Finite Group Databasebeta

← D47×#3550 #27124082

Subgroups — D47×#3550 #27124082

Order 12032.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257802C211yesmaximal, characteristic, complemented
2#20257801C214yesmaximal, complemented
3#20257800C212yesmaximal, complemented
4#20257799C212yesmaximal, complemented
5#20257798C214yesmaximal, complemented
6#20257797C214yesmaximal, complemented
7#20257796C218yesmaximal, complemented
8#20257795C214yesmaximal, complemented
9#20257794C212yesmaximal, complemented
10#563×D47C214yesmaximal, complemented
11#559×D47C212yesmaximal, complemented
12Q82×D47C212yesmaximal, complemented
13#556×D47C214yesmaximal, complemented
14D4×Q8×D47C214yesmaximal, complemented
15#542×D47C218yesmaximal, complemented
16#536×D47C214yesmaximal, complemented
17#533×D47C212yesmaximal, complemented
18#532×D47C211yesmaximal, characteristic
19C47×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D47C2212yes—
21C22×Q8×D47C2214yes—
22#15689877C2218yescomplemented
23#15689876C2218yescomplemented
24#15689875C22116yescomplemented
25#15689874C22116yescomplemented
26#15689873C2214yescomplemented
27#15689872C2218yescomplemented
28#15689859C2212yescomplemented
29#15689858C2214yescomplemented
30#15689857C2218yescomplemented
31#15689856C2218yescomplemented
32#15689855C2218yescomplemented
33Q8×Dic94C2218yescomplemented
34Q8×Dic94C2214yescomplemented
35#15689853C2212yescomplemented
36#15689853C2218yescomplemented
37#15689853C2218yescomplemented
38#15689847C2214yescomplemented
39#15689846C2214yescomplemented
40#15689845C2218yescomplemented
41#15689844C2218yescomplemented
42#15689843C2214yescomplemented
43#15689842C2218yescomplemented
44#15689841C2218yescomplemented
45#15689840C22116yescomplemented
46Q8×D188C2214yescomplemented
47D4×Dic94C2218yescomplemented
48D4×Dic94C2214yescomplemented
49#15689788C2218yescomplemented
50#15689788C2214yescomplemented
51Q8×C22⋊D47C2218yescomplemented
52#15689786C22116yescomplemented
53#15689786C2218yescomplemented
54#15689747C2218yescomplemented
55#15689746C2218yescomplemented
56#15689745C2218yescomplemented
57#15689744C2218yescomplemented
58#15689743C22116yescomplemented
59#15689742C2218yescomplemented
60#15689741C22116yescomplemented
61#15689740C2218yescomplemented
62#15689739C22116yescomplemented
63#15689738C2218yescomplemented
64#15689737C22116yescomplemented
65#15689699C2214yescomplemented
66#15689698C2218yescomplemented
67#15689697C2214yescomplemented
68#15689696C2218yescomplemented
69#15689696C2218yescomplemented
70#15689695C2218yescomplemented
71#15689695C2218yescomplemented
72#15689694C2214yescomplemented
73#15689693C2218yescomplemented
74#15689680C2212yescomplemented
75#15689679C2214yescomplemented
76#15689678C2212yescomplemented
77#15689678C2212yescomplemented
78#15689677C2214yescomplemented
79#15689677C2214yescomplemented
80#15689676C2214yescomplemented
81#15689675C2214yescomplemented
82#15689675C2214yescomplemented
83#15689674C2211yescharacteristic
84#15689673C2211yescharacteristic
85#15689672C2212yes—
86#15689671C2211yescharacteristic
87#15689670C2214yes—
88#15689669C2212yes—
89#15689668C2214yes—
90C4⋊Q8×D47C2212yes—
91C4⋊Q8×D47C2218yes—
92C4⋊Q8×D47C2211yescharacteristic
93C4⋊Q8×D47C2212yes—
94C4⋊Q8×D47C2218yes—
