Finite Group Databasebeta

← D47×#3548 #27124067

Subgroups — D47×#3548 #27124067

Order 12032.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257788C211yesmaximal, characteristic, complemented
2#20257787C214yesmaximal, complemented
3#20257786C212yesmaximal, complemented
4#20257785C214yesmaximal, complemented
5#20257784C214yesmaximal, complemented
6#20257783C218yesmaximal, complemented
7#20257782C214yesmaximal, complemented
8#20257781C214yesmaximal, complemented
9#562×D47C214yesmaximal, complemented
10#554×D47C214yesmaximal, complemented
11#550×D47C214yesmaximal, complemented
12#547×D47C214yesmaximal, complemented
13#540×D47C214yesmaximal, complemented
14#537×D47C218yesmaximal, complemented
15#533×D47C211yesmaximal, characteristic, complemented
16#532×D47C212yesmaximal, complemented
17C47×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D47C2218yes—
19C2×#41×D47C2214yes—
20#15689871C2214yescomplemented
21#15689870C22116yescomplemented
22#15689869C22116yescomplemented
23#15689868C22116yescomplemented
24#15689867C2218yescomplemented
25#15689834C2214yescomplemented
26#15689833C2214yescomplemented
27#15689832C2218yescomplemented
28#15689831C2218yescomplemented
29#15689830C2214yescomplemented
30#15689829C2218yescomplemented
31#15689828C2218yescomplemented
32#15689827C22116yescomplemented
33#15689795C2214yescomplemented
34#15689794C2218yescomplemented
35#15689794C2214yescomplemented
36#15689793C2218yescomplemented
37#15689793C2214yescomplemented
38#15689792C2218yescomplemented
39#15689791C22116yescomplemented
40#15689791C2218yescomplemented
41#15689778C2214yescomplemented
42#15689777C2214yescomplemented
43#15689776C2214yescomplemented
44#15689775C2218yescomplemented
45#15689774C2218yescomplemented
46#15689773C2218yescomplemented
47#15689772C2218yescomplemented
48#15689771C22116yescomplemented
49#15689729C2214yescomplemented
50#15689728C2214yescomplemented
51#15689727C2214yescomplemented
52#15689726C2218yescomplemented
53#15689725C22116yescomplemented
54#15689724C2218yescomplemented
55#15689723C22116yescomplemented
56#15689704C2218yescomplemented
57#15689703C2218yescomplemented
58#15689703C22116yescomplemented
59#15689703C2218yescomplemented
60#15689702C2218yescomplemented
61#15689702C22116yescomplemented
62#15689702C2218yescomplemented
63#15689701C2218yescomplemented
64#15689701C2218yescomplemented
65#15689700C22116yescomplemented
66#15689700C22116yescomplemented
67#15689680C2211yescharacteristic, complemented
68#15689679C2212yescomplemented
69#15689678C2212yescomplemented
70#15689677C2214yescomplemented
71#15689676C2212yescomplemented
72#15689675C2214yescomplemented
73#15689674C2212yescomplemented
74#15689673C2212yescomplemented
75#15689672C2214yescomplemented
76#15689671C2212yescomplemented
77#15689670C2214yescomplemented
78#15689670C2214yescomplemented
79#15689669C2214yescomplemented
80#15689668C2214yescomplemented
81#15689668C2214yescomplemented
82C4⋊Q8×D47C2212yes—
83C4⋊Q8×D47C2212yes—
84#127×D47C2212yes—
85#127×D47C2214yes—
86#125×D47C2214yes—
