Finite Group Databasebeta

← #27400327

Subgroups — #27400327

Order 13568.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic
2C2×C8×C22⋊D53C211yesmaximal, characteristic
3#20277611C211yesmaximal, characteristic
4#20275674C211yesmaximal, characteristic, complemented
5#20275661C211yesmaximal, characteristic, complemented
6#20275135C211yesmaximal, characteristic, complemented
7#20275023C211yesmaximal, characteristic, complemented
8#20275019C211yesmaximal, characteristic, complemented
9#20274804C211yesmaximal, characteristic, complemented
10#20274803C211yesmaximal, characteristic, complemented
11#20274718C211yesmaximal, characteristic, complemented
12#103×Dic53C211yesmaximal, characteristic, complemented
13C2×#16810386C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1892C211yesmaximal, characteristic, complemented
16C22×C8×D53C2211yescharacteristic
17#16811331—24no—
18#16811331C418yescomplemented
19C2×#13133216C2211yescharacteristic
20C2×#13133207—21no—
21C2×#13133197—21no—
22C2×#13133194—21no—
23C2×#13133193C2211yescharacteristic
24C2×Q8×Dic53C2211yescharacteristic
25C2×C4×C22⋊D53C2211yescharacteristic
26C2×#13133177—21no—
27C2×#13133177—21no—
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32C8×C22⋊D53—24no—
33C2×#13133146C2211yescharacteristic
34C2×#13133141C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×C8×Dic53C2211yescharacteristic
39#16810520—21no—
40#16810497—21no—
41#16810495—21no—
42#16810492C2211yescharacteristic
43#16810480C2211yescharacteristic
44C4⋊C4×Dic53C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C22⋊Q8×C53C2211yescharacteristic
57C2×#103×C53C2211yescharacteristic
58C2×#103×C53C2211yescharacteristic
59C53×#380C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C22×Dic106—21no—
63C22×C22⋊D53D411yescharacteristic
64C23×Dic53—21no—
65C23×Dic53—21no—
66C22×C4×D53—21no—
67C22×C4×D53—21no—
68C22×C4×D53C2311yescharacteristic
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C2×C8×D53—22no—
72C2×C8×D53—22no—
73C2×C8×D53—41no—
74#13133216—22no—
75#13133216C2×C414yescomplemented
76#13133207—28no—
77#13133197—28no—
78#13133194—28no—
79#13133193—22no—
80#13133193C2×C414yescomplemented
81Q8×Dic53—22no—
82Q8×Dic53C2×C414yescomplemented
83C4×C22⋊D53C2×C414yes—
84C4×C22⋊D53D414yes—
85#13133177—28no—
86#13133177—44no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—21no—
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—41no—
93C2×C4⋊Dic53C2×C414yescomplemented
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×#11719919—21no—
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C2×#11719919—21no—
104C2×#11719919D411yescharacteristic
105C4⋊C4×D53—22no—
106C4⋊C4×D53—22no—
107C4⋊C4×D53—41no—
108C4⋊C4×D53C2×C414yescomplemented
109C2×C22⋊Dic53D411yescharacteristic
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921D411yescharacteristic
113C2×C4×Dic53—21no—
114C2×C4×Dic53—21no—
115C2×C4×Dic53C2311yescharacteristic
116#13133146—22no—
117#13133141—22no—
118#13133141—41no—
119C22⋊#88322—22no—
120#13133129—22no—
121C8×Dic53—22no—
122#13133124—21no—
123#13133124—21no—
124C22×Q8×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C22×C8×C53—22no—
127C22×C8×C53—22no—
128C22×C8×C53—41no—
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53C2×C414yescomplemented
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53C2311yescharacteristic
135C2×C4⋊C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53—21no—
139#103×C53—22no—
140#103×C53—41no—
141#95×C53—21no—
142C24×C53C2×D411yescharacteristic
143C23×D53C2×D411yescharacteristic
144C2×Q8×C53—21no—
145C2×Q8×C53—21no—
146C2×Q8×C53—21no—
147C2×Q8×C53—21no—
148C2×Q8×C53—21no—
149C2×Q8×C53C22×C412yes—
150C22×C4×C53—21no—
