Finite Group Databasebeta

← #27307268

Subgroups — #27307268

Order 13568.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810523C211yesmaximal, characteristic
2C2×#16810523C211yesmaximal, characteristic
3C2×#16810523C211yesmaximal, characteristic
4C2×#16810515C211yesmaximal, characteristic, complemented
5C2×#16810514C211yesmaximal, characteristic, complemented
6C2×#16810511C211yesmaximal, characteristic, complemented
7C2×#16810492C211yesmaximal, characteristic, complemented
8C2×C4×#11719919C211yesmaximal, characteristic, complemented
9#20272960C211yesmaximal, characteristic, complemented
10#20272959C211yesmaximal, characteristic, complemented
11#20272958C211yesmaximal, characteristic, complemented
12#20272957C211yesmaximal, characteristic, complemented
13#20272943C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C2×C53×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36#16810523—24no—
37#16810523—24no—
38#16810523C418yescomplemented
39#16810515—24no—
40#16810514—24no—
41#16810511—24no—
42#16810492—24no—
43C4×#11719919—24no—
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C53×#388—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⋊D53—22no—
66C22×C22⋊D53—22no—
67C22×C22⋊D53C2×C414yes—
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—41no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—22no—
82C2×#11719919—22no—
83C2×#11719919—22no—
84C2×#11719919—22no—
85C2×#11719919—22no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—41no—
90C2×#11719919—41no—
91C2×#11719919C2×C414yes—
92C2×#11719919D414yes—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C22⋊Dic53C2×C414yes—
102C2×#11719921—22no—
103C2×#11719921—22no—
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921—22no—
112C2×#11719921—22no—
113C2×#11719921—22no—
114C2×#11719921—41no—
115C2×#11719921—41no—
116C2×#11719921—41no—
117C2×#11719921—41no—
118C2×#11719921C2×C414yes—
119C2×#11719921C2×C414yes—
120C2×C4×Dic53—22no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—22no—
123C2×C4×Dic53—22no—
124C2×C4×Dic53—22no—
125C2×C4×Dic53—22no—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53C2×C414yes—
131C2×C4×Dic53D414yes—
132#13133124—22no—
133#13133124—22no—
134#13133124—22no—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124D414yescomplemented
140C25×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C2×C4⋊C4×C53—22no—
148C2×C4⋊C4×C53—22no—
149C2×C4⋊C4×C53—41no—
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—41no—
158C2×C22⋊C4×C53C2×C414yes—
159C2×C42×C53—22no—
160C2×C42×C53—22no—
161C2×C42×C53—22no—
162#95×C53—22no—
163#95×C53D414yescomplemented
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
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×C53C22×C412yes—
179C24×C53C2411yescharacteristic
180C23×D53—21no—
181C23×D53—21no—
182C23×D53—21no—
183C23×D53—21no—
184C23×D53—21no—
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×D53C22×C412yes—
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—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×C53C22×C412yes—
229C22×C4×C53C22×C412yes—
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2×D412yes—
232C22×C4×C53C2×D412yes—
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D412yes—
236C22×C4×C53#4112yes—
237C2×C22⋊D53—28no—
238C2×C22⋊D53—28no—
239C2×C22⋊D53—28no—
240C2×C22⋊D53—44no—
241C2×C22⋊D53—44no—
242C2×C22⋊D53—44no—
