Finite Group Databasebeta

← #26004992

Subgroups — #26004992

Order 11008.

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#19148681C212yesmaximal, complemented
2#19148628C216yesmaximal, complemented
3#19148602C212yesmaximal, complemented
4#19148557C216yesmaximal, complemented
5#19148508C213yesmaximal, complemented
6#19148472C213yesmaximal, complemented
7#19148373C211yesmaximal, characteristic, complemented
8#19148333C216yesmaximal, complemented
9#19148265C212yesmaximal, complemented
10#19148222C212yesmaximal, complemented
11#19148206C216yesmaximal, complemented
12#19148195C212yesmaximal, complemented
13D4×#10621902C216yesmaximal, complemented
14#19148018C216yesmaximal, complemented
15#19147892C213yesmaximal, complemented
16C2×#14583450C213yesmaximal, complemented
17#19147801C212yesmaximal, complemented
18C4×#41×D43C211yesmaximal, characteristic, complemented
19C43×#3503C211yesmaximal, characteristic, complemented
20C2×#13063371C2212yes—
21C22×#10621902C2216yescomplemented
22C2×#41×D43C2211yescharacteristic
23#14583634C2216yescomplemented
24#14583634C2216yescomplemented
25#14583623C2216yescomplemented
26#14583615C22112yescomplemented
27#14583615C2216yescomplemented
28#14583610C2216yescomplemented
29#14583602C22112yescomplemented
30#14583602C22112yescomplemented
31#14583597C22112yescomplemented
32#14583576C22124yescomplemented
33#14583571C2216yescomplemented
34#14583571C2212yescomplemented
35#14583571C2214yescomplemented
36#14583571C2216yescomplemented
37#14583571C2212yescomplemented
38#14583561C2214yescomplemented
39#14583560C22112yescomplemented
40#14583552C22112yescomplemented
41#14583552C2216yescomplemented
42#14583544C22112yescomplemented
43#14583540C22112yescomplemented
44#14583540C22124yescomplemented
45#14583540C22112yescomplemented
46D4×D172C2216yescomplemented
47D4×D172C22112yescomplemented
48D4×D172C2216yescomplemented
49#14583523C22112yescomplemented
50#14583523C22112yescomplemented
51#14583505C22112yescomplemented
52#14583505C22112yescomplemented
53#14583489C22124yescomplemented
54#14583480C2216yescomplemented
55#14583468C2216yescomplemented
56#14583468C2216yescomplemented
57#14583454C2211yescharacteristic, complemented
58#14583454C2213yescomplemented
59#14583450C2216yescomplemented
60#14583450C2216yescomplemented
61#14583450C2216yescomplemented
62#14583450C22112yescomplemented
63#14583450C2216yescomplemented
64#14583450C2213yescomplemented
65#14583450C2216yescomplemented
66#14583450C2216yescomplemented
67#14583450C2216yescomplemented
68#14583450C2213yescomplemented
69#14583449C2213yescomplemented
