Finite Group Databasebeta

← #27305659

Subgroups — #27305659

Order 13568.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×C4×#11719919C212yesmaximal, complemented
4C2×#16810470C211yesmaximal, characteristic, complemented
5#20272953C212yesmaximal, complemented
6#20272952C212yesmaximal, complemented
7#20272943C211yesmaximal, characteristic, complemented
8#20272938C211yesmaximal, characteristic, complemented
9#20272936C211yesmaximal, characteristic, complemented
10#95×Dic53C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—28no—
15C2×C4×C22⋊D53C418yescomplemented
16C22×#11719919C2212yes—
17C22×#11719919C2211yescharacteristic
18C22×C22⋊Dic53C2211yescharacteristic
19C22×C22⋊Dic53C2212yes—
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26#16810523C4116yescomplemented
27C4×#11719919—28no—
28#16810470—24no—
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2212yes—
37C22×C42×C53C2212yes—
38C4×C22⋊C4×C53—24no—
39C2×#95×C53C2211yescharacteristic
40C2×#95×C53C2211yescharacteristic
41C24×D53C2311yescharacteristic
42C22×C22⋊D53—24no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53C2×C418yes—
46C22×C22⋊D53C2×C414yes—
47C23×Dic53C2312yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—24no—
55C22×C4×D53—42no—
56C22×C4×D53C2×C414yes—
57C4×C22⋊D53—232no—
58C2×#11719919—24no—
59C2×#11719919—24no—
60C2×#11719919C2×C414yes—
61C2×#11719919C2×C418yescomplemented
62C2×#11719919D418yes—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—42no—
65C2×C22⋊Dic53—42no—
66C2×C22⋊Dic53C2×C414yes—
67C2×C22⋊Dic53C2×C418yescomplemented
68C2×#11719921—24no—
69C2×#11719921—24no—
70C2×#11719921—24no—
71C2×#11719921—42no—
72C2×#11719921—42no—
73C2×#11719921C2×C414yes—
74C2×#11719921C2×C418yescomplemented
75C2×#11719921C2×C418yescomplemented
76C2×C4×Dic53—24no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53—42no—
82C2×C4×Dic53C2×C414yes—
83C2×C4×Dic53C2×C418yescomplemented
84#13133124—22no—
85#13133124—24no—
86#13133124—22no—
87#13133124—24no—
88#13133124—24no—
89#13133124—42no—
90C25×C53C2311yescharacteristic
91C23×C4×C53—24no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—42no—
95C23×C4×C53C2×C414yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C2×C22⋊C4×C53—24no—
101C2×C22⋊C4×C53—24no—
102C2×C22⋊C4×C53C2×C418yescomplemented
103C2×C42×C53—24no—
104C2×C42×C53—24no—
105C2×C42×C53—42no—
106#95×C53—22no—
107#95×C53D414yescomplemented
108C24×C53—21no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—22no—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53C22×C414yes—
118C24×C53C22×C412yes—
119C24×C53C2411yescharacteristic
120C23×D53—21no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—22no—
128C23×D53—21no—
129C23×D53C22×C412yes—
130C23×D53C22×C414yes—
131C22×C4×C53—21no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—28no—
147C22×C4×C53—28no—
148C22×C4×C53—44no—
149C22×C4×C53—48no—
150C22×C4×C53—48no—
151C22×C4×C53C22×C414yes—
152C22×C4×C53C22×C412yes—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C22×C414yes—
