Finite Group Databasebeta

← #27383622

Subgroups — #27383622

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×#16811105C211yesmaximal, characteristic
2C2×#16810648C211yesmaximal, characteristic, complemented
3C2×#16810623C211yesmaximal, characteristic
4C2×#16810618C211yesmaximal, characteristic
5#20277340C211yesmaximal, characteristic, complemented
6#20274728C211yesmaximal, characteristic, complemented
7#20274724C211yesmaximal, characteristic, complemented
8#20274722C211yesmaximal, characteristic, complemented
9#20274720C211yesmaximal, characteristic, complemented
10#20274718C211yesmaximal, characteristic, complemented
11#20274716C211yesmaximal, characteristic, complemented
12#20274714C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C53×#1805C211yesmaximal, characteristic, complemented
16C22×#11719949C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811105—24no—
20#16811105C418yescomplemented
21C2×Q8×Dic53C2211yescharacteristic
22C2×C4×D212—21no—
23C2×C4×D212C2211yescharacteristic
24C2×#13133179—21no—
25C2×#13133179C2211yescharacteristic
26C2×#13133175C2211yescharacteristic
27C2×#13133174—21no—
28C2×#13133174C2211yescharacteristic
29C2×C4⋊C4×D53—21no—
30C2×C4⋊C4×D53C2211yescharacteristic
31C2×C4⋊C4×D53C2211yescharacteristic
32#16810648—24no—
33C2×C4⋊#88322C2211yescharacteristic
34C2×#13133146C2211yescharacteristic
35C2×#13133146C2211yescharacteristic
36#16810623—24no—
37#16810618—24no—
38C2×#13133141C2211yescharacteristic
39C2×#13133141C2211yescharacteristic
40C2×#13133139C2211yescharacteristic
41C2×#13133139C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×#13133137C2211yescharacteristic
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×Q8×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×#103×C53C2211yescharacteristic
60C2×#103×C53C2211yescharacteristic
61C53×#382C2211yescharacteristic
62C53×#340C2211yescharacteristic
63C53×#340C2211yescharacteristic
64C2×#11719949—22no—
65C2×#11719949—22no—
66C2×#11719949—22no—
67C2×#11719949C2×C414yes—
68C2×#11719949D414yes—
69C2×#11719949Q814yes—
70C22×D212—21no—
71C22×D212C2311yescharacteristic
72C22×C4×D53—21no—
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76C22×C4×D53—21no—
77C22×C4×D53C2311yescharacteristic
78C2×#11719912—22no—
79C2×#11719912—22no—
80C2×#11719912—22no—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C2×C8×D53—22no—
84C2×C8×D53—22no—
85C2×C8×D53—22no—
86Q8×Dic53—22no—
87Q8×Dic53C2×C414yescomplemented
88C4×D212—22no—
89C4×D212—28no—
90C4×D212C2×C414yescomplemented
91#13133179—28no—
92#13133179—22no—
93#13133179C2×C414yescomplemented
94#13133175—22no—
95#13133175—22no—
96#13133174—28no—
97#13133174C2×C414yes—
98#13133174D414yes—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—21no—
101C2×C4⋊Dic53—21no—
102C2×C4⋊Dic53C2311yescharacteristic
103C2×C4⋊Dic53C2311yescharacteristic
104C2×C4⋊Dic53C2311yescharacteristic
105C2×#11719919—21no—
106C2×#11719919—21no—
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×#11719919D411yescharacteristic
110C2×#11719919D411yescharacteristic
111C4⋊C4×D53—28no—
112C4⋊C4×D53—22no—
113C4⋊C4×D53—22no—
114C4⋊C4×D53—22no—
115C4⋊C4×D53C2×C414yes—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921D411yescharacteristic
120C2×#11719921D411yescharacteristic
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123C2×C4×Dic53C2311yescharacteristic
124C4⋊#88322—22no—
125#13133146—22no—
