Finite Group Databasebeta

← #27124108

Subgroups — #27124108

Order 12032.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257812C214yesmaximal, complemented
2#20257802C211yesmaximal, characteristic, complemented
3#20257786C212yesmaximal, complemented
4#20257780C214yesmaximal, complemented
5#20257756C214yesmaximal, complemented
6#20257743C214yesmaximal, complemented
7#20257723C212yesmaximal, complemented
8#20257719C212yesmaximal, complemented
9#20257706C218yesmaximal, complemented
10#20257528C214yesmaximal, complemented
11#20257013C212yesmaximal, complemented
12#20256989C212yesmaximal, complemented
13#20256945C214yesmaximal, complemented
14D4×#10625352C214yesmaximal, complemented
15#20256801C218yesmaximal, complemented
16#20256719C214yesmaximal, complemented
17#20256683C212yesmaximal, complemented
18#532×D47C211yesmaximal, characteristic, complemented
19C47×#3549C211yesmaximal, characteristic, complemented
20C22×#10625352C2214yescomplemented
21C2×#41×D47C2212yescomplemented
22#15689873C2214yescomplemented
23#15689873C2218yescomplemented
24#15689867C22116yescomplemented
25#15689867C2218yescomplemented
26#15689862C2218yescomplemented
27#15689862C22116yescomplemented
28#15689859C2212yescomplemented
29#15689853C2212yescomplemented
30#15689843C2214yescomplemented
31#15689836C2218yescomplemented
32#15689835C2218yescomplemented
33#15689834C2214yescomplemented
34#15689830C2214yescomplemented
35#15689825C2218yescomplemented
36#15689820C2218yescomplemented
37#15689812C2218yescomplemented
38#15689812C2218yescomplemented
39#15689804C2218yescomplemented
40#15689803C22116yescomplemented
41#15689794C2214yescomplemented
42#15689793C2214yescomplemented
43#15689791C2218yescomplemented
44D4×Dic94C2214yescomplemented
45#15689779C2218yescomplemented
46#15689778C2214yescomplemented
47#15689777C2214yescomplemented
48#15689773C2218yescomplemented
49#15689770C2218yescomplemented
50#15689767C2218yescomplemented
51#15689767C2218yescomplemented
52#15689760C22116yescomplemented
53D4×C22⋊D47C2218yescomplemented
54#15689751C2218yescomplemented
55#15689742C22116yescomplemented
56#15689740C2218yescomplemented
57#15689740C2218yescomplemented
58#15689727C22116yescomplemented
59#15689726C2218yescomplemented
60#15689726C2218yescomplemented
61#15689708C22116yescomplemented
62#15689708C22116yescomplemented
63#15689702C2218yescomplemented
64#15689702C2218yescomplemented
65#15689701C2218yescomplemented
66#15689699C2214yescomplemented
67#15689694C2214yescomplemented
68#15689693C2218yescomplemented
69#15689690C2218yescomplemented
70#15689690C2214yescomplemented
71#15689686C2218yescomplemented
72#15689683C2218yescomplemented
73#15689683C2218yescomplemented
74#15689680C2212yescomplemented
75#15689678C2212yescomplemented
76#15689678C2212yescomplemented
77#15689674C2211yescharacteristic, complemented
78#15689673C2211yescharacteristic, complemented
79#15689672C2212yescomplemented
80#15689672C2218yescomplemented
81#15689671C2212yes—
82#15689671C2211yescharacteristic
83#15689671C2218yescomplemented
84#15689671C2212yescomplemented
85#15689670C2214yescomplemented
86#15689669C2212yescomplemented
87#15689668C2214yescomplemented
88#15689668C2218yescomplemented
89C4⋊Q8×D47C2211yescharacteristic, complemented
90#127×D47C2211yescharacteristic
91#15689655C2214yescomplemented
92#15689655C2214yescomplemented
93#15689654C2214yescomplemented
94#15689654C2214yescomplemented
95#15689654C2218yescomplemented
96#15689652C22116yescomplemented
