Finite Group Databasebeta

← #27307115

Subgroups — #27307115

Order 13568.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810517C211yesmaximal, characteristic, complemented
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810499C211yesmaximal, characteristic
4C2×#16810497C211yesmaximal, characteristic, complemented
5C2×#16810483C211yesmaximal, characteristic, complemented
6C2×C4×#11719921C211yesmaximal, characteristic, complemented
7#20272971C211yesmaximal, characteristic, complemented
8#20272962C211yesmaximal, characteristic, complemented
9#20272961C211yesmaximal, characteristic, complemented
10#20272954C211yesmaximal, characteristic
11#20272953C211yesmaximal, characteristic, complemented
12#20272949C211yesmaximal, characteristic, complemented
13#20272948C211yesmaximal, characteristic, complemented
14#20272942C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810517—24no—
31#16810502C418yescomplemented
32#16810499—24no—
33#16810497—24no—
34#16810483—24no—
35C4×#11719921—24no—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C24×C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C42×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C4×C22⋊C4×C53—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C24×D53C2311yescharacteristic
59C22×C22⋊D53—22no—
60C22×C22⋊D53—22no—
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—41no—
64C22×C22⋊D53—41no—
65C22×C22⋊D53C2×C414yes—
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C22×C4×D53—22no—
74C22×C4×D53—22no—
75C22×C4×D53—22no—
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—41no—
79C22×C4×D53—41no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—22no—
84C2×C4⋊Dic53—41no—
85C2×C4⋊Dic53—41no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×C22⋊Dic53—22no—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—22no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—41no—
96C2×C22⋊Dic53—41no—
97C2×C22⋊Dic53C2×C414yescomplemented
98C2×#11719921—22no—
99C2×#11719921—22no—
100C2×#11719921—22no—
101C2×#11719921—22no—
102C2×#11719921—22no—
103C2×#11719921—22no—
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—41no—
110C2×#11719921—41no—
111C2×#11719921C2×C414yes—
112C2×#11719921C2×C414yes—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—22no—
115C2×C4×Dic53—41no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—22no—
124#13133124—41no—
125#13133124—41no—
126#13133124—41no—
127#13133124C2×C414yescomplemented
128#13133124C2×C414yescomplemented
129#13133124D414yescomplemented
130C25×C53C2311yescharacteristic
131C23×C4×C53—22no—
132C23×C4×C53—22no—
133C23×C4×C53—22no—
134C23×C4×C53—22no—
135C23×C4×C53—41no—
136C23×C4×C53—41no—
137C23×C4×C53C2×C414yescomplemented
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53—22no—
149C2×C22⋊C4×C53D414yes—
150C2×C42×C53—22no—
151C2×C42×C53—22no—
152C2×C42×C53—22no—
153C2×C42×C53—22no—
154C2×C42×C53—41no—
155C2×C42×C53—41no—
156#95×C53—22no—
157#95×C53D414yescomplemented
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53C22×C412yes—
171C24×C53C2×D412yes—
172C24×C53#4112yes—
173C24×C53C2411yescharacteristic
174C23×D53—21no—
175C23×D53—21no—
176C23×D53—21no—
177C23×D53—21no—
178C23×D53—21no—
179C23×D53—21no—
