Finite Group Databasebeta

← #27306946

Subgroups — #27306946

Order 13568.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810503C211yesmaximal, characteristic
2C2×#16810503C211yesmaximal, characteristic
3C2×#16810496C211yesmaximal, characteristic, complemented
4C2×#16810496C211yesmaximal, characteristic, complemented
5C2×#16810481C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272978C211yesmaximal, characteristic, complemented
8#20272974C211yesmaximal, characteristic, complemented
9#20272958C211yesmaximal, characteristic, complemented
10#20272958C211yesmaximal, characteristic, complemented
11#20272948C211yesmaximal, characteristic, complemented
12#20272948C211yesmaximal, characteristic, complemented
13#20272938C211yesmaximal, characteristic, complemented
14#20272937C211yesmaximal, characteristic, complemented
15C22×C4×D4×C53C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28#16810503—24no—
29#16810503C418yescomplemented
30#16810496—24no—
31#16810496—24no—
32#16810481—24no—
33C2×#13133124—24no—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
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
50C23×D4×C53C2211yescharacteristic
51C24×C4×C53C2211yescharacteristic
52C24×C4×C53C2211yescharacteristic
53C2×C4×D4×C53—24no—
54C2×C4×D4×C53—24no—
55C2×C4×D4×C53—24no—
56C22×C4⋊C4×C53C2211yescharacteristic
57C22×C22⋊C4×C53C2211yescharacteristic
58C22×C22⋊C4×C53C2211yescharacteristic
59C22×C42×C53C2211yescharacteristic
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53—22no—
65C23×Dic53—22no—
66C23×Dic53—22no—
67C23×Dic53—22no—
68C23×Dic53—22no—
69C23×Dic53—41no—
70C23×Dic53—41no—
71C23×Dic53—41no—
72C23×Dic53—41no—
73C23×Dic53C2×C414yescomplemented
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C2×#11719919—22no—
83C2×#11719919—22no—
84C2×#11719919—22no—
85C2×#11719919—22no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—22no—
90C2×#11719919—41no—
91C2×#11719919—41no—
92C2×#11719919—41no—
93C2×#11719919—41no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—22no—
99C2×C22⋊Dic53—22no—
100C2×C22⋊Dic53—22no—
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53—22no—
103C2×C22⋊Dic53—22no—
104C2×C22⋊Dic53—22no—
105C2×C22⋊Dic53—41no—
106C2×C22⋊Dic53—41no—
107C2×C22⋊Dic53—41no—
108C2×C22⋊Dic53—41no—
109C2×C22⋊Dic53C2×C414yescomplemented
110C2×C22⋊Dic53C2×C414yescomplemented
111C2×C22⋊Dic53C2×C414yescomplemented
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—22no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—41no—
124#13133124—41no—
125#13133124C2×C414yescomplemented
126#13133124C2×C414yescomplemented
127#13133124D414yescomplemented
128C25×C53C2311yescharacteristic
129C25×C53C2311yescharacteristic
130C22×D4×C53—22no—
131C22×D4×C53—22no—
132C22×D4×C53—22no—
133C22×D4×C53—22no—
134C22×D4×C53C2×C414yes—
135C22×D4×C53D414yes—
136C22×D4×C53Q814yes—
137C23×C4×C53—22no—
138C23×C4×C53—22no—
139C23×C4×C53—22no—
140C23×C4×C53—22no—
141C23×C4×C53—22no—
142C23×C4×C53—22no—
