Finite Group Databasebeta

← #27306279

Subgroups — #27306279

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
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810502C211yesmaximal, characteristic
3C2×#16810500C211yesmaximal, characteristic
4C2×#16810498C211yesmaximal, characteristic, complemented
5C2×#16810480C211yesmaximal, characteristic, complemented
6C22×#13133124C211yesmaximal, characteristic, complemented
7#20272969C211yesmaximal, characteristic, complemented
8#20272965C211yesmaximal, characteristic, complemented
9#20272961C211yesmaximal, characteristic, complemented
10#20272957C211yesmaximal, characteristic, complemented
11#20272944C211yesmaximal, characteristic, complemented
12#20272939C211yesmaximal, characteristic, complemented
13#20272937C211yesmaximal, characteristic, complemented
14#20272936C211yesmaximal, characteristic, complemented
15C2×C53×#385C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133177—24no—
21C2×#13133177—24no—
22C2×#13133177C418yescomplemented
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810502—24no—
34#16810500—24no—
35#16810498—24no—
36#16810480—24no—
37C2×#13133124—24no—
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C24×C4×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C4⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C22⋊C4×C53C2211yescharacteristic
57C53×#385—24no—
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C22×C22⋊D53—22no—
62C22×C22⋊D53—22no—
63C22×C22⋊D53—22no—
64C22×C22⋊D53—22no—
65C22×C22⋊D53C2×C414yes—
66C22×C22⋊D53D414yes—
67C22×C22⋊D53Q814yes—
68C23×Dic53—22no—
69C23×Dic53—22no—
70C23×Dic53—22no—
71C23×Dic53—22no—
72C23×Dic53—22no—
73C23×Dic53—22no—
74C23×Dic53—22no—
75C23×Dic53—22no—
76C23×Dic53—22no—
77C23×Dic53—41no—
78C23×Dic53—41no—
79C23×Dic53—41no—
80C23×Dic53—41no—
81C23×Dic53C2×C414yes—
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2311yescharacteristic
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C22×C4×D53—22no—
90C22×C4×D53—22no—
91C22×C4×D53—22no—
92C22×C4×D53—22no—
93C22×C4×D53—41no—
94C22×C4×D53—41no—
95C22×C4×D53C2×C414yescomplemented
96#13133177—232no—
97C2×C4⋊Dic53—22no—
98C2×C4⋊Dic53—22no—
99C2×C4⋊Dic53—22no—
100C2×C4⋊Dic53—22no—
101C2×C4⋊Dic53—41no—
102C2×C4⋊Dic53—41no—
103C2×#11719919—22no—
104C2×#11719919—22no—
105C2×#11719919C2×C414yescomplemented
106C2×C22⋊Dic53—22no—
107C2×C22⋊Dic53—22no—
108C2×C22⋊Dic53—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—22no—
112C2×#11719921—22no—
113C2×#11719921—22no—
114C2×#11719921—22no—
115C2×#11719921—22no—
116C2×#11719921—22no—
117C2×#11719921—22no—
118C2×#11719921—22no—
119C2×#11719921—41no—
120C2×#11719921—41no—
121C2×#11719921—41no—
122C2×#11719921—41no—
123C2×#11719921C2×C414yescomplemented
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53C2×C414yescomplemented
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—22no—
131#13133124—22no—
132#13133124—22no—
133#13133124—22no—
134#13133124—22no—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—41no—
139#13133124—41no—
140#13133124D414yescomplemented
141C25×C53C2311yescharacteristic
142C23×C4×C53—22no—
143C23×C4×C53—22no—
144C23×C4×C53—22no—
145C23×C4×C53—22no—
146C23×C4×C53—22no—
147C23×C4×C53—41no—
148C23×C4×C53—41no—
149C23×C4×C53C2311yescharacteristic
150C23×C4×C53C2311yescharacteristic
151C23×C4×C53C2311yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C23×C4×C53C2311yescharacteristic
