Finite Group Databasebeta

← #27404360

Subgroups — #27404360

Order 13568.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810762C211yesmaximal, characteristic
2C2×#16810721C211yesmaximal, characteristic, complemented
3C22×#13133141C211yesmaximal, characteristic, complemented
4#20277729C211yesmaximal, characteristic
5#20275599C211yesmaximal, characteristic, complemented
6#20275408C211yesmaximal, characteristic, complemented
7#20275353C211yesmaximal, characteristic, complemented
8#20275141C211yesmaximal, characteristic
9#20275070C211yesmaximal, characteristic, complemented
10#20275052C211yesmaximal, characteristic, complemented
11#20274969C211yesmaximal, characteristic, complemented
12#20274902C211yesmaximal, characteristic, complemented
13#20274545C211yesmaximal, characteristic, complemented
14#20274493C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719924C2211yescharacteristic
17C22×#11719924C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×#13133177—21no—
22C22×C4⋊Dic53C2211yescharacteristic
23#16810762C418yescomplemented
24#16810721—24no—
25C2×#13133150C2211yescharacteristic
26C2×#13133150C2211yescharacteristic
27C2×#13133141—24no—
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133137C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133128C2211yescharacteristic
38C2×#13133128C2211yescharacteristic
39#16810525C2211yescharacteristic
40#16810521C2211yescharacteristic
41#16810515—21no—
42#16810500—21no—
43#16810497—21no—
44C4×C4⋊Dic53C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810378C2211yescharacteristic
51C23×Q8×C53C2211yescharacteristic
52C2×C4×Q8×C53C2211yescharacteristic
53C2×C4×Q8×C53C2211yescharacteristic
54C53×#391—21no—
55C53×#391—21no—
56C53×#391C2211yescharacteristic
57C53×#391C2211yescharacteristic
58C53×#380—21no—
59C53×#380C2211yescharacteristic
60C4×C22⋊C4×C53—21no—
61C4×C22⋊C4×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C22×C4×D53—21no—
66C2×#11719924—22no—
67C2×#11719924—22no—
68C2×#11719924—41no—
69C2×#11719924—41no—
70C2×#11719924C2×C414yescomplemented
71C2×#11719924C2×C414yescomplemented
72C22×#88322—22no—
73C22×#88322—22no—
74C22×#88322—41no—
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79#13133191—22no—
80#13133191C2×C414yes—
81C4×D212—22no—
82C4×D212—41no—
83#13133177—44no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—22no—
86C2×C4⋊Dic53—41no—
87C2×C4⋊Dic53C2311yescharacteristic
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×#11719919—21no—
91C2×#11719921—21no—
92C2×#11719921—21no—
93C2×#11719921—21no—
94C2×#11719921—21no—
95C2×C4×Dic53—21no—
96#13133150—22no—
97#13133150—41no—
98#13133141—22no—
99#13133141—22no—
100#13133141—22no—
101#13133141C2×C414yescomplemented
102#13133141C2×C414yescomplemented
103#13133141D414yescomplemented
104#13133137—22no—
105#13133137—41no—
106C22⋊#88322C2×C414yescomplemented
107#13133128—22no—
108#13133128—41no—
109#13133124—21no—
110#13133124—21no—
111C22×Q8×C53—21no—
112C22×Q8×C53—22no—
113C22×Q8×C53—22no—
114C22×Q8×C53—22no—
115C22×Q8×C53—41no—
116C22×Q8×C53—41no—
117C22×Q8×C53C2×C414yescomplemented
118C22×Q8×C53C2311yescharacteristic
119C22×Q8×C53C2311yescharacteristic
120C23×C4×C53—21no—
121C23×C4×C53C2311yescharacteristic
122C4×Q8×C53—22no—
123C4×Q8×C53—22no—
124C4×Q8×C53—41no—
125C4×Q8×C53—41no—
126C2×C4⋊C4×C53—21no—
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53C2311yescharacteristic
129C2×C4⋊C4×C53C2311yescharacteristic
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53D411yescharacteristic
132C2×C22⋊C4×C53D411yescharacteristic
133C2×C42×C53—21no—
134C2×C42×C53—21no—
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137#95×C53—21no—
