Finite Group Databasebeta

← #27306767

Subgroups — #27306767

Order 13568.

1630 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810522C211yesmaximal, characteristic
2C2×#16810521C211yesmaximal, characteristic
3C2×#16810519C211yesmaximal, characteristic
4C2×#16810488C211yesmaximal, characteristic
5C2×C4⋊C4×Dic53C211yesmaximal, characteristic
6C2×C4×#11719919C211yesmaximal, characteristic
7#20272979C212yesmaximal
8#20272978C212yesmaximal
9#20272944C212yesmaximal
10#20272943C212yesmaximal
11C2×C53×#389C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C2211yescharacteristic
16C22×#11719919C2211yescharacteristic
17C22×#11719919C2212yes—
18C22×#11719919C2212yes—
19C22×C4×Dic53C2211yescharacteristic
20C22×C4×Dic53C2212yes—
21C22×C4×Dic53C2211yescharacteristic
22#16810522—24no—
23#16810521—24no—
24#16810519—24no—
25#16810488—24no—
26C4⋊C4×Dic53C418yescomplemented
27C4×#11719919—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2212yes—
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#389—24no—
41C2×#95×C53C2212yes—
42C23×Dic53C2312yes—
43C23×Dic53C2311yescharacteristic
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2312yes—
47C23×Dic53C2311yescharacteristic
48C2×C4⋊Dic53—22no—
49C2×C4⋊Dic53—24no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—24no—
53C2×C4⋊Dic53—42no—
54C2×C4⋊Dic53C2×C414yes—
55C2×C4⋊Dic53D414yes—
56C2×C4⋊Dic53Q814yes—
57C2×#11719919—22no—
58C2×#11719919—22no—
59C2×#11719919—24no—
60C2×#11719919—22no—
61C2×#11719919—22no—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—24no—
67C2×#11719919—42no—
68C2×#11719919—42no—
69C2×C4×Dic53—22no—
70C2×C4×Dic53—22no—
71C2×C4×Dic53—22no—
72C2×C4×Dic53—42no—
73C2×C4×Dic53—42no—
74C2×C4×Dic53C2×C418yes—
75C2×C4×Dic53C2×C414yes—
76C2×C4×Dic53D414yes—
77C2×C4×Dic53Q814yes—
78#13133124—24no—
79#13133124—24no—
80#13133124—24no—
81#13133124—22no—
82#13133124—22no—
83#13133124—24no—
84#13133124—24no—
85#13133124C2×C418yes—
86C23×C4×C53C2312yes—
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2312yes—
90C23×C4×C53C2311yescharacteristic
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—24no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—24no—
96C2×C4⋊C4×C53—42no—
97C2×C4⋊C4×C53C2×C414yes—
98C2×C4⋊C4×C53D414yes—
99C2×C4⋊C4×C53Q814yes—
100C2×C42×C53—22no—
101C2×C42×C53—22no—
102C2×C42×C53—22no—
103#95×C53—24no—
104C24×C53C2411yescharacteristic
105C22×C4×C53—22no—
106C22×C4×C53—22no—
107C22×C4×C53—22no—
108C22×C4×C53—22no—
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—22no—
122C22×C4×C53—22no—
123C22×C4×C53—22no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53C22×C414yes—
129C22×C4×C53C22×C412yes—
130C22×C4×C53C2×D414yes—
131C22×C4×C53C2×D412yes—
132C22×C4×C53C2×D412yes—
133C22×C4×C53C2×D412yes—
134C22×C4×C53C2×Q814yes—
135C22×C4×C53C2×Q812yes—
136C22×C4×C53C2×Q812yes—
137C22×C4×C53C2×Q812yes—
138C22×C4×C53#4112yes—
139C22×C4×C53#4112yes—
140C22×Dic53—21no—
141C22×Dic53—21no—
142C22×Dic53—21no—
