Finite Group Databasebeta

← #27307829

Subgroups — #27307829

Order 13568.

1586 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810521C211yesmaximal, characteristic
2C2×#16810521C211yesmaximal, characteristic
3C2×#16810521C211yesmaximal, characteristic
4C2×#16810518C212yesmaximal
5C2×C4×C4⋊Dic53C211yesmaximal, characteristic
6#20272970C212yesmaximal
7#20272965C212yesmaximal
8#20272950C212yesmaximal
9#20272945C211yesmaximal, characteristic
10#20272945C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4⋊Dic53C2211yescharacteristic
16C22×#11719919C2212yes—
17C22×#11719919C2212yes—
18C22×#11719919C2212yes—
19C22×C4×Dic53C2212yes—
20#16810521—24no—
21#16810521—24no—
22#16810521C418yescomplemented
23#16810518—28no—
24C4×C4⋊Dic53—24no—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C22×C4⋊C4×C53C2211yescharacteristic
34C22×C4⋊C4×C53C2211yescharacteristic
35C22×C42×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C4×C4⋊C4×C53—24no—
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—22no—
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53C2×C414yes—
53C2×C4⋊Dic53C2×C414yes—
54C2×C4⋊Dic53D414yes—
55C2×C4⋊Dic53Q814yes—
56C2×C4⋊Dic53Q814yes—
57C2×#11719919—24no—
58C2×#11719919—24no—
59C2×#11719919—24no—
60C2×#11719919—24no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—42no—
65C2×#11719919C2×C418yes—
66C2×C4×Dic53—24no—
67C2×C4×Dic53—24no—
68C2×C4×Dic53—42no—
69#13133124—24no—
70#13133124—24no—
71#13133124—24no—
72#13133124—24no—
73#13133124—24no—
74#13133124—24no—
75#13133124—42no—
76#13133124C2×C418yes—
77C23×C4×C53C2311yescharacteristic
78C23×C4×C53C2311yescharacteristic
79C23×C4×C53C2311yescharacteristic
80C23×C4×C53C2311yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C2×C4⋊C4×C53—22no—
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—22no—
87C2×C4⋊C4×C53—22no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53D414yes—
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×C53—22no—
97C2×C42×C53C2×C414yes—
98C2×C42×C53D414yes—
99#95×C53—22no—
100#95×C53—22no—
101C24×C53C2411yescharacteristic
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×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53C22×C412yes—
135C22×C4×C53C22×C412yes—
136C22×C4×C53C22×C412yes—
137C22×C4×C53C2×D412yes—
138C22×C4×C53C2×D412yes—
139C22×C4×C53C2×D412yes—
140C22×C4×C53C2×D412yes—
141C22×C4×C53C2×D412yes—
142C22×C4×C53C2×D412yes—
143C22×C4×C53C2×D412yes—
144C22×C4×C53C2×Q812yes—
145C22×C4×C53C2×Q812yes—
146C22×C4×C53#4112yes—
147C22×C4×C53#4112yes—
148C22×C4×C53#4112yes—
149C22×C4×C53#4112yes—
150C22×C4×C53#4112yes—
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×Dic53C22×C414yes—
175C22×Dic53C22×C414yes—
176C22×Dic53C2×D414yes—
177C22×Dic53C2×Q814yes—
178C22×Dic53C2×Q814yes—
179C4⋊C4×C53—28no—
180C4⋊C4×C53—28no—
181C42×C53—28no—
182C42×C53—28no—
183C42×C53—44no—
184C4⋊Dic53—28no—
185C4⋊Dic53—28no—
186C4⋊Dic53—44no—
187C4⋊Dic53C4⋊C4116yescomplemented
188#11719919—216no—
189#11719919—48no—
190#11719919—48no—
191C4×Dic53—48no—
192C23×C53C23×C411yescharacteristic
193C23×C53C22×D411yescharacteristic
194C23×C53C22×D411yescharacteristic
195C23×C53C22×D411yescharacteristic
196C23×C53C22×Q811yescharacteristic
197C23×C53C22×Q811yescharacteristic