143C23×C4×C53—22no—
144C23×C4×C53—22no—
145C23×C4×C53—22no—
146C23×C4×C53—41no—
147C23×C4×C53—41no—
148C23×C4×C53—41no—
149C23×C4×C53—41no—
150C23×C4×C53D414yes—
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C23×C4×C53C2311yescharacteristic
156C4×D4×C53—232no—
157C2×C4⋊C4×C53—22no—
158C2×C4⋊C4×C53—22no—
159C2×C4⋊C4×C53—22no—
160C2×C22⋊C4×C53—22no—
161C2×C22⋊C4×C53—22no—
162C2×C22⋊C4×C53—22no—
163C2×C22⋊C4×C53—22no—
164C2×C22⋊C4×C53—22no—
165C2×C22⋊C4×C53D414yes—
166C2×C42×C53—22no—
167C2×C42×C53—22no—
168C2×C42×C53—22no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53C22×C412yes—
190C24×C53C22×C412yes—
191C24×C53C2×D412yes—
192C24×C53C2×D412yes—
193C24×C53C2×D412yes—
194C24×C53C2×D412yes—
195C24×C53C2×Q812yes—
196C24×C53C2×Q812yes—
197C24×C53#4112yes—
198C24×C53#4112yes—
199C24×C53C2411yescharacteristic
200C2×D4×C53—28no—
201C2×D4×C53—28no—
202C2×D4×C53—28no—
203C2×D4×C53—28no—
204C2×D4×C53—28no—
205C2×D4×C53—28no—
206C2×D4×C53C4⋊C4116yescomplemented
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—28no—
216C22×C4×C53—28no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—28no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53—44no—
240C22×C4×C53—44no—
241C22×C4×C53—44no—
242C22×C4×C53—44no—
243C22×C4×C53—44no—
244C22×C4×C53—44no—
245C22×C4×C53—44no—
246C22×C4×C53—44no—
247C22×C4×C53C22×C412yes—
248C22×C4×C53C2×D412yes—
249C22×C4×C53C2×D412yes—
250C22×C4×C53C2×D412yes—
251C22×C4×C53C2×D412yes—
252C22×C4×C53C2×D412yes—
253C22×C4×C53C2×D412yes—
254C22×C4×C53C2×Q812yes—
255C22×C4×C53#4112yes—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53—28no—
261C22×Dic53—28no—
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×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—21no—
292C22×Dic53—28no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295C22×Dic53—21no—
296C22×Dic53—21no—
297C22×Dic53—21no—
298C22×Dic53—21no—
299C22×Dic53—21no—
300C22×Dic53—21no—
301C22×Dic53—21no—
302C22×Dic53—21no—
303C22×Dic53—21no—
304C22×Dic53—21no—
305C22×Dic53—21no—
306C22×Dic53—21no—
307C22×Dic53—44no—
308C22×Dic53—44no—
309C22×Dic53—44no—
310C22×Dic53—44no—
311C22×Dic53—44no—
312C22×Dic53—44no—
313C22×Dic53—44no—
314C22×Dic53—44no—
315C22×Dic53—44no—
316C22×Dic53—44no—
317C22×Dic53—44no—
318C22×Dic53C22×C412yes—
319C22×Dic53C22×C412yes—
320C22×Dic53C22×C412yes—
321C22×Dic53C22×C412yes—
322C22×Dic53C2×D412yes—
323C22×Dic53C2×D412yes—
324C22×Dic53#4112yes—
325C22×Dic53#4112yes—
326C4⋊C4×C53—28no—
327C22⋊C4×C53—28no—
328C22⋊C4×C53—28no—
329C42×C53—28no—
330C22⋊Dic53—28no—
331C22⋊Dic53—28no—
332C22⋊Dic53—44no—
333C22⋊Dic53—44no—
334C22⋊Dic53—44no—
335C22⋊Dic53—44no—
336#11719919—44no—
337#11719919—44no—
338#11719919—44no—
339#11719919—44no—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53—41no—
395C23×C53—41no—
396C23×C53—41no—
397C23×C53—41no—
398C23×C53—41no—
399C23×C53—41no—
400C23×C53—41no—
401C23×C53—41no—
402C23×C53C2×C4⋊C414yes—
403C23×C53C2×C4⋊C414yes—
