Finite Group Databasebeta

← #27401131

Subgroups — #27401131

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×#16810588C211yesmaximal, characteristic
2#20277203C211yesmaximal, characteristic
3#20275328C211yesmaximal, characteristic, complemented
4#20275327C211yesmaximal, characteristic, complemented
5#20275327C211yesmaximal, characteristic, complemented
6#20275321C211yesmaximal, characteristic, complemented
7#20274896C211yesmaximal, characteristic, complemented
8#20274891C211yesmaximal, characteristic, complemented
9#20274786C211yesmaximal, characteristic, complemented
10#20274693C211yesmaximal, characteristic, complemented
11#20274626C211yesmaximal, characteristic
12#20274498C211yesmaximal, characteristic, complemented
13#20274492C211yesmaximal, characteristic, complemented
14#20274479C211yesmaximal, characteristic, complemented
15C2×C53×#433C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19C22×C4×Dic53C2211yescharacteristic
20C2×#13133146C2211yescharacteristic
21C2×#13133146C2211yescharacteristic
22#16810588—24no—
23C2×C22⋊#88322C2211yescharacteristic
24C2×C22⋊#88322C2211yescharacteristic
25C2×#13133129C2211yescharacteristic
26C2×#13133129C2211yescharacteristic
27C2×#13133129C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133127C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33#16810528C411yescharacteristic
34#16810528C411yescharacteristic
35#16810524C411yescharacteristic
36#16810524C411yescharacteristic
37#16810500C411yescharacteristic
38#16810500C411yescharacteristic
39#16810500C411yescharacteristic
40#16810500C411yescharacteristic
41C4×#11719921C2211yescharacteristic
42C4×#11719921C2211yescharacteristic
43C4×#11719921C2211yescharacteristic
44C4×#11719921C2211yescharacteristic
45#16810378C2211yescharacteristic
46#16810378C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810377C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53C2×#117×C53C2211yescharacteristic
54C53×#433—24no—
55C2×C4⋊C8×C53C2211yescharacteristic
56C2×C4⋊C8×C53C2211yescharacteristic
57C2×C22⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×#97×C53C2211yescharacteristic
60C2×C4×C8×C53C2211yescharacteristic
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
71C23×Dic53C2×C411yescharacteristic
72C23×Dic53C2×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—
85C2×#11719921C2×C411yescharacteristic
86C2×#11719921C2×C411yescharacteristic
87C2×#11719921C2×C411yescharacteristic
88C2×#11719921C2×C411yescharacteristic
89C2×#11719921C2×C411yescharacteristic
90C2×#11719921C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×C4×Dic53—41no—
94C2×C4×Dic53—41no—
95C2×C4×Dic53C2×C411yescharacteristic
96C2×C4×Dic53C2×C411yescharacteristic
97C2×C4×Dic53C2311yescharacteristic
98C2×C4×Dic53C2311yescharacteristic
99#13133146—41no—
100#13133146—41no—
101C22⋊#88322—22no—
102C22⋊#88322—22no—
103#13133129—22no—
104#13133129—22no—
105#13133129—22no—
106#13133129—22no—
107#13133129—41no—
108#13133129—41no—
109#13133127—41no—
110#13133127—41no—
111#13133124C2×C411yescharacteristic
112#13133124C2×C411yescharacteristic
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118#13133124C2×C411yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C22×C8×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C22×C8×C53C2311yescharacteristic
123C22×C8×C53C2311yescharacteristic
124#117×C53—22no—
125#117×C53—22no—
126C2×C4⋊C4×C53C2×C411yescharacteristic
127C2×C4⋊C4×C53C2×C411yescharacteristic
128C2×C22⋊C4×C53C2×C411yescharacteristic
129C2×C22⋊C4×C53C2×C411yescharacteristic
130C2×C42×C53C2311yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C4⋊C8×C53—22no—
133C4⋊C8×C53—22no—
134C22⋊C8×C53—22no—
135C22⋊C8×C53D414yes—
136#97×C53—22no—
137C4×C8×C53—22no—
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×C53C22×C411yescharacteristic
146C22×C4×C53C22×C411yescharacteristic
