Finite Group Databasebeta

← #27124672

Subgroups — #27124672

Order 12032.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257473C212yesmaximal, complemented
2#20257420C216yesmaximal, complemented
3#20257394C212yesmaximal, complemented
4#20257349C216yesmaximal, complemented
5#20257299C213yesmaximal, complemented
6#20257264C213yesmaximal, complemented
7#20257207C211yesmaximal, characteristic, complemented
8#20257166C211yesmaximal, characteristic, complemented
9#20257123C216yesmaximal, complemented
10#20257057C212yesmaximal, complemented
11#20257014C212yesmaximal, complemented
12#20256998C216yesmaximal, complemented
13#20256983C212yesmaximal, complemented
14D4×#10625350C216yesmaximal, complemented
15#20256804C216yesmaximal, complemented
16#20256684C213yesmaximal, complemented
17C2×#15689673C213yesmaximal, complemented
18C4×#13094070C212yesmaximal, complemented
19C2×C4×#41×C47C211yesmaximal, characteristic, complemented
20C2×#13094070C2212yes—
21C22×#10625350C2216yescomplemented
22#15689858C2216yescomplemented
23#15689858C2216yescomplemented
24Q8×Dic94C2212yescomplemented
25#15689852C2212yescomplemented
26#15689846C2216yescomplemented
27#15689838C2216yescomplemented
28#15689836C22112yescomplemented
29#15689833C2216yescomplemented
30#15689830C2216yescomplemented
31#15689821C22112yescomplemented
32#15689819C22112yescomplemented
33#15689817C22112yescomplemented
34#15689797C22124yescomplemented
35#15689795C2212yescomplemented
36#15689795C2212yescomplemented
37#15689794C2216yescomplemented
38#15689794C2216yescomplemented
39#15689792C2214yescomplemented
40D4×Dic94C2216yescomplemented
41#15689784C2214yescomplemented
42#15689782C22112yescomplemented
43#15689778C2216yescomplemented
44#15689774C22112yescomplemented
45#15689769C22112yescomplemented
46#15689769C22112yescomplemented
47#15689763C22124yescomplemented
48#15689761C22112yescomplemented
49D4×D188C2216yescomplemented
50D4×D188C2216yescomplemented
51D4×C22⋊D47C22112yescomplemented
52#15689751C2216yescomplemented
53#15689745C22112yescomplemented
54#15689744C22112yescomplemented
55#15689728C22112yescomplemented
56#15689724C22112yescomplemented
57#15689706C22124yescomplemented
58#15689701C2216yescomplemented
59#15689692C2216yescomplemented
60#15689687C2216yescomplemented
61#15689680C2213yescomplemented
62#15689680C2211yescharacteristic, complemented
63#15689680C2213yescomplemented
64#15689673C2213yescomplemented
65#15689673C2216yescomplemented
66#15689673C2216yescomplemented
67#15689673C2216yescomplemented
68#15689673C2216yescomplemented
69#15689673C2216yescomplemented
70#15689673C2216yescomplemented
71#15689673C2213yescomplemented
72#15689673C2216yescomplemented
73#15689673C2213yescomplemented
74#15689670C22112yescomplemented
75C2×#13094024C2213yescomplemented
76C2×#13094021C2213yescomplemented
77#15689660C22112yescomplemented
78#15689657C2216yescomplemented
79#15689657C2216yescomplemented
80#15689657C2216yescomplemented
81#15689657C2216yescomplemented
82#15689657C2216yescomplemented
83#15689657C2216yescomplemented
84C2×#13094012C2216yescomplemented
85#15689634C2216yescomplemented
86#15689634C2216yescomplemented
87#15689634C2216yescomplemented
88#15689632C22124yescomplemented
89C2×#13093998C2216yescomplemented
90C2×#13093998C2216yescomplemented
91#15689606C2212yes—
92#15689605C2214yescomplemented
93#15689603C2216yescomplemented
94#15689597C2216yescomplemented
95#15689595C22112yescomplemented
