Finite Group Databasebeta

← #27418097

Subgroups — #27418097

Order 13568.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810927C211yesmaximal, characteristic, complemented
2C2×C4×#11719923C211yesmaximal, characteristic, complemented
3#20279624C211yesmaximal, characteristic, complemented
4#20275901C211yesmaximal, characteristic, complemented
5#20275894C211yesmaximal, characteristic, complemented
6#20275718C211yesmaximal, characteristic, complemented
7#20275718C211yesmaximal, characteristic, complemented
8#20275681C211yesmaximal, characteristic, complemented
9#20275510C211yesmaximal, characteristic, complemented
10#20275027C211yesmaximal, characteristic, complemented
11#20275022C211yesmaximal, characteristic, complemented
12#20274914C211yesmaximal, characteristic, complemented
13#20274908C211yesmaximal, characteristic, complemented
14#20274725C211yesmaximal, characteristic, complemented
15C2×C53×#553C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C2×#13133196C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×C4×Dic106C2211yescharacteristic
20#16810927—24no—
21C4×#11719923—24no—
22C2×#13133150C2211yescharacteristic
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×C4⋊#88322C2211yescharacteristic
26C2×#13133140C2211yescharacteristic
27C2×#13133140C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×C22⋊#88322C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37#16810554—21no—
38#16810537—21no—
39#16810511—21no—
40#16810511—21no—
41#16810489C2211yescharacteristic
42#16810483C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50C53×#553—24no—
51C53×#553—24no—
52C2×#126×C53—21no—
53C2×#125×C53C2211yescharacteristic
54C2×#123×C53—21no—
55C2×#121×C53—21no—
56C2×#121×C53C2211yescharacteristic
57C2×#121×C53C2211yescharacteristic
58C2×C4×D4×C53—21no—
59C2×C4×D4×C53C2211yescharacteristic
60C2×C4×D4×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C2×#11719923—22no—
65C2×#11719923—22no—
66C2×#11719923—22no—
67C22×#88322C2311yescharacteristic
68C22×#88322C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71#13133196—22no—
72#13133196—22no—
73#13133196—41no—
74#13133196—41no—
75C4×Dic106—22no—
76C4×Dic106—22no—
77C2×C4⋊Dic53C2311yescharacteristic
78C2×C4⋊Dic53C2311yescharacteristic
79C2×C4⋊Dic53C2311yescharacteristic
80C2×#11719919—21no—
81C2×#11719919—21no—
82C2×#11719919—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88#13133150—22no—
89#13133148—22no—
90#13133148—22no—
91C4⋊#88322—22no—
92#13133140—22no—
93#13133140—22no—
94#13133140—22no—
95#13133138—22no—
96#13133138—41no—
97#13133138—41no—
98C22⋊#88322—22no—
99C22⋊#88322—22no—
100C22⋊#88322—41no—
101C22⋊#88322—41no—
102C4×#88322—22no—
103#13133124—21no—
104#13133124—21no—
105#13133124—21no—
106#13133124—21no—
107C22×D4×C53—21no—
108C22×D4×C53—21no—
109C22×D4×C53D411yescharacteristic
110C22×D4×C53C2311yescharacteristic
111C23×C4×C53—21no—
112C23×C4×C53—21no—
113C23×C4×C53C2311yescharacteristic
114C23×C4×C53C2311yescharacteristic
115#126×C53—28no—
116#125×C53—22no—
117#125×C53D414yes—
118#123×C53—28no—
119#121×C53—28no—
120#121×C53—22no—
121#121×C53—22no—
122#121×C53—22no—
123#121×C53—22no—
124C4×D4×C53—28no—
125C4×D4×C53—22no—
126C4×D4×C53—22no—
127C4×D4×C53—22no—
128C4×D4×C53D414yes—
129#117×C53—22no—
130#117×C53—22no—
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—22no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53D411yescharacteristic
145C2×C22⋊C4×C53D411yescharacteristic
146C2×C42×C53—21no—
147C2×C42×C53C2311yescharacteristic
148C24×C53—21no—
149C24×C53C2×D411yescharacteristic
150C24×C53C2×D411yescharacteristic
151C2×D4×C53—24no—
152C2×D4×C53—22no—
153C2×D4×C53—24no—
154C2×D4×C53—22no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—41no—
161C2×D4×C53—42no—
162C2×D4×C53—42no—
163C2×D4×C53—81no—
164C2×D4×C53—81no—
165C2×D4×C53C2×D412yes—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—24no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—24no—
183C22×C4×C53—81no—
184C22×C4×C53—81no—
185C22×C4×C53—81no—
186C22×C4×C53—81no—
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106—21no—
201C2×Dic106#4112yes—
202C4⋊C4×C53—24no—
203C4⋊C4×C53—24no—
204C4⋊C4×C53—24no—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53—21no—