70C2×#13063322C2213yescomplemented
71#14583436C2216yescomplemented
72#14583436C2216yescomplemented
73#14583435C2216yescomplemented
74#14583435C2216yescomplemented
75#14583434C2216yescomplemented
76#14583434C2216yescomplemented
77#14583434C22112yescomplemented
78C2×#13063314C2216yescomplemented
79#14583412C2216yescomplemented
80#14583412C22124yescomplemented
81#14583412C2216yescomplemented
82#14583411C2216yescomplemented
83C2×#13063300C2216yescomplemented
84C2×#13063300C2216yescomplemented
85#14583381C2214yescomplemented
86#14583380C2216yescomplemented
87#14583373C2216yescomplemented
88#14583371C22112yescomplemented
89#41×Dic43C2211yescharacteristic
90C4×#10621902C2214yescomplemented
91C4×#10621902C2216yescomplemented
92C4×#10621902C2211yescharacteristic, complemented
93C4×#10621902C2216yescomplemented
94C4×#10621902C2211yescharacteristic, complemented
95C4×#10621898C2213yescomplemented
96#14583367C2216yescomplemented
97#14583367C2213yescomplemented
98C4×#10621900C2213yescomplemented
99C4×#10621900C2213yescomplemented
100C4×Q8×D43C2211yescharacteristic, complemented
101C4×Q8×D43C2211yescharacteristic, complemented
102C2×#13063287C2216yescomplemented
103C2×#13063287C2216yescomplemented
104C4×D4×D43C22112yescomplemented
105C4×D4×D43C2213yescomplemented
106C4×D4×D43C2213yescomplemented
107#117×D43C2213yescomplemented
108C2×C42×D43C2213yescomplemented
109Q82×C43C2212yescomplemented
110C43×#557C2212yescomplemented
111C43×#554C2216yescomplemented
112D4×Q8×C43C2216yescomplemented
113C43×#544C2216yescomplemented
114C43×#533C2213yescomplemented
115C2×C4⋊Q8×C43C2213yescomplemented
116C43×#520C2212yes—
117C4×#41×C43C2211yescharacteristic
118#13063371—216no—
119C2×#10621902—424no—
120C2×#10621902C2314yes—
121C2×#10621902C2311yescharacteristic
122C2×#10621902C2316yes—
123C2×#10621902C23112yes—
124C2×#10621902C23112yes—
125C2×#10621902C2316yes—
126C2×#10621902C23112yes—
127C2×#10621898C2313yes—
128C2×#10621898C2316yes—
129C2×#10621900C2313yes—
130#41×D43—28no—
131C2×Q8×D43C2311yescharacteristic
132C22×D172C2316yes—
133C22×D172C2316yes—
134C22×D172C23112yes—
135C22×D172C2316yes—
136C2×D4×D43C2313yes—
137C2×D4×D43C23112yes—
138C22×C4×D43C2313yes—
139C22×C4×D43C2313yes—
140C22×C4×D43C2313yes—
141C22×C4×D43C23112yes—
142#13063325C2311yescharacteristic
143#13063322C23112yes—
144#13063322C2316yes—
145#13063322C2316yes—
146#13063322C2313yes—
147#13063322C2316yes—
148#13063320C23112yes—
149#13063320C23124yes—
150#13063320C23112yes—
151#13063316C2316yes—
152#13063316C2312yes—
153#13063314C23124yes—
154#13063314C23112yes—
155#13063314C23112yes—