143C22×Dic53—21no—
144C22×Dic53—22no—
145C22×Dic53—22no—
146C22×Dic53—21no—
147C22×Dic53—21no—
148C22×Dic53—22no—
149C22×Dic53—22no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
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×Dic53C22×C412yes—
172C22×Dic53C22×C414yes—
173C22×Dic53C22×C412yes—
174C22×Dic53C2×D412yes—
175C22×Dic53C2×D412yes—
176C22×Dic53C2×D414yes—
177C22×Dic53C2×Q812yes—
178C22×Dic53C2×Q812yes—
179C22×Dic53C2×Q814yes—
180C22×Dic53#4112yes—
181C22×Dic53#4112yes—
182C4⋊C4×C53—48no—
183C4⋊C4×C53—44no—
184C4⋊C4×C53C4⋊C4116yescomplemented
185C42×C53—44no—
186C4⋊Dic53—48no—
187C4⋊Dic53—44no—
188C4⋊Dic53C4⋊C4116yescomplemented
189#11719919—28no—
190#11719919—28no—
191#11719919—48no—
192#11719919—48no—
193C4×Dic53—48no—
194C4×Dic53—44no—
195C4×Dic53C4⋊C4116yescomplemented
196C23×C53C23×C411yescharacteristic
197C23×C53C22×D411yescharacteristic
198C23×C53C22×D411yescharacteristic
199C23×C53C22×D411yescharacteristic
200C23×C53C22×Q811yescharacteristic
201C23×C53C22×Q811yescharacteristic
202C23×C53C22×Q811yescharacteristic
203C23×C53C2×#4111yescharacteristic
204C23×C53C2×#4111yescharacteristic
205C23×C53C2×#4111yescharacteristic
206C23×C53C2×#4111yescharacteristic
207C23×C53H(5,𝔽2)11yescharacteristic
208C23×C53H(5,𝔽2)11yescharacteristic
209C23×C532−1+411yescharacteristic
210C23×C532−1+411yescharacteristic
211C2×C4×C53—24no—
212C2×C4×C53—24no—
213C2×C4×C53—24no—
214C2×C4×C53—24no—
215C2×C4×C53—24no—
216C2×C4×C53—24no—
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—41no—
224C2×C4×C53—41no—
225C2×C4×C53—41no—
226C2×C4×C53—41no—
227C2×C4×C53—41no—
228C2×C4×C53—41no—
229C2×C4×C53—41no—
230C2×C4×C53—41no—
231C2×C4×C53—42no—
232C2×C4×C53—42no—
233C2×C4×C53—42no—
234C2×C4×C53—42no—
235C2×C4×C53—42no—
236C2×C4×C53—42no—
237C2×C4×C53—42no—
238C2×C4×C53C2×C4⋊C414yes—
239C2×C4×C53C2×C4⋊C414yes—
240C2×C4×C53C2×C4⋊C418yes—
241C2×C4×C53C2×C4⋊C414yes—
242C2×C4×C53#12714yes—
243C2×C4×C53C4⋊Q814yes—
244C2×C4×C53C4⋊Q814yes—
245C2×C4×C53C4⋊Q814yes—
246C2×Dic53—22no—
247C2×Dic53—24no—
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—22no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—24no—
261C2×Dic53—24no—
262C2×Dic53—24no—
263C2×Dic53—24no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—41no—
271C2×Dic53—41no—
272C2×Dic53—41no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—41no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—42no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53C2×C4⋊C414yes—
286C2×Dic53C2×C4⋊C414yes—
287C2×Dic53C2×C4⋊C418yes—
288#13954—531nomaximal, Sylow
289C22×C53C22×C4⋊C411yescharacteristic
290C22×C53C22×C4⋊C411yescharacteristic
291C22×C53C22×C4⋊C411yescharacteristic
292C22×C53C4×#4111yescharacteristic
293C22×C53C4×#4111yescharacteristic
294C22×C53#51811yescharacteristic
295C22×C53#51911yescharacteristic
296C22×C53#52511yescharacteristic
297C22×C53#52511yescharacteristic
298C22×C53C2×#12711yescharacteristic
299C22×C53C2×C4⋊Q811yescharacteristic
