Finite Group Databasebeta

← C2×#20279900 #27554307

Subgroups — C2×#20279900 #27554307

Order 13568.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D53C211yesmaximal, characteristic
3#20279900C2116yesmaximal, direct product factor
4C2×#16810564C211yesmaximal, characteristic, complemented
5C2×#16810559C211yesmaximal, characteristic, complemented
6C2×#16810543C211yesmaximal, characteristic, complemented
7C2×#16810535C211yesmaximal, characteristic, complemented
8C2×#16810508C211yesmaximal, characteristic, complemented
9C2×#16810504C211yesmaximal, characteristic, complemented
10C2×#16810499C211yesmaximal, characteristic
11C2×#16810499C211yesmaximal, characteristic
12C2×#16810496C211yesmaximal, characteristic, complemented
13C2×#16810482C211yesmaximal, characteristic, complemented
14C2×#16810480C211yesmaximal, characteristic, complemented
15C2×#95×D53C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C22⋊D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C23×C4×D53C2211yescharacteristic
22C2×#13133195—28no—
23C2×#13133195C2218yescomplemented
24C2×C4×C22⋊D53—28no—
25C2×C4×C22⋊D53C2218yes—
26C22×C4⋊Dic53C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C22⋊Dic53C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810564C2218yescomplemented
40#16810559C2218yescomplemented
41#16810543C2218yescomplemented
42#16810535C2218yescomplemented
43#16810508C2218yescomplemented
44#16810504C2218yescomplemented
45#16810499C2218yes—
46#16810499C2218yes—
47#16810496C2218yescomplemented
48#16810482C2218yescomplemented
49#16810480C2218yescomplemented
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60#95×D53C2218yescomplemented
61C24×C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C53×#385C2218yescomplemented
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C22×Dic106—24no—
71C22×Dic106—42no—
72C22×Dic106—42no—
73C22×Dic106C2314yes—
74C22×C22⋊D53—24no—
75C22×C22⋊D53—24no—
76C22×C22⋊D53Q818yescomplemented
77C22×C22⋊D53C2314yes—
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C22×C4×D53—24no—
86C22×C4×D53—24no—
87C22×C4×D53—24no—
88C22×C4×D53—24no—
89C22×C4×D53—42no—
90C22×C4×D53—42no—
91C22×C4×D53—42no—
92C22×C4×D53—42no—
93C22×C4×D53D418yes—
94C22×C4×D53C2314yes—
95C22×C4×D53C2314yes—
96C22×C4×D53C2314yes—
97#13133195—232no—
98C4×C22⋊D53—232no—
99C2×C4⋊Dic53—24no—
100C2×C4⋊Dic53C2314yes—
101C2×#11719919—24no—
102C2×#11719919—24no—
103C2×#11719919—24no—
104C2×#11719919—24no—
105C2×#11719919—42no—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×C22⋊Dic53—24no—
112C2×C22⋊Dic53—24no—
113C2×C22⋊Dic53—42no—
114C2×C22⋊Dic53C2314yes—
115C2×C22⋊Dic53C2314yes—
116C2×C22⋊Dic53C2314yes—
117C2×#11719921—24no—
118C2×#11719921—24no—
119C2×#11719921—24no—
120C2×#11719921C2314yes—
121C2×#11719921C2314yes—
122C2×#11719921C2314yes—
123C2×C4×Dic53—24no—
124C2×C4×Dic53C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133#13133124C2314yes—
134#13133124C2314yes—
135C25×C53C2311yescharacteristic
136C23×C4×C53—24no—
137C23×C4×C53—42no—
138C23×C4×C53—42no—
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2314yes—
