Finite Group Databasebeta

← #27401137

Subgroups — #27401137

Order 13568.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810683C211yesmaximal, characteristic, complemented
2C2×#16810588C211yesmaximal, characteristic
3#20277201C211yesmaximal, characteristic
4#20275331C211yesmaximal, characteristic, complemented
5#20275330C211yesmaximal, characteristic, complemented
6#20275318C211yesmaximal, characteristic, complemented
7#20274896C211yesmaximal, characteristic, complemented
8#20274894C211yesmaximal, characteristic, complemented
9#20274785C211yesmaximal, characteristic, complemented
10#20274694C211yesmaximal, characteristic, complemented
11#20274626C211yesmaximal, characteristic
12#20274500C211yesmaximal, characteristic, complemented
13#20274490C211yesmaximal, characteristic, complemented
14#20274478C211yesmaximal, characteristic, complemented
15C53×#1924C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C2×#13133174C2211yescharacteristic
20C2×C42×D53C2211yescharacteristic
21#16810683—24no—
22C2×C4⋊#88322C2211yescharacteristic
23C2×#13133146C2211yescharacteristic
24C2×#13133146C2211yescharacteristic
25#16810588—24no—
26C2×C22⋊#88322C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35C2×#13133127C2211yescharacteristic
36C2×C8×Dic53C2211yescharacteristic
37#16810527C411yescharacteristic
38#16810527C411yescharacteristic
39#16810523C411yescharacteristic
40#16810523C411yescharacteristic
41#16810501C411yescharacteristic
42#16810501C411yescharacteristic
43#16810499C411yescharacteristic
44#16810499C411yescharacteristic
45C4×#11719921C2211yescharacteristic
46C4×#11719921C2211yescharacteristic
47C4×C22⋊Dic53C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C2×C4⋊C8×C53C2211yescharacteristic
55C2×C22⋊C8×C53C2211yescharacteristic
56C2×C22⋊C8×C53C2211yescharacteristic
57C2×#97×C53C2211yescharacteristic
58C4×C22⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C53×#336C2211yescharacteristic
61C2×#11719945—22no—
62C2×#11719945—22no—
63C2×#11719945—22no—
64C2×#11719945—22no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C22×Dic106C2×C411yescharacteristic
68C22×D212C2×C411yescharacteristic
69C22×C22⋊D53C2×C411yescharacteristic
70C22×C22⋊D53C2×C411yescharacteristic
71C22×C4×D53C2×C411yescharacteristic
72C22×C4×D53C2×C411yescharacteristic
73C22×C4×D53C2311yescharacteristic
74C22×C4×D53C2311yescharacteristic
75C2×#11719912—22no—
76C2×#11719912—22no—
77C2×#11719912—41no—
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C2×C8×D53—22no—
83C2×C8×D53—22no—
84C2×C8×D53—41no—
85#13133174—22no—
86#13133174—22no—
87C2×#11719919C2×C411yescharacteristic
88C2×#11719919C2×C411yescharacteristic
89C2×C22⋊Dic53C2×C411yescharacteristic
90C2×C22⋊Dic53C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×#11719921C2×C411yescharacteristic
94C2×#11719921C2×C411yescharacteristic
95C2×#11719921C2×C411yescharacteristic
96C2×#11719921C2×C411yescharacteristic
97C2×C4×Dic53C2×C411yescharacteristic
98C2×C4×Dic53C2×C411yescharacteristic
99C2×C4×Dic53C2311yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C42×D53—41no—
102C42×D53—41no—
103C4⋊#88322—22no—
104#13133146—41no—
105#13133146—41no—
106C22⋊#88322—22no—
107C22⋊#88322—41no—
108#13133129—22no—
109#13133129—22no—
110#13133129—22no—
111#13133129—22no—
112#13133129—22no—
113#13133129D414yes—
114#13133128—41no—
115#13133127—22no—
116C8×Dic53—22no—
117#13133124C2×C411yescharacteristic
118#13133124C2×C411yescharacteristic
119#13133124C2×C411yescharacteristic
120#13133124C2×C411yescharacteristic
121#13133124C2×C411yescharacteristic
122#13133124C2×C411yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C42×C53C2311yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C4⋊C8×C53—22no—