155C2×C4⋊C4×C53—22no—
156C2×C4⋊C4×C53—22no—
157C2×C4⋊C4×C53—22no—
158C2×C4⋊C4×C53—22no—
159C2×C4⋊C4×C53—41no—
160C2×C4⋊C4×C53—41no—
161C2×C22⋊C4×C53—22no—
162C2×C22⋊C4×C53—22no—
163C2×C22⋊C4×C53—22no—
164C2×C22⋊C4×C53C2×C414yes—
165C2×C22⋊C4×C53D414yes—
166C2×C22⋊C4×C53D414yes—
167#95×C53—22no—
168#95×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×C53C22×C412yes—
178C24×C53C2×D412yes—
179C24×C53C2×D412yes—
180C24×C53C2×D412yes—
181C24×C53C2×Q812yes—
182C24×C53#4112yes—
183C24×C53#4112yes—
184C24×C53C2411yescharacteristic
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C23×D53—21no—
189C23×D53—21no—
190C23×D53—21no—
191C23×D53—21no—
192C23×D53—21no—
193C23×D53—21no—
194C23×D53—21no—
195C23×D53—21no—
196C23×D53—21no—
197C23×D53C22×C412yes—
198C23×D53C2×D412yes—
199C23×D53C2×Q812yes—
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—28no—
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—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—44no—
236C22×C4×C53—44no—
237C22×C4×C53—44no—
238C22×C4×C53—44no—
239C22×C4×C53—44no—
240C22×C4×C53—44no—
241C22×C4×C53C22×C412yes—
242C22×C4×C53C22×C412yes—
243C22×C4×C53C2×D412yes—
244C22×C4×C53C2×D412yes—
245C22×C4×C53C2×D412yes—
246C22×C4×C53C2×D412yes—
247C22×C4×C53C2×D412yes—
248C22×C4×C53#4112yes—
249C2×C22⋊D53—28no—
250C2×C22⋊D53—28no—
251C2×C22⋊D53—28no—
252C2×C22⋊D53—28no—
253C2×C22⋊D53—28no—
254C2×C22⋊D53—28no—
255C2×C22⋊D53C4⋊C4116yescomplemented
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—28no—
265C22×Dic53—28no—
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—28no—
285C22×Dic53—21no—
286C22×Dic53—21no—
287C22×Dic53—21no—
288C22×Dic53—21no—
289C22×Dic53—21no—
290C22×Dic53—21no—
291C22×Dic53—21no—
292C22×Dic53—21no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295C22×Dic53—21no—
296C22×Dic53—21no—
297C22×Dic53—21no—
298C22×Dic53—21no—
299C22×Dic53—44no—
300C22×Dic53—44no—
301C22×Dic53—44no—
302C22×Dic53—44no—
303C22×Dic53—44no—
304C22×Dic53—44no—
305C22×Dic53—44no—
306C22×Dic53—44no—
307C22×Dic53—44no—
308C22×Dic53—44no—
309C22×Dic53—44no—
310C22×Dic53C22×C412yes—
311C22×Dic53C22×C412yes—
312C22×Dic53C22×C412yes—
313C22×Dic53C2×D412yes—
314C22×Dic53C2×D412yes—
315C22×Dic53C2×D412yes—
316C22×Dic53C2×Q812yes—
317C22×Dic53#4112yes—
318C22×Dic53#4112yes—
319C2×C4×D53—28no—
320C2×C4×D53—28no—
321C2×C4×D53—44no—
322C2×C4×D53—44no—
323C2×C4×D53—44no—
324C2×C4×D53—44no—
325C2×C4×D53—44no—
326C4⋊C4×C53—44no—
327C4⋊C4×C53—44no—
328C22⋊C4×C53—44no—
329C22⋊C4×C53C22⋊C4116yescomplemented
330C22⋊Dic53—44no—
331#11719921—28no—
332#11719921—44no—
333#11719921—44no—
334#11719921—44no—
335#11719921—44no—
336C4⋊Dic53—44no—
337C4⋊Dic53—44no—
338#11719919—28no—
339C4×Dic53—28no—
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×C53C2×C22⋊C414yes—
369C23×C53C2×C4⋊C414yes—
370C23×C53#11714yes—
371C23×C53#12114yes—
372C23×C53#12114yes—
373C23×C53C22⋊Q814yes—
374C23×C53C22⋊Q814yes—
375C23×C53C23×C411yescharacteristic
376C23×C53C22×D411yescharacteristic
377C23×C53C22×D411yescharacteristic
378C23×C53C22×D411yescharacteristic
379C23×C53C22×D411yescharacteristic
380C23×C53C22×Q811yescharacteristic
381C23×C53C2×#4111yescharacteristic
382C23×C53C2×#4111yescharacteristic
383C23×C53C2×#4111yescharacteristic
384C23×C53C2×#4111yescharacteristic
385C23×C53C2×#4111yescharacteristic
386C23×C53H(5,𝔽2)11yescharacteristic