96C4×#10625354C2214yescomplemented
97C4×#10625350C2216yescomplemented
98C4×#10625350C2216yescomplemented
99C4×#10625350C2216yescomplemented
100C2×C4×D188C2216yescomplemented
101C2×C4×D188C2216yescomplemented
102C4×D4×D47C22112yescomplemented
103C22×#41×C47C2211yescharacteristic
104C4×#41×C47C2211yescharacteristic
105C4×#41×C47C2211yescharacteristic
106C4×#41×C47C2213yescomplemented
107C4×#41×C47C2213yescomplemented
108C4×#41×C47C2213yescomplemented
109C4×#41×C47C2211yescharacteristic, complemented
110C4×#41×C47C2213yescomplemented
111C4×#41×C47C2211yescharacteristic, complemented
112C2×C4×Q8×C47C2211yescharacteristic, complemented
113C2×C4×Q8×C47C2211yescharacteristic, complemented
114C2×C4×D4×C47C2213yescomplemented
115C2×C4×D4×C47C2213yescomplemented
116C2×#117×C47C2213yescomplemented
117C22×C42×C47C2213yescomplemented
118#13094070—216no—
119C2×#10625354C2314yes—
120C2×#10625350—424no—
121C2×#10625350C2316yes—
122C2×#10625350C2316yes—
123C2×#10625350C23112yes—
124C2×#10625350C2316yes—
125C2×#10625350C23112yes—
126C2×#10625350C23112yes—
127C22×Dic94C2316yes—
128C22×D188C2316yes—
129C22×D188C2316yes—
130C22×D188C2316yes—
131C22×C22⋊D47C23112yes—
132C2×D4×D47C23112yes—
133C22×C4×D47C23112yes—
134#13094024C2316yes—
135#13094024C2316yes—
136#13094024C2316yes—
137#13094024C2313yes—
138#13094024C2311yescharacteristic
139#13094024C2311yescharacteristic
140#13094023C23112yes—
141#13094021C2316yes—
142#13094021C2316yes—
143#13094021C2316yes—
144#13094021C2313yes—
145#13094020C23112yes—
146#13094019C23124yes—
147#13094018C23112yes—
148#13094018C23112yes—
149#13094016C2316yes—
150#13094016C2316yes—
151#13094016C2312yes—
152#13094015C23112yes—
153#13094013C23112yes—
154#13094012C2316yes—
155#13094012C23112yes—
156#13094012C2316yes—
157#13094012C23112yes—
158#13094012C23112yes—
159#13094012C2316yes—
160#13094010C23124yes—
161#13094009C23124yes—
162#13094009C23124yes—
163#13094007C23112yes—
164#13094007C23112yes—
165#13094007C23112yes—
166#13094006C23124yes—
167#13094003C2316yes—
168#13094003C2316yes—
169#13094003C2316yes—
170#13094003C2316yes—
171#13094003C2312yes—
172#13094003C2312yes—
173#13094002C23124yes—
174#13094001C23124yes—
175#13094000C23112yes—
176#13093999C23112yes—
177#13093999C23112yes—
178#13093998C2316yes—
179#13093998C23112yes—
180#13093998C23112yes—
181#13093998C2316yes—
182#13093998C2316yes—
183#13093998C23112yes—
184#13093998C23112yes—
185#13093998C2316yes—
186#13093998C23112yes—
187#13093998C2316yes—
188#13093998C2316yes—
189#13093998C23112yes—
190#13093997C23124yes—
191#13093997C23124yes—
192#13093996C23124yes—
193#13093995C23112yes—
194#13093994C23124yes—
195#13093993C23112yes—
196#13093992C23124yes—
197Q8×Dic47C2314yes—
198C4×Dic94C2316yes—
199C4×Dic94C2316yes—
200C4×Dic94C2316yes—
201C4×Dic94C2316yes—
202C4×Dic94C2312yes—
203C4×Dic94C2312yes—
204C4×D188C2316yes—
205C4×D188C23112yes—
206C4×D188C23112yes—
207C4×D188C2316yes—
208C4×D188C2316yes—
209C4×D188C2316yes—
210C4×D188C23112yes—
211C4×D188C23112yes—
212C4×D188C23112yes—
213C4×D188C2316yes—
214C4×D188C2316yes—
215C4×D188C23112yes—
216D4×Dic47C23112yes—
217#13093986C23112yes—
218#13093986C23112yes—
219C4×C22⋊D47C23112yes—
220C4×C22⋊D47C23112yes—
221C4×C22⋊D47C23112yes—
222C4×C22⋊D47C23112yes—
223C4×C22⋊D47C23112yes—
224C4×C22⋊D47C23112yes—
225(C22⋊D47)⋊C4C23124yes—
226#13093983C2316yes—
227#13093983C2316yes—
228#13093983C2312yes—
229#13093982C23112yes—
230#13093981C23112yes—
