Finite Group Databasebeta

← #27320722

Subgroups — #27320722

Order 13568.

1454 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810556C212yesmaximal
2C2×#16810521C211yesmaximal, characteristic
3C2×#16810521C211yesmaximal, characteristic
4C2×#16810493C211yesmaximal, characteristic
5#20272969C212yesmaximal
6#20272968C212yesmaximal
7#20272967C212yesmaximal
8#20272945C211yesmaximal, characteristic
9#20272945C211yesmaximal, characteristic
10#20272945C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×C4⋊Dic53C2212yes—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×#11719919C2212yes—
20#16810556—28no—
21#16810521—24no—
22#16810521—24no—
23#16810493—24no—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C22×C4⋊C4×C53C2211yescharacteristic
33C22×C4⋊C4×C53C2211yescharacteristic
34C22×C42×C53C2211yescharacteristic
35C22×C42×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C4×C4⋊C4×C53—24no—
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2211yescharacteristic
40C23×Dic53C2312yes—
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C2×C4⋊Dic53—22no—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—24no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—24no—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—24no—
57C2×C4⋊Dic53—24no—
58C2×C4⋊Dic53—42no—
59C2×C4⋊Dic53—42no—
60C2×C4⋊Dic53D414yes—
61C2×C4⋊Dic53Q814yes—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—42no—
68#13133124—24no—
69#13133124—24no—
70#13133124—24no—
71#13133124—24no—
72#13133124—24no—
73#13133124—42no—
74#13133124—42no—
75#13133124—42no—
76C23×C4×C53C2311yescharacteristic
77C23×C4×C53C2311yescharacteristic
78C23×C4×C53C2311yescharacteristic
79C23×C4×C53C2311yescharacteristic
80C23×C4×C53C2311yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C2×C4⋊C4×C53—22no—
84C2×C4⋊C4×C53—22no—
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—22no—
87C2×C4⋊C4×C53D414yes—
88C2×C4⋊C4×C53Q814yes—
89C2×C42×C53—22no—
90C2×C42×C53—22no—
91C2×C42×C53—22no—
92C2×C42×C53—22no—
93C2×C42×C53—22no—
94C2×C42×C53—22no—
95C2×C42×C53—22no—
96C2×C42×C53D414yes—
97C2×C42×C53Q814yes—
98#95×C53—22no—
99#95×C53—22no—
100C24×C53C2411yescharacteristic
101C22×C4×C53—21no—
102C22×C4×C53—21no—
103C22×C4×C53—21no—
104C22×C4×C53—21no—
105C22×C4×C53—21no—
106C22×C4×C53—21no—
107C22×C4×C53—21no—
108C22×C4×C53—21no—
109C22×C4×C53—21no—
110C22×C4×C53—21no—
111C22×C4×C53—21no—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—21no—
115C22×C4×C53—21no—
116C22×C4×C53—21no—
117C22×C4×C53—21no—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53C2×D412yes—
132C22×C4×C53C2×D412yes—
133C22×C4×C53C2×D412yes—
134C22×C4×C53C2×D412yes—
135C22×C4×C53C2×D412yes—
136C22×C4×C53C2×D412yes—
137C22×C4×C53C2×D412yes—
138C22×C4×C53C2×Q812yes—
139C22×C4×C53C2×Q812yes—
140C22×C4×C53C2×Q812yes—
141C22×C4×C53C2×Q812yes—
142C22×C4×C53C2×Q812yes—
