Finite Group Databasebeta

← #27306339

Subgroups — #27306339

Order 13568.

2366 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D53C211yesmaximal, characteristic
2C2×#16810520C211yesmaximal, characteristic, complemented
3C2×#16810518C211yesmaximal, characteristic, complemented
4C2×#16810482C211yesmaximal, characteristic
5C2×#16810482C211yesmaximal, characteristic
6C2×#16810480C211yesmaximal, characteristic
7C2×#16810470C211yesmaximal, characteristic
8#20272968C211yesmaximal, characteristic, complemented
9#20272967C211yesmaximal, characteristic, complemented
10#20272967C211yesmaximal, characteristic, complemented
11#20272943C211yesmaximal, characteristic, complemented
12#20272943C211yesmaximal, characteristic, complemented
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C2×C4⋊C4×D53—24no—
28C2×C4⋊C4×D53—24no—
29C2×C4⋊C4×D53C418yescomplemented
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36#16810520—24no—
37#16810518—24no—
38#16810482—24no—
39#16810482—24no—
40#16810480—24no—
41#16810470—24no—
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C22×C4⋊C4×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C24×D53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C22×C4×D53—22no—
69C22×C4×D53—22no—
70C22×C4×D53—22no—
71C22×C4×D53—22no—
72C22×C4×D53—22no—
73C22×C4×D53—22no—
74C22×C4×D53—22no—
75C22×C4×D53—22no—
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—22no—
79C22×C4×D53—22no—
80C22×C4×D53—41no—
81C22×C4×D53—41no—
82C22×C4×D53—41no—
83C22×C4×D53—41no—
84C22×C4×D53C2×C414yes—
85C22×C4×D53C2×C414yes—
86C22×C4×D53C2×C414yes—
87C22×C4×D53D414yes—
88C22×C4×D53Q814yes—
89C2×C4⋊Dic53—22no—
90C2×C4⋊Dic53—22no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53C2×C414yes—
95C2×#11719919—22no—
96C2×#11719919—22no—
97C2×#11719919—22no—
98C2×#11719919—22no—
99C2×#11719919—22no—
100C2×#11719919—22no—
101C2×#11719919—22no—
102C2×#11719919—22no—
103C2×#11719919—22no—
104C2×#11719919—22no—
105C2×#11719919—22no—
106C2×#11719919—22no—
107C2×#11719919—41no—
108C2×#11719919—41no—
109C2×#11719919C2×C414yes—
110C2×#11719919C2×C414yes—
111C2×#11719919D414yes—
112C2×#11719919D414yes—
113C4⋊C4×D53—232no—
114C2×#11719921—22no—
115C2×#11719921—22no—
116C2×#11719921—22no—
117C2×#11719921—22no—
118C2×#11719921—22no—
119C2×#11719921—22no—
120C2×#11719921—22no—
121C2×#11719921—22no—
122C2×#11719921—22no—
123C2×#11719921—22no—
124C2×#11719921D414yes—
125C2×#11719921Q814yes—
126C2×C4×Dic53—22no—
127C2×C4×Dic53—22no—
128C2×C4×Dic53—22no—
129C2×C4×Dic53—22no—
130C2×C4×Dic53—22no—
131C2×C4×Dic53—22no—
132#13133124—22no—
133#13133124—22no—
134#13133124—22no—
135#13133124—22no—
136#13133124—22no—
137#13133124—22no—
138#13133124—22no—
139#13133124—22no—
140#13133124—41no—
141#13133124—41no—
142#13133124—41no—
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150C2×C4⋊C4×C53—22no—
