Finite Group Databasebeta

← #27389807

Subgroups — #27389807

Order 13568.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811097C211yesmaximal, characteristic, complemented
2C2×#16810756C211yesmaximal, characteristic
3C2×#16810733C211yesmaximal, characteristic, complemented
4C2×C4×#11719922C211yesmaximal, characteristic, complemented
5#20275066C211yesmaximal, characteristic, complemented
6#20275066C211yesmaximal, characteristic, complemented
7#20275038C211yesmaximal, characteristic, complemented
8#20274975C211yesmaximal, characteristic, complemented
9#20274961C211yesmaximal, characteristic, complemented
10#20274912C211yesmaximal, characteristic, complemented
11#20274645C211yesmaximal, characteristic, complemented
12#20274543C211yesmaximal, characteristic, complemented
13C4×#13133137C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2324C211yesmaximal, characteristic, complemented
16C23×D212C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19#16811097—24no—
20#16811097—24no—
21C2×C4×D212C2211yescharacteristic
22C2×C4×D212C2211yescharacteristic
23C2×C4×D212C2211yescharacteristic
24C2×C4×D212C2211yescharacteristic
25C2×#13133179—21no—
26C2×#13133179—21no—
27C2×#13133176C2211yescharacteristic
28C2×C22⋊C4×D53—21no—
29C2×C22⋊C4×D53—21no—
30#16810756C418yescomplemented
31#16810733—24no—
32C4×#11719922—24no—
33C2×#13133150C2211yescharacteristic, complemented
34C2×#13133148C2211yescharacteristic, complemented
35C2×#13133138C2211yescharacteristic, complemented
36C2×#13133138C2211yescharacteristic, complemented
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39C2×#13133137C2211yescharacteristic
40C2×#13133137C2211yescharacteristic
41C2×#13133137C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×C22⋊#88322C2211yescharacteristic
44C2×C22⋊#88322C2211yescharacteristic
45C2×#13133128C2211yescharacteristic, complemented
46C2×C4×#88322C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810385C2211yescharacteristic, complemented
49#16810385C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810378C2211yescharacteristic, complemented
52#16810378C2211yescharacteristic, complemented
53C2×#121×C53C2211yescharacteristic
54C2×C4×D4×C53C2211yescharacteristic, complemented
55C2×#117×C53C2211yescharacteristic
56C53×#390—21no—
57C53×#390C2211yescharacteristic, complemented
58C53×#389C2211yescharacteristic, complemented
59C53×#388—21no—
60C53×#386—21no—
61C53×#385—21no—
62C53×#380C2211yescharacteristic
63C4×C4⋊C4×C53C2211yescharacteristic, complemented
64C24×D53—21no—
65C22×D212—21no—
66C22×D212—22no—
67C22×D212—22no—
68C22×D212—22no—
69C22×D212—22no—
70C22×D212—22no—
71C22×D212C2×C414yescomplemented
72C22×D212C2311yescharacteristic
73C22×D212C2311yescharacteristic
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76C22×C4×D53—21no—
77C22×C4×D53—21no—
78C2×#11719922—22no—
79C2×#11719922—22no—
80C2×#11719922—22no—
81C2×#11719922—22no—
82C2×#11719922C2×C414yescomplemented
83C2×#11719922C2×C414yescomplemented
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C22×#88322C2311yescharacteristic
88C4×D212—22no—
89C4×D212—22no—
90C4×D212—22no—
91C4×D212—22no—
92C4×D212—22no—
93C4×D212—22no—
94C4×D212D414yescomplemented
95C4×D212D414yescomplemented
96#13133179—28no—
97#13133179—28no—
98#13133176—22no—
99#13133176—22no—
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C22⋊Dic53—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C2×#11719921—21no—