300C22×C53C2×C4⋊Q811yescharacteristic
301C22×C53C2×C4⋊Q811yescharacteristic
302C22×C53#53311yescharacteristic
303C22×C53#53311yescharacteristic
304C22×C53#53711yescharacteristic
305C22×C53#53711yescharacteristic
306C22×C53#54411yescharacteristic
307C22×C53#54411yescharacteristic
308C22×C53#54611yescharacteristic
309C22×C53#54611yescharacteristic
310C22×C53#54611yescharacteristic
311C22×C53#54611yescharacteristic
312C22×C53#54811yescharacteristic
313C22×C53#54811yescharacteristic
314C22×C53#54811yescharacteristic
315C22×C53#54811yescharacteristic
316C22×C53#55411yescharacteristic
317C22×C53#55411yescharacteristic
318C22×C53#55411yescharacteristic
319C22×C53#55411yescharacteristic
320C22×C53#55711yescharacteristic
321C22×C53#55711yescharacteristic
322C22×C53#55711yescharacteristic
323C22×C53#55711yescharacteristic
324C4×C53—28no—
325C4×C53—42no—
326C4×C53—42no—
327C4×C53—82no—
328C4×C53#38418yes—
329Dic53—24no—
330Dic53—28no—
331Dic53—24no—
332Dic53—42no—
333Dic53—42no—
334Dic53—82no—
335C2×#389—531no—
336C2×#389—531no—
337C2×#389—531no—
338C2×#389D5311yescharacteristic
339C2×#382—531no—
340C2×C4×C4⋊C4—531no—
341C2×C4×C4⋊C4—531no—
342#1444—532no—
343#1444—532no—
344C4⋊#95—532no—
345C4⋊#95—532no—
346C2×C53C2×#38411yescharacteristic
347C2×C53#229611yescharacteristic
348C2×C53#231611yescharacteristic
349C2×C53#234911yescharacteristic
350C2×C53#234911yescharacteristic
351C2×C53#235111yescharacteristic
352C2×C53#235111yescharacteristic
353C2×C53#254011yescharacteristic
354C2×C53#254011yescharacteristic
355C2×C53#255011yescharacteristic
356C2×C53#255011yescharacteristic
357C2×C53#255011yescharacteristic
358C2×C53#255011yescharacteristic
359C2×C53#258411yescharacteristic
360C2×C53#258411yescharacteristic
361C22×C4⋊C4—531no—
362C22×C4⋊C4—531no—
363C22×C4⋊C4—531no—
364C22×C4⋊C4—531no—
365C22×C4⋊C4—532no—
366C22×C4⋊C4—532no—
367C22×C4⋊C4—532no—
368C22×C4⋊C4C2×D5311yescharacteristic
369C22×C4⋊C4C2×D5312yes—
370C22×C4⋊C4C2×D5311yescharacteristic
371C22×C42—531no—
372C22×C42—532no—
373C22×C42—531no—
374C22×C42C2×D5311yescharacteristic
375#389—24no—
376#389—1064no—
377#389—1064no—
378#389—1064no—
379#382—1064no—
380C4×C4⋊C4—538no—
381C4×C4⋊C4—1064no—
382C2×#95—532no—
383C2×#95—531no—
384C2×#95—531no—
385C2×#95—532no—
386C2×#95—532no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—532no—
390C2×#95C2×D5312yes—
391C53#1395411yescharacteristic, complemented, Sylow
392C23×C4—532no—
393C23×C4—531no—
394C23×C4—531no—
395C23×C4—531no—
396C23×C4—531no—
397C23×C4—532no—
398C23×C4C22×D5312yes—
399C23×C4C22×D5311yescharacteristic
400C23×C4C22×D5311yescharacteristic
401C23×C4C22×D5312yes—
402C23×C4C22×D5311yescharacteristic
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—534no—
410C2×C4⋊C4—534no—
411C2×C4⋊C4—534no—
412C2×C4⋊C4—1062no—
413C2×C4⋊C4—1062no—
414C2×C4⋊C4—1062no—
415C2×C4⋊C4—1062no—
416C2×C4⋊C4—1062no—
417C2×C4⋊C4—1062no—
418C2×C4⋊C4—1064no—
419C2×C4⋊C4—1064no—
420C2×C4⋊C4—1064no—
