Finite Group Databasebeta

← #27124673

Subgroups — #27124673

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#20257474C212yesmaximal, complemented
2#20257421C216yesmaximal, complemented
3#20257395C212yesmaximal, complemented
4#20257350C216yesmaximal, complemented
5#20257301C213yesmaximal, complemented
6#20257265C213yesmaximal, complemented
7#20257166C211yesmaximal, characteristic, complemented
8#20257126C216yesmaximal, complemented
9#20257058C212yesmaximal, complemented
10#20257015C212yesmaximal, complemented
11#20256999C216yesmaximal, complemented
12#20256988C212yesmaximal, complemented
13D4×#10625354C216yesmaximal, complemented
14#20256811C216yesmaximal, complemented
15#20256685C213yesmaximal, complemented
16C2×#15689674C213yesmaximal, complemented
17#20256594C212yesmaximal, complemented
18C4×#41×D47C211yesmaximal, characteristic, complemented
19C47×#3503C211yesmaximal, characteristic, complemented
20C2×#13094070C2212yes—
21C22×#10625354C2216yescomplemented
22C2×#41×D47C2211yescharacteristic
23#15689858C2216yescomplemented
24#15689858C2216yescomplemented
25#15689847C2216yescomplemented
26#15689839C2216yescomplemented
27#15689839C22112yescomplemented
28#15689834C2216yescomplemented
29#15689826C22112yescomplemented
30#15689826C22112yescomplemented
31#15689821C22112yescomplemented
32#15689800C22124yescomplemented
33#15689795C2214yescomplemented
34#15689795C2216yescomplemented
35#15689795C2212yescomplemented
36#15689795C2216yescomplemented
37#15689795C2212yescomplemented
38#15689785C2214yescomplemented
39#15689784C22112yescomplemented
40#15689776C2216yescomplemented
41#15689776C22112yescomplemented
42#15689768C22112yescomplemented
43#15689764C22112yescomplemented
44#15689764C22124yescomplemented
45#15689764C22112yescomplemented
46D4×D188C22112yescomplemented
47D4×D188C2216yescomplemented
48D4×D188C2216yescomplemented
49#15689747C22112yescomplemented
50#15689747C22112yescomplemented
51#15689729C22112yescomplemented
52#15689729C22112yescomplemented
53#15689713C22124yescomplemented
54#15689704C2216yescomplemented
55#15689692C2216yescomplemented
56#15689692C2216yescomplemented
57#15689678C2213yescomplemented
58#15689678C2211yescharacteristic, complemented
59#15689674C2216yescomplemented
60#15689674C2216yescomplemented
61#15689674C22112yescomplemented
62#15689674C2216yescomplemented
63#15689674C2216yescomplemented
64#15689674C2216yescomplemented
65#15689674C2216yescomplemented
66#15689674C2213yescomplemented
67#15689674C2216yescomplemented
68#15689674C2213yescomplemented
69#15689673C2213yescomplemented
70C2×#13094021C2213yescomplemented
71#15689660C2216yescomplemented
72#15689660C2216yescomplemented
73#15689659C2216yescomplemented
74#15689659C2216yescomplemented
75#15689658C2216yescomplemented
76#15689658C22112yescomplemented
77#15689658C2216yescomplemented
78C2×#13094013C2216yescomplemented
79#15689636C22124yescomplemented
80#15689636C2216yescomplemented
81#15689636C2216yescomplemented
82#15689635C2216yescomplemented
83C2×#13093999C2216yescomplemented
84C2×#13093999C2216yescomplemented
85#15689605C2214yescomplemented
86#15689604C2216yescomplemented
87#15689597C2216yescomplemented
88#15689595C22112yescomplemented
89#41×Dic47C2211yescharacteristic
90C4×#10625354C2211yescharacteristic, complemented