87#125×D47C2212yes—
88#124×D47C2214yes—
89#123×D47C22116yes—
90C22⋊Q8×D47C2218yes—
91C22⋊Q8×D47C22116yes—
92C22⋊Q8×D47C2214yes—
93#121×D47C2218yes—
94#121×D47C22116yes—
95#121×D47C2214yes—
96#121×D47C2214yes—
97#121×D47C22116yes—
98C4×Q8×D47C2214yes—
99C4×D4×D47C2214yes—
100C4×D4×D47C2214yes—
101C4×D4×D47C2218yes—
102#117×D47C2212yes—
103C2×C4⋊C4×D47C2218yes—
104C2×C42×D47C2211yescharacteristic
105C47×#562C2214yescomplemented
106C47×#554C2214yescomplemented
107C47×#550C2214yescomplemented
108C47×#547C2214yescomplemented
109C47×#540C2214yescomplemented
110C47×#537C2218yescomplemented
111C47×#533C2211yescharacteristic, complemented
112C47×#532C2212yescomplemented
113C2×#10625354C2318yes—
114C2×#10625354C2314yes—
115C2×#10625350C23116yes—
116C2×#10625350C2318yes—
117C2×#10625350C2314yes—
118C2×#10625350C2318yes—
119C2×#10625352C23116yes—
120C2×#10625352C2318yes—
121C2×#10625352C2318yes—
122C2×#10625352C2314yes—
123#41×D47—416no—
124#41×D47—432no—
125C2×Q8×D47C2314yes—
126C2×Q8×D47C2314yes—
127C2×D4×D47C2314yes—
128C2×D4×D47C2314yes—
129C2×D4×D47C2318yes—
130C2×D4×D47C23116yes—
131C2×D4×D47C2314yes—
132C22×C4×D47C2311yescharacteristic
133C22×C4×D47C2312yes—
134C22×C4×D47C2318yes—
135C22×C4×D47C23116yes—
136#13094024C2312yes—
137#13094024C2312yes—
138#13094023C2314yes—
139#13094023C2314yes—
140#13094023C2314yes—
141#13094023C2314yes—
142#13094022C2314yes—
143#13094022C2314yes—
144#13094021C2314yes—
145#13094021C2312yes—
146#13094020C2314yes—
147#13094020C23116yes—
148#13094020C2314yes—
149#13094020C2314yes—
150#13094020C2318yes—
151#13094016C2314yes—
152#13094016C2312yes—
153#13094015C2318yes—
154#13094015C2314yes—
155#13094014C23116yes—
156#13094014C2318yes—
157#13094013C2314yes—
158#13094012C2314yes—
159#13094011C2314yes—
160#13094010C2318yes—
161#13094010C2318yes—
162#13094009C23116yes—
163#13094009C23116yes—
164#13094008C23116yes—
165#13094007C23116yes—
166#13094006C23116yes—
167#13094006C23116yes—
168#13094005C23116yes—
169#13094004C2318yes—
170#13094004C23116yes—
171#13094004C2314yes—
172#13094003C2318yes—
173#13094003C23116yes—
174#13094003C2314yes—
175#13094002C23116yes—
176#13094002C23116yes—
177#13094002C23116yes—
178#13094002C2318yes—
179#13094001C23116yes—
180#13094001C23116yes—
181#13094001C23116yes—
182#13094001C2318yes—
183#13094000C2318yes—
184#13094000C23116yes—
185#13094000C2314yes—
186#13093999C2314yes—
187#13093999C23116yes—
188#13093999C2318yes—
189#13093999C23116yes—
190#13093999C2314yes—
191#13093998C2314yes—
192#13093998C2318yes—
193#13093998C23116yes—
194#13093998C2314yes—
195#13093998C23116yes—
196#13093997C23116yes—
197#13093997C23116yes—
198#13093997C23116yes—
199#13093997C23116yes—
200#13093997C2318yes—
201#13093997C2318yes—
202#13093997C23116yes—
203#13093996C23116yes—
204#13093996C23116yes—
205#13093996C23116yes—
206#13093996C2318yes—
207#13093996C2318yes—
208#13093996C23116yes—
209#13093996C23116yes—
210#13093995C2318yes—
211#13093995C23116yes—
212#13093995C2314yes—
213#13093995C2314yes—
214#13093995C23116yes—
215Q8×Dic47C2314yes—