133C22⋊C8×C53—22no—
134C22⋊C8×C53—41no—
135#97×C53—41no—
136#95×C53C2×C411yescharacteristic
137#95×C53C2×C411yescharacteristic
138C24×C53C22×C411yescharacteristic
139C23×D53C22×C411yescharacteristic
140C23×D53C22×C411yescharacteristic
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53C22×C411yescharacteristic
148C22×C4×C53C22×C411yescharacteristic
149C22×C4×C53C22×C411yescharacteristic
150C22×C4×C53C22×C411yescharacteristic
151C22×C4×C53C22×C411yescharacteristic
152C22×C4×C53C2411yescharacteristic
153C2×C22⋊D53—22no—
154C2×C22⋊D53—22no—
155C2×C22⋊D53—22no—
156C2×C22⋊D53—22no—
157C2×C22⋊D53—41no—
158C2×C22⋊D53—41no—
159C22×Dic53C22×C411yescharacteristic
160C22×Dic53C22×C411yescharacteristic
161C22×Dic53C22×C411yescharacteristic
162C22×Dic53C22×C411yescharacteristic
163C22×Dic53C22×C411yescharacteristic
164C22×Dic53C22×C411yescharacteristic
165#11719945—44no—
166#11719945—44no—
167#11719945—44no—
168#11719945—44no—
169C2×D212—22no—
170C2×D212—22no—
171C2×D212—41no—
172C2×C4×D53—21no—
173C2×C4×D53—21no—
174C2×C4×D53—21no—
175C2×C4×D53—21no—
176C2×C4×D53—21no—
177C2×C4×D53—21no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—22no—
181C2×C4×D53—41no—
182C2×C4×D53—41no—
183C2×C4×D53—41no—
184C2×C4×D53—41no—
185C2×C4×D53—41no—
186C2×C4×D53C2×D412yes—
187C2×C4×D53#4112yes—
188C2×C4×D53#4112yes—
189C2×C4×D53#4112yes—
190C2×Dic106—22no—
191C2×Dic106—22no—
192C2×Dic106—41no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53C2×D412yes—
205C22⋊C4×C53—41no—
206C22⋊C4×C53—41no—
207C42×C53—21no—
208C42×C53—21no—
209C42×C53—21no—
210C42×C53—21no—
211C22⋊Dic53—22no—
212C22⋊Dic53—41no—
213#11719921—22no—
214#11719921—22no—
215#11719921—22no—
216#11719921—41no—
217#11719921—41no—
218#11719921—41no—
219#11719919—22no—
220#11719919—22no—
221C4×Dic53—21no—
222C4×Dic53—21no—
223C4×Dic53—21no—
224C4×Dic53—21no—
225C4×Dic53—41no—
226C4×Dic53—41no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C2×#88322—21no—
233C2×#88322—21no—
234C2×#88322—21no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322C2×D412yes—
239#11719912—44no—
240C8×D53—44no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53C23×C411yescharacteristic
249C22×D53—21no—
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53—21no—
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53#11712yes—
262C22×D53C4×D412yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53C22×D411yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53H(5,𝔽2)11yescharacteristic
287C2×C4×C53H(5,𝔽2)11yescharacteristic
288C22⋊D53—44no—
289C22⋊D53—44no—
290C2×Dic53—21no—
291C2×Dic53—21no—
292C2×Dic53—21no—
293C2×Dic53—21no—
294C2×Dic53—21no—
295C2×Dic53—21no—
296C2×Dic53—21no—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53#11712yes—
306C2×Dic53C4×D412yes—
307C2×Dic53#13112yes—
308D212—44no—
309C4×D53—22no—
310C4×D53—22no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—44no—
318C4×D53—44no—
319Dic106—44no—
320C8×C53—22no—
321C8×C53—41no—
322C8×C53—41no—
323C8×C53—41no—
324#88322—22no—
325#88322—41no—
326#88322—41no—
327#88322—41no—
328#22561—531nomaximal, Sylow
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53C2×#11711yescharacteristic
337C22×C53C2×C4×D411yescharacteristic
338C22×C53#51811yescharacteristic
339C22×C53C2×#13111yescharacteristic
340C22×C53#56811yescharacteristic
341C22×C53#56811yescharacteristic
342C22×C53#56811yescharacteristic
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—22no—
348C2×D53—22no—
349C2×D53—41no—
350C2×D53—41no—
351C2×D53—41no—
352C2×D53—41no—
353C2×D53—41no—
354C2×D53—41no—
355C2×D53—41no—
356C2×D53—41no—
357C4×C53—41no—
358C4×C53—41no—
359C4×C53—41no—
360C4×C53—41no—
361C4×C53—41no—