243C2×C22⋊D53—44no—
244C22×Dic53—21no—
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×Dic53C22×C412yes—
280C22×Dic53C22×C412yes—
281C22×Dic53C22×C412yes—
282C22×Dic53C2×D412yes—
283C22×Dic53C2×D412yes—
284C22×Dic53C2×D412yes—
285C22×Dic53C2×D412yes—
286C22×Dic53C2×D412yes—
287C22×Dic53C2×D412yes—
288C22×Dic53#4112yes—
289C22×Dic53#4112yes—
290C22×Dic53#4112yes—
291C22×Dic53#4112yes—
292C22×Dic53#4112yes—
293C4⋊C4×C53—44no—
294C22⋊C4×C53—28no—
295C22⋊C4×C53—44no—
296C22⋊C4×C53—44no—
297C42×C53—44no—
298C22⋊Dic53—28no—
299C22⋊Dic53—44no—
300C22⋊Dic53—44no—
301#11719921—28no—
302#11719921—28no—
303#11719921—44no—
304#11719921—44no—
305#11719921—44no—
306#11719921—44no—
307C4⋊Dic53—44no—
308#11719919—28no—
309#11719919—28no—
310#11719919—44no—
311#11719919—44no—
312#11719919—44no—
313C4×Dic53—28no—
314C4×Dic53—28no—
315C4×Dic53—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—41no—
325C23×C53—41no—
326C23×C53—41no—
327C23×C53—41no—
328C23×C53—41no—
329C23×C53—41no—
330C23×C53—41no—
331C23×C53—41no—
332C23×C53—41no—
333C23×C53—41no—
334C23×C53—41no—
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×C53—41no—
352C23×C53C23×C411yescharacteristic
353C23×C53C22×D411yescharacteristic
354C23×C53C22×D411yescharacteristic
355C23×C53C22×D411yescharacteristic
356C23×C53C22×D411yescharacteristic
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×C532−1+411yescharacteristic
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—41no—
375C22×D53—41no—
376C22×D53—41no—
377C22×D53—41no—
378C22×D53—41no—
379C22×D53—41no—
380C22×D53—41no—
381C22×D53—41no—
382C22×D53—41no—
383C22×D53—41no—
384C22×D53—41no—
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—41no—
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—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
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×C53#12714yes—
444C22⋊D53—416no—
445C2×Dic53—22no—
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—22no—
462C2×Dic53—22no—
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#11714yes—
487C2×Dic53C4×D414yes—
488C2×Dic53C4×D414yes—
489C2×Dic53C4×D414yes—
490C2×Dic53#12114yes—
491C2×Dic53#12314yes—
492C2×Dic53#12414yes—
493C2×Dic53#12614yes—
494#14001—531nomaximal, Sylow
495C22×C53—42no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—42no—
499C22×C53—42no—
500C22×C53—42no—
501C22×C53—42no—
502C22×C53—81no—
503C22×C53—81no—
504C22×C53—81no—
505C22×C53—81no—
506C22×C53—81no—
507C22×C53—81no—
508C22×C53—81no—
509C22×C53—81no—
510C22×C53C2×#11711yescharacteristic
511C22×C53C2×C4×D411yescharacteristic
512C22×C53C2×C4×D411yescharacteristic
513C22×C53C2×C4×D411yescharacteristic
514C22×C53C2×C4×D411yescharacteristic
515C22×C53#52011yescharacteristic
516C22×C53#52011yescharacteristic
517C22×C53C2×#12111yescharacteristic
518C22×C53C2×#12311yescharacteristic
519C22×C53C2×#12411yescharacteristic
520C22×C53C2×#12611yescharacteristic
521C22×C53C2×#12711yescharacteristic
522C22×C53#53211yescharacteristic
523C22×C53#53211yescharacteristic
524C22×C53#53211yescharacteristic
525C22×C53#53511yescharacteristic
526C22×C53#53611yescharacteristic
527C22×C53#54211yescharacteristic
528C22×C53#54211yescharacteristic
529C22×C53D4211yescharacteristic
530C22×C53D4211yescharacteristic
531C22×C53#54711yescharacteristic
532C22×C53#54711yescharacteristic
533C22×C53#54711yescharacteristic
534C22×C53#54711yescharacteristic
