Finite Group Databasebeta

← C2×#20257307 #27124782

Subgroups — C2×#20257307 #27124782

Order 12032.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257307C2132yesmaximal, direct product factor
2C2×#15689820C214yesmaximal, complemented
3C2×#15689818C214yesmaximal, complemented
4C2×#15689816C214yesmaximal, complemented
5C2×#15689810C214yesmaximal, complemented
6C2×#15689736C211yesmaximal, characteristic, complemented
7C2×#15689735C211yesmaximal, characteristic, complemented
8C2×#15689727C211yesmaximal, characteristic, complemented
9C2×#15689702C212yesmaximal, complemented
10C2×#15689671C211yesmaximal, characteristic, complemented
11C2×#15689655C212yesmaximal, complemented
12C2×#15689654C212yesmaximal, complemented
13C2×#125×D47C211yesmaximal, characteristic, complemented
14C2×#15689602C212yesmaximal, complemented
15C2×#15689591C211yesmaximal, characteristic, complemented
16C2×C47×#540C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×#10625352C2212yes—
19#15689820C22164yescomplemented
20#15689818C22164yescomplemented
21#15689816C22164yescomplemented
22#15689810C22164yescomplemented
23#15689736C22116yescomplemented
24#15689735C22116yescomplemented
25#15689727C22116yescomplemented
26#15689702C22132yescomplemented
27#15689671C22116yescomplemented
28C2×#13094024C2211yescharacteristic
29#15689655C22132yescomplemented
30#15689654C22132yescomplemented
31C2×#13094019C2214yes—
32C2×#13094017C2214yes—
33C2×#13094017C2214yes—
34C2×#13094017C2214yes—
35C2×#13094016C2211yescharacteristic
36C2×#13094015C2212yes—
37C2×#13094015C2214yes—
38C2×#13094014C2214yes—
39C2×#13094014C2214yes—
40#125×D47C22116yescomplemented
41C2×#13094011C2212yes—
42C2×#13094006C2214yes—
43C2×#13094005C2214yes—
44C2×#13094005C2214yes—
45C2×#13094004C2212yes—
46C2×#13094003C2212yes—
47C2×#13094001C2214yes—
48C2×#13093997C2214yes—
49C2×#13093996C2214yes—
50C2×#13093996C2214yes—
51C2×#13093995C2214yes—
52C2×#13093995C2212yes—
53C2×#13093995C2214yes—
54#15689602C22132yescomplemented
55#15689591C22116yescomplemented
56C2×C4×Dic94C2212yes—
57C2×#13093989C2212yes—
58C2×#13093989C2212yes—
59C2×D4×Dic47C2212yes—
60C2×D4×Dic47C2214yes—
61C2×D4×Dic47C2214yes—
62C2×#13093986C2212yes—
63C2×C4×C22⋊D47C2214yes—
64C2×C4×C22⋊D47C2214yes—
65C2×(C22⋊D47)⋊C4C2212yes—
66C2×(C22⋊D47)⋊C4C2212yes—
67C2×(C22⋊D47)⋊C4C2214yes—
68C2×#13093983C2214yes—
69C2×#13093981C2211yescharacteristic
70C2×#13093981C2211yescharacteristic
71C2×#13093980C2214yes—
72C2×#13093980C2214yes—
73C22×Dic47⋊C4C2214yes—
74C2×C4⋊C4×D47C2212yes—
75C2×C4⋊C4×D47C2214yes—
76C22×C4×Dic47C2211yescharacteristic
77C2×C42×D47C2211yescharacteristic
78C2×C42×D47C2211yescharacteristic
79C47×#540C22116yescomplemented
80C2×#127×C47C2211yescharacteristic
81C2×#125×C47C2211yescharacteristic
82C2×#123×C47C2214yes—
83C2×#121×C47C2214yes—
84C2×#121×C47C2212yes—
85C2×C4×D4×C47C2212yes—
86C2×#117×C47C2211yescharacteristic
87C2×#10625350—28no—
88C2×#10625350C2318yes—
89C2×#10625352—216no—
90C2×#10625352C23116yes—