126#13133146—22no—
127#13133141—22no—
128#13133141—22no—
129#13133139—22no—
130#13133139—22no—
131#13133137—22no—
132#13133137—22no—
133#13133124—21no—
134#13133124—21no—
135C22×Q8×C53C2311yescharacteristic
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C4×Q8×C53—22no—
139C4×Q8×C53C2×C414yescomplemented
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C42×C53—21no—
145C2×C42×C53C2311yescharacteristic
146C4⋊C8×C53—22no—
147#103×C53—22no—
148#103×C53—22no—
149#95×C53—21no—
150#95×C53—21no—
151C23×D53—21no—
152C23×D53C2×D411yescharacteristic
153C2×Q8×C53—21no—
154C2×Q8×C53—21no—
155C2×Q8×C53—21no—
156C2×Q8×C53C22×C412yes—
157C2×Q8×C53C2×D412yes—
158C2×Q8×C53C2×Q812yes—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2411yescharacteristic
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53C2×D411yescharacteristic
170C22×Dic53C2×D411yescharacteristic
171C22×Dic53C2×D411yescharacteristic
172#11719949—28no—
173#11719949—28no—
174#11719949—28no—
175#11719949C4⋊C4116yescomplemented
176C2×D212—24no—
177C2×D212—24no—
178C2×D212—24no—
179C2×D212—21no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212C22×C412yes—
183C2×D212C2×D412yes—
184C2×D212C2×Q812yes—
185C2×C4×D53—24no—
186C2×C4×D53—24no—
187C2×C4×D53—24no—
188C2×C4×D53—24no—
189C2×C4×D53—24no—
190C2×C4×D53—24no—
191C2×C4×D53—42no—
192C2×C4×D53—81no—
193C2×C4×D53—81no—
194C2×C4×D53—81no—
195C2×C4×D53—81no—
196C2×C4×D53—81no—
197C2×C4×D53—81no—
198C2×C4×D53—81no—
199C2×C4×D53—81no—
200C2×C4×D53C22×C412yes—
201C2×C4×D53C2×D412yes—
202C2×C4×D53C2×D412yes—
203C2×C4×D53C2×Q812yes—
204C2×C4×D53#4112yes—
205C2×C4×D53#4112yes—
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—24no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53C22×C412yes—
219C42×C53—24no—
220C42×C53C22×C412yes—
221C42×C53C2×D412yes—
222#11719921—24no—
223#11719921—24no—
224#11719921—42no—
225#11719921C22⋊C414yes—
226#11719921C22⋊C414yes—
227C4⋊Dic53—21no—
228C4⋊Dic53—24no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—81no—
234C4⋊Dic53—81no—
235C4⋊Dic53C22×C412yes—
236#11719919—24no—
237#11719919—42no—
238#11719919—81no—
239#11719919—81no—
240#11719919C22⋊C414yes—
241#11719919C22⋊C414yes—
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×C53C22×D411yescharacteristic
255C22×D53—21no—
256C22×D53—21no—
257C22×D53—21no—
258C22×D53—21no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53C2×C22⋊C412yes—
267C22×D53#12112yes—
268C22×D53C22⋊Q812yes—
269Q8×C53—22no—
270Q8×C53—22no—
271Q8×C53—22no—
272Q8×C53C2×C4⋊C414yes—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—21no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—22no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53C2×C22⋊C412yes—
290C2×C4×C53C2×C22⋊C412yes—
291C2×C4×C53C23×C411yescharacteristic
292C2×C4×C53C22×D411yescharacteristic
293C2×C4×C53C22×D411yescharacteristic
294C2×C4×C53C22×Q811yescharacteristic
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—22no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53C2×C22⋊C412yes—
311C2×Dic53C2×C22⋊C412yes—
312C2×Dic53C2×C22⋊C412yes—
313C2×Dic53#12112yes—
314C2×Dic53C22⋊Q812yes—
315D212—216no—
316D212—22no—
317D212—22no—
318D212—22no—
319D212C2×C4⋊C414yes—
320C4×D53—216no—
321C4×D53—84no—
322C4×D53—84no—
323C4×D53—84no—
324C4×D53—84no—
325C4×D53C2×C4⋊C414yes—
326C4×D53#11714yes—
327C4×D53#12114yes—
328C4×D53C22⋊Q814yes—
329C8×C53—41no—