155C22×C4×C53C2×D414yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D414yes—
158C22×C4×C53#4112yes—
159C22×C4×C53#4114yes—
160C2×C22⋊D53—28no—
161C2×C22⋊D53—28no—
162C2×C22⋊D53—216no—
163C2×C22⋊D53—216no—
164C2×C22⋊D53C42116yescomplemented
165C22×Dic53—21no—
166C22×Dic53—21no—
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—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—21no—
184C22×Dic53C22×C412yes—
185C22×Dic53C22×C414yes—
186C22×Dic53C22×C414yes—
187C22×Dic53C22×C412yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C22×C414yes—
190C22×Dic53C2×D414yes—
191C22×Dic53C2×D414yes—
192C22×Dic53#4112yes—
193C22×Dic53#4112yes—
194C2×C4×D53—28no—
195C2×C4×D53—28no—
196C2×C4×D53—44no—
197C2×C4×D53—48no—
198C2×C4×D53—48no—
199C22⋊C4×C53—216no—
200C42×C53—48no—
201C22⋊Dic53—28no—
202C22⋊Dic53—48no—
203#11719921—28no—
204#11719921—216no—
205#11719921—48no—
206#11719919—216no—
207#11719919C22⋊C4116yescomplemented
208C4×Dic53—28no—
209C4×Dic53—216no—
210C4×Dic53—48no—
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—24no—
214C23×C53—24no—
215C23×C53—22no—
216C23×C53—24no—
217C23×C53—22no—
218C23×C53—24no—
219C23×C53—22no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—22no—
223C23×C53—42no—
224C23×C53—42no—
225C23×C53—41no—
226C23×C53—42no—
227C23×C53—41no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—42no—
233C23×C53C2×C4214yes—
234C23×C53C23×C411yescharacteristic
235C23×C53C23×C412yes—
236C23×C53C22×D412yes—
237C23×C53C22×D411yescharacteristic
238C23×C53C2×#4111yescharacteristic
239C23×C53C2×#4111yescharacteristic
240C23×C53C2×#4111yescharacteristic
241C23×C53C2×#4112yes—
242C23×C53H(5,𝔽2)12yes—
243C23×C53H(5,𝔽2)11yescharacteristic
244C23×C532−1+411yescharacteristic
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—24no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—22no—
252C22×D53—24no—
253C22×D53—22no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—22no—
257C22×D53—42no—
258C22×D53—42no—
259C22×D53—41no—
260C22×D53—42no—
261C22×D53—41no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—42no—
267C22×D53C2×C4214yes—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—24no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—24no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—416no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53C2×C22⋊C414yes—
291C2×C4×C53C4×D414yes—
292C2×C4×C53C4×D418yescomplemented
293C22⋊D53—232no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—22no—
299C2×Dic53—24no—
300C2×Dic53—24no—
301C2×Dic53—24no—
302C2×Dic53—22no—
303C2×Dic53—24no—
304C2×Dic53—24no—
305C2×Dic53—24no—
306C2×Dic53—22no—
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—
317C2×Dic53C2×C4214yes—
318C2×Dic53C2×C22⋊C414yes—
319C2×Dic53C2×C22⋊C414yes—
320C2×Dic53#11714yes—
321C2×Dic53C4×D418yes—
322C2×Dic53C4×D418yes—
323C4×D53—416no—
324#13820—531nomaximal, Sylow
325C22×C53—24no—
326C22×C53—24no—
327C22×C53—24no—