231#13093981C23112yes—
232#13093981C23112yes—
233C2×C4⋊Dic47C2316yes—
234C2×C4⋊Dic47C2316yes—
235C4⋊C4×D47C23112yes—
236C2×(C2×D47)⋊C4C23112yes—
237C2×(C2×D47)⋊C4C23112yes—
238C22⋊C4×D47C23124yes—
239C42×D47C23112yes—
240C2×#41×C47—28no—
241C2×#41×C47C2313yes—
242C2×#41×C47C2311yescharacteristic
243C2×#41×C47C2313yes—
244C2×#41×C47C2311yescharacteristic
245C22×Q8×C47C2311yescharacteristic
246C22×D4×C47C2313yes—
247C23×C4×C47C2313yes—
248C23×C4×C47C2313yes—
249C23×C4×C47C2313yes—
250C4×Q8×C47C2313yes—
251C4×Q8×C47C2311yescharacteristic
252C4×Q8×C47C2311yescharacteristic
253C4×Q8×C47C2311yescharacteristic
254C4×Q8×C47C2311yescharacteristic
255C4×Q8×C47C2313yes—
256C4×Q8×C47C2313yes—
257C4×Q8×C47C2313yes—
258C4×D4×C47C2313yes—
259C4×D4×C47C2313yes—
260C4×D4×C47C2316yes—
261C4×D4×C47C2316yes—
262C4×D4×C47C2313yes—
263C4×D4×C47C2313yes—
264C4×D4×C47C2313yes—
265C4×D4×C47C2313yes—
266C4×D4×C47C2316yes—
267C4×D4×C47C2313yes—
268C4×D4×C47C2316yes—
269C4×D4×C47C2313yes—
270#117×C47C2316yes—
271#117×C47C2313yes—
272#117×C47C2313yes—
273#117×C47C2316yes—
274#117×C47C2313yes—
275#117×C47C2313yes—
276C2×C4⋊C4×C47C2313yes—
277C2×C4⋊C4×C47C2313yes—
278C2×C22⋊C4×C47C2316yes—
279C2×C42×C47C2311yescharacteristic
280C2×C42×C47C2313yes—
281C2×C42×C47C2313yes—
282C2×C42×C47C2313yes—
283C2×C42×C47C2313yes—
284C2×C42×C47C2313yes—
285C2×C42×C47C2313yes—
286C2×C42×C47C2313yes—
287C2×C42×C47C2313yes—
288C2×C42×C47C2313yes—
289C2×C42×C47C2313yes—
290C2×C42×C47C2313yes—
291C24×C47C2413yes—
292C23×D47C24112yes—
293#41×C47—24no—
294#41×C47—212no—
295#41×C47—212no—
296#41×C47#4118yescomplemented
297C2×Q8×C47—24no—
298C2×Q8×C47C2413yes—
299C2×Q8×C47C2411yescharacteristic
300C2×D4×C47—212no—
301C2×D4×C47C2416yes—
302C2×D4×C47C2413yes—
303C2×D4×C47C2413yes—
304C22×C4×C47—212no—
305C22×C4×C47—212no—
306C22×C4×C47—46no—
307C22×C4×C47C2411yescharacteristic
308C22×C4×C47C2411yescharacteristic
309C22×C4×C47C2413yes—
310C22×C4×C47C2413yes—
311C22×C4×C47C2413yes—
312C22×C4×C47C2413yes—
313C22×C4×C47C2413yes—
314C22×C4×C47C2413yes—
315C22×C4×C47C2413yes—
316C22×C4×C47C2413yes—
317C22×C4×C47C2413yes—
318C22×C4×C47C2413yes—
319C22×C4×C47C2413yes—
320C22×C4×C47C2413yes—
321C22×C4×C47C2413yes—
322C22×C4×C47C2413yes—
323C22×C4×C47C2413yes—
324C22×C4×C47C2411yescharacteristic
325C2×C22⋊D47—424no—
326C2×C22⋊D47C24112yes—
327C2×C22⋊D47C24112yes—
328C2×C22⋊D47C24112yes—
329C2×C22⋊D47C24124yes—
330C22×Dic47C24112yes—
331#10625354—216no—
332D4×D47—248no—
333#10625350—224no—
334#10625350—224no—
335#10625350—424no—
336#10625350—412no—
337#10625350—424no—
338#10625350—424no—
339C2×D188—224no—
340C2×D188—412no—
341C2×D188—412no—
342C2×D188C24112yes—
343C2×D188C2416yes—
344C2×D188C2416yes—
345C2×D188C2416yes—
346C2×D188C24112yes—
347C2×D188C24112yes—
348C2×C4×D47—424no—
349C2×C4×D47C24112yes—
350C2×C4×D47C24112yes—
351C2×C4×D47C24112yes—
352C2×C4×D47C24124yes—
353C2×Dic94—412no—
354C2×Dic94C2412yes—
355C2×Dic94C2412yes—
356C2×Dic94C2416yes—
357C2×Dic94C24112yes—
358C4⋊C4×C47C2413yes—
359C4⋊C4×C47C2413yes—
360C4⋊C4×C47C2413yes—
361C4⋊C4×C47C2413yes—
362C4⋊C4×C47C2416yes—
363C4⋊C4×C47C2416yes—
364C22⋊C4×C47C2416yes—
365C22⋊C4×C47C2416yes—
366C22⋊C4×C47C2416yes—
367C22⋊C4×C47C2416yes—
368C42×C47C2411yescharacteristic
369C42×C47C2411yescharacteristic
370C42×C47C2411yescharacteristic
371C42×C47C2411yescharacteristic
372C42×C47C2413yes—
373C42×C47C2413yes—
374C42×C47C2413yes—
375C42×C47C2413yes—