421C2×C4⋊C4—1064no—
422C2×C4⋊C4—1062no—
423C2×C4⋊C4—1062no—
424C2×C4⋊C4—1064no—
425C2×C4⋊C4—1064no—
426C2×C4⋊C4—1062no—
427C2×C4⋊C4—2122no—
428C2×C4⋊C4—2122no—
429C2×C4⋊C4—2122no—
430C2×C4⋊C4Dic10614yes—
431C2×C4⋊C4C4×D5314yes—
432C2×C4⋊C4C22⋊D5314yes—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—534no—
437C2×C42—534no—
438C2×C42—534no—
439C2×C42—538no—
440C2×C42—1062no—
441C2×C42—1062no—
442C2×C42—1062no—
443C2×C42—2122no—
444C2×C42—2122no—
445#95—24no—
446#95—538no—
447#95—1062no—
448#95—1062no—
449#95—1064no—
450#95—1064no—
451#95—1064no—
452#95—1064no—
453#95—1064no—
454C24C23×D5311yescharacteristic
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
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—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—532no—
479C22×C4—534no—
480C22×C4—532no—
481C22×C4—532no—
482C22×C4—532no—
483C22×C4—534no—
484C22×C4—532no—
485C22×C4—532no—
486C22×C4—534no—
487C22×C4—532no—
488C22×C4—532no—
489C22×C4—1062no—
490C22×C4—1061no—
491C22×C4—1061no—
492C22×C4—1061no—
493C22×C4—1062no—
494C22×C4—1061no—
495C22×C4—1061no—
496C22×C4—1062no—
497C22×C4—1061no—
498C22×C4—1062no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1061no—
503C22×C4—1061no—
504C22×C4—1061no—
505C22×C4—1061no—
506C22×C4—1061no—
507C22×C4—1061no—
508C22×C4—1061no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1061no—
512C22×C4—1061no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4C2×Dic10614yes—
521C22×C4C2×Dic10612yes—
522C22×C4C2×C4×D5314yes—
523C22×C4C2×C4×D5312yes—
524C22×C4D4×D5312yes—
525C22×C4D4×D5312yes—
526C22×C4#1171994712yes—
527C22×C4Q8×D5312yes—
528C22×C4Q8×D5312yes—
529C22×C4#1171994912yes—
530C22×C4C2×C22⋊D5314yes—
531C22×C4C2×C22⋊D5312yes—
532C4⋊C4—48no—
533C4⋊C4—44no—
534C4⋊C4—5316no—
535C4⋊C4—1068no—
536C4⋊C4—1068no—
537C4⋊C4—2128no—
538C4⋊C4—2128no—
539C4⋊C4—2128no—
540C4⋊C4—2124no—
541C4⋊C4#11719919116yescomplemented
542C42—44no—
543C42—5316no—
544C42—2128no—
545C42—2124no—
546C23C22×C4×D5311yescharacteristic
547C23C2×D4×D5311yescharacteristic
548C23C2×D4×D5311yescharacteristic
549C23C22×C22⋊D5311yescharacteristic
550C23C2×Q8×D5311yescharacteristic
551C23C2×Q8×D5311yescharacteristic
552C23C22×Dic10611yescharacteristic
553C23#41×D5311yescharacteristic
554C23#41×D5311yescharacteristic
555C23C2×#1171994711yescharacteristic
556C23C2×#1171994911yescharacteristic
557C23#1313326211yescharacteristic
558C23#1313326311yescharacteristic
559C23#1313326411yescharacteristic
560C23#1313326511yescharacteristic
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—534no—
589C2×C4—534no—
590C2×C4—538no—
591C2×C4—1064no—
592C2×C4—1064no—
593C2×C4—1064no—
594C2×C4—1064no—
595C2×C4—1062no—
596C2×C4—1064no—
597C2×C4—1062no—
598C2×C4—1062no—
599C2×C4—1064no—
600C2×C4—1062no—
601C2×C4—1062no—
602C2×C4—1062no—
603C2×C4—1062no—
604C2×C4—1062no—
605C2×C4—1062no—
606C2×C4—1062no—
607C2×C4—1062no—
608C2×C4—1062no—
609C2×C4—1062no—
610C2×C4—1062no—