156#13063314C2316yes—
157#13063314C2316yes—
158#13063314C23112yes—
159#13063313C23112yes—
160#13063313C2316yes—
161#13063310C23112yes—
162#13063310C23124yes—
163#13063310C23124yes—
164#13063310C23124yes—
165#13063310C23112yes—
166#13063309C23112yes—
167#13063305C23112yes—
168#13063305C2312yes—
169#13063305C2316yes—
170#13063301C2316yes—
171#13063301C23124yes—
172#13063301C2312yes—
173#13063300C23112yes—
174#13063300C23112yes—
175#13063300C23112yes—
176#13063300C2316yes—
177#13063300C23112yes—
178#13063300C23112yes—
179#13063300C23112yes—
180#13063300C23124yes—
181#13063300C23124yes—
182#13063300C23112yes—
183#13063300C2316yes—
184#13063300C2316yes—
185#13063300C23112yes—
186#13063300C23112yes—
187#13063300C2316yes—
188#13063299C2316yes—
189#13063299C23124yes—
190#13063299C2316yes—
191#13063295C23124yes—
192#13063295C23112yes—
193#13063295C23124yes—
194Q8×Dic43C2316yes—
195Q8×Dic43C2311yescharacteristic
196Q8×Dic43C2311yescharacteristic
197Q8×Dic43C2312yes—
198C4×Dic86C2313yes—
199C4×Dic86C2313yes—
200#13063290C2313yes—
201#13063290C2313yes—
202#13063290C2312yes—
203#13063290C2316yes—
204C4×D172C2313yes—
205C4×D172C23112yes—
206C4×D172C23112yes—
207C4×D172C2316yes—
208C4×D172C2313yes—
209C4×D172C23112yes—
210C4×D172C23112yes—
211C4×D172C2316yes—
212D4×Dic43C2313yes—
213D4×Dic43C2313yes—
214#13063287C23112yes—
215#13063287C23112yes—
216#13063287C23112yes—
217#13063287C23112yes—
218#13063287C2313yes—
219#13063287C2313yes—
220#13063287C2316yes—
221#13063287C2316yes—
222#13063287C23112yes—
223#13063287C23112yes—
224#13063287C23112yes—
225#13063287C2316yes—
226#13063287C2316yes—
227#13063287C23112yes—
228C4×C22⋊D43C2316yes—
229C4×C22⋊D43C23124yes—
230C4×C22⋊D43C2316yes—
231(C22⋊D43)⋊C4C23112yes—
232(C22⋊D43)⋊C4C2316yes—
233(C22⋊D43)⋊C4C2316yes—
234(C22⋊D43)⋊C4C23112yes—
235#13063284C2313yes—
236#13063283C23112yes—
237#13063283C2316yes—
238#13063283C2313yes—
239#13063283C23112yes—
240#13063283C2313yes—
241#13063283C2312yes—
242#13063283C23112yes—
243#13063282C2316yes—
244#13063282C23112yes—
245#13063281C2316yes—
246C4⋊C4×D43C2313yes—
247C4⋊C4×D43C23112yes—
248C4⋊C4×D43C2313yes—
249C2×(C2×D43)⋊C4C23112yes—
250C2×(C2×D43)⋊C4C23112yes—
251C22⋊C4×D43C23124yes—
252C22⋊C4×D43C2316yes—
253C2×C4×Dic43C2313yes—
254C2×C4×Dic43C2313yes—
255C2×C4×Dic43C2313yes—
256C42×D43C2311yescharacteristic
257C42×D43C2313yes—
258C42×D43C2313yes—
259C42×D43C2313yes—
260C42×D43C2313yes—
261C42×D43C2313yes—
262C42×D43C2313yes—
263C42×D43C2313yes—
264C42×D43C23112yes—
265C2×#41×C43C2311yescharacteristic
266C22×Q8×C43C2316yes—
267C4⋊Q8×C43C2316yes—
268C4⋊Q8×C43C23112yes—
