Finite Group Databasebeta

← #27383620

Subgroups — #27383620

Order 13568.

1462 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811102C211yesmaximal, characteristic
2C2×#16810648C211yesmaximal, characteristic, complemented
3C2×#16810621C211yesmaximal, characteristic
4C2×#16810616C211yesmaximal, characteristic
5#20277340C211yesmaximal, characteristic, complemented
6#20274729C211yesmaximal, characteristic, complemented
7#20274727C211yesmaximal, characteristic, complemented
8#20274723C211yesmaximal, characteristic, complemented
9#20274721C211yesmaximal, characteristic, complemented
10#20274719C211yesmaximal, characteristic, complemented
11#20274715C211yesmaximal, characteristic, complemented
12#20274713C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1804C211yesmaximal, characteristic, complemented
16C22×#11719947C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811102—24no—
20#16811102C418yescomplemented
21C2×C4×Dic106C2211yescharacteristic
22C2×#13133182C2211yescharacteristic
23C2×D4×Dic53C2211yescharacteristic
24C2×C4×C22⋊D53—21no—
25C2×#13133177—21no—
26C2×#13133175C2211yescharacteristic
27C2×#13133174C2211yescharacteristic
28C2×#13133173—21no—
29C22×#11719919—21no—
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32#16810648—24no—
33C2×C4⋊#88322C2211yescharacteristic
34C2×#13133146C2211yescharacteristic
35C2×#13133146C2211yescharacteristic
36#16810621—24no—
37#16810616—24no—
38C2×#13133142C2211yescharacteristic
39C2×#13133142C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×#13133140C2211yescharacteristic
42C2×#13133138C2211yescharacteristic
43C2×#13133138C2211yescharacteristic
44#16810520—21no—
45#16810520—21no—
46#16810497—21no—
47#16810497—21no—
48#16810493C2211yescharacteristic
49#16810492C2211yescharacteristic
50#16810488C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55#16810385C2211yescharacteristic
56#16810385C2211yescharacteristic
57C2×C4×D4×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C53×#382C2211yescharacteristic
62C53×#340C2211yescharacteristic
63C53×#340C2211yescharacteristic
64C2×#11719947—22no—
65C2×#11719947—22no—
66C2×#11719947—22no—
67C2×#11719947C2×C414yes—
68C2×#11719947D414yes—
69C2×#11719947Q814yes—
70C22×Dic106C2311yescharacteristic
71C22×C22⋊D53—21no—
72C23×Dic53—21no—
73C23×Dic53—21no—
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76C22×C4×D53C2311yescharacteristic
77C2×#11719912—22no—
78C2×#11719912—22no—
79C2×#11719912—22no—
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C2×C8×D53—22no—
83C2×C8×D53—22no—
84C2×C8×D53—22no—
85C4×Dic106—22no—
86C4×Dic106C2×C414yescomplemented
87#13133182—22no—
88#13133182C2×C414yescomplemented
89D4×Dic53—22no—
90D4×Dic53C2×C414yescomplemented
91C4×C22⋊D53—28no—
92#13133177—28no—
93#13133175—22no—
94#13133175—22no—
95#13133174C2×C414yes—
96#13133174D414yes—
97#13133173—28no—
98C2×C4⋊Dic53—21no—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C4⋊Dic53C2311yescharacteristic
103C2×#11719919—28no—
104C2×#11719919—21no—
105C2×#11719919—21no—
106C2×#11719919—21no—
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×#11719919—21no—