95#127×D47C2211yescharacteristic
96#126×D47C22116yes—
97#125×D47C2214yes—
98#124×D47C2212yes—
99#124×D47C2218yes—
100#124×D47C2218yes—
101#123×D47C2218yes—
102#123×D47C2218yes—
103C22⋊Q8×D47C2218yes—
104C22⋊Q8×D47C22116yes—
105C22⋊Q8×D47C2214yes—
106C22⋊Q8×D47C2214yes—
107#121×D47C2214yes—
108C4×Q8×D47C2214yes—
109C4×Q8×D47C2214yes—
110C4×Q8×D47C2218yes—
111C4×D4×D47C2214yes—
112C4×D4×D47C2218yes—
113#117×D47C2214yes—
114#117×D47C2214yes—
115C2×C42×D47C2211yescharacteristic
116C47×#563C2214yescomplemented
117C47×#559C2212yescomplemented
118Q82×C47C2212yescomplemented
119C47×#556C2214yescomplemented
120D4×Q8×C47C2214yescomplemented
121C47×#542C2218yescomplemented
122C47×#536C2214yescomplemented
123C47×#533C2212yescomplemented
124C47×#532C2211yescharacteristic
125C2×#10625354C2312yes—
126C2×#10625350C2312yes—
127C2×#10625350C2314yes—
128C2×#10625352C2314yes—
129C2×#10625352C2312yes—
130#41×D47—48no—
131C22×Dic94C2314yes—
132C22×Dic94C2318yes—
133C2×Q8×D47—416no—
134C2×Q8×D47C2314yes—
135C2×Q8×D47C2314yes—
136C2×Q8×D47C2318yes—
137C2×Q8×D47C2318yes—
138C2×Q8×D47C2318yes—
139C2×Q8×D47C2312yes—
140C2×D4×D47C2314yes—
141C2×D4×D47C2314yes—
142C2×D4×D47C2312yes—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2314yes—
146C22×C4×D47C2318yes—
147#13094024C2318yes—
148#13094024C2312yes—
149#13094024C2312yes—
150#13094024C2311yescharacteristic
151#13094024C2318yes—
152#13094023C2318yes—
153#13094023C23116yes—
154#13094023C2318yes—
155#13094023C2314yes—
156#13094023C2314yes—
157#13094023C2314yes—
158#13094023C2314yes—
159#13094023C2314yes—
160#13094023C23116yes—
161#13094023C23116yes—
162#13094022C23116yes—
163#13094022C2314yes—
164#13094022C2314yes—
165#13094022C2312yes—
166#13094022C2318yes—
167#13094022C2318yes—
168#13094021C2311yescharacteristic
169#13094020C2314yes—
170#13094020C2312yes—
171#13094019C23116yes—
172#13094019C23116yes—
173#13094019C23116yes—
174#13094018C23116yes—
175#13094017C23116yes—
176#13094017C23116yes—
177#13094017C23116yes—
178#13094016C2314yes—
179#13094015C2314yes—
180#13094015C2314yes—
181#13094014C2318yes—
182#13094014C2318yes—
183#13094013C2318yes—
184#13094013C2318yes—
185#13094013C2312yes—
186#13094012C2318yes—
187#13094012C2318yes—
188#13094012C2312yes—
189#13094011C2318yes—
190#13094011C2318yes—
191#13094011C2312yes—
192#13094010C23116yes—
193#13094010C23116yes—
194#13094010C23116yes—
195#13094010C23116yes—
196#13094010C2318yes—
197#13094009C23116yes—
198#13094009C23116yes—
199#13094008C2318yes—
200#13094008C2318yes—
201#13094007C2318yes—
202#13094007C2318yes—
203#13094006C23116yes—
204#13094006C23116yes—
205#13094005C2318yes—
206#13094005C2318yes—
207#13094004C2314yes—
208#13094004C23116yes—
209#13094004C2318yes—
210#13094004C2314yes—
211#13094003C23116yes—
212#13094003C2314yes—
213#13094003C2318yes—
214#13094003C2314yes—
215#13094002C2318yes—
216#13094002C23116yes—
217#13094002C23116yes—
218#13094002C23116yes—
219#13094002C2318yes—
220#13094001C2318yes—
221#13094001C23116yes—
222#13094001C23116yes—
223#13094001C23116yes—
224#13094001C2318yes—
225#13094000C23116yes—
226#13094000C2314yes—
227#13094000C2318yes—
228#13094000C2314yes—
229#13093999C2314yes—
230#13093998C2314yes—
231#13093997C2318yes—
232#13093996C2318yes—
233#13093995C2314yes—
