Finite Group Databasebeta

← #26220255

Subgroups — #26220255

Order 12032.

1460 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2#20251977C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689140C211yesmaximal, characteristic, complemented
5C2×#15689096C211yesmaximal, characteristic, complemented
6#20251807C211yesmaximal, characteristic, complemented
7#20244283C218yesmaximal, complemented
8C2×C47×#410C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689921—22no—
11#15689921—22no—
12#15689921—22no—
13#15689921—22no—
14C2×#13094055C412yescomplemented
15C2×#13094054C412yescomplemented
16C2×#13094050C412yescomplemented
17C2×#13094049C412yescomplemented
18C2×#13094044C2214yes—
19C22×#10625329C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21C2×#13093983C2211yescharacteristic
22#15689166—22no—
23#15689163—22no—
24#15689159C2214yescomplemented
25#15689141—22no—
26#15689141C2214yescomplemented
27#15689140—22no—
28#15689140C2214yescomplemented
29C2×#13093952—22no—
30C2×#13093951—22no—
31#15689096—22no—
32#15689096C2214yescomplemented
33C2×#13093938—22no—
34#15689079—22no—
35#15689079C2214yescomplemented
36C4×#10625329—22no—
37C22×#41×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C47×#410—22no—
41C47×#410C2214yescomplemented
42C2×#99×C47—22no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350C2×C412yes—
54C2×#10625350C2312yes—
55C22×Dic94C2×C411yescharacteristic
56C22×D188C2×C411yescharacteristic
57C22×C22⋊D47—21no—
58C22×C4×D47—21no—
59#13094055—24no—
60#13094055—24no—
61#13094054—24no—
62#13094054—24no—
63#13094050—24no—
64#13094050—24no—
65#13094049—24no—
66#13094049—24no—
67#13094044—28no—
68#13094044—28no—
69C2×#10625337C2×C414yescomplemented
70C2×#10625335C2×C414yescomplemented
71C2×#10625336C2×C414yescomplemented
72C2×#10625334C2×C414yescomplemented
73C2×#10625329—21no—
74C2×#10625329—21no—
75C2×#10625329—21no—
76C2×#10625329C2×C412yes—
77C2×#10625329C2×C412yes—
78C2×#10625329D412yes—
79C2×#10625329D412yes—
80C2×#10625329D412yes—
81C2×#10625329D412yes—
82C2×#10625329D412yes—
83C2×#10625329D412yes—
84C2×#10625329C2312yes—
85C22×C47⋊C8—21no—
86C22×C47⋊C8C2312yes—
87#13093983—21no—
88#13093983—21no—
89#13093983—21no—
90#13093983C2312yes—
91C2×C4⋊Dic47—21no—
92C2×C22⋊Dic47—21no—
93C2×C4×Dic47—21no—
94#13093957—24no—
95#13093955—24no—
96#13093952—28no—
97#13093951—28no—
98#13093938—28no—
99#13093935—24no—
100C4×C47⋊C8—24no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47—21no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47—21no—
109C2×#41×C47—21no—
110C2×#41×C47—21no—
111C2×#41×C47C2×C412yes—
112C2×#41×C47C2312yes—
113C22×Q8×C47C2×C411yescharacteristic
114C22×D4×C47—21no—
115C22×D4×C47C2×C411yescharacteristic
116C23×C4×C47—21no—
117C23×C4×C47C2311yescharacteristic
118#117×C47—21no—
119#117×C47—21no—
120#117×C47—21no—
121#117×C47—21no—
122#117×C47—21no—
123#117×C47D412yes—
124#117×C47C2312yes—
125#117×C47C2312yes—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47D412yes—
130C2×C42×C47—21no—
131C2×C42×C47—21no—
132#99×C47—28no—
133C24×C47—21no—
134C24×C47C2×D411yescharacteristic
135C23×D47—21no—
136#41×C47—22no—
137#41×C47—22no—
138#41×C47—22no—
139#41×C47—22no—
140#41×C47—22no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—41no—
145#41×C47—41no—