376C42×C47C2413yes—
377C42×C47C2413yes—
378C42×C47C2413yes—
379C42×C47C2413yes—
380C42×C47C2413yes—
381C42×C47C2413yes—
382C42×C47C2413yes—
383C42×C47C2413yes—
384C22⋊Dic47C24112yes—
385C22⋊Dic47C2414yes—
386C22⋊Dic47C24112yes—
387(C2×D47)⋊C4C24112yes—
388(C2×D47)⋊C4C24124yes—
389(C2×D47)⋊C4C24112yes—
390(C2×D47)⋊C4C24112yes—
391(C2×D47)⋊C4C24124yes—
392(C2×D47)⋊C4C24112yes—
393(C2×D47)⋊C4C24112yes—
394(C2×D47)⋊C4C24112yes—
395C4⋊Dic47C24112yes—
396C4⋊Dic47C2416yes—
397C4⋊Dic47C2416yes—
398C4⋊Dic47C24112yes—
399C4⋊Dic47C2412yes—
400C4⋊Dic47C2412yes—
401C4⋊Dic47C2412yes—
402C4⋊Dic47C2412yes—
403Dic47⋊C4C24112yes—
404Dic47⋊C4C2414yes—
405Dic47⋊C4C2414yes—
406Dic47⋊C4C24112yes—
407Dic47⋊C4C24112yes—
408Dic47⋊C4C24112yes—
409C4×Dic47C2414yes—
410C4×Dic47C24112yes—
411C4×Dic47C24112yes—
412C23×C47—26no—
413C23×C47—26no—
414C23×C47—43no—
415C23×C47C2513yes—
416C23×C47C2513yes—
417C23×C47C2511yescharacteristic
418C22×D47—224no—
419C22×D47—412no—
420C22×D47—412no—
421C22×D47C25112yes—
422Q8×C47—26no—
423Q8×C47C2×#4114yescomplemented
424D4×C47—212no—
425D4×C47—26no—
426D4×C47C2×#41112yescomplemented
427C2×C4×C47—26no—
428C2×C4×C47—26no—
429C2×C4×C47—22no—
430C2×C4×C47—26no—
431C2×C4×C47—26no—
432C2×C4×C47—26no—
433C2×C4×C47—26no—
434C2×C4×C47—26no—
435C2×C4×C47—26no—
436C2×C4×C47—26no—
437C2×C4×C47—26no—
438C2×C4×C47—26no—
439C2×C4×C47—22no—
440C2×C4×C47—43no—
441C2×C4×C47—43no—
442C2×C4×C47—43no—
443C2×C4×C47C2×#41112yescomplemented
444C2×C4×C47H(5,𝔽2)14yescomplemented
445C2×C4×C47C2513yes—
446C2×C4×C47C2513yes—
447C2×C4×C47C2511yescharacteristic
448C2×C4×C47C2511yescharacteristic
449C2×C4×C47C2513yes—
450C2×C4×C47C2513yes—
451C2×C4×C47C2513yes—
452C2×C4×C47C2513yes—
453C2×C4×C47C2511yescharacteristic
454C2×C4×C47C2511yescharacteristic
455C2×C4×C47C2511yescharacteristic
456C2×C4×C47C2511yescharacteristic
457C22⋊D47—224no—
458C22⋊D47—224no—
459C22⋊D47—424no—
460C22⋊D47—412no—
461C2×Dic47—412no—
462C2×Dic47C2514yes—
463C2×Dic47C2514yes—
464C2×Dic47C25112yes—
465D188—212no—
466D188—224no—
467D188—212no—
468D188—212no—
469D188—412no—
470D188—412no—
471C4×D47—224no—
472C4×D47—224no—
473C4×D47—424no—
474C4×D47—412no—
475Dic94—24no—
476Dic94—212no—
477Dic94—24no—
478Dic94—412no—
479#62800—471nomaximal, Sylow
480C22×C47—21no—
481C22×C47—23no—
482C22×C47—21no—
483C22×C47—23no—
484C22×C47—23no—
485C22×C47—23no—
486C22×C47—23no—
487C22×C47—412no—
488C22×C47C22×#4116yes—
489C22×C47C2×H(5,𝔽2)12yes—
490C22×C47C2611yescharacteristic
491C2×D47—212no—
492C2×D47—212no—
493C2×D47—212no—
494C2×D47—824no—
495C4×C47—21no—
496C4×C47—23no—
497C4×C47—23no—
498C4×C47—23no—
499C4×C47—23no—
500C4×C47—23no—
501C4×C47—21no—
502C4×C47C22×#4112yes—
503C4×C47C22×#4116yes—
504C4×C47C2×H(5,𝔽2)12yes—
505C4×C47C2×H(5,𝔽2)12yes—
506C4×C47#58512yes—
507Dic47—24no—
508Dic47—212no—
509Dic47—24no—
510#3522—472no—
511#3519—476no—
512#3517—472no—
513#3514—476no—
514#3511—473no—
515#3508—473no—
516#3503—471no—
517#3498—471no—
518#3494—476no—
519#3488—472no—
520#3483—472no—
521#3481—476no—
522#3480—472no—
523D4×#41—476no—
524#3460—476no—
525#3444—473no—
526C2×#532—473no—
527C4×H(5,𝔽2)—472no—
528C2×C4×#41D4711yescharacteristic, complemented
529C2×C47—26no—
530C2×C47—22no—
531C2×C47—43no—
532C2×C47C23×#4111yescharacteristic
533C2×C47C22×H(5,𝔽2)11yescharacteristic
534C2×C47C2×#58511yescharacteristic
535D47—412no—
536C2×H(5,𝔽2)—472no—
537C22×#41—476no—
538C22×#41C2×D4711yescharacteristic
