Finite Group Databasebeta

← #27124110

Subgroups — #27124110

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#20257817C214yesmaximal, complemented
2#20257793C211yesmaximal, characteristic, complemented
3#20257788C212yesmaximal, complemented
4#20257773C214yesmaximal, complemented
5#20257763C214yesmaximal, complemented
6#20257746C214yesmaximal, complemented
7#20257733C212yesmaximal, complemented
8#20257722C212yesmaximal, complemented
9#20257700C218yesmaximal, complemented
10#20257529C214yesmaximal, complemented
11#20257015C212yesmaximal, complemented
12#20256997C212yesmaximal, complemented
13#20256949C214yesmaximal, complemented
14D4×#10625354C214yesmaximal, complemented
15#20256808C218yesmaximal, complemented
16#20256720C214yesmaximal, complemented
17#20256685C212yesmaximal, complemented
18#532×D47C211yesmaximal, characteristic, complemented
19C47×#3550C211yesmaximal, characteristic, complemented
20C22×#10625354C2214yescomplemented
21C2×#41×D47C2212yescomplemented
22#15689872C2218yescomplemented
23#15689871C2218yescomplemented
24#15689869C22116yescomplemented
25#15689865C2214yescomplemented
26#15689864C22116yescomplemented
27#15689863C2218yescomplemented
28#15689839C2212yescomplemented
29#15689839C2218yescomplemented
30#15689839C2218yescomplemented
31#15689838C2214yescomplemented
32#15689833C2214yescomplemented
33#15689833C2214yescomplemented
34#15689823C2218yescomplemented
35#15689817C2218yescomplemented
36#15689814C2218yescomplemented
37#15689807C2218yescomplemented
38#15689801C2218yescomplemented
39#15689798C22116yescomplemented
40#15689795C2214yescomplemented
41#15689795C2218yescomplemented
42#15689795C2214yescomplemented
43#15689784C2218yescomplemented
44#15689776C2218yescomplemented
45#15689776C2214yescomplemented
46#15689776C2214yescomplemented
47#15689766C2218yescomplemented
48#15689766C2218yescomplemented
49#15689764C2218yescomplemented
50#15689764C22116yescomplemented
51D4×D188C2214yescomplemented
52D4×D188C2218yescomplemented
53#15689758C2212yescomplemented
54#15689750C2218yescomplemented
55#15689745C2218yescomplemented
56#15689743C22116yescomplemented
57#15689728C2218yescomplemented
58#15689725C22116yescomplemented
59#15689724C2218yescomplemented
60#15689712C22116yescomplemented
61#15689707C22116yescomplemented
62#15689703C2218yescomplemented
63#15689703C2218yescomplemented
64#15689703C2218yescomplemented
65#15689698C2218yescomplemented
66#15689697C2214yescomplemented
67#15689692C2214yescomplemented
68#15689691C2218yescomplemented
69#15689691C2218yescomplemented
70#15689689C2218yescomplemented
71#15689687C2214yescomplemented
72#15689684C2218yescomplemented
73#15689684C2218yescomplemented
74#15689678C2212yescomplemented
75#15689678C2212yescomplemented
76#15689674C2212yes—
77#15689674C2218yescomplemented
78#15689674C2211yescharacteristic, complemented
79#15689674C2212yescomplemented
80#15689674C2218yescomplemented
81#15689673C2212yescomplemented
82#15689673C2211yescharacteristic, complemented
83#15689672C2218yescomplemented
84#15689672C2212yescomplemented
85#15689671C2211yescharacteristic
86#15689670C2214yescomplemented
87#15689669C2212yescomplemented
88#15689668C2214yescomplemented
89C4⋊Q8×D47C2211yescharacteristic, complemented
90#127×D47C2211yescharacteristic
91#15689660C2214yescomplemented
92#15689660C2214yescomplemented
93#15689659C2214yescomplemented