387C23×C53H(5,𝔽2)11yescharacteristic
388C23×C53H(5,𝔽2)11yescharacteristic
389C23×C532−1+411yescharacteristic
390C22×D53—22no—
391C22×D53—22no—
392C22×D53—22no—
393C22×D53—22no—
394C22×D53—22no—
395C22×D53—22no—
396C22×D53—22no—
397C22×D53—22no—
398C22×D53—22no—
399C22×D53—22no—
400C22×D53—22no—
401C22×D53—22no—
402C22×D53—22no—
403C22×D53—22no—
404C22×D53—22no—
405C22×D53—22no—
406C22×D53—22no—
407C22×D53—22no—
408C22×D53—41no—
409C22×D53—41no—
410C22×D53—41no—
411C22×D53—41no—
412C22×D53—41no—
413C22×D53—41no—
414C22×D53—41no—
415C22×D53—41no—
416C22×D53—41no—
417C22×D53—41no—
418C22×D53—41no—
419C22×D53—41no—
420C22×D53—41no—
421C22×D53—41no—
422C22×D53—41no—
423C22×D53—41no—
424C22×D53C2×C4⋊C414yes—
425C2×C4×C53—22no—
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—416no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
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×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—41no—
465C2×C4×C53—41no—
466C2×C4×C53C2×C22⋊C414yes—
467C2×C4×C53C2×C22⋊C414yes—
468C22⋊D53—232no—
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—22no—
485C2×Dic53—22no—
486C2×Dic53—22no—
487C2×Dic53—22no—
488C2×Dic53—22no—
489C2×Dic53—22no—
490C2×Dic53—416no—
491C2×Dic53—416no—
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×Dic53C2×C4⋊C414yes—
519C2×Dic53C4×D414yes—
520C4×D53—416no—
521#13899—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#38018yescomplemented
537C22×C53C22×C22⋊C411yescharacteristic
538C22×C53C22×C4⋊C411yescharacteristic
539C22×C53C2×#11711yescharacteristic
540C22×C53C2×C4×D411yescharacteristic
541C22×C53C4×#4111yescharacteristic
542C22×C53#51811yescharacteristic
543C22×C53#52011yescharacteristic
544C22×C53C2×#12111yescharacteristic
545C22×C53C2×#12111yescharacteristic
546C22×C53C2×C22⋊Q811yescharacteristic
547C22×C53C2×C22⋊Q811yescharacteristic
548C22×C53#52511yescharacteristic
549C22×C53#52511yescharacteristic
550C22×C53#52911yescharacteristic
551C22×C53#52911yescharacteristic
552C22×C53#53811yescharacteristic
553C22×C53#53811yescharacteristic
554C22×C53#53911yescharacteristic
555C22×C53#53911yescharacteristic
556C22×C53D4211yescharacteristic
557C22×C53D4211yescharacteristic
558C22×C53D4211yescharacteristic
559C22×C53#54611yescharacteristic
560C22×C53#54611yescharacteristic
561C22×C53#54611yescharacteristic
562C22×C53#54611yescharacteristic
563C22×C53#54611yescharacteristic
564C22×C53#54611yescharacteristic
565C22×C53#54711yescharacteristic
566C22×C53#54711yescharacteristic
567C22×C53#54711yescharacteristic
568C22×C53D4×Q811yescharacteristic
569C22×C53#55411yescharacteristic
570C22×C53#55411yescharacteristic
571C22×C53#55411yescharacteristic
572C2×D53—24no—
573C2×D53—24no—
574C2×D53—24no—
575C2×D53—42no—
576C2×D53—42no—
577C2×D53—42no—
578C2×D53—42no—
579C2×D53—42no—
580C2×D53—42no—
581C2×D53—42no—
582C2×D53—42no—
583C2×D53—42no—
584C2×D53—42no—
585C2×D53—42no—
586C2×D53—42no—
587C4×C53—24no—
588C4×C53—24no—
589C4×C53—42no—
590C4×C53—42no—
591C4×C53—81no—
592C4×C53—81no—
593Dic53—24no—
594Dic53—24no—
595Dic53—42no—
596Dic53—42no—
597Dic53—42no—
598Dic53—81no—
599Dic53—81no—
600C22×C4×D4—531no—
601C2×#386—531no—
602C2×#386—531no—
603C2×#385—531no—
604C2×#385D5311yescharacteristic, complemented
605C2×#380—531no—
606C22×#95—531no—
607#1441—531no—
608#1441—531no—
609#1439—531no—
610#1439—531no—
611C4⋊#95—531no—
