Finite Group Databasebeta

← #27306181

Subgroups — #27306181

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×#16810509C212yesmaximal, complemented
2C2×#16810483C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
4#20272960C212yesmaximal, complemented
5#20272956C212yesmaximal
6#20272952C212yesmaximal, complemented
7#20272942C211yesmaximal, 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#16810509—28no—
19#16810483—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—24no—
65#13133124—24no—
66#13133124—22no—
67#13133124—22no—
68#13133124—22no—
69#13133124—24no—
70#13133124—42no—
71#13133124D414yescomplemented
72C25×C53C2311yescharacteristic
73C25×C53C2311yescharacteristic
74C22×D4×C53—24no—
75C22×D4×C53—22no—
76C22×D4×C53—22no—
77C22×D4×C53—24no—
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×C53C2×C414yes—
96C2×C4⋊C4×C53D418yes—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—24no—
99C2×C22⋊C4×C53C2×C414yes—
100C2×C22⋊C4×C53C2×C414yes—
101C2×C42×C53—24no—
102C2×C42×C53C2×C414yes—
103C24×C53—22no—
104C24×C53—22no—
105C24×C53—21no—
106C24×C53—21no—
107C24×C53—21no—
108C24×C53—21no—
109C24×C53—22no—
110C24×C53—21no—
111C24×C53—21no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53C22×C412yes—
121C24×C53C22×C412yes—
122C24×C53#4114yes—
123C24×C53#4112yes—
124C24×C53#4112yes—
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—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—21no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—21no—
145C22×C4×C53—21no—
146C22×C4×C53—28no—
147C22×C4×C53—28no—
148C22×C4×C53—28no—
149C22×C4×C53—28no—
150C22×C4×C53—44no—
151C22×C4×C53—44no—
152C22×C4×C53—48no—
153C22×C4×C53—48no—
154C22×C4×C53—48no—
155C22×C4×C53—48no—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C22×C412yes—
158C22×C4×C53C22×C412yes—
159C22×C4×C53C22×C412yes—
160C22×C4×C53C22×C412yes—
161C22×C4×C53C2×D414yes—
162C22×C4×C53C2×D414yes—
163C22×C4×C53C2×D414yes—
164C22×C4×C53C2×D412yes—
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×C53C22⋊C4116yescomplemented
195C22⋊C4×C53—28no—
196C22⋊C4×C53—28no—
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—22no—
225C23×C53—22no—
226C23×C53—24no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—24no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—41no—
239C23×C53—42no—
240C23×C53—42no—
241C23×C53—41no—
242C23×C53—42no—
243C23×C53—42no—
244C23×C53—42no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—42no—
248C23×C53#11714yes—
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×C53C2×C22⋊C414yes—
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#13890—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#54611yescharacteristic
356C22×C53#54812yes—
357C22×C53#54811yescharacteristic
358C22×C53#55012yes—
359C22×C53#55112yes—
360C22×C53#55211yescharacteristic
361C22×C53#55311yescharacteristic
362C22×C53#55312yes—
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×#387—532no—
374C2×#380—531no—
375C2×C4×C22⋊C4—531no—
376#1439—532no—
377#1438—532no—
378#1437—532no—
379#1434—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#234111yescharacteristic
390C2×C53#235211yescharacteristic
391C2×C53#235311yescharacteristic
392C2×C53#245612yes—
393C2×C53#246012yes—
394C2×C53#246312yes—
395C2×C53#246712yes—
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#387—1068no—
412#380—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#1389011yescharacteristic, complemented, Sylow
425C25C22×D5311yescharacteristic
426C25C22×D5311yescharacteristic
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—24no—
430C22×D4—24no—
431C22×D4C2×Dic5314yes—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—24no—
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—1064no—
453C2×C4⋊C4—1064no—
454C2×C4⋊C4—2122no—
455C2×C4⋊C4C2×Dic5314yes—
456C2×C4⋊C4C22⋊D5318yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
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—1064no—
467C2×C22⋊C4—2122no—
468C2×C22⋊C4—2122no—
469C2×C22⋊C4—2122no—
470C2×C22⋊C4—2122no—
471C2×C22⋊C4C2×Dic5314yes—
472C2×C22⋊C4C2×Dic5314yes—
473C2×C42—24no—
474C2×C42—1064no—
475C2×C42—1064no—
476C2×C42—2122no—
477C2×C42C2×Dic5314yes—
478#95—534no—
479#95—1064no—
480#95—1062no—
481#95—1062no—
482#95—1062no—
483#95—1064no—
484#95—1064no—
485#95—1064no—
486#95—1064no—
487#95—2122no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24#1171994512yes—
506C24#1171994512yes—
507C24#1171994514yes—
508C24C22×Dic5312yes—
509C24C22×Dic5312yes—
510C24C23×D5311yescharacteristic
511C2×D4—216no—
512C2×D4—216no—
513C2×D4—28no—
514C2×D4—28no—
515C2×D4—28no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—534no—
542C22×C4—534no—
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—1062no—
569C22×C4D4×D5312yes—
570C22×C4#1171994712yes—
571C22×C4C22×Dic5312yes—
572C22×C4C22×Dic5312yes—
573C22×C4C22×Dic5312yes—
574C22×C4C22×Dic5312yes—
575C22×C4C22×Dic5312yes—
576C22×C4C2×C22⋊D5314yes—
577C22×C4C2×C22⋊D5314yes—
578C22×C4C2×C22⋊D5314yes—
579C4⋊C4—2128no—
580C4⋊C4C22⋊Dic53116yescomplemented
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—10616no—
584C22⋊C4—2128no—
585C22⋊C4—2128no—
586C22⋊C4—2128no—
587C42—28no—
588C42—2128no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23#1313317614yes—
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×C4C2×C22⋊Dic5314yes—
701C2×C4D4×Dic5314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
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#1681126712yes—
739C22#1681126911yescharacteristic
740C22#1681128012yes—
741C22#1681128211yescharacteristic
742C22#1681129212yes—
743C22#1681130212yes—
744C22#1681131311yescharacteristic
745C22#1681131911yescharacteristic
746C22#1681132212yes—
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#2027755611yescharacteristic
763C2#2027764411yescharacteristic
764C2#2027765511yescharacteristic
765C2#2027860112yes—
766C2#2027866112yes—
767C2#2027870612yes—
768C2#2027876012yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C4×D4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC22×C4×D4D53
hypocenterC53#13890
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×#16810509C2semidirect
2. C2×#16810483C2semidirect
3. C2×C4×C22⋊Dic53C2semidirect
4. #20272960C2semidirect
6. #20272952C2semidirect
7. #20272942C2semidirect
8. #20272942C2semidirect
9. #20272938C2semidirect
10. #20272938C2semidirect
35. C2×C4×D4×C53C4semidirect
71. #13133124D4semidirect
194. C4⋊C4×C53C22⋊C4semidirect
400. C2×C4×D4Dic53semidirect
424. C53#13890semidirect
580. C4⋊C4C22⋊Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105092
C2×#168104832
C2×C4×C22⋊Dic532
#202729602
#202729562
#202729522
#202729422
#202729382
C22×C4×D4×C532
#1389053