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×C53C22×C412yes—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2411yescharacteristic
162C2×C22⋊D53C22⋊C414yes—
163C2×C22⋊D53SD1614yes—
164C2×C22⋊D53Q1614yes—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—24no—
169C22×Dic53—21no—
170C22×Dic53—42no—
171C22×Dic53—42no—
172C22×Dic53—81no—
173C22×Dic53—81no—
174C22×Dic53—81no—
175C22×Dic53C2×D411yescharacteristic
176C22×Dic53C2×D411yescharacteristic
177C22×Dic53C2×D411yescharacteristic
178C2×C4×D53—21no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—21no—
182C2×C4×D53—24no—
183C2×C4×D53—42no—
184C2×C4×D53—42no—
185C2×C4×D53—81no—
186C2×C4×D53—81no—
187C2×C4×D53—81no—
188C2×C4×D53C22×C412yes—
189C2×C4×D53C2×D412yes—
190C2×Dic106—24no—
191C2×Dic106—81no—
192C2×Dic106—81no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—44no—
199C2×C8×C53#4112yes—
200C4⋊C4×C53—24no—
201C4⋊C4×C53—21no—
202C4⋊C4×C53—21no—
203C4⋊C4×C53—21no—
204C4⋊C4×C53—21no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53C22×C412yes—
207C22⋊C4×C53—24no—
208C22⋊C4×C53—42no—
209C22⋊Dic53C22⋊C414yes—
210#11719921—24no—
211#11719921—42no—
212#11719921C22⋊C414yes—
213C4⋊Dic53—24no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—24no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—42no—
221C4⋊Dic53C22×C412yes—
222C4⋊Dic53C22×C412yes—
223C4⋊Dic53#4112yes—
224#11719919—24no—
225#11719919—24no—
226#11719919—24no—
227#11719919—42no—
228#11719919—42no—
229#11719919—81no—
230#11719919C22⋊C414yes—
231C4×Dic53—24no—
232C4×Dic53—42no—
233C4×Dic53C22×C412yes—
234C4×Dic53C2×D412yes—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C8×D53—44no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53C2×C22⋊C412yes—
247C23×C53C2×SD1612yes—
248C23×C53C2×Q1612yes—
249C23×C53C22×D411yescharacteristic
250C22×D53—21no—
251C22×D53—21no—
252C22×D53—21no—
253C22×D53—21no—
254C22×D53C2×C22⋊C412yes—
255C22×D53C2×SD1612yes—
256C22×D53C2×Q1612yes—
257Q8×C53—22no—
258Q8×C53—22no—
259Q8×C53—41no—
260Q8×C53—41no—
261C2×C4×C53—21no—
262C2×C4×C53—21no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—41no—
270C2×C4×C53—41no—
271C2×C4×C53—41no—
272C2×C4×C53—41no—
273C2×C4×C53—41no—
274C2×C4×C53—41no—
275C2×C4×C53—41no—
276C2×C4×C53—41no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53C2×C22⋊C412yes—
280C2×C4×C53C23×C411yescharacteristic
281C2×C4×C53C22×D411yescharacteristic
282C2×C4×C53C2×#4111yescharacteristic
283C2×C4×C53C2×#4111yescharacteristic
284C2×C4×C53H(5,𝔽2)11yescharacteristic
285C2×C4×C532−1+411yescharacteristic
286C22⋊D53#103116yescomplemented
287C2×Dic53—21no—
288C2×Dic53—21no—
289C2×Dic53—21no—
290C2×Dic53—21no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—84no—
304C2×Dic53—84no—
305C2×Dic53C2×C22⋊C412yes—
306C2×Dic53C2×C22⋊C412yes—
307C2×Dic53C2×C22⋊C412yes—
308C2×Dic53C2×SD1612yes—
309C2×Dic53C2×Q1612yes—
310C4×D53—22no—
311C4×D53—22no—
312C4×D53—22no—
313C4×D53—22no—
314C4×D53—84no—
315C4×D53—84no—
316Dic106—84no—
317C8×C53—22no—
318C8×C53—41no—
319#88322—41no—
320#88322—41no—
321#22487—531nomaximal, Sylow
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53C2×#10314yes—
329C22×C53C22×C22⋊C411yescharacteristic
330C22×C53#54611yescharacteristic
331C22×C53#54711yescharacteristic
332C22×C53C22×SD1611yescharacteristic
333C22×C53C22×Q1611yescharacteristic
334C22×C53#57611yescharacteristic
335C22×C53#57711yescharacteristic
336C2×D53—22no—
337C2×D53—22no—
338C2×D53—22no—
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53C2×#10314yes—
343C4×C53—22no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—81no—
347C4×C53—81no—
348C4×C53C4×#4111yescharacteristic
349C4×C53#52011yescharacteristic
350C4×C53#54611yescharacteristic