234Q8×Dic47C2318yes—
235Q8×Dic47C2314yes—
236Q8×Dic47C2314yes—
237C4×Dic94C23116yes—
238C4×Dic94C2318yes—
239C4×Dic94C2318yes—
240C4×Dic94C2314yes—
241C4×Dic94C2318yes—
242C4×Dic94C2314yes—
243#13093989C2318yes—
244#13093989C23116yes—
245#13093989C2318yes—
246#13093989C2314yes—
247#13093989C2314yes—
248#13093989C2318yes—
249C4×D188C2318yes—
250C4×D188C2314yes—
251D4×Dic47C2318yes—
252D4×Dic47C2314yes—
253#13093986C2318yes—
254#13093986C2314yes—
255C4×C22⋊D47C23116yes—
256C4×C22⋊D47C2318yes—
257(C22⋊D47)⋊C4C23116yes—
258(C22⋊D47)⋊C4C2318yes—
259#13093983C2314yes—
260#13093983C2314yes—
261#13093982C2314yes—
262#13093982C2314yes—
263#13093982C2318yes—
264#13093981C2318yes—
265#13093981C2318yes—
266#13093980C2318yes—
267#13093980C2318yes—
268C4⋊C4×D47C2314yes—
269C4⋊C4×D47C2314yes—
270C4⋊C4×D47C2314yes—
271C4⋊C4×D47C2314yes—
272C4⋊C4×D47C2314yes—
273C4⋊C4×D47C2318yes—
274C4⋊C4×D47C23116yes—
275C4⋊C4×D47C2318yes—
276C22⋊C4×D47C2318yes—
277C22⋊C4×D47C2318yes—
278C22⋊C4×D47C2318yes—
279C22⋊C4×D47C23116yes—
280C2×C4×Dic47C2312yes—
281C2×C4×Dic47C2311yescharacteristic
282C42×D47C2312yes—
283C42×D47C2311yescharacteristic
284C42×D47C2311yescharacteristic
285C42×D47C2312yes—
286C42×D47C2311yescharacteristic
287C42×D47C2311yescharacteristic
288C42×D47C2318yes—
289C42×D47C2318yes—
290C2×#41×C47C2312yes—
291C22×Q8×C47C2314yes—
292C4⋊Q8×C47C2318yes—
293C4⋊Q8×C47C2312yes—
294C4⋊Q8×C47C2311yescharacteristic
295C4⋊Q8×C47C2312yes—
296C4⋊Q8×C47C2318yes—
297#127×C47C2311yescharacteristic
298#126×C47C23116yes—
299#125×C47C2314yes—
300#124×C47C2318yes—
301#124×C47C2318yes—
302#124×C47C2312yes—
303#123×C47C2318yes—
304#123×C47C2318yes—
305C22⋊Q8×C47C23116yes—
306C22⋊Q8×C47C2314yes—
307C22⋊Q8×C47C2318yes—
308C22⋊Q8×C47C2314yes—
309#121×C47C2314yes—
310C4×Q8×C47C2318yes—
311C4×Q8×C47C2314yes—
312C4×Q8×C47C2314yes—
313C4×D4×C47C2318yes—
314C4×D4×C47C2314yes—
315#117×C47C2314yes—
316#117×C47C2314yes—
317C2×C42×C47C2311yescharacteristic
318C23×D47C2414yes—
319C23×D47C2411yescharacteristic
320#41×C47—44no—
321C2×Q8×C47—48no—
322C2×Q8×C47C2414yes—
323C2×Q8×C47C2414yes—
324C2×Q8×C47C2418yes—
325C2×Q8×C47C2412yes—
326C2×D4×C47C2414yes—
327C2×D4×C47C2414yes—
328C2×D4×C47C2412yes—
329C22×C4×C47C2412yes—
330C22×C4×C47C2411yescharacteristic
331C22×C4×C47C2414yes—
332C22×C4×C47C2418yes—
333C2×C22⋊D47C2418yes—
334C2×C22⋊D47C2414yes—
335C2×C22⋊D47C2414yes—
336C2×C22⋊D47C2414yes—
337C22×Dic47C2412yes—
338C22×Dic47C2411yescharacteristic
339C22×Dic47C2414yes—
340C22×Dic47C2418yes—
341#10625354—44no—
342Q8×D47—216no—
343Q8×D47—216no—
344Q8×D47—416no—
345Q8×D47—416no—
346Q8×D47—416no—
347Q8×D47—44no—
348#10625352—44no—
349#10625352—48no—
350D4×D47—216no—
351D4×D47—44no—
352D4×D47—48no—
353#10625350—48no—
354#10625350—44no—
355C2×D188C2414yes—
356C2×D188C2414yes—
357C2×D188C2412yes—
358C2×C4×D47—216no—
359C2×C4×D47—24no—
360C2×C4×D47—28no—
361C2×C4×D47—416no—
362C2×C4×D47C2418yes—
363C2×C4×D47C2412yes—
364C2×C4×D47C2414yes—
365C2×C4×D47C2411yescharacteristic
366C2×C4×D47C2412yes—
367C2×C4×D47C2412yes—
368C2×C4×D47C2411yescharacteristic
369C2×C4×D47C2411yescharacteristic
370C2×C4×D47C2418yes—
371C2×C4×D47C2414yes—
372C2×C4×D47C2414yes—
373C2×C4×D47C24116yes—
374C2×C4×D47C2411yescharacteristic
375C2×C4×D47C2412yes—