146#41×C47—41no—
147#41×C47—41no—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47C22×C412yes—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—41no—
166C2×D4×C47—41no—
167C2×D4×C47—41no—
168C2×D4×C47—41no—
169C2×D4×C47C22×C412yes—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—41no—
175C22×C4×C47—41no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47C22×C411yescharacteristic
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47#4111yescharacteristic
189C22×C4×C47#4111yescharacteristic
190C22×C4×C47#4111yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47C2411yescharacteristic
193C2×C22⋊D47—22no—
194C2×C22⋊D47—22no—
195C2×C22⋊D47—41no—
196C2×C22⋊D47—41no—
197C2×C22⋊D47—41no—
198C2×C22⋊D47—41no—
199C22×Dic47—21no—
200C22×Dic47—41no—
201#10625350—22no—
202#10625350—22no—
203#10625350—22no—
204#10625350—22no—
205#10625350—22no—
206#10625350—22no—
207#10625350—22no—
208#10625350—22no—
209#10625350—41no—
210#10625350—41no—
211#10625350—41no—
212#10625350—41no—
213#10625350—41no—
214#10625350—41no—
215#10625350—41no—
216#10625350—41no—
217C2×D188—21no—
218C2×D188—21no—
219C2×D188—21no—
220C2×D188—21no—
221C2×D188—21no—
222C2×D188C22×C412yes—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—41no—
226C2×C4×D47—41no—
227C2×C4×D47—41no—
228C2×C4×D47—41no—
229C2×Dic94—21no—
230C2×Dic94—21no—
231C2×Dic94—21no—
232C2×Dic94—21no—
233C2×Dic94—21no—
234C2×Dic94C22×C412yes—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—22no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—41no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—41no—
242C22⋊C4×C47C2×D414yes—
243C42×C47—22no—
244C42×C47—22no—
245C42×C47—22no—
246C42×C47—41no—
247C22⋊Dic47—22no—
248C22⋊Dic47—41no—
249#10625337—28no—
250#10625336—28no—
251#10625335—28no—
252#10625334—28no—
253C4⋊Dic47—22no—
254C4⋊Dic47—41no—
255C4×Dic47—22no—
256C4×Dic47—41no—
257#10625329—22no—
258#10625329—22no—
259#10625329—22no—
260#10625329C22⋊C414yes—
261#10625329C22⋊C414yes—
262#10625329C22⋊C414yes—
263#10625329C22⋊C414yes—
264#10625329C2×D414yes—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8C22×C414yes—
269C2×C47⋊C8C2×D414yes—
270C2×C47⋊C8C2×D414yes—
271C23×C47—22no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—81no—
275C23×C47—82no—
276C23×C47C4×D411yescharacteristic
277C23×C47C4×D411yescharacteristic
278C23×C47#12111yescharacteristic
279C23×C47#12111yescharacteristic
280C23×C47#12711yescharacteristic
281C23×C47#12711yescharacteristic
282C23×C47C22×D411yescharacteristic
283C22×D47—22no—
284C22×D47—41no—
285C22×D47—41no—
286C22×D47—82no—
287Q8×C47—22no—
288Q8×C47—22no—
289Q8×C47—41no—
290Q8×C47—41no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—42no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—41no—
298D4×C47—41no—
299C2×C4×C47—22no—
300C2×C4×C47—24no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—82no—
309C2×C4×C47—82no—
310C2×C4×C47C2×C22⋊C411yescharacteristic
311C2×C4×C47C2×C22⋊C411yescharacteristic
312C2×C4×C47C2×C22⋊C411yescharacteristic
313C2×C4×C47C2×C22⋊C411yescharacteristic
314C2×C4×C47C4×D411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47#12111yescharacteristic
321C2×C4×C47#12111yescharacteristic
322C2×C4×C47#12111yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12411yescharacteristic
