Finite Group Databasebeta

← #27124429

Subgroups — #27124429

Order 12032.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257445C218yesmaximal, complemented
2#20257357C214yesmaximal, complemented
3#20257340C214yesmaximal, complemented
4#20257250C212yesmaximal, complemented
5#20257222C214yesmaximal, complemented
6#20257191C211yesmaximal, characteristic, complemented
7#20257107C212yesmaximal, complemented
8#20257085C214yesmaximal, complemented
9#20257028C212yesmaximal, complemented
10#20257000C214yesmaximal, complemented
11#20256989C214yesmaximal, complemented
12#20256939C218yesmaximal, complemented
13#20256816C212yesmaximal, complemented
14#20256794C214yesmaximal, complemented
15#20256683C212yesmaximal, complemented
16C2×#15689654C214yesmaximal, complemented
17H(5,𝔽2)×Dic47C212yesmaximal, complemented
18C2×C4×#10625352C211yesmaximal, characteristic, complemented
19C47×#3496C211yesmaximal, characteristic, complemented
20C22×#10625352C2211yescharacteristic
21#15689859C2214yescomplemented
22#15689848C2214yescomplemented
23#15689844C2218yescomplemented
24#15689843C2214yescomplemented
25#15689842C2218yescomplemented
26#15689837C2218yescomplemented
27#15689832C2218yescomplemented
28#15689830C2214yescomplemented
29#15689830C2214yescomplemented
30#15689825C2218yescomplemented
31#15689825C2218yescomplemented
32#15689816C22116yescomplemented
33#15689815C2218yescomplemented
34#15689813C2218yescomplemented
35#15689810C22116yescomplemented
36#15689810C22116yescomplemented
37#15689808C2218yescomplemented
38#15689804C22116yescomplemented
39#15689804C22116yescomplemented
40#15689799C22116yescomplemented
41D4×Dic94C2214yescomplemented
42#15689779C2218yescomplemented
43#15689772C2218yescomplemented
44#15689772C2218yescomplemented
45#15689767C2218yescomplemented
46#15689767C2218yescomplemented
47#15689767C2218yescomplemented
48#15689754C2212yescomplemented
49#15689749C2214yescomplemented
50#15689740C2218yescomplemented
51#15689733C2218yescomplemented
52#15689718C2218yescomplemented
53#15689718C2218yescomplemented
54#15689717C22116yescomplemented
55#15689710C2218yescomplemented
56#15689708C22116yescomplemented
57#15689694C2214yescomplemented
58#15689682C2218yescomplemented
59#15689680C2212yescomplemented
60#15689678C2212yescomplemented
61#15689678C2212yescomplemented
62#15689675C2218yescomplemented
63#15689671C2212yescomplemented
64#15689671C2212yescomplemented
65#15689655C2214yescomplemented
66#15689655C2214yescomplemented
67#15689654C2218yescomplemented
68#15689654C2218yescomplemented
69#15689654C2218yescomplemented
70#15689654C2214yescomplemented
71#15689654C2218yescomplemented
72#15689654C2214yescomplemented
73#15689654C2218yescomplemented
74#15689654C2218yescomplemented
75#15689654C2218yescomplemented
76#15689654C2218yescomplemented
77#15689652C2214yescomplemented
78#15689652C2214yescomplemented
79#15689650C22116yescomplemented
80C2×#13094017C2218yescomplemented
81C2×#13094015C2214yescomplemented
82C2×#13094011C2214yescomplemented
83#15689633C2214yescomplemented
84#15689633C2214yescomplemented
85#15689630C2214yescomplemented
86#15689629C22116yescomplemented
87C2×#13094005C2218yescomplemented
88C2×#13094003C2214yescomplemented
89#15689606C2218yescomplemented
90#15689606C2214yescomplemented
91#15689598C2212yes—
92#15689598C2218yescomplemented
93#15689598C2218yescomplemented
94#41×Dic47C2214yescomplemented
95#41×Dic47C2218yescomplemented
96C4×#10625352C2214yescomplemented