269C4⋊Q8×C43C2313yes—
270C4⋊Q8×C43C2316yes—
271C4⋊Q8×C43C2316yes—
272C4⋊Q8×C43C2311yescharacteristic
273#125×C43C2316yes—
274#125×C43C23112yes—
275C22⋊Q8×C43C23124yes—
276C22⋊Q8×C43C2316yes—
277C22⋊Q8×C43C2316yes—
278C4×Q8×C43C2314yes—
279C4×Q8×C43C2311yescharacteristic
280C4×Q8×C43C2311yescharacteristic
281C4×Q8×C43C2316yes—
282C4×Q8×C43C2316yes—
283C4×D4×C43C2313yes—
284C4×D4×C43C2313yes—
285C4×D4×C43C23112yes—
286#117×C43C2313yes—
287#117×C43C2316yes—
288C2×C4⋊C4×C43C2316yes—
289C2×C4⋊C4×C43C2316yes—
290C2×C42×C43C2313yes—
291C23×D43C2413yes—
292C23×D43C24112yes—
293#41×C43#4118yescomplemented
294C2×Q8×C43—412no—
295C2×Q8×C43C2412yes—
296C2×Q8×C43C2416yes—
297C2×Q8×C43C24112yes—
298C2×Q8×C43C2411yescharacteristic
299C2×D4×C43C2413yes—
300C22×C4×C43C2413yes—
301C22×C4×C43C2413yes—
302C22×C4×C43C24112yes—
303C22×C4×C43C2413yes—
304C2×C22⋊D43C2416yes—
305C2×C22⋊D43C24112yes—
306C22×Dic43C2413yes—
307C22×Dic43C2413yes—
308C22×Dic43C2413yes—
309#10621902—24no—
310#10621902—216no—
311#10621902—224no—
312#10621902—424no—
313#10621902—424no—
314#10621902—424no—
315#10621902—412no—
316Q8×D43—24no—
317#10621900—212no—
318D4×D43—212no—
319D4×D43—248no—
320#10621898—212no—
321#10621898—224no—
322C2×D172—224no—
323C2×D172—424no—
324C2×D172—412no—
325C2×D172—412no—
326C2×D172C2416yes—
327C2×D172C2416yes—
328C2×D172C24112yes—
329C2×D172C2413yes—
330C2×D172C24112yes—
331C2×D172C2416yes—
332C2×D172C24112yes—
333C2×D172C24112yes—
334C2×D172C24112yes—
335C2×D172C24124yes—
336C2×C4×D43—212no—
337C2×C4×D43—212no—
338C2×C4×D43—424no—
339C2×C4×D43—46no—
340C2×C4×D43C2411yescharacteristic
341C2×C4×D43C2411yescharacteristic
342C2×C4×D43C2413yes—
343C2×C4×D43C2413yes—
344C2×C4×D43C2413yes—
345C2×C4×D43C2413yes—
346C2×C4×D43C2413yes—
347C2×C4×D43C2413yes—
348C2×C4×D43C2413yes—
349C2×C4×D43C24112yes—
350C2×C4×D43C24112yes—
351C2×C4×D43C2413yes—
352C2×C4×D43C2413yes—
353C2×C4×D43C24112yes—
354C2×C4×D43C24124yes—
355C2×C4×D43C2411yescharacteristic
356C2×Dic86C2412yes—
357C2×Dic86C2413yes—
358C4⋊C4×C43C2416yes—
359C4⋊C4×C43C2416yes—
360C4⋊C4×C43C24112yes—
361C4⋊C4×C43C24112yes—
362C4⋊C4×C43C2412yes—
363C4⋊C4×C43C2413yes—
364C4⋊C4×C43C2413yes—
365C4⋊C4×C43C2412yes—
366C4⋊C4×C43C24112yes—
367C4⋊C4×C43C24112yes—
368C22⋊C4×C43C24112yes—
369C22⋊C4×C43C2416yes—
370C42×C43C2411yescharacteristic
371C42×C43C2413yes—
372C42×C43C2413yes—
373C42×C43C2413yes—
374C42×C43C24112yes—
375C22⋊Dic43C2416yes—
376(C2×D43)⋊C4C24112yes—
377(C2×D43)⋊C4C24124yes—
378(C2×D43)⋊C4C2416yes—
379(C2×D43)⋊C4C2416yes—
380(C2×D43)⋊C4C24112yes—
381(C2×D43)⋊C4C24112yes—
382(C2×D43)⋊C4C24124yes—