94#15689659C2214yescomplemented
95#15689658C2214yescomplemented
96#15689658C2214yescomplemented
97#15689656C22116yescomplemented
98#15689652C2218yescomplemented
99#124×D47C2212yescomplemented
100#15689636C22116yescomplemented
101#15689636C2218yescomplemented
102#15689636C2214yescomplemented
103#15689636C2214yescomplemented
104#15689635C2214yescomplemented
105#15689631C2218yescomplemented
106#15689631C2218yescomplemented
107#121×D47C2214yescomplemented
108C4×#10625354C2218yescomplemented
109C4×#10625354C2214yescomplemented
110C4×#10625354C2214yescomplemented
111#15689591C2214yescomplemented
112C4×D4×D47C2218yescomplemented
113C4×D4×D47C2214yescomplemented
114#117×D47C2214yescomplemented
115C2×C42×D47C2211yescharacteristic, complemented
116C47×#563C2214yescomplemented
117C47×#559C2212yescomplemented
118Q82×C47C2212yescomplemented
119C47×#556C2214yescomplemented
120D4×Q8×C47C2214yescomplemented
121C47×#542C2218yescomplemented
122C47×#536C2214yescomplemented
123C47×#533C2212yescomplemented
124C47×#532C2211yescharacteristic
125C2×#10625354—416no—
126C2×#10625354C2314yes—
127C2×#10625354C2318yes—
128C2×#10625354C2318yes—
129C2×#10625354C2314yes—
130C2×#10625354C2318yes—
131C2×#10625354C2318yes—
132C2×#10625354C2312yes—
133C2×#10625350C2314yes—
134C2×#10625350C2312yes—
135C2×#10625350C2314yes—
136C2×#10625352C2312yes—
137C2×#10625352C2314yes—
138#41×D47—48no—
139C2×Q8×D47C2312yes—
140C22×D188C2318yes—
141C22×D188C2314yes—
142C2×D4×D47C2318yes—
143C2×D4×D47C2314yes—
144C2×D4×D47C2314yes—
145C2×D4×D47C2312yes—
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2314yes—
148C22×C4×D47C2312yes—
149C22×C4×D47C2318yes—
150#13094024C2311yescharacteristic
151#13094024C2312yes—
152#13094023C2314yes—
153#13094022C2318yes—
154#13094022C2312yes—
155#13094021C2318yes—
156#13094021C2312yes—
157#13094021C2311yescharacteristic
158#13094021C2318yes—
159#13094020C2312yes—
160#13094020C2314yes—
161#13094020C2318yes—
162#13094019C2318yes—
163#13094019C2318yes—
164#13094018C23116yes—
165#13094017C23116yes—
166#13094016C2318yes—
167#13094015C2314yes—
168#13094015C2314yes—
169#13094014C23116yes—
170#13094013C23116yes—
171#13094013C2314yes—
172#13094013C2314yes—
173#13094013C2312yes—
174#13094013C2318yes—
175#13094013C2318yes—
176#13094012C2318yes—
177#13094012C2314yes—
178#13094012C2312yes—
179#13094011C2312yes—
180#13094010C2318yes—
181#13094010C23116yes—
182#13094009C23116yes—
183#13094009C23116yes—
184#13094009C23116yes—
185#13094009C23116yes—
186#13094009C2318yes—
187#13094009C2318yes—
188#13094008C2318yes—
189#13094007C2318yes—
190#13094007C2318yes—
191#13094006C23116yes—
192#13094006C23116yes—
193#13094004C2314yes—
194#13094004C2314yes—
195#13094002C23116yes—
196#13094002C23116yes—
197#13094002C23116yes—
198#13094000C2318yes—
199#13094000C23116yes—
200#13094000C2314yes—
201#13094000C2318yes—
202#13094000C2314yes—
203#13093999C2318yes—
204#13093999C2314yes—
205#13093999C2318yes—
206#13093999C2314yes—
207#13093999C23116yes—
208#13093999C2318yes—
209#13093999C23116yes—
210#13093999C2314yes—
211#13093999C23116yes—
212#13093999C23116yes—
213#13093999C2314yes—
214#13093999C2314yes—
215#13093998C2314yes—
216#13093998C2314yes—
217#13093998C2318yes—
218#13093998C23116yes—
219#13093998C2314yes—
220#13093997C23116yes—
221#13093997C23116yes—
222#13093997C23116yes—
223#13093997C23116yes—
224#13093997C23116yes—