147C22×C4×C53C22×C411yescharacteristic
148C22×C4×C53C22×C411yescharacteristic
149C22×C4×C53C22×C411yescharacteristic
150C22×C4×C53C2×D412yes—
151C22×C4×C53#4112yes—
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×Dic53—22no—
160C22×Dic53—41no—
161C22×Dic53—41no—
162C22×Dic53—41no—
163C22×Dic53—41no—
164C22×Dic53—41no—
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169C22×Dic53C22×C411yescharacteristic
170C22×Dic53C22×C411yescharacteristic
171#11719945—44no—
172#11719945—44no—
173#11719945—44no—
174#11719945—44no—
175C2×D212—22no—
176C2×D212—22no—
177C2×D212—41no—
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
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×C53C2×D412yes—
204C2×C8×C53C2×D412yes—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—22no—
207C22⋊C4×C53—22no—
208C22⋊C4×C53—22no—
209C42×C53—21no—
210C42×C53—21no—
211C42×C53—21no—
212C42×C53—21no—
213#11719921—22no—
214#11719921—22no—
215#11719921—41no—
216#11719921—41no—
217#11719921—41no—
218#11719921—41no—
219#11719921—41no—
220#11719921—41no—
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×#88322—21no—
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×C53C4×D412yes—
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—21no—
262C22×D53#11712yes—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
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—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53C4×D412yes—
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—21no—
306C2×Dic53—44no—
307C2×Dic53—44no—
308C2×Dic53#11712yes—
309C2×Dic53#13112yes—
310D212—44no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—22no—
315C4×D53—41no—
316C4×D53—41no—
317C4×D53—41no—
318C4×D53—41no—
319Dic106—44no—
320C8×C53—22no—
321C8×C53—22no—
322C8×C53—41no—
323C8×C53—41no—
324#88322—41no—
325#88322—41no—
326#88322—41no—
327#88322—41no—
328#22561—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
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—41no—
347C2×D53—41no—
348C2×D53—41no—
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—22no—
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—41no—
369Dic53—41no—
370Dic53—41no—
371Dic53—41no—
372C2×#433D5311yescharacteristic, complemented
373C2×#408—531no—
374#2297—531no—
375#1924—531no—
376#1924—531no—
377#1924—531no—
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—42no—
388C2×C53#234211yescharacteristic
389C2×C53#292311yescharacteristic
390C2×C53#292511yescharacteristic
391C2×C53#293211yescharacteristic
392C2×C53#293511yescharacteristic
393C2×C53#297611yescharacteristic
394C2×C53#297811yescharacteristic
395D53—42no—
396D53—81no—
397C22×#41—531no—
398C22×M16—531no—
399C23×C8—531no—
400C2×#117C2×D5311yescharacteristic
401C22×C42—531no—
402#433—24no—
403C2×C4⋊C8—531no—
404C2×C4⋊C8—531no—
405C2×C4⋊C8C2×D5311yescharacteristic
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×C8C2×D5311yescharacteristic
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⋊C4—531no—
434#336—531no—
435#336—531no—
436#336—531no—
437#336—531no—
438#336—531no—
439#336—531no—
440#336—531no—
441#336—531no—
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—22no—
473#117—22no—
474C2×C4⋊C4C4×D5311yescharacteristic
475C2×C4⋊C4C4×D5311yescharacteristic
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—22no—
496C4⋊C8—2121no—
497C4⋊C8—2121no—
498C22⋊C8—22no—
499C22⋊C8—1062no—
500C22⋊C8—1062no—
501C22⋊C8—1062no—
502C22⋊C8—1062no—
503C22⋊C8—1062no—
504C22⋊C8—1062no—
505C22⋊C8—2121no—
506C22⋊C8—2121no—
507C22⋊C8C22⋊D5314yes—
508#97—22no—
509#97—2121no—
510#97—2121no—
511C4×C8—22no—
512#95—531no—
513#95—531no—
514#95—531no—
515#95—531no—
516#95—531no—
517#95—531no—
518#95—531no—
519#95—531no—
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—531no—
544C22×C4—531no—
545C22×C4—532no—
546C22×C4—532no—
