Finite Group Databasebeta

← #27307820

Subgroups — #27307820

Order 13568.

1530 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×#16810522C211yesmaximal, characteristic
2C2×#16810522C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic
4C2×C4×C4⋊Dic53C211yesmaximal, characteristic
5#20272980C212yesmaximal
6#20272968C212yesmaximal
7#20272949C212yesmaximal
8#20272945C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10#20272944C212yesmaximal
11C2×C53×#389C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2212yes—
15C22×C4⋊Dic53C2211yescharacteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2212yes—
18C22×C4×Dic53C2211yescharacteristic
19C22×C4×Dic53C2212yes—
20C22×C4×Dic53C2211yescharacteristic
21#16810522—24no—
22#16810522—24no—
23C4⋊C4×Dic53—24no—
24C4×C4⋊Dic53—24no—
25C2×#13133124C2211yescharacteristic
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C22×C4⋊C4×C53C2211yescharacteristic
35C22×C4⋊C4×C53C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C53×#389C418yescomplemented
39C2×#95×C53C2212yes—
40C23×Dic53C2312yes—
41C23×Dic53C2311yescharacteristic
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2312yes—
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
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—22no—
53C2×C4⋊Dic53—22no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—24no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—24no—
59C2×C4⋊Dic53—42no—
60C2×C4⋊Dic53—42no—
61C2×C4⋊Dic53—42no—
62C2×C4⋊Dic53Q814yes—
63C2×C4⋊Dic53Q814yes—
64C2×C4×Dic53—22no—
65C2×C4×Dic53—22no—
66C2×C4×Dic53—22no—
67C2×C4×Dic53—24no—
68C2×C4×Dic53—22no—
69C2×C4×Dic53—22no—
70C2×C4×Dic53—24no—
71C2×C4×Dic53—42no—
72C2×C4×Dic53D414yes—
73#13133124—24no—
74#13133124—24no—
75#13133124—24no—
76#13133124—24no—
77#13133124—22no—
78#13133124—22no—
79#13133124—42no—
80#13133124—42no—
81#13133124—42no—
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2312yes—
84C23×C4×C53C2312yes—
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C2×C4⋊C4×C53—22no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53—42no—
90C2×C4⋊C4×C53—42no—
91C2×C4⋊C4×C53C2×C414yes—
92C2×C4⋊C4×C53C2×C418yes—
93C2×C4⋊C4×C53C2×C414yes—
94C2×C4⋊C4×C53D414yes—
95C2×C4⋊C4×C53Q814yes—
96C2×C42×C53—22no—
97C2×C42×C53—22no—
98C2×C42×C53C2×C414yes—
99#95×C53C2×C418yes—
100C24×C53C2411yescharacteristic
101C22×C4×C53—21no—
102C22×C4×C53—21no—
103C22×C4×C53—22no—
104C22×C4×C53—21no—
105C22×C4×C53—21no—
106C22×C4×C53—22no—
107C22×C4×C53—22no—
108C22×C4×C53—22no—
109C22×C4×C53—21no—
110C22×C4×C53—22no—
111C22×C4×C53—21no—
112C22×C4×C53—22no—
113C22×C4×C53—21no—
114C22×C4×C53—21no—
115C22×C4×C53—22no—
116C22×C4×C53—22no—
117C22×C4×C53—21no—
118C22×C4×C53—22no—
119C22×C4×C53—21no—
120C22×C4×C53—22no—
121C22×C4×C53C22×C414yes—
122C22×C4×C53C22×C412yes—
123C22×C4×C53C22×C414yes—
124C22×C4×C53C22×C412yes—
125C22×C4×C53C22×C412yes—
126C22×C4×C53C2×D414yes—
127C22×C4×C53C2×D412yes—