151C2×C4⋊C4×C53—22no—
152C2×C4⋊C4×C53—22no—
153C2×C4⋊C4×C53—22no—
154C2×C4⋊C4×C53—41no—
155C2×C4⋊C4×C53C2×C414yes—
156#95×C53—22no—
157#95×C53—22no—
158#95×C53—22no—
159#95×C53—22no—
160#95×C53—41no—
161C24×C53C2411yescharacteristic
162C23×D53—21no—
163C23×D53—21no—
164C23×D53—21no—
165C23×D53—21no—
166C23×D53—21no—
167C23×D53—21no—
168C23×D53—21no—
169C23×D53—21no—
170C23×D53C22×C412yes—
171C23×D53C2×D412yes—
172C23×D53C2×D412yes—
173C23×D53C2×Q812yes—
174C23×D53C2×Q812yes—
175C23×D53#4112yes—
176C23×D53#4112yes—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
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×C53C22×C412yes—
218C22×C4×C53C22×C412yes—
219C22×C4×C53C22×C412yes—
220C22×C4×C53C2×D412yes—
221C22×C4×C53C2×D412yes—
222C22×C4×C53C2×D412yes—
223C22×C4×C53C2×D412yes—
224C22×C4×C53C2×Q812yes—
225C22×C4×C53C2×Q812yes—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
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×Dic53C22×C412yes—
263C22×Dic53C22×C412yes—
264C22×Dic53C22×C412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×D412yes—
267C22×Dic53C2×D412yes—
268C22×Dic53C2×D412yes—
269C22×Dic53C2×D412yes—
270C22×Dic53C2×D412yes—
271C22×Dic53C2×Q812yes—
272C22×Dic53C2×Q812yes—
273C22×Dic53#4112yes—
274C22×Dic53#4112yes—
275C2×C4×D53—28no—
276C2×C4×D53—28no—
277C2×C4×D53—28no—
278C2×C4×D53—28no—
279C2×C4×D53—28no—
280C2×C4×D53—28no—
281C2×C4×D53—28no—
282C2×C4×D53—28no—
283C2×C4×D53—28no—
284C2×C4×D53—28no—
285C2×C4×D53—44no—
286C2×C4×D53—44no—
287C2×C4×D53—44no—
288C2×C4×D53—44no—
289C2×C4×D53—44no—
290C2×C4×D53—44no—
291C2×C4×D53—44no—
292C2×C4×D53—44no—
293C2×C4×D53—44no—
294C2×C4×D53—44no—
295C2×C4×D53C4⋊C4116yescomplemented
296C4⋊C4×C53—28no—
297C4⋊C4×C53—44no—
298#11719921—28no—
299#11719921—28no—
300#11719921—44no—
301#11719921—44no—
302C4⋊Dic53—28no—
303C4⋊Dic53—44no—
304#11719919—28no—
305#11719919—44no—
306#11719919—44no—
307#11719919—44no—
308#11719919—44no—
309#11719919C22⋊C4116yescomplemented
310C4×Dic53—44no—
311C4×Dic53—44no—
312C23×C53C23×C411yescharacteristic
313C23×C53C22×D411yescharacteristic
314C23×C53C22×D411yescharacteristic
315C23×C53C22×D411yescharacteristic
316C23×C53C22×D411yescharacteristic
317C23×C53C22×Q811yescharacteristic
318C23×C53C22×Q811yescharacteristic
319C23×C53C2×#4111yescharacteristic
320C23×C53C2×#4111yescharacteristic
321C23×C53C2×#4111yescharacteristic
322C23×C53C2×#4111yescharacteristic
323C23×C53H(5,𝔽2)11yescharacteristic
324C23×C53H(5,𝔽2)11yescharacteristic
325C23×C532−1+411yescharacteristic
326C23×C532−1+411yescharacteristic
327C22×D53—22no—
328C22×D53—22no—
329C22×D53—22no—
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—22no—
337C22×D53—22no—
338C22×D53—22no—
339C22×D53—22no—
340C22×D53—22no—
341C22×D53—22no—
342C22×D53—22no—
343C22×D53—22no—