376C2×Dic94—416no—
377C2×Dic94—48no—
378C2×Dic94C2418yes—
379C2×Dic94C2414yes—
380C2×Dic94C2418yes—
381C2×Dic94C2414yes—
382C2×Dic94C2418yes—
383C2×Dic94C24116yes—
384C2×Dic94C2414yes—
385C2×Dic94C2412yes—
386C4⋊C4×C47C2414yes—
387C4⋊C4×C47C2414yes—
388C4⋊C4×C47C2414yes—
389C4⋊C4×C47C2414yes—
390C4⋊C4×C47C2414yes—
391C4⋊C4×C47C2418yes—
392C4⋊C4×C47C24116yes—
393C4⋊C4×C47C2418yes—
394C22⋊C4×C47C2418yes—
395C22⋊C4×C47C2418yes—
396C22⋊C4×C47C2418yes—
397C22⋊C4×C47C24116yes—
398C42×C47C2412yes—
399C42×C47C2411yescharacteristic
400C42×C47C2411yescharacteristic
401C42×C47C2418yes—
402C42×C47C2418yes—
403C22⋊Dic47C2418yes—
404C22⋊Dic47C2418yes—
405C22⋊Dic47C2418yes—
406C22⋊Dic47C24116yes—
407(C2×D47)⋊C4C2418yes—
408(C2×D47)⋊C4C2418yes—
409(C2×D47)⋊C4C24116yes—
410(C2×D47)⋊C4C2418yes—
411(C2×D47)⋊C4C24116yes—
412(C2×D47)⋊C4C2418yes—
413(C2×D47)⋊C4C24116yes—
414C4⋊Dic47C2414yes—
415C4⋊Dic47C2414yes—
416C4⋊Dic47C2414yes—
417C4⋊Dic47C2414yes—
418C4⋊Dic47C2414yes—
419C4⋊Dic47C2418yes—
420C4⋊Dic47C24116yes—
421C4⋊Dic47C2418yes—
422Dic47⋊C4C2418yes—
423Dic47⋊C4C2418yes—
424Dic47⋊C4C2418yes—
425Dic47⋊C4C2418yes—
426Dic47⋊C4C2418yes—
427Dic47⋊C4C2418yes—
428Dic47⋊C4C24116yes—
429Dic47⋊C4C24116yes—
430Dic47⋊C4C2418yes—
431Dic47⋊C4C2418yes—
432Dic47⋊C4C2418yes—
433C4×Dic47C2412yes—
434C4×Dic47C2412yes—
435C4×Dic47C2412yes—
436C4×Dic47C2411yescharacteristic
437C4×Dic47C2412yes—
438C4×Dic47C2412yes—
439C4×Dic47C2411yescharacteristic
440C4×Dic47C2418yes—
441C4×Dic47C2418yes—
442C4×Dic47C24116yes—
443C4×Dic47C2418yes—
444C4×Dic47C2418yes—
445C23×C47C2514yes—
446C23×C47C2511yescharacteristic
447C22×D47—28no—
448C22×D47—22no—
449C22×D47—24no—
450C22×D47—216no—
451C22×D47C2514yes—
452C22×D47C2511yescharacteristic
453C22×D47C2511yescharacteristic
454Q8×C47—28no—
455Q8×C47—28no—
456Q8×C47—48no—
457Q8×C47—42no—
458D4×C47—28no—
459D4×C47—44no—
460D4×C47—42no—
461C2×C4×C47—28no—
462C2×C4×C47—22no—
463C2×C4×C47—24no—
464C2×C4×C47—48no—
465C2×C4×C47C2518yes—
466C2×C4×C47C2511yescharacteristic
467C2×C4×C47C2514yes—
468C2×C4×C47C2512yes—
469C2×C4×C47C2518yes—
470C2×C4×C47C2511yescharacteristic
471C2×C4×C47C2512yes—
472C22⋊D47—216no—
473C22⋊D47—44no—
474C22⋊D47—44no—
475C22⋊D47—44no—
476C2×Dic47—28no—
477C2×Dic47—22no—
478C2×Dic47—24no—
479C2×Dic47—48no—
480C2×Dic47C2518yes—
481C2×Dic47C2512yes—
482C2×Dic47C2511yescharacteristic
483C2×Dic47C2514yes—
484C2×Dic47C2518yes—
485C2×Dic47C2511yescharacteristic
486C2×Dic47C2512yes—
487D188—28no—
488D188—44no—
489D188—42no—
490C4×D47—22no—
491C4×D47—28no—
492C4×D47—216no—
493C4×D47—24no—
494C4×D47—216no—
495C4×D47—22no—
496C4×D47—28no—
497C4×D47—24no—
498C4×D47—22no—
499C4×D47—28no—
500C4×D47—24no—
501C4×D47—416no—
502C4×D47H(5,𝔽2)14yes—
503C4×D472−1+418yes—
504Dic94—28no—
505Dic94—28no—
506Dic94—216no—
507Dic94—216no—
508Dic94—48no—
509Dic94—416no—
510Dic94—42no—
511Dic94—44no—
512C2×#3550—471nomaximal, Sylow
513C22×C47—24no—
514C22×C47—21no—
515C22×C47—22no—
516C22×C47—28no—
517C22×C47C2611yescharacteristic
518C2×D47—24no—
519C2×D47—21no—
520C2×D47—22no—
521C2×D47—28no—
522C2×D47—416no—
523C2×D47—44no—
524C2×D47C2×H(5,𝔽2)12yes—
525C2×D47C2×2−1+414yes—
526C4×C47—28no—
527C4×C47—24no—
528C4×C47—21no—
529C4×C47—28no—
530C4×C47—22no—
531C4×C47C2×H(5,𝔽2)12yes—