539#559—476no—
540#559—476no—
541Q82—472no—
542#557—472no—
543#556—476no—
544#555—476no—
545#555—4712no—
546#554—476no—
547#554—476no—
548#553—4712no—
549#553—4712no—
550#553—4712no—
551#551—4724no—
552#550—474no—
553#550—472no—
554#550—472no—
555#550—476no—
556#550—476no—
557D4×Q8—476no—
558#548—474no—
559#548—4712no—
560#547—476no—
561#547—4712no—
562#546—4712no—
563#546—4712no—
564#546—4712no—
565#546—4724no—
566D42—4712no—
567D42—476no—
568D42—476no—
569#544—476no—
570#542—4712no—
571#542—4712no—
572#540—4712no—
573#540—4712no—
574#538—4724no—
575#537—476no—
576#535—476no—
577#535—476no—
578#533—471no—
579#533—473no—
580#533—473no—
581#532—4712no—
582#532—473no—
583#532—476no—
584#532—476no—
585#532—476no—
586#532—476no—
587#532—476no—
588#532—476no—
589#532—476no—
590#532—473no—
591#532—473no—
592C2×C4⋊Q8—473no—
593C2×#127—473no—
594#529—4712no—
595#529—476no—
596#529—476no—
597#529—476no—
598#529—476no—
599#529—476no—
600#529—476no—
601C2×#124—476no—
602#525—476no—
603#525—476no—
604#525—476no—
605#525—4724no—
606C2×#121—476no—
607C2×#121—476no—
608#520—472no—
609#520—474no—
610#520—476no—
611#518—4712no—
612#518—476no—
613C4×#41—474no—
614C4×#41—476no—
615C4×#41—476no—
616C4×#41—476no—
617C4×#41C2×D4711yescharacteristic
618C4×#41C2×D4711yescharacteristic
619C4×#41C2×D4713yescomplemented
620C4×#41C2×D4713yescomplemented
621C4×#41C2×D4711yescharacteristic, complemented
622C4×#41C2×D4713yescomplemented
623C4×#41C2×D4713yescomplemented
624C4×#41C2×D4711yescharacteristic, complemented
625C2×C4×Q8C2×D4711yescharacteristic, complemented
626C2×C4×Q8C2×D4711yescharacteristic, complemented
627C2×C4×D4—4712no—
628C2×C4×D4—476no—
629C2×C4×D4—476no—
630C2×C4×D4C2×D4713yescomplemented
631C2×C4×D4C2×D4713yescomplemented
632C2×#117C2×D4713yescomplemented
633C22×C42C2×D4713yescomplemented
634C47#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—9416no—
636C2×#41—28no—
637C2×#41—474no—
638C2×#41—476no—
639C2×#41—476no—
640C2×#41—476no—
641C2×#41—4712no—
642C2×#41—4712no—
643C2×#41—4712no—
644C2×#41—18824no—
645C2×#41C22×D4713yes—
646C2×#41C22×D4713yes—
647C2×#41C22×D4711yescharacteristic
648C2×#41C22×D4711yescharacteristic
649C22×Q8—476no—
650C22×Q8C22×D4711yescharacteristic
651C22×D4—4712no—
652C22×D4—4712no—
653C22×D4—476no—
654C22×D4—476no—
655C22×D4—476no—
656C22×D4C22×D4713yes—
657C23×C4—4712no—
658C23×C4C22×D4713yes—
659C23×C4C22×D4713yes—
660C23×C4C22×D4713yes—
661C4⋊Q8—4712no—
662C4⋊Q8—473no—
663C4⋊Q8—476no—
664C4⋊Q8—476no—
665C4⋊Q8—476no—
666C4⋊Q8—471no—
667C4⋊Q8—471no—
668#127—4712no—
669#127—473no—
670#127—476no—
671#127—476no—
672#127—476no—
673#126—4724no—
674#126—4712no—
675#126—4712no—
676#125—4712no—
677#125—472no—
678#125—476no—
679#125—476no—
680#124—4712no—
681#124—4724no—
682#124—476no—
683#124—4712no—
684#124—4712no—
685#124—4712no—
686#124—476no—
687#124—476no—
688#123—4712no—
689#123—4712no—
690#123—4712no—
691#123—4724no—
692#123—4724no—
693#123—4724no—
694C22⋊Q8—4712no—
695C22⋊Q8—472no—
696C22⋊Q8—472no—
697C22⋊Q8—476no—
698C22⋊Q8—476no—
699C22⋊Q8—476no—
700C22⋊Q8—476no—
701C22⋊Q8—4724no—
702C22⋊Q8—4724no—
703#121—4724no—
704#121—4712no—
705#121—476no—
706#121—476no—
707#121—4712no—
708#121—4712no—
709#121—4712no—
710#121—4712no—
711#121—4712no—
712#121—4712no—
713#121—476no—
714#121—476no—
715#121—476no—
716#121—476no—
717#121—4712no—
718#121—4712no—
719#121—4724no—
720#121—4724no—
721#120—4712no—
722#120—4724no—