91C4×#10625354C2211yescharacteristic, complemented
92C4×#10625354C2214yescomplemented
93C4×#10625354C2216yescomplemented
94C4×#10625354C2216yescomplemented
95C4×#10625350C2213yescomplemented
96#15689591C2213yescomplemented
97#15689591C2216yescomplemented
98C4×#10625352C2213yescomplemented
99C4×#10625352C2213yescomplemented
100C4×Q8×D47C2211yescharacteristic, complemented
101C4×Q8×D47C2211yescharacteristic, complemented
102C2×#13093986C2216yescomplemented
103C2×#13093986C2216yescomplemented
104C4×D4×D47C2213yescomplemented
105C4×D4×D47C2213yescomplemented
106C4×D4×D47C22112yescomplemented
107#117×D47C2213yescomplemented
108C2×C42×D47C2213yescomplemented
109Q82×C47C2212yescomplemented
110C47×#557C2212yescomplemented
111C47×#554C2216yescomplemented
112D4×Q8×C47C2216yescomplemented
113C47×#544C2216yescomplemented
114C47×#533C2213yescomplemented
115C2×C4⋊Q8×C47C2213yescomplemented
116C47×#520C2212yes—
117C4×#41×C47C2211yescharacteristic
118#13094070—216no—
119C2×#10625354—424no—
120C2×#10625354C2314yes—
121C2×#10625354C2311yescharacteristic
122C2×#10625354C2316yes—
123C2×#10625354C23112yes—
124C2×#10625354C2316yes—
125C2×#10625354C23112yes—
126C2×#10625354C23112yes—
127C2×#10625350C2313yes—
128C2×#10625350C2316yes—
129C2×#10625352C2313yes—
130#41×D47—28no—
131C2×Q8×D47C2311yescharacteristic
132C22×D188C2316yes—
133C22×D188C2316yes—
134C22×D188C23112yes—
135C22×D188C2316yes—
136C2×D4×D47C2313yes—
137C2×D4×D47C23112yes—
138C22×C4×D47C2313yes—
139C22×C4×D47C2313yes—
140C22×C4×D47C2313yes—
141C22×C4×D47C23112yes—
142#13094024C2311yescharacteristic
143#13094021C2316yes—
144#13094021C23112yes—
145#13094021C2316yes—
146#13094021C2316yes—
147#13094021C2313yes—
148#13094019C23112yes—
149#13094019C23124yes—
150#13094019C23112yes—
151#13094015C2316yes—
152#13094015C2312yes—
153#13094013C23112yes—
154#13094013C23124yes—
155#13094013C2316yes—
156#13094013C23112yes—
157#13094013C23112yes—
158#13094013C2316yes—
159#13094012C2316yes—
160#13094012C23112yes—
161#13094009C23112yes—
162#13094009C23124yes—
163#13094009C23124yes—
164#13094009C23124yes—
165#13094009C23112yes—
166#13094008C23112yes—
167#13094004C2316yes—
168#13094004C23112yes—
169#13094004C2312yes—
170#13094000C23124yes—
171#13094000C2316yes—
172#13094000C2312yes—
173#13093999C23124yes—
174#13093999C23112yes—
175#13093999C2316yes—
176#13093999C23112yes—
177#13093999C23112yes—
178#13093999C23112yes—
179#13093999C23124yes—
180#13093999C23112yes—
181#13093999C23112yes—
182#13093999C2316yes—
183#13093999C23112yes—
184#13093999C23112yes—
185#13093999C23112yes—
186#13093999C2316yes—
187#13093999C2316yes—
188#13093998C2316yes—
189#13093998C2316yes—
190#13093998C23124yes—
191#13093994C23112yes—
192#13093994C23124yes—
193#13093994C23124yes—
194Q8×Dic47C2316yes—
195Q8×Dic47C2311yescharacteristic
196Q8×Dic47C2311yescharacteristic
197Q8×Dic47C2312yes—
198C4×Dic94C2313yes—
199C4×Dic94C2313yes—
200#13093989C2313yes—
201#13093989C2316yes—
202#13093989C2313yes—
203#13093989C2312yes—
204C4×D188C23112yes—
205C4×D188C2316yes—
206C4×D188C2316yes—
207C4×D188C23112yes—
208C4×D188C2313yes—
209C4×D188C23112yes—
210C4×D188C2313yes—
211C4×D188C23112yes—
212D4×Dic47C2313yes—
213D4×Dic47C2313yes—
214#13093986C2313yes—
215#13093986C2316yes—
216#13093986C23112yes—