110C2×#11719919D411yescharacteristic
111C2×#11719919D411yescharacteristic
112C4⋊C4×D53—22no—
113C4⋊C4×D53—22no—
114C4⋊C4×D53—22no—
115C4⋊C4×D53C2×C414yes—
116C2×C22⋊Dic53—21no—
117C2×#11719921—21no—
118C2×#11719921D411yescharacteristic
119C2×#11719921D411yescharacteristic
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123C2×C4×Dic53C2311yescharacteristic
124C4⋊#88322—22no—
125#13133146—22no—
126#13133146—22no—
127#13133142—22no—
128#13133142—22no—
129#13133140—22no—
130#13133140—22no—
131#13133138—22no—
132#13133138—22no—
133#13133124—21no—
134#13133124—21no—
135C22×D4×C53C2311yescharacteristic
136C23×C4×C53—21no—
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C4×D4×C53—22no—
140C4×D4×C53C2×C414yescomplemented
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C22⋊C4×C53—21no—
145C2×C42×C53C2311yescharacteristic
146C4⋊C8×C53—22no—
147#102×C53—22no—
148#102×C53—22no—
149#95×C53—21no—
150#95×C53—21no—
151C24×C53—21no—
152C23×D53C2×D411yescharacteristic
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53C22×C412yes—
157C2×D4×C53C2×D412yes—
158C2×D4×C53C2×Q812yes—
159C22×C4×C53—21no—
160C22×C4×C53—24no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—81no—
164C22×C4×C53—81no—
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2411yescharacteristic
168C2×C22⋊D53—24no—
169C2×C22⋊D53—24no—
170C2×C22⋊D53—24no—
171C22×Dic53—21no—
172C22×Dic53—24no—
173C22×Dic53—24no—
174C22×Dic53—24no—
175C22×Dic53—21no—
176C22×Dic53—24no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—81no—
180C22×Dic53—81no—
181C22×Dic53C2×D411yescharacteristic
182C22×Dic53C2×D411yescharacteristic
183C22×Dic53C2×D411yescharacteristic
184#11719947—28no—
185#11719947—28no—
186#11719947—28no—
187#11719947C4⋊C4116yescomplemented
188C2×C4×D53—24no—
189C2×C4×D53—42no—
190C2×C4×D53—81no—
191C2×C4×D53—81no—
192C2×C4×D53—81no—
193C2×C4×D53—81no—
194C2×C4×D53C22×C412yes—
195C2×C4×D53C2×D412yes—
196C2×C4×D53C2×D412yes—
197C2×C4×D53C2×Q812yes—
198C2×C4×D53#4112yes—
199C2×C4×D53#4112yes—
200C2×Dic106—21no—
201C2×Dic106—21no—
202C2×Dic106—21no—
203C2×Dic106C22×C412yes—
204C2×Dic106C2×D412yes—
205C2×Dic106C2×Q812yes—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C4⋊C4×C53—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53C22×C412yes—
218C22⋊C4×C53—24no—
219C42×C53C22×C412yes—
220C42×C53C2×D412yes—
221C22⋊Dic53—24no—
222#11719921—42no—
223#11719921C22⋊C414yes—
224#11719921C22⋊C414yes—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—81no—
231C4⋊Dic53—81no—
232C4⋊Dic53C22×C412yes—
233#11719919—24no—
234#11719919—24no—
235#11719919—24no—
236#11719919—42no—
237#11719919—81no—
238#11719919—81no—
239#11719919C22⋊C414yes—
240#11719919C22⋊C414yes—
241C4×Dic53—24no—
242C4×Dic53—24no—
243C4×Dic53—42no—
244C4×Dic53C22×C412yes—
245C4×Dic53C2×D412yes—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252#11719912—44no—
253C8×D53—44no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53C22×D411yescharacteristic
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53—21no—
266C22×D53C2×C22⋊C412yes—
267C22×D53#12112yes—
268C22×D53C22⋊Q812yes—
269D4×C53—22no—
270D4×C53—22no—
271D4×C53—22no—
