Finite Group Databasebeta

← #27441146

Subgroups — #27441146

Order 13568.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810900C211yesmaximal, characteristic, complemented
2C22×#13133137C211yesmaximal, characteristic
3C22⋊C4×D212C211yesmaximal, characteristic
4#20276244C211yesmaximal, characteristic, complemented
5#20276100C211yesmaximal, characteristic, complemented
6#20276100C211yesmaximal, characteristic, complemented
7#20275848C211yesmaximal, characteristic, complemented
8#20274961C211yesmaximal, characteristic, complemented
9#20274961C211yesmaximal, characteristic, complemented
10#20274903C211yesmaximal, characteristic, complemented
11#20274895C211yesmaximal, characteristic, complemented
12#20274742C211yesmaximal, characteristic, complemented
13#20274712C211yesmaximal, characteristic, complemented
14#20274645C211yesmaximal, characteristic
15C53×#2440C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×C4×D212C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×C22⋊C4×D53—21no—
21#16810900—24no—
22C2×#13133150C2211yescharacteristic, complemented
23C2×#13133150C2211yescharacteristic, complemented
24C2×#13133150C2211yescharacteristic, complemented
25C2×#13133150C2211yescharacteristic, complemented
26C2×C4⋊#88322C2211yescharacteristic, complemented
27C2×C4⋊#88322C2211yescharacteristic, complemented
28C2×#13133137—24no—
29C2×#13133137C2211yescharacteristic
30C2×#13133137C2211yescharacteristic
31C2×#13133137C2211yescharacteristic
32C2×#13133137C2211yescharacteristic
33C2×#13133137C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38#16810525C2211yescharacteristic
39#16810525C2211yescharacteristic
40#16810501—21no—
41#16810501—21no—
42#16810483C2211yescharacteristic
43#16810478—21no—
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50C2×C4⋊Q8×C53C2211yescharacteristic, complemented
51C2×C22⋊Q8×C53—21no—
52C22×C4⋊C4×C53C2211yescharacteristic
53C53×#398—21no—
54C53×#395—21no—
55C53×#389C2211yescharacteristic, complemented
56C53×#389C2211yescharacteristic, complemented
57C53×#385—21no—
58C53×#384C2211yescharacteristic, complemented
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C24×D53—21no—
62C22×D212—22no—
63C22×D212—22no—
64C22×D212—21no—
65C22×D212—22no—
66C22×D212—41no—
67C22×D212—41no—
68C22×D212Q814yescomplemented
69C22×D212C2311yescharacteristic
70C22×D212C2311yescharacteristic
71C22×C4×D53—21no—
72C22×C4×D53—21no—
73C22×#88322—22no—
74C22×#88322—22no—
75C22×#88322—41no—
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C4×D212—22no—
81C4×D212—22no—
82C4×D212—41no—
83C4×D212—41no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C22⋊Dic53—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90C2×#11719921—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C22⋊C4×D53—44no—
94#13133150—22no—
95#13133150—22no—
96#13133150—41no—
97#13133150—41no—
98C4⋊#88322—22no—
99C4⋊#88322—41no—
100#13133137—22no—
101#13133137—22no—
102#13133137—22no—
103#13133137—22no—
104#13133137—22no—
105#13133137—41no—
106#13133137—41no—
107#13133137D414yes—
108C22⋊#88322—22no—
109#13133124—21no—
110C22×Q8×C53—21no—
111C23×C4×C53—21no—
112C23×C4×C53C2311yescharacteristic
113C4⋊Q8×C53—22no—
114C4⋊Q8×C53—41no—
115C22⋊Q8×C53—44no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53—21no—
119C2×C4⋊C4×C53—21no—
120C2×C4⋊C4×C53—21no—
121C2×C4⋊C4×C53—21no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—41no—
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C4⋊C4×C53C2311yescharacteristic
126C2×C4⋊C4×C53C2311yescharacteristic
127C2×C4⋊C4×C53C2311yescharacteristic
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C22⋊C4×C53D411yescharacteristic
131C2×C42×C53C2311yescharacteristic
132C2×C42×C53C2311yescharacteristic
133#95×C53—21no—
134#95×C53—21no—
135#95×C53—21no—