128C22×C4×C53C2×D412yes—
129C22×C4×C53C2×Q814yes—
130C22×C4×C53C2×Q812yes—
131C22×C4×C53C2×Q812yes—
132C22×C4×C53C2×Q812yes—
133C22×C4×C53#4112yes—
134C22×C4×C53#4112yes—
135C22×C4×C53#4112yes—
136C22×Dic53—21no—
137C22×Dic53—21no—
138C22×Dic53—21no—
139C22×Dic53—21no—
140C22×Dic53—21no—
141C22×Dic53—21no—
142C22×Dic53—21no—
143C22×Dic53—22no—
144C22×Dic53—21no—
145C22×Dic53—21no—
146C22×Dic53—22no—
147C22×Dic53—21no—
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—22no—
151C22×Dic53—22no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53C2×D412yes—
172C22×Dic53C2×D412yes—
173C22×Dic53C2×Q812yes—
174C22×Dic53C2×Q814yes—
175C22×Dic53C2×Q812yes—
176C22×Dic53#4112yes—
177C22×Dic53#4112yes—
178C4⋊C4×C53—28no—
179C4⋊C4×C53—48no—
180C4⋊C4×C53C4⋊C4116yescomplemented
181C42×C53—28no—
182C4⋊Dic53—28no—
183C4⋊Dic53—28no—
184C4⋊Dic53—28no—
185C4⋊Dic53—48no—
186C4⋊Dic53—48no—
187C4⋊Dic53—44no—
188C4×Dic53—28no—
189C4×Dic53—48no—
190C4×Dic53—44no—
191C23×C53C23×C411yescharacteristic
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×C53H(5,𝔽2)11yescharacteristic
205C23×C532−1+411yescharacteristic
206C2×C4×C53—22no—
207C2×C4×C53—24no—
208C2×C4×C53—22no—
209C2×C4×C53—24no—
210C2×C4×C53—22no—
211C2×C4×C53—22no—
212C2×C4×C53—22no—
213C2×C4×C53—22no—
214C2×C4×C53—24no—
215C2×C4×C53—24no—
216C2×C4×C53—24no—
217C2×C4×C53—24no—
218C2×C4×C53—22no—
219C2×C4×C53—24no—
220C2×C4×C53—24no—
221C2×C4×C53—22no—
222C2×C4×C53—22no—
223C2×C4×C53—24no—
224C2×C4×C53—41no—
225C2×C4×C53—42no—
226C2×C4×C53—41no—
227C2×C4×C53—42no—
228C2×C4×C53—41no—
229C2×C4×C53—42no—
230C2×C4×C53—41no—
231C2×C4×C53—42no—
232C2×C4×C53C2×C4⋊C418yes—
233C2×C4×C53C2×C4⋊C414yes—
234C2×C4×C53C4×D414yes—
235C2×C4×C53C4×Q814yes—
236C2×C4×C53C4×Q814yes—
237C2×C4×C53#12114yes—
238C2×C4×C53C22⋊Q814yes—
239C2×C4×C53#12514yes—
240C2×C4×C53C4⋊Q814yes—
241C2×Dic53—22no—
242C2×Dic53—22no—
243C2×Dic53—22no—
244C2×Dic53—22no—
245C2×Dic53—22no—
246C2×Dic53—22no—
247C2×Dic53—22no—
248C2×Dic53—22no—
249C2×Dic53—24no—
250C2×Dic53—22no—
251C2×Dic53—22no—
252C2×Dic53—22no—
253C2×Dic53—22no—
254C2×Dic53—22no—
255C2×Dic53—22no—
256C2×Dic53—24no—
257C2×Dic53—22no—
258C2×Dic53—24no—
259C2×Dic53—41no—
260C2×Dic53—41no—
261C2×Dic53—42no—
262C2×Dic53—41no—
263C2×Dic53—41no—
264C2×Dic53—42no—
265C2×Dic53—41no—
266C2×Dic53—41no—
267C2×Dic53—42no—
268C2×Dic53—41no—
269C2×Dic53—41no—
270C2×Dic53—42no—
271C2×Dic53—41no—
272C2×Dic53—41no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—42no—
276C2×Dic53—42no—
277C2×Dic53—42no—
278C2×Dic53—42no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53C22⋊Q814yes—
283#14045—531nomaximal, Sylow
284C22×C53C22×C4⋊C411yescharacteristic
285C22×C53C2×C4×D411yescharacteristic
286C22×C53C2×C4×Q811yescharacteristic
287C22×C53C2×C4×Q811yescharacteristic
288C22×C53C4×#4111yescharacteristic
289C22×C53#51811yescharacteristic
290C22×C53#52011yescharacteristic
291C22×C53C2×#12111yescharacteristic