91C22×Dic94C2311yescharacteristic
92C22×Dic94C2312yes—
93C22×D188C2311yescharacteristic
94C22×C22⋊D47C2311yescharacteristic
95C22×C22⋊D47C2311yescharacteristic
96C22×C22⋊D47C2314yes—
97C22×C22⋊D47C2314yes—
98C23×Dic47C2314yes—
99C23×Dic47C2312yes—
100C23×Dic47C2314yes—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2312yes—
103C22×C4×D47C2312yes—
104C22×C4×D47C2314yes—
105C22×C4×D47C2311yescharacteristic
106#13094024C2318yes—
107#13094019C23132yes—
108#13094017C23132yes—
109#13094017C23132yes—
110#13094017C23132yes—
111#13094016C2318yes—
112#13094015C23132yes—
113#13094015C23116yes—
114#13094014C23132yes—
115#13094014C23132yes—
116#13094011C23116yes—
117#13094006C23132yes—
118#13094005C23132yes—
119#13094005C23132yes—
120#13094004C23116yes—
121#13094003C23116yes—
122#13094001C23132yes—
123#13093997C23132yes—
124#13093996C23132yes—
125#13093996C23132yes—
126#13093995C23132yes—
127#13093995C23132yes—
128#13093995C23116yes—
129C4×Dic94C23116yes—
130#13093989C23116yes—
131#13093989C23116yes—
132D4×Dic47C23132yes—
133D4×Dic47C23132yes—
134D4×Dic47C23116yes—
135#13093986C23116yes—
136C4×C22⋊D47C23132yes—
137C4×C22⋊D47C23132yes—
138(C22⋊D47)⋊C4C23116yes—
139(C22⋊D47)⋊C4C23132yes—
140(C22⋊D47)⋊C4C23116yes—
141#13093983C23132yes—
142#13093981C2318yes—
143#13093981C2318yes—
144#13093980C23132yes—
145#13093980C23132yes—
146C2×C4⋊Dic47C2314yes—
147C2×C4⋊Dic47C2312yes—
148C2×C4⋊Dic47C2314yes—
149C2×C4⋊Dic47C2314yes—
150C2×Dic47⋊C4C23132yes—
151C2×Dic47⋊C4C2314yes—
152C2×Dic47⋊C4C2314yes—
153C2×Dic47⋊C4C2314yes—
154C2×Dic47⋊C4C2312yes—
155C2×Dic47⋊C4C2314yes—
156C2×Dic47⋊C4C2314yes—
157C2×Dic47⋊C4C2314yes—
158C2×Dic47⋊C4C2312yes—
159C4⋊C4×D47C23132yes—
160C4⋊C4×D47C23116yes—
161C2×C22⋊Dic47C2314yes—
162C2×C22⋊Dic47C2314yes—
163C2×C22⋊Dic47C2314yes—
164C2×C22⋊Dic47C2314yes—
165C2×C22⋊Dic47C2314yes—
166C2×(C2×D47)⋊C4C2312yes—
167C2×(C2×D47)⋊C4C2312yes—
168C2×(C2×D47)⋊C4C2314yes—
169C2×C4×Dic47C2311yescharacteristic
170C2×C4×Dic47C2312yes—
171C2×C4×Dic47C2312yes—
172C2×C4×Dic47C2312yes—
173C2×C4×Dic47C2311yescharacteristic
174C2×C4×Dic47C2318yes—
175C2×C4×Dic47C2314yes—
176C2×C4×Dic47C2314yes—
177C42×D47C2318yes—
178C42×D47C2318yes—
179C22×D4×C47C2312yes—
180C22×D4×C47C2314yes—
181C22×D4×C47C2314yes—
182C23×C4×C47C2311yescharacteristic
183C23×C4×C47C2314yes—
184#127×C47C2318yes—
185#125×C47C2318yes—
186#123×C47C23132yes—
187#121×C47C23132yes—
188#121×C47C23116yes—
189C4×D4×C47C23116yes—
190#117×C47C2318yes—
191C2×C4⋊C4×C47C2312yes—
192C2×C4⋊C4×C47C2312yes—
193C2×C4⋊C4×C47C2314yes—
194C2×C22⋊C4×C47C2312yes—
195C2×C22⋊C4×C47C2314yes—
196C2×C22⋊C4×C47C2314yes—
197C2×C42×C47C2311yescharacteristic
198C2×C42×C47C2311yescharacteristic
199C24×C47C2414yes—
200C24×C47C2411yescharacteristic
201C23×D47C2411yescharacteristic
202C23×D47C2411yescharacteristic
203C2×D4×C47—28no—
204C2×D4×C47—48no—
205C2×D4×C47—48no—
206C2×D4×C47C2418yes—
207C2×D4×C47C24116yes—
208C2×D4×C47C24116yes—
209C22×C4×C47—24no—
210C22×C4×C47—48no—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2411yescharacteristic