362C4×C53#54611yescharacteristic
363C4×C53#54611yescharacteristic
364C4×C53#55111yescharacteristic
365C4×C53#55111yescharacteristic
366Dic53—22no—
367Dic53—22no—
368Dic53—22no—
369Dic53—41no—
370Dic53—41no—
371Dic53—41no—
372C2×#433—531no—
373C2×#408—531no—
374#2297—531no—
375#1924—531no—
376#1924—531no—
377#1924D5311yescharacteristic, complemented
378#1923—531no—
379#1851—531no—
380#1850—531no—
381#1818—531no—
382#1797—531no—
383#1780—531no—
384#1753—531no—
385#1752—531no—
386#1749—531no—
387C2×C53—81no—
388C2×C53#234211yescharacteristic
389C2×C53#292311yescharacteristic
390C2×C53#292511yescharacteristic
391C2×C53#293211yescharacteristic
392C2×C53#293511yescharacteristic
393C2×C53#297611yescharacteristic
394C2×C53#297811yescharacteristic
395D53—42no—
396D53—42no—
397C22×#41—531no—
398C22×M16—531no—
399C23×C8—531no—
400C2×#117—531no—
401C22×C42—531no—
402#433—1064no—
403C2×C4⋊C8—531no—
404C2×C4⋊C8—531no—
405C2×C4⋊C8—531no—
406C2×C4⋊C8C2×D5311yescharacteristic
407#408—1064no—
408C2×C22⋊C8—531no—
409C2×C22⋊C8—531no—
410C2×C22⋊C8—531no—
411C2×C22⋊C8—531no—
412C2×C22⋊C8—531no—
413C2×C22⋊C8—531no—
414C2×C22⋊C8—531no—
415C2×C22⋊C8—531no—
416C2×C22⋊C8C2×D5311yescharacteristic
417C2×C22⋊C8C2×D5311yescharacteristic
418C2×#97—531no—
419C2×#97—531no—
420C2×#97C2×D5311yescharacteristic
421C2×C4×C8—531no—
422#391—531no—
423#391—531no—
424#390—531no—
425#390—531no—
426#386—531no—
427#386—531no—
428#386—531no—
429#386—531no—
430C4×C22⋊C4—531no—
431C4×C22⋊C4—531no—
432C4×C22⋊C4—531no—
433C4×C22⋊C4C2×D5311yescharacteristic
434#336—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336—531no—
440#336C2×D5311yescharacteristic
441#336C2×D5311yescharacteristic
442C53#2256111yescharacteristic, complemented, Sylow
443C2×#41—1062no—
444C2×#41—1062no—
445C2×#41—1062no—
446C2×#41—1062no—
447C2×#41—2121no—
448C2×#41—2121no—
449C22×Q8—531no—
450C22×D4—531no—
451C22×D4—531no—
452C22×D4—531no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4C22×D5311yescharacteristic
458C2×M16—1062no—
459C2×M16—1062no—
460C2×M16—2121no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22×C8—1062no—
466C22×C8—1062no—
467C22×C8—2121no—
468C22×C8C22×D5311yescharacteristic
469C22×C8C22×D5311yescharacteristic
470C22×C8C22×D5311yescharacteristic
471C22×C8C22×D5311yescharacteristic
472#117—1062no—
473#117—1062no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—531no—
476C2×C22⋊C4—531no—
477C2×C22⋊C4—531no—
478C2×C22⋊C4—531no—
479C2×C22⋊C4—531no—
480C2×C22⋊C4—531no—
481C2×C22⋊C4—531no—
482C2×C22⋊C4—531no—
483C2×C22⋊C4—531no—
484C2×C22⋊C4C4×D5311yescharacteristic
485C2×C22⋊C4C4×D5311yescharacteristic
486C2×C42—531no—
487C2×C42—531no—
488C2×C42—531no—
489C2×C42—531no—
490C2×C42—2121no—
491C2×C42—2121no—
492C2×C42C22×D5311yescharacteristic
493C2×C42C22×D5311yescharacteristic
494C4⋊C8—22no—
495C4⋊C8—1062no—
496C4⋊C8—2121no—
497C4⋊C8—2121no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—534no—
501C22⋊C8—1062no—
502C22⋊C8—1062no—
503C22⋊C8—1062no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C22⋊C8—1062no—
507C22⋊C8—2121no—
508#97—41no—
509#97—1062no—
510#97—2121no—
511C4×C8—1062no—
512#95—531no—
513#95—531no—
514#95—531no—
515#95—531no—
516#95—531no—
517#95—531no—
518#95C4×D5311yescharacteristic
519#95C4×D5311yescharacteristic
520C24—531no—
521C24—531no—
522C24C2×C4×D5311yescharacteristic
523#41—2124no—
524#41—2124no—
525#41—2124no—
526#41—2124no—
527C2×Q8—1062no—
528C2×Q8—1062no—
529C2×Q8—2121no—
530C2×D4—1062no—
531C2×D4—1062no—
532C2×D4—1062no—
533C2×D4—1062no—
534C2×D4—1062no—
535C2×D4—1062no—
536C2×D4—2121no—
537C2×D4—2121no—
538C2×D4—2121no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—531no—
546C22×C4—531no—