383(C2×D43)⋊C4C2414yes—
384(C2×D43)⋊C4C24112yes—
385(C2×D43)⋊C4C24112yes—
386(C2×D43)⋊C4C24112yes—
387(C2×D43)⋊C4C24112yes—
388C4⋊Dic43C2413yes—
389C4⋊Dic43C2413yes—
390C4⋊Dic43C2412yes—
391C4⋊Dic43C2414yes—
392C4⋊Dic43C2412yes—
393C4⋊Dic43C24112yes—
394Dic43⋊C4C24112yes—
395Dic43⋊C4C2416yes—
396Dic43⋊C4C2416yes—
397Dic43⋊C4C2414yes—
398C4×Dic43C2413yes—
399C4×Dic43C2411yescharacteristic
400C4×Dic43C2411yescharacteristic
401C4×Dic43C2411yescharacteristic
402C4×Dic43C2414yes—
403C4×Dic43C2413yes—
404C4×Dic43C2413yes—
405C4×Dic43C2413yes—
406C4×Dic43C2413yes—
407C4×Dic43C2413yes—
408C4×Dic43C2413yes—
409C4×Dic43C2413yes—
410C4×Dic43C2413yes—
411C4×Dic43C24112yes—
412C23×C43C2513yes—
413C22×D43—26no—
414C22×D43—224no—
415C22×D43—26no—
416C22×D43—43no—
417C22×D43—412no—
418C22×D43—412no—
419C22×D43C25112yes—
420C22×D43C2513yes—
421C22×D43C2511yescharacteristic
422Q8×C43—212no—
423Q8×C43—24no—
424Q8×C43—412no—
425Q8×C43C2×#4114yescomplemented
426D4×C43C2×#41112yescomplemented
427C2×C4×C43—26no—
428C2×C4×C43—26no—
429C2×C4×C43—412no—
430C2×C4×C43C2×#41112yescomplemented
431C2×C4×C43C2513yes—
432C2×C4×C43C2513yes—
433C2×C4×C43C2514yes—
434C2×C4×C43C25112yes—
435C2×C4×C43C2511yescharacteristic
436C2×C4×C43C2513yes—
437C2×C4×C43C2511yescharacteristic
438C2×C4×C43C2511yescharacteristic
439C22⋊D43—224no—
440C22⋊D43—212no—
441C2×Dic43—26no—
442C2×Dic43—26no—
443C2×Dic43—43no—
444C2×Dic43C2511yescharacteristic
445C2×Dic43C2513yes—
446C2×Dic43C2511yescharacteristic
447C2×Dic43C2513yes—
448C2×Dic43C2514yes—
449C2×Dic43C2513yes—
450C2×Dic43C2511yescharacteristic
451D172—224no—
452D172—212no—
453D172—224no—
454D172—26no—
455D172—212no—
456D172—212no—
457D172—412no—
458D172—412no—
459D172—424no—
460D172—412no—
461C4×D43—26no—
462C4×D43—22no—
463C4×D43—26no—
464C4×D43—26no—
465C4×D43—26no—
466C4×D43—224no—
467C4×D43—26no—
468C4×D43—22no—
469C4×D43—26no—
470C4×D43—26no—
471C4×D43—224no—
472C4×D43—43no—
473C4×D43—43no—
474C4×D43—424no—
475C4×D43—412no—
476C4×D43H(5,𝔽2)14yescomplemented
477Dic86—24no—
478Dic86—26no—
479#62800—431nomaximal, Sylow
480C22×C43—23no—
481C22×C43—23no—
482C22×C43C22×#4116yes—
483C22×C43C2611yescharacteristic
484C2×D43—21no—
485C2×D43—21no—
486C2×D43—212no—
487C2×D43—23no—
488C2×D43—23no—
489C2×D43—212no—
490C2×D43—212no—
491C2×D43—23no—
492C2×D43—412no—
493C2×D43—824no—
494C2×D43C2×H(5,𝔽2)12yes—
495C4×C43—23no—
496C4×C43—212no—
497C4×C43—24no—
498C4×C43—23no—
499C4×C43C22×#4112yes—
500C4×C43C22×#4116yes—
501C4×C43C2×H(5,𝔽2)12yes—
502C4×C43#58512yes—
503Dic43—23no—
504Dic43—24no—
505Dic43—21no—
506Dic43—23no—