97#15689652C2214yescomplemented
98#15689652C2214yescomplemented
99#124×D47C2212yescomplemented
100#15689633C2218yescomplemented
101#15689633C2214yescomplemented
102#15689633C2214yescomplemented
103#15689630C2214yescomplemented
104#15689629C2218yescomplemented
105#15689629C22116yescomplemented
106#15689629C2218yescomplemented
107#121×D47C2214yescomplemented
108#41×Dic47C2214yescomplemented
109#15689591C2218yescomplemented
110C4×#10625352C2214yescomplemented
111C4×#10625352C2214yescomplemented
112C2×D4×Dic47C2218yescomplemented
113C4×D4×D47C2214yescomplemented
114#117×D47C2214yescomplemented
115C2×C42×D47C2211yescharacteristic, complemented
116C47×H(3,𝔽4)C2214yescomplemented
117C47×#555C2214yescomplemented
118C47×#555C2212yescomplemented
119D42×C47C2214yescomplemented
120D42×C47C2212yescomplemented
121C47×#535C2214yescomplemented
122C47×#535C2218yescomplemented
123C47×#532C2211yescharacteristic
124C47×#532C2212yescomplemented
125C2×#10625354C2312yes—
126C2×#10625350C2318yes—
127C2×#10625350C2312yes—
128C2×#10625350C2314yes—
129C2×#10625352—416no—
130C2×#10625352C2314yes—
131C2×#10625352C2318yes—
132C2×#10625352C2314yes—
133C2×#10625352C2318yes—
134C2×#10625352C2312yes—
135C2×#10625352C2314yes—
136C2×#10625352C2318yes—
137#41×D47—48no—
138C22×Dic94C2314yes—
139C2×Q8×D47C2312yes—
140C22×C22⋊D47C2318yes—
141C2×D4×D47C2314yes—
142C2×D4×D47C2314yes—
143C2×D4×D47C2312yes—
144C23×Dic47C2318yes—
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2314yes—
147C22×C4×D47C2312yes—
148#13094024C2318yes—
149#13094024C2312yes—
150#13094024C2312yes—
151#13094024C2311yescharacteristic
152#13094023C2314yes—
153#13094023C2318yes—
154#13094022C2318yes—
155#13094022C2312yes—
156#13094021C2311yescharacteristic
157#13094020C2318yes—
158#13094020C2318yes—
159#13094020C2312yes—
160#13094020C2314yes—
161#13094017C23116yes—
162#13094017C23116yes—
163#13094017C2318yes—
164#13094017C23116yes—
165#13094017C2318yes—
166#13094016C23116yes—
167#13094016C2314yes—
168#13094015C2314yes—
169#13094015C2318yes—
170#13094015C2314yes—
171#13094013C2312yes—
172#13094012C2318yes—
173#13094012C2312yes—
174#13094011C2314yes—
175#13094011C2318yes—
176#13094011C2318yes—
177#13094011C2318yes—
178#13094011C2314yes—
179#13094011C2312yes—
180#13094010C2318yes—
181#13094010C23116yes—
182#13094008C2318yes—
183#13094008C23116yes—
184#13094008C2318yes—
185#13094006C23116yes—
186#13094006C23116yes—
187#13094006C23116yes—
188#13094006C2318yes—
189#13094006C2318yes—
190#13094005C2318yes—
191#13094005C23116yes—
192#13094005C23116yes—
193#13094005C2318yes—
194#13094005C2318yes—
195#13094004C2314yes—
196#13094004C2318yes—
197#13094004C2314yes—
198#13094003C2314yes—
199#13094003C2318yes—
200#13094003C2318yes—
201#13094003C2314yes—
202#13094001C23116yes—
203#13094001C23116yes—
204#13094001C23116yes—
205#13094001C23116yes—
206#13094000C23116yes—
207#13094000C2314yes—
208#13094000C2314yes—
209#13093999C2314yes—
210#13093998C2318yes—
211#13093998C2314yes—
212#13093997C23116yes—
213#13093997C23116yes—
214#13093997C2318yes—
215#13093996C23116yes—
216#13093996C23116yes—
217#13093996C23116yes—
218#13093996C23116yes—
219#13093996C2318yes—
220#13093996C23116yes—
221#13093995C23116yes—
222#13093995C2314yes—
223#13093995C2314yes—
224#13093995C2314yes—
225#13093995C2318yes—
226#13093995C23116yes—
227#13093995C2314yes—
228#13093995C2314yes—
229#13093995C23116yes—
230#13093993C23116yes—
231#13093993C2318yes—
232#13093993C2318yes—
233#13093992C23116yes—