272D4×C53C2×C4⋊C414yes—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—22no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—84no—
287C2×C4×C53C2×C22⋊C412yes—
288C2×C4×C53C2×C22⋊C412yes—
289C2×C4×C53C23×C411yescharacteristic
290C2×C4×C53C22×D411yescharacteristic
291C2×C4×C53C22×D411yescharacteristic
292C2×C4×C53C22×Q811yescharacteristic
293C2×C4×C53C2×#4111yescharacteristic
294C2×C4×C53C2×#4111yescharacteristic
295C22⋊D53—216no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—216no—
304C2×Dic53—22no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—84no—
314C2×Dic53C2×C22⋊C412yes—
315C2×Dic53C2×C22⋊C412yes—
316C2×Dic53C2×C22⋊C412yes—
317C2×Dic53#12112yes—
318C2×Dic53C22⋊Q812yes—
319C4×D53—84no—
320C4×D53—84no—
321C4×D53C2×C4⋊C414yes—
322C4×D53#11714yes—
323C4×D53#12114yes—
324C4×D53C22⋊Q814yes—
325Dic106—22no—
326Dic106—22no—
327Dic106—22no—
328Dic106C2×C4⋊C414yes—
329C8×C53—41no—
330C8×C53—41no—
331#88322—41no—
332#88322—41no—
333#20652—531nomaximal, Sylow
334C22×C53—24no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53C22×C22⋊C411yescharacteristic
342C22×C53C2×#12111yescharacteristic
343C22×C53C2×C22⋊Q811yescharacteristic
344C22×C53#57611yescharacteristic
345C22×C53#57711yescharacteristic
346C22×C53#57711yescharacteristic
347C22×C53#57811yescharacteristic
348C2×D53—22no—
349C2×D53—22no—
350C2×D53—22no—
351C2×D53—22no—
352C2×D53—22no—
353C2×D53—22no—
354C2×D53#38014yes—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—42no—
358C4×C53—81no—
359C4×C53—81no—
360C4×C53C22×C4⋊C411yescharacteristic
361C4×C53C2×#11711yescharacteristic
362C4×C53C2×#12111yescharacteristic
363C4×C53C2×C22⋊Q811yescharacteristic
364Dic53—22no—
365Dic53—22no—
366Dic53—24no—
367Dic53—42no—
368Dic53—81no—
369Dic53—81no—
370Dic53#38014yes—
371C2×#520—531no—
372C2×#424—531no—
373C2×#417—531no—
374C2×#416—531no—
375#2317—531no—
376#1805—531no—
377#1805—531no—
378#1804—531no—
379#1804D5311yescharacteristic, complemented
380#1803—531no—
381#1803—531no—
382#1802—531no—
383#1802—531no—
384#1736—531no—
385C2×#340—531no—
386C2×C53—44no—
387C2×C53C2×#38011yescharacteristic
388C2×C53#289711yescharacteristic
389C2×C53#289811yescharacteristic
390C2×C53#304511yescharacteristic
391C2×C53#304611yescharacteristic
392C2×C53#308311yescharacteristic
393C2×C53#308411yescharacteristic
394D53—24no—
395C22×#41—531no—
396C22×M16—531no—
397C23×C8—531no—
398#520—538no—
399#520—1064no—
400C2×C4×Q8—531no—
401C2×C4×Q8—531no—
402C2×C4×D4—531no—
403C2×C4×D4—1061no—
404C2×C4×D4—1061no—
405C2×C4×D4C2×D5311yescharacteristic
406C2×#117—531no—
407C2×#117—531no—
408C2×#117—1061no—
409C22×C4⋊C4—531no—
410C22×C4⋊C4—531no—
411C22×C4⋊C4—1061no—
412#424—1064no—
413C2×C4⋊C8—531no—
414C2×C4⋊C8—531no—
415C2×C4⋊C8—531no—
416C2×C4⋊C8C2×D5311yescharacteristic
417#417—1064no—
418#416—1064no—
419C2×#103—531no—
420C2×#103—531no—
421C2×#103—531no—
422C2×#103—531no—
423C2×#102—531no—
424C2×#102—531no—
425C2×#102C2×D5311yescharacteristic
426C2×#102C2×D5311yescharacteristic
427#389—1061no—
428#389—1061no—
429#385—1061no—
430#385—1061no—
431#384—531no—
432#384—531no—
433#382—531no—
434#382C2×D5311yescharacteristic
435#340—531no—