327C2×C4×C47#12411yescharacteristic
328C2×C4×C47#12411yescharacteristic
329C2×C4×C47#12411yescharacteristic
330C2×C4×C47#12711yescharacteristic
331C2×C4×C47#12711yescharacteristic
332C2×C4×C47C23×C411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47C2×#4111yescharacteristic
338C22⋊D47—42no—
339C22⋊D47—42no—
340C22⋊D47—42no—
341C22⋊D47—42no—
342C2×Dic47—22no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—42no—
346C2×Dic47—82no—
347D188—22no—
348D188—22no—
349D188—41no—
350D188—41no—
351C4×D47—42no—
352C4×D47—42no—
353C4×D47—42no—
354C4×D47—42no—
355Dic94—22no—
356Dic94—22no—
357Dic94—41no—
358Dic94—41no—
359C47⋊C8—24no—
360C47⋊C8C2×C22⋊C418yes—
361#21244—471nomaximal, Sylow
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—42no—
370C22×C47—82no—
371C22×C47—82no—
372C22×C47—82no—
373C22×C47#39011yescharacteristic
374C22×C47#39011yescharacteristic
375C22×C47#39011yescharacteristic
376C22×C47#39011yescharacteristic
377C22×C47C2×C4×D411yescharacteristic
378C22×C47C2×#12111yescharacteristic
379C22×C47C2×#12711yescharacteristic
380C2×D47—42no—
381C2×D47—82no—
382C2×D47—82no—
383C2×D47—82no—
384C4×C47—44no—
385C4×C47—42no—
386C4×C47—82no—
387C4×C47#39011yescharacteristic
388C4×C47#39011yescharacteristic
389C4×C47#39011yescharacteristic
390C4×C47#39011yescharacteristic
391C4×C47C22×C22⋊C411yescharacteristic
392C4×C47C2×C4×D411yescharacteristic
393C4×C47C2×#12111yescharacteristic
394C4×C47C2×#12411yescharacteristic
395Dic47—42no—
396Dic47—82no—
397C2×#575—471no—
398#2911—471no—
399C2×#421—471no—
400C2×#421—471no—
401C2×#410—471no—
402C2×#410D4711yescharacteristic, complemented
403#2873—471no—
404#1976—478no—
405C2×C47—21no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—21no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—82no—
413C2×C47C2×#39011yescharacteristic
414D47—82no—
415C22×#41—471no—
416C22×#41C2×D4711yescharacteristic
417#575—942no—
418#575—942no—
419#575—942no—
420#575—942no—
421C2×#137—472no—
422C2×#137—472no—
423C2×AGL(1,ℤ/8)—472no—
424C2×AGL(1,ℤ/8)—472no—
425C2×#135—474no—
426C22×M16—471no—
427C22×M16—471no—
428C2×#117—471no—
429C2×#117C2×D4711yescharacteristic
430C2×#117C2×D4711yescharacteristic
431#428—942no—
432#428—942no—
433#427—474no—
434#421—474no—
435#421—474no—
436#421—942no—
437#421—942no—
438C2×#104—942no—
439C2×#104—942no—
440#410—22no—
441#410—474no—
442#410—942no—
443#410C2×D4714yescomplemented
444C2×#99—22no—
445C2×#99—942no—
446#405—474no—
447#405—942no—
448C4×M16—942no—
449C47#2124411yescharacteristic, complemented, Sylow
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—472no—
461C2×#41—472no—
462C2×#41—941no—
463C2×#41—941no—
464C2×#41—941no—
465C2×#41—941no—
466C2×#41—941no—
467C2×#41—941no—
468C2×#41—941no—
469C2×#41—941no—
470C2×#41—941no—
471C2×#41—941no—
472C2×#41C4×D4712yes—
473C2×#41C22×D4712yes—
474C22×Q8—471no—
475C22×Q8C4×D4711yescharacteristic
476C22×D4—21no—
477C22×D4—471no—
478C22×D4—941no—
479C22×D4C4×D4711yescharacteristic
480C23×C4—21no—
481C23×C4—941no—
482C23×C4C22×D4711yescharacteristic
483#137—944no—
484#137—944no—
485#137—944no—
486#137—944no—
487AGL(1,ℤ/8)—944no—
488AGL(1,ℤ/8)—944no—
489AGL(1,ℤ/8)—944no—
490AGL(1,ℤ/8)—944no—
491#135—948no—
492#135—948no—
493C2×Q16—474no—
494C2×SD16—474no—