216C4×Dic94C2318yes—
217C4×Dic94C2314yes—
218#13093989C2318yes—
219#13093989C2314yes—
220C4×D188C2318yes—
221C4×D188C2314yes—
222C4×D188C2314yes—
223D4×Dic47C2314yes—
224D4×Dic47C2318yes—
225D4×Dic47C2314yes—
226#13093986C2318yes—
227#13093986C2314yes—
228#13093986C2314yes—
229C4×C22⋊D47C2318yes—
230C4×C22⋊D47C23116yes—
231C4×C22⋊D47C2318yes—
232(C22⋊D47)⋊C4C2318yes—
233(C22⋊D47)⋊C4C2318yes—
234(C22⋊D47)⋊C4C23116yes—
235#13093983C2312yes—
236#13093982C2314yes—
237#13093981C2314yes—
238#13093980C2314yes—
239C2×C4⋊Dic47C2318yes—
240C2×Dic47⋊C4C23116yes—
241C4⋊C4×D47C23116yes—
242C4⋊C4×D47C2318yes—
243C4⋊C4×D47C2318yes—
244C4⋊C4×D47C2314yes—
245C4⋊C4×D47C2314yes—
246C4⋊C4×D47C23116yes—
247C4⋊C4×D47C2314yes—
248C4⋊C4×D47C2314yes—
249C4⋊C4×D47C2318yes—
250C22⋊C4×D47C2314yes—
251C22⋊C4×D47C23116yes—
252C22⋊C4×D47C2318yes—
253C22⋊C4×D47C2318yes—
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2312yes—
256C42×D47C2311yescharacteristic
257C42×D47C2312yes—
258C42×D47C2311yescharacteristic
259C42×D47C2311yescharacteristic
260C42×D47C2312yes—
261C42×D47C2311yescharacteristic
262C42×D47C2314yes—
263C2×#41×C47C2318yes—
264C2×#41×C47C2314yes—
265C4⋊Q8×C47C2312yes—
266C4⋊Q8×C47C2312yes—
267#127×C47C2312yes—
268#127×C47C2314yes—
269#125×C47C2314yes—
270#125×C47C2312yes—
271#124×C47C2314yes—
272#123×C47C23116yes—
273C22⋊Q8×C47C2318yes—
274C22⋊Q8×C47C2314yes—
275C22⋊Q8×C47C23116yes—
276#121×C47C2318yes—
277#121×C47C23116yes—
278#121×C47C2314yes—
279#121×C47C2314yes—
280#121×C47C23116yes—
281C4×Q8×C47C2314yes—
282C4×D4×C47C2314yes—
283C4×D4×C47C2314yes—
284C4×D4×C47C2318yes—
285#117×C47C2312yes—
286C2×C4⋊C4×C47C2318yes—
287C2×C42×C47C2311yescharacteristic
288C23×D47C2411yescharacteristic
289C23×D47C2418yes—
290#41×C47—48no—
291#41×C47—416no—
292C2×Q8×C47C2414yes—
293C2×Q8×C47C2414yes—
294C2×D4×C47C2414yes—
295C2×D4×C47C2414yes—
296C2×D4×C47C2418yes—
297C2×D4×C47C24116yes—
298C2×D4×C47C2414yes—
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2412yes—
301C22×C4×C47C2418yes—
302C22×C4×C47C24116yes—
303C2×C22⋊D47C2418yes—
304C2×C22⋊D47C2418yes—
305C2×C22⋊D47C2418yes—
306C2×C22⋊D47C2418yes—
307C2×C22⋊D47C24116yes—
308C2×C22⋊D47C2418yes—
309C2×C22⋊D47C24116yes—
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2412yes—
312C22×Dic47C2418yes—
313C22×Dic47C24116yes—
314#10625354—48no—
315#10625354—416no—
316Q8×D47—216no—
317Q8×D47—48no—
318#10625352—416no—
319#10625352—432no—
320#10625352—416no—
321#10625352—48no—
322D4×D47—216no—
323D4×D47—216no—
324D4×D47—416no—
325D4×D47—48no—
326D4×D47—432no—
327#10625350—432no—
328#10625350—416no—
329#10625350—416no—
330#10625350—48no—
331C2×D188C2414yes—
332C2×D188C2414yes—
333C2×D188C2418yes—
334C2×D188C2414yes—
335C2×D188C24116yes—
336C2×C4×D47—232no—
337C2×C4×D47—28no—
338C2×C4×D47—24no—
339C2×C4×D47—432no—
340C2×C4×D47C2411yescharacteristic
341C2×C4×D47C2412yes—
342C2×C4×D47C2411yescharacteristic
343C2×C4×D47C2411yescharacteristic
344C2×C4×D47C2412yes—
345C2×C4×D47C2412yes—
346C2×C4×D47C2418yes—
347C2×C4×D47C2418yes—
