no—
314Q8×C53—41no—
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—48no—
318D4×C53—48no—
319D4×C53—48no—
320D4×C53—41no—
321D4×C53—41no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—21no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—44no—
341C2×C4×C53—44no—
342C2×C4×C53—44no—
343C2×C4×C53—48no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53#12012yes—
355C2×C4×C53#12312yes—
356C2×C4×C53C22×D411yescharacteristic
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53C2×#4111yescharacteristic
359C2×C4×C53C2×#4111yescharacteristic
360C2×C4×C53H(5,𝔽2)11yescharacteristic
361C2×C4×C53H(5,𝔽2)11yescharacteristic
362C2×Dic53—41no—
363C2×Dic53—41no—
364C2×Dic53—41no—
365C2×Dic53—41no—
366C2×Dic53—41no—
367C2×Dic53—41no—
368C2×Dic53—41no—
369C2×Dic53—41no—
370C2×Dic53—41no—
371C2×Dic53—41no—
372C2×Dic53—41no—
373C2×Dic53—41no—
374#88322—41no—
375#88322—41no—
376#88322—41no—
377#88322—41no—
378#24008—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—22no—
387C22×C53—22no—
388C22×C53—416no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—42no—
402C22×C53—42no—
403C22×C53—42no—
404C22×C53—81no—
405C22×C53—81no—
406C22×C53—81no—
407C22×C53—81no—
408C22×C53C2×#12011yescharacteristic
409C22×C53C2×#12311yescharacteristic
410C22×C53#53411yescharacteristic
411C22×C53C2×#13511yescharacteristic
412C22×C53#57511yescharacteristic
413C22×C53#57511yescharacteristic
414C22×C53#57511yescharacteristic
415C4×C53—22no—
416C4×C53—22no—
417C4×C53—41no—
418C4×C53—42no—
419C4×C53—42no—
420C4×C53—42no—
421C4×C53#54611yescharacteristic
422C4×C53#54611yescharacteristic
423C4×C53#54611yescharacteristic
424C4×C53#54611yescharacteristic
425Dic53—81no—
426Dic53—81no—
427Dic53—81no—
428Dic53—81no—
429C2×#525D5311yescharacteristic
430C2×#485—531no—
431C2×#482—531no—
432#2280—531no—
433#2036—531no—
434#2035—531no—
435#2034—531no—
436#2033—531no—
437#1875—531no—
438#1873—531no—
439#1854—531no—
440#1854—531no—
441#1788—531no—
442#1788—531no—
443#1779—531no—
444C2×C53—42no—
445C2×C53—42no—
446C2×C53—42no—
447C2×C53—82no—
448C2×C53#240511yescharacteristic
449C2×C53#300211yescharacteristic
450C2×C53#300511yescharacteristic
451C2×C53#309111yescharacteristic
452C2×C53#309311yescharacteristic
453C2×C53#319111yescharacteristic
454C2×C53#319711yescharacteristic
455C22×#41C2×D5311yescharacteristic
456C24×C4C2×D5311yescharacteristic
457#525—24no—
458#525—24no—
459C2×#123—21no—
460C2×C22⋊Q8C2×D5311yescharacteristic
461C2×C22⋊Q8C2×D5311yescharacteristic
462C2×#121C2×D5311yescharacteristic
463C2×#121C2×D5311yescharacteristic
464C2×#120—21no—
465C2×C4×D4—21no—
466C2×C4×D4—21no—
467C2×#117—531no—
468C2×#117—531no—
469C2×#117C2×D5311yescharacteristic
470#485—1064no—
471#482—1064no—
472C2×#107—531no—
473C2×#107—531no—
474C2×#106—531no—
475C2×#106—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—531no—
480C2×#102—531no—
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×C22⋊C8—531no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×C22⋊C8—531no—
488C2×C22⋊C8—531no—
489C2×C22⋊C8—531no—
490#381—1061no—
491#380—531no—
492#380—531no—
493#380—531no—
494#380—531no—
495#379—1061no—
496C4×C22⋊C4—1061no—
497C4×C22⋊C4—1061no—
498#340—531no—
499#340—531no—
500#340—531no—
501#340—531no—
502C53#2400811yescharacteristic, complemented, Sylow
503C25C22⋊D5311yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22×D5311yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C22×D5311yescharacteristic
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—21no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C22⋊D5311yescharacteristic
523C23×C4C22⋊D5311yescharacteristic
524C23×C4C22⋊D5311yescharacteristic
525C23×C4C22×D5311yescharacteristic
526C23×C4C22×D5311yescharacteristic
527C23×C4C22×D5311yescharacteristic
528C22×C8—531no—
529C22×C8—531no—
530C22×C8—531no—
531C22×C8—531no—
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8C22⋊D5314yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121C22⋊D5314yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—1062no—
547#117—1062no—
548#117—2121no—
549#117—2121no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C42—21no—