138#95×C53—21no—
139#95×C53—21no—
140#95×C53—21no—
141#95×C53—21no—
142#95×C53D411yescharacteristic
143#95×C53D411yescharacteristic
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C2×Q8×C53—24no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53—21no—
150C2×Q8×C53—21no—
151C2×Q8×C53—28no—
152C2×Q8×C53—21no—
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—42no—
157C2×Q8×C53—42no—
158C2×Q8×C53—44no—
159C2×Q8×C53—44no—
160C2×Q8×C53—44no—
161C2×Q8×C53C22×C412yes—
162C2×Q8×C53C22×C412yes—
163C2×Q8×C53C2×D412yes—
164C2×Q8×C53#4112yes—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—24no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—42no—
175C22×C4×C53—42no—
176C22×C4×C53C22×C412yes—
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53#4112yes—
183C22×C4×C53C2411yescharacteristic
184C2×C22⋊D53—24no—
185C2×C22⋊D53—42no—
186C2×C22⋊D53—42no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—21no—
190C22×Dic53—42no—
191C22×Dic53—42no—
192C22×Dic53—81no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212—21no—
196C2×D212—21no—
197C2×D212—21no—
198C2×D212C22×C412yes—
199C2×C4×D53—42no—
200C2×C4×D53—42no—
201C2×C4×D53—81no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—42no—
207C4⋊C4×C53—42no—
208C22⋊C4×C53—22no—
209C22⋊C4×C53—22no—
210C22⋊C4×C53—42no—
211C42×C53—21no—
212C42×C53—21no—
213C42×C53—21no—
214C42×C53—21no—
215C42×C53—42no—
216C42×C53—42no—
217#11719924—28no—
218#11719924—44no—
219#11719921—24no—
220#11719921—42no—
221#11719921—42no—
222#11719921—81no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—42no—
228C4⋊Dic53C22×C412yes—
229C4⋊Dic53C2×D412yes—
230#11719919—42no—
231C4×Dic53—42no—
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—21no—
241C2×#88322—44no—
242C2×#88322C22×C412yes—
243C2×#88322C22×C412yes—
244C2×#88322C2×D412yes—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53C4×D412yes—
250C23×C53AGL(1,ℤ/8)12yes—
251C23×C53#13712yes—
252C23×C53C22×D411yescharacteristic
253C22×D53—22no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—22no—
264Q8×C53—22no—
265Q8×C53—48no—
266Q8×C53—41no—
267Q8×C53—41no—
268Q8×C53C4×D414yescomplemented
269C2×C4×C53—22no—
270C2×C4×C53—21no—
271C2×C4×C53—22no—
272C2×C4×C53—21no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
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—21no—
290C2×C4×C53—21no—
291C2×C4×C53—48no—
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×C53C4×D412yes—
301C2×C4×C53C23×C411yescharacteristic
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53H(5,𝔽2)11yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C22⋊D53—48no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—84no—
318D212—22no—
319D212—22no—
320D212—41no—
321D212—41no—
322C4×D53—84no—
323#88322—22no—
324#88322—22no—
325#88322—22no—
326#88322—41no—
327#22855—531nomaximal, Sylow
328C22×C53—22no—
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53#44014yescomplemented
335C22×C53C2×C4×D411yescharacteristic
336C22×C53D4211yescharacteristic
337C22×C53#54611yescharacteristic
338C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C53C2×#13711yescharacteristic
340C22×C53#57711yescharacteristic
341C22×C53#57811yescharacteristic
342C2×D53—42no—
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—81no—
346C2×D53—81no—
347C2×D53—81no—
348C2×D53—81no—
349C4×C53—22no—
350C4×C53—24no—
351C4×C53—42no—
352C4×C53—41no—
353C4×C53—41no—
354C4×C53—41no—
355C4×C53—41no—
356C4×C53—81no—
357C4×C53—81no—
358C4×C53C2×C4×D411yescharacteristic
359C4×C53#51811yescharacteristic
360C4×C53#54611yescharacteristic
361C4×C53#55111yescharacteristic
362Dic53—42no—
363Dic53—42no—
364Dic53—81no—
