Finite Group Databasebeta

← #27399718

Subgroups — #27399718

Order 13568.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810701C211yesmaximal, characteristic, complemented
2C2×#16810624C211yesmaximal, characteristic, complemented
3C2×#16810632C211yesmaximal, characteristic, complemented
4#20277644C211yesmaximal, characteristic, complemented
5#20275648C211yesmaximal, characteristic, complemented
6#20275527C211yesmaximal, characteristic, complemented
7#20275154C211yesmaximal, characteristic, complemented
8#20275149C211yesmaximal, characteristic, complemented
9#20275038C211yesmaximal, characteristic, complemented
10#20275023C211yesmaximal, characteristic, complemented
11#20274730C211yesmaximal, characteristic, complemented
12#20274655C211yesmaximal, characteristic, complemented
13#20274650C211yesmaximal, characteristic, complemented
14C4×#13133141C211yesmaximal, characteristic, complemented
15C2×C53×#548C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18C2×#13133176C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20#16810701—24no—
21C2×C4⋊#88322C2211yescharacteristic
22#16810632—24no—
23#16810624—24no—
24C2×#13133141C2211yescharacteristic
25C2×#13133141C2211yescharacteristic
26C2×#13133141C2211yescharacteristic
27C2×#13133141C2211yescharacteristic
28C2×#13133141C2211yescharacteristic
29C2×#13133141C2211yescharacteristic
30C2×#13133141C2211yescharacteristic
31C2×#13133141C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×#13133138C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×C4×#88322C2211yescharacteristic
39#16810516—21no—
40#16810509—21no—
41#16810503—21no—
42#16810489C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45C4×C4⋊Dic53C2211yescharacteristic
46C22⋊C4×Dic53—21no—
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51C22×#41×C53C2211yescharacteristic
52C23×Q8×C53C2211yescharacteristic
53C53×#548—24no—
54C53×#548C418yescomplemented
55C2×#124×C53—21no—
56C2×#124×C53C2211yescharacteristic
57C2×C22⋊Q8×C53—21no—
58C2×C22⋊Q8×C53C2211yescharacteristic
59C2×#121×C53—21no—
60C2×#121×C53C2211yescharacteristic
61C2×C4×Q8×C53C2211yescharacteristic
62C2×C4×D4×C53—21no—
63C2×C4×D4×C53C2211yescharacteristic
64C23×Dic53—21no—
65C2×#11719917—22no—
66C2×#11719917—22no—
67C2×#11719917—22no—
68C2×#11719917—22no—
69C2×#11719917—41no—
70C2×#11719917—41no—
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133176—22no—
76#13133176—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×C22⋊Dic53—21no—
85C2×C22⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89C4⋊#88322—22no—
90#13133141—22no—
91#13133141—22no—
92#13133141—22no—
93#13133141—22no—
94#13133141—22no—
95#13133141—41no—
96#13133141—41no—
97#13133141D414yescomplemented
98#13133138—22no—
99#13133138—22no—
100#13133138—41no—
101#13133138—41no—
102C22⋊#88322—22no—
103C22⋊#88322—22no—
104C4×#88322—22no—
105#13133124—21no—
106#13133124—21no—
107#13133124—21no—
108#13133124—21no—
109#13133124—21no—
110C2×#41×C53—22no—
111C2×#41×C53—22no—
112C2×#41×C53—22no—
113C2×#41×C53—41no—
114C2×#41×C53—41no—
115C2×#41×C53C2×C414yes—
116C22×Q8×C53—21no—
117C22×Q8×C53—22no—
118C22×Q8×C53—22no—
119C22×Q8×C53—22no—
120C22×Q8×C53—41no—
121C22×Q8×C53—41no—
122C22×Q8×C53C2×C414yescomplemented
123C22×Q8×C53C2311yescharacteristic
124C22×Q8×C53C2311yescharacteristic
125C22×D4×C53—21no—
126C22×D4×C53—21no—
127C22×D4×C53D411yescharacteristic
128C22×D4×C53C2311yescharacteristic
129C23×C4×C53—21no—
130C23×C4×C53—21no—
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133#124×C53—28no—
134#124×C53—22no—
135#124×C53C2×C414yescomplemented
136C22⋊Q8×C53—28no—
137C22⋊Q8×C53—22no—
138C22⋊Q8×C53C2×C414yes—
139#121×C53—28no—
140#121×C53—22no—
141#121×C53C2×C414yescomplemented
142C4×Q8×C53—22no—
143C4×Q8×C53C2×C414yescomplemented
144C4×D4×C53—28no—
145C4×D4×C53C2×C414yes—