344C22×D53—22no—
345C22×D53—22no—
346C22×D53—22no—
347C22×D53—22no—
348C22×D53—22no—
349C22×D53—22no—
350C22×D53—22no—
351C22×D53—22no—
352C22×D53—22no—
353C22×D53—22no—
354C22×D53—22no—
355C22×D53C2×C4⋊C414yes—
356C22×D53C4×D414yes—
357C22×D53C4×Q814yes—
358C22×D53#12114yes—
359C22×D53C22⋊Q814yes—
360C22×D53#12514yes—
361C22×D53C4⋊Q814yes—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
382C2×C4×C53—22no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53—41no—
394C2×C4×C53—41no—
395C2×C4×C53—41no—
396C2×C4×C53—41no—
397C2×C4×C53—41no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53C2×C22⋊C414yes—
410C2×C4×C53C2×C4⋊C414yes—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—22no—
415C2×Dic53—22no—
416C2×Dic53—22no—
417C2×Dic53—22no—
418C2×Dic53—22no—
419C2×Dic53—22no—
420C2×Dic53—22no—
421C2×Dic53—22no—
422C2×Dic53—22no—
423C2×Dic53—22no—
424C2×Dic53—22no—
425C2×Dic53—22no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53—41no—
436C2×Dic53—41no—
437C2×Dic53—41no—
438C2×Dic53—41no—
439C2×Dic53—41no—
440C2×Dic53—41no—
441C2×Dic53—41no—
442C2×Dic53—41no—
443C2×Dic53—41no—
444C2×Dic53—41no—
445C2×Dic53—41no—
446C2×Dic53—41no—
447C2×Dic53—41no—
448C2×Dic53—41no—
449C2×Dic53—41no—
450C2×Dic53—41no—
451C2×Dic53—41no—
452C2×Dic53C2×C22⋊C414yes—
453C2×Dic53C2×C22⋊C414yes—
454C2×Dic53C2×C4⋊C414yes—
455C2×Dic53#11714yes—
456C2×Dic53#12114yes—
457C2×Dic53#12114yes—
458C2×Dic53C22⋊Q814yes—
459C2×Dic53C22⋊Q814yes—
460C4×D53—232no—
461C4×D53—416no—
462C4×D53—416no—
463#13907—531nomaximal, Sylow
464C22×C53C22×C22⋊C411yescharacteristic
465C22×C53C22×C4⋊C411yescharacteristic
466C22×C53C2×#11711yescharacteristic
467C22×C53C2×C4×D411yescharacteristic
468C22×C53C2×C4×Q811yescharacteristic
469C22×C53#51811yescharacteristic
470C22×C53#51911yescharacteristic
471C22×C53C2×#12111yescharacteristic
472C22×C53C2×#12111yescharacteristic
473C22×C53C2×#12111yescharacteristic
474C22×C53C2×C22⋊Q811yescharacteristic
475C22×C53C2×C22⋊Q811yescharacteristic
476C22×C53C2×C22⋊Q811yescharacteristic
477C22×C53C2×#12511yescharacteristic
478C22×C53C2×C4⋊Q811yescharacteristic
479C22×C53#53711yescharacteristic
480C22×C53#53711yescharacteristic
481C22×C53#54411yescharacteristic
482C22×C53#54411yescharacteristic
483C22×C53D4211yescharacteristic
484C22×C53D4211yescharacteristic
485C22×C53#54611yescharacteristic
486C22×C53#54611yescharacteristic
487C22×C53#54711yescharacteristic
488C22×C53#54711yescharacteristic
489C22×C53#54811yescharacteristic
490C22×C53#54811yescharacteristic
491C22×C53D4×Q811yescharacteristic
492C22×C53D4×Q811yescharacteristic
493C22×C53#55211yescharacteristic
494C22×C53#55211yescharacteristic
495C22×C53#55311yescharacteristic
496C22×C53#55311yescharacteristic
497C22×C53#55411yescharacteristic
498C22×C53#55411yescharacteristic
499C2×D53—24no—
500C2×D53—24no—