328C22×C53—42no—
329C22×C53—42no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—44no—
333C22×C53—44no—
334C22×C53—44no—
335C22×C53—44no—
336C22×C53C22×C4211yescharacteristic
337C22×C53C22×C22⋊C411yescharacteristic
338C22×C53C2×#11711yescharacteristic
339C22×C53C2×C4×D412yes—
340C22×C53C2×C4×D412yes—
341C22×C53C2×C4×D411yescharacteristic
342C22×C53C2×C4×D412yes—
343C22×C53C4×#4111yescharacteristic
344C22×C53C4×#4112yes—
345C22×C53#51812yes—
346C22×C53#51811yescharacteristic
347C22×C53#52012yes—
348C22×C53#52011yescharacteristic
349C22×C53D4212yes—
350C22×C53#54612yes—
351C22×C53#54711yescharacteristic
352C22×C53#54812yes—
353C22×C53#55011yescharacteristic
354C22×C53#55012yes—
355C22×C53#55312yes—
356C22×C53#55511yescharacteristic
357C22×C53#55611yescharacteristic
358C22×C53#55912yes—
359C2×D53—24no—
360C2×D53—24no—
361C2×D53—24no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—44no—
367C2×D53—44no—
368C2×D53—44no—
369C2×D53—44no—
370C4×C53—24no—
371C4×C53—24no—
372C4×C53—28no—
373C4×C53—44no—
374Dic53—24no—
375Dic53—42no—
376Dic53—44no—
377Dic53—44no—
378Dic53C4×C22⋊C418yescomplemented
379C22×C4×D4—531no—
380C2×#390—532no—
381C2×C4×C4⋊C4—532no—
382C2×C4×C22⋊C4—531no—
383C2×C4×C22⋊C4D5311yescharacteristic, complemented
384#1437—532no—
385#1437—532no—
386C4⋊#95—531no—
387C22⋊#95—531no—
388C22⋊#95—531no—
389C4×#95—531no—
390C2×C53—44no—
391C2×C53C2×C4×C22⋊C411yescharacteristic
392C2×C53C42×D411yescharacteristic
393C2×C53#227511yescharacteristic
394C2×C53D4×C22⋊C411yescharacteristic
395C2×C53#234111yescharacteristic
396C2×C53#235411yescharacteristic
397C2×C53#235711yescharacteristic
398C2×C53#236112yes—
399C2×C53#236312yes—
400C2×C53#236612yes—
401C2×C53#236712yes—
402D53—44no—
403C23×D4—531no—
404C24×C4—531no—
405C24×C4C2×D5311yescharacteristic
406C2×C4×D4—538no—
407C2×C4×D4—1068no—
408C22×C4⋊C4—531no—
409C22×C4⋊C4—532no—
410C22×C22⋊C4—531no—
411C22×C22⋊C4—531no—
412C22×C22⋊C4—532no—
413C22×C22⋊C4—532no—
414C22×C22⋊C4—532no—
415C22×C22⋊C4C2×D5312yes—
416C22×C42—531no—
417C22×C42—532no—
418C22×C42—532no—
419C22×C42C2×D5312yes—
420#390—5316no—
421C4×C4⋊C4—1068no—
422C4×C22⋊C4—24no—
423C4×C22⋊C4—1064no—
424C2×#95—531no—
425C2×#95—532no—
426C2×#95—531no—
427C2×#95—532no—
428C2×#95—532no—
429C2×#95—532no—
430C2×#95C2×D5311yescharacteristic
431C2×#95C2×D5311yescharacteristic
432C53#1382011yescharacteristic, complemented, Sylow
433C25—531no—
434C25C22×D5311yescharacteristic
435C22×D4—534no—
436C22×D4—538no—
437C22×D4—1064no—
438C22×D4—1062no—
439C22×D4—1062no—
440C23×C4—22no—
441C23×C4—24no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—531no—
445C23×C4—531no—
446C23×C4—532no—
447C23×C4—532no—
448C23×C4—531no—
449C23×C4—534no—
450C23×C4—1064no—
451C23×C4—1062no—
452C23×C4—1062no—
453C23×C4—2122no—
454C23×C4C4×D5314yes—
455C23×C4C22×D5312yes—
456C23×C4C22×D5312yes—
457C23×C4C22×D5311yescharacteristic
458C23×C4C22×D5311yescharacteristic
459C4×D4—10632no—
460C2×C4⋊C4—534no—
461C2×C4⋊C4—538no—
