Finite Group Databasebeta

← #27430471

Subgroups — #27430471

Order 13568.

1082 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810862C211yesmaximal, characteristic
2C2×#16810830C211yesmaximal, characteristic, complemented
3C2×#16810779C211yesmaximal, characteristic
4C22×#13133141C211yesmaximal, characteristic
5#20277718C211yesmaximal, characteristic
6#20276110C211yesmaximal, characteristic, complemented
7#20276037C211yesmaximal, characteristic, complemented
8#20275958C211yesmaximal, characteristic, complemented
9#20275815C211yesmaximal, characteristic, complemented
10#20275639C211yesmaximal, characteristic, complemented
11#20275353C211yesmaximal, characteristic, complemented
12#20275059C211yesmaximal, characteristic, complemented
13#20275023C211yesmaximal, characteristic
14#20274895C211yesmaximal, characteristic
15C53×#2434C211yesmaximal, characteristic
16C22×#11719925C2211yescharacteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20C2×#13133196C2211yescharacteristic
21C2×C4×Dic106C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23#16810862—24no—
24#16810830—24no—
25#16810779—24no—
26C2×#13133150C2211yescharacteristic
27C2×C4⋊#88322C2211yescharacteristic
28C2×C4⋊#88322C2211yescharacteristic
29C2×#13133141—24no—
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133141C2211yescharacteristic
33C2×#13133141C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133141C2211yescharacteristic
37C2×#13133141C2211yescharacteristic
38C2×#13133141C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41#16810529C2211yescharacteristic
42#16810521C2211yescharacteristic
43#16810520—21no—
44#16810510—21no—
45#16810495—21no—
46C4×C4⋊Dic53C2211yescharacteristic
47C22⋊C4×Dic53—21no—
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52C23×Q8×C53C2211yescharacteristic
53C2×C4⋊Q8×C53C2211yescharacteristic
54C2×C4⋊Q8×C53C2211yescharacteristic
55C2×C22⋊Q8×C53C2211yescharacteristic
56C53×#395—21no—
57C53×#395—21no—
58C53×#391C2211yescharacteristic
59C53×#391C2211yescharacteristic
60C53×#385—21no—
61C53×#385—21no—
62C4×C22⋊C4×C53C2211yescharacteristic
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C2×#11719925—22no—
66C2×#11719925—22no—
67C2×#11719925—22no—
68C2×#11719925—22no—
69C2×#11719925—22no—
70C2×#11719925—22no—
71C2×#11719925—41no—
72C2×#11719925—41no—
73C2×#11719925—41no—
74C22×#88322—22no—
75C22×#88322—22no—
76C22×#88322—41no—
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79C22×#88322C2311yescharacteristic
80C22×#88322C2311yescharacteristic
81#13133196—22no—
82#13133196D414yes—
83C4×Dic106—22no—
84C4×Dic106—41no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—22no—
87C2×C4⋊Dic53—41no—
88C2×C4⋊Dic53C2311yescharacteristic
89C2×C4⋊Dic53C2311yescharacteristic
90C2×C4⋊Dic53C2311yescharacteristic
91C2×#11719919—21no—
92C2×#11719919—21no—
93C2×#11719919—21no—
94C2×C22⋊Dic53—21no—
95C2×C4×Dic53—21no—
96C2×C4×Dic53—21no—
97#13133150—22no—
98C4⋊#88322—22no—
99C4⋊#88322—41no—
100#13133141—22no—
101#13133141—22no—
102#13133141—22no—
103#13133141—22no—
104#13133141—22no—
105#13133141—22no—
106#13133141—22no—
107#13133141—41no—
108#13133141D414yes—
109#13133140—22no—
110C22⋊#88322—22no—
111#13133124—21no—
112#13133124—21no—
113#13133124—21no—
114#13133124—21no—
115C22×Q8×C53—21no—
116C22×Q8×C53—22no—
117C22×Q8×C53—22no—
118C22×Q8×C53—22no—
119C22×Q8×C53—22no—
120C22×Q8×C53—41no—
121C22×Q8×C53—41no—
122C22×Q8×C53C2311yescharacteristic
123C22×Q8×C53C2311yescharacteristic
124C22×Q8×C53C2311yescharacteristic
125C23×C4×C53—21no—
126C23×C4×C53C2311yescharacteristic