501C2×D53—24no—
502C2×D53—24no—
503C2×D53—24no—
504C2×D53—24no—
505C2×D53—24no—
506C2×D53—24no—
507C2×D53—24no—
508C2×D53—24no—
509C2×D53—24no—
510C2×D53—24no—
511C2×D53—24no—
512C2×D53—24no—
513C2×D53#38918yescomplemented
514C4×C53—24no—
515C4×C53—24no—
516C4×C53—42no—
517C4×C53—42no—
518C4×C53—42no—
519C4×C53—81no—
520C4×C53—81no—
521Dic53—24no—
522Dic53—42no—
523Dic53—42no—
524Dic53—42no—
525Dic53—81no—
526Dic53—81no—
527Dic53#38018yescomplemented
528C23×C4⋊C4—531no—
529C2×#389—531no—
530C2×#389—531no—
531C2×#380—531no—
532C2×#380—531no—
533C2×#380—531no—
534C2×C4×C22⋊C4—531no—
535#1441—531no—
536#1441—531no—
537#1441—531no—
538#1441D5311yescharacteristic, complemented
539C4⋊#95—531no—
540C4⋊#95—531no—
541C22⋊#95—531no—
542C22⋊#95—531no—
543C2×C53C2×#38011yescharacteristic
544C2×C53C2×#38911yescharacteristic
545C2×C53#231611yescharacteristic
546C2×C53D4×C22⋊C411yescharacteristic
547C2×C53Q8×C22⋊C411yescharacteristic
548C2×C53#234411yescharacteristic
549C2×C53#234511yescharacteristic
550C2×C53#241611yescharacteristic
551C2×C53#241611yescharacteristic
552C2×C53#241711yescharacteristic
553C2×C53#241711yescharacteristic
554C2×C53#244011yescharacteristic
555C2×C53#244011yescharacteristic
556C2×C53#244211yescharacteristic
557C2×C53#244211yescharacteristic
558D53—28no—
559C24×C4—531no—
560C24×C4—531no—
561C24×C4—531no—
562C22×C4⋊C4—531no—
563C22×C4⋊C4—531no—
564C22×C4⋊C4—531no—
565C22×C4⋊C4—538no—
566C22×C4⋊C4—531no—
567C22×C4⋊C4—531no—
568C22×C4⋊C4—531no—
569C22×C4⋊C4—531no—
570C22×C4⋊C4—531no—
571C22×C4⋊C4—1064no—
572C22×C4⋊C4—1064no—
573C22×C4⋊C4C2×D5311yescharacteristic
574C22×C4⋊C4C2×D5311yescharacteristic
575C22×C22⋊C4—531no—
576C22×C22⋊C4—531no—
577C22×C22⋊C4—531no—
578C22×C22⋊C4—531no—
579C22×C42—531no—
580C22×C42—531no—
581#389—1064no—
582#389—1064no—
583#380—1064no—
584#380—1064no—
585#380—1064no—
586C4×C22⋊C4—1064no—
587C2×#95—531no—
588C2×#95—531no—
589C2×#95—531no—
590C2×#95—531no—
591C2×#95—531no—
592C2×#95—531no—
593C2×#95—531no—
594C2×#95—531no—
595C2×#95—531no—
596C2×#95—531no—
597C2×#95—531no—
598C2×#95C2×D5311yescharacteristic
599C2×#95C2×D5311yescharacteristic
600C2×#95C2×D5311yescharacteristic
601C2×#95C2×D5311yescharacteristic
602C2×#95C2×D5311yescharacteristic
603C53#1390711yescharacteristic, complemented, Sylow
604C25—531no—
605C23×C4—531no—
606C23×C4—531no—
607C23×C4—534no—
608C23×C4—534no—
609C23×C4—534no—
610C23×C4—531no—
611C23×C4—531no—
612C23×C4—531no—
613C23×C4—534no—
614C23×C4—534no—
615C23×C4—531no—
616C23×C4—531no—
617C23×C4—1062no—
618C23×C4—1062no—
619C23×C4—1062no—
620C23×C4—1062no—
621C23×C4—1062no—
622C23×C4—1062no—
623C23×C4—1062no—
624C23×C4—1062no—
625C23×C4—1062no—
626C23×C4—1062no—
627C23×C4—1062no—
628C23×C4—1062no—
629C23×C4—2121no—
630C23×C4—2121no—
631C23×C4—2121no—
632C23×C4—2121no—
633C23×C4C22×D5311yescharacteristic