198C23×C53C2×#4111yescharacteristic
199C23×C53C2×#4111yescharacteristic
200C23×C53C2×#4111yescharacteristic
201C23×C53C2×#4111yescharacteristic
202C23×C53C2×#4111yescharacteristic
203C23×C53H(5,𝔽2)11yescharacteristic
204C23×C532−1+411yescharacteristic
205C23×C532−1+411yescharacteristic
206C23×C532−1+411yescharacteristic
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—41no—
232C2×C4×C53—41no—
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—41no—
246C2×C4×C53—41no—
247C2×C4×C53C2×C4⋊C414yes—
248C2×C4×C53C4×D414yes—
249C2×C4×C53C4×D414yes—
250C2×C4×C53C4×Q814yes—
251C2×C4×C53#12114yes—
252C2×C4×C53#12114yes—
253C2×C4×C53C22⋊Q814yes—
254C2×C4×C53#12514yes—
255C2×C4×C53C4⋊Q814yes—
256C2×Dic53—24no—
257C2×Dic53—24no—
258C2×Dic53—24no—
259C2×Dic53—24no—
260C2×Dic53—24no—
261C2×Dic53—24no—
262C2×Dic53—24no—
263C2×Dic53—24no—
264C2×Dic53—24no—
265C2×Dic53—24no—
266C2×Dic53—24no—
267C2×Dic53—24no—
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—
283C2×Dic53C2×C4⋊C418yes—
284#14046—531nomaximal, Sylow
285C22×C53C22×C4⋊C411yescharacteristic
286C22×C53C2×C4×D411yescharacteristic
287C22×C53C2×C4×D411yescharacteristic
288C22×C53C2×C4×Q811yescharacteristic
289C22×C53C4×#4111yescharacteristic
290C22×C53#51911yescharacteristic
291C22×C53#52011yescharacteristic
292C22×C53C2×#12111yescharacteristic
293C22×C53C2×#12111yescharacteristic
294C22×C53C2×C22⋊Q811yescharacteristic
295C22×C53#52511yescharacteristic
296C22×C53C2×#12511yescharacteristic
297C22×C53#52911yescharacteristic
298C22×C53C2×C4⋊Q811yescharacteristic
299C22×C53#53211yescharacteristic
300C22×C53#53611yescharacteristic
301C22×C53#53711yescharacteristic
302C22×C53#54111yescharacteristic
303C22×C53#54211yescharacteristic
304C22×C53D4211yescharacteristic
305C22×C53#54711yescharacteristic
306C22×C53#54711yescharacteristic
307C22×C53#54811yescharacteristic
308C22×C53#54811yescharacteristic
309C22×C53D4×Q811yescharacteristic
310C22×C53D4×Q811yescharacteristic
311C22×C53#55211yescharacteristic
312C22×C53#55311yescharacteristic
313C22×C53#55411yescharacteristic
314C22×C53#55411yescharacteristic
315C22×C53#55611yescharacteristic
316C22×C53#55711yescharacteristic
317C22×C53#55711yescharacteristic
318C22×C53#55711yescharacteristic
319C22×C53#55711yescharacteristic
320C4×C53—24no—
321C4×C53—24no—
322C4×C53—42no—
323C4×C53—42no—
324C4×C53—42no—
325C4×C53—42no—
326C4×C53#38918yescomplemented
327Dic53—28no—
328Dic53—44no—
329Dic53—44no—
330Dic53—82no—
331C2×#389—531no—
332C2×#389—531no—
333C2×#389—531no—
334C2×#389—532no—
335C2×C4×C4⋊C4—531no—
336C2×C4×C4⋊C4D5311yescharacteristic
337#1442—532no—
338#1441—532no—
339#1436—532no—
340C4⋊#95—531no—
341C4⋊#95—531no—
342C2×C53C2×#38911yescharacteristic
343C2×C53C4×#12111yescharacteristic
344C2×C53#232311yescharacteristic
345C2×C53D4×C4⋊C411yescharacteristic
346C2×C53#235111yescharacteristic
347C2×C53#236511yescharacteristic
348C2×C53#237011yescharacteristic
349C2×C53#241511yescharacteristic
350C2×C53#241611yescharacteristic
351C2×C53#245211yescharacteristic
352C2×C53#245311yescharacteristic
353C2×C53#250611yescharacteristic
354C2×C53#250911yescharacteristic
355C2×C53#254611yescharacteristic
356C2×C53#258411yescharacteristic
357C22×C4⋊C4—531no—