146C4×D4×C53D414yes—
147C2×C4⋊C4×C53—21no—
148C2×C4⋊C4×C53—21no—
149C2×C4⋊C4×C53D411yescharacteristic
150C2×C4⋊C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53D411yescharacteristic
156C2×C22⋊C4×C53D411yescharacteristic
157C2×C42×C53—21no—
158C2×C42×C53C2311yescharacteristic
159C24×C53—21no—
160C24×C53C2×D411yescharacteristic
161C24×C53C2×D411yescharacteristic
162#41×C53—28no—
163#41×C53—44no—
164#41×C53—44no—
165#41×C53—44no—
166C2×Q8×C53—24no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—28no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53—21no—
175C2×Q8×C53—21no—
176C2×Q8×C53—42no—
177C2×Q8×C53—42no—
178C2×Q8×C53—44no—
179C2×Q8×C53—44no—
180C2×Q8×C53—44no—
181C2×Q8×C53C22×C412yes—
182C2×Q8×C53C22×C412yes—
183C2×Q8×C53C2×D412yes—
184C2×Q8×C53#4112yes—
185C2×D4×C53—24no—
186C2×D4×C53—24no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—41no—
193C2×D4×C53—41no—
194C2×D4×C53—42no—
195C2×D4×C53—42no—
196C2×D4×C53—42no—
197C2×D4×C53—42no—
198C2×D4×C53C22⋊C414yes—
199C2×D4×C53C22×C412yes—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—24no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—24no—
213C22×C4×C53—42no—
214C22×C4×C53—42no—
215C22×C4×C53—42no—
216C22×C4×C53—42no—
217C22×C4×C53C22×C412yes—
218C22×C4×C53C22×C412yes—
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D412yes—
224C22×C4×C53C2×D412yes—
225C22×C4×C53C2411yescharacteristic
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—42no—
231C22×Dic53—42no—
232C22×Dic53—81no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53C22⋊C414yes—
237C4⋊C4×C53C22×C412yes—
238C22⋊C4×C53—24no—
239C22⋊C4×C53—24no—
240C22⋊C4×C53—24no—
241C22⋊C4×C53—24no—
242C22⋊C4×C53C22⋊C414yes—
243C22⋊C4×C53C22⋊C414yes—
244C42×C53—24no—
245C42×C53C22×C412yes—
246C42×C53C2×D412yes—
247C22⋊Dic53—42no—
248C22⋊Dic53—42no—
249C22⋊Dic53—81no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—42no—
258C4⋊Dic53C2×D412yes—
259C4×Dic53—42no—
260C4×Dic53—81no—
261#11719917—44no—
262#11719917—44no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322C2×D412yes—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—22no—
288C23×C53—41no—
289C23×C53—41no—
290C23×C53—41no—
291C23×C53—41no—
292C23×C53—41no—
293C23×C53—41no—
294C23×C53C2×C22⋊C412yes—
295C23×C53C2×C22⋊C412yes—
296C23×C53C22×D411yescharacteristic
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53—48no—
303Q8×C53—41no—
304Q8×C53—41no—
305Q8×C53C4×D414yes—
306D4×C53—22no—
307D4×C53—22no—
308D4×C53—44no—
309D4×C53—48no—
310D4×C53—48no—
311D4×C53—41no—
312D4×C53—41no—
313C2×C4×C53—22no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—22no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—22no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—48no—
335C2×C4×C53—48no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53C2×C22⋊C412yes—
341C2×C4×C53C2×C22⋊C412yes—
342C2×C4×C53C2×C22⋊C412yes—
343C2×C4×C53C2×C22⋊C412yes—
344C2×C4×C53C23×C411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C2×#4111yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C2×C4×C53H(5,𝔽2)11yescharacteristic
350C2×Dic53—22no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—41no—
361C2×Dic53—41no—
362C2×Dic53—84no—
363#88322—22no—
364#88322—41no—
365#88322—41no—
366#88322—41no—
367#22429—531nomaximal, Sylow
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—41no—
375C22×C53—41no—
376C22×C53—41no—
377C22×C53—41no—
378C22×C53—41no—
379C22×C53—41no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53—42no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—81no—
386C22×C53—81no—
387C22×C53—81no—
388C22×C53—81no—
389C22×C53C22×C22⋊C411yescharacteristic
390C22×C53D4211yescharacteristic
391C22×C53#54611yescharacteristic
392C22×C53#57511yescharacteristic
393C22×C53#57511yescharacteristic
394C22×C53#57711yescharacteristic