634C23×C4C22×D5311yescharacteristic
635C23×C4C22×D5311yescharacteristic
636C23×C4C22×D5311yescharacteristic
637C23×C4C22×D5311yescharacteristic
638C23×C4C22×D5311yescharacteristic
639C23×C4C22×D5311yescharacteristic
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—534no—
646C2×C4⋊C4—534no—
647C2×C4⋊C4—534no—
648C2×C4⋊C4—534no—
649C2×C4⋊C4—534no—
650C2×C4⋊C4—10632no—
651C2×C4⋊C4—1062no—
652C2×C4⋊C4—1062no—
653C2×C4⋊C4—1062no—
654C2×C4⋊C4—1062no—
655C2×C4⋊C4—1062no—
656C2×C4⋊C4—1062no—
657C2×C4⋊C4—1062no—
658C2×C4⋊C4—1062no—
659C2×C4⋊C4—1062no—
660C2×C4⋊C4—1062no—
661C2×C4⋊C4—1062no—
662C2×C4⋊C4—1062no—
663C2×C4⋊C4—1062no—
664C2×C4⋊C4—1062no—
665C2×C4⋊C4—1062no—
666C2×C4⋊C4—1062no—
667C2×C4⋊C4—2121no—
668C2×C4⋊C4—2121no—
669C2×C4⋊C4—2121no—
670C2×C4⋊C4C4×D5314yes—
671C2×C22⋊C4—534no—
672C2×C22⋊C4—534no—
673C2×C22⋊C4—1062no—
674C2×C22⋊C4—1062no—
675C2×C22⋊C4—1062no—
676C2×C22⋊C4—1062no—
677C2×C22⋊C4—1062no—
678C2×C22⋊C4—1062no—
679C2×C22⋊C4—1062no—
680C2×C22⋊C4—1062no—
681C2×C22⋊C4—1062no—
682C2×C22⋊C4—1062no—
683C2×C42—1062no—
684C2×C42—1062no—
685C2×C42—1062no—
686C2×C42—1062no—
687C2×C42—1062no—
688C2×C42—1062no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—41no—
694#95—1062no—
695#95—1062no—
696#95—1062no—
697#95—1062no—
698#95—1062no—
699#95—1062no—
700#95—1062no—
701#95—1062no—
702#95—2121no—
703#95—2121no—
704#95—2121no—
705C24—532no—
706C24—532no—
707C24—532no—
708C24—532no—
709C24—532no—
710C24—532no—
711C24—532no—
712C24—1061no—
713C24—1061no—
714C24—1061no—
715C24—1061no—
716C24—1061no—
717C24—1061no—
718C24—1061no—
719C24—1061no—
720C24C23×D5311yescharacteristic
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—532no—
762C22×C4—532no—
763C22×C4—532no—
764C22×C4—532no—
765C22×C4—532no—
766C22×C4—532no—
767C22×C4—532no—
768C22×C4—532no—
769C22×C4—532no—
770C22×C4—532no—
771C22×C4—5316no—
772C22×C4—532no—
773C22×C4—532no—
774C22×C4—532no—
775C22×C4—1068no—
776C22×C4—1068no—
777C22×C4—1068no—
778C22×C4—1068no—
779C22×C4—1068no—
780C22×C4—1068no—
781C22×C4—1068no—
782C22×C4—1068no—
783C22×C4—1068no—
784C22×C4—1061no—
785C22×C4—1061no—
786C22×C4—1061no—
787C22×C4—1061no—
788C22×C4—1061no—
789C22×C4—1061no—
790C22×C4—1061no—
791C22×C4—1061no—
792C22×C4—1061no—
793C22×C4—1061no—
794C22×C4—1061no—
795C22×C4—1061no—
796C22×C4—1061no—
797C22×C4—1061no—
798C22×C4—1061no—
799C22×C4—1061no—
800C22×C4—1061no—
801C22×C4—1061no—
802C22×C4—1061no—
803C22×C4—1061no—
804C22×C4—1061no—
805C22×C4—1061no—
806C22×C4—1068no—
807C22×C4—1061no—
808C22×C4—1061no—
809C22×C4—1061no—
810C22×C4—1061no—
811C22×C4—1061no—
812C22×C4—1061no—
813C22×C4—1061no—
814C22×C4—1061no—
815C22×C4—1061no—
816C22×C4—1061no—
817C22×C4—1061no—
818C22×C4—1061no—
819C22×C4—1061no—
820C22×C4—1061no—
821C22×C4—2124no—
822C22×C4—2124no—
823C22×C4—2124no—