358C22×C4⋊C4—532no—
359C22×C4⋊C4—531no—
360C22×C4⋊C4—531no—
361C22×C4⋊C4—532no—
362C22×C4⋊C4—531no—
363C22×C4⋊C4—532no—
364C22×C4⋊C4C2×D5311yescharacteristic
365C22×C4⋊C4C2×D5311yescharacteristic
366C22×C42—532no—
367C22×C42C2×D5311yescharacteristic
368C22×C42C2×D5311yescharacteristic
369C22×C42C2×D5311yescharacteristic
370#389—538no—
371#389—1064no—
372#389—1068no—
373#389—1064no—
374C4×C4⋊C4—24no—
375C4×C4⋊C4—1064no—
376C2×#95—532no—
377C2×#95—532no—
378C2×#95—532no—
379C2×#95—532no—
380C2×#95—532no—
381C2×#95—532no—
382C2×#95—532no—
383C2×#95—532no—
384C2×#95C2×D5311yescharacteristic
385C2×#95C2×D5311yescharacteristic
386C53#1404611yescharacteristic, complemented, Sylow
387C23×C4—532no—
388C23×C4—532no—
389C23×C4—532no—
390C23×C4—532no—
391C23×C4C22×D5311yescharacteristic
392C23×C4C22×D5311yescharacteristic
393C23×C4C22×D5311yescharacteristic
394C23×C4C22×D5311yescharacteristic
395C23×C4C22×D5311yescharacteristic
396C23×C4C22×D5311yescharacteristic
397C23×C4C22×D5311yescharacteristic
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—534no—
404C2×C4⋊C4—534no—
405C2×C4⋊C4—534no—
406C2×C4⋊C4—538no—
407C2×C4⋊C4—534no—
408C2×C4⋊C4—534no—
409C2×C4⋊C4—1064no—
410C2×C4⋊C4—1064no—
411C2×C4⋊C4—1062no—
412C2×C4⋊C4—1062no—
413C2×C4⋊C4—1062no—
414C2×C4⋊C4—1062no—
415C2×C4⋊C4—1064no—
416C2×C4⋊C4—1064no—
417C2×C4⋊C4—1064no—
418C2×C4⋊C4—1064no—
419C2×C4⋊C4—1062no—
420C2×C4⋊C4—1062no—
421C2×C4⋊C4—1064no—
422C2×C4⋊C4—1062no—
423C2×C4⋊C4—2122no—
424C2×C4⋊C4D21214yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—1064no—
433C2×C42—1064no—
434C2×C42—2122no—
435C2×C42C4×D5314yes—
436C2×C42C22⋊D5314yes—
437#95—22no—
438#95—22no—
439#95—538no—
440#95—1064no—
441#95—1064no—
442#95—1064no—
443#95—1064no—
444#95—1064no—
445#95—1064no—
446#95—2122no—
447C24C23×D5311yescharacteristic
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—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—534no—
481C22×C4—534no—
482C22×C4—534no—
483C22×C4—534no—
484C22×C4—534no—
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×C4—1062no—
505C22×C4—1062no—
506C22×C4—1062no—
507C22×C4—1062no—
508C22×C4C2×C4×D5312yes—
509C22×C4C2×C4×D5312yes—
510C22×C4C2×C4×D5312yes—
511C22×C4C2×D21212yes—
512C22×C4C2×D21212yes—
513C22×C4C2×D21212yes—
514C22×C4#1171994512yes—
515C22×C4#1171994512yes—
516C22×C4#1171994512yes—
517C22×C4#1171994512yes—
518C22×C4D4×D5312yes—
519C22×C4#1171994712yes—
520C22×C4Q8×D5312yes—
521C22×C4Q8×D5312yes—
522C22×C4C2×C22⋊D5312yes—
523C22×C4C2×C22⋊D5312yes—
524C22×C4C2×C22⋊D5312yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—5316no—
528C4⋊C4—1068no—
529C4⋊C4—10616no—
530C4⋊C4—1068no—
531C4⋊C4—2128no—
532C4⋊C4—2124no—
533C4⋊C4—2128no—
534C42—28no—
535C42—28no—
536C42—44no—
537C42—2128no—
538C23C22×C4×D5311yescharacteristic
539C23C2×D4×D5311yescharacteristic
540C23C22×C22⋊D5311yescharacteristic
541C23C22×D21211yescharacteristic
542C23C2×Q8×D5311yescharacteristic
543C23C2×Q8×D5311yescharacteristic
544C23C2×#1171994711yescharacteristic
545C23C2×#1171994511yescharacteristic
546C23C2×#1171994511yescharacteristic
547C23C2×#1171994511yescharacteristic
548C23C2×#1171994511yescharacteristic
549C23#1313326311yescharacteristic
550C23#1313326411yescharacteristic