395C22×C53#57811yescharacteristic
396C4×C53—22no—
397C4×C53—22no—
398C4×C53—24no—
399C4×C53—22no—
400C4×C53—22no—
401C4×C53—42no—
402C4×C53—42no—
403C4×C53C2×C4×D411yescharacteristic
404C4×C53#51811yescharacteristic
405C4×C53D4211yescharacteristic
406C4×C53#54611yescharacteristic
407Dic53—42no—
408Dic53—81no—
409Dic53—81no—
410Dic53—81no—
411C2×#548D5311yescharacteristic
412C2×#436—531no—
413C2×#417—531no—
414C2×#419—531no—
415#2352—531no—
416#1983—531no—
417#1958—531no—
418#1895—531no—
419#1894—531no—
420#1875—531no—
421#1872—531no—
422#1805—531no—
423#1788—531no—
424#1787—531no—
425C4×#103—531no—
426C2×C53—42no—
427C2×C53—42no—
428C2×C53—82no—
429C2×C53D4×C22⋊C411yescharacteristic
430C2×C53#289611yescharacteristic
431C2×C53#289811yescharacteristic
432C2×C53#327511yescharacteristic
433C2×C53#327711yescharacteristic
434C2×C53#332611yescharacteristic
435C2×C53#332711yescharacteristic
436C22×#41C2×D5311yescharacteristic
437C23×Q8C2×D5311yescharacteristic
438C22×M16—531no—
439C22×M16—531no—
440#548—24no—
441#548Dic5318yescomplemented
442C2×#124—21no—
443C2×#124C2×D5311yescharacteristic
444C2×C22⋊Q8—21no—
445C2×C22⋊Q8C2×D5311yescharacteristic
446C2×#121—21no—
447C2×#121C2×D5311yescharacteristic
448C2×C4×Q8C2×D5311yescharacteristic
449C2×C4×D4—21no—
450C2×C4×D4C2×D5311yescharacteristic
451C2×#117—531no—
452C22×C4⋊C4—531no—
453#436—1064no—
454C2×C4⋊C8—531no—
455#419—1064no—
456#417—1064no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102—531no—
468C2×#102—531no—
469C2×C22⋊C8—531no—
470C2×C22⋊C8—531no—
471C2×C4×C8—531no—
472#388—1061no—
473#387—1061no—
474#386—1061no—
475#382—531no—
476#380—531no—
477#380—531no—
478C4×C4⋊C4—531no—
479C4×C22⋊C4—1061no—
480#340—531no—
481#340—531no—
482#340—531no—
483#340—531no—
484C53#2242911yescharacteristic, complemented, Sylow
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41C2×Dic5314yes—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C2×Dic5314yescomplemented
498C22×Q8C22×D5311yescharacteristic
499C22×Q8C22×D5311yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C22⋊D5311yescharacteristic
503C22×D4C22×D5311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—1061no—
507C23×C4C22×D5311yescharacteristic
508C23×C4C22×D5311yescharacteristic
509C2×M16—1062no—
510C2×M16—1062no—
511C2×M16—1062no—
512C2×M16—1062no—
513C2×M16—2121no—
514C2×M16—2121no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8—531no—
519#124—28no—
520#124—22no—
521#124C2×Dic5314yescomplemented
522C22⋊Q8—22no—
523C22⋊Q8—28no—
524C22⋊Q8C2×Dic5314yes—
525#121—28no—
526#121—22no—
527#121C2×Dic5314yescomplemented
528C4×Q8—22no—
529C4×Q8C2×Dic5314yescomplemented
530C4×D4—28no—
531C4×D4C2×Dic5314yes—
532C4×D4C22⋊D5314yes—
533#117—1062no—
534#117—2121no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—531no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—1062no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—2121no—
544C2×C4⋊C4C22⋊D5311yescharacteristic
545C2×C4⋊C4C22×D5311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4C22⋊D5311yescharacteristic
554C2×C22⋊C4C22⋊D5311yescharacteristic
555C2×C42—21no—
556C2×C42—1061no—
557C2×C42—1061no—
558C2×C42C22×D5311yescharacteristic
559C4⋊C8—1062no—
560#103—534no—
561#103—1062no—
562#103—1062no—
563#103—1062no—
564#103—1062no—
565#103—1062no—
566#103—2121no—
567#103—2121no—
568#102—1062no—
569#102—1062no—
570#102—2121no—
571#102—2121no—
572C22⋊C8—1062no—
573C22⋊C8—1062no—
574C4×C8—1062no—
575#95—1061no—
576#95—1061no—
577#95—1061no—
578#95—1061no—
579#95—1061no—
580C24—21no—
581C24C2×C22⋊D5311yescharacteristic
582C24C2×C22⋊D5311yescharacteristic
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—28no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8D4×D5312yes—
603C2×Q8#1171994712yes—
604C2×Q8C22×Dic5312yes—
605C2×Q8C22×Dic5312yes—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4C22⋊Dic5314yes—