214C22×C4×C47C2414yes—
215C22×C4×C47C2414yes—
216C22×C4×C47C24116yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—216no—
219C2×C22⋊D47—24no—
220C2×C22⋊D47—24no—
221C2×C22⋊D47—48no—
222C2×C22⋊D47C2414yes—
223C2×C22⋊D47C2414yes—
224C2×C22⋊D47C24116yes—
225C2×C22⋊D47C24116yes—
226C22×Dic47—216no—
227C22×Dic47—44no—
228C22×Dic47—48no—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2414yes—
232C22×Dic47C2411yescharacteristic
233C22×Dic47C2414yes—
234C22×Dic47C24116yes—
235C22×Dic47C2418yes—
236C22×Dic47C24116yes—
237C22×Dic47C2411yescharacteristic
238#10625352—264no—
239#10625350—232no—
240C2×D188—24no—
241C2×D188C2414yes—
242C2×C4×D47—24no—
243C2×C4×D47—44no—
244C2×C4×D47—44no—
245C2×C4×D47—48no—
246C2×C4×D47#4118yes—
247C2×C4×D47C2414yes—
248C2×C4×D47C2418yes—
249C2×C4×D47C2418yes—
250C2×C4×D47C24116yes—
251C2×C4×D47C2414yes—
252C2×Dic94—28no—
253C2×Dic94—24no—
254C2×Dic94C2414yes—
255C2×Dic94C2418yes—
256C4⋊C4×C47C2418yes—
257C4⋊C4×C47C2418yes—
258C4⋊C4×C47C24116yes—
259C22⋊C4×C47C2418yes—
260C22⋊C4×C47C24116yes—
261C22⋊C4×C47C24116yes—
262C42×C47C2414yes—
263C42×C47C2414yes—
264C22⋊Dic47C24116yes—
265C22⋊Dic47C24116yes—
266C22⋊Dic47C24116yes—
267C22⋊Dic47C24116yes—
268C22⋊Dic47C24116yes—
269(C2×D47)⋊C4C2418yes—
270(C2×D47)⋊C4C2418yes—
271(C2×D47)⋊C4C24116yes—
272C4⋊Dic47C24116yes—
273C4⋊Dic47C2418yes—
274C4⋊Dic47C24116yes—
275C4⋊Dic47C24116yes—
276Dic47⋊C4C24116yes—
277Dic47⋊C4C24116yes—
278Dic47⋊C4C24116yes—
279Dic47⋊C4C2418yes—
280Dic47⋊C4C24116yes—
281Dic47⋊C4C24116yes—
282Dic47⋊C4C24116yes—
283Dic47⋊C4C2418yes—
284C4×Dic47C2414yes—
285C4×Dic47C2418yes—
286C4×Dic47C2418yes—
287C4×Dic47C2418yes—
288C4×Dic47C2414yes—
289C4×Dic47C24116yes—
290C4×Dic47C24116yes—
291C23×C47—28no—
292C23×C47—22no—
293C23×C47—28no—
294C23×C47—24no—
295C23×C47—28no—
296C23×C47C2518yes—
297C23×C47C2512yes—
298C23×C47C2511yescharacteristic
299C22×D47—24no—
300C22×D47—22no—
301C22×D47—24no—
302C22×D47C2×#4114yes—
303C22×D47C2512yes—
304C22×D47C2512yes—
305D4×C47—216no—
306D4×C47—416no—
307D4×C47—416no—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—28no—
311C2×C4×C47—24no—
312C2×C4×C47—28no—
313C2×C4×C47—416no—
314C2×C4×C47C2×#4114yes—
315C2×C4×C47C2514yes—
316C2×C4×C47C2512yes—
317C2×C4×C47C2514yes—
318C2×C4×C47C2518yes—
319C2×C4×C47C2512yes—
320C22⋊D47—28no—
321C22⋊D47—232no—
322C22⋊D47—28no—
323C22⋊D47—416no—
324C2×Dic47—22no—
325C2×Dic47—28no—
326C2×Dic47—24no—
327C2×Dic47—28no—
328C2×Dic47—24no—
329C2×Dic47—232no—
330C2×Dic47—48no—
331C2×Dic47—416no—
332C2×Dic47C2×#4114yes—
333C2×Dic47C2514yes—
334C2×Dic47C2514yes—
335C2×Dic47C2518yes—
336C2×Dic47C2512yes—
337C2×Dic47C2518yes—
338C2×Dic47C2512yes—
339D188—28no—
340C4×D47—28no—
341C4×D47—48no—
342C4×D47—48no—
343C4×D47—416no—
344C4×D47C2×#41116yes—
345Dic94—216no—
346Dic94—28no—
347C2×#3512—471nomaximal, Sylow
348C22×C47—28no—
349C22×C47—22no—
350C22×C47—28no—
351C22×C47—24no—
352C22×C47—28no—
353C22×C47—416no—
354C22×C47—44no—
