Finite Group Databasebeta

← #26218175

Subgroups — #26218175

Order 12032.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2#20256591C211yesmaximal, characteristic, complemented
3C2×#15689139C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic, complemented
5#20243880C214yesmaximal, complemented
6#20243873C214yesmaximal, complemented
7C2×#15688895C211yesmaximal, characteristic, complemented
8C2×#15688879C211yesmaximal, characteristic, complemented
9C47×#2896C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11#15689921—22no—
12#15689921—22no—
13#15689921—22no—
14#15689921—22no—
15C2×#13094055C2212yes—
16C2×#13094054C412yescomplemented
17C2×#13094050C2212yes—
18C2×#13094049C412yescomplemented
19C2×#13094044C414yescomplemented
20C22×#10625329C2211yescharacteristic
21#15689606—22no—
22#15689606—22no—
23#15689601C2212yescomplemented
24#15689598—22no—
25#15689598C2212yescomplemented
26#41×Dic47—22no—
27#41×Dic47—22no—
28C2×#13093983—22no—
29C2×#13093983C2211yescharacteristic
30C2×#13093983C2211yescharacteristic
31#15689139—22no—
32#15689139C2214yes—
33C2×#13093950—22no—
34#15689096—22no—
35#15689096C2214yes—
36C2×#13093938—22no—
37#15688895C2214yescomplemented
38#15688879C2214yescomplemented
39C22×#41×C47C2211yescharacteristic
40C22×M16×C47C2211yescharacteristic
41C2×#117×C47C2211yescharacteristic
42C47×#419C2212yescomplemented
43C47×#418C2212yescomplemented
44C47×#417—22no—
45C47×#416—22no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350—21no—
55C2×#10625350—21no—
56C2×#10625350C2×C412yescomplemented
57C2×#10625350C2312yes—
58C22×Dic94C2×C411yescharacteristic, complemented
59C22×D188C2×C411yescharacteristic, complemented
60C22×C22⋊D47—21no—
61C22×C4×D47—21no—
62#13094055—24no—
63#13094055—24no—
64#13094054—24no—
65#13094054—24no—
66#13094050—24no—
67#13094050—24no—
68#13094049—24no—
69#13094049—24no—
70#13094044—28no—
71#13094044—28no—
72C2×#10625337C2×C414yescomplemented
73C2×#10625335C2×C414yescomplemented
74C2×#10625336C2×C414yescomplemented
75C2×#10625334C2×C414yescomplemented
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329C2×C412yescomplemented
81C2×#10625329C2312yes—
82C22×C47⋊C8C2×C412yescomplemented
83Q8×Dic47—24no—
84Q8×Dic47—24no—
85D4×Dic47—28no—
86D4×Dic47—28no—
87D4×Dic47—24no—
88D4×Dic47—24no—
89#13093983—24no—
90#13093983—24no—
91#13093983—21no—
92#13093983—21no—
93#13093983—21no—
94#13093983—21no—
95#13093983—24no—
96#13093983D412yes—
97#13093983D412yes—
98#13093983C2312yes—
99#13093983C2312yes—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47—21no—
102C2×C4⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47—24no—
105C2×C22⋊Dic47D412yes—
106C2×C4×Dic47—24no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47D412yes—
109#13093950—28no—
110#13093938—28no—
111C2×#41×C47—21no—
112C2×#41×C47—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—21no—
117C2×#41×C47C2×C412yes—
118C2×#41×C47C2×C412yes—
119C2×#41×C47D412yes—
120C2×#41×C47D412yes—
121C2×#41×C47D412yes—
122C2×#41×C47D412yes—
123C22×Q8×C47C2311yescharacteristic
124C22×D4×C47—21no—
125C22×D4×C47C2311yescharacteristic
126C23×C4×C47—21no—
127C23×C4×C47C2311yescharacteristic
128C2×M16×C47—21no—
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47—21no—
132C2×M16×C47—21no—
133C2×M16×C47C2312yes—
134C22×C8×C47—21no—
135#117×C47—21no—
136#117×C47—21no—
137#117×C47—21no—
138#117×C47C2312yes—
139C2×C4⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C42×C47—21no—
142#103×C47—24no—
143#102×C47—24no—
144C24×C47—21no—
145C24×C47C2×D411yescharacteristic
146C23×D47—21no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—22no—