824C22×C4—2124no—
825C22×C4—2124no—
826C22×C4—2124no—
827C22×C4—2124no—
828C22×C4—2124no—
829C22×C4—2124no—
830C22×C4—2124no—
831C22×C4C2×C4×D5312yes—
832C22×C4C2×C4×D5312yes—
833C22×C4C2×C4×D5312yes—
834C22×C4D4×D5312yes—
835C22×C4D4×D5312yes—
836C22×C4D4×D5312yes—
837C22×C4D4×D5312yes—
838C22×C4Q8×D5312yes—
839C22×C4Q8×D5312yes—
840C4⋊C4—28no—
841C4⋊C4—44no—
842C4⋊C4—5316no—
843C4⋊C4—1068no—
844C4⋊C4—1068no—
845C4⋊C4—2124no—
846C4⋊C4—2124no—
847C4⋊C4—2124no—
848C4⋊C4—2124no—
849C4⋊C4—2124no—
850C22⋊C4—1068no—
851C22⋊C4—1068no—
852C22⋊C4—2124no—
853C22⋊C4—2124no—
854C42—2124no—
855C42—2124no—
856C23—534no—
857C23—534no—
858C23—534no—
859C23—534no—
860C23—534no—
861C23—534no—
862C23—534no—
863C23—1062no—
864C23—1062no—
865C23—1062no—
866C23—1062no—
867C23—1062no—
868C23—1062no—
869C23—1062no—
870C23—1062no—
871C23—1062no—
872C23—1062no—
873C23—1062no—
874C23—1062no—
875C23—1062no—
876C23—1062no—
877C23—1062no—
878C23—1062no—
879C23—1062no—
880C23—1062no—
881C23—1062no—
882C23—1062no—
883C23—1062no—
884C23—1062no—
885C23—1062no—
886C23—1062no—
887C23—1062no—
888C23—1062no—
889C23—1062no—
890C23—1062no—
891C23C22×C4×D5311yescharacteristic
892C23C2×D4×D5311yescharacteristic
893C23C2×D4×D5311yescharacteristic
894C23C2×D4×D5311yescharacteristic
895C23C2×D4×D5311yescharacteristic
896C23C2×Q8×D5311yescharacteristic
897C23C2×Q8×D5311yescharacteristic
898C23#41×D5311yescharacteristic
899C23#41×D5311yescharacteristic
900C23#41×D5311yescharacteristic
901C23#41×D5311yescharacteristic
902C23#1313326211yescharacteristic
903C23#1313326311yescharacteristic
904C23#1313326411yescharacteristic
905C23#1313326511yescharacteristic
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—534no—
954C2×C4—534no—
955C2×C4—534no—
956C2×C4—534no—
957C2×C4—534no—
958C2×C4—534no—
959C2×C4—534no—
960C2×C4—534no—
961C2×C4—10632no—
962C2×C4—1062no—
963C2×C4—1062no—
964C2×C4—1062no—
965C2×C4—1062no—
966C2×C4—1062no—
967C2×C4—1062no—
968C2×C4—1062no—
969C2×C4—1062no—
970C2×C4—1062no—
971C2×C4—1062no—
972C2×C4—1062no—
973C2×C4—1062no—
974C2×C4—1062no—
975C2×C4—1062no—
976C2×C4—1062no—
977C2×C4—21216no—
978C2×C4—21216no—
979C2×C4—2121no—
980C2×C4—2121no—
981C2×C4—2121no—
982C2×C4—2121no—
983C2×C4—2121no—
984C2×C4—2121no—
985C2×C4—2121no—
986C2×C4—2121no—
987C2×C4—2121no—
988C2×C4—2121no—
989C2×C4—2121no—
990C2×C4—2121no—
991C2×C4—2121no—
992C2×C4—2121no—
993C2×C4—2121no—
994C2×C4—2121no—
995C2×C4—2121no—
996C2×C4—2121no—
997C2×C4—2121no—
998C2×C4—2121no—
999C2×C4—2121no—
1000C2×C4—2121no—
1001C2×C4—2121no—
1002C2×C4—2121no—
1003C2×C4—2121no—
1004C2×C4—2121no—
1005C2×C4C22⋊C4×D5314yes—
1006C2×C4C4⋊C4×D5314yes—
1007C22—538no—
1008C22—1064no—
1009C22—1064no—
1010C22—1064no—
1011C22—1064no—
1012C22—1064no—
1013C22—1064no—
1014C22—1064no—
1015C22—1064no—
1016C22—1064no—
1017C22—1064no—
1018C22—1064no—