146C2×C4⋊C4×C53—24no—
147C2×C4⋊C4×C53—42no—
148C2×C4⋊C4×C53C2314yes—
149C2×C4⋊C4×C53C2314yes—
150C2×C22⋊C4×C53—24no—
151C2×C22⋊C4×C53—42no—
152C2×C22⋊C4×C53C2314yes—
153C2×C22⋊C4×C53C2314yes—
154#95×C53C2314yes—
155#95×C53C2314yes—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53C2×Q814yes—
163C24×C53C2412yes—
164C24×C53C2411yescharacteristic
165C23×D53—22no—
166C23×D53—22no—
167C23×D53—22no—
168C23×D53—22no—
169C23×D53C2×D414yes—
170C23×D53C2×Q814yes—
171C23×D53#4114yes—
172C23×D53C2412yes—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—28no—
190C22×C4×C53—44no—
191C22×C4×C53—44no—
192C22×C4×C53—416no—
193C22×C4×C53C2×D414yes—
194C22×C4×C53#4114yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2412yes—
197C22×C4×C53C2412yes—
198C22×C4×C53C2412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2412yes—
201C2×C22⋊D53—232no—
202C2×C22⋊D53—28no—
203C2×C22⋊D53—28no—
204C2×C22⋊D53C2×Q8116yescomplemented
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53—22no—
218C22×Dic53—22no—
219C22×Dic53—22no—
220C22×Dic53—22no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53C2×D414yes—
224C22×Dic53C2×Q814yes—
225C22×Dic53#4114yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C2×C4×D53—28no—
234C2×C4×D53—28no—
235C2×C4×D53—28no—
236C2×C4×D53—28no—
237C2×C4×D53—416no—
238C2×C4×D53—44no—
239C2×C4×D53—44no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×C4×D53—416no—
243C2×C4×D53—416no—
244C2×C4×D53C2×D4116yes—
245C2×Dic106—28no—
246C2×Dic106—44no—
247C2×Dic106—44no—
248C2×Dic106—416no—
249C4⋊C4×C53—28no—
250C4⋊C4×C53—44no—
251C22⋊C4×C53—28no—
252C22⋊C4×C53—44no—
253C22⋊Dic53—28no—
254C22⋊Dic53—28no—
255C22⋊Dic53—44no—
256#11719921—28no—
257#11719921—28no—
258#11719921—28no—
259C4⋊Dic53—28no—
260#11719919—28no—
261#11719919—28no—
262#11719919—28no—
263#11719919—28no—
264#11719919—44no—
265C4×Dic53—28no—
266C23×C53—28no—
267C23×C53—28no—
268C23×C53—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—44no—
279C23×C53C22×D412yes—
280C23×C53C22×Q814yes—
281C23×C53C22×Q812yes—
282C23×C53C2×#4112yes—
283C23×C53C2×#4112yes—
284C23×C53C2×#4112yes—
285C23×C53H(5,𝔽2)12yes—
286C23×C53H(5,𝔽2)12yes—
287C23×C53C2511yescharacteristic
288C22×D53—28no—
289C22×D53—28no—
290C22×D53—28no—
291C22×D53—28no—
292C22×D53—28no—
293C22×D53—28no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53C22⋊Q8116yes—
299C22×D53C22×D414yes—
300C22×D53C22×Q814yes—
301C22×D53C2×#4114yes—
302C2×C4×C53—28no—
303C2×C4×C53—28no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—416no—
321C2×C4×C53—44no—
322C2×C4×C53—44no—
323C2×C4×C53—44no—
324C2×C4×C53—44no—
325C2×C4×C53C22×D414yes—
326C2×C4×C53C2×#4114yes—
327C22⋊D53—232no—
328C2×Dic53—28no—
329C2×Dic53—28no—
330C2×Dic53—28no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—44no—
350C2×Dic53—44no—
351C2×Dic53—44no—
352C2×Dic53—44no—
353C2×Dic53C22×D414yes—
354C2×Dic53C22×Q814yes—
355C2×Dic53C2×#4114yes—
356C4×D53—416no—
357C4×D53—416no—
358C4×D53—416no—
359Dic106—416no—
360C2×#2564—531nomaximal, Sylow
361C22×C53—24no—