97C4×#10625352C2214yescomplemented
98C4×#10625352C2214yescomplemented
99C4×#10625352C2214yescomplemented
100C4×#10625352C2214yescomplemented
101C4×#10625352C2214yescomplemented
102C2×C4×Dic94C2211yescharacteristic, complemented
103C2×#13093989C2211yescharacteristic, complemented
104C2×#13093989C2214yescomplemented
105C2×D4×Dic47C2211yescharacteristic
106C2×D4×Dic47C2218yescomplemented
107C2×D4×Dic47C2218yescomplemented
108C2×D4×Dic47C2214yescomplemented
109C2×C4×C22⋊D47C2212yescomplemented
110C2×(C22⋊D47)⋊C4C2212yescomplemented
111C2×#13093982C2211yescharacteristic, complemented
112C2×#13093980C2212yescomplemented
113C2×#13093980C2218yescomplemented
114C22×C4×Dic47C2212yescomplemented
115C2×C42×D47C2211yescharacteristic, complemented
116C2×H(5,𝔽2)×C47C2212yes—
117C47×#547C2214yescomplemented
118C47×#546C2218yescomplemented
119D42×C47C2214yescomplemented
120C47×#537C2212yes—
121C47×#534C2214yes—
122C47×#532C2212yes—
123C2×#121×C47C2214yes—
124C2×C4×D4×C47C2211yescharacteristic
125C2×#10625352—28no—
126C2×#10625352C2314yes—
127C2×#10625352C2314yes—
128C2×#10625352C2314yes—
129C2×#10625352C2314yes—
130C22×Dic94C2311yescharacteristic
131C22×Dic94C2314yes—
132C22×C22⋊D47C2312yes—
133C23×Dic47C2312yes—
134C23×Dic47C2312yes—
135C23×Dic47C2318yes—
136C22×C4×D47C2311yescharacteristic
137C22×C4×D47C2311yescharacteristic
138C22×C4×D47C2311yescharacteristic
139#13094024C2312yes—
140#13094024C2312yes—
141#13094023C2318yes—
142#13094022C2318yes—
143#13094019C23116yes—
144#13094017C23116yes—
145#13094017C23116yes—
146#13094017C23116yes—
147#13094017C2318yes—
148#13094017C23116yes—
149#13094017C23116yes—
150#13094017C2318yes—
151#13094016C2314yes—
152#13094015C2318yes—
153#13094015C2318yes—
154#13094015C2318yes—
155#13094015C2314yes—
156#13094015C2318yes—
157#13094015C2314yes—
158#13094014C23116yes—
159#13094014C23116yes—
160#13094011C2318yes—
161#13094011C2318yes—
162#13094011C2318yes—
163#13094011C2314yes—
164#13094011C2318yes—
165#13094011C2314yes—
166#13094010C23116yes—
167#13094008C23116yes—
168#13094007C23116yes—
169#13094006C2318yes—
170#13094006C2318yes—
171#13094005C23116yes—
172#13094005C23116yes—
173#13094005C23116yes—
174#13094005C23116yes—
175#13094005C2318yes—
176#13094005C23116yes—
177#13094004C2314yes—
178#13094004C2314yes—
179#13094003C2318yes—
180#13094003C2318yes—
181#13094003C2314yes—
182#13094003C2318yes—
183#13094003C2318yes—
184#13094003C2318yes—
185#13094003C2314yes—
186#13094001C23116yes—
187#13094001C23116yes—
188#13094001C23116yes—
189#13094001C23116yes—
190#13094000C2314yes—
191#13094000C2314yes—
192#13093996C23116yes—
193#13093996C23116yes—
194#13093996C23116yes—
195#13093995C2314yes—
196#13093995C2314yes—
197#13093995C2314yes—
198#13093995C2314yes—
199#13093993C23116yes—
200#13093992C2318yes—
201Q8×Dic47C2314yes—
202Q8×Dic47C2318yes—
203Q8×Dic47C2314yes—
204C4×Dic94C2314yes—
205C4×Dic94C2314yes—
206C4×Dic94C2314yes—
207C4×Dic94C2314yes—
208#13093989C2314yes—
209#13093989C2318yes—
210#13093989C2314yes—
211#13093989C2318yes—
212#13093989C2314yes—
213#13093989C2314yes—
214#13093989C2318yes—
215D4×Dic47C2314yes—
216D4×Dic47C2318yes—
217D4×Dic47C2318yes—
218D4×Dic47C2318yes—
219D4×Dic47C23116yes—
220D4×Dic47C2314yes—
221D4×Dic47C2318yes—
222D4×Dic47C23116yes—
223D4×Dic47C2318yes—
224D4×Dic47C2314yes—
225D4×Dic47C2314yes—
226D4×Dic47C2314yes—
227D4×Dic47C23116yes—
228D4×Dic47C2318yes—
229D4×Dic47C2314yes—
230D4×Dic47C23116yes—
231D4×Dic47C23116yes—
232D4×Dic47C2318yes—