127C4⋊Q8×C53—22no—
128C4⋊Q8×C53—22no—
129C4⋊Q8×C53—41no—
130C4⋊Q8×C53—41no—
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53—22no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—21no—
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C22⋊C4×C53—21no—
140C2×C22⋊C4×C53D411yescharacteristic
141C2×C22⋊C4×C53D411yescharacteristic
142C2×C42×C53C2311yescharacteristic
143C2×C42×C53C2311yescharacteristic
144#95×C53—21no—
145#95×C53—21no—
146#95×C53—21no—
147#95×C53—21no—
148#95×C53D411yescharacteristic
149#95×C53D411yescharacteristic
150C24×C53C2×D411yescharacteristic
151C2×Q8×C53—21no—
152C2×Q8×C53—21no—
153C2×Q8×C53—28no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53—21no—
157C2×Q8×C53—21no—
158C2×Q8×C53—21no—
159C2×Q8×C53—21no—
160C2×Q8×C53—21no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—42no—
169C2×Q8×C53—42no—
170C2×Q8×C53—44no—
171C2×Q8×C53—44no—
172C2×Q8×C53—44no—
173C2×Q8×C53—42no—
174C2×Q8×C53C2×D412yes—
175C2×Q8×C53#4112yes—
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—21no—
183C22×C4×C53—21no—
184C22×C4×C53—42no—
185C22×C4×C53—42no—
186C22×C4×C53—42no—
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D412yes—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53#4112yes—
194C22×C4×C53C2411yescharacteristic
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—42no—
200C22×Dic53—42no—
201C22×Dic53—81no—
202C2×Dic106—21no—
203C2×Dic106—21no—
204C2×Dic106—21no—
205C2×Dic106—21no—
206C2×Dic106—21no—
207C2×Dic106C2×D412yes—
208C4⋊C4×C53—21no—
209C4⋊C4×C53—21no—
210C4⋊C4×C53—42no—
211C4⋊C4×C53—42no—
212C4⋊C4×C53—42no—
213C4⋊C4×C53—42no—
214C4⋊C4×C53—42no—
215C22⋊C4×C53—22no—
216C22⋊C4×C53—42no—
217C22⋊C4×C53Q1614yescomplemented
218C42×C53—21no—
219C42×C53—21no—
220C42×C53—21no—
221C42×C53—21no—
222C22⋊Dic53—24no—
223#11719925—44no—
224#11719925—44no—
225#11719925—44no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—42no—
231C4⋊Dic53C2×D412yes—
232C4⋊Dic53C2×D412yes—
233#11719919—24no—
234#11719919—42no—
235#11719919—81no—
236C4×Dic53—42no—
237C4×Dic53—81no—
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—21no—
248C2×#88322—21no—
249C2×#88322—44no—
250C2×#88322C2×D412yes—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53#12112yes—
256C23×C53C2×Q1612yes—
257C23×C53#13712yes—
258C23×C53C22×D411yescharacteristic
259Q8×C53—22no—
260Q8×C53—22no—
261Q8×C53—22no—
262Q8×C53—22no—
263Q8×C53—48no—
264Q8×C53—41no—
265Q8×C53—41no—
266Q8×C53—41no—
267Q8×C53—41no—
268Q8×C53—41no—
269Q8×C53—41no—
270Q8×C53—41no—
271Q8×C53—41no—
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—22no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—48no—
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#12112yes—
302C2×C4×C53C2×Q1612yes—
303C2×C4×C53C2×Q1612yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53C2×#4111yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×C4×C53H(5,𝔽2)11yescharacteristic
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—41no—
316C2×Dic53—41no—
317C2×Dic53—41no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—84no—
323Dic106—22no—
324Dic106—22no—
325Dic106—41no—
326Dic106—41no—
327#88322—22no—
328#88322—41no—
329#88322—41no—
330#88322—41no—
331#25082—531nomaximal, Sylow
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—22no—
338C22×C53#46214yescomplemented
339C22×C53C2×#12111yescharacteristic
340C22×C53D4211yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53C22×Q1611yescharacteristic
343C22×C53C2×#13711yescharacteristic
344C22×C53#57711yescharacteristic