107C22⋊C4×D53—28no—
108C22⋊C4×D53—28no—
109C2×C4×Dic53—21no—
110#13133150—22no—
111#13133148—22no—
112#13133138—22no—
113#13133138—22no—
114#13133137—22no—
115#13133137—22no—
116#13133137—22no—
117#13133137—22no—
118#13133137C2×C414yescomplemented
119#13133137C2×C414yescomplemented
120C22⋊#88322—22no—
121C22⋊#88322C2×C414yescomplemented
122#13133128—22no—
123C4×#88322—22no—
124C22×D4×C53—21no—
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128#121×C53—22no—
129#121×C53C2×C414yescomplemented
130C4×D4×C53—22no—
131C4×D4×C53—22no—
132#117×C53—22no—
133#117×C53—22no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53D411yescharacteristic
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53D411yescharacteristic
146C2×C22⋊C4×C53D411yescharacteristic
147C2×C42×C53—21no—
148C2×C42×C53C2311yescharacteristic
149C2×C42×C53C2311yescharacteristic
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153C24×C53—21no—
154C24×C53C2×D411yescharacteristic
155C23×D53—21no—
156C23×D53—21no—
157C23×D53—24no—
158C23×D53—24no—
159C23×D53—24no—
160C23×D53—81no—
161C23×D53—81no—
162C23×D53—81no—
163C23×D53—81no—
164C2×D4×C53—24no—
165C2×D4×C53—21no—
166C2×D4×C53—21no—
167C2×D4×C53—21no—
168C2×D4×C53—21no—
169C2×D4×C53—21no—
170C2×D4×C53—81no—
171C2×D4×C53—81no—
172C2×D4×C53C22×C412yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—42no—
181C22×C4×C53—81no—
182C22×C4×C53—81no—
183C22×C4×C53C22×C412yes—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53#4112yes—
190C22×C4×C53C2411yescharacteristic
191C22×Dic53—21no—
192C22×Dic53—21no—
193C2×D212—24no—
194C2×D212—24no—
195C2×D212—28no—
196C2×D212—28no—
197C2×D212—24no—
198C2×D212—21no—
199C2×D212—21no—
200C2×D212—21no—
201C2×D212—21no—
202C2×D212—21no—
203C2×D212—21no—
204C2×D212—28no—
205C2×D212—28no—
206C2×D212C22×C412yes—
207C2×D212C22×C412yes—
208C2×D212C2×D412yes—
209C2×D212C2×D412yes—
210C2×D212#4112yes—
211C2×D212#4112yes—
212C2×C4×D53—24no—
213C2×C4×D53—24no—
214C2×C4×D53—24no—
215C2×C4×D53—24no—
216C2×C4×D53—81no—
217C2×C4×D53—81no—
218C2×C4×D53—81no—
219C2×C4×D53—81no—
220C2×C4×D53—81no—
221C2×C4×D53—81no—
222C2×C4×D53—81no—
223C2×C4×D53—81no—
224C4⋊C4×C53—22no—
225C4⋊C4×C53—22no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53—21no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—81no—
232C4⋊C4×C53C22×C412yes—
233C22⋊C4×C53—24no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C22⋊C4×C53—42no—
237C22⋊C4×C53—81no—
238C22⋊C4×C53—81no—
239C22⋊C4×C53—81no—
240C42×C53—21no—
241C42×C53—21no—
242C42×C53—81no—
243C42×C53C2×D412yes—
244C42×C53C2×D412yes—
245C22⋊Dic53—24no—
246#11719922—28no—
247#11719922—28no—
248#11719921—24no—
249#11719921—24no—
250#11719921—24no—
251#11719921—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53C2×D412yes—
255C4⋊Dic53C2×D412yes—
256C4×Dic53—24no—
257C2×#88322—21no—
258C2×#88322—21no—
259C2×#88322—21no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322C22×C412yes—
268C2×#88322C22×C412yes—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—22no—
276C23×C53—41no—
277C23×C53—41no—
278C23×C53—41no—
279C23×C53—41no—
280C23×C53—41no—
281C23×C53—41no—
282C23×C53C4×D412yes—
283C23×C53C22×D411yescharacteristic
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—216no—
291C22×D53—41no—
292C22×D53—41no—
293C22×D53—41no—
294C22×D53—41no—
295C22×D53—41no—