462C2×C4⋊C4—538no—
463C2×C4⋊C4—1064no—
464C2×C4⋊C4—1064no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—534no—
468C2×C22⋊C4—534no—
469C2×C22⋊C4—538no—
470C2×C22⋊C4—538no—
471C2×C22⋊C4—538no—
472C2×C22⋊C4—1064no—
473C2×C22⋊C4—1064no—
474C2×C22⋊C4—1064no—
475C2×C22⋊C4—1064no—
476C2×C22⋊C4—2122no—
477C2×C22⋊C4—2122no—
478C2×C22⋊C4—2122no—
479C2×C22⋊C4—2122no—
480C2×C22⋊C4C4×D5318yescomplemented
481C2×C42—24no—
482C2×C42—24no—
483C2×C42—42no—
484C2×C42—534no—
485C2×C42—538no—
486C2×C42—1064no—
487C2×C42—1064no—
488C2×C42—1064no—
489C2×C42—1064no—
490C2×C42—1064no—
491C2×C42—2122no—
492#95—22no—
493#95—1064no—
494#95—1062no—
495#95—1064no—
496#95—1064no—
497#95—1062no—
498#95—2122no—
499#95C22⋊D5314yescomplemented
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—534no—
510C24—532no—
511C24—1062no—
512C24—1061no—
513C24—1061no—
514C24—1061no—
515C24—1062no—
516C24—1061no—
517C24—1062no—
518C24—1061no—
519C24—1061no—
520C24C2×C4×D5314yes—
521C24C2×C4×D5312yes—
522C24C23×D5311yescharacteristic
523C2×D4—5316no—
524C2×D4—1068no—
525C2×D4—1068no—
526C2×D4—10616no—
527C2×D4—10616no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—532no—
549C22×C4—534no—
550C22×C4—534no—
551C22×C4—532no—
552C22×C4—532no—
553C22×C4—532no—
554C22×C4—534no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—534no—
558C22×C4—1068no—
559C22×C4—1061no—
560C22×C4—1061no—
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×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1061no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1061no—
578C22×C4—1068no—
579C22×C4—2124no—
580C22×C4—2128no—
581C22×C4—2128no—
582C22×C4C2×C4×D5314yes—
583C22×C4C2×C4×D5312yes—
584C22×C4C2×C4×D5312yes—
585C22×C4C2×C4×D5314yes—
586C22×C4#1171994512yes—
587C22×C4#1171994514yes—
588C22×C4D4×D5314yes—
589C22×C4C2×C22⋊D5312yes—
590C22×C4C2×C22⋊D5314yes—
591C4⋊C4—5316no—
592C4⋊C4—10616no—
593C22⋊C4—216no—
594C22⋊C4—1068no—
595C22⋊C4—1068no—
596C22⋊C4—10616no—
597C22⋊C4—2128no—
598C22⋊C4—2128no—
599C42—48no—
600C42—1068no—
601C42—10616no—
602C42—2128no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—534no—
626C23—1062no—
627C23—1062no—
628C23—1064no—
629C23—1064no—
630C23—1064no—
631C23—1062no—
632C23—1064no—
633C23—1062no—
634C23—1064no—
635C23—1062no—
636C23—1064no—
637C23—1062no—
638C23—2121no—
639C23—2122no—
640C23—2121no—
641C23—2122no—
642C23—2122no—
643C23—2121no—
644C23—2121no—
645C23—2122no—
646C23—2122no—
647C23—2122no—
648C23C42×D5314yes—
649C23C22×C4×D5311yescharacteristic
650C23C22×C4×D5312yes—
651C23C2×D4×D5312yes—
652C23C22×C22⋊D5311yescharacteristic
653C23#41×D5311yescharacteristic
654C23#41×D5311yescharacteristic
655C23C2×#1171994512yes—
656C23C2×#1171994511yescharacteristic
657C23#1313326212yes—
658C23#1313326311yescharacteristic
659C23#1313326411yescharacteristic
660D4—10632no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—534no—
684C2×C4—534no—
685C2×C4—534no—
686C2×C4—538no—
687C2×C4—538no—