217#13093986C23112yes—
218#13093986C23112yes—
219#13093986C2316yes—
220#13093986C23112yes—
221#13093986C23112yes—
222#13093986C23112yes—
223#13093986C2313yes—
224#13093986C2316yes—
225#13093986C2316yes—
226#13093986C23112yes—
227#13093986C23112yes—
228C4×C22⋊D47C2316yes—
229C4×C22⋊D47C2316yes—
230C4×C22⋊D47C23124yes—
231(C22⋊D47)⋊C4C23112yes—
232(C22⋊D47)⋊C4C2316yes—
233(C22⋊D47)⋊C4C2316yes—
234(C22⋊D47)⋊C4C23112yes—
235#13093983C2313yes—
236#13093982C23112yes—
237#13093982C2316yes—
238#13093982C2313yes—
239#13093982C23112yes—
240#13093982C2313yes—
241#13093982C2312yes—
242#13093982C23112yes—
243#13093981C2316yes—
244#13093981C23112yes—
245#13093980C2316yes—
246C4⋊C4×D47C2313yes—
247C4⋊C4×D47C23112yes—
248C4⋊C4×D47C2313yes—
249C2×(C2×D47)⋊C4C23112yes—
250C2×(C2×D47)⋊C4C23112yes—
251C22⋊C4×D47C2316yes—
252C22⋊C4×D47C23124yes—
253C2×C4×Dic47C2313yes—
254C2×C4×Dic47C2313yes—
255C2×C4×Dic47C2313yes—
256C42×D47C2311yescharacteristic
257C42×D47C2313yes—
258C42×D47C2313yes—
259C42×D47C2313yes—
260C42×D47C2313yes—
261C42×D47C2313yes—
262C42×D47C2313yes—
263C42×D47C2313yes—
264C42×D47C23112yes—
265C2×#41×C47C2311yescharacteristic
266C22×Q8×C47C2316yes—
267C4⋊Q8×C47C2316yes—
268C4⋊Q8×C47C23112yes—
269C4⋊Q8×C47C2316yes—
270C4⋊Q8×C47C2313yes—
271C4⋊Q8×C47C2316yes—
272C4⋊Q8×C47C2311yescharacteristic
273#125×C47C2316yes—
274#125×C47C23112yes—
275C22⋊Q8×C47C2316yes—
276C22⋊Q8×C47C2316yes—
277C22⋊Q8×C47C23124yes—
278C4×Q8×C47C2314yes—
279C4×Q8×C47C2311yescharacteristic
280C4×Q8×C47C2311yescharacteristic
281C4×Q8×C47C2316yes—
282C4×Q8×C47C2316yes—
283C4×D4×C47C2313yes—
284C4×D4×C47C2313yes—
285C4×D4×C47C23112yes—
286#117×C47C2313yes—
287#117×C47C2316yes—
288C2×C4⋊C4×C47C2316yes—
289C2×C4⋊C4×C47C2316yes—
290C2×C42×C47C2313yes—
291C23×D47C2413yes—
292C23×D47C24112yes—
293#41×C47#4118yescomplemented
294C2×Q8×C47—412no—
295C2×Q8×C47C2412yes—
296C2×Q8×C47C2416yes—
297C2×Q8×C47C24112yes—
298C2×Q8×C47C2411yescharacteristic
299C2×D4×C47C2413yes—
300C22×C4×C47C2413yes—
301C22×C4×C47C2413yes—
302C22×C4×C47C24112yes—
303C22×C4×C47C2413yes—
304C2×C22⋊D47C2416yes—
305C2×C22⋊D47C24112yes—
306C22×Dic47C2413yes—
307C22×Dic47C2413yes—
308C22×Dic47C2413yes—
309#10625354—24no—
310#10625354—216no—
311#10625354—224no—
312#10625354—424no—
313#10625354—424no—
314#10625354—424no—
315#10625354—412no—
316Q8×D47—24no—
317#10625352—212no—
318D4×D47—212no—
319D4×D47—248no—
320#10625350—212no—
321#10625350—224no—
322C2×D188—224no—
323C2×D188—412no—
324C2×D188—412no—
325C2×D188—424no—
326C2×D188C2416yes—
327C2×D188C2416yes—
328C2×D188C24112yes—
329C2×D188C2413yes—
330C2×D188C24112yes—
331C2×D188C2416yes—
332C2×D188C24112yes—
333C2×D188C24112yes—
334C2×D188C24112yes—
335C2×D188C24124yes—
336C2×C4×D47—212no—
337C2×C4×D47—212no—
338C2×C4×D47—424no—
339C2×C4×D47—46no—
340C2×C4×D47C2411yescharacteristic
341C2×C4×D47C2411yescharacteristic
342C2×C4×D47C2413yes—
343C2×C4×D47C2413yes—
344C2×C4×D47C2413yes—
345C2×C4×D47C2413yes—
346C2×C4×D47C2413yes—
347C2×C4×D47C2413yes—
348C2×C4×D47C2413yes—
349C2×C4×D47C24112yes—
350C2×C4×D47C24112yes—
351C2×C4×D47C2413yes—
352C2×C4×D47C2413yes—
353C2×C4×D47C24112yes—
354C2×C4×D47C24124yes—
355C2×C4×D47C2411yescharacteristic
356C2×Dic94C2412yes—
357C2×Dic94C2413yes—
358C4⋊C4×C47C2416yes—
359C4⋊C4×C47C2416yes—