154#41×C47—22no—
155#41×C47—22no—
156#41×C47—22no—
157#41×C47—22no—
158#41×C47—22no—
159#41×C47C22⋊C414yes—
160#41×C47C22⋊C414yes—
161#41×C47C22⋊C414yes—
162#41×C47C22⋊C414yes—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47C22×C412yes—
167C2×Q8×C47C2×D412yes—
168C2×Q8×C47C2×D412yes—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—22no—
172C2×D4×C47—22no—
173C2×D4×C47—22no—
174C2×D4×C47—22no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47C22×C412yes—
179C2×D4×C47C2×D412yes—
180C2×D4×C47C2×D412yes—
181C22×C4×C47—21no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—41no—
189C22×C4×C47C22×C411yescharacteristic
190C22×C4×C47C22×C411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47#4111yescharacteristic
199C22×C4×C47#4111yescharacteristic
200C22×C4×C47#4111yescharacteristic
201C22×C4×C47#4111yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—22no—
204C2×C22⋊D47—22no—
205C2×C22⋊D47—41no—
206C2×C22⋊D47—41no—
207C2×C22⋊D47—41no—
208C2×C22⋊D47—41no—
209C22×Dic47—21no—
210C22×Dic47—28no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350—22no—
217#10625350—22no—
218#10625350—22no—
219#10625350—22no—
220#10625350—22no—
221#10625350—41no—
222#10625350—41no—
223#10625350—41no—
224#10625350—41no—
225#10625350—41no—
226#10625350—41no—
227#10625350—41no—
228#10625350—41no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188—21no—
232C2×D188—21no—
233C2×D188—21no—
234C2×D188C22×C412yes—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—41no—
238C2×C4×D47—41no—
239C2×C4×D47—41no—
240C2×C4×D47—41no—
241C2×Dic94—21no—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—21no—
245C2×Dic94—21no—
246C2×Dic94C22×C412yes—
247M16×C47—22no—
248M16×C47—22no—
249M16×C47—41no—
250M16×C47—41no—
251C2×C8×C47—22no—
252C2×C8×C47—41no—
253C2×C8×C47—41no—
254C4⋊C4×C47—22no—
255C4⋊C4×C47—41no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—41no—
258C42×C47—22no—
259C42×C47—41no—
260C22⋊Dic47—28no—
261C22⋊Dic47—22no—
262C22⋊Dic47—22no—
263C22⋊Dic47—22no—
264C22⋊Dic47C2×D414yes—
265#10625337—28no—
266#10625336—28no—
267#10625335—28no—
268#10625334—28no—
269C4⋊Dic47—28no—
270C4⋊Dic47—22no—
271C4⋊Dic47—22no—
272C4⋊Dic47—22no—
273C4⋊Dic47—22no—
274C4×Dic47—28no—
275C4×Dic47—22no—
276C4×Dic47—22no—
277C4×Dic47—22no—
278C4×Dic47C2×D414yes—
279#10625329—22no—
280#10625329—22no—
281#10625329—22no—
282#10625329—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8C22×C414yes—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—81no—
290C23×C47—82no—
291C23×C47C4×D411yescharacteristic
292C23×C47C4×D411yescharacteristic
293C23×C47#12011yescharacteristic
294C23×C47#12011yescharacteristic
295C23×C47#12111yescharacteristic
296C23×C47#12111yescharacteristic
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—41no—
300C22×D47—41no—
301C22×D47—82no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47C2×C22⋊C414yes—
306D4×C47—24no—
307D4×C47—24no—
308D4×C47—24no—
309D4×C47—24no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47C2×C22⋊C414yes—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—24no—
318C2×C4×C47—24no—
319C2×C4×C47—24no—
320C2×C4×C47—24no—
321C2×C4×C47—42no—
322C2×C4×C47—82no—
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C2×C4×C47C2×C22⋊C411yescharacteristic
326C2×C4×C47C2×C22⋊C411yescharacteristic
327C2×C4×C47C4×D411yescharacteristic
328C2×C4×C47C4×D411yescharacteristic
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47C4×D411yescharacteristic
331C2×C4×C47C4×D411yescharacteristic
332C2×C4×C47C4×D411yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12011yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12111yescharacteristic