233D4×Dic47C2318yes—
234C4×C22⋊D47C2318yes—
235C4×C22⋊D47C2318yes—
236C4×C22⋊D47C2318yes—
237C4×C22⋊D47C2318yes—
238(C22⋊D47)⋊C4C2318yes—
239(C22⋊D47)⋊C4C2318yes—
240(C22⋊D47)⋊C4C2318yes—
241(C22⋊D47)⋊C4C2318yes—
242#13093983C2318yes—
243#13093983C2314yes—
244#13093983C23116yes—
245#13093983C2318yes—
246#13093982C2314yes—
247#13093982C2314yes—
248#13093982C2314yes—
249#13093982C2314yes—
250#13093980C23116yes—
251#13093980C2318yes—
252#13093980C2318yes—
253#13093980C2318yes—
254#13093980C23116yes—
255#13093980C2318yes—
256#13093980C23116yes—
257C2×C4⋊Dic47C2318yes—
258C2×C4⋊Dic47C2314yes—
259C2×C4⋊Dic47C2311yescharacteristic
260C2×C4⋊Dic47C2318yes—
261C2×Dic47⋊C4C2318yes—
262C2×Dic47⋊C4C2318yes—
263C2×Dic47⋊C4C2318yes—
264C2×Dic47⋊C4C2312yes—
265C2×Dic47⋊C4C2312yes—
266C2×C22⋊Dic47C2318yes—
267C2×C22⋊Dic47C2318yes—
268C2×C22⋊Dic47C2318yes—
269C2×C22⋊Dic47C23116yes—
270C2×C22⋊Dic47C2312yes—
271C2×C22⋊Dic47C2318yes—
272C2×(C2×D47)⋊C4C2312yes—
273C2×C4×Dic47C2311yescharacteristic
274C2×C4×Dic47C2311yescharacteristic
275C2×C4×Dic47C2311yescharacteristic
276C2×C4×Dic47C2314yes—
277C2×C4×Dic47C2312yes—
278C2×C4×Dic47C2312yes—
279C2×C4×Dic47C2312yes—
280C2×C4×Dic47C2314yes—
281C2×C4×Dic47C2314yes—
282C2×C4×Dic47C2314yes—
283C2×C4×Dic47C2318yes—
284C2×C4×Dic47C2318yes—
285C42×D47C2312yes—
286C42×D47C2312yes—
287C42×D47C2312yes—
288C42×D47C2312yes—
289H(5,𝔽2)×C47—216no—
290C2×#41×C47C2318yes—
291C2×#41×C47C2314yes—
292C22×D4×C47C2318yes—
293C22×D4×C47C2318yes—
294C22×D4×C47C2314yes—
295C22×D4×C47C2311yescharacteristic
296C23×C4×C47C2312yes—
297C4⋊Q8×C47C2312yes—
298#127×C47C2312yes—
299#124×C47C2314yes—
300#123×C47C23116yes—
301C22⋊Q8×C47C2318yes—
302#121×C47C2318yes—
303#121×C47C2318yes—
304#121×C47C2314yes—
305#121×C47C2318yes—
306#121×C47C2318yes—
307#121×C47C2314yes—
308#120×C47C23116yes—
309C4×D4×C47C2314yes—
310C4×D4×C47C2314yes—
311C4×D4×C47C2314yes—
312C4×D4×C47C2314yes—
313C2×C4⋊C4×C47C2311yescharacteristic
314C2×C4⋊C4×C47C2314yes—
315C2×C22⋊C4×C47C2312yes—
316C2×C22⋊C4×C47C2318yes—
317C2×C42×C47C2311yescharacteristic
318C24×C47C2418yes—
319C24×C47C2412yes—
320C23×D47C2411yescharacteristic
321#41×C47—232no—
322#41×C47—216no—
323C2×Q8×C47C2414yes—
324C2×D4×C47—232no—
325C2×D4×C47—232no—
326C2×D4×C47—48no—
327C2×D4×C47#4118yescomplemented
328C2×D4×C47C2414yes—
329C2×D4×C47C24116yes—
330C2×D4×C47C2418yes—
331C2×D4×C47C2414yes—
332C2×D4×C47C2414yes—
333C2×D4×C47C2418yes—
334C2×D4×C47C2414yes—
335C22×C4×C47—44no—
336C22×C4×C47C2411yescharacteristic
337C22×C4×C47C2418yes—
338C22×C4×C47C2414yes—
339C22×C4×C47C2418yes—
340C22×C4×C47C2411yescharacteristic
341C22×C4×C47C2414yes—
342C22×C4×C47C2412yes—
343C22×C4×C47C2411yescharacteristic
344C2×C22⋊D47—28no—
345C2×C22⋊D47C2418yes—
346C2×C22⋊D47C2418yes—
347C2×C22⋊D47C2418yes—
348C22×Dic47—28no—
349C22×Dic47—44no—
350C22×Dic47—416no—
351C22×Dic47C2414yes—
352C22×Dic47C2411yescharacteristic
353C22×Dic47C2411yescharacteristic
354C22×Dic47C2414yes—
355C22×Dic47C2414yes—
356C22×Dic47C2412yes—
357C22×Dic47C2418yes—
358C22×Dic47C2412yes—
359C22×Dic47C2411yescharacteristic
360C22×Dic47C2414yes—
361C22×Dic47C2418yes—
362C22×Dic47C2418yes—
363C22×Dic47C2418yes—
364C22×Dic47C24116yes—
365#10625352—216no—
366#10625352—216no—
367#10625352—48no—
368#10625352—48no—
369C2×C4×D47—24no—
370C2×C4×D47—42no—
371C2×C4×D47—42no—
372C2×C4×D47C2412yes—
373C2×C4×D47C2412yes—
374C2×C4×D47C2412yes—
375C2×C4×D47C2412yes—
376C2×C4×D47C2412yes—