180C23×D53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53C22×C412yes—
187C23×D53#4112yes—
188C23×D53#4112yes—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—28no—
220C22×C4×C53—28no—
221C22×C4×C53—44no—
222C22×C4×C53—44no—
223C22×C4×C53—44no—
224C22×C4×C53—44no—
225C22×C4×C53—44no—
226C22×C4×C53C22×C412yes—
227C22×C4×C53C22×C412yes—
228C22×C4×C53C2×D412yes—
229C22×C4×C53C2×D412yes—
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53#4112yes—
235C22×C4×C53#4112yes—
236C22×C4×C53#4112yes—
237C22×C4×C53#4112yes—
238C2×C22⋊D53—28no—
239C2×C22⋊D53—28no—
240C2×C22⋊D53—44no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53—44no—
243C2×C22⋊D53—44no—
244C2×C22⋊D53—44no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—21no—
261C22×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53—21no—
283C22×Dic53—21no—
284C22×Dic53—21no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53C22×C412yes—
290C22×Dic53C22×C412yes—
291C22×Dic53C22×C412yes—
292C22×Dic53C2×D412yes—
293C22×Dic53C2×D412yes—
294C2×C4×D53—28no—
295C2×C4×D53—44no—
296C2×C4×D53—44no—
297C2×C4×D53—44no—
298C2×C4×D53—44no—
299C2×C4×D53—44no—
300C2×C4×D53—44no—
301C22⋊C4×C53—28no—
302C22⋊C4×C53—28no—
303C42×C53—44no—
304C42×C53—44no—
305C22⋊Dic53—28no—
306C22⋊Dic53—44no—
307C22⋊Dic53—44no—
308#11719921—28no—
309#11719921—28no—
310#11719921—28no—
311#11719921—44no—
312#11719921—44no—
313C4⋊Dic53—44no—
314C4⋊Dic53—44no—
315#11719919—44no—
316C4×Dic53—44no—
317C23×C53—22no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—41no—
336C23×C53—41no—
337C23×C53—41no—
338C23×C53—41no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53C4×D414yes—
352C23×C53C23×C411yescharacteristic
353C23×C53C22×D411yescharacteristic
354C23×C53C22×D411yescharacteristic
355C23×C53C22×D411yescharacteristic
356C23×C53C2×#4111yescharacteristic
357C23×C53C2×#4111yescharacteristic
358C23×C53C2×#4111yescharacteristic
359C23×C53C2×#4111yescharacteristic
360C23×C53C2×#4111yescharacteristic
361C23×C53C2×#4111yescharacteristic
362C23×C53C2×#4111yescharacteristic
363C23×C53H(5,𝔽2)11yescharacteristic
364C23×C53H(5,𝔽2)11yescharacteristic
365C23×C53H(5,𝔽2)11yescharacteristic
366C23×C532−1+411yescharacteristic
367C22×D53—22no—
368C22×D53—22no—
369C22×D53—22no—
370C22×D53—22no—
371C22×D53—22no—
372C22×D53—22no—
373C22×D53—22no—
374C22×D53—22no—
375C22×D53—22no—
376C22×D53—22no—
377C22×D53—22no—
378C22×D53—22no—
379C22×D53—22no—
380C22×D53—22no—
381C22×D53—22no—
382C22×D53—22no—
383C22×D53—22no—
384C22×D53—22no—
385C22×D53—41no—
386C22×D53—41no—
387C22×D53—41no—
388C22×D53—41no—
389C22×D53—41no—
390C22×D53—41no—
391C22×D53—41no—
392C22×D53—41no—
393C22×D53—41no—
394C22×D53—41no—
395C22×D53—41no—
396C22×D53—41no—
397C22×D53—41no—
398C22×D53—41no—
399C22×D53—41no—
400C22×D53—41no—
401C22×D53#11714yes—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—416no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53—41no—
435C2×C4×C53—41no—
436C2×C4×C53—41no—
437C2×C4×C53—41no—
438C2×C4×C53—41no—
439C2×C4×C53—41no—
440C2×C4×C53—41no—
441C2×C4×C53—41no—
442C2×C4×C53C4×D414yes—
443C2×C4×C53C4×D414yes—
444C2×C4×C53#12114yes—
445C22⋊D53—416no—
446C2×Dic53—22no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—41no—
462C2×Dic53—41no—
463C2×Dic53—41no—
464C2×Dic53—41no—
465C2×Dic53—41no—