234#13093992C2318yes—
235Q8×Dic47C2314yes—
236Q8×Dic47C2314yes—
237C4×Dic94C2314yes—
238C4×Dic94C2314yes—
239#13093989C2318yes—
240#13093989C2314yes—
241#13093989C2314yes—
242C4×D188C2314yes—
243D4×Dic47C2318yes—
244D4×Dic47C2318yes—
245D4×Dic47C23116yes—
246D4×Dic47C2314yes—
247D4×Dic47C2314yes—
248D4×Dic47C2314yes—
249D4×Dic47C23116yes—
250D4×Dic47C2314yes—
251D4×Dic47C2318yes—
252D4×Dic47C2318yes—
253D4×Dic47C2314yes—
254#13093986C2318yes—
255#13093986C2314yes—
256C4×C22⋊D47C2318yes—
257C4×C22⋊D47C2318yes—
258C4×C22⋊D47C2318yes—
259(C22⋊D47)⋊C4C2318yes—
260(C22⋊D47)⋊C4C23116yes—
261(C22⋊D47)⋊C4C2318yes—
262(C22⋊D47)⋊C4C2318yes—
263(C22⋊D47)⋊C4C23116yes—
264#13093983C2314yes—
265#13093983C2318yes—
266#13093983C2314yes—
267#13093982C2314yes—
268#13093982C2314yes—
269#13093981C23116yes—
270#13093981C2318yes—
271#13093980C2318yes—
272#13093980C2318yes—
273#13093980C2318yes—
274C2×C4⋊Dic47C2318yes—
275C4⋊C4×D47C2314yes—
276C4⋊C4×D47C2318yes—
277C2×C22⋊Dic47C23116yes—
278C22⋊C4×D47C2318yes—
279C22⋊C4×D47C2318yes—
280C2×C4×Dic47C2312yes—
281C2×C4×Dic47C2311yescharacteristic
282C2×C4×Dic47C2318yes—
283C42×D47C2312yes—
284C42×D47C2311yescharacteristic
285C42×D47C2311yescharacteristic
286C42×D47C2311yescharacteristic
287C42×D47C2311yescharacteristic
288C42×D47C2312yes—
289C42×D47C2318yes—
290C2×#41×C47C2312yes—
291C2×#41×C47C2314yes—
292C22×D4×C47C2318yes—
293C22×D4×C47C2314yes—
294C4⋊Q8×C47C2311yescharacteristic
295C4⋊Q8×C47C2312yes—
296#127×C47C2312yes—
297#127×C47C2311yescharacteristic
298#127×C47C2318yes—
299#124×C47C23116yes—
300#124×C47C2312yes—
301#124×C47C2314yes—
302#124×C47C2318yes—
303#121×C47C2314yes—
304#121×C47C2318yes—
305#121×C47C2318yes—
306#121×C47C2318yes—
307#121×C47C2314yes—
308#121×C47C2314yes—
309#120×C47C23116yes—
310#120×C47C2318yes—
311#120×C47C2318yes—
312C4×D4×C47C2314yes—
313C4×D4×C47C2314yes—
314C4×D4×C47C2314yes—
315#117×C47C2318yes—
316#117×C47C2314yes—
317C2×C42×C47C2311yescharacteristic
318C24×C47C2418yes—
319C23×D47C2414yes—
320C23×D47C2411yescharacteristic
321#41×C47—48no—
322#41×C47—44no—
323C2×Q8×C47C2414yes—
324C2×Q8×C47C2412yes—
325C2×D4×C47—416no—
326C2×D4×C47—48no—
327C2×D4×C47C2414yes—
328C2×D4×C47C2414yes—
329C2×D4×C47C2414yes—
330C2×D4×C47C2414yes—
331C2×D4×C47C2412yes—
332C2×D4×C47C24116yes—
333C2×D4×C47C2418yes—
334C2×D4×C47C2418yes—
335C2×D4×C47C2414yes—
336C22×C4×C47C2412yes—
337C22×C4×C47C2411yescharacteristic
338C22×C4×C47C2418yes—
339C22×C4×C47C2414yes—
340C2×C22⋊D47—416no—
341C2×C22⋊D47C2418yes—
342C2×C22⋊D47C24116yes—
343C2×C22⋊D47C2418yes—
344C2×C22⋊D47C2418yes—
345C2×C22⋊D47C2414yes—
346C2×C22⋊D47C2414yes—
347C2×C22⋊D47C24116yes—
348C2×C22⋊D47C2414yes—
349C22×Dic47—416no—
350C22×Dic47C2411yescharacteristic
351C22×Dic47C2418yes—
352C22×Dic47C2414yes—
353C22×Dic47C2412yes—
354C22×Dic47C2418yes—
355C22×Dic47C24116yes—
356C22×Dic47C2418yes—
357#10625354—44no—
358Q8×D47—44no—
359#10625352—216no—
360#10625352—416no—
361#10625352—48no—
362#10625352—48no—
363#10625352—44no—
364#10625352—416no—
365#10625352—416no—
366D4×D47—48no—
367D4×D47—44no—
368D4×D47—48no—
369#10625350—416no—
370#10625350—48no—
371#10625350—44no—
372C2×D188C2414yes—
373C2×D188C2412yes—
374C2×D188C2414yes—
375C2×C4×D47—24no—
376C2×C4×D47—216no—
377C2×C4×D47—44no—
378C2×C4×D47C2412yes—
379C2×C4×D47C2412yes—
380C2×C4×D47C2411yescharacteristic
381C2×C4×D47C2414yes—
382C2×C4×D47C2411yescharacteristic
383C2×C4×D47C2411yescharacteristic
384C2×C4×D47C2414yes—