532C4×C47C2×2−1+414yes—
533Dic47—28no—
534Dic47—24no—
535Dic47—21no—
536Dic47—28no—
537Dic47—22no—
538Dic47C2×H(5,𝔽2)12yes—
539Dic47C2×2−1+414yes—
540#3550—474no—
541#3550—472no—
542#3550—472no—
543#3550—474no—
544#3550—474no—
545#3550—478no—
546#3550—474no—
547#3550—472no—
548#3550—471no—
549#3550D4711yescharacteristic, direct product factor
550C2×#563—474no—
551C2×#559—472no—
552C2×Q82—472no—
553C2×#556—474no—
554C2×D4×Q8—474no—
555C2×#542—478no—
556C2×#536—474no—
557C2×#533—472no—
558C2×#532—471no—
559C2×C47—44no—
560C2×C47—41no—
561C2×C47C22×H(5,𝔽2)11yescharacteristic
562C2×C47C22×2−1+412yes—
563D47—44no—
564D47—41no—
565D47#355014yesdirect product factor
566C22×#41—472no—
567C23×Q8—474no—
568#563—478no—
569#563—4716no—
570#563—478no—
571#563—474no—
572#563—478no—
573#563—4716no—
574#563C2×D4714yescomplemented
575#559—472no—
576#559—478no—
577#559—478no—
578#559—474no—
579#559—478no—
580#559C2×D4712yescomplemented
581Q82—478no—
582Q82—478no—
583Q82—472no—
584Q82—478no—
585Q82—474no—
586Q82C2×D4712yescomplemented
587#556—474no—
588#556—4716no—
589#556—478no—
590#556—478no—
591#556—478no—
592#556—474no—
593#556—474no—
594#556—478no—
595#556C2×D4714yescomplemented
596D4×Q8—478no—
597D4×Q8—478no—
598D4×Q8—474no—
599D4×Q8—478no—
600D4×Q8—4716no—
601D4×Q8—474no—
602D4×Q8—478no—
603D4×Q8—474no—
604D4×Q8C2×D4714yescomplemented
605#542—478no—
606#542—4716no—
607#542—4716no—
608#542—478no—
609#542—4716no—
610#542—4716no—
611#542—478no—
612#542—478no—
613#542—478no—
614#542—478no—
615#542—478no—
616#542C2×D4718yescomplemented
617#536—474no—
618#536—474no—
619#536—478no—
620#536—478no—
621#536—478no—
622#536—478no—
623#536—478no—
624#536—478no—
625#536—474no—
626#536C2×D4714yescomplemented
627#533—472no—
628#533—472no—
629#533—474no—
630#533—474no—
631#533—474no—
632#533—474no—
633#533—474no—
634#533—474no—
635#533—472no—
636#533C2×D4712yescomplemented
637#532—472no—
638#532—471no—
639#532—471no—
640#532—472no—
641#532—474no—
642#532—474no—
643#532—471no—
644#532C2×D4711yescharacteristic
645C2×C4⋊Q8—471no—
646C2×C4⋊Q8—472no—
647C2×C4⋊Q8—472no—
648C2×C4⋊Q8—478no—
649C2×C4⋊Q8—478no—
650C2×#127—471no—
651C2×#126—4716no—
652C2×#125—474no—
653C2×#124—472no—
654C2×#124—478no—
655C2×#124—478no—
656C2×#123—478no—
657C2×#123—478no—
658C2×C22⋊Q8—474no—
659C2×C22⋊Q8—474no—
660C2×C22⋊Q8—478no—
661C2×C22⋊Q8—4716no—
662C2×#121—474no—
663C2×C4×Q8—474no—
664C2×C4×Q8—474no—
665C2×C4×Q8—478no—
666C2×C4×D4—474no—
667C2×C4×D4—478no—
668C2×#117—474no—
669C2×#117—474no—
670C22×C42—471no—
671C47C2×#355011yescharacteristic, complemented, Sylow
672C2×#41—472no—
673C2×#41—474no—
674C2×#41—472no—
675C2×#41—474no—
676C2×#41—472no—
677C2×#41—1888no—
678C2×#41C22×D4712yes—
679C22×Q8—474no—
680C22×Q8—474no—
681C22×Q8—478no—
682C22×Q8—472no—
683C22×Q8—478no—
684C22×Q8—478no—
685C22×Q8—478no—
686C22×Q8—474no—
687C22×Q8—18816no—
688C22×Q8C22×D4714yes—
689C22×D4—474no—
690C22×D4—474no—
691C22×D4—472no—
692C23×C4—472no—
693C23×C4—474no—
694C23×C4—471no—
695C23×C4—478no—
696C4⋊Q8—472no—
697C4⋊Q8—474no—
698C4⋊Q8—474no—
699C4⋊Q8—478no—
700C4⋊Q8—478no—
701C4⋊Q8—4716no—
702C4⋊Q8—474no—
703C4⋊Q8—474no—
704C4⋊Q8—474no—
705C4⋊Q8—474no—
706C4⋊Q8—474no—
707C4⋊Q8—4716no—
708C4⋊Q8—4716no—
709C4⋊Q8—4716no—