507Dic43—23no—
508Dic43—21no—
509Dic43C2×H(5,𝔽2)12yes—
510#3522—432no—
511#3519—436no—
512#3517—432no—
513#3514—436no—
514#3511—433no—
515#3508—433no—
516#3503D4311yescharacteristic, complemented
517#3498—431no—
518#3494—436no—
519#3488—432no—
520#3483—432no—
521#3481—436no—
522#3480—432no—
523D4×#41—436no—
524#3460—436no—
525#3444—433no—
526C2×#532—433no—
527C4×H(5,𝔽2)—432no—
528C2×C4×#41—431no—
529C2×C43—26no—
530C2×C43C23×#4111yescharacteristic
531C2×C43C22×H(5,𝔽2)11yescharacteristic
532C2×C43C2×#58511yescharacteristic
533D43—22no—
534D43—43no—
535D43—412no—
536C2×H(5,𝔽2)—432no—
537C22×#41—431no—
538C22×#41—436no—
539#559—436no—
540#559—436no—
541Q82C2×D4312yescomplemented
542#557C2×D4312yescomplemented
543#556—436no—
544#555—4312no—
545#555—436no—
546#554—436no—
547#554C2×D4316yescomplemented
548#553—4312no—
549#553—4312no—
550#553—4312no—
551#551—4324no—
552#550—436no—
553#550—432no—
554#550—434no—
555#550—432no—
556#550—436no—
557D4×Q8C2×D4316yescomplemented
558#548—4312no—
559#548—434no—
560#547—4312no—
561#547—436no—
562#546—4324no—
563#546—4312no—
564#546—4312no—
565#546—4312no—
566D42—4312no—
567D42—436no—
568D42—436no—
569#544C2×D4316yescomplemented
570#542—4312no—
571#542—4312no—
572#540—4312no—
573#540—4312no—
574#538—4324no—
575#537—436no—
576#535—436no—
577#535—436no—
578#533—431no—
579#533—433no—
580#533C2×D4313yescomplemented
581#532—433no—
582#532—436no—
583#532—436no—
584#532—436no—
585#532—436no—
586#532—436no—
587#532—436no—
588#532—436no—
589#532—433no—
590#532—4312no—
591#532—433no—
592C2×C4⋊Q8C2×D4313yescomplemented
593C2×#127—433no—
594#529—436no—
595#529—436no—
596#529—4312no—
597#529—436no—
598#529—436no—
599#529—436no—
600#529—436no—
601C2×#124—436no—
602#525—436no—
603#525—436no—
604#525—4324no—
605#525—436no—
606C2×#121—436no—
607C2×#121—436no—
608#520—434no—
609#520—436no—
610#520C2×D4312yes—
611#518—4312no—
612#518—436no—
613C4×#41—431no—
614C4×#41—431no—
615C4×#41—431no—
616C4×#41—434no—
617C4×#41—436no—
618C4×#41—436no—
619C4×#41—433no—
620C4×#41—433no—
621C4×#41—433no—
622C4×#41—436no—
623C4×#41—433no—
624C4×#41C2×D4311yescharacteristic
625C2×C4×Q8—431no—
626C2×C4×Q8—431no—
627C2×C4×D4—433no—
628C2×C4×D4—433no—
629C2×C4×D4—4312no—
630C2×C4×D4—436no—
631C2×C4×D4—436no—
632C2×#117—433no—
633C22×C42—433no—
634C43#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—8616no—
636C2×#41—431no—
637C2×#41—434no—
638C2×#41—436no—
639C2×#41—436no—
640C2×#41—4312no—
641C2×#41—4312no—
642C2×#41—4312no—
643C2×#41—433no—
644C2×#41—433no—
645C2×#41—436no—
646C2×#41—868no—
647C2×#41—17224no—