688C2×C4—534no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1064no—
692C2×C4—1064no—
693C2×C4—1062no—
694C2×C4—1064no—
695C2×C4—1064no—
696C2×C4—1064no—
697C2×C4—1062no—
698C2×C4—1064no—
699C2×C4—1064no—
700C2×C4—1064no—
701C2×C4—1062no—
702C2×C4—21216no—
703C2×C4—2122no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2122no—
709C2×C4—2122no—
710C2×C4—2122no—
711C2×C4—2122no—
712C2×C4—2122no—
713C2×C4C22⋊C4×D5314yes—
714C2×C4C4×C22⋊D5314yes—
715C2×C4C4×C22⋊D5318yescomplemented
716C22—24no—
717C22—24no—
718C22—24no—
719C22—44no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—44no—
726C22—44no—
727C22—1064no—
728C22—1064no—
729C22—1064no—
730C22—2124no—
731C22—2124no—
732C22—2122no—
733C22—2122no—
734C22—2122no—
735C22—2122no—
736C22—2124no—
737C22—2124no—
738C22C2×C42×D5311yescharacteristic
739C22C2×C22⋊C4×D5311yescharacteristic
740C22#117×D5311yescharacteristic
741C22C4×D4×D5312yes—
742C22C4×D4×D5312yes—
743C22C2×C4×C22⋊D5312yes—
744C22C2×C4×C22⋊D5311yescharacteristic
745C22C4×#1171994512yes—
746C22C4×#1171994511yescharacteristic
747C22#1681109512yes—
748C22#1681109611yescharacteristic
749C22#1681110212yes—
750C22#1681110311yescharacteristic
751C22D4×C22⋊D5312yes—
752C22#1681126312yes—
753C22#1681127211yescharacteristic
754C22#1681128212yes—
755C22#1681129211yescharacteristic
756C22#1681129412yes—
757C22#1681132212yes—
758C22#1681133611yescharacteristic
759C22#1681134111yescharacteristic
760C22#1681135612yes—
761C4—24no—
762C4—24no—
763C4—28no—
764C4—44no—
765C4—538no—
766C4—1064no—
767C4—2124no—
768C4—2122no—
769C4—2124no—
770C2—44no—
771C2—2124no—
772C2C4×C22⋊C4×D5311yescharacteristic
773C2C42×C22⋊D5311yescharacteristic
774C2#2027707411yescharacteristic
775C2C22⋊C4×C22⋊D5311yescharacteristic
776C2#2027755511yescharacteristic
777C2#2027766511yescharacteristic
778C2#2027768911yescharacteristic
779C2#2027773212yes—
780C2#2027775412yes—
781C2#2027777712yes—
782C2#2027778712yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13820
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11719919C2semidirect
4. C2×#16810470C2semidirect
5. #20272953C2semidirect
6. #20272952C2semidirect
7. #20272943C2semidirect
8. #20272938C2semidirect
9. #20272936C2semidirect
10. #95×Dic53C2semidirect
11. C2×C4×C22⋊C4×C53C2semidirect
15. C2×C4×C22⋊D53C4semidirect
26. #16810523C4semidirect
61. C2×#11719919C2×C4semidirect
67. C2×C22⋊Dic53C2×C4semidirect
74. C2×#11719921C2×C4semidirect
75. C2×#11719921C2×C4semidirect
83. C2×C4×Dic53C2×C4semidirect
102. C2×C22⋊C4×C53C2×C4semidirect
107. #95×C53D4semidirect
164. C2×C22⋊D53C42semidirect
207. #11719919C22⋊C4semidirect
292. C2×C4×C53C4×D4semidirect
378. Dic53C4×C22⋊C4semidirect
383. C2×C4×C22⋊C4D53semidirect
432. C53#13820semidirect
480. C2×C22⋊C4C4×D53semidirect
499. #95C22⋊D53semidirect
715. C2×C4C4×C22⋊D53semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C2×#168105232
C2×C4×#117199192
C2×#168104702
#202729532
#202729522
#202729432
#202729382
#202729362
#95×Dic532
C2×C4×C22⋊C4×C532
#1382053