710C4⋊Q8—478no—
711C4⋊Q8—478no—
712C4⋊Q8—471no—
713C4⋊Q8—472no—
714C4⋊Q8—472no—
715C4⋊Q8—478no—
716C4⋊Q8—478no—
717C4⋊Q8C22×D4711yescharacteristic
718C4⋊Q8C22×D4712yes—
719C4⋊Q8C22×D4712yes—
720C4⋊Q8C22×D4718yes—
721C4⋊Q8C22×D4718yes—
722#127—472no—
723#127—474no—
724#127—471no—
725#127C22×D4711yescharacteristic
726#126—4716no—
727#126—4716no—
728#126—4716no—
729#126—4716no—
730#126—4716no—
731#126—4716no—
732#126—4716no—
733#126C22×D47116yes—
734#125—478no—
735#125—478no—
736#125—474no—
737#125—474no—
738#125—474no—
739#125C22×D4714yes—
740#124—472no—
741#124—478no—
742#124—478no—
743#124—472no—
744#124—478no—
745#124—478no—
746#124—478no—
747#124—4716no—
748#124—4716no—
749#124—4716no—
750#124—4716no—
751#124—472no—
752#124—478no—
753#124—478no—
754#124C22×D4712yes—
755#124C22×D4718yes—
756#124C22×D4718yes—
757#123—478no—
758#123—478no—
759#123—478no—
760#123—478no—
761#123—4716no—
762#123—4716no—
763#123—4716no—
764#123—478no—
765#123—4716no—
766#123—478no—
767#123C22×D4718yes—
768#123C22×D4718yes—
769C22⋊Q8—474no—
770C22⋊Q8—474no—
771C22⋊Q8—478no—
772C22⋊Q8—4716no—
773C22⋊Q8—474no—
774C22⋊Q8—474no—
775C22⋊Q8—478no—
776C22⋊Q8—4716no—
777C22⋊Q8—478no—
778C22⋊Q8—474no—
779C22⋊Q8—478no—
780C22⋊Q8—474no—
781C22⋊Q8—4716no—
782C22⋊Q8—478no—
783C22⋊Q8—4716no—
784C22⋊Q8—4716no—
785C22⋊Q8—4716no—
786C22⋊Q8—478no—
787C22⋊Q8—478no—
788C22⋊Q8—4716no—
789C22⋊Q8—4716no—
790C22⋊Q8—4716no—
791C22⋊Q8C22×D4714yes—
792C22⋊Q8C22×D4714yes—
793C22⋊Q8C22×D4718yes—
794C22⋊Q8C22×D47116yes—
795#121—474no—
796#121—478no—
797#121—474no—
798#121—474no—
799#121—478no—
800#121C22×D4714yes—
801C4×Q8—474no—
802C4×Q8—474no—
803C4×Q8—478no—
804C4×Q8—478no—
805C4×Q8—474no—
806C4×Q8—478no—
807C4×Q8—474no—
808C4×Q8—4716no—
809C4×Q8—478no—
810C4×Q8—478no—
811C4×Q8—474no—
812C4×Q8—478no—
813C4×Q8—474no—
814C4×Q8—4716no—
815C4×Q8—478no—
816C4×Q8C22×D4714yes—
817C4×Q8C22×D4714yes—
818C4×Q8C22×D4718yes—
819C4×D4—474no—
820C4×D4—478no—
821C4×D4—478no—
822C4×D4—4716no—
823C4×D4—474no—
824C4×D4—478no—
825C4×D4—478no—
826C4×D4—4716no—
827C4×D4—474no—
828C4×D4—478no—
829C4×D4C22×D4714yes—
830C4×D4C22×D4718yes—
831#117—474no—
832#117—474no—
833#117—474no—
834#117—474no—
835#117—478no—
836#117—478no—
837#117—478no—
838#117—478no—
839#117—478no—
840#117C22×D4714yes—
841#117C22×D4714yes—
842C2×C4⋊C4—474no—
843C2×C4⋊C4—474no—
844C2×C4⋊C4—474no—
845C2×C4⋊C4—474no—
846C2×C4⋊C4—474no—
847C2×C4⋊C4—478no—
848C2×C4⋊C4—4716no—
849C2×C4⋊C4—478no—
850C2×C22⋊C4—478no—
851C2×C22⋊C4—478no—
852C2×C22⋊C4—478no—
853C2×C22⋊C4—4716no—
854C2×C42—471no—
855C2×C42—472no—
856C2×C42—478no—
857C2×C42—478no—
858C2×C42—472no—
859C2×C42—471no—
860C2×C42—471no—
861C2×C42—471no—
862C2×C42—471no—
863C2×C42—472no—
864C2×C42C22×D4711yescharacteristic
865C24—474no—
866C24—471no—
867#41—44no—
868#41—1888no—
869#41—1884no—
870#41—1888no—
871#41—1884no—
872#41—1884no—
873C2×Q8—48no—
874C2×Q8—478no—
875C2×Q8—474no—
876C2×Q8—478no—
877C2×Q8—474no—
878C2×Q8—4716no—
879C2×Q8—478no—
880C2×Q8—472no—
881C2×Q8—474no—
882C2×Q8—9416no—
883C2×Q8—9416no—
884C2×Q8—1888no—
885C2×Q8—18816no—
886C2×Q8—18816no—
887C2×Q8—1884no—
888C2×Q8—18816no—
889C2×Q8—18816no—
890C2×Q8C23×D4714yes—
891C2×Q8C23×D4714yes—
892C2×Q8C23×D4718yes—
893C2×Q8C23×D4712yes—
894C2×D4—478no—