209C4⋊C4×C53C2×D412yes—
210C4⋊C4×C53C2×D412yes—
211C4⋊C4×C53C2×D412yes—
212C22⋊C4×C53—24no—
213C22⋊C4×C53—24no—
214C22⋊C4×C53—24no—
215C22⋊C4×C53—24no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C42×C53—24no—
219C42×C53C2×D412yes—
220C42×C53C2×D412yes—
221C22⋊Dic53—42no—
222C22⋊Dic53—42no—
223C22⋊Dic53—42no—
224C22⋊Dic53—42no—
225#11719923—28no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232#11719919—42no—
233#11719919—42no—
234#11719919—42no—
235C4×Dic53—42no—
236C2×#88322—21no—
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×#88322—21no—
247C2×#88322#4112yes—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53#13512yes—
269C23×C53C22×D411yescharacteristic
270D4×C53—22no—
271D4×C53—22no—
272D4×C53—44no—
273D4×C53—48no—
274D4×C53—41no—
275D4×C53—41no—
276D4×C53—84no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—22no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
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—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—84no—
305C2×C4×C53—84no—
306C2×C4×C53#12012yes—
307C2×C4×C53#12012yes—
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C22×D411yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×C4×C53H(5,𝔽2)11yescharacteristic
313C2×C4×C532−1+411yescharacteristic
314C2×Dic53—22no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326Dic106—22no—
327Dic106—22no—
328Dic106—41no—
329Dic106—41no—
330#88322—22no—
331#88322—41no—
332#88322—41no—
333#88322—41no—
334#24126—531nomaximal, Sylow
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53—41no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—42no—
346C22×C53—41no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—41no—
350C22×C53—41no—
351C22×C53—41no—
352C22×C53—81no—
353C22×C53—81no—
354C22×C53—81no—
355C22×C53—81no—
356C22×C53C2×#12011yescharacteristic
357C22×C53#54611yescharacteristic
358C22×C53#54711yescharacteristic
359C22×C53C2×#13511yescharacteristic
360C22×C53#57511yescharacteristic
361C22×C53#57711yescharacteristic
362C22×C53#57711yescharacteristic
363C4×C53—22no—
364C4×C53—22no—
365C4×C53—41no—
366C4×C53—41no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#52511yescharacteristic
371C4×C53#53711yescharacteristic
372C4×C53#54811yescharacteristic
373C4×C53#55011yescharacteristic
374Dic53—42no—
375Dic53—81no—
376Dic53—81no—
377Dic53—81no—
378C2×#553D5311yescharacteristic
379C2×#479—531no—
380C2×C4×SD16—531no—
381#2536—531no—
382#2034—531no—
383#2033—531no—
384#2000—531no—
385#2000—531no—
386#1991—531no—
387#1954—531no—
388#1873—531no—
389#1872—531no—
390#1854—531no—
391#1853—531no—
392#1804—531no—
393C2×C53—42no—
394C2×C53—81no—
395C2×C53—82no—
396C2×C53#240711yescharacteristic
397C2×C53#300211yescharacteristic
398C2×C53#300911yescharacteristic
399C2×C53#330111yescharacteristic
400C2×C53#332611yescharacteristic
401C2×C53#333711yescharacteristic
402C2×C53#335111yescharacteristic
403C22×SD16—531no—
404#553—24no—
405#553—24no—
406C2×#126—21no—
407C2×#125C2×D5311yescharacteristic
408C2×#123—21no—
409C2×C22⋊Q8—531no—
410C2×C22⋊Q8—531no—
411C2×#121—21no—
412C2×#121C2×D5311yescharacteristic
413C2×#121C2×D5311yescharacteristic
414C2×C4×Q8—531no—
415C2×C4×D4—21no—
416C2×C4×D4C2×D5311yescharacteristic
417C2×C4×D4C2×D5311yescharacteristic
418C2×#117C2×D5311yescharacteristic
419C22×C4⋊C4C2×D5311yescharacteristic
420#479—1064no—
421C4×SD16—1064no—
422C2×#107—531no—
423C2×#106—531no—
424C2×#106—531no—
425C2×C4⋊C8—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×C22⋊C8—531no—
433C2×C22⋊C8—531no—
434C2×C22⋊C8—531no—
435C2×C22⋊C8—531no—
436C2×C4×C8—531no—
437#398—1061no—
438#394—1061no—
439#388—1061no—
440#388—1061no—
441#382—531no—
442#380—531no—
443#380—531no—
444#340—531no—
445#340—531no—
446#340—531no—
447#340—531no—
448#340—531no—
449#340—531no—
450C53#2412611yescharacteristic, complemented, Sylow
451C22×Q8—531no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22⋊D5311yescharacteristic
455C22×D4C22×D5311yescharacteristic
456C23×C4—21no—
457C23×C4—21no—
458C23×C4C22×D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C2×SD16—1062no—
461C2×SD16—1062no—
462C2×SD16—1062no—
463C22×C8—531no—
464C22×C8—531no—
465C22×C8—531no—
466C22×C8—531no—
467#126—28no—
468#125—22no—