330C8×C53—41no—
331#88322—41no—
332#88322—41no—
333#20652—531nomaximal, Sylow
334C22×C53C22×C22⋊C411yescharacteristic
335C22×C53C2×#12111yescharacteristic
336C22×C53C2×C22⋊Q811yescharacteristic
337C22×C53#57611yescharacteristic
338C22×C53#57711yescharacteristic
339C22×C53#57711yescharacteristic
340C22×C53#57811yescharacteristic
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—22no—
345C2×D53—22no—
346C2×D53—22no—
347C2×D53—24no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—42no—
353C2×D53—42no—
354C2×D53#38014yes—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—24no—
358C4×C53—42no—
359C4×C53—81no—
360C4×C53—81no—
361C4×C53C22×C4⋊C411yescharacteristic
362C4×C53C2×#11711yescharacteristic
363C4×C53C2×#12111yescharacteristic
364C4×C53C2×C22⋊Q811yescharacteristic
365Dic53—22no—
366Dic53—22no—
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#1805D5311yescharacteristic, complemented
378#1804—531no—
379#1804—531no—
380#1803—531no—
381#1803—531no—
382#1802—531no—
383#1802—531no—
384#1736—531no—
385C2×#340—531no—
386C2×C53C2×#38011yescharacteristic
387C2×C53#289711yescharacteristic
388C2×C53#289811yescharacteristic
389C2×C53#304511yescharacteristic
390C2×C53#304611yescharacteristic
391C2×C53#308311yescharacteristic
392C2×C53#308411yescharacteristic
393D53—24no—
394D53—44no—
395C22×#41—531no—
396C22×M16—531no—
397C23×C8—531no—
398#520—538no—
399#520—1064no—
400C2×C4×Q8—531no—
401C2×C4×Q8C2×D5311yescharacteristic
402C2×C4×D4—531no—
403C2×C4×D4—531no—
404C2×C4×D4—1061no—
405C2×C4×D4—1061no—
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×#103C2×D5311yescharacteristic
422C2×#103C2×D5311yescharacteristic
423C2×#102—531no—
424C2×#102—531no—
425C2×#102—531no—
426C2×#102—531no—
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×Q8C22×D5311yescharacteristic
451C22×D4—531no—
452C22×D4—1061no—
453C23×C4—531no—
454C23×C4—1061no—
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—22no—
470C4×Q8—534no—
471C4×Q8—1062no—
472C4×Q8C4×D5314yescomplemented
473C4×D4—534no—
474C4×D4—534no—
475C4×D4—1068no—
476C4×D4—1062no—
477C4×D4—1068no—
478C4×D4—1062no—
479#117—534no—
480#117—534no—
481#117—1068no—
482#117—1062no—
483#117—1062no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—531no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—534no—
489C2×C4⋊C4—531no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—1068no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1062no—
494C2×C4⋊C4—1062no—
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—531no—
506C2×C22⋊C4—531no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C42—21no—
511C2×C42—531no—
512C2×C42—1061no—
513C2×C42—1061no—
514C2×C42C22×D5311yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1062no—
517C4⋊C8—1062no—
518C4⋊C8—1062no—
519#103—22no—
520#103—22no—
521#103—1062no—
522#103—1062no—
523#102—1062no—
524#102—1062no—
525#102—1062no—
526#102—1062no—
527#95—21no—
528#95—21no—
529#95—1061no—
530#95—1061no—
531C24—531no—
532C24—1061no—
533#41—5316no—
534#41—1068no—
535#41—1068no—
536#41—1068no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D5312yes—
541C2×Q8D4×D5312yes—
542C2×Q8Q8×D5312yes—
543C2×D4—532no—
544C2×D4—532no—
545C2×D4—532no—
546C2×D4—1064no—
547C2×D4—1064no—
548C2×D4—1064no—
549C2×D4—1061no—
550C2×D4—1061no—
551C2×D4—1061no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—531no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—1064no—
