Finite Group Databasebeta

← #27306342

Subgroups — #27306342

Order 13568.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D53C211yesmaximal, characteristic
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810480C211yesmaximal, characteristic
4C2×#16810480C212yesmaximal
5C2×C4×#11719921C211yesmaximal, characteristic
6#20272969C212yesmaximal, complemented
7#20272965C212yesmaximal, complemented
8#20272945C211yesmaximal, characteristic, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272936C212yesmaximal
11C2×C53×#389C211yesmaximal, characteristic, complemented
12C23×C4×D53C2212yes—
13C23×C4×D53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4⋊Dic53C2212yes—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719919C2212yes—
18C2×C4⋊C4×D53—24no—
19C2×C4⋊C4×D53—24no—
20C2×C4⋊C4×D53C418yescomplemented
21C22×#11719921C2212yes—
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25#16810522—24no—
26#16810480—24no—
27#16810480—28no—
28C4×#11719921—24no—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#389—24no—
42C2×#95×C53C2212yes—
43C24×D53C2311yescharacteristic
44C23×Dic53C2312yes—
45C23×Dic53C2312yes—
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53—22no—
53C22×C4×D53—24no—
54C22×C4×D53—24no—
55C22×C4×D53—24no—
56C22×C4×D53—24no—
57C22×C4×D53—42no—
58C22×C4×D53—42no—
59C22×C4×D53C2×C418yes—
60C22×C4×D53C2×C414yes—
61C22×C4×D53D414yes—
62C22×C4×D53Q814yes—
63C2×C4⋊Dic53—22no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53—24no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—24no—
70C2×C4⋊Dic53—42no—
71C2×C4⋊Dic53C2×C414yes—
72C2×#11719919—24no—
73C2×#11719919—24no—
74C2×#11719919C2×C418yes—
75C4⋊C4×D53—232no—
76C2×#11719921—22no—
77C2×#11719921—22no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921—22no—
81C2×#11719921—22no—
82C2×#11719921—24no—
83C2×#11719921D414yes—
84C2×#11719921Q814yes—
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88#13133124—24no—
89#13133124—24no—
90#13133124—22no—
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—42no—
95#13133124—42no—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2312yes—
100C23×C4×C53C2311yescharacteristic
101C2×C4⋊C4×C53—24no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—24no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53—42no—
107C2×C4⋊C4×C53C2×C414yes—
108C2×C4⋊C4×C53D414yes—
109C2×C4⋊C4×C53D414yes—
110C2×C42×C53—22no—
111C2×C42×C53—22no—
112C2×C42×C53—22no—
113#95×C53—24no—
114C24×C53C2411yescharacteristic
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53—21no—
122C23×D53—21no—
123C23×D53C22×C412yes—
124C23×D53C2×D412yes—
125C23×D53C2×D412yes—
126C23×D53C2×Q812yes—
127C23×D53C2×Q812yes—
128C23×D53#4112yes—
129C23×D53#4112yes—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53C22×C414yes—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D414yes—
157C22×C4×C53C2×D414yes—
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×D412yes—
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×Q812yes—
162C22×C4×C53C2×Q812yes—
163C22×C4×C53#4112yes—
164C22×C4×C53#4112yes—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—22no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—22no—
181C22×Dic53—21no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53C22×C414yes—
195C22×Dic53C22×C412yes—
196C22×Dic53C2×D412yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×Q812yes—
199C22×Dic53C2×Q812yes—
200C2×C4×D53—28no—
201C2×C4×D53—28no—
202C2×C4×D53—28no—
203C2×C4×D53—28no—
204C2×C4×D53—28no—
205C2×C4×D53—28no—
206C2×C4×D53—216no—
207C2×C4×D53—216no—
208C2×C4×D53—48no—
209C2×C4×D53—48no—
210C2×C4×D53—48no—
211C2×C4×D53—48no—
212C2×C4×D53—48no—
213C2×C4×D53C4⋊C4116yescomplemented
214C4⋊C4×C53—48no—
215C4⋊C4×C53—44no—
216C4⋊C4×C53C22⋊C4116yescomplemented
217C42×C53—44no—
218#11719921—28no—
219#11719921—28no—