341C2×C4×C47#12311yescharacteristic
342C2×C4×C47#12311yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47#12311yescharacteristic
345C2×C4×C47C23×C411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C22⋊D47—42no—
352C22⋊D47—42no—
353C22⋊D47—42no—
354C22⋊D47—42no—
355C2×Dic47—22no—
356C2×Dic47—24no—
357C2×Dic47—24no—
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—82no—
361C2×Dic47—82no—
362C2×Dic47—88no—
363D188—22no—
364D188—22no—
365D188—41no—
366D188—41no—
367C4×D47—42no—
368C4×D47—42no—
369C4×D47—42no—
370C4×D47—42no—
371Dic94—22no—
372Dic94—22no—
373Dic94—41no—
374Dic94—41no—
375C8×C47—42no—
376C47⋊C8—24no—
377#20998—471nomaximal, Sylow
378C22×C47—24no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—44no—
387C22×C47—82no—
388C22×C47—82no—
389C22×C47#38611yescharacteristic
390C22×C47#38611yescharacteristic
391C22×C47#38611yescharacteristic
392C22×C47#38611yescharacteristic
393C22×C47C2×C4×D411yescharacteristic
394C22×C47C2×#12011yescharacteristic
395C22×C47C2×#12111yescharacteristic
396C2×D47—42no—
397C2×D47—82no—
398C2×D47—82no—
399C2×D47—82no—
400C4×C47—24no—
401C4×C47—82no—
402C4×C47#38611yescharacteristic
403C4×C47#38611yescharacteristic
404C4×C47#38611yescharacteristic
405C4×C47#38611yescharacteristic
406C4×C47C22×C22⋊C411yescharacteristic
407C4×C47C2×C4×D411yescharacteristic
408C4×C47C2×#12111yescharacteristic
409C4×C47C2×#12311yescharacteristic
410Dic47—44no—
411Dic47—44no—
412Dic47—42no—
413C2×#575—471no—
414#3428—471no—
415C2×#421—471no—
416#2896D4711yescharacteristic, complemented
417C2×#410—471no—
418#1905—474no—
419#1904—474no—
420C2×#344—471no—
421C2×H(3,ℤ/4)—471no—
422C2×C47—21no—
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—21no—
426C2×C47—21no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—44no—
430C2×C47C2×#38611yescharacteristic
431D47—82no—
432C22×#41—471no—
433C22×#41C2×D4711yescharacteristic
434#575—942no—
435#575—942no—
436#575—942no—
437#575—942no—
438C2×#137—472no—
439C2×#137—472no—
440C2×AGL(1,ℤ/8)—472no—
441C2×AGL(1,ℤ/8)—472no—
442C2×#135—474no—
443C22×M16—471no—
444C22×M16C2×D4711yescharacteristic
445#520—942no—
446#520—942no—
447#519—472no—
448#518—472no—
449#518—942no—
450C4×#41—942no—
451C4×#41—942no—
452C2×#117—471no—
453C2×#117—471no—
454C2×#117—942no—
455C2×#117C2×D4711yescharacteristic
456#421—474no—
457#421—942no—
458C2×#104—942no—
459#419C2×D4712yescomplemented
460#418C2×D4712yescomplemented
461#417—22no—
462#416—22no—
463#410—474no—
464#410—942no—
465C2×#99—942no—
466#344—474no—
467H(3,ℤ/4)—474no—
468C47#2099811yescharacteristic, complemented, Sylow
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—472no—
476C2×#41—472no—
477C2×#41—941no—
478C2×#41—941no—
479C2×#41—941no—
480C2×#41—941no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—941no—
484C2×#41—941no—
485C2×#41—941no—
486C2×#41—941no—
487C2×#41C4×D4712yes—
488C2×#41C4×D4712yes—
489C2×#41D18812yes—
490C2×#41D18812yes—
491C2×#41C22⋊D4712yes—
492C2×#41C22⋊D4712yes—
493C22×Q8—471no—
494C22×Q8C22×D4711yescharacteristic
495C22×D4—21no—
496C22×D4—471no—
497C22×D4—941no—
498C22×D4C22×D4711yescharacteristic
499C23×C4—21no—
500C23×C4—941no—
501C23×C4C22×D4711yescharacteristic
502#137—944no—
503#137—944no—
504#137—944no—
505#137—944no—
506AGL(1,ℤ/8)—944no—
507AGL(1,ℤ/8)—944no—
508AGL(1,ℤ/8)—944no—
509AGL(1,ℤ/8)—944no—
510#135—948no—
511#135—948no—
512C2×Q16—474no—
513C2×SD16—474no—
514C2×SD16—474no—
515C2×D8—474no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—472no—
522C2×M16—472no—
523C2×M16—941no—
524C2×M16—941no—