377C2×C4×D47C2412yes—
378C2×Dic94—24no—
379C2×Dic94—48no—
380C2×Dic94C2414yes—
381C2×Dic94C2414yes—
382C2×Dic94C2418yes—
383C2×Dic94C2414yes—
384C4⋊C4×C47C2414yes—
385C4⋊C4×C47C2414yes—
386C4⋊C4×C47C2418yes—
387C4⋊C4×C47C2414yes—
388C22⋊C4×C47C2418yes—
389C22⋊C4×C47C2418yes—
390C22⋊C4×C47C24116yes—
391C22⋊C4×C47C2418yes—
392C42×C47C2412yes—
393C42×C47C2412yes—
394C22⋊Dic47C2418yes—
395C22⋊Dic47C2418yes—
396C22⋊Dic47C2418yes—
397C22⋊Dic47C2418yes—
398C22⋊Dic47C24116yes—
399C22⋊Dic47C2418yes—
400C22⋊Dic47C2418yes—
401C22⋊Dic47C24116yes—
402C22⋊Dic47C24116yes—
403C22⋊Dic47C24116yes—
404(C2×D47)⋊C4C2418yes—
405(C2×D47)⋊C4C2418yes—
406(C2×D47)⋊C4C2418yes—
407C4⋊Dic47C2414yes—
408C4⋊Dic47C2414yes—
409C4⋊Dic47C2414yes—
410C4⋊Dic47C24116yes—
411C4⋊Dic47C2418yes—
412C4⋊Dic47C2418yes—
413C4⋊Dic47C2414yes—
414C4⋊Dic47C2414yes—
415C4⋊Dic47C2418yes—
416Dic47⋊C4C2418yes—
417Dic47⋊C4C2418yes—
418Dic47⋊C4C2418yes—
419Dic47⋊C4C2418yes—
420Dic47⋊C4C2418yes—
421Dic47⋊C4C24116yes—
422Dic47⋊C4C24116yes—
423Dic47⋊C4C24116yes—
424Dic47⋊C4C2418yes—
425C4×Dic47C2411yescharacteristic
426C4×Dic47C2411yescharacteristic
427C4×Dic47C2412yes—
428C4×Dic47C2411yescharacteristic
429C4×Dic47C2411yescharacteristic
430C4×Dic47C2412yes—
431C4×Dic47C2412yes—
432C4×Dic47C2412yes—
433C4×Dic47C2414yes—
434C4×Dic47C2414yes—
435C4×Dic47C2414yes—
436C4×Dic47C2418yes—
437C4×Dic47C2414yes—
438C4×Dic47C2414yes—
439C4×Dic47C2414yes—
440C4×Dic47C24116yes—
441C4×Dic47C2418yes—
442C4×Dic47C2418yes—
443C23×C47—216no—
444C23×C47—42no—
445C23×C47—42no—
446C23×C47—48no—
447C23×C47—48no—
448C23×C47C2×#4118yes—
449C23×C47C2518yes—
450C23×C47C2511yescharacteristic
451C23×C47C2514yes—
452C22×D47—22no—
453C22×D47—41no—
454C22×D47—41no—
455C22×D47C2512yes—
456Q8×C47—28no—
457D4×C47—216no—
458D4×C47—232no—
459D4×C47—28no—
460D4×C47—28no—
461D4×C47—44no—
462D4×C47—48no—
463D4×C47C2×#41116yes—
464C2×C4×C47—216no—
465C2×C4×C47—216no—
466C2×C4×C47—28no—
467C2×C4×C47—22no—
468C2×C4×C47—41no—
469C2×C4×C47—42no—
470C2×C4×C47—44no—
471C2×C4×C47C2×#4114yes—
472C2×C4×C47C2511yescharacteristic
473C2×C4×C47C2518yes—
474C2×C4×C47C2514yes—
475C2×C4×C47C2512yes—
476C2×C4×C47C2512yes—
477C2×C4×C47C2511yescharacteristic
478C22⋊D47—216no—
479C22⋊D47—48no—
480C22⋊D47—48no—
481C2×Dic47—24no—
482C2×Dic47—22no—
483C2×Dic47—28no—
484C2×Dic47—28no—
485C2×Dic47—22no—
486C2×Dic47—216no—
487C2×Dic47—28no—
488C2×Dic47—48no—
489C2×Dic47—41no—
490C2×Dic47—48no—
491C2×Dic47—48no—
492C2×Dic47—416no—
493C2×Dic47—44no—
494C2×Dic47—42no—
495C2×Dic47C2511yescharacteristic
496C2×Dic47C2511yescharacteristic
497C2×Dic47C2512yes—
498C2×Dic47C2514yes—
499C2×Dic47C2511yescharacteristic
500C2×Dic47C2514yes—
501C2×Dic47C2518yes—
502C2×Dic47C2518yes—
503C2×Dic47C2511yescharacteristic
504C4×D47—24no—
505C4×D47—24no—
506C4×D47—24no—
507C4×D47—24no—
508C4×D47—42no—
509C4×D47—42no—
510Dic94—28no—
511Dic94—28no—
512Dic94—48no—
513Dic94—44no—
514#62781—471nomaximal, Sylow
515C22×C47—24no—
516C22×C47—21no—
517C22×C47—24no—
518C22×C47—21no—
519C22×C47—28no—
520C22×C47—28no—
521C22×C47—28no—
522C22×C47—48no—
523C22×C47—816no—
524C22×C47C22×#4112yes—
525C22×C47C22×#4118yes—
526C22×C47C2611yescharacteristic
527C2×D47—22no—
528C2×D47—22no—
529C2×D47—22no—
530C2×D47—44no—
531C4×C47—28no—
532C4×C47—22no—
533C4×C47—24no—
534C4×C47—21no—
535C4×C47C22×#4114yes—
536C4×C47#58512yes—
537Dic47—24no—
538Dic47—21no—
539Dic47—21no—
540Dic47—28no—
541Dic47—28no—
542Dic47—22no—
543Dic47—21no—