351C4×C53#54711yescharacteristic
352Dic53—22no—
353Dic53—22no—
354Dic53—42no—
355Dic53—42no—
356Dic53—42no—
357Dic53—81no—
358Dic53C2×#10314yes—
359C2×#554—531no—
360C2×C8×D4—531no—
361D4×C4⋊C4—531no—
362#1990—531no—
363#1987—531no—
364#1892—531no—
365#1892D5311yescharacteristic, complemented
366#1872—531no—
367#1872—531no—
368#1824—531no—
369#1824—531no—
370#1803—531no—
371C4×#103—531no—
372C2×#340—531no—
373C2×#340—531no—
374C2×C53—24no—
375C2×C53#233911yescharacteristic
376C2×C53C22×#10311yescharacteristic
377C2×C53#289711yescharacteristic
378C2×C53#329511yescharacteristic
379C2×C53#329911yescharacteristic
380C2×C53#333511yescharacteristic
381C2×C53#333811yescharacteristic
382D53—24no—
383C23×C8—531no—
384C23×C8C2×D5311yescharacteristic
385#554—538no—
386#554—1064no—
387C2×C4⋊Q8—531no—
388C2×#125—1061no—
389C2×C22⋊Q8—531no—
390C2×C22⋊Q8—1061no—
391C2×C22⋊Q8—1061no—
392C2×C22⋊Q8C2×D5311yescharacteristic
393C2×C4×Q8—531no—
394C2×C4×D4—531no—
395C2×C4×D4—1061no—
396C2×C4×D4—1061no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C8×D4—1064no—
402C2×C4⋊C8—531no—
403C2×#103—531no—
404C2×#103—531no—
405C2×#103C2×D5311yescharacteristic
406C2×#103C2×D5311yescharacteristic
407C2×C22⋊C8—531no—
408C2×C22⋊C8—531no—
409C2×C4×C8—531no—
410#389—1061no—
411#385—1061no—
412#385—1061no—
413#384—531no—
414#380—531no—
415#380C2×D5311yescharacteristic
416C4×C4⋊C4—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340—531no—
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#340C2×D5311yescharacteristic
428#340C2×D5311yescharacteristic
429C53#2248711yescharacteristic, complemented, Sylow
430C22×Q8—1061no—
431C22×Q8C22×D5311yescharacteristic
432C22×D4—531no—
433C23×C4—531no—
434C23×C4—1061no—
435C23×C4—1061no—
436C23×C4—1061no—
437C23×C4—1061no—
438C23×C4C22×D5311yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—1062no—
445C22×C8—1062no—
446C22×C8—2121no—
447C22×C8C22×D5311yescharacteristic
448C22×C8C22×D5311yescharacteristic
449C4⋊Q8—534no—
450C4⋊Q8—1062no—
451#125—1068no—
452C22⋊Q8—22no—
453C22⋊Q8—534no—
454C22⋊Q8—1068no—
455C22⋊Q8—1068no—
456C22⋊Q8—1062no—
457C22⋊Q8C4×D5314yescomplemented
458C4×Q8—534no—
459C4×Q8—1062no—
460C4×D4—534no—
461C4×D4—534no—
462C4×D4—1068no—
463C4×D4—2124no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—534no—
467C2×C4⋊C4—531no—
468C2×C4⋊C4—531no—
469C2×C4⋊C4—531no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—531no—
472C2×C4⋊C4—1062no—
473C2×C4⋊C4—1062no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1062no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4—1061no—
484C2×C4⋊C4—1061no—
485C2×C4⋊C4—2121no—
486C2×C4⋊C4—2121no—
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C4⋊C4C22×D5311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—531no—
493C2×C22⋊C4—531no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C42—531no—
497C2×C42—1061no—
498C2×C42—1061no—
499C4⋊C8—1062no—
500#103—22no—
501#103—41no—
502#103—1062no—
503#103—2121no—
504C22⋊C8—1062no—
505C22⋊C8—1062no—
506C4×C8—1062no—
507#95—21no—
508#95—1061no—
509#95—1061no—
510C24—531no—
511C24D4×D5311yescharacteristic
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—1064no—
518C2×Q8—4241no—
519C2×Q8—4241no—
520C2×Q8C2×C4×D5312yes—
521C2×D4—534no—
522C2×D4—534no—
523C2×D4—534no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—531no—
533C22×C4—531no—
534C22×C4—531no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—1064no—
538C22×C4—1061no—
539C22×C4—1061no—
540C22×C4—1061no—
541C22×C4—1061no—
542C22×C4—1064no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4—4241no—
548C22×C4—4241no—
549C22×C4—4241no—
550C22×C4—4241no—
551C22×C4—4241no—
552C22×C4—4241no—
553C22×C4—2122no—