469#125C22⋊D5314yes—
470#123—28no—
471C22⋊Q8—1062no—
472C22⋊Q8—1062no—
473C22⋊Q8—2121no—
474C22⋊Q8—2121no—
475#121—28no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480C4×Q8—1062no—
481C4×Q8—1062no—
482C4×D4—28no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4C22⋊D5314yes—
487#117—22no—
488#117—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4C22⋊D5311yescharacteristic
501C2×C4⋊C4C22×D5311yescharacteristic
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4C22⋊D5311yescharacteristic
513C2×C22⋊C4C22⋊D5311yescharacteristic
514C2×C42—21no—
515C2×C42—1061no—
516C2×C42C22×D5311yescharacteristic
517#107—1062no—
518#106—1062no—
519#106—1062no—
520C4⋊C8—1062no—
521#103—1062no—
522#103—1062no—
523#103—1062no—
524#102—1062no—
525#102—2121no—
526#102—2121no—
527C22⋊C8—1062no—
528C22⋊C8—1062no—
529C22⋊C8—2121no—
530C22⋊C8—2121no—
531C4×C8—1062no—
532#95—1061no—
533#95—1061no—
534#95—1061no—
535#95—1061no—
536C24—21no—
537C24C2×C22⋊D5311yescharacteristic
538C24C2×C22⋊D5311yescharacteristic
539C2×Q8—532no—
540C2×Q8—1061no—
541C2×Q8—1061no—
542C2×Q8—1061no—
543C2×Q8—1061no—
544C2×Q8—1061no—
545C2×D4—24no—
546C2×D4—22no—
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—41no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4C2×C22⋊D5312yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—24no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4C2×C22⋊D5311yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C2×C22⋊D5311yescharacteristic
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591C2×C8—532no—
592C2×C8—1061no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—2122no—
617C4⋊C4—2122no—
618C4⋊C4—2122no—
619C4⋊C4C2×C22⋊D5312yes—
620C4⋊C4C2×C22⋊D5312yes—
621C4⋊C4C2×C22⋊D5312yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—2122no—
629C22⋊C4—2122no—
630C22⋊C4—2122no—
631C22⋊C4—2122no—
632C42—24no—
633C42—2122no—
634C42C2×C22⋊D5312yes—
635C42C2×C22⋊D5312yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#1313323712yes—
657C23C22×C22⋊D5311yescharacteristic
658Q8—1062no—
659Q8—1062no—
660Q8—2121no—
661Q8—2121no—
662D4—22no—
663D4—22no—
664D4—44no—
665D4—48no—
666D4—41no—
667D4—41no—
668D4—84no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—1062no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4—2121no—
705C2×C4—2121no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4#1313318612yes—
711C2×C4#1313318612yes—
712C2×C4C22×C22⋊D5311yescharacteristic
713C2×C4C22×C22⋊D5311yescharacteristic
714C2×C4#41×D5311yescharacteristic
715C2×C4#41×D5311yescharacteristic
716C2×C4#1313326311yescharacteristic
717C2×C4#1313326411yescharacteristic
718C8—1062no—
719C8—2121no—
720C8—2121no—
721C8—2121no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#1313318611yescharacteristic
744C22#1681126111yescharacteristic
745C22#1681127211yescharacteristic
746C22C2×#1313323711yescharacteristic
747C22#1681142111yescharacteristic
748C22#1681143411yescharacteristic
749C22#1681143411yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—42no—
757C4—4241no—
758C4—4241no—
759C4—4241no—
760C4—2122no—
761C4#1681113011yescharacteristic
762C4#1681120111yescharacteristic
763C4#1681128011yescharacteristic
764C4#1681129211yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2#2027805411yescharacteristic
769C2#2028393311yescharacteristic
770C2#2028399211yescharacteristic
771C2#2028661111yescharacteristic
772C2#2028696211yescharacteristic
773C2#2028708811yescharacteristic
774C2#2028726911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#553C2
socleC23×C53C22×D4
hypercenterC2×#553D53
hypocenterC53#24126
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16810927C2semidirect
2. C2×C4×#11719923C2semidirect
3. #20279624C2semidirect
4. #20275901C2semidirect
5. #20275894C2semidirect
6. #20275718C2semidirect
7. #20275718C2semidirect
8. #20275681C2semidirect
9. #20275510C2semidirect
10. #20275027C2semidirect
11. #20275022C2semidirect
12. #20274914C2semidirect
13. #20274908C2semidirect
14. #20274725C2semidirect
450. C53#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#168109272
C2×C4×#117199232
#202796242
#202759012
#202758942
#202757182
#202756812
#202755102
#202750272
#202750222
#202749142
#202749082
#202747252
C2×C53×#5532
#2412653