348C2×C4×D47C2418yes—
349C2×C4×D47C2418yes—
350C2×C4×D47C24116yes—
351C2×C4×D47C24116yes—
352C2×C4×D47C2412yes—
353C2×C4×D47C2411yescharacteristic
354C2×Dic94C2418yes—
355C2×Dic94C2414yes—
356C2×Dic94C2414yes—
357C2×Dic94C2418yes—
358C4⋊C4×C47C2414yes—
359C4⋊C4×C47C2414yes—
360C4⋊C4×C47C24116yes—
361C4⋊C4×C47C2414yes—
362C4⋊C4×C47C2414yes—
363C4⋊C4×C47C2418yes—
364C22⋊C4×C47C2414yes—
365C22⋊C4×C47C24116yes—
366C22⋊C4×C47C2418yes—
367C22⋊C4×C47C2418yes—
368C42×C47C2411yescharacteristic
369C42×C47C2412yes—
370C42×C47C2411yescharacteristic
371C42×C47C2414yes—
372C22⋊Dic47C2414yes—
373C22⋊Dic47C24116yes—
374C22⋊Dic47C2418yes—
375C22⋊Dic47C2418yes—
376(C2×D47)⋊C4C2418yes—
377(C2×D47)⋊C4C2418yes—
378(C2×D47)⋊C4C24116yes—
379(C2×D47)⋊C4C2418yes—
380(C2×D47)⋊C4C24116yes—
381(C2×D47)⋊C4C2418yes—
382(C2×D47)⋊C4C2418yes—
383C4⋊Dic47C2414yes—
384C4⋊Dic47C2414yes—
385C4⋊Dic47C24116yes—
386C4⋊Dic47C2414yes—
387C4⋊Dic47C2414yes—
388C4⋊Dic47C2418yes—
389Dic47⋊C4C2418yes—
390Dic47⋊C4C2418yes—
391Dic47⋊C4C24116yes—
392Dic47⋊C4C24116yes—
393Dic47⋊C4C2418yes—
394Dic47⋊C4C2418yes—
395Dic47⋊C4C2418yes—
396Dic47⋊C4C2418yes—
397C4×Dic47C2411yescharacteristic
398C4×Dic47C2412yes—
399C4×Dic47C2412yes—
400C4×Dic47C2412yes—
401C4×Dic47C2412yes—
402C4×Dic47C2411yescharacteristic
403C4×Dic47C2412yes—
404C4×Dic47C2418yes—
405C4×Dic47C2414yes—
406C23×C47C2511yescharacteristic
407C23×C47C2518yes—
408C22×D47—24no—
409C22×D47—216no—
410C22×D47—216no—
411C22×D47—22no—
412C22×D47—216no—
413C22×D47C2511yescharacteristic
414C22×D47C2518yes—
415C22×D47C2511yescharacteristic
416Q8×C47—28no—
417Q8×C47—44no—
418D4×C47—28no—
419D4×C47—28no—
420D4×C47—416no—
421D4×C47—44no—
422D4×C47—48no—
423C2×C4×C47—24no—
424C2×C4×C47—216no—
425C2×C4×C47—22no—
426C2×C4×C47—416no—
427C2×C4×C47C2512yes—
428C2×C4×C47C2511yescharacteristic
429C2×C4×C47C2518yes—
430C2×C4×C47C2518yes—
431C2×C4×C47C2512yes—
432C2×C4×C47C2511yescharacteristic
433C22⋊D47—216no—
434C22⋊D47—216no—
435C22⋊D47—416no—
436C22⋊D47—416no—
437C22⋊D47—48no—
438C22⋊D47—48no—
439C22⋊D47—48no—
440C2×Dic47—24no—
441C2×Dic47—216no—
442C2×Dic47—22no—
443C2×Dic47—416no—
444C2×Dic47C2511yescharacteristic
445C2×Dic47C2512yes—
446C2×Dic47C2518yes—
447C2×Dic47C2518yes—
448C2×Dic47C2512yes—
449C2×Dic47C2511yescharacteristic
450D188—28no—
451D188—28no—
452D188—416no—
453D188—44no—
454D188—48no—
455C4×D47—216no—
456C4×D47—24no—
457C4×D47—216no—
458C4×D47—22no—
459C4×D47—24no—
460C4×D47—216no—
461C4×D47—22no—
462C4×D47—216no—
463C4×D47—24no—
464C4×D47—22no—
465C4×D47—416no—
466C4×D47—416no—
467C4×D47H(5,𝔽2)18yes—
468C4×D472−1+414yes—
469Dic94—28no—
470Dic94—216no—
471Dic94—48no—
472Dic94—44no—
473C2×#3548—471nomaximal, Sylow
474C22×C47—22no—
475C22×C47—28no—
476C22×C47—28no—
477C22×C47—21no—
478C22×C47—28no—
479C22×C47C2611yescharacteristic
480C2×D47—22no—
481C2×D47—28no—
482C2×D47—28no—
483C2×D47—21no—
484C2×D47—28no—
485C2×D47—44no—
486C2×D47—432no—
487C2×D47C2×H(5,𝔽2)14yes—
488C2×D47C2×2−1+412yes—
489C4×C47—28no—
490C4×C47—22no—
491C4×C47—28no—
492C4×C47—21no—