723#120—4724no—
724C4×Q8—474no—
725C4×Q8—472no—
726C4×Q8—472no—
727C4×Q8—476no—
728C4×Q8—476no—
729C4×Q8—476no—
730C4×Q8—476no—
731C4×Q8C22×D4711yescharacteristic
732C4×Q8C22×D4711yescharacteristic
733C4×Q8C22×D4711yescharacteristic
734C4×Q8C22×D4711yescharacteristic
735C4×Q8C22×D4713yes—
736C4×Q8C22×D4713yes—
737C4×Q8C22×D4713yes—
738C4×Q8C22×D4713yes—
739C4×D4—4712no—
740C4×D4—4712no—
741C4×D4—4712no—
742C4×D4—4712no—
743C4×D4—4712no—
744C4×D4—4712no—
745C4×D4—4712no—
746C4×D4—4712no—
747C4×D4—4712no—
748C4×D4—4724no—
749C4×D4—4712no—
750C4×D4—476no—
751C4×D4—476no—
752C4×D4—4712no—
753C4×D4—4712no—
754C4×D4—4712no—
755C4×D4—4712no—
756C4×D4—4712no—
757C4×D4—476no—
758C4×D4—476no—
759C4×D4—476no—
760C4×D4—476no—
761C4×D4C22×D4713yes—
762C4×D4C22×D4713yes—
763C4×D4C22×D4713yes—
764C4×D4C22×D4713yes—
765C4×D4C22×D4716yes—
766C4×D4C22×D4713yes—
767C4×D4C22×D4716yes—
768C4×D4C22×D4713yes—
769C4×D4C22×D4716yes—
770C4×D4C22×D4716yes—
771C4×D4C22×D4713yes—
772C4×D4C22×D4713yes—
773#117—472no—
774#117—476no—
775#117—476no—
776#117—4712no—
777#117—4712no—
778#117—4712no—
779#117—4712no—
780#117C22×D4713yes—
781#117C22×D4713yes—
782#117C22×D4716yes—
783#117C22×D4716yes—
784#117C22×D4713yes—
785#117C22×D4713yes—
786C2×C4⋊C4—476no—
787C2×C4⋊C4—476no—
788C2×C4⋊C4—4712no—
789C2×C4⋊C4C22×D4713yes—
790C2×C4⋊C4C22×D4713yes—
791C2×C22⋊C4—4712no—
792C2×C22⋊C4—4712no—
793C2×C22⋊C4—4724no—
794C2×C22⋊C4C22×D4716yes—
795C2×C42—4712no—
796C2×C42C22×D4713yes—
797C2×C42C22×D4713yes—
798C2×C42C22×D4713yes—
799C2×C42C22×D4713yes—
800C2×C42C22×D4713yes—
801C2×C42C22×D4713yes—
802C2×C42C22×D4713yes—
803C2×C42C22×D4713yes—
804C2×C42C22×D4713yes—
805C2×C42C22×D4713yes—
806C2×C42C22×D4713yes—
807C2×C42C22×D4711yescharacteristic
808C24—4712no—
809C24C23×D4713yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—9416no—
814#41—9424no—
815#41—9424no—
816#41—18824no—
817#41—18824no—
818#41—18812no—
819#41—18824no—
820#41#1062535018yescomplemented
821C2×Q8—24no—
822C2×Q8—472no—
823C2×Q8—472no—
824C2×Q8—476no—
825C2×Q8—4712no—
826C2×Q8—18812no—
827C2×Q8C23×D4713yes—
828C2×Q8C23×D4711yescharacteristic
829C2×D4—212no—
830C2×D4—4712no—
831C2×D4—4712no—
832C2×D4—4712no—
833C2×D4—4724no—
834C2×D4—4712no—
835C2×D4—476no—
836C2×D4—476no—
837C2×D4—476no—
838C2×D4—4712no—
839C2×D4—4712no—
840C2×D4—9448no—
841C2×D4—9424no—
842C2×D4—18812no—
843C2×D4—18812no—
844C2×D4—18824no—
845C2×D4C23×D4716yes—
846C2×D4C23×D4713yes—
847C2×D4C23×D4713yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—4712no—
852C22×C4—4712no—
853C22×C4—4712no—
854C22×C4—4712no—
855C22×C4—4724no—
856C22×C4—18824no—
857C22×C4C23×D4711yescharacteristic
858C22×C4C23×D4711yescharacteristic
859C22×C4C23×D4713yes—
860C22×C4C23×D4713yes—
861C22×C4C23×D4713yes—
862C22×C4C23×D4713yes—
863C22×C4C23×D4713yes—
864C22×C4C23×D4713yes—
865C22×C4C23×D4713yes—
866C22×C4C23×D4713yes—
867C22×C4C23×D4713yes—
868C22×C4C23×D4713yes—
869C22×C4C23×D4713yes—
870C22×C4C23×D4713yes—
871C22×C4C23×D4713yes—
872C22×C4C23×D4713yes—
873C22×C4C23×D4713yes—
874C22×C4C23×D4711yescharacteristic
875C4⋊C4—4712no—
876C4⋊C4—474no—
877C4⋊C4—474no—
878C4⋊C4—4712no—
879C4⋊C4—4712no—
880C4⋊C4—4712no—
881C4⋊C4—4712no—
882C4⋊C4—476no—
883C4⋊C4—476no—
884C4⋊C4—4712no—
885C4⋊C4—472no—
886C4⋊C4—472no—
887C4⋊C4—472no—
888C4⋊C4—472no—
889C4⋊C4C23×D4713yes—
890C4⋊C4C23×D4713yes—
891C4⋊C4C23×D4713yes—
892C4⋊C4C23×D4713yes—
893C4⋊C4C23×D4716yes—
894C4⋊C4C23×D4716yes—