385C2×C4×D47C2414yes—
386C2×C4×D47C2412yes—
387C2×C4×D47C2412yes—
388C2×C4×D47C24116yes—
389C2×C4×D47C2411yescharacteristic
390C2×Dic94—48no—
391C2×Dic94C2414yes—
392C2×Dic94C2414yes—
393C2×Dic94C2412yes—
394C2×Dic94C2414yes—
395C2×Dic94C2418yes—
396C4⋊C4×C47C2414yes—
397C4⋊C4×C47C2414yes—
398C4⋊C4×C47C2414yes—
399C22⋊C4×C47C2418yes—
400C22⋊C4×C47C24116yes—
401C22⋊C4×C47C2418yes—
402C22⋊C4×C47C2418yes—
403C22⋊C4×C47C2418yes—
404C42×C47C2412yes—
405C42×C47C2411yescharacteristic
406C42×C47C2411yescharacteristic
407C42×C47C2418yes—
408C22⋊Dic47C2418yes—
409C22⋊Dic47C2418yes—
410C22⋊Dic47C2418yes—
411C22⋊Dic47C24116yes—
412C22⋊Dic47C24116yes—
413C22⋊Dic47C2418yes—
414C22⋊Dic47C2418yes—
415C22⋊Dic47C2418yes—
416C22⋊Dic47C2418yes—
417(C2×D47)⋊C4C2418yes—
418(C2×D47)⋊C4C2418yes—
419(C2×D47)⋊C4C2418yes—
420(C2×D47)⋊C4C24116yes—
421(C2×D47)⋊C4C2418yes—
422C4⋊Dic47C2414yes—
423C4⋊Dic47C2414yes—
424C4⋊Dic47C2414yes—
425C4⋊Dic47C24116yes—
426C4⋊Dic47C2418yes—
427C4⋊Dic47C2418yes—
428C4⋊Dic47C2414yes—
429C4⋊Dic47C2414yes—
430Dic47⋊C4C24116yes—
431Dic47⋊C4C2418yes—
432Dic47⋊C4C2418yes—
433Dic47⋊C4C2418yes—
434Dic47⋊C4C2418yes—
435Dic47⋊C4C2418yes—
436Dic47⋊C4C24116yes—
437C4×Dic47C2412yes—
438C4×Dic47C2411yescharacteristic
439C4×Dic47C2412yes—
440C4×Dic47C2418yes—
441C4×Dic47C2412yes—
442C4×Dic47C2412yes—
443C4×Dic47C2412yes—
444C4×Dic47C2411yescharacteristic
445C4×Dic47C2418yes—
446C4×Dic47C2418yes—
447C4×Dic47C2418yes—
448C23×C47—48no—
449C23×C47—416no—
450C23×C47C2514yes—
451C23×C47C2511yescharacteristic
452C23×C47C2518yes—
453C22×D47—22no—
454C22×D47—28no—
455C22×D47—42no—
456C22×D47—48no—
457C22×D47C2511yescharacteristic
458C22×D47C2514yes—
459C22×D47C2511yescharacteristic
460Q8×C47—42no—
461Q8×C47—44no—
462D4×C47—28no—
463D4×C47—28no—
464D4×C47—28no—
465D4×C47—44no—
466D4×C47—42no—
467D4×C47—48no—
468D4×C47—416no—
469D4×C47—48no—
470D4×C47—44no—
471C2×C4×C47—28no—
472C2×C4×C47—22no—
473C2×C4×C47—24no—
474C2×C4×C47—216no—
475C2×C4×C47C2511yescharacteristic
476C2×C4×C47C2514yes—
477C2×C4×C47C2512yes—
478C2×C4×C47C2518yes—
479C2×C4×C47C2511yescharacteristic
480C2×C4×C47C2512yes—
481C22⋊D47—216no—
482C22⋊D47—44no—
483C22⋊D47—44no—
484C22⋊D47—44no—
485C22⋊D47—416no—
486C22⋊D47—48no—
487C22⋊D47—416no—
488C22⋊D47—48no—
489C2×Dic47—22no—
490C2×Dic47—28no—
491C2×Dic47—216no—
492C2×Dic47—48no—
493C2×Dic47—42no—
494C2×Dic47—416no—
495C2×Dic47—48no—
496C2×Dic47C2512yes—
497C2×Dic47C2512yes—
498C2×Dic47C2518yes—
499C2×Dic47C2511yescharacteristic
500C2×Dic47C2518yes—
501C2×Dic47C2514yes—
502C2×Dic47C2511yescharacteristic
503D188—28no—
504D188—44no—
505D188—42no—
506C4×D47—22no—
507C4×D47—28no—
508C4×D47—22no—
509C4×D47—28no—
510C4×D47—24no—
511C4×D47—24no—
512C4×D47—28no—
513C4×D47—22no—
514C4×D47—42no—
515C4×D47—42no—
516C4×D47—416no—
517C4×D47H(5,𝔽2)14yes—
518Dic94—28no—
519Dic94—28no—
520Dic94—48no—
521Dic94—44no—
522Dic94—42no—
523#62759—471nomaximal, Sylow
524C22×C47—28no—
525C22×C47—24no—
526C22×C47—21no—
527C22×C47—28no—
528C22×C47—22no—
529C22×C47—28no—
530C22×C47—28no—
531C22×C47—816no—
532C22×C47C2611yescharacteristic
533C2×D47—22no—
534C2×D47—21no—
535C2×D47—24no—
536C2×D47—22no—
537C2×D47—28no—
538C2×D47—44no—
539C2×D47—88no—
540C2×D47C2×H(5,𝔽2)12yes—
541C4×C47—24no—
542C4×C47—21no—
543C4×C47—28no—
544C4×C47—22no—
545C4×C47C2×H(5,𝔽2)12yes—
546C4×C47#58514yes—
547Dic47—28no—
548Dic47—21no—
549Dic47—24no—
550Dic47—28no—
551Dic47—22no—
552Dic47—22no—
553Dic47C2×H(5,𝔽2)12yes—
554#3551—474no—