345C22×C53#57811yescharacteristic
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—42no—
350C4×C53—42no—
351C4×C53—41no—
352C4×C53—41no—
353C4×C53—81no—
354C4×C53—81no—
355C4×C53#52511yescharacteristic
356C4×C53#53811yescharacteristic
357C4×C53D4211yescharacteristic
358C4×C53#54611yescharacteristic
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—81no—
363C2×#467—531no—
364C2×#462—531no—
365C2×#451—531no—
366C22×#103—531no—
367#2434D5311yescharacteristic
368#2360—531no—
369#2068—531no—
370#2056—531no—
371#2043—531no—
372#2016—531no—
373#1981—531no—
374#1928—531no—
375#1878—531no—
376#1872—531no—
377#1850—531no—
378C2×C53—24no—
379C2×C53#242411yescharacteristic
380C2×C53C2×#46211yescharacteristic
381C2×C53#304611yescharacteristic
382C2×C53#326611yescharacteristic
383C2×C53D4×Q1611yescharacteristic
384C2×C53#329911yescharacteristic
385C2×C53#331211yescharacteristic
386C23×Q8C2×D5311yescharacteristic
387C22×Q16—531no—
388C22×Q16—531no—
389C22×Q16—531no—
390C23×C8—531no—
391C2×C4⋊Q8C2×D5311yescharacteristic
392C2×C4⋊Q8C2×D5311yescharacteristic
393C2×C22⋊Q8—531no—
394C2×C22⋊Q8C2×D5311yescharacteristic
395C2×C4×Q8—531no—
396C22×C4⋊C4—531no—
397#467—1064no—
398#462—1064no—
399#451—1064no—
400C2×#107—531no—
401C2×C4⋊C8—531no—
402C2×C4⋊C8—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103—531no—
406C2×#103—531no—
407C2×#103—531no—
408C2×#103—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#103—531no—
413C2×#103—1064no—
414C2×C22⋊C8—531no—
415#395—21no—
416#395—21no—
417#391—531no—
418#391C2×D5311yescharacteristic
419#391C2×D5311yescharacteristic
420#389—531no—
421#389—1061no—
422#387—1061no—
423#385—21no—
424#385—21no—
425#385—1061no—
426C4×C4⋊C4—531no—
427C4×C22⋊C4—1061no—
428C4×C22⋊C4C2×D5311yescharacteristic
429#340—531no—
430#340—531no—
431#336—531no—
432#336—531no—
433C53#2508211yescharacteristic, complemented, Sylow
434C22×Q8—21no—
435C22×Q8—22no—
436C22×Q8—22no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—41no—
440C22×Q8—41no—
441C22×Q8—531no—
442C22×Q8C22×D5311yescharacteristic
443C22×Q8C22×D5311yescharacteristic
444C22×Q8C22×D5311yescharacteristic
445C23×C4—21no—
446C23×C4—1061no—
447C23×C4C22×D5311yescharacteristic
448C2×Q16—1062no—
449C2×Q16—1062no—
450C2×Q16—1062no—
451C2×Q16—1062no—
452C2×Q16—1062no—
453C2×Q16—1062no—
454C2×Q16—2121no—
455C2×Q16—2121no—
456C2×Q16—2121no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—531no—
460C22×C8—531no—
461C22×C8—1062no—
462C22×C8—1062no—
463C22×C8—2121no—
464C4⋊Q8—22no—
465C4⋊Q8—22no—
466C4⋊Q8—41no—
467C4⋊Q8—41no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—534no—
471C22⋊Q8—1062no—
472C4×Q8—1062no—
473C4×Q8—2121no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—1062no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—2121no—
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4C22⋊D5311yescharacteristic
492C2×C22⋊C4C22⋊D5311yescharacteristic
493C2×C42—1061no—
494C2×C42—1061no—
495C2×C42C22×D5311yescharacteristic
496C2×C42C22×D5311yescharacteristic
497#107—1062no—
498C4⋊C8—1062no—
499C4⋊C8—2121no—
500#103—534no—
501#103—1062no—
502#103—1062no—
503#103—1062no—
504#103—1062no—
505#103—1062no—
506#103—1062no—
507#103—1062no—
508#103—1062no—
509#103—2121no—
510C22⋊C8—1062no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—1061no—
516#95—1061no—
517#95—1061no—
518#95—1061no—
519#95C22⋊D5311yescharacteristic
520#95C22⋊D5311yescharacteristic
521C24C2×C22⋊D5311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8—44no—
542C2×Q8—44no—
543C2×Q8—44no—
544C2×Q8—42no—
545C2×Q8—532no—
546C2×Q8—1061no—