648C2×#41C22×D4311yescharacteristic
649C22×Q8—431no—
650C22×Q8C22×D4316yes—
651C22×D4—433no—
652C22×D4—4312no—
653C22×D4—436no—
654C22×D4—436no—
655C22×D4—4312no—
656C22×D4—436no—
657C23×C4—433no—
658C23×C4—433no—
659C23×C4—4312no—
660C23×C4—433no—
661C4⋊Q8—431no—
662C4⋊Q8C22×D4313yes—
663C4⋊Q8C22×D4316yes—
664C4⋊Q8C22×D4316yes—
665C4⋊Q8C22×D4316yes—
666C4⋊Q8C22×D4311yescharacteristic
667C4⋊Q8C22×D43112yes—
668#127—433no—
669#127—436no—
670#127—436no—
671#127—436no—
672#127—4312no—
673#126—4312no—
674#126—4312no—
675#126—4324no—
676#125—432no—
677#125—436no—
678#125C22×D4316yes—
679#125C22×D43112yes—
680#124—436no—
681#124—4312no—
682#124—4312no—
683#124—4312no—
684#124—436no—
685#124—4324no—
686#124—436no—
687#124—4312no—
688#123—4312no—
689#123—4312no—
690#123—4324no—
691#123—4324no—
692#123—4324no—
693#123—4312no—
694C22⋊Q8—432no—
695C22⋊Q8—436no—
696C22⋊Q8—4324no—
697C22⋊Q8—432no—
698C22⋊Q8—436no—
699C22⋊Q8—4312no—
700C22⋊Q8C22×D4316yes—
701C22⋊Q8C22×D4316yes—
702C22⋊Q8C22×D43124yes—
703#121—436no—
704#121—436no—
705#121—4324no—
706#121—436no—
707#121—436no—
708#121—4312no—
709#121—4312no—
710#121—4312no—
711#121—4312no—
712#121—4312no—
713#121—4312no—
714#121—436no—
715#121—436no—
716#121—4324no—
717#121—4312no—
718#121—4312no—
719#121—4312no—
720#121—4324no—
721#120—4312no—
722#120—4324no—
723#120—4324no—
724C4×Q8—431no—
725C4×Q8—431no—
726C4×Q8—432no—
727C4×Q8—436no—
728C4×Q8—433no—
729C4×Q8—433no—
730C4×Q8—432no—
731C4×Q8—436no—
732C4×Q8—433no—
733C4×Q8—433no—
734C4×Q8C22×D4311yescharacteristic
735C4×Q8C22×D4311yescharacteristic
736C4×Q8C22×D4314yes—
737C4×Q8C22×D4316yes—
738C4×Q8C22×D4316yes—
739C4×D4—433no—
740C4×D4—433no—
741C4×D4—436no—
742C4×D4—436no—
743C4×D4—4324no—
744C4×D4—4312no—
745C4×D4—436no—
746C4×D4—436no—
747C4×D4—433no—
748C4×D4—433no—
749C4×D4—4312no—
750C4×D4—4312no—
751C4×D4—4312no—
752C4×D4—4312no—
753C4×D4—4312no—
754C4×D4—436no—
755C4×D4—4312no—
756C4×D4—4312no—
757C4×D4—436no—
758C4×D4—4312no—
759C4×D4—436no—
760C4×D4—436no—
761C4×D4—4312no—
762C4×D4—433no—
763C4×D4—433no—
764C4×D4—4312no—
765C4×D4—4312no—
766C4×D4—4312no—
767C4×D4—4312no—
768C4×D4—436no—
769C4×D4—436no—
770C4×D4C22×D4313yes—
771C4×D4C22×D4313yes—
772C4×D4C22×D43112yes—
773#117—433no—
774#117—433no—
775#117—433no—
776#117—432no—
777#117—4312no—
778#117—4312no—
779#117—436no—
780#117—4312no—
781#117—436no—
782#117—436no—
783#117—4312no—
784#117C22×D4313yes—
785#117C22×D4316yes—
786C2×C4⋊C4—433no—
787C2×C4⋊C4—433no—
788C2×C4⋊C4—4312no—
789C2×C4⋊C4C22×D4316yes—
790C2×C4⋊C4C22×D4316yes—
791C2×C22⋊C4—4312no—
792C2×C22⋊C4—4312no—
793C2×C22⋊C4—436no—