555#3550—471no—
556#3549D4711yescharacteristic, complemented
557#3548—472no—
558#3547—474no—
559#3546—474no—
560#3545—474no—
561#3544—472no—
562#3543—472no—
563#3542—478no—
564#3529—474no—
565#3483—472no—
566#3481—472no—
567#3475—474no—
568D4×#41—474no—
569#3460—478no—
570#3449—474no—
571#3444—472no—
572C2×#532—471no—
573C2×C47—41no—
574C2×C47—44no—
575C2×C47—48no—
576C2×C47C22×H(5,𝔽2)11yescharacteristic
577C2×C47C2×#58512yes—
578D47—22no—
579D47—41no—
580D47—44no—
581C22×#41—472no—
582C22×#41—474no—
583#563—478no—
584#563—474no—
585#562—4716no—
586#562—478no—
587H(3,𝔽4)C2×D4714yescomplemented
588#560—4716no—
589#560—478no—
590#559—472no—
591Q82—472no—
592#556—474no—
593#555—478no—
594#555—478no—
595#555C2×D4714yescomplemented
596#555C2×D4712yescomplemented
597#554—474no—
598#554—474no—
599#553—478no—
600#553—478no—
601#552—478no—
602#552—478no—
603#551—4716no—
604#551—478no—
605#550—474no—
606#550—478no—
607#550—474no—
608D4×Q8—474no—
609#548—478no—
610#547—478no—
611#547—474no—
612#547—474no—
613#546—478no—
614#546—478no—
615#546—478no—
616#546—4716no—
617D42—478no—
618D42C2×D4714yescomplemented
619D42C2×D4712yescomplemented
620#544—478no—
621#542—4716no—
622#542—478no—
623#542—478no—
624#540—4716no—
625#540—478no—
626#540—478no—
627#538—4716no—
628#538—4716no—
629#537—478no—
630#537—478no—
631#537—478no—
632#536—474no—
633#536—478no—
634#536—474no—
635#535—474no—
636#535—478no—
637#535—478no—
638#535C2×D4714yescomplemented
639#535C2×D4718yescomplemented
640#534—478no—
641#534—478no—
642#533—472no—
643#533—472no—
644#533—472no—
645#532—472no—
646#532—471no—
647#532—471no—
648#532—472no—
649#532—472no—
650#532—478no—
651#532—472no—
652#532—478no—
653#532—474no—
654#532—478no—
655#532—474no—
656#532—471no—
657#532C2×D4711yescharacteristic
658#532C2×D4712yescomplemented
659C2×C4⋊Q8—471no—
660C2×#127—471no—
661#529—474no—
662#529—474no—
663#529—4716no—
664#529—474no—
665#529—474no—
666#529—478no—
667#529—474no—
668#529—474no—
669C2×#124—472no—
670#525—474no—
671#525—474no—
672#525—474no—
673#525—478no—
674#525—478no—
675#525—478no—
676#525—4716no—
677C2×#121—474no—
678C4×#41—474no—
679C4×#41—474no—
680C4×#41—474no—
681C4×#41—478no—
682C2×C4×D4—478no—
683C2×C4×D4—474no—
684C2×#117—474no—
685C22×C42—471no—
686C47#6275911yescharacteristic, complemented, Sylow
687C2×#41—472no—
688C2×#41—474no—
689C2×#41—474no—
690C2×#41—472no—
691C2×#41—474no—
692C2×#41—478no—
693C2×#41—478no—
694C2×#41—478no—
695C2×#41—478no—
696C2×#41—474no—
697C2×#41—472no—
698C2×#41—1888no—
699C2×#41—18816no—
700C2×#41C22×D4714yes—
701C2×#41C22×D4712yes—
702C22×Q8—472no—
703C22×Q8—474no—
704C22×D4—478no—
705C22×D4—474no—
706C22×D4—474no—
707C22×D4—472no—
708C22×D4C22×D4718yes—
709C22×D4C22×D4714yes—
710C23×C4—478no—
711C23×C4—474no—
712C23×C4—471no—
713C23×C4—472no—
714C4⋊Q8—472no—
715C4⋊Q8—478no—
716C4⋊Q8—474no—
717C4⋊Q8—478no—
718C4⋊Q8—471no—
719C4⋊Q8—472no—
720C4⋊Q8—472no—
721C4⋊Q8—478no—
722C4⋊Q8C22×D4711yescharacteristic
723C4⋊Q8C22×D4712yes—
724#127—474no—
725#127—472no—
726#127—478no—
727#127—478no—
728#127—471no—
729#127C22×D4711yescharacteristic
730#127C22×D4712yes—
731#127C22×D4718yes—
732#126—478no—
733#126—478no—
734#126—4716no—
735#126—4716no—
736#126—4716no—
737#125—474no—
738#125—474no—
739#125—478no—
740#125—474no—
741#125—4716no—
742#124—472no—
743#124—472no—
744#124—474no—
745#124—474no—
746#124—478no—
747#124—478no—
748#124—478no—
749#124—478no—
750#124—4716no—
751#124—472no—
752#124—478no—