220#11719921—48no—
221C4⋊Dic53—28no—
222C4⋊Dic53—48no—
223C4⋊Dic53—44no—
224#11719919—216no—
225C4×Dic53—44no—
226C23×C53C23×C411yescharacteristic
227C23×C53C22×D411yescharacteristic
228C23×C53C22×D411yescharacteristic
229C23×C53C22×D411yescharacteristic
230C23×C53C22×D411yescharacteristic
231C23×C53C22×Q811yescharacteristic
232C23×C53C22×Q811yescharacteristic
233C23×C53C2×#4111yescharacteristic
234C23×C53C2×#4111yescharacteristic
235C23×C53C2×#4111yescharacteristic
236C23×C53C2×#4111yescharacteristic
237C23×C53H(5,𝔽2)11yescharacteristic
238C23×C53H(5,𝔽2)11yescharacteristic
239C23×C532−1+411yescharacteristic
240C23×C532−1+411yescharacteristic
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53C2×C4⋊C414yes—
270C22×D53C4×D414yes—
271C22×D53C4×Q814yes—
272C22×D53#12114yes—
273C22×D53C22⋊Q814yes—
274C22×D53#12514yes—
275C22×D53C4⋊Q814yes—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53C2×C22⋊C418yes—
304C2×C4×C53C2×C22⋊C414yes—
305C2×C4×C53C2×C4⋊C414yes—
306C2×C4×C53#11714yes—
307C2×C4×C53#12114yes—
308C2×C4×C53#12114yes—
309C2×C4×C53C22⋊Q814yes—
310C2×C4×C53C22⋊Q814yes—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—24no—
318C2×Dic53—24no—
319C2×Dic53—24no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53C2×C4⋊C414yes—
346C4×D53—232no—
347C4×D53—432no—
348#13907—531nomaximal, Sylow
349C22×C53C22×C22⋊C411yescharacteristic
350C22×C53C22×C4⋊C411yescharacteristic
351C22×C53C2×#11711yescharacteristic
352C22×C53C2×C4×D411yescharacteristic
353C22×C53C2×C4×Q811yescharacteristic
354C22×C53#51811yescharacteristic
355C22×C53#51911yescharacteristic
356C22×C53C2×#12111yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×#12111yescharacteristic
359C22×C53C2×C22⋊Q811yescharacteristic
360C22×C53C2×C22⋊Q811yescharacteristic
361C22×C53C2×C22⋊Q811yescharacteristic
362C22×C53C2×#12511yescharacteristic
363C22×C53C2×C4⋊Q811yescharacteristic
364C22×C53#53711yescharacteristic
365C22×C53#53711yescharacteristic
366C22×C53#54411yescharacteristic
367C22×C53#54411yescharacteristic
368C22×C53D4211yescharacteristic
369C22×C53D4211yescharacteristic
370C22×C53#54611yescharacteristic
371C22×C53#54611yescharacteristic
372C22×C53#54711yescharacteristic
373C22×C53#54711yescharacteristic
374C22×C53#54811yescharacteristic
375C22×C53#54811yescharacteristic
376C22×C53D4×Q811yescharacteristic
377C22×C53D4×Q811yescharacteristic
378C22×C53#55211yescharacteristic
379C22×C53#55211yescharacteristic
380C22×C53#55311yescharacteristic
381C22×C53#55311yescharacteristic
382C22×C53#55411yescharacteristic
383C22×C53#55411yescharacteristic
384C2×D53—24no—
385C2×D53—24no—
386C2×D53—24no—
387C2×D53—24no—
388C2×D53—24no—
389C2×D53—24no—
390C2×D53—24no—
391C2×D53—24no—
392C2×D53—24no—
393C2×D53—24no—
394C2×D53—24no—
395C2×D53—24no—
396C2×D53—24no—
397C2×D53—24no—
398C2×D53#38918yescomplemented
399C4×C53—28no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53—82no—
403C4×C53#38018yescomplemented
404Dic53—24no—
405Dic53—44no—
406Dic53—42no—
407Dic53—42no—
408Dic53—82no—
409C23×C4⋊C4—531no—
410C2×#389—531no—
411C2×#389D5311yescharacteristic, complemented
412C2×#380—532no—
413C2×#380—531no—
414C2×C4×C22⋊C4—531no—
415#1441—532no—
416#1441—532no—
417C4⋊#95—531no—
418C4⋊#95—531no—
419C22⋊#95—532no—
420C2×C53C2×#38011yescharacteristic
421C2×C53C2×#38911yescharacteristic
422C2×C53#231611yescharacteristic
423C2×C53D4×C22⋊C411yescharacteristic
424C2×C53Q8×C22⋊C411yescharacteristic
425C2×C53#234411yescharacteristic
426C2×C53#234511yescharacteristic
427C2×C53#241611yescharacteristic
428C2×C53#241611yescharacteristic
429C2×C53#241711yescharacteristic
430C2×C53#241711yescharacteristic
431C2×C53#244011yescharacteristic
432C2×C53#244011yescharacteristic
433C2×C53#244211yescharacteristic
434C2×C53#244211yescharacteristic
435D53—28no—
436C24×C4—531no—
437C24×C4—532no—