535C22×C53#54811yescharacteristic
536C22×C53#54811yescharacteristic
537C22×C53#55011yescharacteristic
538C22×C53#55011yescharacteristic
539C22×C53#55311yescharacteristic
540C22×C53#55311yescharacteristic
541C22×C53#55511yescharacteristic
542C22×C53#55511yescharacteristic
543C22×C53#55611yescharacteristic
544C22×C53#55611yescharacteristic
545C2×D53—42no—
546C2×D53—42no—
547C2×D53—42no—
548C2×D53—42no—
549C2×D53—42no—
550C2×D53—42no—
551C2×D53—42no—
552C2×D53—81no—
553C2×D53—81no—
554C2×D53—81no—
555C2×D53—81no—
556C2×D53—81no—
557C2×D53—81no—
558C2×D53—81no—
559C2×D53—81no—
560C4×C53—24no—
561C4×C53—24no—
562C4×C53—42no—
563C4×C53—42no—
564C4×C53—42no—
565C4×C53—81no—
566Dic53—24no—
567Dic53—42no—
568Dic53—42no—
569Dic53—42no—
570Dic53—42no—
571Dic53—81no—
572Dic53#38818yescomplemented
573C2×#390—531no—
574C2×#390—531no—
575C2×#390—531no—
576C2×#388—531no—
577C2×#388—531no—
578C2×#388—531no—
579C2×#388D5311yescharacteristic, complemented
580C2×#384—531no—
581C2×C4×C4⋊C4—531no—
582#1439—531no—
583#1439—531no—
584#1439—531no—
585#1439—531no—
586C4⋊#95—531no—
587C4×#95—531no—
588C2×C53—82no—
589C2×C53C2×#38811yescharacteristic
590C2×C53C4×#12711yescharacteristic
591C2×C53#232611yescharacteristic
592C2×C53#235411yescharacteristic
593C2×C53#235411yescharacteristic
594C2×C53#236111yescharacteristic
595C2×C53#236111yescharacteristic
596C2×C53#249111yescharacteristic
597C2×C53#249111yescharacteristic
598C2×C53#250011yescharacteristic
599C2×C53#250111yescharacteristic
600C2×C53#251211yescharacteristic
601C2×C53#251211yescharacteristic
602C2×C53#254111yescharacteristic
603C2×C53#254511yescharacteristic
604D53—82no—
605C23×D4—531no—
606C22×C4⋊C4—531no—
607C22×C4⋊C4—531no—
608C22×C4⋊C4—531no—
609C22×C4⋊C4—531no—
610C22×C4⋊C4—531no—
611C22×C4⋊C4—531no—
612C22×C4⋊C4C2×D5311yescharacteristic
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⋊C4—531no—
622C22×C22⋊C4C2×D5311yescharacteristic
623C22×C22⋊C4C2×D5311yescharacteristic
624C22×C22⋊C4C2×D5311yescharacteristic
625C22×C42—531no—
626C22×C42—531no—
627C22×C42—531no—
628C22×C42—531no—
629C22×C42C2×D5311yescharacteristic
630#390—538no—
631#390—1064no—
632#390—1064no—
633#388—24no—
634#388—1064no—
635#388—1064no—
636#388—1064no—
637#384—1064no—
638C4×C4⋊C4—1064no—
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#1400111yescharacteristic, complemented, Sylow
650C25—531no—
651C25C22×D5311yescharacteristic
652C22×D4—534no—
653C22×D4—1062no—
654C22×D4—1062no—
655C22×D4—1062no—
656C22×D4—1062no—
657C22×D4—1062no—
658C22×D4—1062no—
659C23×C4—531no—
660C23×C4—531no—
661C23×C4—531no—
662C23×C4—531no—
663C23×C4—531no—
664C23×C4—531no—
665C23×C4—531no—
666C23×C4C22×D5311yescharacteristic
667C23×C4C22×D5311yescharacteristic
668C23×C4C22×D5311yescharacteristic
669C23×C4C22×D5311yescharacteristic
670C23×C4C22×D5311yescharacteristic
671C23×C4C22×D5311yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—534no—
676C2×C4⋊C4—534no—
677C2×C4⋊C4—1062no—
678C2×C4⋊C4—1062no—
679C2×C4⋊C4—1062no—
680C2×C4⋊C4—1062no—
681C2×C4⋊C4—1062no—
682C2×C4⋊C4—1062no—
683C2×C4⋊C4—1062no—
684C2×C4⋊C4—1062no—
685C2×C4⋊C4—1062no—
686C2×C4⋊C4—1062no—
687C2×C4⋊C4—1062no—
688C2×C4⋊C4—1062no—
689C2×C4⋊C4—1062no—
690C2×C4⋊C4—2121no—
691C2×C4⋊C4—2121no—
692C2×C4⋊C4—2121no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—534no—
703C2×C22⋊C4—534no—
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—1062no—