753#124C22×D4712yes—
754#124C22×D4714yes—
755#124C22×D47116yes—
756#124C22×D4718yes—
757#123—478no—
758#123—478no—
759#123—478no—
760#123—4716no—
761#123—4716no—
762#123—478no—
763#123—478no—
764#123—478no—
765#123—4716no—
766#123—478no—
767#123—4716no—
768#123—4716no—
769#123—4716no—
770C22⋊Q8—474no—
771C22⋊Q8—474no—
772C22⋊Q8—4716no—
773C22⋊Q8—474no—
774C22⋊Q8—474no—
775C22⋊Q8—478no—
776C22⋊Q8—478no—
777C22⋊Q8—474no—
778C22⋊Q8—474no—
779C22⋊Q8—478no—
780C22⋊Q8—4716no—
781C22⋊Q8—4716no—
782C22⋊Q8—4716no—
783C22⋊Q8—4716no—
784#121—478no—
785#121—474no—
786#121—474no—
787#121—474no—
788#121—474no—
789#121—474no—
790#121—4716no—
791#121—478no—
792#121—4716no—
793#121—4716no—
794#121—4716no—
795#121—4716no—
796#121—4716no—
797#121—4716no—
798#121—4716no—
799#121—474no—
800#121—478no—
801#121—474no—
802#121—478no—
803#121—4716no—
804#121—4716no—
805#121C22×D4714yes—
806#121C22×D4714yes—
807#121C22×D4714yes—
808#121C22×D4718yes—
809#121C22×D4718yes—
810#121C22×D4718yes—
811#120—478no—
812#120—478no—
813#120—4716no—
814#120—478no—
815#120—4716no—
816#120C22×D4718yes—
817#120C22×D4718yes—
818#120C22×D47116yes—
819C4×Q8—474no—
820C4×Q8—474no—
821C4×Q8—474no—
822C4×Q8—474no—
823C4×Q8—478no—
824C4×Q8—474no—
825C4×Q8—474no—
826C4×D4—474no—
827C4×D4—474no—
828C4×D4—4716no—
829C4×D4—478no—
830C4×D4—478no—
831C4×D4—4716no—
832C4×D4—474no—
833C4×D4—478no—
834C4×D4—478no—
835C4×D4—474no—
836C4×D4—474no—
837C4×D4—478no—
838C4×D4—478no—
839C4×D4—478no—
840C4×D4—474no—
841C4×D4—478no—
842C4×D4—478no—
843C4×D4—478no—
844C4×D4—4716no—
845C4×D4—478no—
846C4×D4—4716no—
847C4×D4—474no—
848C4×D4C22×D4714yes—
849C4×D4C22×D4714yes—
850C4×D4C22×D4714yes—
851#117—474no—
852#117—474no—
853#117—478no—
854#117—474no—
855#117—474no—
856#117—478no—
857#117—478no—
858#117—478no—
859#117—478no—
860#117—4716no—
861#117C22×D4714yes—
862#117C22×D4718yes—
863C2×C4⋊C4—478no—
864C2×C4⋊C4—478no—
865C2×C4⋊C4—474no—
866C2×C22⋊C4—4716no—
867C2×C22⋊C4—478no—
868C2×C22⋊C4—478no—
869C2×C42—478no—
870C2×C42—472no—
871C2×C42—471no—
872C2×C42—478no—
873C2×C42—472no—
874C2×C42—471no—
875C2×C42—471no—
876C2×C42—471no—
877C2×C42—471no—
878C2×C42—472no—
879C2×C42C22×D4711yescharacteristic
880C24—474no—
881C24—471no—
882C24C23×D4718yes—
883#41—44no—
884#41—48no—
885#41—9416no—
886#41—1888no—
887#41—1884no—
888#41—18816no—
889#41—1884no—
890#41—1888no—
891#41—18816no—
892#41—1884no—
893#41—1888no—
894#41—18816no—
895#41—18816no—
896C2×Q8—474no—
897C2×Q8—474no—
898C2×Q8—472no—
899C2×Q8—474no—
900C2×Q8—478no—
901C2×Q8—1888no—
902C2×Q8—1884no—
903C2×Q8C23×D4714yes—
904C2×Q8C23×D4712yes—
905C2×D4—416no—
906C2×D4—48no—
907C2×D4—478no—
908C2×D4—4716no—
909C2×D4—478no—
910C2×D4—478no—
911C2×D4—474no—
912C2×D4—474no—
913C2×D4—4716no—
914C2×D4—474no—
915C2×D4—474no—
916C2×D4—474no—
917C2×D4—472no—
918C2×D4—1888no—
919C2×D4—1884no—
920C2×D4—1888no—
921C2×D4—18816no—
922C2×D4C23×D4714yes—
923C2×D4C23×D4714yes—
924C2×D4C23×D4714yes—
925C2×D4C23×D47116yes—
926C2×D4C23×D4718yes—
927C2×D4C23×D4714yes—
928C2×D4C23×D4712yes—
929C2×D4C23×D4714yes—
930C2×D4C23×D4718yes—
931C22×C4—471no—
932C22×C4—471no—
933C22×C4—478no—
934C22×C4—474no—
935C22×C4—472no—
936C22×C4—478no—
937C22×C4—4716no—
938C22×C4—478no—
939C22×C4—472no—
940C22×C4—472no—
941C22×C4—474no—
942C22×C4—471no—
943C22×C4—471no—
944C22×C4—471no—
945C22×C4—474no—
946C22×C4—474no—
947C22×C4—472no—
948C22×C4—472no—
949C22×C4—4716no—
950C22×C4—9416no—
951C22×C4—944no—
952C22×C4—1884no—
953C22×C4—18816no—