466C2×Dic53—41no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53—41no—
490C2×Dic53—41no—
491C2×Dic53—41no—
492C2×Dic53—41no—
493C2×Dic53—41no—
494C2×Dic53—41no—
495C4×D53—416no—
496#13988—531nomaximal, Sylow
497C22×C53—24no—
498C22×C53—24no—
499C22×C53—24no—
500C22×C53—42no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53C2×#11711yescharacteristic
513C22×C53C2×C4×D411yescharacteristic
514C22×C53C2×C4×D411yescharacteristic
515C22×C53C2×C4×D411yescharacteristic
516C22×C53C4×#4111yescharacteristic
517C22×C53#51811yescharacteristic
518C22×C53#52011yescharacteristic
519C22×C53C2×#12111yescharacteristic
520C22×C53#52511yescharacteristic
521C22×C53#52511yescharacteristic
522C22×C53#52511yescharacteristic
523C22×C53#52911yescharacteristic
524C22×C53#52911yescharacteristic
525C22×C53#52911yescharacteristic
526C22×C53#53211yescharacteristic
527C22×C53#53811yescharacteristic
528C22×C53#53911yescharacteristic
529C22×C53#54011yescharacteristic
530C22×C53#54211yescharacteristic
531C22×C53D4211yescharacteristic
532C22×C53D4211yescharacteristic
533C22×C53#54611yescharacteristic
534C22×C53#54611yescharacteristic
535C22×C53#54611yescharacteristic
536C22×C53#54611yescharacteristic
537C22×C53#54611yescharacteristic
538C22×C53#54711yescharacteristic
539C22×C53#54811yescharacteristic
540C22×C53#54811yescharacteristic
541C22×C53#55111yescharacteristic
542C22×C53#55111yescharacteristic
543C22×C53#55111yescharacteristic
544C22×C53#55211yescharacteristic
545C22×C53#55311yescharacteristic
546C22×C53#55311yescharacteristic
547C2×D53—24no—
548C2×D53—24no—
549C2×D53—24no—
550C2×D53—42no—
551C2×D53—42no—
552C2×D53—42no—
553C2×D53—42no—
554C2×D53—42no—
555C2×D53—42no—
556C2×D53—42no—
557C2×D53—42no—
558C2×D53—42no—
559C2×D53—42no—
560C2×D53—42no—
561C2×D53—42no—
562C4×C53—24no—
563C4×C53—24no—
564C4×C53—24no—
565C4×C53—42no—
566C4×C53—42no—
567C4×C53—42no—
568Dic53—42no—
569Dic53—42no—
570Dic53—42no—
571Dic53—42no—
572Dic53—42no—
573Dic53—81no—
574Dic53—81no—
575C2×#388—531no—
576C2×#386—531no—
577C2×#386—531no—
578C2×#385—531no—
579C2×#380—531no—
580C2×C4×C22⋊C4—531no—
581C2×C4×C22⋊C4D5311yescharacteristic, complemented
582#1442—531no—
583#1440—531no—
584#1439—531no—
585#1438—531no—
586#1437—531no—
587#1436—531no—
588#1436—531no—
589#1434—531no—
590C2×C53—44no—
591C2×C53#229011yescharacteristic
592C2×C53C4×#12111yescharacteristic
593C2×C53#233511yescharacteristic
594C2×C53#234211yescharacteristic
595C2×C53#235211yescharacteristic
596C2×C53#235811yescharacteristic
597C2×C53#236111yescharacteristic
598C2×C53#242411yescharacteristic
599C2×C53#242711yescharacteristic
600C2×C53#245711yescharacteristic
601C2×C53#246311yescharacteristic
602C2×C53#246411yescharacteristic
603C2×C53#247711yescharacteristic
604C2×C53#255311yescharacteristic
605C2×C53#257811yescharacteristic
606D53—44no—
607C23×D4—531no—
608C24×C4—531no—
609C24×C4C2×D5311yescharacteristic
610C22×C4⋊C4—531no—
611C22×C4⋊C4—531no—
612C22×C4⋊C4—531no—
613C22×C22⋊C4—531no—
614C22×C22⋊C4—531no—
615C22×C22⋊C4—531no—
616C22×C22⋊C4—531no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—531no—
619C22×C22⋊C4—531no—
620C22×C22⋊C4—531no—
621C22×C22⋊C4C2×D5311yescharacteristic
622C22×C22⋊C4C2×D5311yescharacteristic
623C22×C42—531no—