547C2×Q8—1061no—
548C2×Q8—1061no—
549C2×Q8—1061no—
550C2×Q8—1061no—
551C2×Q8D4×D5312yes—
552C2×Q8#1171994712yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—4241no—
569C22×C4—2122no—
570C22×C4—2122no—
571C22×C4D4×D5312yes—
572C22×C4#1171994712yes—
573C22×C4C2×C22⋊D5311yescharacteristic
574C22×C4C2×C22⋊D5311yescharacteristic
575C22×C4C2×C22⋊D5311yescharacteristic
576C22×C4C2×C22⋊D5311yescharacteristic
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C23×D5311yescharacteristic
579Q16—2124no—
580Q16—2124no—
581Q16—2124no—
582C2×C8—532no—
583C2×C8—1061no—
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—2124no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—1064no—
605C4⋊C4—1061no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—4241no—
610C4⋊C4—2122no—
611C4⋊C4—2122no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—1064no—
615C22⋊C4#1171992514yescomplemented
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—4241no—
621C42—2122no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23#1313318812yes—
627C23C2×#1171992512yes—
628C23#1313324812yes—
629C23C22×C22⋊D5311yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—48no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—1062no—
644Q8—1062no—
645Q8—2121no—
646Q8—2121no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—48no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—4244no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4—2121no—
685C2×C4—2121no—
686C2×C4—2121no—
687C2×C4—2121no—
688C2×C4—2121no—
689C2×C4#1313318812yes—
690C2×C4C2×#1171992512yes—
691C2×C4C2×#1171992512yes—
692C2×C4C2×D4×D5311yescharacteristic
693C2×C4C2×D4×D5311yescharacteristic
694C2×C4C2×#1171994711yescharacteristic
695C2×C4C2×#1171994711yescharacteristic
696C2×C4#1313326211yescharacteristic
697C2×C4#1313326211yescharacteristic
698C8—1062no—
699C8—2121no—
700C8—2121no—
701C8—2121no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22#1681083014yescomplemented
709C22C2×#1313318811yescharacteristic
710C22D4×C22⋊D5311yescharacteristic
711C22#1681126711yescharacteristic
712C22C22×#1171992511yescharacteristic
713C22C2×#1313324811yescharacteristic
714C22#1681143111yescharacteristic
715C22#1681143811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—81no—
724C4—81no—
725C4—4241no—
726C4—2122no—
727C4—2122no—
728C4—2122no—
729C4#1681112911yescharacteristic
730C4#1681120811yescharacteristic
731C4#1681125511yescharacteristic
732C4#1681126011yescharacteristic
733C2—24no—
734C2#2027824711yescharacteristic
735C2C2×#1681083011yescharacteristic
736C2#2028426111yescharacteristic
737C2#2028622611yescharacteristic
738C2D4×#1171992511yescharacteristic
739C2#2028659111yescharacteristic
740C2#2028676611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2434C2
socleC23×C53C22×D4
prime radicalC24×C53C2×D4
hypercenter#2434D53
hypocenterC53#25082
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
2. C2×#16810830C2semidirect
6. #20276110C2semidirect
7. #20276037C2semidirect
8. #20275958C2semidirect
9. #20275815C2semidirect
10. #20275639C2semidirect
11. #20275353C2semidirect
12. #20275059C2semidirect
217. C22⋊C4×C53Q16semidirect
338. C22×C53#462semidirect
433. C53#25082semidirect
615. C22⋊C4#11719925semidirect
708. C22#16810830semidirect

Maximal subgroups

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

subgroupindex
C2×#168108622
C2×#168108302
C2×#168107792
C22×#131331412
#202777182
#202761102
#202760372
#202759582
#202758152
#202756392
#202753532
#202750592
#202750232
#202748952
C53×#24342
#2508253