296C22×D53—41no—
297C22×D53—41no—
298C22×D53—41no—
299C22×D53—84no—
300C22×D53—84no—
301C22×D53—84no—
302C22×D53—84no—
303C22×D53—84no—
304C22×D53—84no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—41no—
308D4×C53—41no—
309D4×C53—84no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—41no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53—84no—
336C2×C4×C53C4×D412yes—
337C2×C4×C53#12012yes—
338C2×C4×C53#12012yes—
339C2×C4×C53C23×C411yescharacteristic
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53C22×D411yescharacteristic
342C2×C4×C53C2×#4111yescharacteristic
343C2×C4×C53C2×#4111yescharacteristic
344C2×C4×C53C2×#4111yescharacteristic
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351D212—216no—
352D212—22no—
353D212—22no—
354D212—22no—
355D212—22no—
356D212—22no—
357D212—22no—
358D212C4×D414yes—
359D212C4×D414yes—
360C4×D53—84no—
361C4×D53—84no—
362C4×D53—84no—
363C4×D53—84no—
364#88322—22no—
365#88322—22no—
366#88322—41no—
367#88322—41no—
368#21458—531nomaximal, Sylow
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—81no—
380C22×C53—81no—
381C22×C53—81no—
382C22×C53—81no—
383C22×C53C2×C4×D411yescharacteristic
384C22×C53C2×#12011yescharacteristic
385C22×C53#52511yescharacteristic
386C22×C53#57611yescharacteristic
387C22×C53#57611yescharacteristic
388C22×C53#57611yescharacteristic
389C22×C53#57711yescharacteristic
390C2×D53—24no—
391C2×D53—24no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—816no—
405C4×C53—22no—
406C4×C53—22no—
407C4×C53—22no—
408C4×C53—42no—
409C4×C53—41no—
410C4×C53—41no—
411C4×C53—81no—
412C4×C53—81no—
413C4×C53C2×C4×D411yescharacteristic
414C4×C53C2×C4×D411yescharacteristic
415C4×C53#52511yescharacteristic
416C4×C53#52511yescharacteristic
417Dic53—42no—
418Dic53—42no—
419C2×#518—531no—
420C2×#447—531no—
421C2×#442—531no—
422C2×C4×D8—531no—
423#2324D5311yescharacteristic, complemented
424#1879—531no—
425#1879—531no—
426#1875—531no—
427#1864—531no—
428#1862—531no—
429#1854—531no—
430#1786—531no—
431#1762—531no—
432C4×#102—531no—
433#1750—531no—
434C2×C53—42no—
435C2×C53—82no—
436C2×C53C4×#12011yescharacteristic
437C2×C53#294611yescharacteristic
438C2×C53#294811yescharacteristic
439C2×C53#300811yescharacteristic
440C2×C53#301211yescharacteristic
441C2×C53#311811yescharacteristic
442C2×C53#312211yescharacteristic
443D53—44no—
444D53—44no—
445C23×D4—531no—
446C22×D8—531no—
447C22×D8—531no—
448C2×#121C2×D5311yescharacteristic
449#518—1064no—
450#518—1064no—
451C2×C4×D4—531no—
452C2×C4×D4—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—1061no—
456C2×C4×D4—1061no—
457C2×C4×D4C2×D5311yescharacteristic, complemented
458C2×#117—531no—
459C2×#117C2×D5311yescharacteristic
460C22×C22⋊C4—1061no—
461C22×C22⋊C4—1061no—
462#447—538no—
463#442—1064no—
464C4×D8—1064no—
465C2×#107—531no—
466C2×#106—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×C22⋊C8—531no—
476C2×C22⋊C8—531no—
477C2×#97—531no—
478C2×C4×C8—531no—
479#390—21no—
480#390C2×D5311yescharacteristic, complemented
481#389C2×D5311yescharacteristic, complemented
482#388—21no—
483#386—21no—
484#385—21no—
485#380C2×D5311yescharacteristic
486C4×C4⋊C4C2×D5311yescharacteristic, complemented
487#340—531no—
488#340—531no—
489#340—531no—
490#340—531no—
491#336—531no—
492#336—531no—
493C53#2145811yescharacteristic, complemented, Sylow
494C25—1061no—
495C22×D4—21no—
496C22×D4—534no—
497C22×D4—531no—