495C2×SD16—474no—
496C2×D8—474no—
497C2×M16—472no—
498C2×M16—472no—
499C2×M16—472no—
500C2×M16—472no—
501C2×M16—472no—
502C2×M16—472no—
503C2×M16—472no—
504C2×M16—472no—
505C2×M16—472no—
506C2×M16—941no—
507C2×M16—941no—
508C2×M16—941no—
509C22×C8—472no—
510C22×C8—941no—
511#117—21no—
512#117—21no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—472no—
517#117—941no—
518#117—941no—
519#117—941no—
520#117C22⋊D4712yes—
521#117C22×D4712yes—
522#117C22×D4712yes—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—941no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—941no—
528C2×C22⋊C4C22⋊D4712yes—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—941no—
532#107—944no—
533#106—944no—
534#104—948no—
535#104—948no—
536#99—28no—
537#99—948no—
538#97—944no—
539C4×C8—944no—
540C24—21no—
541C24—941no—
542C24C2×C22⋊D4711yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—942no—
560#41—942no—
561#41—942no—
562#41—942no—
563#41—942no—
564#41—942no—
565#41—942no—
566#41—942no—
567#41—1881no—
568#41—1881no—
569#41—1881no—
570#41—1881no—
571#41—1881no—
572#41—1881no—
573#41—1881no—
574#41—1881no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—472no—
581C2×Q8—941no—
582C2×Q8—941no—
583C2×Q8—941no—
584C2×Q8—941no—
585C2×Q8—941no—
586C2×Q8C2×C4×D4712yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—472no—
599C2×D4—942no—
600C2×D4—942no—
601C2×D4—941no—
602C2×D4—941no—
603C2×D4—941no—
604C2×D4—941no—
605C2×D4—941no—
606C2×D4—1881no—
607C2×D4—1881no—
608C2×D4—1881no—
609C2×D4—1881no—
610C2×D4C2×C4×D4712yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—941no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—1881no—
624C22×C4—1881no—
625C22×C4—1881no—
626C22×C4—1881no—
627C22×C4—1881no—
628C22×C4C2×C4×D4711yescharacteristic
629C22×C4C2×C4×D4711yescharacteristic
630C22×C4#1062535011yescharacteristic
631C22×C4#1062535011yescharacteristic
632C22×C4D4×D4711yescharacteristic
633C22×C4D4×D4711yescharacteristic
634C22×C4D4×D4711yescharacteristic
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4D4×D4711yescharacteristic
638C22×C4#1062535211yescharacteristic
639C22×C4#1062535211yescharacteristic
640C22×C4C2×C22⋊D4711yescharacteristic
641C22×C4C23×D4711yescharacteristic
642Q16—948no—
643SD16—948no—
644SD16—948no—
645D8—948no—
646M16—474no—
647M16—474no—
648M16—474no—
649M16—474no—
650M16—474no—
651M16—942no—
652M16—942no—
653M16—942no—
654C2×C8—474no—
655C2×C8—474no—
656C2×C8—474no—
657C2×C8—942no—
658C2×C8—942no—
659C2×C8—942no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—41no—
664C4⋊C4—942no—
665C4⋊C4—1881no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—41no—
669C22⋊C4—942no—
670C22⋊C4—1881no—
671C22⋊C4C2×C22⋊D4714yes—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—41no—
676C42—942no—
677C42—1881no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—942no—
684C23—3762no—
685C23—1881no—
686C23—1881no—
687C23C4×C22⋊D4711yescharacteristic
688C23C4×C22⋊D4711yescharacteristic
689C23#1309399611yescharacteristic
690C23#1309399611yescharacteristic
691C23#1309402011yescharacteristic
692C23#1309402011yescharacteristic
693C23C22×C22⋊D4711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—942no—
699Q8—942no—
700Q8—1881no—
701Q8—1881no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—942no—