362C22×C53—24no—
363C22×C53—24no—
364C22×C53—416no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53C2×C22⋊Q814yes—
370C22×C53#53214yes—
371C22×C53#53414yes—
372C22×C53#55114yes—
373C22×C53#55114yes—
374C22×C53#55414yes—
375C22×C53#55414yes—
376C22×C53C23×D411yescharacteristic
377C22×C53C23×Q811yescharacteristic
378C22×C53C22×#4111yescharacteristic
379C22×C53C22×#4111yescharacteristic
380C22×C53C22×#4111yescharacteristic
381C22×C53C2×H(5,𝔽2)11yescharacteristic
382C22×C53C2×H(5,𝔽2)11yescharacteristic
383C2×D53—232no—
384C2×D53—24no—
385C2×D53—24no—
386C2×D53—24no—
387C2×D53—24no—
388C2×D53—24no—
389C2×D53—24no—
390C2×D53C2×C22⋊Q818yes—
391C4×C53—24no—
392C4×C53—24no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53—42no—
397Dic53—24no—
398Dic53—24no—
399Dic53—24no—
400Dic53—42no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C22×C22⋊Q8—531no—
405C22×C4×D4—531no—
406#2564—5316no—
407C2×#400—531no—
408C2×#399—531no—
409C2×#395—531no—
410C2×#393—531no—
411C2×#387—531no—
412C2×#387—531no—
413C2×#386—531no—
414C2×#386—531no—
415C2×#385—531no—
416C2×#385D5311yescharacteristic, complemented
417C2×#380—531no—
418C2×#380—531no—
419C22×#95—531no—
420C2×C53—44no—
421C2×C53#256418yescomplemented
422C2×C53C22×C22⋊Q811yescharacteristic
423C2×C53C2×#53211yescharacteristic
424C2×C53C2×#53411yescharacteristic
425C2×C53C2×#55111yescharacteristic
426C2×C53C2×#55111yescharacteristic
427C2×C53C2×#55411yescharacteristic
428C2×C53C2×#55411yescharacteristic
429D53—28no—
430C23×Q8—531no—
431C23×D4—531no—
432C24×C4—531no—
433C24×C4—531no—
434C24×C4—531no—
435C24×C4C2×D5311yescharacteristic
436C2×C22⋊Q8—538no—
437C2×C22⋊Q8—1068no—
438C2×C4×D4—538no—
439C2×C4×D4—1068no—
440C22×C4⋊C4—531no—
441C22×C4⋊C4—531no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—531no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4—531no—
446C22×C4⋊C4C2×D5311yescharacteristic
447C22×C4⋊C4C2×D5311yescharacteristic
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—531no—
452C22×C22⋊C4—531no—
453C22×C22⋊C4—531no—
454C22×C22⋊C4C2×D5311yescharacteristic
455C22×C22⋊C4C2×D5311yescharacteristic
456C22×C42—531no—
457#400—538no—
458#399—538no—
459#395—538no—
460#393—538no—
461#387—538no—
462#387—538no—
463#386—538no—
464#386—538no—
465#385—538no—
466#385C2×D5318yescomplemented
467#380—538no—
468#380—538no—
469C2×#95—531no—
470C2×#95—531no—
471C2×#95—531no—
472C2×#95—531no—
473C2×#95—531no—
474C2×#95—531no—
475C2×#95—531no—
476C2×#95—531no—
477C2×#95—531no—
478C2×#95—531no—
479C2×#95—538no—
480C2×#95C2×D5311yescharacteristic
481C2×#95C2×D5311yescharacteristic
482C53C2×#256411yescharacteristic, complemented, Sylow
483C25—531no—
484C25C22×D5311yescharacteristic
485C22×Q8—534no—
486C22×Q8—1064no—
487C22×Q8—2122no—
488C22×Q8—2122no—
489C22×D4—538no—
490C22×D4—534no—
491C22×D4—1064no—
492C22×D4—1064no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—42no—
496C23×C4—531no—
497C23×C4—531no—
498C23×C4—531no—
499C23×C4—538no—
500C23×C4—534no—
501C23×C4—531no—
502C23×C4—531no—
503C23×C4—531no—
504C23×C4—531no—
505C23×C4—534no—