360C4⋊C4×C47C24112yes—
361C4⋊C4×C47C24112yes—
362C4⋊C4×C47C2412yes—
363C4⋊C4×C47C2413yes—
364C4⋊C4×C47C2413yes—
365C4⋊C4×C47C2412yes—
366C4⋊C4×C47C24112yes—
367C4⋊C4×C47C24112yes—
368C22⋊C4×C47C24112yes—
369C22⋊C4×C47C2416yes—
370C42×C47C2411yescharacteristic
371C42×C47C2413yes—
372C42×C47C2413yes—
373C42×C47C2413yes—
374C42×C47C24112yes—
375C22⋊Dic47C2416yes—
376(C2×D47)⋊C4C24112yes—
377(C2×D47)⋊C4C24124yes—
378(C2×D47)⋊C4C2416yes—
379(C2×D47)⋊C4C2416yes—
380(C2×D47)⋊C4C24112yes—
381(C2×D47)⋊C4C24112yes—
382(C2×D47)⋊C4C24124yes—
383(C2×D47)⋊C4C2414yes—
384(C2×D47)⋊C4C24112yes—
385(C2×D47)⋊C4C24112yes—
386(C2×D47)⋊C4C24112yes—
387(C2×D47)⋊C4C24112yes—
388C4⋊Dic47C2413yes—
389C4⋊Dic47C2413yes—
390C4⋊Dic47C2412yes—
391C4⋊Dic47C2414yes—
392C4⋊Dic47C2412yes—
393C4⋊Dic47C24112yes—
394Dic47⋊C4C24112yes—
395Dic47⋊C4C2416yes—
396Dic47⋊C4C2416yes—
397Dic47⋊C4C2414yes—
398C4×Dic47C2413yes—
399C4×Dic47C2411yescharacteristic
400C4×Dic47C2411yescharacteristic
401C4×Dic47C2411yescharacteristic
402C4×Dic47C2414yes—
403C4×Dic47C2413yes—
404C4×Dic47C2413yes—
405C4×Dic47C2413yes—
406C4×Dic47C2413yes—
407C4×Dic47C2413yes—
408C4×Dic47C2413yes—
409C4×Dic47C2413yes—
410C4×Dic47C2413yes—
411C4×Dic47C24112yes—
412C23×C47C2513yes—
413C22×D47—26no—
414C22×D47—224no—
415C22×D47—26no—
416C22×D47—43no—
417C22×D47—412no—
418C22×D47—412no—
419C22×D47C25112yes—
420C22×D47C2513yes—
421C22×D47C2511yescharacteristic
422Q8×C47—212no—
423Q8×C47—24no—
424Q8×C47—412no—
425Q8×C47C2×#4114yescomplemented
426D4×C47C2×#41112yescomplemented
427C2×C4×C47—26no—
428C2×C4×C47—26no—
429C2×C4×C47—412no—
430C2×C4×C47C2×#41112yescomplemented
431C2×C4×C47C2513yes—
432C2×C4×C47C2513yes—
433C2×C4×C47C2514yes—
434C2×C4×C47C25112yes—
435C2×C4×C47C2511yescharacteristic
436C2×C4×C47C2513yes—
437C2×C4×C47C2511yescharacteristic
438C2×C4×C47C2511yescharacteristic
439C22⋊D47—224no—
440C22⋊D47—212no—
441C2×Dic47—26no—
442C2×Dic47—26no—
443C2×Dic47—43no—
444C2×Dic47C2511yescharacteristic
445C2×Dic47C2513yes—
446C2×Dic47C2511yescharacteristic
447C2×Dic47C2513yes—
448C2×Dic47C2514yes—
449C2×Dic47C2513yes—
450C2×Dic47C2511yescharacteristic
451D188—224no—
452D188—212no—
453D188—224no—
454D188—26no—
455D188—212no—
456D188—212no—
457D188—412no—
458D188—412no—
459D188—424no—
460D188—412no—
461C4×D47—26no—
462C4×D47—22no—
463C4×D47—26no—
464C4×D47—26no—
465C4×D47—26no—
466C4×D47—224no—
467C4×D47—26no—
468C4×D47—22no—
469C4×D47—26no—
470C4×D47—26no—
471C4×D47—224no—
472C4×D47—43no—
473C4×D47—43no—
474C4×D47—424no—
475C4×D47—412no—
476C4×D47H(5,𝔽2)14yescomplemented
477Dic94—24no—
478Dic94—26no—
479#62800—471nomaximal, Sylow
480C22×C47—23no—
481C22×C47—23no—
482C22×C47C22×#4116yes—
483C22×C47C2611yescharacteristic
484C2×D47—21no—
485C2×D47—21no—
486C2×D47—23no—
487C2×D47—212no—
488C2×D47—23no—
489C2×D47—212no—
490C2×D47—23no—
491C2×D47—212no—
492C2×D47—412no—
493C2×D47—824no—
494C2×D47C2×H(5,𝔽2)12yes—
495C4×C47—23no—
496C4×C47—212no—
497C4×C47—24no—
498C4×C47—23no—
499C4×C47C22×#4112yes—
500C4×C47C22×#4116yes—
501C4×C47C2×H(5,𝔽2)12yes—
502C4×C47#58512yes—
503Dic47—23no—
504Dic47—24no—
505Dic47—21no—
506Dic47—23no—
507Dic47—23no—
508Dic47—21no—
509Dic47C2×H(5,𝔽2)12yes—
510#3522—472no—
511#3519—476no—
512#3517—472no—
513#3514—476no—
514#3511—473no—
515#3508—473no—