493C4×C47C2×H(5,𝔽2)14yes—
494C4×C47C2×2−1+412yes—
495Dic47—28no—
496Dic47—22no—
497Dic47—28no—
498Dic47—21no—
499Dic47C2×H(5,𝔽2)14yes—
500Dic47C2×2−1+412yes—
501#3548—474no—
502#3548—474no—
503#3548—474no—
504#3548—474no—
505#3548—474no—
506#3548—478no—
507#3548—471no—
508#3548—472no—
509#3548D4711yescharacteristic, direct product factor
510C2×#562—474no—
511C2×#554—474no—
512C2×#550—474no—
513C2×#547—474no—
514C2×#540—474no—
515C2×#537—478no—
516C2×#533—471no—
517C2×#532—472no—
518C2×C47—41no—
519C2×C47—48no—
520C2×C47C22×H(5,𝔽2)12yes—
521C2×C47C22×2−1+411yescharacteristic
522D47—41no—
523D47—48no—
524D47#354814yesdirect product factor
525C22×#41—474no—
526C22×#41—478no—
527#562—474no—
528#562—478no—
529#562—4716no—
530#562—4716no—
531#562—4716no—
532#562C2×D4714yescomplemented
533#554—474no—
534#554—478no—
535#554—4716no—
536#554—478no—
537#554—474no—
538#554—474no—
539#554—478no—
540#554—478no—
541#554C2×D4714yescomplemented
542#550—478no—
543#550—478no—
544#550—474no—
545#550—478no—
546#550—4716no—
547#550—474no—
548#550—478no—
549#550—474no—
550#550C2×D4714yescomplemented
551#547—478no—
552#547—474no—
553#547—4716no—
554#547—478no—
555#547—478no—
556#547—474no—
557#547—474no—
558#547—478no—
559#547C2×D4714yescomplemented
560#540—474no—
561#540—474no—
562#540—4716no—
563#540—4716no—
564#540—478no—
565#540—478no—
566#540—474no—
567#540C2×D4714yescomplemented
568#537—478no—
569#537—478no—
570#537—478no—
571#537—4716no—
572#537—478no—
573#537—4716no—
574#537—4716no—
575#537—478no—
576#537—4716no—
577#537—478no—
578#537—478no—
579#537C2×D4718yescomplemented
580#533—472no—
581#533—472no—
582#533—474no—
583#533—474no—
584#533—472no—
585#533—471no—
586#533C2×D4711yescharacteristic, complemented
587#532—474no—
588#532—472no—
589#532—472no—
590#532—474no—
591#532—474no—
592#532—474no—
593#532—474no—
594#532—474no—
595#532—472no—
596#532C2×D4712yescomplemented
597C2×C4⋊Q8—472no—
598C2×C4⋊Q8—472no—
599C2×#127—472no—
600C2×#127—474no—
601C2×#125—472no—
602C2×#125—474no—
603C2×#124—474no—
604C2×#123—4716no—
605C2×C22⋊Q8—474no—
606C2×C22⋊Q8—478no—
607C2×C22⋊Q8—4716no—
608C2×#121—474no—
609C2×#121—474no—
610C2×#121—4716no—
611C2×#121—478no—
612C2×#121—4716no—
613C2×C4×Q8—474no—
614C2×C4×D4—474no—
615C2×C4×D4—474no—
616C2×C4×D4—478no—
617C2×#117—472no—
618C22×C4⋊C4—478no—
619C22×C42—471no—
620C47C2×#354811yescharacteristic, complemented, Sylow
621C2×#41—474no—
622C2×#41—478no—
623C2×#41—478no—
624C2×#41—474no—
625C2×#41—4716no—
626C2×#41—478no—
627C2×#41—478no—
628C2×#41—474no—
629C2×#41—4716no—
630C2×#41—478no—
631C2×#41—18816no—
632C2×#41—18832no—
633C2×#41C22×D4714yes—
634C2×#41C22×D4718yes—
635C22×Q8—474no—
636C22×Q8—474no—
637C22×D4—474no—
638C22×D4—474no—
639C22×D4—478no—
640C22×D4—4716no—
641C22×D4—474no—
642C23×C4—478no—
643C23×C4—471no—
644C23×C4—472no—
645C23×C4—4716no—
646C4⋊Q8—474no—
647C4⋊Q8—474no—
648C4⋊Q8—474no—
649C4⋊Q8—474no—
650C4⋊Q8—474no—
651C4⋊Q8—474no—
652C4⋊Q8—472no—
653C4⋊Q8—472no—
654C4⋊Q8C22×D4712yes—
655C4⋊Q8C22×D4712yes—
656#127—474no—