611C2×C4—1062no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—2122no—
616C2×C4—2122no—
617C2×C4—2122no—
618C2×C4—2122no—
619C2×C4—2122no—
620C2×C4—2122no—
621C2×C4—2122no—
622C2×C4—2121no—
623C2×C4—2121no—
624C2×C4—2121no—
625C2×C4—2121no—
626C2×C4—2121no—
627C2×C4—2121no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4C4⋊C4×D5314yes—
631C2×C4C4⋊C4×D5314yes—
632C2×C4C2×#1171991918yes—
633C2×C4C2×#1171991914yes—
634C2×C4#1313321314yes—
635C2×C4#1313321514yes—
636C2×C4#1313321614yes—
637C2×C4#1313321614yes—
638C22C2×C4⋊C4×D5311yescharacteristic
639C22C2×C4⋊C4×D5311yescharacteristic
640C22C22×#1171991911yescharacteristic
641C22C4×#1171994711yescharacteristic
642C22C4×#1171994911yescharacteristic
643C22#1681109511yescharacteristic
644C22#1681109911yescharacteristic
645C22#1681113311yescharacteristic
646C22#1681113611yescharacteristic
647C22C2×#1313321311yescharacteristic
648C22C2×#1313321511yescharacteristic
649C22C2×#1313321611yescharacteristic
650C22C2×#1313321611yescharacteristic
651C22#1681117811yescharacteristic
652C22#1681117911yescharacteristic
653C22#1681120211yescharacteristic
654C22#1681120311yescharacteristic
655C22#1681125011yescharacteristic
656C22#1681125311yescharacteristic
657C22#1681126111yescharacteristic
658C22#1681126411yescharacteristic
659C22#1681126711yescharacteristic
660C22#1681127011yescharacteristic
661C22#1681127911yescharacteristic
662C22#1681128011yescharacteristic
663C22#1681128311yescharacteristic
664C22#1681128411yescharacteristic
665C22#1681132911yescharacteristic
666C22#1681133011yescharacteristic
667C22#1681133211yescharacteristic
668C22#1681133411yescharacteristic
669C22#1681134811yescharacteristic
670C22#1681134911yescharacteristic
671C22#1681135011yescharacteristic
672C22#1681135211yescharacteristic
673C4—28no—
674C4—42no—
675C4—42no—
676C4—82no—
677C4—1064no—
678C4—1068no—
679C4—1064no—
680C4—4242no—
681C4—2122no—
682C4—2122no—
683C4#1681049218yes—
684C2C2×#1681049211yescharacteristic
685C2#2027719611yescharacteristic
686C2#2027733011yescharacteristic
687C2#2027762011yescharacteristic
688C2#2027762411yescharacteristic
689C2#2027763311yescharacteristic
690C2#2027763411yescharacteristic
691C2#2027965111yescharacteristic
692C2#2027965311yescharacteristic
693C2#2027973211yescharacteristic
694C2#2027973411yescharacteristic
695C2#2027973811yescharacteristic
696C2#2027973911yescharacteristic
697C2#2028010011yescharacteristic
698C2#2028010211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, prime radical, cosocleC24×C53C24
hypercenterC2×#389D53
hypocenterC53#13954
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
26. C4⋊C4×Dic53C4semidirect
184. C4⋊C4×C53C4⋊C4semidirect
188. C4⋊Dic53C4⋊C4semidirect
195. C4×Dic53C4⋊C4semidirect
391. C53#13954semidirect
541. C4⋊C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168105222
C2×#168105212
C2×#168105192
C2×#168104882
C2×C4⋊C4×Dic532
C2×C4×#117199192
#202729792
#202729782
#202729442
#202729432
C2×C53×#3892
#1395453