954C22×C4C23×D4712yes—
955C22×C4C23×D4711yescharacteristic
956C22×C4C23×D4718yes—
957C22×C4C23×D4714yes—
958C4⋊C4—4716no—
959C4⋊C4—478no—
960C4⋊C4—478no—
961C4⋊C4—478no—
962C4⋊C4—478no—
963C4⋊C4—4716no—
964C4⋊C4—478no—
965C4⋊C4—474no—
966C4⋊C4—474no—
967C4⋊C4—474no—
968C4⋊C4—4716no—
969C4⋊C4—478no—
970C4⋊C4—478no—
971C4⋊C4—474no—
972C4⋊C4—474no—
973C4⋊C4C23×D4714yes—
974C4⋊C4C23×D4714yes—
975C4⋊C4C23×D4714yes—
976C22⋊C4—478no—
977C22⋊C4—478no—
978C22⋊C4—478no—
979C22⋊C4—4716no—
980C22⋊C4—4716no—
981C22⋊C4—478no—
982C22⋊C4—478no—
983C22⋊C4—478no—
984C22⋊C4—478no—
985C22⋊C4—478no—
986C22⋊C4—478no—
987C22⋊C4—478no—
988C22⋊C4—4716no—
989C22⋊C4—478no—
990C22⋊C4C23×D4718yes—
991C22⋊C4C23×D4718yes—
992C22⋊C4C23×D4718yes—
993C22⋊C4C23×D4718yes—
994C22⋊C4C23×D47116yes—
995C42—472no—
996C42—471no—
997C42—478no—
998C42—472no—
999C42—472no—
1000C42—472no—
1001C42—472no—
1002C42—471no—
1003C42—478no—
1004C42—478no—
1005C42—478no—
1006C42C23×D4712yes—
1007C42C23×D4711yescharacteristic
1008C42C23×D4711yescharacteristic
1009C42C23×D4718yes—
1010C23—48no—
1011C23—416no—
1012C23—471no—
1013C23—471no—
1014C23—474no—
1015C23—948no—
1016C23—942no—
1017C23—1888no—
1018C23—1882no—
1019C23C24×D4714yes—
1020C23C24×D4711yescharacteristic
1021C23C24×D4718yes—
1022Q8—42no—
1023Q8—44no—
1024Q8—948no—
1025Q8—948no—
1026Q8—1884no—
1027Q8—1888no—
1028Q8—1882no—
1029D4—28no—
1030D4—28no—
1031D4—28no—
1032D4—416no—
1033D4—48no—
1034D4—44no—
1035D4—42no—
1036D4—48no—
1037D4—44no—
1038D4—9416no—
1039D4—948no—
1040D4—1884no—
1041D4—1882no—
1042D4—1888no—
1043D4—1884no—
1044D4—1884no—
1045D4—1884no—
1046D4—18816no—
1047D4—18816no—
1048D4—1888no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—216no—
1053C2×C4—471no—
1054C2×C4—474no—
1055C2×C4—472no—
1056C2×C4—478no—
1057C2×C4—472no—
1058C2×C4—471no—
1059C2×C4—478no—
1060C2×C4—474no—
1061C2×C4—948no—
1062C2×C4—942no—
1063C2×C4—942no—
1064C2×C4—948no—
1065C2×C4—948no—
1066C2×C4—942no—
1067C2×C4—9416no—
1068C2×C4—948no—
1069C2×C4—942no—
1070C2×C4—944no—
1071C2×C4—944no—
1072C2×C4—1882no—
1073C2×C4—1882no—
1074C2×C4—18816no—
1075C2×C4—1882no—
1076C2×C4—1888no—
1077C2×C4—18816no—
1078C2×C4—1888no—
1079C2×C4C24×D4712yes—
1080C2×C4C24×D4718yes—
1081C2×C4C24×D4714yes—
1082C2×C4C24×D4711yescharacteristic
1083C2×C4C24×D4711yescharacteristic
1084C2×C4C24×D4712yes—
1085C22—24no—
1086C22—21no—
1087C22—28no—
1088C22—22no—
1089C22—28no—
1090C22—28no—
1091C22—28no—
1092C22—816no—
1093C22—472no—
1094C22—942no—
1095C22—944no—
1096C22—941no—
1097C22—942no—
1098C22—948no—
1099C22—3768no—
1100C22—1884no—
1101C22C25×D4711yescharacteristic
1102C4—24no—
1103C4—21no—
1104C4—28no—
1105C4—22no—
1106C4—472no—
1107C4—944no—
1108C4—941no—
1109C4—948no—
1110C4—942no—
1111C4—942no—
1112C4—948no—
1113C4H(5,𝔽2)×D4712yes—
1114C4#1568995814yes—
1115C2—44no—
1116C2—48no—
1117C2—41no—
1118C2—942no—
1119C2—1884no—
1120C2—1881no—
1121C2C2×H(5,𝔽2)×D4711yescharacteristic
1122C2C2×#1568995812yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3549C2
hypercenter#3549D47
hypocenterC47#62759
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #20257812C2semidirect
2. #20257802C2semidirect
3. #20257786C2semidirect
4. #20257780C2semidirect
5. #20257756C2semidirect
6. #20257743C2semidirect
7. #20257723C2semidirect
8. #20257719C2semidirect
9. #20257706C2semidirect
10. #20257528C2semidirect
11. #20257013C2semidirect
12. #20256989C2semidirect
13. #20256945C2semidirect
14. D4×#10625352C2semidirect