292C22×C53C2×C22⋊Q811yescharacteristic
293C22×C53C2×C22⋊Q811yescharacteristic
294C22×C53#52511yescharacteristic
295C22×C53C2×#12511yescharacteristic
296C22×C53#52911yescharacteristic
297C22×C53C2×C4⋊Q811yescharacteristic
298C22×C53#53311yescharacteristic
299C22×C53#53511yescharacteristic
300C22×C53#53711yescharacteristic
301C22×C53#54011yescharacteristic
302C22×C53#54211yescharacteristic
303C22×C53#54611yescharacteristic
304C22×C53#54611yescharacteristic
305C22×C53D4×Q811yescharacteristic
306C22×C53#55011yescharacteristic
307C22×C53#55211yescharacteristic
308C22×C53#55311yescharacteristic
309C22×C53#55411yescharacteristic
310C22×C53#55411yescharacteristic
311C22×C53#55411yescharacteristic
312C22×C53#55411yescharacteristic
313C22×C53#55411yescharacteristic
314C22×C53#55511yescharacteristic
315C22×C53#55711yescharacteristic
316C22×C53#55711yescharacteristic
317C22×C53Q8211yescharacteristic
318C22×C53Q8211yescharacteristic
319C4×C53—28no—
320C4×C53—24no—
321C4×C53—42no—
322C4×C53—44no—
323C4×C53#38918yes—
324Dic53—24no—
325Dic53—42no—
326Dic53—42no—
327Dic53—42no—
328Dic53—44no—
329Dic53—82no—
330C2×#389—531no—
331C2×#389—531no—
332C2×#389D5311yescharacteristic
333C2×C4×C4⋊C4—531no—
334C2×C4×C4⋊C4—531no—
335#1444—532no—
336#1441—532no—
337#1436—532no—
338C4⋊#95—531no—
339C4⋊#95—531no—
340C4⋊#95—532no—
341C2×C53C2×#38911yescharacteristic
342C2×C53C4×C22⋊Q811yescharacteristic
343C2×C53#232411yescharacteristic
344C2×C53#234911yescharacteristic
345C2×C53Q8×C4⋊C411yescharacteristic
346C2×C53#236911yescharacteristic
347C2×C53#237011yescharacteristic
348C2×C53#241411yescharacteristic
349C2×C53#241711yescharacteristic
350C2×C53#245111yescharacteristic
351C2×C53#245411yescharacteristic
352C2×C53#250711yescharacteristic
353C2×C53#250811yescharacteristic
354C2×C53#256711yescharacteristic
355C2×C53#258411yescharacteristic
356C22×C4⋊C4—531no—
357C22×C4⋊C4—531no—
358C22×C4⋊C4—531no—
359C22×C4⋊C4—531no—
360C22×C4⋊C4—532no—
361C22×C4⋊C4—532no—
362C22×C4⋊C4C2×D5311yescharacteristic
363C22×C4⋊C4C2×D5312yes—
364C22×C4⋊C4C2×D5311yescharacteristic
365C22×C42—531no—
366C22×C42—531no—
367C22×C42—532no—
368C22×C42C2×D5311yescharacteristic
369#389—1064no—
370#389—1064no—
371#389Dic5318yescomplemented
372C4×C4⋊C4—1064no—
373C4×C4⋊C4—1064no—
374C2×#95—531no—
375C2×#95—532no—
376C2×#95—532no—
377C2×#95—532no—
378C2×#95—531no—
379C2×#95—532no—
380C2×#95—532no—
381C2×#95—532no—
382C2×#95—532no—
383C2×#95C2×D5312yes—
384C53#1404511yescharacteristic, complemented, Sylow
385C23×C4—531no—
386C23×C4—531no—
387C23×C4—531no—
388C23×C4—531no—
389C23×C4—532no—
390C23×C4—532no—
391C23×C4C22×D5312yes—
392C23×C4C22×D5311yescharacteristic
393C23×C4C22×D5312yes—
394C23×C4C22×D5311yescharacteristic
395C23×C4C22×D5311yescharacteristic
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4—42no—
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—1062no—
407C2×C4⋊C4—1062no—
408C2×C4⋊C4—1062no—
409C2×C4⋊C4—1064no—
410C2×C4⋊C4—1064no—