566C22×C4—1064no—
567C22×C4—1064no—
568C22×C4—1064no—
569C22×C4—1064no—
570C22×C4—1061no—
571C22×C4—1064no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—4241no—
575C22×C4—4241no—
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—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—534no—
607C4⋊C4—534no—
608C4⋊C4—532no—
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—534no—
623C22⋊C4—534no—
624C22⋊C4—1064no—
625C22⋊C4—1064no—
626C22⋊C4—2122no—
627C42—24no—
628C42—532no—
629C42—532no—
630C42—1064no—
631C42—2122no—
632C42C2×C4×D5312yes—
633C42D4×D5312yes—
634C23—532no—
635C23—532no—
636C23—532no—
637C23—1061no—
638C23—1061no—
639C23—1061no—
640C23—1061no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—2121no—
645C23—2121no—
646C23—2121no—
647C23—2121no—
648C23C2×D4×D5311yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C4⋊C4×D5314yes—
653D4—534no—
654D4—10616no—
655D4—1062no—
656D4—1062no—
657D4—1062no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
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—532no—
675C2×C4—532no—
676C2×C4—532no—
677C2×C4—534no—
678C2×C4—534no—
679C2×C4—534no—
680C2×C4—534no—
681C2×C4—532no—
682C2×C4—532no—
683C2×C4—10616no—
684C2×C4—1061no—
685C2×C4—1061no—
686C2×C4—1061no—
687C2×C4—1061no—
688C2×C4—1062no—
689C2×C4—4244no—
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—534no—
714C22—1062no—
715C22—1062no—
716C22—1062no—
717C22—1062no—
718C22—1062no—
719C22—1062no—
720C22—1064no—
721C22—2122no—
722C22—2122no—
723C22—2122no—
724C22—2122no—
725C22—2122no—
726C22—2122no—
727C22C2×C22⋊C4×D5311yescharacteristic
728C22#121×D5311yescharacteristic
729C22C22⋊Q8×D5311yescharacteristic
730C22#1681142511yescharacteristic
731C22#1681143011yescharacteristic
732C22#1681143211yescharacteristic
733C22#1681143911yescharacteristic
734C4—24no—
735C4—22no—
736C4—22no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—534no—
741C4—1062no—
742C4—1062no—
743C4—4241no—
744C4—4241no—
745C4—2122no—
746C4C2×C4⋊C4×D5311yescharacteristic
747C4#117×D5311yescharacteristic
748C4#121×D5311yescharacteristic
749C4C22⋊Q8×D5311yescharacteristic
750C2—1064no—
751C2—2124no—
752C2#380×D5311yescharacteristic
753C2#2028323711yescharacteristic
754C2#2028324711yescharacteristic
755C2#2028425711yescharacteristic
756C2#2028426811yescharacteristic
757C2#2028456911yescharacteristic
758C2#2028458011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1805C2
socleC23×C53C22×D4
prime radicalC22×#11719949C22
cosocleC22×C4×C53C24
hypercenter#1805D53
hypocenterC53#20652
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#16810648C2semidirect
5. #20277340C2semidirect
6. #20274728C2semidirect
7. #20274724C2semidirect
8. #20274722C2semidirect
9. #20274720C2semidirect
10. #20274718C2semidirect
11. #20274716C2semidirect
12. #20274714C2semidirect
13. #20274433C2semidirect
14. #340×D53C2semidirect
15. C53×#1805C2semidirect
20. #16811105C4semidirect
87. Q8×Dic53C2×C4semidirect
90. C4×D212C2×C4semidirect
93. #13133179C2×C4semidirect
139. C4×Q8×C53C2×C4semidirect
175. #11719949C4⋊C4semidirect
377. #1805D53semidirect
443. C53#20652semidirect
472. C4×Q8C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168111052
C2×#168106482
C2×#168106232
C2×#168106182
#202773402
#202747282
#202747242
#202747222
#202747202
#202747182
#202747162
#202747142
#202744332
#340×D532
C53×#18052
#2065253