498C22×D4—531no—
499C22×D4—1062no—
500C22×D4—1062no—
501C22×D4—1062no—
502C22×D4—1062no—
503C22×D4—1062no—
504C22×D4—1061no—
505C22×D4C22×D5311yescharacteristic
506C23×C4—21no—
507C23×C4—1061no—
508C23×C4—1061no—
509C23×C4—1061no—
510C23×C4—1061no—
511C23×C4C22×D5311yescharacteristic
512C2×D8—534no—
513C2×D8—534no—
514C2×D8—1062no—
515C2×D8—1062no—
516C2×D8—1062no—
517C2×D8—1062no—
518C22×C8—531no—
519C22×C8—531no—
520C22×C8—531no—
521C22×C8—531no—
522#121—22no—
523#121C4×D5314yescomplemented
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—534no—
527C4×D4—534no—
528C4×D4—1062no—
529C4×D4—1062no—
530C4×D4—1062no—
531C4×D4—1062no—
532C4×D4—1068no—
533C4×D4—1068no—
534C4×D4—1062no—
535C4×D4—1062no—
536#117—22no—
537#117—22no—
538#117—1062no—
539#117—1062no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4C22⋊D5311yescharacteristic
544C2×C4⋊C4C22⋊D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1068no—
554C2×C22⋊C4—1068no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4C22⋊D5311yescharacteristic
561C2×C22⋊C4C22⋊D5311yescharacteristic
562C2×C42—21no—
563C2×C42—1061no—
564C2×C42C22×D5311yescharacteristic
565C2×C42C22×D5311yescharacteristic
566#107—1062no—
567#106—1062no—
568#102—534no—
569#102—534no—
570#102—1062no—
571#102—1062no—
572#102—1062no—
573#102—1062no—
574#102—1062no—
575#102—1062no—
576C22⋊C8—534no—
577C22⋊C8—1062no—
578#97—1062no—
579C4×C8—1062no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—1064no—
585C24—1064no—
586C24—1064no—
587C24—1061no—
588C24—1061no—
589C24—4241no—
590C24—4241no—
591C24—4241no—
592C24—4241no—
593C24C2×C22⋊D5311yescharacteristic
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—532no—
603C2×D4—532no—
604C2×D4—532no—
605C2×D4—532no—
606C2×D4—532no—
607C2×D4—532no—
608C2×D4—1068no—
609C2×D4—1068no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1068no—
613C2×D4—1068no—
614C2×D4—1064no—
615C2×D4—1061no—
616C2×D4—1061no—
617C2×D4—1061no—
618C2×D4—1061no—
619C2×D4—1061no—
620C2×D4—1061no—
621C2×D4C2×C4×D5312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4—1064no—
633C22×C4—1064no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1064no—
637C22×C4—1064no—
638C22×C4—4241no—
639C22×C4—4241no—
640C22×C4—4241no—
641C22×C4—4241no—
642C22×C4—4241no—
643C22×C4—4241no—
644C22×C4—4241no—
645C22×C4—4241no—
646C22×C4C2×C4×D5312yes—
647C22×C4#1171994512yes—
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5311yescharacteristic
654D8—1068no—
655D8—1068no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—1061no—
667C2×C8—1061no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—81no—
676C4⋊C4—532no—
677C4⋊C4—532no—
678C4⋊C4—1061no—
679C4⋊C4—1061no—
680C4⋊C4C2×C4×D5312yes—
681C22⋊C4—24no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—1064no—
697C42D4×D5312yes—
698C42D4×D5312yes—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—10616no—
713C23—1062no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—1062no—
719C23—4244no—
720C23—4244no—
721C23—4244no—
722C23—4244no—
723C23—4244no—
724C23—4244no—
725C23—2121no—
726C23—2121no—
727C23—2121no—
728C23—2121no—
729C23—2121no—
730C23—2121no—
731C23—2121no—
732C23—2121no—
733C23C4×C22⋊D5312yes—
734C23C22×C22⋊D5311yescharacteristic
735D4—22no—
736D4—22no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—534no—
741D4—534no—
742D4—10616no—
743D4—1062no—
744D4—1062no—
745D4—1062no—