225#13093997C2318yes—
226#13093996C2318yes—
227#13093995C2318yes—
228#13093995C2314yes—
229#13093994C23116yes—
230#13093994C23116yes—
231#13093994C23116yes—
232#13093994C2318yes—
233#13093994C2318yes—
234#13093994C2318yes—
235#13093992C2318yes—
236#13093992C2318yes—
237Q8×Dic47C2314yes—
238Q8×Dic47C2314yes—
239#13093989C2314yes—
240#13093989C2314yes—
241C4×D188C2318yes—
242C4×D188C2318yes—
243C4×D188C2314yes—
244C4×D188C2318yes—
245C4×D188C2314yes—
246C4×D188C2318yes—
247C4×D188C2314yes—
248C4×D188C23116yes—
249D4×Dic47C2314yes—
250#13093986C2318yes—
251#13093986C2314yes—
252#13093986C2314yes—
253#13093986C2314yes—
254#13093986C2314yes—
255#13093986C2314yes—
256#13093986C2318yes—
257#13093986C23116yes—
258C4×C22⋊D47C23116yes—
259C4×C22⋊D47C2318yes—
260(C22⋊D47)⋊C4C23116yes—
261(C22⋊D47)⋊C4C2318yes—
262(C22⋊D47)⋊C4C2318yes—
263(C22⋊D47)⋊C4C2318yes—
264#13093983C2314yes—
265#13093982C23116yes—
266#13093982C2318yes—
267#13093982C2318yes—
268#13093982C2314yes—
269#13093982C2314yes—
270#13093982C2318yes—
271#13093981C2318yes—
272#13093981C2318yes—
273#13093980C2318yes—
274C4⋊C4×D47C2318yes—
275C4⋊C4×D47C2314yes—
276C4⋊C4×D47C2318yes—
277C22⋊C4×D47C23116yes—
278C22⋊C4×D47C2318yes—
279C22⋊C4×D47C2318yes—
280C2×C4×Dic47C2312yes—
281C2×C4×Dic47C2311yescharacteristic
282C42×D47C2312yes—
283C42×D47C2311yescharacteristic
284C42×D47C2311yescharacteristic
285C42×D47C2311yescharacteristic
286C42×D47C2311yescharacteristic
287C42×D47C2312yes—
288C42×D47C2318yes—
289C42×D47C2318yes—
290C2×#41×C47C2312yes—
291C22×Q8×C47C2314yes—
292C4⋊Q8×C47C2318yes—
293C4⋊Q8×C47C2312yes—
294C4⋊Q8×C47C2312yes—
295C4⋊Q8×C47C2311yescharacteristic
296C4⋊Q8×C47C2318yes—
297#127×C47C2311yescharacteristic
298#126×C47C23116yes—
299#125×C47C2314yes—
300#124×C47C2318yes—
301#124×C47C2312yes—
302#124×C47C2318yes—
303#123×C47C2318yes—
304#123×C47C2318yes—
305C22⋊Q8×C47C23116yes—
306C22⋊Q8×C47C2318yes—
307C22⋊Q8×C47C2314yes—
308C22⋊Q8×C47C2314yes—
309#121×C47C2314yes—
310C4×Q8×C47C2318yes—
311C4×Q8×C47C2314yes—
312C4×Q8×C47C2314yes—
313C4×D4×C47C2314yes—
314C4×D4×C47C2318yes—
315#117×C47C2314yes—
316#117×C47C2314yes—
317C2×C42×C47C2311yescharacteristic
318C23×D47C2414yes—
319C23×D47C2411yescharacteristic
320C23×D47C2418yes—
321#41×C47—44no—
322C2×Q8×C47—48no—
323C2×Q8×C47C2414yes—
324C2×Q8×C47C2414yes—
325C2×Q8×C47C2418yes—
326C2×Q8×C47C2412yes—
327C2×D4×C47C2414yes—
328C2×D4×C47C2414yes—
329C2×D4×C47C2412yes—
330C22×C4×C47C2412yes—
331C22×C4×C47C2411yescharacteristic
332C22×C4×C47C2414yes—
333C22×C4×C47C2418yes—
334C2×C22⋊D47C2418yes—
335C2×C22⋊D47C24116yes—
336C2×C22⋊D47C2418yes—
337C2×C22⋊D47C2414yes—
338C2×C22⋊D47C2414yes—
339C2×C22⋊D47C2414yes—
340C22×Dic47C2411yescharacteristic
341C22×Dic47C2414yes—
342C22×Dic47C2412yes—
343#10625354—216no—
344#10625354—44no—
345#10625354—416no—
346#10625354—416no—
347#10625354—416no—
348#10625354—48no—
349#10625354—416no—
350Q8×D47—44no—
351#10625352—44no—
352#10625352—48no—
353D4×D47—48no—
354D4×D47—416no—
355D4×D47—44no—
356D4×D47—48no—
357#10625350—48no—
358#10625350—44no—
359#10625350—48no—
360C2×D188—48no—
361C2×D188—416no—
362C2×D188C2414yes—
363C2×D188C2414yes—
364C2×D188C2418yes—
365C2×D188C2414yes—
366C2×D188C2414yes—
367C2×D188C2418yes—
368C2×D188C24116yes—
369C2×D188C2418yes—
370C2×D188C24116yes—
371C2×D188C2414yes—
372C2×D188C2412yes—
373C2×C4×D47—24no—
374C2×C4×D47—216no—