657#127—474no—
658#127—474no—
659#127—4716no—
660#127—478no—
661#127—472no—
662#127—474no—
663#127C22×D4712yes—
664#127C22×D4714yes—
665#125—478no—
666#125—474no—
667#125—4716no—
668#125—478no—
669#125—472no—
670#125—474no—
671#125C22×D4712yes—
672#125C22×D4714yes—
673#124—474no—
674#124—474no—
675#124—478no—
676#124—478no—
677#124—474no—
678#124C22×D4714yes—
679#123—4716no—
680#123—4716no—
681#123—4716no—
682#123—4716no—
683#123—4716no—
684#123—4716no—
685#123—4716no—
686#123C22×D47116yes—
687C22⋊Q8—474no—
688C22⋊Q8—478no—
689C22⋊Q8—4716no—
690C22⋊Q8—474no—
691C22⋊Q8—478no—
692C22⋊Q8—4716no—
693C22⋊Q8—478no—
694C22⋊Q8—474no—
695C22⋊Q8—4716no—
696C22⋊Q8—478no—
697C22⋊Q8—4716no—
698C22⋊Q8—4716no—
699C22⋊Q8—4716no—
700C22⋊Q8—478no—
701C22⋊Q8—4716no—
702C22⋊Q8—4716no—
703C22⋊Q8—4716no—
704C22⋊Q8C22×D4714yes—
705C22⋊Q8C22×D4718yes—
706C22⋊Q8C22×D47116yes—
707#121—474no—
708#121—478no—
709#121—474no—
710#121—478no—
711#121—4716no—
712#121—4716no—
713#121—4716no—
714#121—478no—
715#121—4716no—
716#121—4716no—
717#121—4716no—
718#121—4716no—
719#121—474no—
720#121—474no—
721#121—4716no—
722#121—478no—
723#121—4716no—
724#121—474no—
725#121—474no—
726#121—4716no—
727#121—478no—
728#121—4716no—
729#121—478no—
730#121—478no—
731#121—4716no—
732#121—4716no—
733#121—4716no—
734#121—4716no—
735#121—4716no—
736#121C22×D4714yes—
737#121C22×D4714yes—
738#121C22×D47116yes—
739#121C22×D4718yes—
740#121C22×D47116yes—
741C4×Q8—474no—
742C4×Q8—478no—
743C4×Q8—474no—
744C4×Q8—478no—
745C4×Q8—474no—
746C4×Q8C22×D4714yes—
747C4×D4—474no—
748C4×D4—474no—
749C4×D4—478no—
750C4×D4—478no—
751C4×D4—478no—
752C4×D4—4716no—
753C4×D4—474no—
754C4×D4—474no—
755C4×D4—478no—
756C4×D4—478no—
757C4×D4—478no—
758C4×D4—4716no—
759C4×D4—474no—
760C4×D4—474no—
761C4×D4—478no—
762C4×D4C22×D4714yes—
763C4×D4C22×D4714yes—
764C4×D4C22×D4718yes—
765#117—472no—
766#117—474no—
767#117—474no—
768#117—474no—
769#117C22×D4712yes—
770C2×C4⋊C4—4716no—
771C2×C4⋊C4—478no—
772C2×C4⋊C4—474no—
773C2×C4⋊C4—474no—
774C2×C4⋊C4—4716no—
775C2×C4⋊C4—4716no—
776C2×C4⋊C4—478no—
777C2×C4⋊C4—478no—
778C2×C4⋊C4—474no—
779C2×C4⋊C4—474no—
780C2×C4⋊C4—478no—
781C2×C4⋊C4C22×D4718yes—
782C2×C22⋊C4—474no—
783C2×C22⋊C4—4716no—
784C2×C22⋊C4—478no—
785C2×C22⋊C4—478no—
786C2×C42—472no—
787C2×C42—471no—
788C2×C42—474no—
789C2×C42—471no—
790C2×C42—472no—
791C2×C42—471no—
792C2×C42—471no—
793C2×C42—472no—
794C2×C42—471no—
795C2×C42C22×D4711yescharacteristic
796C24—471no—
797C24—478no—
798#41—48no—
799#41—416no—
800#41—18816no—
801#41—1888no—
802#41—18816no—
803#41—18832no—
804#41—18816no—
805#41—1888no—
806#41—1888no—
807#41—18816no—
808#41—18832no—
809#41—18816no—
810C2×Q8—478no—
811C2×Q8—474no—
812C2×Q8—478no—
813C2×Q8—474no—
814C2×Q8—9416no—
815C2×Q8—1888no—
816C2×Q8C23×D4714yes—
817C2×Q8C23×D4714yes—
818C2×D4—478no—
819C2×D4—478no—
820C2×D4—478no—
821C2×D4—478no—
822C2×D4—4716no—
823C2×D4—4716no—
824C2×D4—478no—
825C2×D4—474no—
826C2×D4—474no—
827C2×D4—478no—
828C2×D4—4716no—
829C2×D4—474no—
830C2×D4—9416no—
831C2×D4—9416no—