136#95×C53D411yescharacteristic
137#95×C53D411yescharacteristic
138C24×C53C2×D411yescharacteristic
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—24no—
142C23×D53—42no—
143C23×D53—42no—
144C23×D53—42no—
145C23×D53—42no—
146C23×D53—81no—
147C23×D53—81no—
148C2×Q8×C53—42no—
149C2×Q8×C53—42no—
150C2×Q8×C53—81no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—42no—
160C22×C4×C53—42no—
161C22×C4×C53—81no—
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×Q812yes—
168C22×C4×C53#4112yes—
169C22×C4×C53C2411yescharacteristic
170C22×Dic53—21no—
171C22×Dic53—21no—
172C2×D212—21no—
173C2×D212—21no—
174C2×D212—21no—
175C2×D212—21no—
176C2×D212—21no—
177C2×D212—21no—
178C2×D212—21no—
179C2×D212—28no—
180C2×D212—24no—
181C2×D212—21no—
182C2×D212—44no—
183C2×D212—44no—
184C2×D212—44no—
185C2×D212—42no—
186C2×D212—42no—
187C2×D212C2×D412yes—
188C2×D212C2×Q812yes—
189C2×D212C2×Q812yes—
190C2×D212#4112yes—
191C2×C4×D53—42no—
192C2×C4×D53—42no—
193C2×C4×D53—42no—
194C2×C4×D53—42no—
195C2×C4×D53—81no—
196C2×C4×D53—81no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C4⋊C4×C53—21no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—42no—
205C4⋊C4×C53—42no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53—42no—
208C4⋊C4×C53—42no—
209C4⋊C4×C53—81no—
210C4⋊C4×C53C2×D412yes—
211C22⋊C4×C53—22no—
212C22⋊C4×C53—42no—
213C22⋊C4×C53D814yes—
214C42×C53—21no—
215C42×C53—21no—
216C42×C53—21no—
217C42×C53—21no—
218C22⋊Dic53—42no—
219#11719921—42no—
220#11719921—42no—
221#11719921—42no—
222#11719921—42no—
223#11719921—81no—
224#11719921—81no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—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—
239C2×#88322—21no—
240C2×#88322—44no—
241C2×#88322C2×D412yes—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53C22⋊Q812yes—
247C23×C53C2×D812yes—
248C23×C53#13712yes—
249C23×C53C22×D411yescharacteristic
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—48no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—48no—
266C22×D53—84no—
267C22×D53—84no—
268C22×D53—84no—
269C22×D53—84no—
270C22×D53—84no—
271Q8×C53—84no—
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—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
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—41no—
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—84no—
301C2×C4×C53C22⋊Q812yes—
302C2×C4×C53C2×D812yes—
303C2×C4×C53C2×D812yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×Q811yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53C2×#4111yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×C4×C53H(5,𝔽2)11yescharacteristic
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316D212—22no—
317D212—22no—
318D212—22no—
319D212—22no—
320D212—22no—
321D212—48no—
322D212—41no—
323D212—41no—
324D212C22⋊Q814yescomplemented
325C4×D53—84no—
326C4×D53—84no—
327#88322—22no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#25950—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53#47414yescomplemented
339C22×C53C2×C22⋊Q811yescharacteristic
340C22×C53D4211yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53C22×D811yescharacteristic
343C22×C53C2×#13711yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57711yescharacteristic
346C2×D53—24no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53—42no—
355C2×D53—42no—
356C2×D53—816no—
357C2×D53—81no—
358C2×D53—81no—
359C2×D53—81no—
360C2×D53—81no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—22no—
364C4×C53—41no—
365C4×C53—42no—
366C4×C53—41no—
367C4×C53—81no—
368C4×C53—81no—
369C4×C53—81no—
370C4×C53C2×C22⋊Q811yescharacteristic
371C4×C53#54311yescharacteristic
372C4×C53#54611yescharacteristic
373C4×C53#55111yescharacteristic
374Dic53—81no—
375Dic53—81no—
376C2×#474—531no—
377C22×#102—531no—