375C2×C4×D47—416no—
376C2×C4×D47—44no—
377C2×C4×D47C2412yes—
378C2×C4×D47C2412yes—
379C2×C4×D47C2414yes—
380C2×C4×D47C2411yescharacteristic
381C2×C4×D47C2411yescharacteristic
382C2×C4×D47C2411yescharacteristic
383C2×C4×D47C2418yes—
384C2×C4×D47C2418yes—
385C2×C4×D47C2414yes—
386C2×C4×D47C2414yes—
387C2×C4×D47C2412yes—
388C2×C4×D47C2412yes—
389C2×C4×D47C2418yes—
390C2×C4×D47C24116yes—
391C2×C4×D47C24116yes—
392C2×C4×D47C2411yescharacteristic
393C2×Dic94C2414yes—
394C2×Dic94C2412yes—
395C2×Dic94C2414yes—
396C4⋊C4×C47C2414yes—
397C4⋊C4×C47C2414yes—
398C4⋊C4×C47C2414yes—
399C4⋊C4×C47C2414yes—
400C4⋊C4×C47C2414yes—
401C4⋊C4×C47C2418yes—
402C4⋊C4×C47C24116yes—
403C4⋊C4×C47C2418yes—
404C22⋊C4×C47C2418yes—
405C22⋊C4×C47C2418yes—
406C22⋊C4×C47C2418yes—
407C22⋊C4×C47C24116yes—
408C42×C47C2412yes—
409C42×C47C2411yescharacteristic
410C42×C47C2411yescharacteristic
411C42×C47C2418yes—
412C42×C47C2418yes—
413C22⋊Dic47C2418yes—
414C22⋊Dic47C2418yes—
415(C2×D47)⋊C4C2418yes—
416(C2×D47)⋊C4C2418yes—
417(C2×D47)⋊C4C2418yes—
418(C2×D47)⋊C4C24116yes—
419(C2×D47)⋊C4C2418yes—
420(C2×D47)⋊C4C2418yes—
421(C2×D47)⋊C4C2418yes—
422(C2×D47)⋊C4C2418yes—
423(C2×D47)⋊C4C24116yes—
424(C2×D47)⋊C4C2418yes—
425(C2×D47)⋊C4C2418yes—
426(C2×D47)⋊C4C2418yes—
427(C2×D47)⋊C4C24116yes—
428C4⋊Dic47C2414yes—
429C4⋊Dic47C2414yes—
430C4⋊Dic47C2414yes—
431C4⋊Dic47C2418yes—
432C4⋊Dic47C2418yes—
433Dic47⋊C4C24116yes—
434Dic47⋊C4C2418yes—
435Dic47⋊C4C24116yes—
436Dic47⋊C4C2418yes—
437Dic47⋊C4C2418yes—
438C4×Dic47C2412yes—
439C4×Dic47C2418yes—
440C4×Dic47C2412yes—
441C4×Dic47C2411yescharacteristic
442C4×Dic47C2412yes—
443C4×Dic47C2412yes—
444C4×Dic47C2412yes—
445C4×Dic47C2411yescharacteristic
446C4×Dic47C2418yes—
447C4×Dic47C2418yes—
448C23×C47C2514yes—
449C23×C47C2511yescharacteristic
450C22×D47—22no—
451C22×D47—28no—
452C22×D47—42no—
453C22×D47—48no—
454C22×D47—48no—
455C22×D47—416no—
456C22×D47C2518yes—
457C22×D47C2514yes—
458C22×D47C2511yescharacteristic
459C22×D47C2511yescharacteristic
460Q8×C47—28no—
461Q8×C47—28no—
462Q8×C47—42no—
463Q8×C47—48no—
464D4×C47—28no—
465D4×C47—42no—
466D4×C47—44no—
467C2×C4×C47—28no—
468C2×C4×C47—22no—
469C2×C4×C47—24no—
470C2×C4×C47—48no—
471C2×C4×C47C2514yes—
472C2×C4×C47C2512yes—
473C2×C4×C47C2511yescharacteristic
474C2×C4×C47C2518yes—
475C2×C4×C47C2518yes—
476C2×C4×C47C2511yescharacteristic
477C2×C4×C47C2512yes—
478C22⋊D47—44no—
479C22⋊D47—44no—
480C22⋊D47—44no—
481C22⋊D47—48no—
482C22⋊D47—416no—
483C22⋊D47—48no—
484C2×Dic47—28no—
485C2×Dic47—22no—
486C2×Dic47—42no—
487C2×Dic47C2512yes—
488C2×Dic47C2512yes—
489C2×Dic47C2511yescharacteristic
490C2×Dic47C2518yes—
491C2×Dic47C2514yes—
492C2×Dic47C2511yescharacteristic
493D188—216no—
494D188—28no—
495D188—28no—
496D188—28no—
497D188—48no—
498D188—416no—
499D188—44no—
500D188—42no—
501D188—44no—
502D188—48no—
503D188—416no—
504C4×D47—22no—
505C4×D47—28no—
506C4×D47—22no—
507C4×D47—28no—
508C4×D47—24no—
509C4×D47—24no—
510C4×D47—216no—
511C4×D47—22no—
512C4×D47—28no—
513C4×D47—216no—
514C4×D47—42no—
515C4×D47—42no—
516C4×D47—416no—
517C4×D47—416no—
518C4×D47—48no—
519C4×D47H(5,𝔽2)14yes—
520Dic94—44no—
521Dic94—44no—
522Dic94—42no—
523#62759—471nomaximal, Sylow
524C22×C47—21no—
525C22×C47—24no—
526C22×C47—22no—
527C22×C47—28no—
528C22×C47C2611yescharacteristic
529C2×D47—22no—
530C2×D47—24no—
531C2×D47—21no—
532C2×D47—28no—
533C2×D47—22no—