832C2×D4—18816no—
833C2×D4—1888no—
834C2×D4—18832no—
835C2×D4C23×D4714yes—
836C2×D4C23×D4714yes—
837C2×D4C23×D4718yes—
838C2×D4C23×D47116yes—
839C2×D4C23×D4714yes—
840C22×C4—471no—
841C22×C4—472no—
842C22×C4—471no—
843C22×C4—472no—
844C22×C4—478no—
845C22×C4—4716no—
846C22×C4—471no—
847C22×C4—472no—
848C22×C4—471no—
849C22×C4—471no—
850C22×C4—472no—
851C22×C4—472no—
852C22×C4—478no—
853C22×C4—478no—
854C22×C4—478no—
855C22×C4—478no—
856C22×C4—4716no—
857C22×C4—4716no—
858C22×C4—944no—
859C22×C4—9432no—
860C22×C4—948no—
861C22×C4—18832no—
862C22×C4C23×D4711yescharacteristic
863C22×C4C23×D4712yes—
864C22×C4C23×D4718yes—
865C22×C4C23×D47116yes—
866C4⋊C4—478no—
867C4⋊C4—478no—
868C4⋊C4—4716no—
869C4⋊C4—4716no—
870C4⋊C4—478no—
871C4⋊C4—478no—
872C4⋊C4—478no—
873C4⋊C4—478no—
874C4⋊C4—474no—
875C4⋊C4—474no—
876C4⋊C4—4716no—
877C4⋊C4—474no—
878C4⋊C4—474no—
879C4⋊C4—478no—
880C4⋊C4C23×D4714yes—
881C4⋊C4C23×D4714yes—
882C4⋊C4C23×D47116yes—
883C4⋊C4C23×D4714yes—
884C4⋊C4C23×D4714yes—
885C4⋊C4C23×D4718yes—
886C22⋊C4—474no—
887C22⋊C4—4716no—
888C22⋊C4—478no—
889C22⋊C4—478no—
890C22⋊C4—478no—
891C22⋊C4—4716no—
892C22⋊C4—4716no—
893C22⋊C4—478no—
894C22⋊C4—478no—
895C22⋊C4—478no—
896C22⋊C4—478no—
897C22⋊C4C23×D4714yes—
898C22⋊C4C23×D47116yes—
899C22⋊C4C23×D4718yes—
900C22⋊C4C23×D4718yes—
901C42—471no—
902C42—472no—
903C42—472no—
904C42—472no—
905C42—472no—
906C42—472no—
907C42—471no—
908C42—478no—
909C42—474no—
910C42C23×D4711yescharacteristic
911C42C23×D4712yes—
912C42C23×D4711yescharacteristic
913C42C23×D4714yes—
914C23—471no—
915C23—471no—
916C23—478no—
917C23—944no—
918C23—9416no—
919C23—942no—
920C23—9416no—
921C23—9416no—
922C23C24×D4711yescharacteristic
923C23C24×D4718yes—
924Q8—28no—
925Q8—44no—
926Q8—9416no—
927Q8—948no—
928Q8—1888no—
929Q8—1884no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—9416no—
936D4—9416no—
937D4—948no—
938D4—948no—
939D4—1888no—
940D4—1884no—
941D4—18816no—
942D4—1888no—
943D4—1888no—
944D4—1888no—
945D4—18816no—
946D4—18816no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—471no—
952C2×C4—472no—
953C2×C4—478no—
954C2×C4—474no—
955C2×C4—471no—
956C2×C4—472no—
957C2×C4—478no—
958C2×C4—478no—
959C2×C4—942no—
960C2×C4—9416no—
961C2×C4—944no—
962C2×C4—942no—
963C2×C4—9416no—
964C2×C4—944no—
965C2×C4—9416no—
966C2×C4—942no—
967C2×C4—9416no—
968C2×C4—944no—
969C2×C4—9416no—
970C2×C4—944no—
971C2×C4—942no—
972C2×C4—18816no—
973C2×C4—18816no—
974C2×C4—18816no—
975C2×C4C24×D4711yescharacteristic
976C2×C4C24×D4712yes—
977C2×C4C24×D4718yes—
978C2×C4C24×D4718yes—
979C2×C4C24×D4712yes—
980C2×C4C24×D4711yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—474no—
987C22—472no—
988C22—942no—
989C22—948no—
990C22—948no—
991C22—941no—
992C22—948no—
993C22—1884no—
994C22—18832no—
995C22C25×D4711yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—474no—
1001C4—472no—
1002C4—948no—
1003C4—942no—
1004C4—948no—
1005C4—941no—
1006C4H(5,𝔽2)×D4714yes—
1007C42−1+4×D4712yes—
1008C2—41no—
1009C2—48no—
1010C2—474no—
1011C2—1881no—
1012C2—1888no—