411C2×C4⋊C4—1064no—
412C2×C4⋊C4—1062no—
413C2×C4⋊C4—1062no—
414C2×C4⋊C4—1062no—
415C2×C4⋊C4—2122no—
416C2×C4⋊C4—2122no—
417C2×C4⋊C4—2122no—
418C2×C4⋊C4Dic10614yes—
419C2×C4⋊C4D21214yes—
420C2×C4⋊C4C2×Dic5314yes—
421C2×C4⋊C4C2×Dic5318yes—
422C2×C4⋊C4C2×Dic5314yes—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—534no—
426C2×C42—1062no—
427C2×C42—1062no—
428C2×C42—1064no—
429C2×C42—1064no—
430C2×C42—1062no—
431C2×C42—1062no—
432C2×C42—1062no—
433C2×C42—2122no—
434C2×C42C2×Dic5314yes—
435#95—1062no—
436#95—1062no—
437#95—1064no—
438#95—1064no—
439#95—1064no—
440#95—1064no—
441#95—2122no—
442#95—2122no—
443#95—2122no—
444#95C2×Dic5318yes—
445C24C23×D5311yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—532no—
467C22×C4—532no—
468C22×C4—532no—
469C22×C4—532no—
470C22×C4—532no—
471C22×C4—534no—
472C22×C4—532no—
473C22×C4—1061no—
474C22×C4—1061no—
475C22×C4—1061no—
476C22×C4—1061no—
477C22×C4—1061no—
478C22×C4—1061no—
479C22×C4—1061no—
480C22×C4—1061no—
481C22×C4—1062no—
482C22×C4—1061no—
483C22×C4—1062no—
484C22×C4—1061no—
485C22×C4—1061no—
486C22×C4—1062no—
487C22×C4—1062no—
488C22×C4—1061no—
489C22×C4—1061no—
490C22×C4—1061no—
491C22×C4—1061no—
492C22×C4—1061no—
493C22×C4—1061no—
494C22×C4—1062no—
495C22×C4—1061no—
496C22×C4—1061no—
497C22×C4—1061no—
498C22×C4—1062no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1062no—
502C22×C4—1062no—
503C22×C4—1062no—
504C22×C4—1062no—
505C22×C4—1062no—
506C22×C4—1062no—
507C22×C4—1062no—
508C22×C4C2×Dic10614yes—
509C22×C4C2×Dic10612yes—
510C22×C4C2×D21214yes—
511C22×C4C2×D21212yes—
512C22×C4D4×D5312yes—
513C22×C4#1171994712yes—
514C22×C4Q8×D5312yes—
515C22×C4Q8×D5312yes—
516C22×C4#1171994912yes—
517C22×C4#1171994912yes—
518C22×C4C22×Dic5314yes—
519C22×C4C22×Dic5312yes—
520C22×C4C22×Dic5314yes—
521C22×C4C22×Dic5312yes—
522C22×C4C22×Dic5312yes—
523C4⋊C4—28no—
524C4⋊C4—48no—
525C4⋊C4—1068no—
526C4⋊C4—1068no—
527C4⋊C4—1068no—
528C4⋊C4—2128no—
529C4⋊C4—2128no—
530C4⋊C4—2124no—
531C4⋊C4C4⋊Dic53116yescomplemented
532C42—28no—
533C42—1068no—
534C42—2128no—
535C42—2124no—
536C23C23×Dic5311yescharacteristic
537C23C2×D4×D5311yescharacteristic
538C23C22×D21211yescharacteristic
539C23C2×Q8×D5311yescharacteristic
540C23C2×Q8×D5311yescharacteristic
541C23C22×Dic10611yescharacteristic
542C23#41×D5311yescharacteristic
543C23#41×D5311yescharacteristic
544C23C2×#1171994711yescharacteristic
545C23C2×#1171994911yescharacteristic
546C23C2×#1171994911yescharacteristic
547C23#1313326211yescharacteristic
548C23#1313326211yescharacteristic
549C23#1313326311yescharacteristic
550C23#1313326411yescharacteristic
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—534no—
578C2×C4—1062no—
579C2×C4—1062no—
580C2×C4—1062no—
581C2×C4—1062no—
582C2×C4—1062no—
583C2×C4—1062no—
584C2×C4—1062no—
585C2×C4—1062no—
586C2×C4—1062no—
587C2×C4—1064no—
588C2×C4—1064no—
589C2×C4—1062no—
590C2×C4—1062no—
591C2×C4—1062no—
592C2×C4—1064no—
593C2×C4—1062no—