547C22×C4—531no—
548C22×C4—532no—
549C22×C4—532no—
550C22×C4—532no—
551C22×C4—532no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—1062no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—1061no—
563C22×C4—1061no—
564C22×C4—2121no—
565C22×C4—2121no—
566C22×C4—2121no—
567C22×C4—2121no—
568C22×C4—2121no—
569C22×C4C2×C4×D5311yescharacteristic
570C22×C4C2×C4×D5311yescharacteristic
571C22×C4C2×C4×D5311yescharacteristic
572C22×C4C2×C4×D5311yescharacteristic
573C22×C4C2×C4×D5311yescharacteristic
574C22×C4C23×D5311yescharacteristic
575M16—2124no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
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—1061no—
598C2×C8—1061no—
599C2×C8—2124no—
600C2×C8D4×D5312yes—
601C4⋊C4—1062no—
602C4⋊C4—1062no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—1062no—
608C22⋊C4—1062no—
609C22⋊C4—2121no—
610C22⋊C4—2121no—
611C22⋊C4—2121no—
612C22⋊C4—2121no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—1061no—
618C42—1061no—
619C42—1061no—
620C42—1061no—
621C42—2121no—
622C42—2121no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—532no—
631C23—532no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1061no—
642C23—1061no—
643C23—1061no—
644C23C22×C4×D5311yescharacteristic
645Q8—2124no—
646D4—2124no—
647D4—2124no—
648D4—2124no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—532no—
669C2×C4—532no—
670C2×C4—532no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1061no—
674C2×C4—1061no—
675C2×C4—1061no—
676C2×C4—1061no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
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—2124no—
695C2×C4—2124no—
696C2×C4C2×D4×D5311yescharacteristic
697C2×C4#41×D5311yescharacteristic
698C2×C4#41×D5311yescharacteristic
699C2×C4#41×D5311yescharacteristic
700C2×C4#1313326211yescharacteristic
701C2×C4#1313326311yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—1062no—
707C8—2121no—
708C8—2121no—
709C8—2121no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—1062no—
721C22—1062no—
722C22—1062no—
723C22—2121no—
724C22—2121no—
725C22—2121no—
726C22—2121no—
727C22—2121no—
728C22—2121no—
729C22—2121no—
730C22—2121no—
731C22#117×D5311yescharacteristic
732C22C4×D4×D5311yescharacteristic
733C22#1681109511yescharacteristic
734C22#131×D5311yescharacteristic
735C22#1681138811yescharacteristic
736C22#1681138911yescharacteristic
737C22#1681138911yescharacteristic
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—1062no—
744C4—1062no—
745C4—1062no—
746C4—2121no—
747C4—2121no—
748C4—2121no—
749C4#1681126211yescharacteristic
750C4#1681126611yescharacteristic
751C4#1681129811yescharacteristic
752C4#1681130111yescharacteristic
753C2—81no—
754C2—2122no—
755C2—2122no—
756C2#2027756311yescharacteristic
757C2#2028336111yescharacteristic
758C2#2028337811yescharacteristic
759C2#2028342911yescharacteristic
760C2#2028345611yescharacteristic
761C2#2028375911yescharacteristic
762C2#2028377411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1924C2
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1924D53
hypocenterC53#22561
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#16810683C2semidirect
4. #20275331C2semidirect
5. #20275330C2semidirect
6. #20275318C2semidirect
7. #20274896C2semidirect
8. #20274894C2semidirect
9. #20274785C2semidirect
10. #20274694C2semidirect
12. #20274500C2semidirect
13. #20274490C2semidirect
14. #20274478C2semidirect
15. C53×#1924C2semidirect
377. #1924D53semidirect
442. C53#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#168106832
C2×#168105882
#202772012
#202753312
#202753302
#202753182
#202748962
#202748942
#202747852
#202746942
#202746262
#202745002
#202744902
#202744782
C53×#19242
#2256153