612#1434—531no—
613C22⋊#95—531no—
614C22⋊#95—531no—
615C2×C53—28no—
616C2×C53C2×#38011yescharacteristic
617C2×C53#229011yescharacteristic
618C2×C53#231811yescharacteristic
619C2×C53D4×C22⋊C411yescharacteristic
620C2×C53#233911yescharacteristic
621C2×C53D4×C4⋊C411yescharacteristic
622C2×C53#234911yescharacteristic
623C2×C53#242411yescharacteristic
624C2×C53#242411yescharacteristic
625C2×C53#242511yescharacteristic
626C2×C53#242511yescharacteristic
627C2×C53#244911yescharacteristic
628C2×C53#244911yescharacteristic
629C2×C53#245011yescharacteristic
630C2×C53#245011yescharacteristic
631D53—44no—
632C23×D4—531no—
633C24×C4—531no—
634C24×C4—531no—
635C24×C4—531no—
636C24×C4C2×D5311yescharacteristic
637C2×C4×D4—538no—
638C2×C4×D4—1064no—
639C2×C4×D4—1064no—
640C22×C4⋊C4—531no—
641C22×C4⋊C4—531no—
642C22×C4⋊C4—531no—
643C22×C4⋊C4C2×D5311yescharacteristic
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×C42—531no—
654#386—1064no—
655#386—1064no—
656#385—24no—
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—1064no—
674C2×#95C2×D5311yescharacteristic
675C2×#95C2×D5311yescharacteristic
676C53#1389911yescharacteristic, complemented, Sylow
677C25—531no—
678C25C22×D5311yescharacteristic
679C22×D4—534no—
680C22×D4—534no—
681C22×D4—534no—
682C22×D4—1062no—
683C22×D4—1062no—
684C22×D4—1062no—
685C22×D4—1062no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—22no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4—531no—
694C23×C4—531no—
695C23×C4—531no—
696C23×C4—531no—
697C23×C4—531no—
698C23×C4—534no—
699C23×C4—534no—
700C23×C4—531no—
701C23×C4—531no—
702C23×C4—1062no—
703C23×C4—1062no—
704C23×C4—1062no—
705C23×C4—1062no—
706C23×C4—1062no—
707C23×C4—1062no—
708C23×C4—1062no—
709C23×C4—1062no—
710C23×C4—1062no—
711C23×C4—1062no—
712C23×C4—1062no—
713C23×C4—1062no—
714C23×C4—1062no—
715C23×C4—2121no—
716C23×C4—2121no—
717C23×C4—2121no—
718C23×C4—2121no—
719C23×C4—2121no—
720C23×C4—2121no—
721C23×C4C22×D5311yescharacteristic
722C23×C4C22×D5311yescharacteristic
723C23×C4C22×D5311yescharacteristic
724C23×C4C22×D5311yescharacteristic
725C23×C4C22×D5311yescharacteristic
726C23×C4C22×D5311yescharacteristic
727C4×D4—10632no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—41no—
733C2×C4⋊C4—41no—
734C2×C4⋊C4—534no—
735C2×C4⋊C4—1062no—
736C2×C4⋊C4—1062no—
737C2×C4⋊C4—1062no—
738C2×C4⋊C4—1062no—
739C2×C4⋊C4—1062no—
740C2×C4⋊C4—1062no—
741C2×C4⋊C4—2121no—
742C2×C4⋊C4—2121no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—534no—
747C2×C22⋊C4—1062no—
748C2×C22⋊C4—1062no—
749C2×C22⋊C4—1062no—
750C2×C22⋊C4—1062no—
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—2121no—
761C2×C22⋊C4—2121no—
762C2×C22⋊C4—2121no—
763C2×C22⋊C4—2121no—
764C2×C22⋊C4C4×D5314yes—
765C2×C22⋊C4D21214yes—
766C2×C22⋊C4C22⋊D5314yes—
767C2×C42—534no—
768C2×C42—1062no—
769C2×C42—1062no—
770#95—22no—
771#95—22no—
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—532no—
795C24—532no—
796C24—532no—
797C24—1061no—
798C24—1061no—
799C24—1061no—
800C24—1061no—
801C24—1061no—
802C24—1061no—
803C24—1061no—
804C24—1061no—
805C24—1061no—
806C24—1061no—
807C24—1061no—
808C24—1061no—
809C24C2×C4×D5312yes—
810C24C2×D21212yes—
811C24D4×D5312yes—
812C24#1171994712yes—
813C24Q8×D5312yes—
814C24#1171994912yes—
815C24C2×C22⋊D5312yes—
816C24C23×D5311yescharacteristic
817C2×D4—5316no—
818C2×D4—1068no—
819C2×D4—1068no—
820C2×D4—1068no—
821C2×D4—1068no—