436#340—531no—
437#340—531no—
438#340—531no—
439#340—531no—
440#340—531no—
441#340C2×D5311yescharacteristic
442#340C2×D5311yescharacteristic
443C53#2065211yescharacteristic, complemented, Sylow
444C2×#41—534no—
445C2×#41—534no—
446C2×#41—534no—
447C2×#41—1062no—
448C2×#41—1062no—
449C2×#41—1062no—
450C22×Q8—531no—
451C22×D4—1061no—
452C22×D4C22×D5311yescharacteristic
453C23×C4—21no—
454C23×C4—531no—
455C23×C4—1061no—
456C23×C4—1061no—
457C23×C4—1061no—
458C23×C4—1061no—
459C2×M16—1062no—
460C2×M16—1062no—
461C2×M16—1062no—
462C22×C8—531no—
463C22×C8—531no—
464C22×C8—1062no—
465C22×C8—1062no—
466C22×C8—1062no—
467C22×C8C22×D5311yescharacteristic
468C22×C8C22×D5311yescharacteristic
469C4×Q8—534no—
470C4×Q8—534no—
471C4×Q8—1062no—
472C4×Q8—1062no—
473C4×D4—22no—
474C4×D4—534no—
475C4×D4—1062no—
476C4×D4—1068no—
477C4×D4—1068no—
478C4×D4C4×D5314yescomplemented
479#117—534no—
480#117—534no—
481#117—1068no—
482#117—1062no—
483#117—1062no—
484C2×C4⋊C4—531no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—534no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1062no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1068no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—531no—
507C2×C22⋊C4—531no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C42—531no—
511C2×C42—1061no—
512C2×C42—1061no—
513C2×C42—1061no—
514C2×C42C22×D5311yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1062no—
517C4⋊C8—1062no—
518C4⋊C8—1062no—
519#103—1062no—
520#103—1062no—
521#103—1062no—
522#103—1062no—
523#102—22no—
524#102—22no—
525#102—1062no—
526#102—1062no—
527#95—21no—
528#95—21no—
529#95—1061no—
530#95—1061no—
531C24—21no—
532C24—531no—
533#41—5316no—
534#41—1068no—
535#41—1068no—
536#41—1068no—
537C2×Q8—532no—
538C2×Q8—532no—
539C2×Q8—532no—
540C2×Q8—1061no—
541C2×Q8—1061no—
542C2×Q8—1061no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—1064no—
547C2×D4—1064no—
548C2×D4—1064no—
549C2×D4C2×C4×D5312yes—
550C2×D4D4×D5312yes—
551C2×D4Q8×D5312yes—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—531no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—531no—
566C22×C4—531no—
567C22×C4—1064no—
568C22×C4—1064no—
569C22×C4—1064no—
570C22×C4—1064no—
571C22×C4—1064no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—4241no—
577C22×C4—4241no—
578C22×C4—4241no—
579C22×C4—4241no—
580C22×C4—4241no—
581C22×C4—4241no—
582C22×C4—2122no—
583C22×C4D4×D5311yescharacteristic
584C22×C4D4×D5311yescharacteristic
585C22×C4C23×D5311yescharacteristic
586M16—2124no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—1061no—
594C2×C8—1061no—
595C2×C8—1061no—
596C2×C8—1061no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—2124no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—534no—
606C4⋊C4—534no—
607C4⋊C4—532no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1061no—
612C4⋊C4—1061no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1061no—
616C4⋊C4—4241no—
617C4⋊C4—4241no—
618C4⋊C4—4241no—
619C4⋊C4—4241no—
620C4⋊C4—2122no—
621C4⋊C4C2×C4×D5312yes—
622C22⋊C4—24no—
623C22⋊C4—534no—
624C22⋊C4—534no—
625C22⋊C4—1064no—
626C22⋊C4—2122no—
627C42—532no—
628C42—532no—