404C23×C53C4×D414yes—
405C23×C53C4×D414yes—
406C23×C53#12014yes—
407C23×C53C22⋊Q814yes—
408C23×C53C22⋊Q814yes—
409C23×C53#12314yes—
410C23×C53C23×C411yescharacteristic
411C23×C53C22×D411yescharacteristic
412C23×C53C22×D411yescharacteristic
413C23×C53C22×D411yescharacteristic
414C23×C53C22×D411yescharacteristic
415C23×C53C22×Q811yescharacteristic
416C23×C53C2×#4111yescharacteristic
417C23×C53C2×#4111yescharacteristic
418C23×C53C2×#4111yescharacteristic
419C23×C53C2×#4111yescharacteristic
420C23×C53C2×#4111yescharacteristic
421C23×C53H(5,𝔽2)11yescharacteristic
422C23×C53H(5,𝔽2)11yescharacteristic
423C23×C53H(5,𝔽2)11yescharacteristic
424C23×C532−1+411yescharacteristic
425D4×C53—232no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—22no—
446C2×C4×C53—22no—
447C2×C4×C53—416no—
448C2×C4×C53—416no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53C2×C4⋊C414yes—
462C2×C4×C53#12114yes—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—22no—
467C2×Dic53—22no—
468C2×Dic53—22no—
469C2×Dic53—22no—
470C2×Dic53—22no—
471C2×Dic53—22no—
472C2×Dic53—22no—
473C2×Dic53—22no—
474C2×Dic53—22no—
475C2×Dic53—22no—
476C2×Dic53—22no—
477C2×Dic53—22no—
478C2×Dic53—22no—
479C2×Dic53—22no—
480C2×Dic53—22no—
481C2×Dic53—22no—
482C2×Dic53—22no—
483C2×Dic53—22no—
484C2×Dic53—416no—
485C2×Dic53—416no—
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—
495C2×Dic53—41no—
496C2×Dic53—41no—
497C2×Dic53—41no—
498C2×Dic53—41no—
499C2×Dic53—41no—
500C2×Dic53—41no—
501C2×Dic53—41no—
502C2×Dic53—41no—
503C2×Dic53—41no—
504C2×Dic53—41no—
505C2×Dic53—41no—
506C2×Dic53—41no—
507C2×Dic53—41no—
508C2×Dic53—41no—
509C2×Dic53—41no—
510C2×Dic53—41no—
511C2×Dic53—41no—
512C2×Dic53—41no—
513C2×Dic53—41no—
514C2×Dic53—41no—
515C2×Dic53—41no—
516C2×Dic53—41no—
517C2×Dic53—41no—
518C2×Dic53—41no—
519C2×Dic53—41no—
520C2×Dic53C4×D414yescomplemented
521#13975—531nomaximal, Sylow
522C22×C53—24no—
523C22×C53—24no—
524C22×C53—24no—
525C22×C53—24no—
526C22×C53—24no—
527C22×C53—24no—
528C22×C53—24no—
529C22×C53—24no—
530C22×C53—24no—
531C22×C53—24no—
532C22×C53—24no—
533C22×C53—24no—
534C22×C53—24no—
535C22×C53—24no—
536C22×C53—24no—
537C22×C53—24no—
538C22×C53—24no—
539C22×C53—42no—
540C22×C53—42no—
541C22×C53—42no—
542C22×C53—42no—
543C22×C53—42no—
544C22×C53—42no—
545C22×C53—42no—
546C22×C53—42no—
547C22×C53—42no—
548C22×C53—42no—
549C22×C53—42no—
550C22×C53—42no—
551C22×C53#38518yescomplemented
552C22×C53C22×C4⋊C411yescharacteristic
553C22×C53C2×C4×D411yescharacteristic
554C22×C53C2×C4×D411yescharacteristic
555C22×C53C2×C4×D411yescharacteristic
556C22×C53C4×#4111yescharacteristic
557C22×C53#51811yescharacteristic
558C22×C53#52011yescharacteristic
559C22×C53C2×#12011yescharacteristic
560C22×C53C2×#12111yescharacteristic
561C22×C53C2×C22⋊Q811yescharacteristic
562C22×C53C2×C22⋊Q811yescharacteristic
563C22×C53C2×#12311yescharacteristic
564C22×C53#52511yescharacteristic
565C22×C53#52911yescharacteristic
566C22×C53#53211yescharacteristic