570C2×C42—1061no—
571C2×C42—1061no—
572#107—1062no—
573#107—1062no—
574#106—1062no—
575#106—1062no—
576#103—1062no—
577#103—1062no—
578#103—2121no—
579#103—2121no—
580#102—1062no—
581#102—1062no—
582#102—2121no—
583#102—2121no—
584C22⋊C8—1062no—
585C22⋊C8—1062no—
586C22⋊C8—1062no—
587C22⋊C8—1062no—
588C22⋊C8—2121no—
589C22⋊C8—2121no—
590#95—1061no—
591#95—1061no—
592#95—1061no—
593#95—1061no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×C22⋊D5311yescharacteristic
603C24C2×C22⋊D5311yescharacteristic
604C24C2×C22⋊D5311yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C22⋊D5312yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×C22⋊D5312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—1061no—
667C22×C4#1171994712yes—
668C22×C4#1171994712yes—
669C22×C4C2×C22⋊D5311yescharacteristic
670C22×C4C2×C22⋊D5311yescharacteristic
671C22×C4C2×C22⋊D5312yes—
672C22×C4C2×C22⋊D5312yes—
673C22×C4C2×C22⋊D5311yescharacteristic
674C22×C4C23×D5311yescharacteristic
675C2×C8—1061no—
676C2×C8—1061no—
677C2×C8—1061no—
678C2×C8—1061no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—1061no—
684C2×C8—1061no—
685C2×C8—1061no—
686C2×C8—1061no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—1061no—
698C4⋊C4—1061no—
699C4⋊C4C2×C22⋊D5312yes—
700C4⋊C4C2×C22⋊D5312yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—2122no—
707C22⋊C4—2122no—
708C22⋊C4—2122no—
709C22⋊C4—2122no—
710C22⋊C4—2122no—
711C22⋊C4—2122no—
712C42—24no—
713C42—2122no—
714C42—2122no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#1313318612yes—
748C23#1313319812yes—
749C23#1313323712yes—
750C23C22×C22⋊D5311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4—2121no—
802C2×C4—2121no—
803C2×C4—2121no—
804C2×C4—2121no—
805C2×C4—2121no—
806C2×C4#1313318612yes—
807C2×C4#1313319812yes—
808C2×C4C22×C22⋊D5311yescharacteristic
809C2×C4C22×C22⋊D5311yescharacteristic
810C2×C4C2×#1171994711yescharacteristic
811C2×C4C2×#1171994711yescharacteristic
812C2×C4#1313326211yescharacteristic
813C2×C4#1313326211yescharacteristic
814C8—2121no—
815C8—2121no—
816C8—2121no—
817C8—2121no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#1313318611yescharacteristic
848C22C2×#1313319811yescharacteristic
849C22#1681118211yescharacteristic
850C22C2×#1313323711yescharacteristic
851C22#1681142111yescharacteristic
852C22#1681142111yescharacteristic
853C22#1681142111yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—4241no—
861C4—4241no—
862C4—4241no—
863C4—4241no—
864C4#1681126711yescharacteristic
865C4#1681126711yescharacteristic
866C4#1681126711yescharacteristic
867C4#1681126711yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2#2027803811yescharacteristic
873C2#2028393311yescharacteristic
874C2#2028395711yescharacteristic
875C2#2028462411yescharacteristic
876C2#2028464411yescharacteristic
877C2#2028550311yescharacteristic
878C2#2028555211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#525C2
socleC23×C53C22×D4
hypercenterC2×#525D53
hypocenterC53#24008
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16810961C2semidirect
2. C2×#16810944C2semidirect
3. #20277098C2semidirect
4. #20275915C2semidirect
5. #20275908C2semidirect
6. #20275901C2semidirect
7. #20275894C2semidirect
8. #20275038C2semidirect
9. #20275028C2semidirect
10. #20274914C2semidirect
11. #20274914C2semidirect
12. #20274655C2semidirect
13. #20274655C2semidirect
14. #20274625C2semidirect
20. C2×#13133150C22semidirect
21. C2×#13133150C22semidirect
22. C2×#13133148C22semidirect
23. C2×#13133148C22semidirect
24. C2×#13133141C22semidirect
25. C2×#13133141C22semidirect
26. C2×#13133141C22semidirect
27. C2×#13133141C22semidirect
28. C2×#13133138C22semidirect
29. C2×#13133138C22semidirect
30. C2×#13133138C22semidirect
31. C2×#13133138C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
502. C53#24008semidirect

Maximal subgroups

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

subgroupindex
C2×#168109612
C2×#168109442
#202770982
#202759152
#202759082
#202759012
#202758942
#202750382
#202750282
#202749142
#202746552
#202746252
C2×C53×#5252
#2400853