534C2×D47—28no—
535C2×D47—28no—
536C2×D47—28no—
537C2×D47—44no—
538C2×D47—88no—
539C2×D47—816no—
540C2×D47C2×H(5,𝔽2)12yes—
541C4×C47—21no—
542C4×C47—24no—
543C4×C47—28no—
544C4×C47—22no—
545C4×C47—28no—
546C4×C47C2×H(5,𝔽2)12yes—
547C4×C47#58514yes—
548Dic47—21no—
549Dic47—24no—
550Dic47—28no—
551Dic47—22no—
552Dic47—22no—
553Dic47C2×H(5,𝔽2)12yes—
554#3551—474no—
555#3550D4711yescharacteristic, complemented
556#3549—471no—
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×C47C22×H(5,𝔽2)11yescharacteristic
576C2×C47C2×#58512yes—
577D47—22no—
578D47—41no—
579D47—44no—
580D47—48no—
581C22×#41—472no—
582C22×#41—474no—
583#563—478no—
584#563C2×D4714yescomplemented
585#562—478no—
586#562—4716no—
587H(3,𝔽4)—474no—
588#560—4716no—
589#560—478no—
590#559C2×D4712yescomplemented
591Q82C2×D4712yescomplemented
592#556C2×D4714yescomplemented
593#555—478no—
594#555—472no—
595#555—478no—
596#555—474no—
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×Q8C2×D4714yescomplemented
609#548—478no—
610#547—478no—
611#547—474no—
612#547—474no—
613#546—478no—
614#546—478no—
615#546—4716no—
616#546—478no—
617D42—472no—
618D42—478no—
619D42—474no—
620#544—478no—
621#542—4716no—
622#542—478no—
623#542C2×D4718yescomplemented
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#536C2×D4714yescomplemented
635#535—474no—
636#535—478no—
637#535—478no—
638#535—478no—
639#535—474no—
640#534—478no—
641#534—478no—
642#533—472no—
643#533—472no—
644#533C2×D4712yescomplemented
645#532—472no—
646#532—471no—
647#532—472no—
648#532—472no—
649#532—478no—
650#532—478no—
651#532—471no—
652#532—472no—
653#532—478no—
654#532—474no—
655#532—474no—
656#532—471no—
657#532—472no—
658#532C2×D4711yescharacteristic
659C2×C4⋊Q8—471no—
660C2×#127—471no—
661#529—4716no—
662#529—474no—
663#529—474no—
664#529—478no—
665#529—474no—
666#529—474no—
667#529—474no—
668#529—474no—
669C2×#124—472no—
670#525—478no—
671#525—478no—
672#525—474no—
673#525—474no—
674#525—478no—
675#525—4716no—
676#525—474no—
677C2×#121—474no—
678C4×#41—474no—
679C4×#41—474no—
680C4×#41—478no—
681C4×#41—474no—
682C2×C4×D4—474no—
683C2×C4×D4—478no—
684C2×#117—474no—
685C22×C42—471no—
686C47#6275911yescharacteristic, complemented, Sylow
687C2×#41—474no—
688C2×#41—474no—
689C2×#41—478no—
690C2×#41—478no—
691C2×#41—472no—
692C2×#41—478no—
693C2×#41—478no—
694C2×#41—472no—
695C2×#41—474no—
696C2×#41—474no—
697C2×#41—474no—
698C2×#41—472no—
699C2×#41—1888no—
700C2×#41—18816no—
701C2×#41C22×D4712yes—
702C22×Q8—472no—
703C22×Q8C22×D4714yes—
704C22×D4—474no—
705C22×D4—478no—
706C22×D4—474no—
707C22×D4—472no—
708C22×D4—478no—
709C22×D4—474no—
710C23×C4—474no—
711C23×C4—471no—
712C23×C4—478no—
713C23×C4—472no—
714C4⋊Q8—472no—
715C4⋊Q8—478no—
716C4⋊Q8—474no—
717C4⋊Q8—471no—
718C4⋊Q8—472no—
719C4⋊Q8C22×D4711yescharacteristic
720C4⋊Q8C22×D4712yes—
721C4⋊Q8C22×D4712yes—
722C4⋊Q8C22×D4718yes—
723C4⋊Q8C22×D4718yes—
724#127—474no—
725#127—472no—
726#127—478no—
727#127—471no—
728#127—472no—
729#127—478no—
730#127—478no—
731#127C22×D4711yescharacteristic
732#126—478no—
733#126—478no—
734#126—4716no—
735#126—4716no—
736#126C22×D47116yes—
737#125—474no—
738#125—474no—
739#125—4716no—
740#125—478no—
741#125C22×D4714yes—
742#124—472no—
743#124—474no—
744#124—474no—
745#124—478no—
746#124—478no—
747#124—4716no—
748#124—472no—
749#124—478no—
750#124—4716no—
751#124—472no—