1019C22—1064no—
1020C22—1064no—
1021C22—1064no—
1022C22C2×C22⋊C4×D5311yescharacteristic
1023C22C2×C4⋊C4×D5311yescharacteristic
1024C22#117×D5311yescharacteristic
1025C22C4×D4×D5311yescharacteristic
1026C22C4×Q8×D5311yescharacteristic
1027C22#1681109511yescharacteristic
1028C22#1681109911yescharacteristic
1029C22#121×D5311yescharacteristic
1030C22#121×D5311yescharacteristic
1031C22#121×D5311yescharacteristic
1032C22C22⋊Q8×D5311yescharacteristic
1033C22C22⋊Q8×D5311yescharacteristic
1034C22C22⋊Q8×D5311yescharacteristic
1035C22#125×D5311yescharacteristic
1036C22C4⋊Q8×D5311yescharacteristic
1037C22#1681120211yescharacteristic
1038C22#1681120311yescharacteristic
1039C22#1681125011yescharacteristic
1040C22#1681125311yescharacteristic
1041C22#1681125511yescharacteristic
1042C22#1681125711yescharacteristic
1043C22#1681126211yescharacteristic
1044C22#1681126511yescharacteristic
1045C22#1681127111yescharacteristic
1046C22#1681127511yescharacteristic
1047C22#1681128111yescharacteristic
1048C22#1681128311yescharacteristic
1049C22#1681128611yescharacteristic
1050C22#1681128811yescharacteristic
1051C22#1681130511yescharacteristic
1052C22#1681130911yescharacteristic
1053C22#1681131811yescharacteristic
1054C22#1681132411yescharacteristic
1055C22#1681132711yescharacteristic
1056C22#1681132911yescharacteristic
1057C4—24no—
1058C4—24no—
1059C4—42no—
1060C4—42no—
1061C4—42no—
1062C4—81no—
1063C4—81no—
1064C4—538no—
1065C4—1064no—
1066C4—4241no—
1067C4—4241no—
1068C4—2122no—
1069C4—2122no—
1070C4—2122no—
1071C2—1068no—
1072C2#380×D5311yescharacteristic
1073C2#389×D5311yescharacteristic
1074C2#2027733011yescharacteristic
1075C2#2027753311yescharacteristic
1076C2#2027754911yescharacteristic
1077C2#2027758111yescharacteristic
1078C2#2027758911yescharacteristic
1079C2#2027814811yescharacteristic
1080C2#2027815011yescharacteristic
1081C2#2027815911yescharacteristic
1082C2#2027816111yescharacteristic
1083C2#2027841011yescharacteristic
1084C2#2027841211yescharacteristic
1085C2#2027843211yescharacteristic
1086C2#2027843411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1441C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1441D53
hypocenterC53#13907
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#16810520C2semidirect
3. C2×#16810518C2semidirect
8. #20272968C2semidirect
9. #20272967C2semidirect
10. #20272967C2semidirect
11. #20272943C2semidirect
12. #20272943C2semidirect
15. C53×#1441C2semidirect
29. C2×C4⋊C4×D53C4semidirect
295. C2×C4×D53C4⋊C4semidirect
309. #11719919C22⋊C4semidirect
513. C2×D53#389semidirect
527. Dic53#380semidirect
538. #1441D53semidirect
603. C53#13907semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D532
C2×#168105202
C2×#168105182
C2×#168104822
C2×#168104802
C2×#168104702
#202729682
#202729672
#202729432
#202729362
C53×#14412
#1390753