547C22×C4—531no—
548C22×C4—531no—
549C22×C4—531no—
550C22×C4—531no—
551C22×C4—1062no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1061no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—2121no—
563C22×C4—2121no—
564C22×C4—2121no—
565C22×C4—2121no—
566C22×C4—2121no—
567C22×C4C2×C4×D5311yescharacteristic
568C22×C4C2×C4×D5311yescharacteristic
569C22×C4C2×C4×D5311yescharacteristic
570C22×C4C2×C4×D5311yescharacteristic
571C22×C4C2×C4×D5311yescharacteristic
572C22×C4#1171994512yes—
573C22×C4C2×C22⋊D5312yes—
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—1061no—
587C2×C8—1061no—
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—2124no—
599C2×C8C2×C22⋊D5312yes—
600C2×C8C2×C22⋊D5312yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—1062no—
606C22⋊C4—1062no—
607C22⋊C4—2121no—
608C22⋊C4—2121no—
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—532no—
630C23—1061no—
631C23—1061no—
632C23—1061no—
633C23—1061no—
634C23—1061no—
635C23—1061no—
636C23—1061no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1061no—
642C23—1061no—
643C23C4×C22⋊D5312yes—
644C23C22×C4×D5311yescharacteristic
645Q8—2124no—
646D4—2124no—
647D4—2124no—
648D4—2124no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
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—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—532no—
668C2×C4—532no—
669C2×C4—1061no—
670C2×C4—1061no—
671C2×C4—1061no—
672C2×C4—1061no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1061no—
678C2×C4—1061no—
679C2×C4—1061no—
680C2×C4—1061no—
681C2×C4—1061no—
682C2×C4—1061no—
683C2×C4—1061no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—2124no—
690C2×C4—2124no—
691C2×C4—2121no—
692C2×C4—2121no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4C4×C22⋊D5312yes—
696C2×C4C22×C22⋊D5311yescharacteristic
697C2×C4#41×D5311yescharacteristic
698C2×C4#41×D5311yescharacteristic
699C2×C4C2×#1171994511yescharacteristic
700C2×C4#1313326311yescharacteristic
701C2×C4#1313326311yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—2121no—
707C8—2121no—
708C8—2121no—
709C8—2121no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—2121no—
721C22—2121no—
722C22—2121no—
723C22—2121no—
724C22—2121no—
725C22—2121no—
726C22—2121no—
727C22—2121no—
728C22—2121no—
729C22—2121no—
730C22—2121no—
731C22#117×D5311yescharacteristic
732C22C2×C4×C22⋊D5311yescharacteristic
733C22#1681109711yescharacteristic
734C22#131×D5311yescharacteristic
735C22#1681138811yescharacteristic
736C22#1681138811yescharacteristic
737C22#1681138811yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—1062no—
744C4—1062no—
745C4—2121no—
746C4—2121no—
747C4—2121no—
748C4—2121no—
749C4#1681126111yescharacteristic
750C4#1681126111yescharacteristic
751C4#1681129711yescharacteristic
752C4#1681129711yescharacteristic
753C2—42no—
754C2—4241no—
755C2—2122no—
756C2#2027756511yescharacteristic
757C2#2028336311yescharacteristic
758C2#2028337811yescharacteristic
759C2#2028343111yescharacteristic
760C2#2028345711yescharacteristic
761C2#2028376111yescharacteristic
762C2#2028377611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#433C2
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenterC2×#433D53
hypocenterC53#22561
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #20275328C2semidirect
4. #20275327C2semidirect
5. #20275327C2semidirect
6. #20275321C2semidirect
7. #20274896C2semidirect
8. #20274891C2semidirect
9. #20274786C2semidirect
10. #20274693C2semidirect
12. #20274498C2semidirect
13. #20274492C2semidirect
14. #20274479C2semidirect
15. C2×C53×#433C2semidirect
372. C2×#433D53semidirect
442. C53#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#168105882
#202772032
#202753282
#202753272
#202753212
#202748962
#202748912
#202747862
#202746932
#202746262
#202744982
#202744922
#202744792
C2×C53×#4332
#2256153