506C23×C4—534no—
507C23×C4—1064no—
508C23×C4—1064no—
509C23×C4—1064no—
510C23×C4—1064no—
511C23×C4—2122no—
512C23×C4—2122no—
513C23×C4—2122no—
514C23×C4—2122no—
515C23×C4C22×D5311yescharacteristic
516C23×C4C22×D5311yescharacteristic
517C23×C4C22×D5311yescharacteristic
518C23×C4C22×D5311yescharacteristic
519C23×C4C22×D5311yescharacteristic
520C23×C4C22×D5311yescharacteristic
521C23×C4C22×D5314yes—
522C22⋊Q8—10632no—
523C4×D4—10632no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—42no—
526C2×C4⋊C4—534no—
527C2×C4⋊C4—534no—
528C2×C4⋊C4—534no—
529C2×C4⋊C4—534no—
530C2×C4⋊C4—534no—
531C2×C4⋊C4—534no—
532C2×C4⋊C4—1064no—
533C2×C4⋊C4—1064no—
534C2×C4⋊C4—1064no—
535C2×C4⋊C4—1064no—
536C2×C4⋊C4—1064no—
537C2×C4⋊C4—2122no—
538C2×C4⋊C4C22×D5314yes—
539C2×C4⋊C4C22×D5314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—534no—
543C2×C22⋊C4—534no—
544C2×C22⋊C4—534no—
545C2×C22⋊C4—534no—
546C2×C22⋊C4—534no—
547C2×C22⋊C4—534no—
548C2×C22⋊C4—1064no—
549C2×C22⋊C4—1064no—
550C2×C22⋊C4—1064no—
551C2×C22⋊C4—1064no—
552C2×C22⋊C4—1064no—
553C2×C22⋊C4—2122no—
554C2×C22⋊C4C22×D5314yes—
555C2×C22⋊C4C22×D5314yes—
556C2×C42—534no—
557C2×C42—1064no—
558#95—534no—
559#95—534no—
560#95—534no—
561#95—534no—
562#95—534no—
563#95—534no—
564#95—534no—
565#95—534no—
566#95—534no—
567#95—534no—
568#95C22×D5314yes—
569#95C22×D5314yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—534no—
577C24—534no—
578C24—534no—
579C24—532no—
580C24—1062no—
581C24—1062no—
582C24—1062no—
583C24—1062no—
584C24Q8×D5314yes—
585C24C23×D5312yes—
586C24C23×D5311yescharacteristic
587C2×Q8—1068no—
588C2×Q8—2124no—
589C2×Q8—2124no—
590C2×Q8—21216no—
591C2×D4—5316no—
592C2×D4—1068no—
593C2×D4—10632no—
594C2×D4—1068no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—28no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—416no—
615C22×C4—534no—
616C22×C4—534no—
617C22×C4—534no—
618C22×C4—532no—
619C22×C4—532no—
620C22×C4—532no—
621C22×C4—5316no—
622C22×C4—532no—
623C22×C4—532no—
624C22×C4—532no—
625C22×C4—532no—
626C22×C4—1068no—
627C22×C4—1068no—
628C22×C4—1068no—
629C22×C4—1062no—
630C22×C4—1062no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1062no—
637C22×C4—1062no—
638C22×C4—1062no—
639C22×C4—1062no—
640C22×C4—1062no—
641C22×C4—1062no—
642C22×C4—1062no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1068no—
648C22×C4—21216no—
649C22×C4—2124no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4—21216no—
654C22×C4—21216no—
655C22×C4#1171994514yes—
656C22×C4D4×D5314yes—
657C22×C4C23×D5312yes—
658C22×C4C23×D5312yes—
659C22×C4C23×D5312yes—
660C22×C4C23×D5312yes—
661C22×C4C23×D5312yes—
662C22×C4C23×D5312yes—
663C4⋊C4—28no—
664C4⋊C4—44no—
665C4⋊C4—1068no—
666C4⋊C4—1068no—
667C4⋊C4—1068no—
668C4⋊C4—1068no—
669C4⋊C4—1068no—
670C4⋊C4—2124no—
671C22⋊C4—28no—
672C22⋊C4—44no—
673C22⋊C4—1068no—
674C22⋊C4—1068no—
675C22⋊C4—1068no—
676C22⋊C4—1068no—
677C22⋊C4—1068no—
678C22⋊C4—2124no—
679C42—1068no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—5316no—
694C23—534no—
695C23—534no—
696C23—534no—
697C23—1068no—
698C23—1068no—