746D4—1062no—
747D4—1062no—
748D4—1062no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—4244no—
778C2×C4—4244no—
779C2×C4—4244no—
780C2×C4—4244no—
781C2×C4—2121no—
782C2×C4—2121no—
783C2×C4—2121no—
784C2×C4—2121no—
785C2×C4C4×C22⋊D5312yes—
786C2×C4#1313318512yes—
787C2×C4#1313318512yes—
788C2×C4C22×C4×D5311yescharacteristic
789C2×C4C2×D4×D5311yescharacteristic
790C2×C4C2×D4×D5311yescharacteristic
791C2×C4#41×D5311yescharacteristic
792C2×C4#41×D5311yescharacteristic
793C2×C4C2×#1171994511yescharacteristic
794C8—1062no—
795C8—1062no—
796C8—2121no—
797C8—2121no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—1064no—
813C22—1064no—
814C22—42416no—
815C22—2122no—
816C22—2122no—
817C22—2122no—
818C22—2122no—
819C22—2122no—
820C22—2122no—
821C22—2122no—
822C22—2122no—
823C22—2122no—
824C22—2122no—
825C22—2122no—
826C22—2122no—
827C22C2×C4×C22⋊D5311yescharacteristic
828C22C2×#1313318511yescharacteristic
829C22#1681113011yescharacteristic
830C22#1681142611yescharacteristic
831C22#1681142611yescharacteristic
832C22#1681142611yescharacteristic
833C22#1681143111yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—41no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4—2122no—
843C4—2122no—
844C4C4×D4×D5311yescharacteristic
845C4C4×D4×D5311yescharacteristic
846C4#1681113211yescharacteristic
847C4#1681113211yescharacteristic
848C2—42no—
849C2—82no—
850C2—2124no—
851C2—2124no—
852C2C4×#1313318511yescharacteristic
853C2#2028354311yescharacteristic
854C2#2028356511yescharacteristic
855C2#2028398111yescharacteristic
856C2#2028401611yescharacteristic
857C2#2028489311yescharacteristic
858C2#2028495311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2324C2
socleC23×C53C22×D4
prime radicalC2×#16810756C2
cosocleC22×C4×C53C24
hypercenter#2324D53
hypocenterC53#21458
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#16811097C2semidirect
3. C2×#16810733C2semidirect
4. C2×C4×#11719922C2semidirect
5. #20275066C2semidirect
6. #20275066C2semidirect
7. #20275038C2semidirect
8. #20274975C2semidirect
9. #20274961C2semidirect
10. #20274912C2semidirect
11. #20274645C2semidirect
12. #20274543C2semidirect
13. C4×#13133137C2semidirect
14. #20274481C2semidirect
15. C53×#2324C2semidirect
30. #16810756C4semidirect
33. C2×#13133150C22semidirect
34. C2×#13133148C22semidirect
35. C2×#13133138C22semidirect
36. C2×#13133138C22semidirect
45. C2×#13133128C22semidirect
46. C2×C4×#88322C22semidirect
47. #16810385C22semidirect
48. #16810385C22semidirect
49. #16810385C22semidirect
50. #16810385C22semidirect
51. #16810378C22semidirect
52. #16810378C22semidirect
54. C2×C4×D4×C53C22semidirect
57. C53×#390C22semidirect
58. C53×#389C22semidirect
63. C4×C4⋊C4×C53C22semidirect
71. C22×D212C2×C4semidirect
82. C2×#11719922C2×C4semidirect
83. C2×#11719922C2×C4semidirect
94. C4×D212D4semidirect
95. C4×D212D4semidirect
118. #13133137C2×C4semidirect
119. #13133137C2×C4semidirect
121. C22⋊#88322C2×C4semidirect
129. #121×C53C2×C4semidirect
423. #2324D53semidirect
457. C2×C4×D4C2×D53semidirect
480. #390C2×D53semidirect
481. #389C2×D53semidirect
486. C4×C4⋊C4C2×D53semidirect
493. C53#21458semidirect
523. #121C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168110972
C2×#168107562
C2×#168107332
C2×C4×#117199222
#202750662
#202750382
#202749752
#202749612
#202749122
#202746452
#202745432
C4×#131331372
#202744812
C53×#23242
#2145853