516#3503D4711yescharacteristic, complemented
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×#41—471no—
529C2×C47—26no—
530C2×C47C23×#4111yescharacteristic
531C2×C47C22×H(5,𝔽2)11yescharacteristic
532C2×C47C2×#58511yescharacteristic
533D47—22no—
534D47—43no—
535D47—412no—
536C2×H(5,𝔽2)—472no—
537C22×#41—471no—
538C22×#41—476no—
539#559—476no—
540#559—476no—
541Q82C2×D4712yescomplemented
542#557C2×D4712yescomplemented
543#556—476no—
544#555—4712no—
545#555—476no—
546#554—476no—
547#554C2×D4716yescomplemented
548#553—4712no—
549#553—4712no—
550#553—4712no—
551#551—4724no—
552#550—476no—
553#550—472no—
554#550—474no—
555#550—472no—
556#550—476no—
557D4×Q8C2×D4716yescomplemented
558#548—4712no—
559#548—474no—
560#547—4712no—
561#547—476no—
562#546—4724no—
563#546—4712no—
564#546—4712no—
565#546—4712no—
566D42—4712no—
567D42—476no—
568D42—476no—
569#544C2×D4716yescomplemented
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#533C2×D4713yescomplemented
581#532—473no—
582#532—476no—
583#532—476no—
584#532—476no—
585#532—476no—
586#532—476no—
587#532—476no—
588#532—476no—
589#532—473no—
590#532—4712no—
591#532—473no—
592C2×C4⋊Q8C2×D4713yescomplemented
593C2×#127—473no—
594#529—476no—
595#529—476no—
596#529—4712no—
597#529—476no—
598#529—476no—
599#529—476no—
600#529—476no—
601C2×#124—476no—
602#525—476no—
603#525—476no—
604#525—4724no—
605#525—476no—
606C2×#121—476no—
607C2×#121—476no—
608#520—474no—
609#520—476no—
610#520C2×D4712yes—
611#518—4712no—
612#518—476no—
613C4×#41—471no—
614C4×#41—471no—
615C4×#41—471no—
616C4×#41—474no—
617C4×#41—476no—
618C4×#41—476no—
619C4×#41—473no—
620C4×#41—473no—
621C4×#41—473no—
622C4×#41—476no—
623C4×#41—473no—
624C4×#41C2×D4711yescharacteristic
625C2×C4×Q8—471no—
626C2×C4×Q8—471no—
627C2×C4×D4—473no—
628C2×C4×D4—473no—
629C2×C4×D4—4712no—
630C2×C4×D4—476no—
631C2×C4×D4—476no—
632C2×#117—473no—
633C22×C42—473no—
634C47#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—9416no—
636C2×#41—471no—
637C2×#41—474no—
638C2×#41—476no—
639C2×#41—476no—
640C2×#41—4712no—
641C2×#41—4712no—
642C2×#41—4712no—
643C2×#41—473no—
644C2×#41—473no—
645C2×#41—476no—
646C2×#41—948no—
647C2×#41—18824no—
648C2×#41C22×D4711yescharacteristic
649C22×Q8—471no—
650C22×Q8C22×D4716yes—
651C22×D4—473no—
652C22×D4—4712no—
653C22×D4—476no—
654C22×D4—476no—
655C22×D4—4712no—
656C22×D4—476no—
657C23×C4—473no—
658C23×C4—473no—
659C23×C4—4712no—
660C23×C4—473no—
661C4⋊Q8—471no—
662C4⋊Q8C22×D4713yes—
663C4⋊Q8C22×D4716yes—
664C4⋊Q8C22×D4716yes—
665C4⋊Q8C22×D4716yes—
666C4⋊Q8C22×D4711yescharacteristic
667C4⋊Q8C22×D47112yes—
668#127—473no—
669#127—476no—
670#127—476no—
671#127—476no—
672#127—4712no—
673#126—4712no—
674#126—4712no—
675#126—4724no—
676#125—472no—
677#125—476no—
678#125C22×D4716yes—
679#125C22×D47112yes—
680#124—476no—
681#124—4712no—
682#124—4712no—
683#124—4712no—
684#124—476no—
685#124—4724no—
686#124—476no—
687#124—4712no—
688#123—4712no—
689#123—4712no—
690#123—4724no—
691#123—4724no—
692#123—4724no—
693#123—4712no—
694C22⋊Q8—472no—
695C22⋊Q8—476no—
696C22⋊Q8—4724no—
697C22⋊Q8—472no—
698C22⋊Q8—476no—
699C22⋊Q8—4712no—
700C22⋊Q8C22×D4716yes—
701C22⋊Q8C22×D4716yes—
702C22⋊Q8C22×D47124yes—
703#121—476no—
704#121—476no—
705#121—4724no—
706#121—476no—
707#121—476no—
708#121—4712no—