544Dic47—24no—
545Dic47#58512yes—
546#3521—478no—
547#3515—474no—
548#3514—474no—
549#3507—472no—
550#3505—474no—
551#3501—471no—
552#3496D4711yescharacteristic, complemented
553#3493—472no—
554#3491—474no—
555#3485—472no—
556#3482—474no—
557#3481—474no—
558#3475—478no—
559#3461—472no—
560#3459—474no—
561#3444—472no—
562C2×#529—474no—
563C4×H(5,𝔽2)—472no—
564C2×C4×#41—471no—
565C2×C47—22no—
566C2×C47—28no—
567C2×C47—48no—
568C2×C47C23×#4111yescharacteristic
569C2×C47C2×#58511yescharacteristic
570C2×C47C2×#58511yescharacteristic
571D47—42no—
572C2×H(5,𝔽2)C2×D4712yes—
573C22×#41—471no—
574#559—474no—
575#557—474no—
576#556—478no—
577#556—478no—
578#556—474no—
579#555—478no—
580#554—474no—
581#554—474no—
582#554—478no—
583#553—4716no—
584#553—478no—
585#553—478no—
586#552—4716no—
587#552—4716no—
588#552—478no—
589#552—478no—
590#552—478no—
591#551—4716no—
592#551—4716no—
593#551—4716no—
594D4×Q8—474no—
595#548—478no—
596#547—478no—
597#547—478no—
598#547C2×D4714yescomplemented
599#546—478no—
600#546—478no—
601#546—478no—
602#546C2×D4718yescomplemented
603D42C2×D4714yescomplemented
604#544—472no—
605#543—474no—
606#542—478no—
607#541—478no—
608#539—4716no—
609#539—478no—
610#539—478no—
611#538—478no—
612#538—4716no—
613#537C2×D4712yes—
614#536—474no—
615#534—478no—
616#534C2×D4714yes—
617#533—472no—
618#533—472no—
619#533—478no—
620#533—472no—
621#532—472no—
622#532—472no—
623#532C2×D4712yes—
624#529—474no—
625#529—474no—
626#529—4716no—
627#529—474no—
628#529—478no—
629#529—478no—
630#529—478no—
631#529—478no—
632#529—478no—
633#529—478no—
634#529—478no—
635#529—474no—
636#529—478no—
637#529—474no—
638#529—474no—
639C2×#126—478no—
640C2×#125—474no—
641C2×#124—474no—
642#525—474no—
643#525—474no—
644#525—474no—
645#525—4716no—
646C2×#123—478no—
647C2×C22⋊Q8—474no—
648C2×#121C2×D4714yes—
649#520—474no—
650#520—478no—
651#518—472no—
652#518—478no—
653#518—478no—
654C4×#41—474no—
655C4×#41—478no—
656C4×#41—474no—
657C4×#41—474no—
658C4×#41—474no—
659C4×#41—474no—
660C4×#41—474no—
661C4×#41—474no—
662C2×C4×Q8—471no—
663C2×C4×Q8—474no—
664C2×C4×Q8—471no—
665C2×C4×D4—471no—
666C2×C4×D4—478no—
667C2×C4×D4—478no—
668C2×C4×D4—474no—
669C2×C4×D4—472no—
670C2×C4×D4—472no—
671C2×C4×D4C2×D4711yescharacteristic
672C2×#117—471no—
673C2×#117—472no—
674C2×#117—478no—
675C22×C42—472no—
676C22×C42—471no—
677C47#6278111yescharacteristic, complemented, Sylow
678H(5,𝔽2)—216no—
679C2×#41—474no—
680C2×#41—474no—
681C2×#41—474no—
682C2×#41—474no—
683C2×#41—948no—
684C2×#41C22×D4714yes—
685C2×#41C22×D4718yes—
686C22×Q8—471no—
687C22×Q8—474no—
688C22×D4—472no—
689C22×D4C22×D4718yes—
690C22×D4C22×D4718yes—
691C22×D4C22×D4714yes—
692C22×D4C22×D4711yescharacteristic
693C23×C4—472no—
694C23×C4—478no—
695C23×C4—472no—
696C23×C4—471no—
697C23×C4—471no—
698C23×C4—471no—
699C23×C4C22×D4712yes—
700C4⋊Q8—478no—
701C4⋊Q8—478no—
702C4⋊Q8—472no—
703C4⋊Q8—472no—
704C4⋊Q8C22×D4712yes—
705#127C22×D4712yes—
706#126—4716no—
707#126—478no—
708#126—4716no—
709#126—4716no—
710#126—4716no—
711#126—478no—
712#126—4716no—
713#126—4716no—
714#125—474no—
715#125—478no—
716#125—478no—
717#125—478no—
718#125—474no—
719#125—4716no—
720#125—478no—
721#125—4716no—
722#125—474no—
723#124—474no—
724#124—478no—
725#124—478no—
726#124—478no—
727#124—474no—
728#124—478no—
729#124—4716no—
730#124C22×D4714yes—
731#123—478no—
732#123—4716no—
733#123—4716no—
734#123—4716no—
735#123—4716no—
736#123—4716no—
737#123—4716no—
738#123—478no—