365C2×#448—531no—
366C2×#440—531no—
367C22×#103—531no—
368#2361—531no—
369Q8×C22⋊C4D5311yescharacteristic, complemented
370#1973—531no—
371#1935—531no—
372#1928—531no—
373#1893—531no—
374#1880—531no—
375#1877—531no—
376#1863—531no—
377#1852—531no—
378#1763—531no—
379#1752—531no—
380C2×C53—24no—
381C2×C53#235811yescharacteristic
382C2×C53C2×#44011yescharacteristic
383C2×C53#294711yescharacteristic
384C2×C53#326511yescharacteristic
385C2×C53#327011yescharacteristic
386C2×C53#330811yescharacteristic
387C2×C53#332011yescharacteristic
388D53—82no—
389C23×Q8C2×D5311yescharacteristic
390C22×SD16—531no—
391C22×SD16—531no—
392C23×C8—531no—
393C2×#121—531no—
394C2×C4×Q8C2×D5311yescharacteristic
395C2×C4×Q8C2×D5311yescharacteristic
396C2×C4×D4—531no—
397C2×C4×D4—1061no—
398C22×C4⋊C4—531no—
399#448—538no—
400#440—1064no—
401C2×#107—531no—
402C2×#107—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—1064no—
410C2×#102—531no—
411C2×#102—531no—
412C2×C22⋊C8—531no—
413C2×#97—531no—
414C2×#97—531no—
415#391—21no—
416#391—21no—
417#391C2×D5311yescharacteristic
418#391C2×D5311yescharacteristic
419#390—531no—
420#389—531no—
421#388—1061no—
422#386—1061no—
423#385—1061no—
424#380—21no—
425#380C2×D5311yescharacteristic
426C4×C4⋊C4—531no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2×D5311yescharacteristic
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#336—531no—
434#336—531no—
435C53#2285511yescharacteristic, complemented, Sylow
436C22×Q8—22no—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C4×D5314yescomplemented
443C22×Q8C22×D5311yescharacteristic
444C22×Q8C22×D5311yescharacteristic
445C22×D4—531no—
446C22×D4—1061no—
447C23×C4—21no—
448C23×C4—1061no—
449C23×C4—1061no—
450C23×C4C22×D5311yescharacteristic
451C2×SD16—534no—
452C2×SD16—534no—
453C2×SD16—1062no—
454C2×SD16—1062no—
455C2×SD16—2121no—
456C2×SD16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—2121no—
464#121—534no—
465#121—1062no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×D4—1062no—
471C4×D4—2121no—
472C4×D4—2124no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—531no—
476C2×C4⋊C4—531no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—1062no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—2121no—
482C2×C4⋊C4C22×D5311yescharacteristic
483C2×C4⋊C4C22×D5311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1061no—
486C2×C22⋊C4—1061no—
487C2×C22⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C22⋊C4C22⋊D5311yescharacteristic
490C2×C22⋊C4C22⋊D5311yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—1061no—
494C2×C42C22×D5311yescharacteristic
495C2×C42C22×D5311yescharacteristic
496#107—1062no—
497#107—2121no—
498#103—534no—
499#103—534no—
500#103—534no—
501#103—1062no—
502#103—1062no—
503#103—1062no—
504#102—1062no—
505#102—2121no—
506C22⋊C8—534no—
507#97—1062no—
508#97—2121no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—1061no—
515#95—1061no—
516#95C22⋊D5311yescharacteristic
517#95C22⋊D5311yescharacteristic
518C24—1061no—
519C24C2×C22⋊D5311yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D5312yes—
536C2×Q8C2×C4×D5312yes—
537C2×Q8D4×D5312yes—
538C2×Q8#1171994712yes—
539C2×D4—532no—
540C2×D4—1064no—
541C2×D4—1061no—
542C2×D4—1061no—
543C2×D4—1061no—
544C2×D4—1061no—
545C2×D4—1061no—
546C2×D4—2122no—
547C2×D4—2122no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—4241no—
563C22×C4—4241no—
564C22×C4—2122no—
565C22×C4—2122no—
566C22×C4—2122no—
567C22×C4—2122no—
568C22×C4C2×C4×D5312yes—
569C22×C4#1171994512yes—
570C22×C4C2×C22⋊D5311yescharacteristic
571C22×C4C2×C22⋊D5311yescharacteristic
572C22×C4C2×C22⋊D5311yescharacteristic