752#124—474no—
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—4716no—
765#123—478no—
766#123—4716no—
767#123—4716no—
768#123C22×D4718yes—
769#123C22×D4718yes—
770C22⋊Q8—474no—
771C22⋊Q8—474no—
772C22⋊Q8—478no—
773C22⋊Q8—4716no—
774C22⋊Q8—478no—
775C22⋊Q8—474no—
776C22⋊Q8—474no—
777C22⋊Q8—4716no—
778C22⋊Q8—4716no—
779C22⋊Q8—4716no—
780C22⋊Q8C22×D4714yes—
781C22⋊Q8C22×D4714yes—
782C22⋊Q8C22×D4718yes—
783C22⋊Q8C22×D47116yes—
784#121—478no—
785#121—474no—
786#121—478no—
787#121—474no—
788#121—474no—
789#121—474no—
790#121—478no—
791#121—4716no—
792#121—474no—
793#121—474no—
794#121—474no—
795#121—474no—
796#121—474no—
797#121—478no—
798#121—4716no—
799#121—4716no—
800#121—4716no—
801#121—478no—
802#121—478no—
803#121—4716no—
804#121—478no—
805#121—4716no—
806#121—4716no—
807#121—4716no—
808#121—4716no—
809#121—4716no—
810#121C22×D4714yes—
811#120—478no—
812#120—478no—
813#120—478no—
814#120—478no—
815#120—4716no—
816#120—478no—
817#120—4716no—
818#120—4716no—
819C4×Q8—474no—
820C4×Q8—474no—
821C4×Q8—474no—
822C4×Q8—474no—
823C4×Q8C22×D4714yes—
824C4×Q8C22×D4714yes—
825C4×Q8C22×D4718yes—
826C4×D4—474no—
827C4×D4—478no—
828C4×D4—4716no—
829C4×D4—474no—
830C4×D4—474no—
831C4×D4—474no—
832C4×D4—478no—
833C4×D4—4716no—
834C4×D4—478no—
835C4×D4—474no—
836C4×D4—474no—
837C4×D4—4716no—
838C4×D4—478no—
839C4×D4—478no—
840C4×D4—478no—
841C4×D4—474no—
842C4×D4—478no—
843C4×D4—478no—
844C4×D4—478no—
845C4×D4—474no—
846C4×D4—474no—
847C4×D4—4716no—
848C4×D4—478no—
849C4×D4C22×D4714yes—
850C4×D4C22×D4718yes—
851#117—474no—
852#117—474no—
853#117—478no—
854#117—474no—
855#117—478no—
856#117—478no—
857#117—4716no—
858#117—478no—
859#117—478no—
860#117—478no—
861#117C22×D4714yes—
862#117C22×D4714yes—
863C2×C4⋊C4—478no—
864C2×C4⋊C4—474no—
865C2×C4⋊C4—478no—
866C2×C22⋊C4—478no—
867C2×C22⋊C4—478no—
868C2×C22⋊C4—4716no—
869C2×C42—472no—
870C2×C42—471no—
871C2×C42—478no—
872C2×C42—472no—
873C2×C42—478no—
874C2×C42—471no—
875C2×C42—471no—
876C2×C42—471no—
877C2×C42—471no—
878C2×C42—472no—
879C2×C42C22×D4711yescharacteristic
880C24—474no—
881C24—471no—
882C24—478no—
883#41—44no—
884#41—9416no—
885#41—1888no—
886#41—1888no—
887#41—1884no—
888#41—1884no—
889#41—1888no—
890#41—1884no—
891#41—18816no—
892#41—18816no—
893#41—1888no—
894#41—18816no—
895#41—18816no—
896C2×Q8—48no—
897C2×Q8—474no—
898C2×Q8—472no—
899C2×Q8—474no—
900C2×Q8—1884no—
901C2×Q8C23×D4714yes—
902C2×Q8C23×D4714yes—
903C2×Q8C23×D4718yes—
904C2×Q8C23×D4712yes—
905C2×D4—4716no—
906C2×D4—478no—
907C2×D4—478no—
908C2×D4—474no—
909C2×D4—474no—
910C2×D4—474no—
911C2×D4—474no—
912C2×D4—474no—
913C2×D4—478no—
914C2×D4—474no—
915C2×D4—474no—
916C2×D4—478no—
917C2×D4—4716no—
918C2×D4—478no—
919C2×D4—4716no—
920C2×D4—472no—
921C2×D4—474no—
922C2×D4—1888no—
923C2×D4—18816no—
924C2×D4—1888no—
925C2×D4—18816no—
926C2×D4—1884no—
927C2×D4—1888no—
928C2×D4C23×D4714yes—
929C2×D4C23×D4712yes—
930C2×D4C23×D4714yes—
931C22×C4—471no—
932C22×C4—471no—
933C22×C4—474no—
934C22×C4—472no—
935C22×C4—472no—
936C22×C4—472no—
937C22×C4—471no—
938C22×C4—474no—
939C22×C4—471no—
940C22×C4—471no—
941C22×C4—478no—
942C22×C4—478no—
943C22×C4—474no—
944C22×C4—474no—
945C22×C4—472no—
946C22×C4—472no—
947C22×C4—478no—
948C22×C4—4716no—
949C22×C4—4716no—
950C22×C4—9416no—
951C22×C4—944no—
952C22×C4—1884no—
953C22×C4—18816no—
954C22×C4C23×D4712yes—
955C22×C4C23×D4711yescharacteristic