624C22×C42C2×D5311yescharacteristic
625C22×C42C2×D5311yescharacteristic
626#388—1064no—
627#386—538no—
628#386—1064no—
629#385—1064no—
630#380—1064no—
631C4×C22⋊C4—24no—
632C4×C22⋊C4—1064no—
633C2×#95—531no—
634C2×#95—531no—
635C2×#95—531no—
636C2×#95—531no—
637C2×#95—531no—
638C2×#95—531no—
639C2×#95—531no—
640C2×#95—531no—
641C2×#95—531no—
642C2×#95—531no—
643C2×#95—531no—
644C2×#95—531no—
645C2×#95—531no—
646C2×#95—531no—
647C2×#95C2×D5311yescharacteristic
648C2×#95C2×D5311yescharacteristic
649C53#1398811yescharacteristic, complemented, Sylow
650C25—531no—
651C25C22×D5311yescharacteristic
652C22×D4—534no—
653C22×D4—1062no—
654C22×D4—1062no—
655C22×D4—1062no—
656C22×D4—1062no—
657C22×D4—2121no—
658C22×D4—2121no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—41no—
664C23×C4—41no—
665C23×C4—531no—
666C23×C4—531no—
667C23×C4—531no—
668C23×C4—531no—
669C23×C4—531no—
670C23×C4—531no—
671C23×C4—531no—
672C23×C4—1062no—
673C23×C4—1062no—
674C23×C4—1062no—
675C23×C4—1062no—
676C23×C4—1062no—
677C23×C4—2121no—
678C23×C4—2121no—
679C23×C4C4×D5314yescomplemented
680C23×C4C22×D5311yescharacteristic
681C23×C4C22×D5311yescharacteristic
682C23×C4C22×D5311yescharacteristic
683C23×C4C22×D5311yescharacteristic
684C23×C4C22×D5311yescharacteristic
685C23×C4C22×D5311yescharacteristic
686C2×C4⋊C4—1062no—
687C2×C4⋊C4—1062no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—1062no—
691C2×C4⋊C4—1062no—
692C2×C4⋊C4—1062no—
693C2×C4⋊C4—2121no—
694C2×C4⋊C4—2121no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—534no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—534no—
703C2×C22⋊C4—1062no—
704C2×C22⋊C4—1062no—
705C2×C22⋊C4—1062no—
706C2×C22⋊C4—1062no—
707C2×C22⋊C4—1062no—
708C2×C22⋊C4—1062no—
709C2×C22⋊C4—1062no—
710C2×C22⋊C4—1062no—
711C2×C22⋊C4—1062no—
712C2×C22⋊C4—1062no—
713C2×C22⋊C4—1062no—
714C2×C22⋊C4—1062no—
715C2×C22⋊C4—1062no—
716C2×C22⋊C4—1062no—
717C2×C22⋊C4—1062no—
718C2×C22⋊C4—1062no—
719C2×C22⋊C4—1062no—
720C2×C22⋊C4—2121no—
721C2×C22⋊C4—2121no—
722C2×C22⋊C4—2121no—
723C2×C22⋊C4—2121no—
724C2×C22⋊C4D21214yes—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—41no—
731C2×C42—1062no—
732C2×C42—1062no—
733C2×C42—2121no—
734#95—22no—
735#95—534no—
736#95—534no—
737#95—534no—
738#95—1062no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—1062no—
744#95—1062no—
745#95—1062no—
746#95—2121no—
747#95—2121no—
748#95—2121no—
749#95C22⋊D5314yescomplemented
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—532no—
763C24—532no—
764C24—532no—
765C24—1061no—
766C24—1061no—
767C24—1061no—
768C24—1061no—
769C24—1061no—
770C24—1061no—
771C24—1061no—
772C24—1061no—
773C24—1061no—
774C24—1061no—
775C24—1061no—
776C24—1061no—
777C24C2×C4×D5312yes—
778C24C2×D21212yes—
779C24#1171994512yes—
780C24C23×D5311yescharacteristic
781C2×D4—1068no—
782C2×D4—1068no—
783C2×D4—2124no—
784C2×D4—2124no—
785C2×D4—2124no—
786C2×D4—2124no—
787C2×D4—2124no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—28no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—532no—
826C22×C4—532no—
827C22×C4—532no—
828C22×C4—532no—
829C22×C4—532no—
830C22×C4—1068no—
831C22×C4—1061no—
832C22×C4—1061no—
833C22×C4—1061no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