525C2×M16—941no—
526C2×M16—941no—
527C2×M16C22×D4712yes—
528C22×C8—21no—
529C22×C8—472no—
530C4×Q8—944no—
531C4×Q8—944no—
532C4×D4—944no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—944no—
536#117—21no—
537#117—21no—
538#117—21no—
539#117—472no—
540#117—472no—
541#117—472no—
542#117—472no—
543#117—944no—
544#117—944no—
545#117—944no—
546#117—941no—
547#117—941no—
548#117—941no—
549#117—941no—
550#117C22×D4712yes—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—944no—
553C2×C4⋊C4—941no—
554C2×C4⋊C4—941no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—472no—
557C2×C22⋊C4—944no—
558C2×C22⋊C4—941no—
559C2×C42—21no—
560C2×C42—472no—
561C2×C42—944no—
562C2×C42—941no—
563#104—948no—
564#103—24no—
565#102—24no—
566#99—948no—
567C24—21no—
568C24—941no—
569C24D4×D4711yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—942no—
583#41—942no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—1881no—
591#41—1881no—
592#41—1881no—
593#41—1881no—
594#41—1881no—
595#41—1881no—
596#41—1881no—
597#41—1881no—
598#41(C2×D47)⋊C414yes—
599#41(C2×D47)⋊C414yes—
600#41(C2×D47)⋊C414yes—
601#41(C2×D47)⋊C414yes—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—472no—
606C2×Q8—941no—
607C2×Q8—941no—
608C2×Q8—941no—
609C2×Q8—941no—
610C2×Q8—941no—
611C2×Q8C2×C4×D4712yes—
612C2×Q8C2×D18812yes—
613C2×Q8C2×C22⋊D4712yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—472no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—941no—
627C2×D4—941no—
628C2×D4—941no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4—1881no—
632C2×D4—1881no—
633C2×D4—1881no—
634C2×D4—1881no—
635C2×D4C2×C4×D4712yes—
636C2×D4C2×D18812yes—
637C2×D4C2×C22⋊D4712yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—41no—
646C22×C4—948no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—941no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—1881no—
653C22×C4—1881no—
654C22×C4—1881no—
655C22×C4—1881no—
656C22×C4C2×C4×D4711yescharacteristic
657C22×C4C2×C4×D4711yescharacteristic
658C22×C4C2×D18811yescharacteristic
659C22×C4C2×D18811yescharacteristic
660C22×C4D4×D4711yescharacteristic
661C22×C4D4×D4711yescharacteristic
662C22×C4D4×D4711yescharacteristic
663C22×C4#1062535211yescharacteristic
664C22×C4#1062535211yescharacteristic
665C22×C4#1062535211yescharacteristic
666C22×C4#1062535211yescharacteristic
667C22×C4C2×C22⋊D4711yescharacteristic
668C22×C4C2×C22⋊D4711yescharacteristic
669C22×C4C23×D4711yescharacteristic
670Q16—948no—
671SD16—948no—
672SD16—948no—
673D8—948no—
674M16—22no—
675M16—22no—
676M16—41no—
677M16—41no—
678M16—942no—
679M16—942no—
680M16—942no—
681M16—942no—
682C2×C8—22no—
683C2×C8—41no—
684C2×C8—41no—
685C2×C8—474no—
686C2×C8—942no—
687C2×C8—942no—
688C4⋊C4—22no—
689C4⋊C4—41no—
690C4⋊C4—948no—
691C4⋊C4—942no—
692C4⋊C4—942no—
693C4⋊C4—942no—
694C4⋊C4—942no—
695C22⋊C4—22no—
696C22⋊C4—41no—
697C22⋊C4—474no—
698C22⋊C4—948no—
699C22⋊C4—942no—
700C22⋊C4—942no—
701C22⋊C4—942no—
702C42—22no—
703C42—41no—
704C42—474no—
705C42—948no—
706C42—942no—
707C42—942no—
708C42—942no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—81no—
713C23—82no—
714C23—942no—
715C23—3762no—
716C23—1881no—
717C23—1881no—
718C23(C22⋊D47)⋊C411yescharacteristic
719C23(C22⋊D47)⋊C411yescharacteristic
720C23#1309399411yescharacteristic
721C23#1309399411yescharacteristic
722C23#1309399611yescharacteristic
723C23#1309399611yescharacteristic
724C23C2×D4×D4711yescharacteristic
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—942no—
729Q8—942no—
730Q8—1881no—
731Q8—1881no—
732Q8C2×(C2×D47)⋊C414yes—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—942no—