895C22⋊C4—4712no—
896C22⋊C4—474no—
897C22⋊C4—4712no—
898C22⋊C4—4712no—
899C22⋊C4—4724no—
900C22⋊C4—4712no—
901C22⋊C4—4712no—
902C22⋊C4—4724no—
903C22⋊C4—4712no—
904C22⋊C4—4712no—
905C22⋊C4—4712no—
906C22⋊C4C23×D4716yes—
907C22⋊C4C23×D4716yes—
908C22⋊C4C23×D4716yes—
909C22⋊C4C23×D4716yes—
910C42—4712no—
911C42—4712no—
912C42—474no—
913C42C23×D4711yescharacteristic
914C42C23×D4711yescharacteristic
915C42C23×D4713yes—
916C42C23×D4713yes—
917C42C23×D4713yes—
918C42C23×D4713yes—
919C42C23×D4713yes—
920C42C23×D4713yes—
921C42C23×D4713yes—
922C42C23×D4713yes—
923C42C23×D4713yes—
924C42C23×D4713yes—
925C42C23×D4713yes—
926C42C23×D4711yescharacteristic
927C42C23×D4711yescharacteristic
928C42C23×D4713yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—4712no—
933C23—9424no—
934C23—18812no—
935C23—18812no—
936C23C24×D4713yes—
937C23C24×D4713yes—
938C23C24×D4711yescharacteristic
939Q8—26no—
940Q8—944no—
941Q8—9412no—
942Q8—944no—
943Q8—18812no—
944Q8C2×#1062535014yescomplemented
945D4—212no—
946D4—26no—
947D4—9424no—
948D4—9424no—
949D4—9412no—
950D4—9424no—
951D4—9412no—
952D4—9412no—
953D4—18812no—
954D4—18812no—
955D4—18824no—
956D4—18812no—
957D4C2×#10625350112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—26no—
964C2×C4—26no—
965C2×C4—26no—
966C2×C4—26no—
967C2×C4—26no—
968C2×C4—22no—
969C2×C4—26no—
970C2×C4—26no—
971C2×C4—43no—
972C2×C4—43no—
973C2×C4—43no—
974C2×C4—474no—
975C2×C4—474no—
976C2×C4—4712no—
977C2×C4—9424no—
978C2×C4—9424no—
979C2×C4—18824no—
980C2×C4—18812no—
981C2×C4—18812no—
982C2×C4C2×#10625350112yescomplemented
983C2×C4#1309407014yescomplemented
984C2×C4C24×D4713yes—
985C2×C4C24×D4711yescharacteristic
986C2×C4C24×D4711yescharacteristic
987C2×C4C24×D4713yes—
988C2×C4C24×D4713yes—
989C2×C4C24×D4713yes—
990C2×C4C24×D4713yes—
991C2×C4C24×D4713yes—
992C2×C4C24×D4711yescharacteristic
993C2×C4C24×D4711yescharacteristic
994C2×C4C24×D4711yescharacteristic
995C2×C4C24×D4711yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—9412no—
1005C22—9412no—
1006C22—9412no—
1007C22—37624no—
1008C22C22×#1062535016yes—
1009C22C2×#1309407012yes—
1010C22C25×D4711yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—944no—
1019C4—9412no—
1020C4—944no—
1021C4C22×#1062535012yes—
1022C4C22×#1062535016yes—
1023C4C2×#1309407012yes—
1024C4C2×#1309407012yes—
1025C4#1568995912yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—18812no—
1030C2C23×#1062535011yescharacteristic
1031C2C22×#1309407011yescharacteristic
1032C2C2×#1568995911yescharacteristic
subgroupG/H
centerC2×C4C24×D47
commutator, socle, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C4×#41×C47C2
hypercenterC2×C4×#41D47
hypocenterC47#62800
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20257473C2semidirect
2. #20257420C2semidirect
3. #20257394C2semidirect
4. #20257349C2semidirect
5. #20257299C2semidirect
6. #20257264C2semidirect
7. #20257207C2semidirect
8. #20257166C2semidirect
9. #20257123C2semidirect
10. #20257057C2semidirect
11. #20257014C2semidirect
12. #20256998C2semidirect
13. #20256983C2semidirect
14. D4×#10625350C2semidirect
15. #20256804C2semidirect
16. #20256684C2semidirect
17. C2×#15689673C2semidirect
18. C4×#13094070C2semidirect
19. C2×C4×#41×C47C2semidirect
21. C22×#10625350C22semidirect
22. #15689858C22semidirect
23. #15689858C22semidirect
24. Q8×Dic94C22semidirect
25. #15689852C22semidirect
26. #15689846C22semidirect
27. #15689838C22semidirect