567C22×C53#53411yescharacteristic
568C22×C53#53711yescharacteristic
569C22×C53#53811yescharacteristic
570C22×C53#53911yescharacteristic
571C22×C53D4211yescharacteristic
572C22×C53D4211yescharacteristic
573C22×C53#54611yescharacteristic
574C22×C53#54611yescharacteristic
575C22×C53#54611yescharacteristic
576C22×C53#54611yescharacteristic
577C22×C53#54611yescharacteristic
578C22×C53#54711yescharacteristic
579C22×C53#54711yescharacteristic
580C22×C53D4×Q811yescharacteristic
581C22×C53#55111yescharacteristic
582C22×C53#55111yescharacteristic
583C22×C53#55211yescharacteristic
584C22×C53#55411yescharacteristic
585C22×C53#55411yescharacteristic
586C22×C53#55411yescharacteristic
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—42no—
590C4×C53—42no—
591C4×C53—42no—
592Dic53—24no—
593Dic53—42no—
594Dic53—42no—
595Dic53—42no—
596Dic53—42no—
597Dic53—42no—
598Dic53—81no—
599Dic53—81no—
600C22×C4×D4D5311yescharacteristic
601C2×#386—531no—
602C2×#386—531no—
603C2×#385—531no—
604C2×#385—531no—
605C2×#380—531no—
606C22×#95—531no—
607#1444—531no—
608#1442—531no—
609#1439—531no—
610#1439—531no—
611#1436—531no—
612#1436—531no—
613C22⋊#95—531no—
614C22⋊#95—531no—
615C2×C53—28no—
616C2×C53—44no—
617C2×C53C2×#38511yescharacteristic
618C2×C53C4×#12111yescharacteristic
619C2×C53#232511yescharacteristic
620C2×C53D4×C4⋊C411yescharacteristic
621C2×C53#234911yescharacteristic
622C2×C53#235811yescharacteristic
623C2×C53#235911yescharacteristic
624C2×C53#241011yescharacteristic
625C2×C53#241711yescharacteristic
626C2×C53#241811yescharacteristic
627C2×C53#241911yescharacteristic
628C2×C53#243011yescharacteristic
629C2×C53#244911yescharacteristic
630C2×C53#245011yescharacteristic
631C2×C53#256411yescharacteristic
632C23×D4C2×D5311yescharacteristic
633C24×C4—531no—
634C24×C4—531no—
635C24×C4C2×D5311yescharacteristic
636C24×C4C2×D5311yescharacteristic
637C2×C4×D4—24no—
638C2×C4×D4—24no—
639C2×C4×D4—24no—
640C22×C4⋊C4—531no—
641C22×C4⋊C4—531no—
642C22×C4⋊C4—531no—
643C22×C4⋊C4—531no—
644C22×C4⋊C4C2×D5311yescharacteristic
645C22×C22⋊C4—531no—
646C22×C22⋊C4—531no—
647C22×C22⋊C4—531no—
648C22×C22⋊C4—531no—
649C22×C22⋊C4—531no—
650C22×C22⋊C4—531no—
651C22×C22⋊C4C2×D5311yescharacteristic
652C22×C22⋊C4C2×D5311yescharacteristic
653C22×C42C2×D5311yescharacteristic
654#386—538no—
655#386—1064no—
656#385—1064no—
657#385—1064no—
658#380—1064no—
659C2×#95—531no—
660C2×#95—531no—
661C2×#95—531no—
662C2×#95—531no—
663C2×#95—531no—
664C2×#95—531no—
665C2×#95—531no—
666C2×#95—531no—
667C2×#95—531no—
668C2×#95—531no—
669C2×#95—531no—
670C2×#95—531no—
671C2×#95—531no—
672C2×#95—531no—
673C2×#95—531no—
674C2×#95—531no—
675C2×#95—1064no—
676C53#1397511yescharacteristic, complemented, Sylow
677C25C22×D5311yescharacteristic
678C25C22×D5311yescharacteristic
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4Dic10614yes—
684C22×D4C4×D5314yes—
685C22×D4C22⋊D5314yes—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—22no—
691C23×C4—22no—
692C23×C4—22no—