739#123—478no—
740#123—4716no—
741#123C22×D47116yes—
742C22⋊Q8—474no—
743C22⋊Q8—474no—
744C22⋊Q8—474no—
745C22⋊Q8—478no—
746C22⋊Q8—478no—
747C22⋊Q8—478no—
748C22⋊Q8—474no—
749C22⋊Q8—478no—
750C22⋊Q8—478no—
751C22⋊Q8—474no—
752C22⋊Q8—474no—
753C22⋊Q8—4716no—
754C22⋊Q8—4716no—
755C22⋊Q8—4716no—
756C22⋊Q8—4716no—
757C22⋊Q8C22×D4718yes—
758#121—474no—
759#121—474no—
760#121—474no—
761#121—474no—
762#121—4716no—
763#121—4716no—
764#121—4716no—
765#121C22×D4714yes—
766#121C22×D4718yes—
767#121C22×D4718yes—
768#121C22×D4718yes—
769#121C22×D4714yes—
770#121C22×D4718yes—
771#120—4716no—
772#120—478no—
773#120C22×D47116yes—
774C4×Q8—474no—
775C4×Q8—474no—
776C4×Q8—478no—
777C4×Q8—474no—
778C4×Q8—474no—
779C4×Q8—474no—
780C4×Q8—478no—
781C4×Q8—478no—
782C4×Q8—478no—
783C4×Q8—474no—
784C4×Q8—474no—
785C4×Q8—474no—
786C4×Q8—474no—
787C4×Q8—474no—
788C4×D4—474no—
789C4×D4—478no—
790C4×D4—4716no—
791C4×D4—474no—
792C4×D4—474no—
793C4×D4—474no—
794C4×D4—4716no—
795C4×D4—4716no—
796C4×D4—478no—
797C4×D4—4716no—
798C4×D4—478no—
799C4×D4—478no—
800C4×D4—478no—
801C4×D4—478no—
802C4×D4—478no—
803C4×D4—474no—
804C4×D4—478no—
805C4×D4—4716no—
806C4×D4—474no—
807C4×D4—478no—
808C4×D4—478no—
809C4×D4—478no—
810C4×D4—478no—
811C4×D4—478no—
812C4×D4—478no—
813C4×D4—478no—
814C4×D4—478no—
815C4×D4C22×D4714yes—
816C4×D4C22×D4714yes—
817C4×D4C22×D4714yes—
818C4×D4C22×D4714yes—
819#117—474no—
820#117—478no—
821#117—4716no—
822#117—478no—
823#117—474no—
824#117—474no—
825#117—474no—
826#117—474no—
827#117—478no—
828#117—478no—
829#117—478no—
830#117—4716no—
831#117—4716no—
832#117—4716no—
833#117—478no—
834C2×C4⋊C4—471no—
835C2×C4⋊C4—472no—
836C2×C4⋊C4—472no—
837C2×C4⋊C4—478no—
838C2×C4⋊C4—478no—
839C2×C4⋊C4—478no—
840C2×C4⋊C4—478no—
841C2×C4⋊C4—474no—
842C2×C4⋊C4—478no—
843C2×C4⋊C4C22×D4711yescharacteristic
844C2×C4⋊C4C22×D4714yes—
845C2×C22⋊C4—472no—
846C2×C22⋊C4—478no—
847C2×C22⋊C4—478no—
848C2×C22⋊C4—478no—
849C2×C22⋊C4—4716no—
850C2×C22⋊C4—478no—
851C2×C22⋊C4—472no—
852C2×C22⋊C4C22×D4712yes—
853C2×C22⋊C4C22×D4718yes—
854C2×C42—474no—
855C2×C42—472no—
856C2×C42—471no—
857C2×C42—478no—
858C2×C42—471no—
859C2×C42—474no—
860C2×C42—472no—
861C2×C42—472no—
862C2×C42—478no—
863C2×C42—474no—
864C2×C42—474no—
865C2×C42—471no—
866C2×C42—472no—
867C2×C42—472no—
868C2×C42—472no—
869C2×C42—472no—
870C2×C42C22×D4711yescharacteristic
871C24—471no—
872C24C23×D4718yes—
873C24C23×D4712yes—
874#41—232no—
875#41—216no—
876#41—9416no—
877#41—9416no—
878#41—1888no—
879#41—1888no—
880C2×Q8—474no—
881C2×Q8—474no—
882C2×Q8—474no—
883C2×Q8—478no—
884C2×Q8—944no—
885C2×Q8—1888no—
886C2×Q8C23×D4714yes—
887C2×D4—232no—
888C2×D4—232no—
889C2×D4—48no—
890C2×D4—478no—
891C2×D4—478no—
892C2×D4—478no—
893C2×D4—948no—
894C2×D4#1062535218yescomplemented
895C2×D4C23×D4718yes—
896C2×D4C23×D47116yes—
897C2×D4C23×D4714yes—
898C2×D4C23×D4714yes—
899C2×D4C23×D4718yes—
900C2×D4C23×D4714yes—
901C2×D4C23×D4714yes—
902C22×C4—44no—
903C22×C4—471no—
904C22×C4—474no—
905C22×C4—471no—
906C22×C4—474no—
907C22×C4—474no—
908C22×C4—472no—
909C22×C4—478no—
910C22×C4—472no—
911C22×C4—471no—
912C22×C4—474no—
913C22×C4—478no—
914C22×C4—478no—
915C22×C4—478no—
916C22×C4—4716no—
917C22×C4—472no—
918C22×C4—472no—
919C22×C4—472no—
920C22×C4—472no—
921C22×C4—472no—
922C22×C4—472no—
923C22×C4—948no—
924C22×C4—944no—
925C22×C4—1882no—
926C22×C4—1882no—
927C22×C4—1884no—
928C22×C4—18816no—
929C22×C4C23×D4711yescharacteristic
930C22×C4C23×D4714yes—