378#2440D5311yescharacteristic, complemented
379D4×C22⋊C4—531no—
380#2093—531no—
381#2067—531no—
382#2067—531no—
383#2023—531no—
384#1862—531no—
385#1862—531no—
386#1852—531no—
387#1850—531no—
388#1808—531no—
389#1802—531no—
390#1786—531no—
391C2×C53—24no—
392C2×C53#243711yescharacteristic
393C2×C53C2×#47411yescharacteristic
394C2×C53#308111yescharacteristic
395C2×C53#326611yescharacteristic
396C2×C53D4×D811yescharacteristic
397C2×C53#329411yescharacteristic
398C2×C53#331411yescharacteristic
399D53—44no—
400D53—82no—
401C23×D4—531no—
402C23×C8—531no—
403C2×C4⋊Q8C2×D5311yescharacteristic, complemented
404C2×C22⋊Q8—21no—
405C2×C4×D4—531no—
406C2×C4×D4—531no—
407C22×C4⋊C4C2×D5311yescharacteristic
408C22×C22⋊C4—1061no—
409#474—1064no—
410C2×#107—531no—
411C2×#107—531no—
412C2×#107—531no—
413C2×#107—531no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×#102—531no—
417C2×#102—531no—
418C2×#102—531no—
419C2×#102—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#102—531no—
424C2×#102—1064no—
425C2×C22⋊C8—531no—
426#398—21no—
427#395—21no—
428#390—531no—
429#390—531no—
430#389C2×D5311yescharacteristic, complemented
431#389C2×D5311yescharacteristic, complemented
432#386—1061no—
433#386—1061no—
434#385—21no—
435#384C2×D5311yescharacteristic, complemented
436#380—531no—
437#380C2×D5311yescharacteristic
438#379—1061no—
439C4×C22⋊C4C2×D5311yescharacteristic
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#336—531no—
445#336—531no—
446C53#2595011yescharacteristic, complemented, Sylow
447C25—1061no—
448C22×Q8—21no—
449C22×D4—534no—
450C22×D4—531no—
451C22×D4—531no—
452C22×D4—1062no—
453C22×D4—1062no—
454C22×D4—1062no—
455C22×D4—1061no—
456C22×D4—2121no—
457C22×D4—2121no—
458C23×C4—21no—
459C23×C4—1061no—
460C23×C4—1061no—
461C23×C4C22×D5311yescharacteristic
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—531no—
465C22×C8—531no—
466C22×C8—1062no—
467C22×C8—1062no—
468C22×C8—2121no—
469C4⋊Q8—22no—
470C4⋊Q8—41no—
471C22⋊Q8—44no—
472C4×D4—1062no—
473C4×D4—1062no—
474C4×D4—2121no—
475C4×D4—2121no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—2124no—
499C2×C22⋊C4C22⋊D5311yescharacteristic
500C2×C22⋊C4C22⋊D5311yescharacteristic
501C2×C42C22×D5311yescharacteristic
502C2×C42C22×D5311yescharacteristic
503#107—1062no—
504#107—1062no—
505#107—2121no—
506#107—2121no—
507C4⋊C8—1062no—
508C4⋊C8—2121no—
509#102—534no—
510#102—1062no—
511#102—1062no—
512#102—1062no—
513#102—1062no—
514#102—1062no—
515#102—2121no—
516#102—2121no—
517C22⋊C8—1062no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—1061no—
522#95C22⋊D5311yescharacteristic
523#95C22⋊D5311yescharacteristic
524C24—1061no—
525C24—1064no—
526C24—1061no—
527C24—4241no—
528C24—4241no—
529C24—2122no—
530C24—2122no—
531C24—2122no—
532C24—2122no—
533C24C2×C22⋊D5311yescharacteristic
534C2×Q8—42no—
535C2×Q8—42no—
536C2×Q8—81no—
537C2×D4—532no—
538C2×D4—532no—
539C2×D4—532no—
540C2×D4—532no—
541C2×D4—1068no—
542C2×D4—1064no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—1061no—
546C2×D4—1061no—
547C2×D4—1061no—
548C2×D4—1061no—
549C2×D4—1061no—
550C2×D4—1061no—
551C2×D4—2124no—
552C2×D4—2124no—
553C2×D4—2124no—
554C2×D4—2122no—
555C2×D4—2122no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—81no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—4241no—
570C22×C4—4241no—
571C22×C4—2122no—
572C22×C4—2122no—
573C22×C4—2122no—
574C22×C4—2122no—
575C22×C4Q8×D5312yes—
576C22×C4#1171994912yes—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C23×D5311yescharacteristic
583C2×C8—532no—
584C2×C8—1061no—
585C2×C8—1061no—
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—2124no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—81no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4D4×D5312yes—