709#121—4712no—
710#121—4712no—
711#121—4712no—
712#121—4712no—
713#121—4712no—
714#121—476no—
715#121—476no—
716#121—4724no—
717#121—4712no—
718#121—4712no—
719#121—4712no—
720#121—4724no—
721#120—4712no—
722#120—4724no—
723#120—4724no—
724C4×Q8—471no—
725C4×Q8—471no—
726C4×Q8—472no—
727C4×Q8—476no—
728C4×Q8—473no—
729C4×Q8—473no—
730C4×Q8—472no—
731C4×Q8—476no—
732C4×Q8—473no—
733C4×Q8—473no—
734C4×Q8C22×D4711yescharacteristic
735C4×Q8C22×D4711yescharacteristic
736C4×Q8C22×D4714yes—
737C4×Q8C22×D4716yes—
738C4×Q8C22×D4716yes—
739C4×D4—473no—
740C4×D4—473no—
741C4×D4—476no—
742C4×D4—476no—
743C4×D4—4724no—
744C4×D4—4712no—
745C4×D4—476no—
746C4×D4—476no—
747C4×D4—473no—
748C4×D4—473no—
749C4×D4—4712no—
750C4×D4—4712no—
751C4×D4—4712no—
752C4×D4—4712no—
753C4×D4—4712no—
754C4×D4—476no—
755C4×D4—4712no—
756C4×D4—4712no—
757C4×D4—476no—
758C4×D4—4712no—
759C4×D4—476no—
760C4×D4—476no—
761C4×D4—4712no—
762C4×D4—473no—
763C4×D4—473no—
764C4×D4—4712no—
765C4×D4—4712no—
766C4×D4—4712no—
767C4×D4—4712no—
768C4×D4—476no—
769C4×D4—476no—
770C4×D4C22×D4713yes—
771C4×D4C22×D4713yes—
772C4×D4C22×D47112yes—
773#117—473no—
774#117—473no—
775#117—473no—
776#117—472no—
777#117—4712no—
778#117—4712no—
779#117—476no—
780#117—4712no—
781#117—476no—
782#117—476no—
783#117—4712no—
784#117C22×D4713yes—
785#117C22×D4716yes—
786C2×C4⋊C4—473no—
787C2×C4⋊C4—473no—
788C2×C4⋊C4—4712no—
789C2×C4⋊C4C22×D4716yes—
790C2×C4⋊C4C22×D4716yes—
791C2×C22⋊C4—4712no—
792C2×C22⋊C4—4712no—
793C2×C22⋊C4—476no—
794C2×C22⋊C4—4724no—
795C2×C42—473no—
796C2×C42—473no—
797C2×C42—473no—
798C2×C42—473no—
799C2×C42—473no—
800C2×C42—473no—
801C2×C42—4712no—
802C2×C42—473no—
803C2×C42—473no—
804C2×C42—473no—
805C2×C42—473no—
806C2×C42—471no—
807C2×C42C22×D4713yes—
808C24—473no—
809C24—4712no—
810#41—9424no—
811#41—944no—
812#41—9416no—
813#41—9412no—
814#41—9412no—
815#41—9424no—
816#41—18824no—
817#41—18824no—
818#41—18812no—
819#41—18824no—
820#41#1062535418yescomplemented
821C2×Q8—412no—
822C2×Q8—473no—
823C2×Q8—472no—
824C2×Q8—944no—
825C2×Q8C23×D4712yes—
826C2×Q8C23×D4716yes—
827C2×Q8C23×D47112yes—
828C2×Q8C23×D4711yescharacteristic
829C2×D4—476no—
830C2×D4—4712no—
831C2×D4—476no—
832C2×D4—4712no—
833C2×D4—476no—
834C2×D4—473no—
835C2×D4—4712no—
836C2×D4—476no—
837C2×D4—4712no—
838C2×D4—4712no—
839C2×D4—4712no—
840C2×D4—4724no—
841C2×D4—9412no—
842C2×D4—9448no—
843C2×D4—9424no—
844C2×D4—18812no—
845C2×D4—18812no—
846C2×D4—18824no—
847C2×D4C23×D4713yes—
848C22×C4—471no—
849C22×C4—473no—
850C22×C4—473no—
851C22×C4—473no—
852C22×C4—471no—
853C22×C4—471no—
854C22×C4—473no—
855C22×C4—473no—
856C22×C4—473no—
857C22×C4—473no—
858C22×C4—473no—
859C22×C4—473no—
860C22×C4—473no—
861C22×C4—4712no—
862C22×C4—4712no—
863C22×C4—473no—
864C22×C4—473no—
865C22×C4—4712no—
866C22×C4—4724no—
867C22×C4—9412no—
868C22×C4—9412no—
869C22×C4—1886no—
870C22×C4—18824no—
871C22×C4C23×D4713yes—
872C22×C4C23×D4713yes—
873C22×C4C23×D47112yes—
874C22×C4C23×D4713yes—
875C4⋊C4—4712no—
876C4⋊C4—476no—
877C4⋊C4—476no—
878C4⋊C4—474no—
879C4⋊C4—473no—
880C4⋊C4—473no—
881C4⋊C4—472no—
882C4⋊C4—474no—
883C4⋊C4—472no—
884C4⋊C4—4712no—
885C4⋊C4C23×D47112yes—
886C4⋊C4C23×D4713yes—
887C4⋊C4C23×D4713yes—
888C4⋊C4C23×D4716yes—
889C4⋊C4C23×D4716yes—
890C4⋊C4C23×D47112yes—
