Finite Group Databasebeta

← #27306137

Subgroups — #27306137

Order 13568.

2330 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810516C212yesmaximal, complemented
2C2×#16810486C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
4#20272960C212yesmaximal, complemented
5#20272956C212yesmaximal
6#20272947C212yesmaximal, complemented
7#20272945C211yesmaximal, characteristic, complemented
8#20272942C211yesmaximal, characteristic, complemented
9#20272938C211yesmaximal, characteristic, complemented
10#20272938C211yesmaximal, characteristic, complemented
11C22×C4×D4×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2212yes—
13C22×C22⋊Dic53C2212yes—
14C22×C22⋊Dic53C2212yes—
15C22×C22⋊Dic53C2212yes—
16C22×C22⋊Dic53C2212yes—
17C22×C4×Dic53C2212yes—
18#16810516—28no—
19#16810486—24no—
20C4×C22⋊Dic53—24no—
21C2×#13133124C2211yescharacteristic
22C2×#13133124C2211yescharacteristic
23C2×#13133124C2211yescharacteristic
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2211yescharacteristic
31C23×D4×C53C2211yescharacteristic
32C24×C4×C53C2211yescharacteristic
33C24×C4×C53C2211yescharacteristic
34C2×C4×D4×C53—28no—
35C2×C4×D4×C53C418yescomplemented
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C23×Dic53C2312yes—
41C23×Dic53C2312yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C2×C4⋊Dic53—24no—
45C2×C4⋊Dic53—24no—
46C2×C4⋊Dic53—42no—
47C2×C22⋊Dic53—24no—
48C2×C22⋊Dic53—24no—
49C2×C22⋊Dic53—24no—
50C2×C22⋊Dic53—24no—
51C2×C22⋊Dic53—24no—
52C2×C22⋊Dic53—24no—
53C2×C22⋊Dic53—24no—
54C2×C22⋊Dic53—24no—
55C2×C22⋊Dic53—42no—
56C2×C22⋊Dic53—42no—
57C2×C22⋊Dic53—42no—
58C2×C22⋊Dic53—42no—
59C2×C4×Dic53—24no—
60C2×C4×Dic53—24no—
61C2×C4×Dic53—42no—
62#13133124—24no—
63#13133124—24no—
64#13133124—22no—
65#13133124—22no—
66#13133124—24no—
67#13133124—24no—
68#13133124—22no—
69#13133124—24no—
70#13133124—42no—
71#13133124D414yescomplemented
72C25×C53C2311yescharacteristic
73C25×C53C2311yescharacteristic
74C22×D4×C53—24no—
75C22×D4×C53—24no—
76C22×D4×C53—22no—
77C22×D4×C53—22no—
78C22×D4×C53C2×C414yes—
79C23×C4×C53—24no—
80C23×C4×C53—24no—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—22no—
85C23×C4×C53—42no—
86C23×C4×C53—42no—
87C23×C4×C53C2×C414yes—
88C23×C4×C53C2×C414yes—
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C4×D4×C53—232no—
95C2×C4⋊C4×C53—24no—
96C2×C4⋊C4×C53C2×C414yes—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53C2×C414yes—
99C2×C22⋊C4×C53C2×C414yes—
100C2×C22⋊C4×C53D418yes—
101C2×C42×C53—24no—
102C2×C42×C53C2×C414yes—
103C24×C53—22no—
104C24×C53—21no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—22no—
109C24×C53—21no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53C22×C412yes—
122C24×C53C22×C412yes—
123C24×C53C2×D414yes—
124C24×C53#4114yes—
125C24×C53C2411yescharacteristic
126C2×D4×C53—216no—
127C2×D4×C53—216no—
128C2×D4×C53—28no—
129C2×D4×C53—28no—
130C2×D4×C53—28no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—28no—
142C22×C4×C53—22no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—28no—
147C22×C4×C53—28no—
148C22×C4×C53—28no—
149C22×C4×C53—44no—
150C22×C4×C53—44no—
151C22×C4×C53—48no—
152C22×C4×C53—48no—
153C22×C4×C53—48no—