1013C2C2×H(5,𝔽2)×D4712yes—
1014C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3548C2
hypercenter#3548D47
hypocenterC47C2×#3548
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #20257788C2semidirect
2. #20257787C2semidirect
3. #20257786C2semidirect
4. #20257785C2semidirect
5. #20257784C2semidirect
6. #20257783C2semidirect
7. #20257782C2semidirect
8. #20257781C2semidirect
9. #562×D47C2semidirect
10. #554×D47C2semidirect
11. #550×D47C2semidirect
12. #547×D47C2semidirect
13. #540×D47C2semidirect
14. #537×D47C2semidirect
15. #533×D47C2semidirect
16. #532×D47C2semidirect
17. C47×#3548C2semidirect
20. #15689871C22semidirect
21. #15689870C22semidirect
22. #15689869C22semidirect
23. #15689868C22semidirect
24. #15689867C22semidirect
25. #15689834C22semidirect
26. #15689833C22semidirect
27. #15689832C22semidirect
28. #15689831C22semidirect
29. #15689830C22semidirect
30. #15689829C22semidirect
31. #15689828C22semidirect
32. #15689827C22semidirect
33. #15689795C22semidirect
34. #15689794C22semidirect
35. #15689794C22semidirect
36. #15689793C22semidirect
37. #15689793C22semidirect
38. #15689792C22semidirect
39. #15689791C22semidirect
40. #15689791C22semidirect
41. #15689778C22semidirect
42. #15689777C22semidirect
43. #15689776C22semidirect
44. #15689775C22semidirect
45. #15689774C22semidirect
46. #15689773C22semidirect
47. #15689772C22semidirect
48. #15689771C22semidirect
49. #15689729C22semidirect
50. #15689728C22semidirect
51. #15689727C22semidirect
52. #15689726C22semidirect
53. #15689725C22semidirect
54. #15689724C22semidirect
55. #15689723C22semidirect
56. #15689704C22semidirect
57. #15689703C22semidirect
58. #15689703C22semidirect
59. #15689703C22semidirect
60. #15689702C22semidirect
61. #15689702C22semidirect
62. #15689702C22semidirect
63. #15689701C22semidirect
64. #15689701C22semidirect
65. #15689700C22semidirect
66. #15689700C22semidirect
67. #15689680C22semidirect
68. #15689679C22semidirect
69. #15689678C22semidirect
70. #15689677C22semidirect
71. #15689676C22semidirect
72. #15689675C22semidirect
73. #15689674C22semidirect
74. #15689673C22semidirect
75. #15689672C22semidirect
76. #15689671C22semidirect
77. #15689670C22semidirect
78. #15689670C22semidirect
79. #15689669C22semidirect
80. #15689668C22semidirect
81. #15689668C22semidirect
105. C47×#562C22semidirect
106. C47×#554C22semidirect
107. C47×#550C22semidirect
108. C47×#547C22semidirect
109. C47×#540C22semidirect
110. C47×#537C22semidirect
111. C47×#533C22semidirect
112. C47×#532C22semidirect
509. #3548D47direct (N × H)
524. D47#3548direct (N × H)
532. #562C2×D47semidirect
541. #554C2×D47semidirect
550. #550C2×D47semidirect
559. #547C2×D47semidirect
567. #540C2×D47semidirect
579. #537C2×D47semidirect
586. #533C2×D47semidirect
596. #532C2×D47semidirect
620. C47C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#202577882
#202577872
#202577862
#202577852
#202577842
#202577832
#202577822
#202577812
#562×D472
#554×D472
#550×D472
#547×D472
#540×D472
#537×D472
#533×D472
#532×D472
C47×#35482
C2×#354847