721C2×C22⋊C4—2121no—
722C2×C22⋊C4—2121no—
723C2×C22⋊C4—2121no—
724C2×C22⋊C4—2121no—
725C2×C22⋊C4—2121no—
726C2×C22⋊C4—2121no—
727C2×C22⋊C4—2121no—
728C2×C22⋊C4C4×D5314yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—534no—
733C2×C42—534no—
734C2×C42—1062no—
735C2×C42—1062no—
736C2×C42—1062no—
737C2×C42—1062no—
738C2×C42—1062no—
739C2×C42—1062no—
740C2×C42—1062no—
741C2×C42—1062no—
742C2×C42—1062no—
743C2×C42—1062no—
744#95—22no—
745#95—534no—
746#95—1062no—
747#95—1062no—
748#95—1062no—
749#95—1062no—
750#95—1062no—
751#95—1062no—
752#95—1062no—
753#95C22⋊D5314yescomplemented
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—532no—
769C24—1061no—
770C24—1061no—
771C24—1061no—
772C24—1061no—
773C24—1061no—
774C24—1061no—
775C24—1061no—
776C24—1061no—
777C24—1061no—
778C24—1061no—
779C24—1061no—
780C24—1061no—
781C24—1061no—
782C24—1061no—
783C24C2×C4×D5312yes—
784C24C23×D5311yescharacteristic
785C2×D4—1068no—
786C2×D4—1068no—
787C2×D4—1068no—
788C2×D4—2124no—
789C2×D4—2124no—
790C2×D4—2124no—
791C2×D4—2124no—
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—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—532no—
826C22×C4—532no—
827C22×C4—532no—
828C22×C4—532no—
829C22×C4—532no—
830C22×C4—532no—
831C22×C4—532no—
832C22×C4—532no—
833C22×C4—532no—
834C22×C4—532no—
835C22×C4—532no—
836C22×C4—532no—
837C22×C4—532no—
838C22×C4—532no—
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×C4C2×C4×D5312yes—
875C22×C4C2×C4×D5312yes—
876C22×C4#1171994512yes—
877C22×C4D4×D5312yes—
878C22×C4D4×D5312yes—
879C22×C4D4×D5312yes—
880C22×C4C2×C22⋊D5312yes—
881C22×C4C2×C22⋊D5312yes—
882C22×C4C2×C22⋊D5312yes—
883C4⋊C4—44no—
884C4⋊C4—1068no—
885C4⋊C4—1068no—
886C4⋊C4—2124no—
887C4⋊C4—2124no—
888C4⋊C4—2124no—
889C4⋊C4—2124no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—1068no—
894C22⋊C4—1068no—
895C22⋊C4—1068no—
896C22⋊C4—2124no—
897C22⋊C4—2124no—
898C22⋊C4—2124no—
899C22⋊C4—2124no—
900C22⋊C4—2124no—
901C22⋊C4—2124no—
902C42—44no—
903C42—1068no—
904C42—1068no—
905C42—2124no—
906C42—2124no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
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—1062no—
943C23—1062no—
944C23—1062no—
945C23—1062no—
946C23—1062no—
947C23—1062no—
948C23—1062no—
949C23—2121no—
950C23—2121no—
951C23—2121no—
952C23—2121no—
953C23—2121no—
954C23—2121no—
955C23—2121no—
956C23—2121no—
957C23—2121no—
958C23—2121no—
959C23—2121no—
960C23—2121no—
961C23—2121no—
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—
977C23C22×C4×D5311yescharacteristic
978C23C2×D4×D5311yescharacteristic
979C23C2×D4×D5311yescharacteristic
980C23C2×D4×D5311yescharacteristic
981C23C22×C22⋊D5311yescharacteristic
982C23#41×D5311yescharacteristic
983C23#41×D5311yescharacteristic
984C23#41×D5311yescharacteristic
985C23#41×D5311yescharacteristic
986C23#41×D5311yescharacteristic
987C23C2×#1171994511yescharacteristic
988C23#1313326211yescharacteristic
989C23#1313326311yescharacteristic
990C23#1313326411yescharacteristic
991C23#1313326411yescharacteristic
992D4—21216no—
993C2×C4—22no—
994C2×C4—22no—
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—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
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—534no—
1034C2×C4—534no—
1035C2×C4—534no—
1036C2×C4—534no—
1037C2×C4—534no—
1038C2×C4—534no—
1039C2×C4—534no—
1040C2×C4—534no—