931C22×C4C23×D4718yes—
932C22×C4C23×D4718yes—
933C22×C4C23×D4712yes—
934C22×C4C23×D4714yes—
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C4⋊C4—478no—
938C4⋊C4—478no—
939C4⋊C4—478no—
940C4⋊C4—478no—
941C4⋊C4—478no—
942C4⋊C4—4716no—
943C4⋊C4—4716no—
944C4⋊C4—4716no—
945C4⋊C4—478no—
946C4⋊C4—474no—
947C4⋊C4—474no—
948C4⋊C4—474no—
949C4⋊C4—4716no—
950C4⋊C4—478no—
951C4⋊C4—478no—
952C4⋊C4—474no—
953C4⋊C4—478no—
954C4⋊C4—474no—
955C4⋊C4C23×D4714yes—
956C4⋊C4C23×D4714yes—
957C4⋊C4C23×D4718yes—
958C4⋊C4C23×D4714yes—
959C22⋊C4—478no—
960C22⋊C4—478no—
961C22⋊C4—478no—
962C22⋊C4—4716no—
963C22⋊C4—478no—
964C22⋊C4—478no—
965C22⋊C4—478no—
966C22⋊C4—4716no—
967C22⋊C4—4716no—
968C22⋊C4—4716no—
969C22⋊C4—478no—
970C22⋊C4—478no—
971C22⋊C4—478no—
972C22⋊C4C23×D4718yes—
973C22⋊C4C23×D4718yes—
974C22⋊C4C23×D47116yes—
975C22⋊C4C23×D4718yes—
976C42—471no—
977C42—472no—
978C42—471no—
979C42—471no—
980C42—471no—
981C42—474no—
982C42—472no—
983C42—478no—
984C42—474no—
985C42—472no—
986C42—474no—
987C42—472no—
988C42—474no—
989C42—474no—
990C42—474no—
991C42—478no—
992C42—4716no—
993C42—478no—
994C42C23×D4712yes—
995C42C23×D4712yes—
996C23—216no—
997C23—42no—
998C23—42no—
999C23—48no—
1000C23—48no—
1001C23—472no—
1002C23—942no—
1003C23—1881no—
1004C23—1881no—
1005C23C2×#1062535218yes—
1006C23C24×D4718yes—
1007C23C24×D4711yescharacteristic
1008C23C24×D4714yes—
1009Q8—28no—
1010Q8—948no—
1011Q8—948no—
1012Q8—1888no—
1013Q8—1884no—
1014D4—232no—
1015D4—216no—
1016D4—28no—
1017D4—28no—
1018D4—48no—
1019D4—44no—
1020D4—9416no—
1021D4—1888no—
1022D4—1888no—
1023D4C2×#10625352116yes—
1024C2×C4—216no—
1025C2×C4—216no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—44no—
1029C2×C4—42no—
1030C2×C4—41no—
1031C2×C4—471no—
1032C2×C4—471no—
1033C2×C4—471no—
1034C2×C4—474no—
1035C2×C4—471no—
1036C2×C4—472no—
1037C2×C4—478no—
1038C2×C4—474no—
1039C2×C4—478no—
1040C2×C4—944no—
1041C2×C4—942no—
1042C2×C4—948no—
1043C2×C4—9416no—
1044C2×C4—942no—
1045C2×C4—944no—
1046C2×C4—948no—
1047C2×C4—948no—
1048C2×C4—944no—
1049C2×C4—944no—
1050C2×C4—944no—
1051C2×C4—1882no—
1052C2×C4—1882no—
1053C2×C4—1882no—
1054C2×C4—1884no—
1055C2×C4—18816no—
1056C2×C4—1888no—
1057C2×C4—1881no—
1058C2×C4—1888no—
1059C2×C4—1888no—
1060C2×C4C2×#1062535214yes—
1061C2×C4C24×D4711yescharacteristic
1062C2×C4C24×D4714yes—
1063C2×C4C24×D4718yes—
1064C2×C4C24×D4712yes—
1065C2×C4C24×D4712yes—
1066C2×C4C24×D4711yescharacteristic
1067C22—21no—
1068C22—24no—
1069C22—21no—
1070C22—24no—
1071C22—28no—
1072C22—28no—
1073C22—28no—
1074C22—48no—
1075C22—816no—
1076C22—942no—
1077C22—942no—
1078C22—942no—
1079C22—1884no—
1080C22C22×#1062535218yes—
1081C22C22×#1062535212yes—
1082C22C25×D4711yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—472no—
1088C4—941no—
1089C4—941no—
1090C4—944no—
1091C4—941no—
1092C4—944no—
1093C4—948no—
1094C4—942no—
1095C4—948no—
1096C4C22×#1062535214yes—
1097C4#1568995812yes—
1098C2—22no—
1099C2—28no—
1100C2—48no—
1101C2—1882no—
1102C2C23×#1062535211yescharacteristic
1103C2#585×D4711yescharacteristic
1104C2C2×#1568995811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3496C2
hypercenter#3496D47
hypocenterC47#62781
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #20257445C2semidirect
2. #20257357C2semidirect
3. #20257340C2semidirect
4. #20257250C2semidirect
5. #20257222C2semidirect
6. #20257191C2semidirect
7. #20257107C2semidirect
8. #20257085C2semidirect
9. #20257028C2semidirect
10. #20257000C2semidirect