822C2×D4—1068no—
823C2×D4—1068no—
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—21no—
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—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—532no—
866C22×C4—532no—
867C22×C4—532no—
868C22×C4—532no—
869C22×C4—532no—
870C22×C4—532no—
871C22×C4—532no—
872C22×C4—532no—
873C22×C4—532no—
874C22×C4—1068no—
875C22×C4—1068no—
876C22×C4—1061no—
877C22×C4—1061no—
878C22×C4—1061no—
879C22×C4—1061no—
880C22×C4—1061no—
881C22×C4—1061no—
882C22×C4—1061no—
883C22×C4—1061no—
884C22×C4—1068no—
885C22×C4—1068no—
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—1068no—
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—2124no—
920C22×C4—2124no—
921C22×C4—2124no—
922C22×C4—2124no—
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×C4—2124no—
935C22×C4C2×C4×D5312yes—
936C22×C4C2×C4×D5312yes—
937C22×C4C2×D21212yes—
938C22×C4C2×D21212yes—
939C22×C4D4×D5312yes—
940C22×C4#1171994712yes—
941C22×C4C2×C22⋊D5312yes—
942C22×C4C2×C22⋊D5312yes—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—1068no—
946C4⋊C4—2124no—
947C4⋊C4—2124no—
948C22⋊C4—44no—
949C22⋊C4—1068no—
950C22⋊C4—2124no—
951C22⋊C4—2124no—
952C22⋊C4—2124no—
953C22⋊C4—2124no—
954C22⋊C4—2124no—
955C22⋊C4#11719921116yescomplemented
956C42—1068no—
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—534no—
986C23—1062no—
987C23—1062no—
988C23—1062no—
989C23—1062no—
990C23—1062no—
991C23—1062no—
992C23—1062no—
993C23—1062no—
994C23—1062no—
995C23—1062no—
996C23—1062no—
997C23—1062no—
998C23—1062no—
999C23—1062no—
1000C23—1062no—
1001C23—1062no—
1002C23—1062no—
1003C23—1062no—
1004C23—2121no—
1005C23—2121no—
1006C23—2121no—
1007C23—2121no—
1008C23—2121no—
1009C23—2121no—
1010C23—2121no—
1011C23—2121no—
1012C23—2121no—
1013C23—2121no—
1014C23—2121no—
1015C23—2121no—
1016C23—2121no—
1017C23—2121no—
1018C23—2121no—
1019C23—2121no—
1020C23C2×#1171992114yes—
1021C23C4⋊C4×D5314yes—
1022C23#1313317514yes—
1023C23#1313318814yes—
1024C23#1313319214yes—
1025C23#1313319314yes—
1026C23#1313319714yes—
1027C23C22×C4×D5311yescharacteristic
1028C23C2×D4×D5311yescharacteristic
1029C23C2×D4×D5311yescharacteristic
1030C23C22×C22⋊D5311yescharacteristic
1031C23C22×D21211yescharacteristic
1032C23C2×Q8×D5311yescharacteristic
1033C23#41×D5311yescharacteristic
1034C23#41×D5311yescharacteristic
1035C23C2×#1171994711yescharacteristic
1036C23C2×#1171994711yescharacteristic
1037C23C2×#1171994911yescharacteristic
1038C23#1313326211yescharacteristic
1039C23#1313326211yescharacteristic
1040C23#1313326311yescharacteristic
1041C23#1313326411yescharacteristic
1042D4—10632no—
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—416no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
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—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—534no—
1085C2×C4—534no—
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—1062no—
1101C2×C4—1062no—
1102C2×C4—1062no—
1103C2×C4—1062no—
1104C2×C4—1062no—
1105C2×C4—1062no—
1106C2×C4—1062no—
1107C2×C4—21216no—
1108C2×C4—21216no—
1109C2×C4—2121no—
1110C2×C4—2121no—
1111C2×C4—2121no—
1112C2×C4—2121no—
1113C2×C4—2121no—
1114C2×C4—2121no—
1115C2×C4—2121no—
1116C2×C4—2121no—
1117C2×C4—2121no—
1118C2×C4—2121no—
1119C2×C4—2121no—
1120C2×C4—2121no—
1121C2×C4—2121no—
1122C2×C4—2121no—
1123C2×C4—21216no—
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×#1171992114yes—