554C22×C4—2122no—
555C22×C4—2122no—
556C22×C4—2122no—
557C22×C4C2×C4×D5312yes—
558C22×C4D4×D5311yescharacteristic
559C22×C4D4×D5312yes—
560C22×C4C23×D5311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—2124no—
574C2×C8#1171994712yes—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—534no—
582C4⋊C4—532no—
583C4⋊C4—532no—
584C4⋊C4—532no—
585C4⋊C4—1064no—
586C4⋊C4—1064no—
587C4⋊C4—1064no—
588C4⋊C4—1064no—
589C4⋊C4—1064no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—4241no—
596C4⋊C4—2122no—
597C4⋊C4—2122no—
598C4⋊C4—2122no—
599C4⋊C4C2×C4×D5312yes—
600C22⋊C4—24no—
601C22⋊C4—42no—
602C22⋊C4—534no—
603C22⋊C4—534no—
604C22⋊C4—1064no—
605C22⋊C4—2122no—
606C42—532no—
607C42—532no—
608C42—1064no—
609C42—2122no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—532no—
615C23—532no—
616C23—532no—
617C23—1061no—
618C23—1061no—
619C23—1061no—
620C23—1061no—
621C23C22⋊C4×D5312yes—
622C23SD16×D5312yes—
623C23Q16×D5312yes—
624C23C2×D4×D5311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—4244no—
630D4—5316no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—532no—
650C2×C4—532no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—532no—
654C2×C4—1061no—
655C2×C4—1061no—
656C2×C4—1061no—
657C2×C4—1061no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—4244no—
666C2×C4—4244no—
667C2×C4—4244no—
668C2×C4—4244no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4C22⋊C4×D5312yes—
679C2×C4C22×C4×D5311yescharacteristic
680C2×C4C2×D4×D5311yescharacteristic
681C2×C4#41×D5311yescharacteristic
682C2×C4C2×#1171994711yescharacteristic
683C2×C4#1313326211yescharacteristic
684C2×C4#1313326411yescharacteristic
685C8—22no—
686C8—41no—
687C8—2121no—
688C8—2121no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—534no—
696C22—1062no—
697C22—1062no—
698C22—1062no—
699C22—1062no—
700C22—1062no—
701C22—1062no—
702C22#103×D5314yes—
703C22C2×C22⋊C4×D5311yescharacteristic
704C22#1681126211yescharacteristic
705C22#1681127311yescharacteristic
706C22C2×SD16×D5311yescharacteristic
707C22C2×Q16×D5311yescharacteristic
708C22#1681142511yescharacteristic
709C22#1681143011yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—81no—
714C4—81no—
715C4—534no—
716C4—1062no—
717C4—1062no—
718C4—4241no—
719C4—2122no—
720C4—2122no—
721C4—2122no—
722C4C4×#1171994711yescharacteristic
723C4#1681110211yescharacteristic
724C4#1681126011yescharacteristic
725C4#1681127111yescharacteristic
726C2—24no—
727C2—1064no—
728C2#2027754111yescharacteristic
729C2C2×#103×D5311yescharacteristic
730C2#2028323711yescharacteristic
731C2#2028653411yescharacteristic
732C2#2028658611yescharacteristic
733C2#2028706711yescharacteristic
734C2#2028710411yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1892C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenter#1892D53
hypocenterC53#22487
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
4. #20275674C2semidirect
5. #20275661C2semidirect
6. #20275135C2semidirect
7. #20275023C2semidirect
8. #20275019C2semidirect
9. #20274804C2semidirect
10. #20274803C2semidirect
11. #20274718C2semidirect
12. #103×Dic53C2semidirect
13. C2×#16810386C2semidirect
14. #340×D53C2semidirect
15. C53×#1892C2semidirect
18. #16811331C4semidirect
75. #13133216C2×C4semidirect
80. #13133193C2×C4semidirect
82. Q8×Dic53C2×C4semidirect
93. C2×C4⋊Dic53C2×C4semidirect
108. C4⋊C4×D53C2×C4semidirect
132. C22⋊Q8×C53C2×C4semidirect
286. C22⋊D53#103semidirect
365. #1892D53semidirect
429. C53#22487semidirect
457. C22⋊Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×C8×C22⋊D532
#202776112
#202756742
#202756612
#202751352
#202750232
#202750192
#202748042
#202748032
#202747182
#103×Dic532
C2×#168103862
#340×D532
C53×#18922
#2248753