841C22×C4—1061no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1061no—
846C22×C4—1061no—
847C22×C4—1061no—
848C22×C4—1061no—
849C22×C4—1061no—
850C22×C4—1061no—
851C22×C4—1061no—
852C22×C4—1061no—
853C22×C4—1061no—
854C22×C4—1061no—
855C22×C4—1061no—
856C22×C4—1061no—
857C22×C4—1061no—
858C22×C4—1061no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—2124no—
876C22×C4—2124no—
877C22×C4—2124no—
878C22×C4—2124no—
879C22×C4—2124no—
880C22×C4—2124no—
881C22×C4C2×C4×D5312yes—
882C22×C4C2×C4×D5312yes—
883C22×C4C2×D21212yes—
884C22×C4C2×D21212yes—
885C22×C4#1171994512yes—
886C22×C4#1171994512yes—
887C22×C4#1171994512yes—
888C22×C4D4×D5312yes—
889C22×C4#1171994712yes—
890C22×C4C2×C22⋊D5312yes—
891C22×C4C2×C22⋊D5312yes—
892C22×C4C2×C22⋊D5312yes—
893C4⋊C4—2124no—
894C4⋊C4—2124no—
895C4⋊C4—2124no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—1068no—
899C22⋊C4—1068no—
900C22⋊C4—1068no—
901C22⋊C4—1068no—
902C22⋊C4—2124no—
903C22⋊C4—2124no—
904C22⋊C4—2124no—
905C22⋊C4—2124no—
906C42—44no—
907C42—44no—
908C42—2124no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—534no—
944C23—1062no—
945C23—1062no—
946C23—1062no—
947C23—1062no—
948C23—1062no—
949C23—1062no—
950C23—1062no—
951C23—1062no—
952C23—1062no—
953C23—1062no—
954C23—1062no—
955C23—1062no—
956C23—1062no—
957C23—1062no—
958C23—1062no—
959C23—1062no—
960C23—1062no—
961C23—1062no—
962C23—2121no—
963C23—2121no—
964C23—2121no—
965C23—2121no—
966C23—2121no—
967C23—2121no—
968C23—2121no—
969C23—2121no—
970C23—2121no—
971C23—2121no—
972C23—2121no—
973C23—2121no—
974C23—2121no—
975C23—2121no—
976C23—2121no—
977C23—2121no—
978C23C4×D21214yes—
979C23C22×C4×D5311yescharacteristic
980C23C2×D4×D5311yescharacteristic
981C23C22×C22⋊D5311yescharacteristic
982C23C22×D21211yescharacteristic
983C23#41×D5311yescharacteristic
984C23#41×D5311yescharacteristic
985C23C2×#1171994711yescharacteristic
986C23C2×#1171994511yescharacteristic
987C23C2×#1171994511yescharacteristic
988C23C2×#1171994511yescharacteristic
989C23C2×#1171994511yescharacteristic
990C23#1313326211yescharacteristic
991C23#1313326211yescharacteristic
992C23#1313326311yescharacteristic
993C23#1313326411yescharacteristic
994D4—21216no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—416no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—1062no—
1036C2×C4—1062no—
1037C2×C4—1062no—
1038C2×C4—1062no—
1039C2×C4—1062no—
1040C2×C4—1062no—
1041C2×C4—1062no—
1042C2×C4—1062no—
1043C2×C4—1062no—
1044C2×C4—1062no—
1045C2×C4—1062no—
1046C2×C4—1062no—
1047C2×C4—1062no—
1048C2×C4—1062no—
1049C2×C4—1062no—
1050C2×C4—21216no—
1051C2×C4—2121no—
1052C2×C4—2121no—
1053C2×C4—2121no—
1054C2×C4—2121no—
1055C2×C4—2121no—
1056C2×C4—2121no—
1057C2×C4—2121no—
1058C2×C4—2121no—
1059C2×C4—2121no—
1060C2×C4—2121no—
1061C2×C4—2121no—
1062C2×C4—2121no—
1063C2×C4—2121no—
1064C2×C4—2121no—
1065C2×C4—2121no—
1066C2×C4—2121no—
1067C2×C4—2121no—
1068C2×C4—2121no—
1069C2×C4—2121no—
1070C2×C4—2121no—
1071C2×C4—2121no—
1072C2×C4—2121no—
1073C2×C4—2121no—
1074C2×C4—2121no—
1075C2×C4—2121no—
1076C2×C4—2121no—
1077C2×C4—2121no—
1078C2×C4—2121no—
1079C2×C4—2121no—
1080C2×C4—2121no—
1081C2×C4—2121no—
1082C2×C4—2121no—
1083C2×C4—2121no—
1084C2×C4—2121no—
1085C2×C4#1313317714yes—
1086C2×C4C4×C22⋊D5314yes—