143C22×C4×C53C2×Q812yes—
144C22×C4×C53C2×Q812yes—
145C22×C4×C53#4112yes—
146C22×C4×C53#4112yes—
147C22×C4×C53#4112yes—
148C22×C4×C53#4112yes—
149C22×C4×C53#4112yes—
150C22×Dic53—22no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53C2×D414yes—
177C22×Dic53C2×Q814yes—
178C4⋊C4×C53—28no—
179C4⋊C4×C53—28no—
180C42×C53—28no—
181C42×C53—28no—
182C42×C53—44no—
183C4⋊Dic53—28no—
184C4⋊Dic53—28no—
185C4⋊Dic53—48no—
186C4⋊Dic53—48no—
187C4⋊Dic53—44no—
188C4⋊Dic53—44no—
189#11719919—48no—
190#11719919—48no—
191C23×C53C22×D411yescharacteristic
192C23×C53C22×D411yescharacteristic
193C23×C53C22×D411yescharacteristic
194C23×C53C22×Q811yescharacteristic
195C23×C53C22×Q811yescharacteristic
196C23×C53C22×Q811yescharacteristic
197C23×C53C2×#4111yescharacteristic
198C23×C53C2×#4111yescharacteristic
199C23×C53C2×#4111yescharacteristic
200C23×C53C2×#4111yescharacteristic
201C23×C53C2×#4111yescharacteristic
202C23×C53H(5,𝔽2)11yescharacteristic
203C23×C53H(5,𝔽2)11yescharacteristic
204C23×C532−1+411yescharacteristic
205C23×C532−1+411yescharacteristic
206C2×C4×C53—22no—
207C2×C4×C53—22no—
208C2×C4×C53—22no—
209C2×C4×C53—22no—
210C2×C4×C53—22no—
211C2×C4×C53—22no—
212C2×C4×C53—22no—
213C2×C4×C53—22no—
214C2×C4×C53—22no—
215C2×C4×C53—22no—
216C2×C4×C53—22no—
217C2×C4×C53—22no—
218C2×C4×C53—22no—
219C2×C4×C53—22no—
220C2×C4×C53—22no—
221C2×C4×C53—22no—
222C2×C4×C53—22no—
223C2×C4×C53—22no—
224C2×C4×C53—22no—
225C2×C4×C53—22no—
226C2×C4×C53—22no—
227C2×C4×C53—22no—
228C2×C4×C53—22no—
229C2×C4×C53—22no—
230C2×C4×C53—22no—
231C2×C4×C53—22no—
232C2×C4×C53—22no—
233C2×C4×C53—41no—
234C2×C4×C53—41no—
235C2×C4×C53—41no—
236C2×C4×C53—41no—
237C2×C4×C53—41no—
238C2×C4×C53—41no—
239C2×C4×C53—41no—
240C2×C4×C53—41no—
241C2×C4×C53—41no—
242C2×C4×C53—41no—
243C2×C4×C53—41no—
244C2×C4×C53—41no—
245C2×C4×C53#12114yes—
246C2×C4×C53#12114yes—
247C2×C4×C53C22⋊Q814yes—
248C2×C4×C53C22⋊Q814yes—
249C2×C4×C53C22⋊Q814yes—
250C2×C4×C53#12314yes—
251C2×C4×C53#12514yes—
252C2×C4×C53#12514yes—
253C2×C4×C53C4⋊Q814yes—
254C2×C4×C53C4⋊Q814yes—
255C2×Dic53—24no—
256C2×Dic53—24no—
257C2×Dic53—24no—
258C2×Dic53—24no—
259C2×Dic53—24no—
260C2×Dic53—24no—
261C2×Dic53—42no—
262C2×Dic53—42no—
263C2×Dic53—42no—
264C2×Dic53—42no—
265C2×Dic53—42no—
266C2×Dic53—42no—
267C2×Dic53—42no—
268C2×Dic53—42no—
269C2×Dic53—42no—
270C2×Dic53—42no—
271C2×Dic53—42no—
272C2×Dic53—42no—
273C2×Dic53—42no—
274C2×Dic53—42no—
275C2×Dic53—42no—
276C2×Dic53—42no—
277C2×Dic53—42no—
278C2×Dic53—42no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283#15133—531nomaximal, Sylow
284C22×C53C2×#12111yescharacteristic
285C22×C53C2×#12111yescharacteristic
286C22×C53C2×C22⋊Q811yescharacteristic
287C22×C53C2×C22⋊Q811yescharacteristic
288C22×C53C2×C22⋊Q811yescharacteristic
289C22×C53C2×#12311yescharacteristic
290C22×C53C2×#12511yescharacteristic
291C22×C53C2×#12511yescharacteristic
292C22×C53C2×C4⋊Q811yescharacteristic