891C4⋊C4C23×D4712yes—
892C4⋊C4C23×D47112yes—
893C4⋊C4C23×D47112yes—
894C4⋊C4C23×D4712yes—
895C22⋊C4—476no—
896C22⋊C4—4712no—
897C22⋊C4—4724no—
898C22⋊C4—4712no—
899C22⋊C4—4712no—
900C22⋊C4—476no—
901C22⋊C4—476no—
902C22⋊C4—4724no—
903C22⋊C4—474no—
904C22⋊C4—4712no—
905C22⋊C4—4712no—
906C22⋊C4—4712no—
907C22⋊C4—4712no—
908C22⋊C4C23×D47112yes—
909C22⋊C4C23×D4716yes—
910C42—471no—
911C42—473no—
912C42—471no—
913C42—471no—
914C42—473no—
915C42—473no—
916C42—474no—
917C42—473no—
918C42—473no—
919C42—473no—
920C42—473no—
921C42—473no—
922C42—473no—
923C42—4712no—
924C42C23×D4711yescharacteristic
925C42C23×D4713yes—
926C42C23×D4713yes—
927C42C23×D4713yes—
928C42C23×D47112yes—
929C23—471no—
930C23—4712no—
931C23—473no—
932C23—946no—
933C23—9424no—
934C23—946no—
935C23—18812no—
936C23—18812no—
937C23—1883no—
938C23C24×D4713yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—946no—
943Q8—944no—
944Q8C2×#1062535414yescomplemented
945D4—9424no—
946D4—9424no—
947D4—9412no—
948D4—9424no—
949D4—9412no—
950D4—946no—
951D4—9412no—
952D4—9412no—
953D4—18812no—
954D4—18812no—
955D4—18824no—
956D4—18812no—
957D4C2×#10625354112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—471no—
962C2×C4—474no—
963C2×C4—471no—
964C2×C4—471no—
965C2×C4—473no—
966C2×C4—473no—
967C2×C4—474no—
968C2×C4—473no—
969C2×C4—946no—
970C2×C4—9424no—
971C2×C4—946no—
972C2×C4—946no—
973C2×C4—946no—
974C2×C4—942no—
975C2×C4—946no—
976C2×C4—946no—
977C2×C4—946no—
978C2×C4—9424no—
979C2×C4—946no—
980C2×C4—942no—
981C2×C4—946no—
982C2×C4—1883no—
983C2×C4—1883no—
984C2×C4—18824no—
985C2×C4—18812no—
986C2×C4—1883no—
987C2×C4C2×#10625354112yescomplemented
988C2×C4C24×D4713yes—
989C2×C4C24×D4713yes—
990C2×C4C24×D4714yes—
991C2×C4C24×D47112yes—
992C2×C4C24×D4711yescharacteristic
993C2×C4C24×D4713yes—
994C2×C4C24×D4711yescharacteristic
995C2×C4C24×D4711yescharacteristic
996C22—23no—
997C22—23no—
998C22—472no—
999C22—941no—
1000C22—941no—
1001C22—943no—
1002C22—9412no—
1003C22—943no—
1004C22—9412no—
1005C22—943no—
1006C22—9412no—
1007C22—37624no—
1008C22—18812no—
1009C22C22×#1062535416yes—
1010C22C25×D4711yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—472no—
1016C4—941no—
1017C4—944no—
1018C4—943no—
1019C4—943no—
1020C4—941no—
1021C4—943no—
1022C4C22×#1062535416yes—
1023C4C22×#1062535412yes—
1024C4H(5,𝔽2)×D4712yes—
1025C4#1568996012yes—
1026C2—26no—
1027C2—942no—
1028C2—18812no—
1029C2—1883no—
1030C2C23×#1062535411yescharacteristic
1031C2C2×H(5,𝔽2)×D4711yescharacteristic
1032C2C2×#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3503C2
hypercenter#3503D47
hypocenterC47#62800
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #20257474C2semidirect
2. #20257421C2semidirect
3. #20257395C2semidirect
4. #20257350C2semidirect
5. #20257301C2semidirect
6. #20257265C2semidirect
7. #20257166C2semidirect
8. #20257126C2semidirect
9. #20257058C2semidirect
10. #20257015C2semidirect
11. #20256999C2semidirect
12. #20256988C2semidirect
13. D4×#10625354C2semidirect
14. #20256811C2semidirect
15. #20256685C2semidirect
16. C2×#15689674C2semidirect
17. #20256594C2semidirect
18. C4×#41×D47C2semidirect
19. C47×#3503C2semidirect
21. C22×#10625354C22semidirect
23. #15689858C22semidirect
24. #15689858C22semidirect
25. #15689847C22semidirect
26. #15689839C22semidirect