594C2×C4—1062no—
595C2×C4—1062no—
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—2121no—
605C2×C4—2121no—
606C2×C4—2122no—
607C2×C4—2121no—
608C2×C4—2121no—
609C2×C4—2121no—
610C2×C4—2121no—
611C2×C4—2121no—
612C2×C4—2121no—
613C2×C4—2121no—
614C2×C4—2121no—
615C2×C4—2122no—
616C2×C4—2121no—
617C2×C4—2121no—
618C2×C4—2122no—
619C2×C4C2×C4⋊Dic5318yes—
620C2×C4C2×C4⋊Dic5314yes—
621C2×C4D4×Dic5314yes—
622C2×C4Q8×Dic5314yes—
623C2×C4Q8×Dic5314yes—
624C2×C4#1313319214yes—
625C2×C4#1313319714yes—
626C2×C4#1313320814yes—
627C2×C4#1313321614yes—
628C22C22×C4⋊Dic5311yescharacteristic
629C22C2×D4×Dic5311yescharacteristic
630C22C2×Q8×Dic5311yescharacteristic
631C22C2×Q8×Dic5311yescharacteristic
632C22#41×Dic5311yescharacteristic
633C22#1681109811yescharacteristic
634C22#1681110611yescharacteristic
635C22C2×#1313319211yescharacteristic
636C22C22⋊Q8×D5311yescharacteristic
637C22C2×#1313319711yescharacteristic
638C22#1681113611yescharacteristic
639C22C2×#1313320811yescharacteristic
640C22#1681115911yescharacteristic
641C22C2×#1313321611yescharacteristic
642C22#1681117511yescharacteristic
643C22#1681118911yescharacteristic
644C22#1681120211yescharacteristic
645C22#1681122611yescharacteristic
646C22#1681124011yescharacteristic
647C22#1681126811yescharacteristic
648C22#1681126811yescharacteristic
649C22Q8×D21211yescharacteristic
650C22#1681129511yescharacteristic
651C22#1681131111yescharacteristic
652C22#1681132611yescharacteristic
653C22#1681132911yescharacteristic
654C22#1681133211yescharacteristic
655C22#1681133211yescharacteristic
656C22#1681133411yescharacteristic
657C22#1681133411yescharacteristic
658C22#1681133911yescharacteristic
659C22#1681135011yescharacteristic
660C22#1681135211yescharacteristic
661C22#1681135311yescharacteristic
662C22Q8×Dic10611yescharacteristic
663C4—24no—
664C4—28no—
665C4—42no—
666C4—44no—
667C4—1064no—
668C4—4242no—
669C4—2124no—
670C4—2122no—
671C4—2122no—
672C4—2122no—
673C4#1681052218yes—
674C2C2×#1681052211yescharacteristic
675C2C22⋊Q8×Dic5311yescharacteristic
676C2#2027741011yescharacteristic
677C2#2027762511yescharacteristic
678C2Q8×C4⋊Dic5311yescharacteristic
679C2#2027780511yescharacteristic
680C2#2027781511yescharacteristic
681C2#2027813111yescharacteristic
682C2#2027816411yescharacteristic
683C2#2027855211yescharacteristic
684C2#2027858511yescharacteristic
685C2#2027924511yescharacteristic
686C2#2027925611yescharacteristic
687C2#2027992211yescharacteristic
688C2#2028010211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, prime radical, cosocleC24×C53C24
hypercenterC2×#389D53
hypocenterC53#14045
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
38. C53×#389C4semidirect
180. C4⋊C4×C53C4⋊C4semidirect
371. #389Dic53semidirect
384. C53#14045semidirect
531. C4⋊C4C4⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105222
C2×C4⋊C4×Dic532
C2×C4×C4⋊Dic532
#202729802
#202729682
#202729492
#202729452
#202729442
C2×C53×#3892
#1404553