28. #15689836C22semidirect
29. #15689833C22semidirect
30. #15689830C22semidirect
31. #15689821C22semidirect
32. #15689819C22semidirect
33. #15689817C22semidirect
34. #15689797C22semidirect
35. #15689795C22semidirect
36. #15689795C22semidirect
37. #15689794C22semidirect
38. #15689794C22semidirect
39. #15689792C22semidirect
40. D4×Dic94C22semidirect
41. #15689784C22semidirect
42. #15689782C22semidirect
43. #15689778C22semidirect
44. #15689774C22semidirect
45. #15689769C22semidirect
46. #15689769C22semidirect
47. #15689763C22semidirect
48. #15689761C22semidirect
49. D4×D188C22semidirect
50. D4×D188C22semidirect
51. D4×C22⋊D47C22semidirect
52. #15689751C22semidirect
53. #15689745C22semidirect
54. #15689744C22semidirect
55. #15689728C22semidirect
56. #15689724C22semidirect
57. #15689706C22semidirect
58. #15689701C22semidirect
59. #15689692C22semidirect
60. #15689687C22semidirect
61. #15689680C22semidirect
62. #15689680C22semidirect
63. #15689680C22semidirect
64. #15689673C22semidirect
65. #15689673C22semidirect
66. #15689673C22semidirect
67. #15689673C22semidirect
68. #15689673C22semidirect
69. #15689673C22semidirect
70. #15689673C22semidirect
71. #15689673C22semidirect
72. #15689673C22semidirect
73. #15689673C22semidirect
74. #15689670C22semidirect
75. C2×#13094024C22semidirect
76. C2×#13094021C22semidirect
77. #15689660C22semidirect
78. #15689657C22semidirect
79. #15689657C22semidirect
80. #15689657C22semidirect
81. #15689657C22semidirect
82. #15689657C22semidirect
83. #15689657C22semidirect
84. C2×#13094012C22semidirect
85. #15689634C22semidirect
86. #15689634C22semidirect
87. #15689634C22semidirect
88. #15689632C22semidirect
89. C2×#13093998C22semidirect
90. C2×#13093998C22semidirect
92. #15689605C22semidirect
93. #15689603C22semidirect
94. #15689597C22semidirect
95. #15689595C22semidirect
96. C4×#10625354C22semidirect
97. C4×#10625350C22semidirect
98. C4×#10625350C22semidirect
99. C4×#10625350C22semidirect
100. C2×C4×D188C22semidirect
101. C2×C4×D188C22semidirect
102. C4×D4×D47C22semidirect
106. C4×#41×C47C22semidirect
107. C4×#41×C47C22semidirect
108. C4×#41×C47C22semidirect
109. C4×#41×C47C22semidirect
110. C4×#41×C47C22semidirect
111. C4×#41×C47C22semidirect
112. C2×C4×Q8×C47C22semidirect
113. C2×C4×Q8×C47C22semidirect
114. C2×C4×D4×C47C22semidirect
115. C2×C4×D4×C47C22semidirect
116. C2×#117×C47C22semidirect
117. C22×C42×C47C22semidirect
296. #41×C47#41semidirect
423. Q8×C47C2×#41semidirect
426. D4×C47C2×#41semidirect
443. C2×C4×C47C2×#41semidirect
444. C2×C4×C47H(5,𝔽2)semidirect
528. C2×C4×#41D47semidirect
619. C4×#41C2×D47semidirect
620. C4×#41C2×D47semidirect
621. C4×#41C2×D47semidirect
622. C4×#41C2×D47semidirect
623. C4×#41C2×D47semidirect
624. C4×#41C2×D47semidirect
625. C2×C4×Q8C2×D47semidirect
626. C2×C4×Q8C2×D47semidirect
630. C2×C4×D4C2×D47semidirect
631. C2×C4×D4C2×D47semidirect
632. C2×#117C2×D47semidirect
633. C22×C42C2×D47semidirect
634. C47#62800semidirect
820. #41#10625350semidirect
944. Q8C2×#10625350semidirect
957. D4C2×#10625350semidirect
982. C2×C4C2×#10625350semidirect
983. C2×C4#13094070semidirect

Maximal subgroups

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

subgroupindex
#202574732
#202574202
#202573942
#202573492
#202572992
#202572642
#202572072
#202571662
#202571232
#202570572
#202570142
#202569982
#202569832
D4×#106253502
#202568042
#202566842
C2×#156896732
C4×#130940702
C2×C4×#41×C472
#6280047