956C22×C4C23×D4714yes—
957C22×C4C23×D4718yes—
958C4⋊C4—4716no—
959C4⋊C4—478no—
960C4⋊C4—4716no—
961C4⋊C4—478no—
962C4⋊C4—478no—
963C4⋊C4—474no—
964C4⋊C4—474no—
965C4⋊C4—474no—
966C4⋊C4—478no—
967C4⋊C4—478no—
968C4⋊C4C23×D4714yes—
969C4⋊C4C23×D4714yes—
970C4⋊C4C23×D4714yes—
971C4⋊C4C23×D4718yes—
972C4⋊C4C23×D4718yes—
973C4⋊C4C23×D47116yes—
974C4⋊C4C23×D4714yes—
975C4⋊C4C23×D4714yes—
976C22⋊C4—478no—
977C22⋊C4—478no—
978C22⋊C4—478no—
979C22⋊C4—478no—
980C22⋊C4—478no—
981C22⋊C4—4716no—
982C22⋊C4—478no—
983C22⋊C4—478no—
984C22⋊C4—478no—
985C22⋊C4—4716no—
986C22⋊C4—478no—
987C22⋊C4—478no—
988C22⋊C4—478no—
989C22⋊C4—478no—
990C22⋊C4—4716no—
991C22⋊C4C23×D4718yes—
992C22⋊C4C23×D47116yes—
993C22⋊C4C23×D4718yes—
994C22⋊C4C23×D4718yes—
995C42—472no—
996C42—471no—
997C42—478no—
998C42—472no—
999C42—472no—
1000C42—472no—
1001C42—472no—
1002C42—471no—
1003C42—478no—
1004C42—478no—
1005C42C23×D4712yes—
1006C42C23×D4711yescharacteristic
1007C42C23×D4711yescharacteristic
1008C42C23×D4718yes—
1009C42C23×D4718yes—
1010C23—471no—
1011C23—478no—
1012C23—471no—
1013C23—474no—
1014C23—948no—
1015C23—942no—
1016C23—1888no—
1017C23—1888no—
1018C23—18816no—
1019C23—1882no—
1020C23C24×D4714yes—
1021C23C24×D4711yescharacteristic
1022Q8—28no—
1023Q8—28no—
1024Q8—48no—
1025Q8—42no—
1026Q8—1882no—
1027Q8—1884no—
1028Q8—1884no—
1029D4—28no—
1030D4—42no—
1031D4—44no—
1032D4—9416no—
1033D4—948no—
1034D4—948no—
1035D4—948no—
1036D4—1882no—
1037D4—1884no—
1038D4—1888no—
1039D4—18816no—
1040D4—1884no—
1041D4—1888no—
1042D4—18816no—
1043D4—1888no—
1044D4—18816no—
1045D4—1884no—
1046D4—1884no—
1047D4—1884no—
1048D4—1888no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—48no—
1053C2×C4—471no—
1054C2×C4—474no—
1055C2×C4—472no—
1056C2×C4—478no—
1057C2×C4—472no—
1058C2×C4—471no—
1059C2×C4—474no—
1060C2×C4—942no—
1061C2×C4—948no—
1062C2×C4—9416no—
1063C2×C4—942no—
1064C2×C4—948no—
1065C2×C4—948no—
1066C2×C4—942no—
1067C2×C4—948no—
1068C2×C4—942no—
1069C2×C4—944no—
1070C2×C4—944no—
1071C2×C4—9416no—
1072C2×C4—1882no—
1073C2×C4—1882no—
1074C2×C4—18816no—
1075C2×C4—1888no—
1076C2×C4—18816no—
1077C2×C4—1882no—
1078C2×C4C24×D4712yes—
1079C2×C4C24×D4711yescharacteristic
1080C2×C4C24×D4714yes—
1081C2×C4C24×D4718yes—
1082C2×C4C24×D4718yes—
1083C2×C4C24×D4711yescharacteristic
1084C2×C4C24×D4712yes—
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—472no—
1090C22—942no—
1091C22—944no—
1092C22—941no—
1093C22—948no—
1094C22—942no—
1095C22—948no—
1096C22—948no—
1097C22—948no—
1098C22—3768no—
1099C22—37616no—
1100C22—1884no—
1101C22C25×D4711yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—472no—
1108C4—944no—
1109C4—941no—
1110C4—942no—
1111C4—942no—
1112C4—948no—
1113C4H(5,𝔽2)×D4712yes—
1114C4#1568996014yes—
1115C2—44no—
1116C2—41no—
1117C2—942no—
1118C2—1888no—
1119C2—1884no—
1120C2—1881no—
1121C2C2×H(5,𝔽2)×D4711yescharacteristic
1122C2C2×#1568996012yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3550C2
hypercenter#3550D47
hypocenterC47#62759
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #20257817C2semidirect
2. #20257793C2semidirect
3. #20257788C2semidirect
4. #20257773C2semidirect
5. #20257763C2semidirect
6. #20257746C2semidirect
7. #20257733C2semidirect
8. #20257722C2semidirect
9. #20257700C2semidirect
10. #20257529C2semidirect
11. #20257015C2semidirect
12. #20256997C2semidirect