15. #20256801C2semidirect
16. #20256719C2semidirect
17. #20256683C2semidirect
18. #532×D47C2semidirect
19. C47×#3549C2semidirect
20. C22×#10625352C22semidirect
21. C2×#41×D47C22semidirect
22. #15689873C22semidirect
23. #15689873C22semidirect
24. #15689867C22semidirect
25. #15689867C22semidirect
26. #15689862C22semidirect
27. #15689862C22semidirect
28. #15689859C22semidirect
29. #15689853C22semidirect
30. #15689843C22semidirect
31. #15689836C22semidirect
32. #15689835C22semidirect
33. #15689834C22semidirect
34. #15689830C22semidirect
35. #15689825C22semidirect
36. #15689820C22semidirect
37. #15689812C22semidirect
38. #15689812C22semidirect
39. #15689804C22semidirect
40. #15689803C22semidirect
41. #15689794C22semidirect
42. #15689793C22semidirect
43. #15689791C22semidirect
44. D4×Dic94C22semidirect
45. #15689779C22semidirect
46. #15689778C22semidirect
47. #15689777C22semidirect
48. #15689773C22semidirect
49. #15689770C22semidirect
50. #15689767C22semidirect
51. #15689767C22semidirect
52. #15689760C22semidirect
53. D4×C22⋊D47C22semidirect
54. #15689751C22semidirect
55. #15689742C22semidirect
56. #15689740C22semidirect
57. #15689740C22semidirect
58. #15689727C22semidirect
59. #15689726C22semidirect
60. #15689726C22semidirect
61. #15689708C22semidirect
62. #15689708C22semidirect
63. #15689702C22semidirect
64. #15689702C22semidirect
65. #15689701C22semidirect
66. #15689699C22semidirect
67. #15689694C22semidirect
68. #15689693C22semidirect
69. #15689690C22semidirect
70. #15689690C22semidirect
71. #15689686C22semidirect
72. #15689683C22semidirect
73. #15689683C22semidirect
74. #15689680C22semidirect
75. #15689678C22semidirect
76. #15689678C22semidirect
77. #15689674C22semidirect
78. #15689673C22semidirect
79. #15689672C22semidirect
80. #15689672C22semidirect
83. #15689671C22semidirect
84. #15689671C22semidirect
85. #15689670C22semidirect
86. #15689669C22semidirect
87. #15689668C22semidirect
88. #15689668C22semidirect
89. C4⋊Q8×D47C22semidirect
91. #15689655C22semidirect
92. #15689655C22semidirect
93. #15689654C22semidirect
94. #15689654C22semidirect
95. #15689654C22semidirect
96. #15689652C22semidirect
97. #15689652C22semidirect
98. #15689652C22semidirect
99. #124×D47C22semidirect
100. #15689633C22semidirect
101. #15689633C22semidirect
102. #15689633C22semidirect
103. #15689630C22semidirect
104. #15689629C22semidirect
105. #15689629C22semidirect
106. #15689629C22semidirect
107. #121×D47C22semidirect
108. #41×Dic47C22semidirect
109. #15689591C22semidirect
110. C4×#10625352C22semidirect
111. C4×#10625352C22semidirect
112. C2×D4×Dic47C22semidirect
113. C4×D4×D47C22semidirect
114. #117×D47C22semidirect
115. C2×C42×D47C22semidirect
116. C47×H(3,𝔽4)C22semidirect
117. C47×#555C22semidirect
118. C47×#555C22semidirect
119. D42×C47C22semidirect
120. D42×C47C22semidirect
121. C47×#535C22semidirect
122. C47×#535C22semidirect
124. C47×#532C22semidirect
556. #3549D47semidirect
587. H(3,𝔽4)C2×D47semidirect
595. #555C2×D47semidirect
596. #555C2×D47semidirect
618. D42C2×D47semidirect
619. D42C2×D47semidirect
638. #535C2×D47semidirect
639. #535C2×D47semidirect
658. #532C2×D47semidirect
686. C47#62759semidirect

Maximal subgroups

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

subgroupindex
#202578122
#202578022
#202577862
#202577802
#202577562
#202577432
#202577232
#202577192
#202577062
#202575282
#202570132
#202569892
#202569452
D4×#106253522
#202568012
#202567192
#202566832
#532×D472
C47×#35492
#6275947