1137C2×C4C2×#1171992114yes—
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—1064no—
1153C22—1064no—
1154C22—1064no—
1155C22—2122no—
1156C22—2122no—
1157C22—2122no—
1158C22—2122no—
1159C22—2122no—
1160C22—2122no—
1161C22—2122no—
1162C22—2122no—
1163C22—2122no—
1164C22—2122no—
1165C22—2122no—
1166C22—2122no—
1167C22#1681048018yescomplemented
1168C22C22×#1171992111yescharacteristic
1169C22C2×C4⋊C4×D5311yescharacteristic
1170C22C2×#1313317511yescharacteristic
1171C22C4×D4×D5311yescharacteristic
1172C22C4×#1171994711yescharacteristic
1173C22#1681109511yescharacteristic
1174C22#1681110211yescharacteristic
1175C22C2×#1313318811yescharacteristic
1176C22C2×#1313319211yescharacteristic
1177C22C2×#1313319311yescharacteristic
1178C22C2×#1313319711yescharacteristic
1179C22#1681112911yescharacteristic
1180C22#1681113611yescharacteristic
1181C22#1681115011yescharacteristic
1182C22#1681115911yescharacteristic
1183C22#1681120811yescharacteristic
1184C22#1681121311yescharacteristic
1185C22#1681121711yescharacteristic
1186C22#1681122211yescharacteristic
1187C22#1681125511yescharacteristic
1188C22D4×C22⋊D5311yescharacteristic
1189C22D4×D21211yescharacteristic
1190C22#1681126011yescharacteristic
1191C22#1681126111yescharacteristic
1192C22#1681126511yescharacteristic
1193C22#1681126711yescharacteristic
1194C22#1681126811yescharacteristic
1195C22#1681126811yescharacteristic
1196C22#1681127111yescharacteristic
1197C22#1681127211yescharacteristic
1198C22#1681127711yescharacteristic
1199C22#1681128611yescharacteristic
1200C22#1681132711yescharacteristic
1201C22#1681132711yescharacteristic
1202C22#1681133111yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—1064no—
1210C4—1064no—
1211C4—4241no—
1212C4—4241no—
1213C4—2122no—
1214C4—2122no—
1215C4—2122no—
1216C2—28no—
1217C2—2124no—
1218C2C2×#1681048011yescharacteristic
1219C2#2027715111yescharacteristic
1220C2#2027734311yescharacteristic
1221C2D4×#1171992111yescharacteristic
1222C2#2027754011yescharacteristic
1223C2#2027761311yescharacteristic
1224C2#2027762111yescharacteristic
1225C2#2027824711yescharacteristic
1226C2#2027824911yescharacteristic
1227C2#2027826211yescharacteristic
1228C2#2027826411yescharacteristic
1229C2#2027852011yescharacteristic
1230C2#2027852211yescharacteristic
1231C2#2027853511yescharacteristic
1232C2#2027853711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53#13899
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#16810498C2semidirect
5. C2×#16810480C2semidirect
6. C22×#13133124C2semidirect
7. #20272969C2semidirect
8. #20272965C2semidirect
9. #20272961C2semidirect
10. #20272957C2semidirect
11. #20272944C2semidirect
12. #20272939C2semidirect
13. #20272937C2semidirect
14. #20272936C2semidirect
15. C2×C53×#385C2semidirect
22. C2×#13133177C4semidirect
95. C22×C4×D53C2×C4semidirect
105. C2×#11719919C2×C4semidirect
123. C2×#11719921C2×C4semidirect
126. C2×C4×Dic53C2×C4semidirect
140. #13133124D4semidirect
255. C2×C22⋊D53C4⋊C4semidirect
329. C22⋊C4×C53C22⋊C4semidirect
536. C22×C53#380semidirect
604. C2×#385D53semidirect
676. C53#13899semidirect
955. C22⋊C4#11719921semidirect
1167. C22#16810480semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105022
C2×#168105002
C2×#168104982
C2×#168104802
C22×#131331242
#202729692
#202729652
#202729612
#202729572
#202729442
#202729392
#202729372
#202729362
C2×C53×#3852
#1389953