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—1062no—
1051C2×C4—1062no—
1052C2×C4—1062no—
1053C2×C4—1062no—
1054C2×C4—1062no—
1055C2×C4—1062no—
1056C2×C4—1062no—
1057C2×C4—1062no—
1058C2×C4—1062no—
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×C4C4×C22⋊D5314yes—
1083C2×C4#1313321314yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—4241no—
1100C22—4241no—
1101C22—4241no—
1102C22—4241no—
1103C22—4241no—
1104C22—4241no—
1105C22—4241no—
1106C22—4241no—
1107C22—2122no—
1108C22—2122no—
1109C22—2122no—
1110C22—2122no—
1111C22—2122no—
1112C22—2122no—
1113C22—2122no—
1114C22#117×D5311yescharacteristic
1115C22C4×D4×D5311yescharacteristic
1116C22C4×D4×D5311yescharacteristic
1117C22C4×D4×D5311yescharacteristic
1118C22C2×C4×C22⋊D5311yescharacteristic
1119C22#1681110211yescharacteristic
1120C22#1681110311yescharacteristic
1121C22#121×D5311yescharacteristic
1122C22#123×D5311yescharacteristic
1123C22#124×D5311yescharacteristic
1124C22#126×D5311yescharacteristic
1125C22C2×#1313321311yescharacteristic
1126C22#1681116911yescharacteristic
1127C22#1681117011yescharacteristic
1128C22#1681117011yescharacteristic
1129C22#1681118911yescharacteristic
1130C22#1681119511yescharacteristic
1131C22#1681123711yescharacteristic
1132C22#1681123911yescharacteristic
1133C22D4×C22⋊D5311yescharacteristic
1134C22#1681125711yescharacteristic
1135C22#1681127111yescharacteristic
1136C22#1681127111yescharacteristic
1137C22#1681127211yescharacteristic
1138C22#1681127211yescharacteristic
1139C22#1681128111yescharacteristic
1140C22#1681128211yescharacteristic
1141C22#1681129111yescharacteristic
1142C22#1681129211yescharacteristic
1143C22#1681132211yescharacteristic
1144C22#1681132411yescharacteristic
1145C22#1681133511yescharacteristic
1146C22#1681133611yescharacteristic
1147C22#1681134011yescharacteristic
1148C22#1681134111yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—538no—
1156C4—1064no—
1157C4—4241no—
1158C4—2122no—
1159C4—2122no—
1160C4—2122no—
1161C4—2122no—
1162C2—82no—
1163C2—4242no—
1164C2#388×D5311yescharacteristic
1165C2C4×#1313321311yescharacteristic
1166C2#2027742411yescharacteristic
1167C2#2027766111yescharacteristic
1168C2#2027766511yescharacteristic
1169C2#2027772811yescharacteristic
1170C2#2027773211yescharacteristic
1171C2#2027907511yescharacteristic
1172C2#2027907711yescharacteristic
1173C2#2027917511yescharacteristic
1174C2#2027918411yescharacteristic
1175C2#2027929811yescharacteristic
1176C2#2027930011yescharacteristic
1177C2#2027965811yescharacteristic
1178C2#2027969311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#388D53
hypocenterC53#14001
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#16810515C2semidirect
5. C2×#16810514C2semidirect
6. C2×#16810511C2semidirect
7. C2×#16810492C2semidirect
8. C2×C4×#11719919C2semidirect
9. #20272960C2semidirect
10. #20272959C2semidirect
11. #20272958C2semidirect
12. #20272957C2semidirect
13. #20272943C2semidirect
14. #95×Dic53C2semidirect
15. C2×C53×#388C2semidirect
38. #16810523C4semidirect
139. #13133124D4semidirect
163. #95×C53D4semidirect
572. Dic53#388semidirect
579. C2×#388D53semidirect
649. C53#14001semidirect
753. #95C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105232
C2×#168105152
C2×#168105142
C2×#168105112
C2×#168104922
C2×C4×#117199192
#202729602
#202729592
#202729582
#202729572
#202729432
#95×Dic532
C2×C53×#3882
#1400153