895C2×D4—474no—
896C2×D4—474no—
897C2×D4—474no—
898C2×D4—474no—
899C2×D4—474no—
900C2×D4—472no—
901C2×D4—9416no—
902C2×D4—1884no—
903C2×D4—1888no—
904C2×D4C23×D4714yes—
905C2×D4C23×D4714yes—
906C2×D4C23×D4712yes—
907C22×C4—472no—
908C22×C4—471no—
909C22×C4—472no—
910C22×C4—471no—
911C22×C4—474no—
912C22×C4—478no—
913C22×C4—478no—
914C22×C4—472no—
915C22×C4—474no—
916C22×C4—471no—
917C22×C4—472no—
918C22×C4—472no—
919C22×C4—471no—
920C22×C4—471no—
921C22×C4—478no—
922C22×C4—474no—
923C22×C4—474no—
924C22×C4—4716no—
925C22×C4—948no—
926C22×C4—9416no—
927C22×C4—944no—
928C22×C4—18816no—
929C22×C4C23×D4712yes—
930C22×C4C23×D4711yescharacteristic
931C22×C4C23×D4714yes—
932C22×C4C23×D4718yes—
933C4⋊C4—478no—
934C4⋊C4—478no—
935C4⋊C4—478no—
936C4⋊C4—478no—
937C4⋊C4—478no—
938C4⋊C4—478no—
939C4⋊C4—478no—
940C4⋊C4—4716no—
941C4⋊C4—4716no—
942C4⋊C4—478no—
943C4⋊C4—478no—
944C4⋊C4—474no—
945C4⋊C4—474no—
946C4⋊C4—474no—
947C4⋊C4—474no—
948C4⋊C4—474no—
949C4⋊C4—478no—
950C4⋊C4—4716no—
951C4⋊C4—478no—
952C4⋊C4C23×D4714yes—
953C4⋊C4C23×D4714yes—
954C4⋊C4C23×D4714yes—
955C4⋊C4C23×D4714yes—
956C4⋊C4C23×D4714yes—
957C4⋊C4C23×D4718yes—
958C4⋊C4C23×D47116yes—
959C4⋊C4C23×D4718yes—
960C22⋊C4—478no—
961C22⋊C4—478no—
962C22⋊C4—478no—
963C22⋊C4—4716no—
964C22⋊C4—478no—
965C22⋊C4—478no—
966C22⋊C4—4716no—
967C22⋊C4—478no—
968C22⋊C4—478no—
969C22⋊C4—4716no—
970C22⋊C4—4716no—
971C22⋊C4C23×D4718yes—
972C22⋊C4C23×D4718yes—
973C22⋊C4C23×D4718yes—
974C22⋊C4C23×D47116yes—
975C42—472no—
976C42—472no—
977C42—472no—
978C42—471no—
979C42—472no—
980C42—471no—
981C42—472no—
982C42—478no—
983C42—478no—
984C42—478no—
985C42—478no—
986C42—4716no—
987C42C23×D4712yes—
988C42C23×D4711yescharacteristic
989C42C23×D4711yescharacteristic
990C42C23×D4718yes—
991C42C23×D4718yes—
992C23—471no—
993C23—474no—
994C23—471no—
995C23—948no—
996C23—942no—
997C23—944no—
998C23—9416no—
999C23C24×D4714yes—
1000C23C24×D4711yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—9416no—
1006Q8—9416no—
1007Q8—948no—
1008Q8—948no—
1009Q8—1888no—
1010Q8—18816no—
1011Q8—1882no—
1012Q8—1884no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—9416no—
1017D4—948no—
1018D4—1882no—
1019D4—1884no—
1020D4—1884no—
1021D4—1884no—
1022D4—1884no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—472no—
1028C2×C4—471no—
1029C2×C4—474no—
1030C2×C4—478no—
1031C2×C4—478no—
1032C2×C4—472no—
1033C2×C4—474no—
1034C2×C4—471no—
1035C2×C4—478no—
1036C2×C4—944no—
1037C2×C4—948no—
1038C2×C4—942no—
1039C2×C4—944no—
1040C2×C4—942no—
1041C2×C4—948no—
1042C2×C4—9416no—
1043C2×C4—9416no—
1044C2×C4—944no—
1045C2×C4—948no—
1046C2×C4—942no—
1047C2×C4—948no—
1048C2×C4—942no—
1049C2×C4—944no—
1050C2×C4—18816no—
1051C2×C4—1888no—
1052C2×C4C24×D4718yes—
1053C2×C4C24×D4712yes—
1054C2×C4C24×D4714yes—
1055C2×C4C24×D4711yescharacteristic
1056C2×C4C24×D4718yes—
1057C2×C4C24×D4711yescharacteristic
1058C2×C4C24×D4712yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—472no—
1064C22—474no—
1065C22—944no—
1066C22—941no—
1067C22—942no—
1068C22—948no—
1069C22—18816no—
1070C22—1884no—
1071C22C25×D4711yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—472no—
1078C4—474no—
1079C4—941no—
1080C4—944no—
1081C4—948no—
1082C4—942no—
1083C4—948no—
1084C4H(5,𝔽2)×D4712yes—