293C22×C53C2×C4⋊Q811yescharacteristic
294C22×C53#53211yescharacteristic
295C22×C53#53311yescharacteristic
296C22×C53#53311yescharacteristic
297C22×C53#53711yescharacteristic
298C22×C53#53711yescharacteristic
299C22×C53#54011yescharacteristic
300C22×C53#54111yescharacteristic
301C22×C53#54411yescharacteristic
302C22×C53#54411yescharacteristic
303C22×C53D4211yescharacteristic
304C22×C53#54611yescharacteristic
305C22×C53#54711yescharacteristic
306C22×C53#54811yescharacteristic
307C22×C53D4×Q811yescharacteristic
308C22×C53D4×Q811yescharacteristic
309C22×C53#55011yescharacteristic
310C22×C53#55211yescharacteristic
311C22×C53#55311yescharacteristic
312C22×C53#55411yescharacteristic
313C22×C53#55411yescharacteristic
314C22×C53#55611yescharacteristic
315C22×C53#55711yescharacteristic
316C22×C53#55711yescharacteristic
317C22×C53Q8211yescharacteristic
318C22×C53#55911yescharacteristic
319C4×C53—24no—
320C4×C53—24no—
321C4×C53—24no—
322C4×C53—42no—
323C4×C53—42no—
324C4×C53—42no—
325C4×C53#39818yescomplemented
326Dic53—44no—
327Dic53—44no—
328Dic53—82no—
329Dic53—82no—
330C2×#398—532no—
331C2×#389—531no—
332C2×#389—531no—
333C2×#384—531no—
334C2×C4×C4⋊C4D5311yescharacteristic
335#1441—532no—
336#1441—532no—
337#1441—532no—
338C4⋊#95—531no—
339C4⋊#95—531no—
340C4⋊#95—531no—
341C2×C53C2×#39811yescharacteristic
342C2×C53#241611yescharacteristic
343C2×C53#241711yescharacteristic
344C2×C53#244511yescharacteristic
345C2×C53#244611yescharacteristic
346C2×C53#250611yescharacteristic
347C2×C53#250711yescharacteristic
348C2×C53#253811yescharacteristic
349C2×C53#255011yescharacteristic
350C2×C53#255111yescharacteristic
351C2×C53#255211yescharacteristic
352C2×C53#257011yescharacteristic
353C2×C53#258211yescharacteristic
354C2×C53#262911yescharacteristic
355C2×C53#285711yescharacteristic
356C22×C4⋊C4—531no—
357C22×C4⋊C4—531no—
358C22×C4⋊C4—532no—
359C22×C4⋊C4—531no—
360C22×C4⋊C4—531no—
361C22×C4⋊C4—532no—
362C22×C4⋊C4—532no—
363C22×C4⋊C4—532no—
364C22×C4⋊C4C2×D5311yescharacteristic
365C22×C4⋊C4C2×D5311yescharacteristic
366C22×C42C2×D5311yescharacteristic
367C22×C42C2×D5311yescharacteristic
368C22×C42C2×D5311yescharacteristic
369#398—1068no—
370#389—1064no—
371#389—1064no—
372#384—1064no—
373C4×C4⋊C4—24no—
374C2×#95—532no—
375C2×#95—532no—
376C2×#95—532no—
377C2×#95—532no—
378C2×#95—532no—
379C2×#95—532no—
380C2×#95—532no—
381C2×#95—532no—
382C2×#95C2×D5311yescharacteristic
383C2×#95C2×D5311yescharacteristic
384C53#1513311yescharacteristic, complemented, Sylow
385C23×C4—532no—
386C23×C4—532no—
387C23×C4—532no—
388C23×C4—532no—
389C23×C4C22×D5311yescharacteristic
390C23×C4C22×D5311yescharacteristic
391C23×C4C22×D5311yescharacteristic
392C23×C4C22×D5311yescharacteristic
393C23×C4C22×D5311yescharacteristic
394C23×C4C22×D5311yescharacteristic
395C23×C4C22×D5311yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—534no—