551C23#1313326411yescharacteristic
552C23#1313326411yescharacteristic
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—41no—
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—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—538no—
594C2×C4—1064no—
595C2×C4—1064no—
596C2×C4—1064no—
597C2×C4—1064no—
598C2×C4—1064no—
599C2×C4—1064no—
600C2×C4—1064no—
601C2×C4—1064no—
602C2×C4—1064no—
603C2×C4—1064no—
604C2×C4—1064no—
605C2×C4—1064no—
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—2122no—
619C2×C4—2122no—
620C2×C4—2122no—
621C2×C4C4⋊C4×D5314yes—
622C2×C4C4×C22⋊D5314yes—
623C2×C4C4×D21214yes—
624C2×C4#1313318214yes—
625C2×C4#1313318914yes—
626C2×C4#1313319114yes—
627C2×C4#1313319514yes—
628C2×C4#1313320714yes—
629C2×C4#1313321514yes—
630C22C2×C4⋊C4×D5311yescharacteristic
631C22C2×C4×C22⋊D5311yescharacteristic
632C22C2×C4×D21211yescharacteristic
633C22C2×#1313318211yescharacteristic
634C22C4×#1171994511yescharacteristic
635C22#1681110011yescharacteristic
636C22#1681110311yescharacteristic
637C22C2×#1313318911yescharacteristic
638C22C2×#1313319111yescharacteristic
639C22C2×#1313319511yescharacteristic
640C22#1681113411yescharacteristic
641C22C2×#1313320711yescharacteristic
642C22#1681115711yescharacteristic
643C22C2×#1313321511yescharacteristic
644C22#1681117311yescharacteristic
645C22#1681119411yescharacteristic
646C22#1681120111yescharacteristic
647C22#1681123511yescharacteristic
648C22#1681124411yescharacteristic
649C22D4×D21211yescharacteristic
650C22#1681127711yescharacteristic
651C22#1681127811yescharacteristic
652C22#1681128211yescharacteristic
653C22#1681128211yescharacteristic
654C22Q8×D21211yescharacteristic
655C22Q8×D21211yescharacteristic
656C22#1681131311yescharacteristic
657C22#1681131911yescharacteristic
658C22#1681133311yescharacteristic
659C22#1681133311yescharacteristic
660C22#1681134311yescharacteristic
661C22#1681135111yescharacteristic
662C22#1681135111yescharacteristic
663C22#1681135111yescharacteristic
664C22#1681135111yescharacteristic
665C4—24no—
666C4—24no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—1068no—
672C4—4242no—
673C4—2124no—
674C4—2124no—
675C4#1681051818yescomplemented
676C2C2×#1681051811yescharacteristic
677C2C4×#1313319111yescharacteristic
678C2#2027739711yescharacteristic
679C2C4⋊C4×D21211yescharacteristic
680C2#2027763511yescharacteristic
681C2#2027777311yescharacteristic
682C2#2027780911yescharacteristic
683C2#2027814411yescharacteristic
684C2#2027815511yescharacteristic
685C2#2027856511yescharacteristic
686C2#2027857611yescharacteristic
687C2#2027923111yescharacteristic
688C2#2027926411yescharacteristic
689C2#2027970011yescharacteristic
690C2#2028010311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C4×C4⋊C4×C53C2
socle, prime radical, cosocleC24×C53C24
hypercenterC2×C4×C4⋊C4D53
hypocenterC53#14046
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #16810521C4semidirect
187. C4⋊Dic53C4⋊C4semidirect
326. C4×C53#389semidirect
386. C53#14046semidirect
675. C4#16810518semidirect

Maximal subgroups

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

subgroupindex
C2×#168105212
C2×#168105182
C2×C4×C4⋊Dic532
#202729702
#202729652
#202729502
#202729452
C2×C4×C4⋊C4×C532
#1404653