614C22⋊C4—22no—
615C22⋊C4—42no—
616C22⋊C4—4241no—
617C22⋊C4—4241no—
618C22⋊C4—2122no—
619C22⋊C4—2122no—
620C22⋊C4—2122no—
621C22⋊C4—2122no—
622C22⋊C4—2122no—
623C22⋊C4#1171992214yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1062no—
633C23—1062no—
634C23—1062no—
635C23—1062no—
636C23—4244no—
637C23—4244no—
638C23—4244no—
639C23—4244no—
640C23—4244no—
641C23—2128no—
642C23—2121no—
643C23—2128no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23—2121no—
649C23—2121no—
650C23—2121no—
651C23—2121no—
652C23—2121no—
653C23#1313319312yes—
654C23C2×#1171992212yes—
655C23#1313324812yes—
656C23C22×C22⋊D5311yescharacteristic
657Q8—84no—
658D4—534no—
659D4—1062no—
660D4—1062no—
661D4—1062no—
662D4—1062no—
663D4—1062no—
664D4—2128no—
665D4—2121no—
666D4—2121no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
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—84no—
696C2×C4—4244no—
697C2×C4—4244no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4—2121no—
702C2×C4—2121no—
703C2×C4—2121no—
704C2×C4#1313319312yes—
705C2×C4C2×#1171992212yes—
706C2×C4C2×#1171992212yes—
707C2×C4C2×D4×D5311yescharacteristic
708C2×C4C2×Q8×D5311yescharacteristic
709C2×C4#41×D5311yescharacteristic
710C2×C4C2×#1171994911yescharacteristic
711C2×C4#1313326211yescharacteristic
712C2×C4#1313326311yescharacteristic
713C8—1062no—
714C8—2121no—
715C8—2121no—
716C8—2121no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—1064no—
724C22—42416no—
725C22—4241no—
726C22—4241no—
727C22—4241no—
728C22—4241no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22#1681090014yescomplemented
739C22C2×#1313319311yescharacteristic
740C22D4×C22⋊D5311yescharacteristic
741C22#1681126111yescharacteristic
742C22C22×#1171992211yescharacteristic
743C22C2×#1313324811yescharacteristic
744C22#1681142611yescharacteristic
745C22#1681143111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—42no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—4241no—
756C4—4241no—
757C4C22⋊Q8×D5311yescharacteristic
758C4#1681124811yescharacteristic
759C4#1681126411yescharacteristic
760C4#1681130011yescharacteristic
761C2—24no—
762C2—4242no—
763C2—2124no—
764C2#2027837811yescharacteristic
765C2C2×#1681090011yescharacteristic
766C2#2028454011yescharacteristic
767C2#2028622611yescharacteristic
768C2D4×#1171992211yescharacteristic
769C2#2028652211yescharacteristic
770C2#2028679011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2440C2
socleC23×C53C22×D4
prime radicalC23×D212C22
hypercenter#2440D53
hypocenterC53#25950
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#16810900C2semidirect
4. #20276244C2semidirect
5. #20276100C2semidirect
6. #20276100C2semidirect
7. #20275848C2semidirect
8. #20274961C2semidirect
9. #20274961C2semidirect
10. #20274903C2semidirect
11. #20274895C2semidirect
12. #20274742C2semidirect
13. #20274712C2semidirect
15. C53×#2440C2semidirect
22. C2×#13133150C22semidirect
23. C2×#13133150C22semidirect
24. C2×#13133150C22semidirect
25. C2×#13133150C22semidirect
26. C2×C4⋊#88322C22semidirect
27. C2×C4⋊#88322C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810378C22semidirect
49. #16810378C22semidirect
50. C2×C4⋊Q8×C53C22semidirect
55. C53×#389C22semidirect
56. C53×#389C22semidirect
58. C53×#384C22semidirect
68. C22×D212Q8semidirect
324. D212C22⋊Q8semidirect
338. C22×C53#474semidirect
378. #2440D53semidirect
403. C2×C4⋊Q8C2×D53semidirect
430. #389C2×D53semidirect
431. #389C2×D53semidirect
435. #384C2×D53semidirect
446. C53#25950semidirect
738. C22#16810900semidirect

Maximal subgroups

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

subgroupindex
C2×#168109002
C22×#131331372
C22⋊C4×D2122
#202762442
#202761002
#202758482
#202749612
#202749032
#202748952
#202747422
#202747122
#202746452
C53×#24402
#2595053