27. #15689839C22semidirect
28. #15689834C22semidirect
29. #15689826C22semidirect
30. #15689826C22semidirect
31. #15689821C22semidirect
32. #15689800C22semidirect
33. #15689795C22semidirect
34. #15689795C22semidirect
35. #15689795C22semidirect
36. #15689795C22semidirect
37. #15689795C22semidirect
38. #15689785C22semidirect
39. #15689784C22semidirect
40. #15689776C22semidirect
41. #15689776C22semidirect
42. #15689768C22semidirect
43. #15689764C22semidirect
44. #15689764C22semidirect
45. #15689764C22semidirect
46. D4×D188C22semidirect
47. D4×D188C22semidirect
48. D4×D188C22semidirect
49. #15689747C22semidirect
50. #15689747C22semidirect
51. #15689729C22semidirect
52. #15689729C22semidirect
53. #15689713C22semidirect
54. #15689704C22semidirect
55. #15689692C22semidirect
56. #15689692C22semidirect
57. #15689678C22semidirect
58. #15689678C22semidirect
59. #15689674C22semidirect
60. #15689674C22semidirect
61. #15689674C22semidirect
62. #15689674C22semidirect
63. #15689674C22semidirect
64. #15689674C22semidirect
65. #15689674C22semidirect
66. #15689674C22semidirect
67. #15689674C22semidirect
68. #15689674C22semidirect
69. #15689673C22semidirect
70. C2×#13094021C22semidirect
71. #15689660C22semidirect
72. #15689660C22semidirect
73. #15689659C22semidirect
74. #15689659C22semidirect
75. #15689658C22semidirect
76. #15689658C22semidirect
77. #15689658C22semidirect
78. C2×#13094013C22semidirect
79. #15689636C22semidirect
80. #15689636C22semidirect
81. #15689636C22semidirect
82. #15689635C22semidirect
83. C2×#13093999C22semidirect
84. C2×#13093999C22semidirect
85. #15689605C22semidirect
86. #15689604C22semidirect
87. #15689597C22semidirect
88. #15689595C22semidirect
90. C4×#10625354C22semidirect
91. C4×#10625354C22semidirect
92. C4×#10625354C22semidirect
93. C4×#10625354C22semidirect
94. C4×#10625354C22semidirect
95. C4×#10625350C22semidirect
96. #15689591C22semidirect
97. #15689591C22semidirect
98. C4×#10625352C22semidirect
99. C4×#10625352C22semidirect
100. C4×Q8×D47C22semidirect
101. C4×Q8×D47C22semidirect
102. C2×#13093986C22semidirect
103. C2×#13093986C22semidirect
104. C4×D4×D47C22semidirect
105. C4×D4×D47C22semidirect
106. C4×D4×D47C22semidirect
107. #117×D47C22semidirect
108. C2×C42×D47C22semidirect
109. Q82×C47C22semidirect
110. C47×#557C22semidirect
111. C47×#554C22semidirect
112. D4×Q8×C47C22semidirect
113. C47×#544C22semidirect
114. C47×#533C22semidirect
115. C2×C4⋊Q8×C47C22semidirect
293. #41×C47#41semidirect
425. Q8×C47C2×#41semidirect
426. D4×C47C2×#41semidirect
430. C2×C4×C47C2×#41semidirect
476. C4×D47H(5,𝔽2)semidirect
516. #3503D47semidirect
541. Q82C2×D47semidirect
542. #557C2×D47semidirect
547. #554C2×D47semidirect
557. D4×Q8C2×D47semidirect
569. #544C2×D47semidirect
580. #533C2×D47semidirect
592. C2×C4⋊Q8C2×D47semidirect
634. C47#62800semidirect
820. #41#10625354semidirect
944. Q8C2×#10625354semidirect
957. D4C2×#10625354semidirect
987. C2×C4C2×#10625354semidirect

Maximal subgroups

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

subgroupindex
#202574742
#202574212
#202573952
#202573502
#202573012
#202572652
#202571662
#202571262
#202570582
#202570152
#202569992
#202569882
D4×#106253542
#202568112
#202566852
C2×#156896742
#202565942
C4×#41×D472
C47×#35032
#6280047