1087C2×C4#1313319114yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—1064no—
1104C22—1064no—
1105C22—1064no—
1106C22—2122no—
1107C22—2122no—
1108C22—2122no—
1109C22—2122no—
1110C22—2122no—
1111C22—2122no—
1112C22—2122no—
1113C22—2122no—
1114C22—2122no—
1115C22—2122no—
1116C22—2122no—
1117C22—2122no—
1118C22#117×D5311yescharacteristic
1119C22C2×#1313317711yescharacteristic
1120C22C2×C4×C22⋊D5311yescharacteristic
1121C22C2×C4×D21211yescharacteristic
1122C22C4×#1171994511yescharacteristic
1123C22#1681109611yescharacteristic
1124C22#1681110311yescharacteristic
1125C22C2×#1313319111yescharacteristic
1126C22#1681113211yescharacteristic
1127C22#1681113211yescharacteristic
1128C22#1681113411yescharacteristic
1129C22#1681115511yescharacteristic
1130C22#1681115511yescharacteristic
1131C22#1681115711yescharacteristic
1132C22#1681117311yescharacteristic
1133C22#1681120611yescharacteristic
1134C22#1681121511yescharacteristic
1135C22#1681122411yescharacteristic
1136C22#1681123811yescharacteristic
1137C22D4×C22⋊D5311yescharacteristic
1138C22D4×D21211yescharacteristic
1139C22#1681126111yescharacteristic
1140C22#1681126311yescharacteristic
1141C22#1681126711yescharacteristic
1142C22#1681126811yescharacteristic
1143C22#1681126811yescharacteristic
1144C22#1681127711yescharacteristic
1145C22#1681128011yescharacteristic
1146C22#1681128211yescharacteristic
1147C22#1681129911yescharacteristic
1148C22#1681130211yescharacteristic
1149C22#1681130211yescharacteristic
1150C22#1681131211yescharacteristic
1151C22#1681131711yescharacteristic
1152C22#1681131911yescharacteristic
1153C4—24no—
1154C4—24no—
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—4241no—
1160C4—4241no—
1161C4—2122no—
1162C4—2122no—
1163C4—2122no—
1164C4—2122no—
1165C4—2122no—
1166C2—44no—
1167C2—2124no—
1168C2#2027716111yescharacteristic
1169C2C4×#1313319111yescharacteristic
1170C2#2027750511yescharacteristic
1171C2#2027756711yescharacteristic
1172C2#2027764511yescharacteristic
1173C2#2027769411yescharacteristic
1174C2#2027772911yescharacteristic
1175C2#2027824511yescharacteristic
1176C2#2027828611yescharacteristic
1177C2#2027861611yescharacteristic
1178C2#2027870611yescharacteristic
1179C2#2027872111yescharacteristic
1180C2#2027891611yescharacteristic
1181C2#2027975411yescharacteristic
1182C2#2028004911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13988
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16810517C2semidirect
4. C2×#16810497C2semidirect
5. C2×#16810483C2semidirect
6. C2×C4×#11719921C2semidirect
7. #20272971C2semidirect
8. #20272962C2semidirect
9. #20272961C2semidirect
11. #20272953C2semidirect
12. #20272949C2semidirect
13. #20272948C2semidirect
14. #20272942C2semidirect
15. C2×C4×C22⋊C4×C53C2semidirect
31. #16810502C4semidirect
97. C2×C22⋊Dic53C2×C4semidirect
127. #13133124C2×C4semidirect
128. #13133124C2×C4semidirect
129. #13133124D4semidirect
137. C23×C4×C53C2×C4semidirect
157. #95×C53D4semidirect
581. C2×C4×C22⋊C4D53semidirect
649. C53#13988semidirect
679. C23×C4C4×D53semidirect
749. #95C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105172
C2×#168105022
C2×#168104992
C2×#168104972
C2×#168104832
C2×C4×#117199212
#202729712
#202729622
#202729612
#202729542
#202729532
#202729492
#202729482
#202729422
C2×C4×C22⋊C4×C532
#1398853