1085C42−1+4×D4714yes—
1086C2—44no—
1087C2—41no—
1088C2—474no—
1089C2—1884no—
1090C2—1881no—
1091C2C2×H(5,𝔽2)×D4711yescharacteristic
1092C2C2×2−1+4×D4712yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3550C2
prime radical#532×D47C2
hypercenter#3550D47
hypocenterC47C2×#3550
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #20257802C2semidirect
2. #20257801C2semidirect
3. #20257800C2semidirect
4. #20257799C2semidirect
5. #20257798C2semidirect
6. #20257797C2semidirect
7. #20257796C2semidirect
8. #20257795C2semidirect
9. #20257794C2semidirect
10. #563×D47C2semidirect
11. #559×D47C2semidirect
12. Q82×D47C2semidirect
13. #556×D47C2semidirect
14. D4×Q8×D47C2semidirect
15. #542×D47C2semidirect
16. #536×D47C2semidirect
17. #533×D47C2semidirect
19. C47×#3550C2semidirect
22. #15689877C22semidirect
23. #15689876C22semidirect
24. #15689875C22semidirect
25. #15689874C22semidirect
26. #15689873C22semidirect
27. #15689872C22semidirect
28. #15689859C22semidirect
29. #15689858C22semidirect
30. #15689857C22semidirect
31. #15689856C22semidirect
32. #15689855C22semidirect
33. Q8×Dic94C22semidirect
34. Q8×Dic94C22semidirect
35. #15689853C22semidirect
36. #15689853C22semidirect
37. #15689853C22semidirect
38. #15689847C22semidirect
39. #15689846C22semidirect
40. #15689845C22semidirect
41. #15689844C22semidirect
42. #15689843C22semidirect
43. #15689842C22semidirect
44. #15689841C22semidirect
45. #15689840C22semidirect
46. Q8×D188C22semidirect
47. D4×Dic94C22semidirect
48. D4×Dic94C22semidirect
49. #15689788C22semidirect
50. #15689788C22semidirect
51. Q8×C22⋊D47C22semidirect
52. #15689786C22semidirect
53. #15689786C22semidirect
54. #15689747C22semidirect
55. #15689746C22semidirect
56. #15689745C22semidirect
57. #15689744C22semidirect
58. #15689743C22semidirect
59. #15689742C22semidirect
60. #15689741C22semidirect
61. #15689740C22semidirect
62. #15689739C22semidirect
63. #15689738C22semidirect
64. #15689737C22semidirect
65. #15689699C22semidirect
66. #15689698C22semidirect
67. #15689697C22semidirect
68. #15689696C22semidirect
69. #15689696C22semidirect
70. #15689695C22semidirect
71. #15689695C22semidirect
72. #15689694C22semidirect
73. #15689693C22semidirect
74. #15689680C22semidirect
75. #15689679C22semidirect
76. #15689678C22semidirect
77. #15689678C22semidirect
78. #15689677C22semidirect
79. #15689677C22semidirect
80. #15689676C22semidirect
81. #15689675C22semidirect
82. #15689675C22semidirect
116. C47×#563C22semidirect
117. C47×#559C22semidirect
118. Q82×C47C22semidirect
119. C47×#556C22semidirect
120. D4×Q8×C47C22semidirect
121. C47×#542C22semidirect
122. C47×#536C22semidirect
123. C47×#533C22semidirect
549. #3550D47direct (N × H)
565. D47#3550direct (N × H)
574. #563C2×D47semidirect
580. #559C2×D47semidirect
586. Q82C2×D47semidirect
595. #556C2×D47semidirect
604. D4×Q8C2×D47semidirect
616. #542C2×D47semidirect
626. #536C2×D47semidirect
636. #533C2×D47semidirect
671. C47C2×#3550semidirect

Maximal subgroups

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

subgroupindex
#202578022
#202578012
#202578002
#202577992
#202577982
#202577972
#202577962
#202577952
#202577942
#563×D472
#559×D472
Q82×D472
#556×D472
D4×Q8×D472
#542×D472
#536×D472
#533×D472
#532×D472
C47×#35502
C2×#355047