629C42—1064no—
630C42—1064no—
631C42—2122no—
632C42C2×C4×D5312yes—
633C42D4×D5312yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—532no—
642C23—532no—
643C23—532no—
644C23—1061no—
645C23—1061no—
646C23—1061no—
647C23—1061no—
648C23C2×D4×D5311yescharacteristic
649Q8—534no—
650Q8—1062no—
651Q8—1062no—
652Q8—1062no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—10616no—
657D4C4⋊C4×D5314yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—532no—
673C2×C4—532no—
674C2×C4—532no—
675C2×C4—534no—
676C2×C4—534no—
677C2×C4—534no—
678C2×C4—534no—
679C2×C4—532no—
680C2×C4—532no—
681C2×C4—10616no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1061no—
689C2×C4—1062no—
690C2×C4—4244no—
691C2×C4—4244no—
692C2×C4—4244no—
693C2×C4—2121no—
694C2×C4—2121no—
695C2×C4—2121no—
696C2×C4—2121no—
697C2×C4—2121no—
698C2×C4—2121no—
699C2×C4—2121no—
700C2×C4—2121no—
701C2×C4C22⋊C4×D5312yes—
702C2×C4C22⋊C4×D5312yes—
703C2×C4C22×C4×D5311yescharacteristic
704C2×C4C2×D4×D5311yescharacteristic
705C2×C4C2×D4×D5311yescharacteristic
706C2×C4C2×Q8×D5311yescharacteristic
707C2×C4#41×D5311yescharacteristic
708C2×C4#41×D5311yescharacteristic
709C8—41no—
710C8—41no—
711C8—2121no—
712C8—2121no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—534no—
721C22—1062no—
722C22—1062no—
723C22—1062no—
724C22—1062no—
725C22—1062no—
726C22—1062no—
727C22C2×C22⋊C4×D5311yescharacteristic
728C22#121×D5311yescharacteristic
729C22C22⋊Q8×D5311yescharacteristic
730C22#1681142711yescharacteristic
731C22#1681143011yescharacteristic
732C22#1681143311yescharacteristic
733C22#1681143711yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—81no—
738C4—81no—
739C4—534no—
740C4—1064no—
741C4—1062no—
742C4—1062no—
743C4—4241no—
744C4—4241no—
745C4—2122no—
746C4C2×C4⋊C4×D5311yescharacteristic
747C4#117×D5311yescharacteristic
748C4#121×D5311yescharacteristic
749C4C22⋊Q8×D5311yescharacteristic
750C2—44no—
751C2—1064no—
752C2#380×D5311yescharacteristic
753C2#2028324011yescharacteristic
754C2#2028324411yescharacteristic
755C2#2028425511yescharacteristic
756C2#2028426611yescharacteristic
757C2#2028456711yescharacteristic
758C2#2028457811yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1804C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
cosocleC22×C4×C53C24
hypercenter#1804D53
hypocenterC53#20652
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#16810648C2semidirect
5. #20277340C2semidirect
6. #20274729C2semidirect
7. #20274727C2semidirect
8. #20274723C2semidirect
9. #20274721C2semidirect
10. #20274719C2semidirect
11. #20274715C2semidirect
12. #20274713C2semidirect
13. #20274433C2semidirect
14. #340×D53C2semidirect
15. C53×#1804C2semidirect
20. #16811102C4semidirect
86. C4×Dic106C2×C4semidirect
88. #13133182C2×C4semidirect
90. D4×Dic53C2×C4semidirect
140. C4×D4×C53C2×C4semidirect
187. #11719947C4⋊C4semidirect
379. #1804D53semidirect
443. C53#20652semidirect
478. C4×D4C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111022
C2×#168106482
C2×#168106212
C2×#168106162
#202773402
#202747292
#202747272
#202747232
#202747212
#202747192
#202747152
#202747132
#202744332
#340×D532
C53×#18042
#2065253