401C2×C4⋊C4—534no—
402C2×C4⋊C4—1062no—
403C2×C4⋊C4—1062no—
404C2×C4⋊C4—1062no—
405C2×C4⋊C4—1062no—
406C2×C4⋊C4—1064no—
407C2×C4⋊C4—1064no—
408C2×C4⋊C4—1064no—
409C2×C4⋊C4—1064no—
410C2×C4⋊C4—1064no—
411C2×C4⋊C4—1064no—
412C2×C4⋊C4—1064no—
413C2×C4⋊C4—1064no—
414C2×C4⋊C4—1062no—
415C2×C4⋊C4—1062no—
416C2×C4⋊C4—1062no—
417C2×C4⋊C4—1062no—
418C2×C4⋊C4—1062no—
419C2×C4⋊C4—1064no—
420C2×C4⋊C4—1062no—
421C2×C4⋊C4—2122no—
422C2×C4⋊C4—2122no—
423C2×C4⋊C4—2122no—
424C2×C4⋊C4Dic10614yes—
425C2×C4⋊C4D21214yes—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42Dic10614yes—
434C2×C42C22⋊D5314yes—
435#95—22no—
436#95—22no—
437#95—1064no—
438#95—1064no—
439#95—1064no—
440#95—1064no—
441#95—1064no—
442#95—2122no—
443#95—2122no—
444#95—2122no—
445C24C23×D5311yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—534no—
477C22×C4—534no—
478C22×C4—1062no—
479C22×C4—1062no—
480C22×C4—1062no—
481C22×C4—1062no—
482C22×C4—1062no—
483C22×C4—1062no—
484C22×C4—1062no—
485C22×C4—1062no—
486C22×C4—1062no—
487C22×C4—1062no—
488C22×C4—1062no—
489C22×C4—1062no—
490C22×C4—1062no—
491C22×C4—1062no—
492C22×C4—1062no—
493C22×C4—1062no—
494C22×C4—1062no—
495C22×C4—1062no—
496C22×C4—1062no—
497C22×C4—1062no—
498C22×C4—1062no—
499C22×C4—1062no—
500C22×C4—1062no—
501C22×C4—1062no—
502C22×C4—1062no—
503C22×C4—1062no—
504C22×C4C2×Dic10612yes—
505C22×C4C2×Dic10612yes—
506C22×C4C2×Dic10612yes—
507C22×C4C2×Dic10612yes—
508C22×C4C2×Dic10612yes—
509C22×C4C2×Dic10612yes—
510C22×C4C2×D21212yes—
511C22×C4C2×D21212yes—
512C22×C4C2×D21212yes—
513C22×C4#1171994512yes—
514C22×C4#1171994512yes—
515C22×C4#1171994512yes—
516C22×C4D4×D5312yes—
517C22×C4#1171994712yes—
518C22×C4Q8×D5312yes—
519C22×C4#1171994912yes—
520C22×C4C2×C22⋊D5312yes—
521C22×C4C2×C22⋊D5312yes—
522C22×C4C2×C22⋊D5312yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—1068no—
526C4⋊C4—1068no—
527C4⋊C4—2128no—
528C4⋊C4—2128no—
529C4⋊C4—2128no—
530C4⋊C4—2124no—
531C4⋊C4—2128no—
532C4⋊C4—2124no—
533C42—28no—
534C42—28no—
535C42—44no—
536C23C2×D4×D5311yescharacteristic
537C23C22×C22⋊D5311yescharacteristic
538C23C22×D21211yescharacteristic
539C23C2×Q8×D5311yescharacteristic
540C23C22×Dic10611yescharacteristic
541C23C22×Dic10611yescharacteristic
542C23C2×#1171994711yescharacteristic
543C23C2×#1171994511yescharacteristic
544C23C2×#1171994511yescharacteristic
545C23C2×#1171994511yescharacteristic
546C23C2×#1171994911yescharacteristic
547C23#1313326311yescharacteristic
548C23#1313326311yescharacteristic
549C23#1313326411yescharacteristic
550C23#1313326411yescharacteristic
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—1064no—
591C2×C4—1064no—
592C2×C4—1064no—
593C2×C4—1064no—
594C2×C4—1064no—
595C2×C4—1064no—
596C2×C4—2122no—
597C2×C4—2122no—
598C2×C4—2122no—
599C2×C4—2122no—
600C2×C4—2122no—
601C2×C4—2122no—
602C2×C4—2122no—
603C2×C4—2122no—
604C2×C4—2122no—
605C2×C4—2122no—