355C22×C47C22×#4112yes—
356C22×C47#58514yes—
357C22×C47C2611yescharacteristic
358C2×D47—24no—
359C2×D47—28no—
360C2×D47—22no—
361C2×D47—24no—
362C2×D47—44no—
363C2×D47C22×#4114yes—
364C4×C47—22no—
365C4×C47—24no—
366C4×C47—28no—
367C4×C47—24no—
368C4×C47C22×#4114yes—
369Dic47—22no—
370Dic47—28no—
371Dic47—24no—
372Dic47—28no—
373Dic47—24no—
374Dic47C22×#4114yes—
375#3512—4732no—
376C2×#553—474no—
377C2×#553—474no—
378C2×#553—474no—
379C2×#552—474no—
380C2×#541—471no—
381C2×#541—471no—
382C2×#540—471no—
383C2×#540D4711yescharacteristic, complemented
384C2×#537—472no—
385C2×#532—471no—
386C2×#529—472no—
387C2×#529—472no—
388C22×#125—471no—
389C2×#520—472no—
390C2×C4×#41—471no—
391C2×C47—48no—
392C2×C47—42no—
393C2×C47#351214yescomplemented
394C2×C47C23×#4111yescharacteristic
395C2×C47C2×#58512yes—
396D47—24no—
397D47—42no—
398C22×#41—472no—
399C22×#41—471no—
400#553—4764no—
401#553—4764no—
402#553—4764no—
403#552—4764no—
404#541—4716no—
405#541—4716no—
406#540—4716no—
407#540C2×D47116yescomplemented
408#537—4732no—
409#532—4716no—
410C2×C4⋊Q8—471no—
411C2×#127C2×D4711yescharacteristic
412#529—4732no—
413#529—4732no—
414C2×#126—474no—
415C2×#126—474no—
416C2×#126—474no—
417C2×#126—474no—
418C2×#125—4716no—
419C2×#125—472no—
420C2×#125—474no—
421C2×#125—474no—
422C2×#125—474no—
423C2×#125—471no—
424C2×#125C2×D4711yescharacteristic
425C2×#124—472no—
426C2×#123—474no—
427C2×#123—474no—
428C2×#123—474no—
429C2×#123C2×D4714yes—
430C2×C22⋊Q8—472no—
431C2×C22⋊Q8—472no—
432C2×C22⋊Q8—474no—
433C2×#121—472no—
434C2×#121—474no—
435C2×#121—474no—
436C2×#121—474no—
437C2×#121—474no—
438C2×#121—474no—
439C2×#121C2×D4712yes—
440C2×#121C2×D4714yes—
441#520—4732no—
442C4×#41—4716no—
443C2×C4×Q8—472no—
444C2×C4×Q8—472no—
445C2×C4×Q8—472no—
446C2×C4×D4—472no—
447C2×C4×D4—474no—
448C2×C4×D4—474no—
449C2×C4×D4—474no—
450C2×C4×D4—474no—
451C2×C4×D4—472no—
452C2×C4×D4—472no—
453C2×C4×D4—472no—
454C2×C4×D4—474no—
455C2×C4×D4C2×D4712yes—
456C2×#117—474no—
457C2×#117—474no—
458C2×#117—474no—
459C2×#117—471no—
460C2×#117—471no—
461C2×#117C2×D4711yescharacteristic
462C22×C4⋊C4—474no—
463C22×C4⋊C4—472no—
464C22×C4⋊C4—474no—
465C22×C42—471no—
466C22×C42—471no—
467C22×C42—471no—
468C47C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—4716no—
470C2×#41—478no—
471C2×#41—948no—
472C2×#41—9416no—
473C22×Q8—471no—
474C22×Q8—472no—
475C22×D4—471no—
476C22×D4—474no—
477C22×D4—471no—
478C22×D4—474no—
479C22×D4—471no—
480C22×D4C22×D4712yes—
481C22×D4C22×D4714yes—
482C22×D4C22×D4714yes—
483C23×C4—471no—
484C23×C4—474no—
485C23×C4—474no—
486C23×C4—472no—
487C23×C4—471no—
488C23×C4—474no—
489C23×C4—472no—
490C23×C4—472no—
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4714yes—
493C4⋊Q8—478no—
494#127C22×D4718yes—
495#126—4732no—
496#126—4732no—
497#126—4732no—
498#126—4732no—
499#125—4716no—
500#125—4732no—
501#125—4732no—
502#125—4732no—
503#125—478no—
504#125C22×D4718yes—
505#124—4716no—
506#123—4732no—
507#123—4732no—
508#123—4732no—