693C23×C4—22no—
694C23×C4—22no—
695C23×C4—41no—
696C23×C4—41no—
697C23×C4—41no—
698C23×C4—41no—
699C23×C4—531no—
700C23×C4—531no—
701C23×C4—531no—
702C23×C4—531no—
703C23×C4—531no—
704C23×C4—531no—
705C23×C4—534no—
706C23×C4—531no—
707C23×C4—531no—
708C23×C4—1062no—
709C23×C4—1062no—
710C23×C4—1062no—
711C23×C4—1062no—
712C23×C4—1062no—
713C23×C4—1062no—
714C23×C4—1062no—
715C23×C4—1062no—
716C23×C4—1062no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4—2121no—
721C23×C4C22⋊D5314yes—
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C4×D4—232no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—1062no—
732C2×C4⋊C4—1062no—
733C2×C4⋊C4—1062no—
734C2×C4⋊C4—1062no—
735C2×C4⋊C4—1062no—
736C2×C4⋊C4—1062no—
737C2×C4⋊C4—1062no—
738C2×C4⋊C4—1062no—
739C2×C4⋊C4—2121no—
740C2×C4⋊C4—2121no—
741C2×C4⋊C4—2121no—
742C2×C4⋊C4—2121no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—534no—
749C2×C22⋊C4—534no—
750C2×C22⋊C4—534no—
751C2×C22⋊C4—1062no—
752C2×C22⋊C4—1062no—
753C2×C22⋊C4—1062no—
754C2×C22⋊C4—1062no—
755C2×C22⋊C4—1062no—
756C2×C22⋊C4—1062no—
757C2×C22⋊C4—1062no—
758C2×C22⋊C4—1062no—
759C2×C22⋊C4—1062no—
760C2×C22⋊C4—1062no—
761C2×C22⋊C4—1062no—
762C2×C22⋊C4—2121no—
763C2×C22⋊C4—2121no—
764C2×C22⋊C4—2121no—
765C2×C22⋊C4—2121no—
766C2×C22⋊C4C22⋊D5314yes—
767C2×C42—22no—
768C2×C42—22no—
769C2×C42—22no—
770#95—534no—
771#95—534no—
772#95—534no—
773#95—1062no—
774#95—1062no—
775#95—1062no—
776#95—1062no—
777#95—1062no—
778#95—1062no—
779#95—1062no—
780#95—1062no—
781#95—1062no—
782#95—1062no—
783#95—1062no—
784#95—2121no—
785#95—2121no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×Dic10612yes—
807C24C2×Dic10612yes—
808C24C2×C4×D5312yes—
809C24C2×C4×D5312yes—
810C24#1171994512yes—
811C24#1171994512yes—
812C24C2×C22⋊D5312yes—
813C24C2×C22⋊D5312yes—
814C24C2×C22⋊D5312yes—
815C24C2×C22⋊D5312yes—
816C24C23×D5311yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4#11719919116yescomplemented
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—28no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—532no—
865C22×C4—532no—
866C22×C4—532no—
867C22×C4—532no—
868C22×C4—532no—
869C22×C4—532no—
870C22×C4—532no—
871C22×C4—532no—
872C22×C4—1068no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4—1068no—
878C22×C4—1068no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1061no—
885C22×C4—1061no—
886C22×C4—1061no—
887C22×C4—1061no—
888C22×C4—1061no—
889C22×C4—1061no—
890C22×C4—1061no—
891C22×C4—1061no—
892C22×C4—1061no—
893C22×C4—1061no—
894C22×C4—1061no—
895C22×C4—1061no—
896C22×C4—1061no—
897C22×C4—1061no—
898C22×C4—1061no—
899C22×C4—1061no—
900C22×C4—1061no—
901C22×C4—1061no—
902C22×C4—1061no—
903C22×C4—1061no—
904C22×C4—1061no—
905C22×C4—1061no—
906C22×C4—1061no—
907C22×C4—1061no—
908C22×C4—1061no—
909C22×C4—1061no—
910C22×C4—1061no—
911C22×C4—1061no—
912C22×C4—1061no—
913C22×C4—1061no—
914C22×C4—1061no—
915C22×C4—1061no—
916C22×C4—1061no—
917C22×C4—1061no—
918C22×C4—1061no—
919C22×C4—1061no—