438C22×C4⋊C4—532no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—538no—
441C22×C4⋊C4—531no—
442C22×C4⋊C4—532no—
443C22×C4⋊C4—1064no—
444C22×C4⋊C4—1064no—
445C22×C4⋊C4C2×D5311yescharacteristic
446C22×C4⋊C4C2×D5312yes—
447C22×C4⋊C4C2×D5311yescharacteristic
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—532no—
451C22×C42—531no—
452C22×C42C2×D5311yescharacteristic
453#389—24no—
454#389—1064no—
455#380—1068no—
456#380—1064no—
457C4×C22⋊C4—1064no—
458C2×#95—532no—
459C2×#95—532no—
460C2×#95—532no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—532no—
464C2×#95—532no—
465C2×#95—532no—
466C2×#95C2×D5312yes—
467C53#1390711yescharacteristic, complemented, Sylow
468C25—531no—
469C23×C4—531no—
470C23×C4—534no—
471C23×C4—534no—
472C23×C4—534no—
473C23×C4—531no—
474C23×C4—531no—
475C23×C4—532no—
476C23×C4—538no—
477C23×C4—532no—
478C23×C4—1064no—
479C23×C4—1064no—
480C23×C4—1062no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4—1062no—
484C23×C4—1064no—
485C23×C4—1064no—
486C23×C4—2122no—
487C23×C4—2122no—
488C23×C4C22×D5312yes—
489C23×C4C22×D5311yescharacteristic
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5312yes—
492C23×C4C22×D5311yescharacteristic
493C2×C4⋊C4—24no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—538no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—1062no—
505C2×C4⋊C4—10632no—
506C2×C4⋊C4—1064no—
507C2×C4⋊C4—1064no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1062no—
510C2×C4⋊C4—1062no—
511C2×C4⋊C4—2122no—
512C2×C4⋊C4C4×D5314yes—
513C2×C4⋊C4D21214yes—
514C2×C4⋊C4C22⋊D5314yes—
515C2×C22⋊C4—534no—
516C2×C22⋊C4—534no—
517C2×C22⋊C4—1062no—
518C2×C22⋊C4—1062no—
519C2×C22⋊C4—1062no—
520C2×C22⋊C4—1062no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—1064no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—1062no—
528C2×C42—1062no—
529C2×C42—1062no—
530#95—24no—
531#95—1062no—
532#95—1062no—
533#95—1064no—
534#95—1064no—
535#95—1064no—
536#95—1064no—
537#95—2122no—
538#95—2122no—
539C24—532no—
540C24—532no—
541C24—532no—
542C24—532no—
543C24—532no—
544C24—532no—
545C24—532no—
546C24—1061no—
547C24—1061no—
548C24—1061no—
549C24—1061no—
550C24—1061no—
551C24—1061no—
552C24—1061no—
553C24—1061no—
554C24C23×D5311yescharacteristic
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—532no—
581C22×C4—5316no—
582C22×C4—534no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—10616no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1068no—
591C22×C4—1068no—
592C22×C4—1068no—
593C22×C4—1068no—
594C22×C4—1068no—
595C22×C4—1068no—
596C22×C4—1062no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1062no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—10616no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—2128no—
623C22×C4—2128no—
624C22×C4—2128no—
625C22×C4—2128no—
626C22×C4—2128no—
627C22×C4C2×C4×D5314yes—
628C22×C4C2×C4×D5312yes—
629C22×C4C2×D21214yes—
630C22×C4C2×D21212yes—
631C22×C4D4×D5312yes—
632C22×C4D4×D5312yes—
633C22×C4#1171994712yes—
634C22×C4Q8×D5312yes—
635C22×C4Q8×D5312yes—
636C22×C4#1171994912yes—
637C22×C4C2×C22⋊D5314yes—
638C22×C4C2×C22⋊D5312yes—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—10616no—
642C4⋊C4—1068no—
643C4⋊C4—2128no—
644C4⋊C4—2124no—
645C4⋊C4#11719921116yescomplemented
646C22⋊C4—1068no—
647C22⋊C4—1068no—
648C22⋊C4—2128no—
649C42—44no—
650C42—2124no—
651C23—534no—
652C23—534no—
653C23—534no—
654C23—534no—
655C23—534no—
656C23—534no—
657C23—534no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—1062no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1062no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23—1062no—
681C23—1062no—
682C23—1062no—
683C23—1062no—
684C23—1062no—
685C23—1062no—
686C23C22×C4×D5311yescharacteristic
687C23C2×D4×D5311yescharacteristic
688C23C2×D4×D5311yescharacteristic
689C23C22×C22⋊D5311yescharacteristic
690C23C22×D21211yescharacteristic