154C22×C4×C53—48no—
155C22×C4×C53C22×C412yes—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C22×C412yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C22×C412yes—
160C22×C4×C53C2×D414yes—
161C22×C4×C53C2×D414yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53#4112yes—
164C22×C4×C53#4112yes—
165C22×C4×C53#4112yes—
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×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53C2×D414yes—
193C22×Dic53#4114yes—
194C4⋊C4×C53—28no—
195C22⋊C4×C53—28no—
196C22⋊C4×C53C22⋊C4116yescomplemented
197C42×C53—28no—
198C22⋊Dic53—216no—
199C22⋊Dic53—48no—
200C22⋊Dic53—48no—
201C22⋊Dic53—48no—
202C4⋊Dic53—48no—
203C4×Dic53—48no—
204C23×C53—22no—
205C23×C53—22no—
206C23×C53—22no—
207C23×C53—22no—
208C23×C53—22no—
209C23×C53—22no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—41no—
237C23×C53—41no—
238C23×C53—41no—
239C23×C53—41no—
240C23×C53—42no—
241C23×C53—42no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—42no—
247C23×C53—42no—
248C23×C53C2×C22⋊C414yes—
249C23×C53#11714yes—
250C23×C53C23×C411yescharacteristic
251C23×C53C22×D411yescharacteristic
252C23×C53C22×D412yes—
253C23×C53C2×#4112yes—
254C23×C53C2×#4111yescharacteristic
255C23×C53C2×#4112yes—
256C23×C53C2×#4111yescharacteristic
257C23×C53C2×#4111yescharacteristic
258C23×C53H(5,𝔽2)12yes—
259C23×C53H(5,𝔽2)11yescharacteristic
260C23×C532−1+411yescharacteristic
261D4×C53—232no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—24no—
273C2×C4×C53—24no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—416no—
282C2×C4×C53—416no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53C2×C22⋊C414yes—
286C2×C4×C53C2×C22⋊C414yes—
287C2×C4×C53#11714yes—
288C2×C4×C53C4×D414yes—
289C2×Dic53—24no—
290C2×Dic53—24no—
291C2×Dic53—24no—
292C2×Dic53—24no—
293C2×Dic53—24no—
294C2×Dic53—24no—
295C2×Dic53—42no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317#13886—531nomaximal, Sylow
318C22×C53—24no—
319C22×C53—24no—
320C22×C53—24no—
321C22×C53—24no—
322C22×C53—24no—
323C22×C53—24no—
324C22×C53—42no—
325C22×C53—42no—
326C22×C53—42no—
327C22×C53—42no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—44no—
332C22×C53—44no—
333C22×C53—44no—
334C22×C53—44no—
335C22×C53—44no—
336C22×C53—44no—
337C22×C53—44no—
338C22×C53—44no—
339C22×C53—42no—
340C22×C53C22×C22⋊C411yescharacteristic
341C22×C53C2×#11711yescharacteristic
342C22×C53C2×#11711yescharacteristic
343C22×C53C2×C4×D411yescharacteristic
344C22×C53C4×#4111yescharacteristic
345C22×C53#51811yescharacteristic
346C22×C53#52011yescharacteristic
347C22×C53#52512yes—
348C22×C53#52512yes—
349C22×C53#52512yes—
350C22×C53#52912yes—
351C22×C53#53812yes—
352C22×C53#53912yes—
353C22×C53D4212yes—
354C22×C53#54612yes—
355C22×C53#54612yes—
356C22×C53#54712yes—
357C22×C53#54711yescharacteristic
358C22×C53#55011yescharacteristic
359C22×C53#55312yes—
360C22×C53#55511yescharacteristic
361C22×C53#55611yescharacteristic
362C22×C53#55912yes—
363C4×C53—24no—
364C4×C53—24no—
365C4×C53—24no—
366C4×C53—24no—
367C4×C53—42no—
368Dic53—44no—
369Dic53—44no—
370Dic53—82no—
371Dic53—82no—
372C22×C4×D4D5311yescharacteristic
373C2×#388—532no—
374C2×#381—531no—