741D4—942no—
742D4—1882no—
743D4—1882no—
744D4—1882no—
745D4—1882no—
746D4—1881no—
747D4—1881no—
748D4C2×(C2×D47)⋊C414yes—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—42no—
757C2×C4—82no—
758C2×C4—942no—
759C2×C4—944no—
760C2×C4—944no—
761C2×C4—3762no—
762C2×C4—3762no—
763C2×C4—3768no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4—1882no—
769C2×C4—1882no—
770C2×C4C2×(C2×D47)⋊C411yescharacteristic
771C2×C4C2×(C2×D47)⋊C411yescharacteristic
772C2×C4C2×(C2×D47)⋊C411yescharacteristic
773C2×C4C2×(C2×D47)⋊C411yescharacteristic
774C2×C4(C22⋊D47)⋊C411yescharacteristic
775C2×C4(C22⋊D47)⋊C411yescharacteristic
776C2×C4(C22⋊D47)⋊C411yescharacteristic
777C2×C4(C22⋊D47)⋊C411yescharacteristic
778C2×C4(C22⋊D47)⋊C411yescharacteristic
779C2×C4(C22⋊D47)⋊C411yescharacteristic
780C2×C4#1309399411yescharacteristic
781C2×C4#1309399411yescharacteristic
782C2×C4#1309399611yescharacteristic
783C2×C4#1309399611yescharacteristic
784C2×C4#1309399611yescharacteristic
785C2×C4#1309399611yescharacteristic
786C2×C4#1309399611yescharacteristic
787C2×C4#1309399611yescharacteristic
788C2×C4#1309400811yescharacteristic
789C2×C4#1309400811yescharacteristic
790C2×C4#1309400811yescharacteristic
791C2×C4#1309400811yescharacteristic
792C2×C4C22×C4×D4711yescharacteristic
793C2×C4C2×D4×D4711yescharacteristic
794C2×C4C22×C22⋊D4711yescharacteristic
795C2×C4C22×D18811yescharacteristic
796C2×C4C2×#1062535211yescharacteristic
797C2×C4C2×#1062535211yescharacteristic
798C8—42no—
799C8—944no—
800C22—24no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—82no—
810C22—82no—
811C22—3762no—
812C22—3762no—
813C22—3762no—
814C22—1882no—
815C22#1568900011yescharacteristic
816C22#1568900011yescharacteristic
817C22#1568900011yescharacteristic
818C22#1568900011yescharacteristic
819C22C2×(C22⋊D47)⋊C411yescharacteristic
820C22C2×#1309399411yescharacteristic
821C22C2×#1309399611yescharacteristic
822C4—24no—
823C4—82no—
824C4—1884no—
825C4—1884no—
826C4—1882no—
827C4#1568900011yescharacteristic
828C4#1568900011yescharacteristic
829C4#1568900011yescharacteristic
830C4#1568900011yescharacteristic
831C4C22×(C2×D47)⋊C411yescharacteristic
832C4C2×(C22⋊D47)⋊C411yescharacteristic
833C4C2×#1309399611yescharacteristic
834C4C2×#1309400811yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—44no—
843C2—3762no—
844C2C2×#1568900011yescharacteristic
subgroupG/H
centerC4#15689000
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2896C2
socleC2×C47C2×#386
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenter#2896D47
hypocenterC47#20998
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. #20256591C2semidirect
3. C2×#15689139C2semidirect
4. C2×#15689096C2semidirect
5. #20243880C2semidirect
6. #20243873C2semidirect
7. C2×#15688895C2semidirect
8. C2×#15688879C2semidirect
9. C47×#2896C2semidirect
16. C2×#13094054C4semidirect
18. C2×#13094049C4semidirect
19. C2×#13094044C4semidirect
23. #15689601C22semidirect
25. #15689598C22semidirect
37. #15688895C22semidirect
38. #15688879C22semidirect
42. C47×#419C22semidirect
43. C47×#418C22semidirect
56. C2×#10625350C2×C4semidirect
58. C22×Dic94C2×C4semidirect
59. C22×D188C2×C4semidirect
72. C2×#10625337C2×C4semidirect
73. C2×#10625335C2×C4semidirect
74. C2×#10625336C2×C4semidirect
75. C2×#10625334C2×C4semidirect
80. C2×#10625329C2×C4semidirect
82. C22×C47⋊C8C2×C4semidirect
416. #2896D47semidirect
459. #419C2×D47semidirect
460. #418C2×D47semidirect
468. C47#20998semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
#202565912
C2×#156891392
C2×#156890962
#202438802
#202438732
C2×#156888952
C2×#156888792
C47×#28962
#2099847