13. #20256949C2semidirect
14. D4×#10625354C2semidirect
15. #20256808C2semidirect
16. #20256720C2semidirect
17. #20256685C2semidirect
18. #532×D47C2semidirect
19. C47×#3550C2semidirect
20. C22×#10625354C22semidirect
21. C2×#41×D47C22semidirect
22. #15689872C22semidirect
23. #15689871C22semidirect
24. #15689869C22semidirect
25. #15689865C22semidirect
26. #15689864C22semidirect
27. #15689863C22semidirect
28. #15689839C22semidirect
29. #15689839C22semidirect
30. #15689839C22semidirect
31. #15689838C22semidirect
32. #15689833C22semidirect
33. #15689833C22semidirect
34. #15689823C22semidirect
35. #15689817C22semidirect
36. #15689814C22semidirect
37. #15689807C22semidirect
38. #15689801C22semidirect
39. #15689798C22semidirect
40. #15689795C22semidirect
41. #15689795C22semidirect
42. #15689795C22semidirect
43. #15689784C22semidirect
44. #15689776C22semidirect
45. #15689776C22semidirect
46. #15689776C22semidirect
47. #15689766C22semidirect
48. #15689766C22semidirect
49. #15689764C22semidirect
50. #15689764C22semidirect
51. D4×D188C22semidirect
52. D4×D188C22semidirect
53. #15689758C22semidirect
54. #15689750C22semidirect
55. #15689745C22semidirect
56. #15689743C22semidirect
57. #15689728C22semidirect
58. #15689725C22semidirect
59. #15689724C22semidirect
60. #15689712C22semidirect
61. #15689707C22semidirect
62. #15689703C22semidirect
63. #15689703C22semidirect
64. #15689703C22semidirect
65. #15689698C22semidirect
66. #15689697C22semidirect
67. #15689692C22semidirect
68. #15689691C22semidirect
69. #15689691C22semidirect
70. #15689689C22semidirect
71. #15689687C22semidirect
72. #15689684C22semidirect
73. #15689684C22semidirect
74. #15689678C22semidirect
75. #15689678C22semidirect
77. #15689674C22semidirect
78. #15689674C22semidirect
79. #15689674C22semidirect
80. #15689674C22semidirect
81. #15689673C22semidirect
82. #15689673C22semidirect
83. #15689672C22semidirect
84. #15689672C22semidirect
86. #15689670C22semidirect
87. #15689669C22semidirect
88. #15689668C22semidirect
89. C4⋊Q8×D47C22semidirect
91. #15689660C22semidirect
92. #15689660C22semidirect
93. #15689659C22semidirect
94. #15689659C22semidirect
95. #15689658C22semidirect
96. #15689658C22semidirect
97. #15689656C22semidirect
98. #15689652C22semidirect
99. #124×D47C22semidirect
100. #15689636C22semidirect
101. #15689636C22semidirect
102. #15689636C22semidirect
103. #15689636C22semidirect
104. #15689635C22semidirect
105. #15689631C22semidirect
106. #15689631C22semidirect
107. #121×D47C22semidirect
108. C4×#10625354C22semidirect
109. C4×#10625354C22semidirect
110. C4×#10625354C22semidirect
111. #15689591C22semidirect
112. C4×D4×D47C22semidirect
113. C4×D4×D47C22semidirect
114. #117×D47C22semidirect
115. C2×C42×D47C22semidirect
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
555. #3550D47semidirect
584. #563C2×D47semidirect
590. #559C2×D47semidirect
591. Q82C2×D47semidirect
592. #556C2×D47semidirect
608. D4×Q8C2×D47semidirect
623. #542C2×D47semidirect
634. #536C2×D47semidirect
644. #533C2×D47semidirect
686. C47#62759semidirect

Maximal subgroups

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

subgroupindex
#202578172
#202577932
#202577882
#202577732
#202577632
#202577462
#202577332
#202577222
#202577002
#202575292
#202570152
#202569972
#202569492
D4×#106253542
#202568082
#202567202
#202566852
#532×D472
C47×#35502
#6275947