375C2×C4×C22⋊C4—531no—
376#1439—532no—
377#1438—532no—
378#1436—532no—
379C4⋊#95—531no—
380#1434—531no—
381C22⋊#95—531no—
382C22⋊#95—531no—
383C2×C53—44no—
384C2×C53—44no—
385C2×C53#228011yescharacteristic
386C2×C53#229011yescharacteristic
387C2×C53#231811yescharacteristic
388C2×C53D4×C22⋊C411yescharacteristic
389C2×C53#233911yescharacteristic
390C2×C53#235411yescharacteristic
391C2×C53#235711yescharacteristic
392C2×C53#245512yes—
393C2×C53#245612yes—
394C2×C53#245912yes—
395C2×C53#246612yes—
396C23×D4C2×D5311yescharacteristic
397C24×C4C2×D5311yescharacteristic
398C24×C4C2×D5311yescharacteristic
399C2×C4×D4—28no—
400C2×C4×D4Dic5318yescomplemented
401C22×C4⋊C4—532no—
402C22×C4⋊C4C2×D5311yescharacteristic
403C22×C22⋊C4—532no—
404C22×C22⋊C4—532no—
405C22×C22⋊C4—532no—
406C22×C22⋊C4—532no—
407C22×C22⋊C4C2×D5311yescharacteristic
408C22×C22⋊C4C2×D5311yescharacteristic
409C22×C42—532no—
410C22×C42C2×D5311yescharacteristic
411#388—1068no—
412#381—1064no—
413C4×C22⋊C4—1064no—
414C2×#95—531no—
415C2×#95—531no—
416C2×#95—531no—
417C2×#95—531no—
418C2×#95—532no—
419C2×#95—532no—
420C2×#95—532no—
421C2×#95—532no—
422C2×#95—532no—
423C2×#95—532no—
424C53#1388611yescharacteristic, complemented, Sylow
425C25C22×D5311yescharacteristic
426C25C22×D5311yescharacteristic
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4C2×Dic5314yes—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—24no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—532no—
441C23×C4—532no—
442C23×C4—532no—
443C23×C4—532no—
444C23×C4C2×Dic5314yes—
445C23×C4C2×Dic5314yes—
446C23×C4C22×D5311yescharacteristic
447C23×C4C22×D5311yescharacteristic
448C23×C4C22×D5311yescharacteristic
449C23×C4C22×D5311yescharacteristic
450C23×C4C22×D5311yescharacteristic
451C4×D4—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—1064no—
454C2×C4⋊C4—1064no—
455C2×C4⋊C4—2122no—
456C2×C4⋊C4C2×Dic5314yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—1064no—
459C2×C22⋊C4—1064no—
460C2×C22⋊C4—1064no—
461C2×C22⋊C4—1064no—
462C2×C22⋊C4—1064no—
463C2×C22⋊C4—1064no—
464C2×C22⋊C4—1064no—
465C2×C22⋊C4—1064no—
466C2×C22⋊C4—2122no—
467C2×C22⋊C4—2122no—
468C2×C22⋊C4—2122no—
469C2×C22⋊C4—2122no—
470C2×C22⋊C4C2×Dic5314yes—
471C2×C22⋊C4C2×Dic5314yes—
472C2×C22⋊C4C22⋊D5318yes—
473C2×C42—24no—
474C2×C42—1064no—
475C2×C42—1064no—
476C2×C42—2122no—
477C2×C42C2×Dic5314yes—
478#95—534no—
479#95—1064no—
480#95—1064no—
481#95—1064no—
482#95—1062no—
483#95—1062no—
484#95—1062no—
485#95—1064no—
486#95—1064no—
487#95—2122no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24#1171994514yes—
507C24C22×Dic5312yes—
508C24C22×Dic5312yes—
509C24C2×C22⋊D5314yes—
510C24C23×D5311yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—28no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—534no—
541C22×C4—534no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4#1171994512yes—
569C22×C4#1171994512yes—
570C22×C4D4×D5312yes—
571C22×C4#1171994712yes—
572C22×C4C22×Dic5312yes—
573C22×C4C22×Dic5312yes—
574C22×C4C22×Dic5312yes—
575C22×C4C22×Dic5312yes—
576C22×C4C22×Dic5312yes—
577C22×C4C2×C22⋊D5314yes—
578C22×C4C2×C22⋊D5314yes—
579C4⋊C4—28no—
580C4⋊C4—2128no—
581C22⋊C4—28no—
582C22⋊C4—10616no—