691C23C2×Q8×D5311yescharacteristic
692C23C2×Q8×D5311yescharacteristic
693C23#41×D5311yescharacteristic
694C23#41×D5311yescharacteristic
695C23C2×#1171994711yescharacteristic
696C23C2×#1171994911yescharacteristic
697C23#1313326211yescharacteristic
698C23#1313326311yescharacteristic
699C23#1313326411yescharacteristic
700C23#1313326511yescharacteristic
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—534no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—10632no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1064no—
739C2×C4—1062no—
740C2×C4—1064no—
741C2×C4—1064no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—21232no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4—2121no—
754C2×C4—2122no—
755C2×C4—2121no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4—2122no—
765C2×C4C2×#1171992118yes—
766C2×C4C2×#1171992114yes—
767C2×C4C4⋊C4×D5314yes—
768C2×C4#1313317514yes—
769C2×C4#1313318814yes—
770C2×C4#1313319214yes—
771C2×C4#1313319314yes—
772C2×C4#1313319714yes—
773C22—538no—
774C22—1064no—
775C22—1064no—
776C22—1064no—
777C22—1064no—
778C22—1064no—
779C22—1064no—
780C22—1064no—
781C22—1064no—
782C22—1064no—
783C22—1064no—
784C22—1064no—
785C22—1064no—
786C22—1064no—
787C22—1064no—
788C22C22×#1171992111yescharacteristic
789C22C2×C4⋊C4×D5311yescharacteristic
790C22C2×#1313317511yescharacteristic
791C22C4×D4×D5311yescharacteristic
792C22C4×Q8×D5311yescharacteristic
793C22#1681109511yescharacteristic
794C22#1681109911yescharacteristic
795C22#121×D5311yescharacteristic
796C22C2×#1313318811yescharacteristic
797C22C2×#1313319211yescharacteristic
798C22C22⋊Q8×D5311yescharacteristic
799C22C2×#1313319311yescharacteristic
800C22C2×#1313319711yescharacteristic
801C22#125×D5311yescharacteristic
802C22C4⋊Q8×D5311yescharacteristic
803C22#1681120211yescharacteristic
804C22#1681120311yescharacteristic
805C22#1681125011yescharacteristic
806C22#1681125311yescharacteristic
807C22D4×C22⋊D5311yescharacteristic
808C22D4×D21211yescharacteristic
809C22#1681126111yescharacteristic
810C22#1681126811yescharacteristic
811C22#1681127311yescharacteristic
812C22#1681127611yescharacteristic
813C22#1681128011yescharacteristic
814C22#1681128511yescharacteristic
815C22Q8×C22⋊D5311yescharacteristic
816C22Q8×D21211yescharacteristic
817C22#1681130711yescharacteristic
818C22#1681131111yescharacteristic
819C22#1681132011yescharacteristic
820C22#1681132611yescharacteristic
821C22#1681133111yescharacteristic
822C22#1681133411yescharacteristic
823C4—28no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—1064no—
828C4—4242no—
829C4—2124no—
830C4—2122no—
831C4—2122no—
832C4#1681048018yescomplemented
833C2—1068no—
834C2C2×#1681048011yescharacteristic
835C2#389×D5311yescharacteristic
836C2#2027733011yescharacteristic
837C2D4×#1171992111yescharacteristic
838C2Q8×#1171992111yescharacteristic
839C2#2027758311yescharacteristic
840C2#2027759111yescharacteristic
841C2#2027815111yescharacteristic
842C2#2027815311yescharacteristic
843C2#2027816211yescharacteristic
844C2#2027816411yescharacteristic
845C2#2027841311yescharacteristic
846C2#2027841511yescharacteristic
847C2#2027843511yescharacteristic
848C2#2027843711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53#13907
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
6. #20272969C2semidirect
7. #20272965C2semidirect
8. #20272945C2semidirect
9. #20272944C2semidirect
11. C2×C53×#389C2semidirect
20. C2×C4⋊C4×D53C4semidirect
213. C2×C4×D53C4⋊C4semidirect
216. C4⋊C4×C53C22⋊C4semidirect
398. C2×D53#389semidirect
403. C4×C53#380semidirect
411. C2×#389D53semidirect
467. C53#13907semidirect
645. C4⋊C4#11719921semidirect
832. C4#16810480semidirect

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×#168105222
C2×#168104802
C2×C4×#117199212
#202729692
#202729652
#202729452
#202729442
#202729362
C2×C53×#3892
#1390753