699C23—1068no—
700C23—1068no—
701C23—1068no—
702C23—1068no—
703C23—1062no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23C2×D4×D5312yes—
708C23C2×Q8×D5314yes—
709C23C2×Q8×D5312yes—
710C23#41×D5312yes—
711C23#41×D5312yes—
712C23C2×#1171994512yes—
713C23#1313326212yes—
714C23#1313326212yes—
715C23C24×D5311yescharacteristic
716Q8—21216no—
717D4—10632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—534no—
742C2×C4—534no—
743C2×C4—534no—
744C2×C4—1068no—
745C2×C4—1068no—
746C2×C4—1068no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—21216no—
766C2×C4—21216no—
767C2×C4—21216no—
768C2×C4—2124no—
769C2×C4—2124no—
770C2×C4—2124no—
771C2×C4—2124no—
772C2×C4C2×D4×D5314yes—
773C2×C4C2×#1171994514yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—416no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—538no—
783C22—1064no—
784C22—10632no—
785C22—1064no—
786C22—1064no—
787C22—1064no—
788C22—1064no—
789C22—1064no—
790C22C22⋊Q8×D5314yes—
791C22#1681117014yes—
792C22#1681118314yes—
793C22#1681130114yes—
794C22#1681130214yes—
795C22#1681132714yes—
796C22#1681132814yes—
797C22C22×D4×D5311yescharacteristic
798C22C22×Q8×D5311yescharacteristic
799C22C2×#41×D5311yescharacteristic
800C22C2×#41×D5311yescharacteristic
801C22C22×#1171994511yescharacteristic
802C22C2×#1313326211yescharacteristic
803C22C2×#1313326211yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—1064no—
811C4—1064no—
812C4—1064no—
813C4—2122no—
814C4—2122no—
815C4—2122no—
816C4—2122no—
817C2—44no—
818C2—1068no—
819C2#2027990018yesdirect product factor
820C2C2×C22⋊Q8×D5311yescharacteristic
821C2C2×#1681117011yescharacteristic
822C2C2×#1681118311yescharacteristic
823C2C2×#1681130111yescharacteristic
824C2C2×#1681130211yescharacteristic
825C2C2×#1681132711yescharacteristic
826C2C2×#1681132811yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53C2×#2564
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13133195C2semidirect
3. #20279900C2direct (N × H)
4. C2×#16810564C2semidirect
5. C2×#16810559C2semidirect
6. C2×#16810543C2semidirect
7. C2×#16810535C2semidirect
8. C2×#16810508C2semidirect
9. C2×#16810504C2semidirect
12. C2×#16810496C2semidirect
13. C2×#16810482C2semidirect
14. C2×#16810480C2semidirect
15. C2×#95×D53C2semidirect
16. C2×C53×#385C2semidirect
23. C2×#13133195C22semidirect
39. #16810564C22semidirect
40. #16810559C22semidirect
41. #16810543C22semidirect
42. #16810535C22semidirect
43. #16810508C22semidirect
44. #16810504C22semidirect
47. #16810496C22semidirect
48. #16810482C22semidirect
49. #16810480C22semidirect
60. #95×D53C22semidirect
66. C53×#385C22semidirect
76. C22×C22⋊D53Q8semidirect
204. C2×C22⋊D53C2×Q8semidirect
416. C2×#385D53semidirect
421. C2×C53#2564semidirect
466. #385C2×D53semidirect
482. C53C2×#2564semidirect
819. C2#20279900direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331952
C22×C4×C22⋊D532
#202799002
C2×#168105642
C2×#168105592
C2×#168105432
C2×#168105352
C2×#168105082
C2×#168105042
C2×#168104992
C2×#168104962
C2×#168104822
C2×#168104802
C2×#95×D532
C2×C53×#3852
C2×#256453