509#123C22×D47132yes—
510C22⋊Q8—4716no—
511C22⋊Q8—4716no—
512C22⋊Q8—4732no—
513#121—4716no—
514#121—4732no—
515#121—4732no—
516#121—4732no—
517#121—4732no—
518#121—4732no—
519#121C22×D47116yes—
520#121C22×D47132yes—
521C4×Q8—4716no—
522C4×Q8—4716no—
523C4×Q8—4716no—
524C4×D4—4716no—
525C4×D4—4732no—
526C4×D4—4732no—
527C4×D4—4732no—
528C4×D4—4732no—
529C4×D4—4716no—
530C4×D4—4716no—
531C4×D4—4716no—
532C4×D4—4732no—
533C4×D4C22×D47116yes—
534#117—4732no—
535#117—4732no—
536#117—4732no—
537#117—478no—
538#117—478no—
539#117C22×D4718yes—
540C2×C4⋊C4—472no—
541C2×C4⋊C4—474no—
542C2×C4⋊C4—474no—
543C2×C4⋊C4—474no—
544C2×C4⋊C4—472no—
545C2×C4⋊C4—474no—
546C2×C4⋊C4—474no—
547C2×C4⋊C4—4732no—
548C2×C4⋊C4—474no—
549C2×C4⋊C4—472no—
550C2×C4⋊C4—474no—
551C2×C4⋊C4—474no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—4716no—
554C2×C4⋊C4—4732no—
555C2×C4⋊C4C22×D4712yes—
556C2×C4⋊C4C22×D4714yes—
557C2×C4⋊C4C22×D4712yes—
558C2×C22⋊C4—474no—
559C2×C22⋊C4—474no—
560C2×C22⋊C4—474no—
561C2×C22⋊C4—474no—
562C2×C22⋊C4—474no—
563C2×C22⋊C4—472no—
564C2×C22⋊C4—472no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4C22×D4714yes—
567C2×C22⋊C4C22×D4714yes—
568C2×C22⋊C4C22×D4712yes—
569C2×C42—471no—
570C2×C42—474no—
571C2×C42—474no—
572C2×C42—472no—
573C2×C42—472no—
574C2×C42—472no—
575C2×C42—478no—
576C2×C42—471no—
577C2×C42—478no—
578C2×C42—478no—
579C2×C42C22×D4711yescharacteristic
580C2×C42C22×D4711yescharacteristic
581C24—471no—
582C24—471no—
583C24C23×D4711yescharacteristic
584C24C23×D4714yes—
585#41—9432no—
586#41—9464no—
587C2×Q8—474no—
588C2×Q8—478no—
589C2×Q8—944no—
590C2×Q8—948no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—474no—
595C2×D4—474no—
596C2×D4—4716no—
597C2×D4—4716no—
598C2×D4—474no—
599C2×D4—944no—
600C2×D4—944no—
601C2×D4—944no—
602C2×D4—9416no—
603C2×D4—1888no—
604C2×D4C23×D4718yes—
605C2×D4C23×D47116yes—
606C2×D4C23×D47116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—471no—
610C22×C4—478no—
611C22×C4—474no—
612C22×C4—4716no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—474no—
616C22×C4—471no—
617C22×C4—474no—
618C22×C4—478no—
619C22×C4—4716no—
620C22×C4—474no—
621C22×C4—478no—
622C22×C4—478no—
623C22×C4—4716no—
624C22×C4—9416no—
625C22×C4—944no—
626C22×C4—1884no—
627C22×C4—1888no—
628C22×C4—1884no—
629C22×C4—1884no—
630C22×C4—1888no—
631C22×C4C23×D4714yes—
632C22×C4C23×D4712yes—
633C22×C4C23×D4711yescharacteristic
634C22×C4C23×D4712yes—
635C22×C4C23×D4714yes—
636C22×C4C23×D47116yes—
637C22×C4C23×D4711yescharacteristic
638C4⋊C4—478no—
639C4⋊C4—4716no—
640C4⋊C4—4716no—
641C4⋊C4—4716no—
642C4⋊C4—4716no—
643C4⋊C4—4716no—
644C4⋊C4—478no—
645C4⋊C4—4716no—
646C4⋊C4—4716no—
647C4⋊C4—478no—
648C4⋊C4—4716no—
649C4⋊C4—4716no—
650C4⋊C4C23×D4718yes—
651C4⋊C4C23×D47116yes—
652C4⋊C4C23×D4718yes—
653C22⋊C4—4716no—
654C22⋊C4—4716no—
655C22⋊C4—4716no—
656C22⋊C4—4716no—
657C22⋊C4—4716no—
658C22⋊C4—478no—
659C22⋊C4—478no—
660C22⋊C4—4716no—
661C22⋊C4C23×D47116yes—
662C22⋊C4C23×D47116yes—
663C22⋊C4C23×D4718yes—