920C22×C4—1061no—
921C22×C4—1061no—
922C22×C4—1061no—
923C22×C4—2124no—
924C22×C4—2124no—
925C22×C4—2124no—
926C22×C4—2124no—
927C22×C4—2124no—
928C22×C4—2124no—
929C22×C4—2124no—
930C22×C4—2124no—
931C22×C4—2124no—
932C22×C4—2124no—
933C22×C4—2124no—
934C22×C4C2×Dic10612yes—
935C22×C4C2×C4×D5312yes—
936C22×C4D4×D5312yes—
937C22×C4#1171994712yes—
938C22×C4C2×C22⋊D5312yes—
939C22×C4C2×C22⋊D5312yes—
940C22×C4C2×C22⋊D5312yes—
941C22×C4C2×C22⋊D5312yes—
942C22×C4C2×C22⋊D5312yes—
943C4⋊C4—28no—
944C4⋊C4—2124no—
945C4⋊C4—2124no—
946C4⋊C4—2124no—
947C4⋊C4—2124no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—1068no—
951C22⋊C4—1068no—
952C22⋊C4—2124no—
953C22⋊C4—2124no—
954C22⋊C4—2124no—
955C22⋊C4—2124no—
956C42—28no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×#1171991914yes—
1020C23C2×#1171991914yes—
1021C23C4×C22⋊D5314yes—
1022C23C4×C22⋊D5314yes—
1023C23#1313318614yes—
1024C23#1313319614yes—
1025C23#1313319614yes—
1026C23#1313320014yes—
1027C23C22×C4×D5311yescharacteristic
1028C23C2×D4×D5311yescharacteristic
1029C23C22×C22⋊D5311yescharacteristic
1030C23C22×C22⋊D5311yescharacteristic
1031C23C22×C22⋊D5311yescharacteristic
1032C23C22×Dic10611yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23C2×#1171994711yescharacteristic
1036C23C2×#1171994511yescharacteristic
1037C23C2×#1171994511yescharacteristic
1038C23#1313326211yescharacteristic
1039C23#1313326211yescharacteristic
1040C23#1313326311yescharacteristic
1041C23#1313326411yescharacteristic
1042D4—232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—416no—
1065C2×C4—416no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—534no—
1079C2×C4—1062no—
1080C2×C4—1062no—
1081C2×C4—1062no—
1082C2×C4—1062no—
1083C2×C4—1062no—
1084C2×C4—1062no—
1085C2×C4—1062no—
1086C2×C4—1062no—
1087C2×C4—1062no—
1088C2×C4—1062no—
1089C2×C4—1062no—
1090C2×C4—1062no—
1091C2×C4—1062no—
1092C2×C4—1062no—
1093C2×C4—1062no—
1094C2×C4—1062no—
1095C2×C4—1062no—
1096C2×C4—1062no—
1097C2×C4—1062no—
1098C2×C4—1062no—
1099C2×C4—1062no—
1100C2×C4—21216no—
1101C2×C4—2121no—
1102C2×C4—2121no—
1103C2×C4—2121no—
1104C2×C4—2121no—
1105C2×C4—2121no—
1106C2×C4—2121no—
1107C2×C4—2121no—
1108C2×C4—2121no—
1109C2×C4—2121no—
1110C2×C4—2121no—
1111C2×C4—2121no—
1112C2×C4—2121no—
1113C2×C4—2121no—
1114C2×C4—2121no—
1115C2×C4—21216no—
1116C2×C4—2121no—
1117C2×C4—2121no—
1118C2×C4—2121no—
1119C2×C4—2121no—
1120C2×C4—2121no—
1121C2×C4—2121no—
1122C2×C4—2121no—
1123C2×C4—2121no—
1124C2×C4—2121no—
1125C2×C4—2121no—
1126C2×C4—2121no—
1127C2×C4—2121no—
1128C2×C4—2121no—
1129C2×C4—2121no—
1130C2×C4—2121no—
1131C2×C4—2121no—
1132C2×C4—2121no—
1133C2×C4—2121no—
1134C2×C4—2121no—
1135C2×C4—2121no—
1136C2×C4C2×#1171991914yes—
1137C2×C4#1313318914yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22#1681049618yescomplemented
1168C22C22×#1171991911yescharacteristic
1169C22C4×D4×D5311yescharacteristic
1170C22C2×C4×C22⋊D5311yescharacteristic
1171C22C2×C4×C22⋊D5311yescharacteristic