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C23×D5311yescharacteristic
576SD16—1068no—
577SD16—2124no—
578C2×C8—532no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—1061no—
582C2×C8—1061no—
583C2×C8—1061no—
584C2×C8—1061no—
585C2×C8—1061no—
586C2×C8—1061no—
587C2×C8—1061no—
588C2×C8—1061no—
589C2×C8—1061no—
590C2×C8—2124no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—532no—
598C4⋊C4—532no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—2122no—
604C4⋊C4—2122no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—1064no—
609C22⋊C4—4241no—
610C22⋊C4—2122no—
611C22⋊C4—2122no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—2122no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—1062no—
624C23—2121no—
625C23—2121no—
626C23—2121no—
627C23—2121no—
628C23—2121no—
629C23—2121no—
630C23C4×C22⋊D5312yes—
631C23#1313324212yes—
632C23#1313324812yes—
633C23C22×C22⋊D5311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8#1313317714yescomplemented
643D4—1062no—
644D4—1062no—
645D4—2128no—
646D4—2121no—
647D4—2121no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—4244no—
682C2×C4—4244no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4—2121no—
690C2×C4C4×C22⋊D5312yes—
691C2×C4C22×C4×D5311yescharacteristic
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4C2×#1171994711yescharacteristic
694C2×C4C2×#1171994511yescharacteristic
695C2×C4#1313326211yescharacteristic
696C2×C4#1313326211yescharacteristic
697C8—1062no—
698C8—1062no—
699C8—1062no—
700C8—2121no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—4241no—
708C22—4241no—
709C22—4241no—
710C22—4241no—
711C22—2122no—
712C22—2122no—
713C22—2122no—
714C22#1681072114yescomplemented
715C22C2×C4×C22⋊D5311yescharacteristic
716C22D4×C22⋊D5311yescharacteristic
717C22#1681126711yescharacteristic
718C22C2×#1313324211yescharacteristic
719C22C2×#1313324811yescharacteristic
720C22#1681143111yescharacteristic
721C22#1681143811yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—4241no—
732C4—2122no—
733C4—2122no—
734C4C2×#1313317711yescharacteristic
735C4#1681109611yescharacteristic
736C4#1681126311yescharacteristic
737C4#1681129911yescharacteristic
738C2—24no—
739C2—4242no—
740C2#2027769411yescharacteristic
741C2C2×#1681072111yescharacteristic
742C2#2028355811yescharacteristic
743C2#2028621111yescharacteristic
744C2#2028628611yescharacteristic
745C2#2028670611yescharacteristic
746C2#2028688611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingQ8×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#13133191C22
cosocleC22×C4×C53C24
hypercenterQ8×C22⋊C4D53
hypocenterC53#22855
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810721C2semidirect
3. C22×#13133141C2semidirect
5. #20275599C2semidirect
6. #20275408C2semidirect
7. #20275353C2semidirect
9. #20275070C2semidirect
10. #20275052C2semidirect
11. #20274969C2semidirect
12. #20274902C2semidirect
13. #20274545C2semidirect
14. #20274493C2semidirect
15. Q8×C22⋊C4×C53C2semidirect
23. #16810762C4semidirect
70. C2×#11719924C2×C4semidirect
71. C2×#11719924C2×C4semidirect
101. #13133141C2×C4semidirect
102. #13133141C2×C4semidirect
103. #13133141D4semidirect
106. C22⋊#88322C2×C4semidirect
117. C22×Q8×C53C2×C4semidirect
268. Q8×C53C4×D4semidirect
334. C22×C53#440semidirect
369. Q8×C22⋊C4D53semidirect
435. C53#22855semidirect
442. C22×Q8C4×D53semidirect
642. Q8#13133177semidirect
714. C22#16810721semidirect

Maximal subgroups

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

subgroupindex
C2×#168107622
C2×#168107212
C22×#131331412
#202777292
#202755992
#202754082
#202753532
#202751412
#202750702
#202750522
#202749692
#202749022
#202745452
#202744932
Q8×C22⋊C4×C532
#2285553