620C2×D4C22×Dic5312yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—4241no—
643C22×C4—2122no—
644C22×C4—2122no—
645C22×C4C22×Dic5312yes—
646C22×C4C22×Dic5312yes—
647C22×C4C2×C22⋊D5311yescharacteristic
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5312yes—
652C22×C4C2×C22⋊D5312yes—
653C22×C4C23×D5311yescharacteristic
654M16—2124no—
655M16—2124no—
656C2×C8—532no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—1061no—
664C2×C8—1061no—
665C2×C8—1061no—
666C2×C8—1061no—
667C2×C8—1061no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—532no—
672C4⋊C4—1061no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4—1061no—
679C4⋊C4—2122no—
680C4⋊C4C22⋊Dic5314yes—
681C4⋊C4C22×Dic5312yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—4241no—
687C22⋊C4—2122no—
688C22⋊C4—2122no—
689C22⋊C4C22⋊Dic5314yes—
690C22⋊C4C22⋊Dic5314yes—
691C42—24no—
692C42—4241no—
693C42—2122no—
694C42C22×Dic5312yes—
695C42C2×C22⋊D5312yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic5312yes—
716C23C2×C22⋊Dic5312yes—
717C23C22×C22⋊D5311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8D4×Dic5314yes—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4—41no—
733D4—41no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—1062no—
762C2×C4—4244no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4—2121no—
769C2×C4—2121no—
770C2×C4—2121no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4—2121no—
774C2×C4C2×C22⋊Dic5312yes—
775C2×C4C2×C22⋊Dic5312yes—
776C2×C4C2×C22⋊Dic5312yes—
777C2×C4C2×C22⋊Dic5312yes—
778C2×C4C23×Dic5311yescharacteristic
779C2×C4C2×D4×D5311yescharacteristic
780C2×C4C22×C22⋊D5311yescharacteristic
781C2×C4C2×#1171994711yescharacteristic
782C2×C4#1313326211yescharacteristic
783C2×C4#1313326211yescharacteristic
784C8—1062no—
785C8—2121no—
786C8—2121no—
787C8—2121no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22C22×C22⋊Dic5311yescharacteristic
810C22D4×C22⋊D5311yescharacteristic
811C22#1681126711yescharacteristic
812C22#1681142111yescharacteristic
813C22#1681142111yescharacteristic
814C22#1681143111yescharacteristic
815C22#1681143811yescharacteristic
816C4—22no—
817C4—22no—
818C4—24no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—4241no—
824C4—4241no—
825C4—4241no—
826C4—2122no—
827C4C2×D4×Dic5311yescharacteristic
828C4#1681109811yescharacteristic
829C4D4×C22⋊D5311yescharacteristic
830C4#1681126711yescharacteristic
831C2—42no—
832C2—42no—
833C2—82no—
834C2D4×C22⋊Dic5311yescharacteristic
835C2#2028323411yescharacteristic
836C2#2028324811yescharacteristic
837C2#2028634711yescharacteristic
838C2#2028636811yescharacteristic
839C2#2028696811yescharacteristic
840C2#2028698311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC2×C53×#548C2
socleC23×C53C22×D4
cosocleC22×C4×C53C24
hypercenterC2×#548D53
hypocenterC53#22429
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16810701C2semidirect
2. C2×#16810624C2semidirect
3. C2×#16810632C2semidirect
4. #20277644C2semidirect
5. #20275648C2semidirect
6. #20275527C2semidirect
7. #20275154C2semidirect
8. #20275149C2semidirect
9. #20275038C2semidirect
10. #20275023C2semidirect
11. #20274730C2semidirect
12. #20274655C2semidirect
13. #20274650C2semidirect
14. C4×#13133141C2semidirect
54. C53×#548C4semidirect
97. #13133141D4semidirect
122. C22×Q8×C53C2×C4semidirect
135. #124×C53C2×C4semidirect
141. #121×C53C2×C4semidirect
143. C4×Q8×C53C2×C4semidirect
441. #548Dic53semidirect
484. C53#22429semidirect
497. C22×Q8C2×Dic53semidirect
521. #124C2×Dic53semidirect
527. #121C2×Dic53semidirect
529. C4×Q8C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168107012
C2×#168106242
C2×#168106322
#202776442
#202756482
#202755272
#202751542
#202751492
#202750382
#202750232
#202747302
#202746552
#202746502
C4×#131331412
C2×C53×#5482
#2242953