1172C22C4×#1171994711yescharacteristic
1173C22#1681109511yescharacteristic
1174C22#1681110211yescharacteristic
1175C22C2×#1313318611yescharacteristic
1176C22C2×#1313318911yescharacteristic
1177C22C2×#1313319611yescharacteristic
1178C22C2×#1313319611yescharacteristic
1179C22C2×#1313320011yescharacteristic
1180C22#1681113211yescharacteristic
1181C22#1681115311yescharacteristic
1182C22#1681116911yescharacteristic
1183C22#1681118211yescharacteristic
1184C22#1681120111yescharacteristic
1185C22#1681120611yescharacteristic
1186C22#1681121511yescharacteristic
1187C22D4×C22⋊D5311yescharacteristic
1188C22D4×C22⋊D5311yescharacteristic
1189C22#1681126111yescharacteristic
1190C22#1681126111yescharacteristic
1191C22#1681126711yescharacteristic
1192C22#1681126711yescharacteristic
1193C22#1681126911yescharacteristic
1194C22#1681127211yescharacteristic
1195C22#1681127211yescharacteristic
1196C22D4×Dic10611yescharacteristic
1197C22#1681130211yescharacteristic
1198C22#1681130211yescharacteristic
1199C22#1681131311yescharacteristic
1200C22#1681133011yescharacteristic
1201C22#1681133211yescharacteristic
1202C22#1681133211yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—1064no—
1209C4—4241no—
1210C4—4241no—
1211C4—2122no—
1212C4—2122no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1681049611yescharacteristic
1219C2C4×#1313318911yescharacteristic
1220C2#2027741311yescharacteristic
1221C2D4×#1171991911yescharacteristic
1222C2#2027762011yescharacteristic
1223C2#2027769211yescharacteristic
1224C2#2027770111yescharacteristic
1225C2#2027808911yescharacteristic
1226C2#2027816611yescharacteristic
1227C2#2027817111yescharacteristic
1228C2#2027818611yescharacteristic
1229C2#2027831911yescharacteristic
1230C2#2027851811yescharacteristic
1231C2#2027853311yescharacteristic
1232C2#2027989111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C4×D4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×C4×D4D53
hypocenterC53#13975
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#16810496C2semidirect
4. C2×#16810496C2semidirect
5. C2×#16810481C2semidirect
6. C22×#13133124C2semidirect
7. #20272978C2semidirect
8. #20272974C2semidirect
9. #20272958C2semidirect
10. #20272958C2semidirect
11. #20272948C2semidirect
12. #20272948C2semidirect
13. #20272938C2semidirect
14. #20272937C2semidirect
29. #16810503C4semidirect
73. C23×Dic53C2×C4semidirect
109. C2×C22⋊Dic53C2×C4semidirect
110. C2×C22⋊Dic53C2×C4semidirect
111. C2×C22⋊Dic53C2×C4semidirect
125. #13133124C2×C4semidirect
126. #13133124C2×C4semidirect
127. #13133124D4semidirect
206. C2×D4×C53C4⋊C4semidirect
520. C2×Dic53C4×D4semidirect
551. C22×C53#385semidirect
676. C53#13975semidirect
823. C2×D4#11719919semidirect
1167. C22#16810496semidirect

Maximal subgroups

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

subgroupindex
C2×#168105032
C2×#168104962
C2×#168104812
C22×#131331242
#202729782
#202729742
#202729582
#202729482
#202729382
#202729372
C22×C4×D4×C532
#1397553