711D4—942no—
712D4—1882no—
713D4—1882no—
714D4—1882no—
715D4—1882no—
716D4—1881no—
717D4—1881no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—942no—
730C2×C4—3762no—
731C2×C4—1882no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4C22⋊C4×D4711yescharacteristic
739C2×C4C22⋊C4×D4711yescharacteristic
740C2×C4C22⋊C4×D4711yescharacteristic
741C2×C4C22⋊C4×D4711yescharacteristic
742C2×C4(C22⋊D47)⋊C411yescharacteristic
743C2×C4(C22⋊D47)⋊C411yescharacteristic
744C2×C4(C22⋊D47)⋊C411yescharacteristic
745C2×C4(C22⋊D47)⋊C411yescharacteristic
746C2×C4C4×C22⋊D4711yescharacteristic
747C2×C4C4×C22⋊D4711yescharacteristic
748C2×C4#1309399611yescharacteristic
749C2×C4#1309399611yescharacteristic
750C2×C4#1309399711yescharacteristic
751C2×C4#1309399711yescharacteristic
752C2×C4#1309399711yescharacteristic
753C2×C4#1309399711yescharacteristic
754C2×C4#1309401011yescharacteristic
755C2×C4#1309401011yescharacteristic
756C2×C4#1309401011yescharacteristic
757C2×C4#1309401011yescharacteristic
758C2×C4#1309402011yescharacteristic
759C2×C4#1309402011yescharacteristic
760C2×C4C22×C4×D4711yescharacteristic
761C2×C4C2×D4×D4711yescharacteristic
762C2×C4C2×D4×D4711yescharacteristic
763C2×C4C2×D4×D4711yescharacteristic
764C2×C4C2×#1062535211yescharacteristic
765C2×C4C2×#1062535011yescharacteristic
766C8—478no—
767C8—944no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—3762no—
780C22—3762no—
781C22—3762no—
782C22—1882no—
783C22#1568902311yescharacteristic
784C22#1568902311yescharacteristic
785C22#1568902311yescharacteristic
786C22#1568902311yescharacteristic
787C22C2×C4×C22⋊D4711yescharacteristic
788C22C2×#1309399611yescharacteristic
789C22C2×#1309402011yescharacteristic
790C4—44no—
791C4—42no—
792C4—82no—
793C4—3762no—
794C4—1882no—
795C4#1568902311yescharacteristic
796C4#1568902311yescharacteristic
797C4#1568902311yescharacteristic
798C4#1568902311yescharacteristic
799C4C2×C22⋊C4×D4711yescharacteristic
800C4C2×(C22⋊D47)⋊C411yescharacteristic
801C4C2×#1309399711yescharacteristic
802C4C2×#1309401011yescharacteristic
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—82no—
811C2—3762no—
812C2C2×#1568902311yescharacteristic
subgroupG/H
centerC4C2×#13093997
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#410C2
socleC2×C47C2×#390
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenterC2×#410D47
hypocenterC47#21244
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #20251977C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689140C2semidirect
5. C2×#15689096C2semidirect
6. #20251807C2semidirect
7. #20244283C2semidirect
8. C2×C47×#410C2semidirect
14. C2×#13094055C4semidirect
15. C2×#13094054C4semidirect
16. C2×#13094050C4semidirect
17. C2×#13094049C4semidirect
24. #15689159C22semidirect
26. #15689141C22semidirect
28. #15689140C22semidirect
32. #15689096C22semidirect
35. #15689079C22semidirect
41. C47×#410C22semidirect
69. C2×#10625337C2×C4semidirect
70. C2×#10625335C2×C4semidirect
71. C2×#10625336C2×C4semidirect
72. C2×#10625334C2×C4semidirect
402. C2×#410D47semidirect
443. #410C2×D47semidirect
449. C47#21244semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
#202519772
C2×#156891412
C2×#156891402
C2×#156890962
#202518072
#202442832
C2×C47×#4102
#2124447