583C22⋊C4—2128no—
584C22⋊C4—2128no—
585C22⋊C4—2128no—
586C22⋊C4C22⋊Dic53116yescomplemented
587C42—28no—
588C42—2128no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23C2×C22⋊Dic5314yes—
634C23#1313317614yes—
635C23C23×Dic5311yescharacteristic
636C23C2×D4×D5311yescharacteristic
637C23C22×C22⋊D5312yes—
638C23#41×D5312yes—
639C23C2×#1171994711yescharacteristic
640C23C2×#1171994511yescharacteristic
641C23C2×#1171994511yescharacteristic
642C23C2×#1171994512yes—
643C23#1313326212yes—
644C23#1313326311yescharacteristic
645C23#1313326411yescharacteristic
646D4—232no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—416no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—1064no—
671C2×C4—1064no—
672C2×C4—1064no—
673C2×C4—1064no—
674C2×C4—1064no—
675C2×C4—1064no—
676C2×C4—2122no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2122no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4—2122no—
687C2×C4—2122no—
688C2×C4—2122no—
689C2×C4—2122no—
690C2×C4—2122no—
691C2×C4—2122no—
692C2×C4—2122no—
693C2×C4—2122no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2122no—
698C2×C4C2×C22⋊Dic5314yes—
699C2×C4C2×C22⋊Dic5314yes—
700C2×C4#1313317614yes—
701C2×C4D4×Dic5314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—44no—
723C22—44no—
724C22C22×C22⋊Dic5311yescharacteristic
725C22C2×#1313317611yescharacteristic
726C22C2×#1313317611yescharacteristic
727C22C2×D4×Dic5311yescharacteristic
728C22#41×Dic5311yescharacteristic
729C22#1681109811yescharacteristic
730C22#1681110611yescharacteristic
731C22#1681113212yes—
732C22#1681113412yes—
733C22#1681113412yes—
734C22#1681115312yes—
735C22#1681120612yes—
736C22#1681121512yes—
737C22D4×C22⋊D5312yes—
738C22#1681126112yes—
739C22#1681126712yes—
740C22#1681127212yes—
741C22#1681127811yescharacteristic
742C22#1681129411yescharacteristic
743C22#1681132312yes—
744C22#1681133811yescharacteristic
745C22#1681134311yescharacteristic
746C22#1681135612yes—
747C4—24no—
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—4242no—
753C4—4242no—
754C4—2124no—
755C4—2124no—
756C2—44no—
757C2—44no—
758C2#2027709811yescharacteristic
759C2#2027716011yescharacteristic
760C2#2027734811yescharacteristic
761C2D4×C22⋊Dic5311yescharacteristic
762C2#2027754511yescharacteristic
763C2#2027766411yescharacteristic
764C2#2027768811yescharacteristic
765C2#2027859212yes—
766C2#2027860712yes—
767C2#2027864612yes—
768C2#2027874512yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C4×D4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×C4×D4D53
hypocenterC53#13886
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16810516C2semidirect
2. C2×#16810486C2semidirect
3. C2×C4×C22⋊Dic53C2semidirect
4. #20272960C2semidirect
6. #20272947C2semidirect
7. #20272945C2semidirect
8. #20272942C2semidirect
9. #20272938C2semidirect
10. #20272938C2semidirect
35. C2×C4×D4×C53C4semidirect
71. #13133124D4semidirect
196. C22⋊C4×C53C22⋊C4semidirect
400. C2×C4×D4Dic53semidirect
424. C53#13886semidirect
586. C22⋊C4C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105162
C2×#168104862
C2×C4×C22⋊Dic532
#202729602
#202729562
#202729472
#202729452
#202729422
#202729382
C22×C4×D4×C532
#1388653