664C42—474no—
665C42—474no—
666C42—478no—
667C42—478no—
668C42—478no—
669C42—4716no—
670C42—4716no—
671C42C23×D4714yes—
672C42C23×D4714yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—474no—
679C23—472no—
680C23—472no—
681C23—944no—
682C23—942no—
683C23—944no—
684C23C24×D4712yes—
685C23C24×D4718yes—
686C23C24×D4711yescharacteristic
687Q8—948no—
688Q8—9416no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—948no—
693D4—948no—
694D4—948no—
695D4—9432no—
696D4—18816no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—474no—
704C2×C4—472no—
705C2×C4—4716no—
706C2×C4—474no—
707C2×C4—474no—
708C2×C4—478no—
709C2×C4—472no—
710C2×C4—478no—
711C2×C4—9432no—
712C2×C4—942no—
713C2×C4—948no—
714C2×C4—944no—
715C2×C4—944no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—1888no—
719C2×C4—18816no—
720C2×C4—1888no—
721C2×C4—1888no—
722C2×C4—18816no—
723C2×C4#41×D4714yes—
724C2×C4C24×D4714yes—
725C2×C4C24×D4712yes—
726C2×C4C24×D4714yes—
727C2×C4C24×D4718yes—
728C2×C4C24×D4712yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—474no—
737C22—948no—
738C22—944no—
739C22—942no—
740C22—944no—
741C22—1884no—
742C22C2×#41×D4712yes—
743C22#1568995814yes—
744C22C25×D4711yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—474no—
750C4—948no—
751C4—942no—
752C4—944no—
753C4—944no—
754C4—948no—
755C4C2×#41×D4714yes—
756C2—42no—
757C2—48no—
758C2—944no—
759C2—1882no—
760C2#2025730714yesdirect product factor
761C2C22×#41×D4711yescharacteristic
762C2C2×#1568995812yes—
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#540C2
socleC23×C47C25
hypercenterC2×#540D47
hypocenterC47C2×#3512
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #20257307C2direct (N × H)
2. C2×#15689820C2semidirect
3. C2×#15689818C2semidirect
4. C2×#15689816C2semidirect
5. C2×#15689810C2semidirect
6. C2×#15689736C2semidirect
7. C2×#15689735C2semidirect
8. C2×#15689727C2semidirect
9. C2×#15689702C2semidirect
10. C2×#15689671C2semidirect
11. C2×#15689655C2semidirect
12. C2×#15689654C2semidirect
13. C2×#125×D47C2semidirect
14. C2×#15689602C2semidirect
15. C2×#15689591C2semidirect
16. C2×C47×#540C2semidirect
19. #15689820C22semidirect
20. #15689818C22semidirect
21. #15689816C22semidirect
22. #15689810C22semidirect
23. #15689736C22semidirect
24. #15689735C22semidirect
25. #15689727C22semidirect
26. #15689702C22semidirect
27. #15689671C22semidirect
29. #15689655C22semidirect
30. #15689654C22semidirect
40. #125×D47C22semidirect
54. #15689602C22semidirect
55. #15689591C22semidirect
79. C47×#540C22semidirect
383. C2×#540D47semidirect
393. C2×C47#3512semidirect
407. #540C2×D47semidirect
468. C47C2×#3512semidirect
760. C2#20257307direct (N × H)

Maximal subgroups

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

subgroupindex
#202573072
C2×#156898202
C2×#156898182
C2×#156898162
C2×#156898102
C2×#156897362
C2×#156897352
C2×#156897272
C2×#156897022
C2×#156896712
C2×#156896552
C2×#156896542
C2×#125×D472
C2×#156896022
C2×#156895912
C2×C47×#5402
C2×#351247