606C2×C4—2122no—
607C2×C4—2122no—
608C2×C4—2122no—
609C2×C4—2122no—
610C2×C4—2122no—
611C2×C4—2122no—
612C2×C4—2122no—
613C2×C4—2122no—
614C2×C4—2122no—
615C2×C4—2122no—
616C2×C4—2122no—
617C2×C4—2122no—
618C2×C4#1313318914yes—
619C2×C4#1313319114yes—
620C2×C4#1313319314yes—
621C2×C4#1313319614yes—
622C2×C4#1313319614yes—
623C2×C4#1313320214yes—
624C2×C4#1313320714yes—
625C2×C4#1313320814yes—
626C2×C4#1313321614yes—
627C2×C4#1313321714yes—
628C22C2×#1313318911yescharacteristic
629C22C2×#1313319111yescharacteristic
630C22C2×#1313319311yescharacteristic
631C22C2×#1313319611yescharacteristic
632C22C2×#1313319611yescharacteristic
633C22C2×#1313320211yescharacteristic
634C22C2×#1313320711yescharacteristic
635C22C2×#1313320811yescharacteristic
636C22C2×#1313321611yescharacteristic
637C22C2×#1313321711yescharacteristic
638C22#1681117311yescharacteristic
639C22#1681118011yescharacteristic
640C22#1681118011yescharacteristic
641C22#1681120111yescharacteristic
642C22#1681120111yescharacteristic
643C22#1681122811yescharacteristic
644C22#1681123511yescharacteristic
645C22#1681125111yescharacteristic
646C22#1681125111yescharacteristic
647C22D4×D21211yescharacteristic
648C22#1681126911yescharacteristic
649C22#1681127711yescharacteristic
650C22#1681128211yescharacteristic
651C22D4×Dic10611yescharacteristic
652C22Q8×D21211yescharacteristic
653C22#1681129511yescharacteristic
654C22#1681131311yescharacteristic
655C22#1681131911yescharacteristic
656C22#1681133011yescharacteristic
657C22#1681133311yescharacteristic
658C22#1681134611yescharacteristic
659C22#1681135111yescharacteristic
660C22#1681135211yescharacteristic
661C22Q8×Dic10611yescharacteristic
662C22#1681135811yescharacteristic
663C4—24no—
664C4—24no—
665C4—24no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—4242no—
670C4—4242no—
671C4—2124no—
672C4—2124no—
673C4#1681055618yescomplemented
674C2C2×#1681055611yescharacteristic
675C2#2027815511yescharacteristic
676C2#2027816611yescharacteristic
677C2#2027848011yescharacteristic
678C2#2027849111yescharacteristic
679C2#2027923111yescharacteristic
680C2#2027924211yescharacteristic
681C2#2027963311yescharacteristic
682C2#2027973611yescharacteristic
683C2#2027974111yescharacteristic
684C2#2027974611yescharacteristic
685C2#2027994911yescharacteristic
686C2#2028008511yescharacteristic
687C2#2028054511yescharacteristic
688C2#2028306711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, prime radical, cosocleC24×C53C24
FittingC2×C4×C4⋊C4×C53C2
hypercenterC2×C4×C4⋊C4D53
hypocenterC53#15133
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
325. C4×C53#398semidirect
384. C53#15133semidirect
673. C4#16810556semidirect

Maximal subgroups

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

subgroupindex
C2×#168105562
C2×#168105212
C2×#168104932
#202729692
#202729682
#202729672
#202729452
C2×C4×C4⋊C4×C532
#1513353