11. #20256989C2semidirect
12. #20256939C2semidirect
13. #20256816C2semidirect
14. #20256794C2semidirect
15. #20256683C2semidirect
16. C2×#15689654C2semidirect
17. H(5,𝔽2)×Dic47C2semidirect
18. C2×C4×#10625352C2semidirect
19. C47×#3496C2semidirect
21. #15689859C22semidirect
22. #15689848C22semidirect
23. #15689844C22semidirect
24. #15689843C22semidirect
25. #15689842C22semidirect
26. #15689837C22semidirect
27. #15689832C22semidirect
28. #15689830C22semidirect
29. #15689830C22semidirect
30. #15689825C22semidirect
31. #15689825C22semidirect
32. #15689816C22semidirect
33. #15689815C22semidirect
34. #15689813C22semidirect
35. #15689810C22semidirect
36. #15689810C22semidirect
37. #15689808C22semidirect
38. #15689804C22semidirect
39. #15689804C22semidirect
40. #15689799C22semidirect
41. D4×Dic94C22semidirect
42. #15689779C22semidirect
43. #15689772C22semidirect
44. #15689772C22semidirect
45. #15689767C22semidirect
46. #15689767C22semidirect
47. #15689767C22semidirect
48. #15689754C22semidirect
49. #15689749C22semidirect
50. #15689740C22semidirect
51. #15689733C22semidirect
52. #15689718C22semidirect
53. #15689718C22semidirect
54. #15689717C22semidirect
55. #15689710C22semidirect
56. #15689708C22semidirect
57. #15689694C22semidirect
58. #15689682C22semidirect
59. #15689680C22semidirect
60. #15689678C22semidirect
61. #15689678C22semidirect
62. #15689675C22semidirect
63. #15689671C22semidirect
64. #15689671C22semidirect
65. #15689655C22semidirect
66. #15689655C22semidirect
67. #15689654C22semidirect
68. #15689654C22semidirect
69. #15689654C22semidirect
70. #15689654C22semidirect
71. #15689654C22semidirect
72. #15689654C22semidirect
73. #15689654C22semidirect
74. #15689654C22semidirect
75. #15689654C22semidirect
76. #15689654C22semidirect
77. #15689652C22semidirect
78. #15689652C22semidirect
79. #15689650C22semidirect
80. C2×#13094017C22semidirect
81. C2×#13094015C22semidirect
82. C2×#13094011C22semidirect
83. #15689633C22semidirect
84. #15689633C22semidirect
85. #15689630C22semidirect
86. #15689629C22semidirect
87. C2×#13094005C22semidirect
88. C2×#13094003C22semidirect
89. #15689606C22semidirect
90. #15689606C22semidirect
92. #15689598C22semidirect
93. #15689598C22semidirect
94. #41×Dic47C22semidirect
95. #41×Dic47C22semidirect
96. C4×#10625352C22semidirect
97. C4×#10625352C22semidirect
98. C4×#10625352C22semidirect
99. C4×#10625352C22semidirect
100. C4×#10625352C22semidirect
101. C4×#10625352C22semidirect
102. C2×C4×Dic94C22semidirect
103. C2×#13093989C22semidirect
104. C2×#13093989C22semidirect
106. C2×D4×Dic47C22semidirect
107. C2×D4×Dic47C22semidirect
108. C2×D4×Dic47C22semidirect
109. C2×C4×C22⋊D47C22semidirect
110. C2×(C22⋊D47)⋊C4C22semidirect
111. C2×#13093982C22semidirect
112. C2×#13093980C22semidirect
113. C2×#13093980C22semidirect
114. C22×C4×Dic47C22semidirect
115. C2×C42×D47C22semidirect
117. C47×#547C22semidirect
118. C47×#546C22semidirect
119. D42×C47C22semidirect
327. C2×D4×C47#41semidirect
552. #3496D47semidirect
598. #547C2×D47semidirect
602. #546C2×D47semidirect
603. D42C2×D47semidirect
677. C47#62781semidirect
894. C2×D4#10625352semidirect

Maximal subgroups

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

subgroupindex
#202574452
#202573572
#202573402
#202572502
#202572222
#202571912
#202571072
#202570852
#202570282
#202570002
#202569892
#202569392
#202568162
#202567942
#202566832
C2×#156896542
H(5,𝔽2)×Dic472
C2×C4×#106253522
C47×#34962
#6278147