794C2×C22⋊C4—4324no—
795C2×C42—433no—
796C2×C42—433no—
797C2×C42—433no—
798C2×C42—433no—
799C2×C42—433no—
800C2×C42—433no—
801C2×C42—4312no—
802C2×C42—433no—
803C2×C42—433no—
804C2×C42—433no—
805C2×C42—433no—
806C2×C42—431no—
807C2×C42C22×D4313yes—
808C24—433no—
809C24—4312no—
810#41—8624no—
811#41—864no—
812#41—8616no—
813#41—8612no—
814#41—8612no—
815#41—8624no—
816#41—17224no—
817#41—17224no—
818#41—17224no—
819#41—17212no—
820#41#1062190218yescomplemented
821C2×Q8—412no—
822C2×Q8—433no—
823C2×Q8—432no—
824C2×Q8—864no—
825C2×Q8C23×D4312yes—
826C2×Q8C23×D4316yes—
827C2×Q8C23×D43112yes—
828C2×Q8C23×D4311yescharacteristic
829C2×D4—436no—
830C2×D4—4312no—
831C2×D4—436no—
832C2×D4—4312no—
833C2×D4—436no—
834C2×D4—433no—
835C2×D4—4312no—
836C2×D4—436no—
837C2×D4—4312no—
838C2×D4—4312no—
839C2×D4—4312no—
840C2×D4—4324no—
841C2×D4—8612no—
842C2×D4—8648no—
843C2×D4—8624no—
844C2×D4—17212no—
845C2×D4—17212no—
846C2×D4—17224no—
847C2×D4C23×D4313yes—
848C22×C4—431no—
849C22×C4—433no—
850C22×C4—433no—
851C22×C4—433no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—433no—
855C22×C4—433no—
856C22×C4—433no—
857C22×C4—433no—
858C22×C4—433no—
859C22×C4—433no—
860C22×C4—433no—
861C22×C4—4312no—
862C22×C4—4312no—
863C22×C4—433no—
864C22×C4—433no—
865C22×C4—4312no—
866C22×C4—4324no—
867C22×C4—8612no—
868C22×C4—8612no—
869C22×C4—1726no—
870C22×C4—17224no—
871C22×C4C23×D4313yes—
872C22×C4C23×D4313yes—
873C22×C4C23×D43112yes—
874C22×C4C23×D4313yes—
875C4⋊C4—433no—
876C4⋊C4—4312no—
877C4⋊C4—433no—
878C4⋊C4—436no—
879C4⋊C4—436no—
880C4⋊C4—432no—
881C4⋊C4—434no—
882C4⋊C4—434no—
883C4⋊C4—432no—
884C4⋊C4—4312no—
885C4⋊C4C23×D43112yes—
886C4⋊C4C23×D4313yes—
887C4⋊C4C23×D4313yes—
888C4⋊C4C23×D4316yes—
889C4⋊C4C23×D4316yes—
890C4⋊C4C23×D43112yes—
891C4⋊C4C23×D4312yes—
892C4⋊C4C23×D43112yes—
893C4⋊C4C23×D43112yes—
894C4⋊C4C23×D4312yes—
895C22⋊C4—436no—
896C22⋊C4—4312no—
897C22⋊C4—4312no—
898C22⋊C4—4324no—
899C22⋊C4—4312no—
900C22⋊C4—436no—
901C22⋊C4—436no—
902C22⋊C4—4324no—
903C22⋊C4—434no—
904C22⋊C4—4312no—
905C22⋊C4—4312no—
906C22⋊C4—4312no—
907C22⋊C4—4312no—
908C22⋊C4C23×D43112yes—
909C22⋊C4C23×D4316yes—
910C42—431no—
911C42—433no—
912C42—431no—
913C42—431no—
914C42—433no—
915C42—433no—
916C42—434no—
917C42—433no—
918C42—433no—
919C42—433no—
920C42—433no—
921C42—433no—
922C42—433no—
923C42—4312no—
924C42C23×D4311yescharacteristic
925C42C23×D4313yes—
926C42C23×D4313yes—
927C42C23×D4313yes—
928C42C23×D43112yes—
929C23—431no—
930C23—4312no—
931C23—433no—
932C23—866no—
933C23—8624no—
934C23—866no—
935C23—17212no—
936C23—17212no—
937C23—1723no—
938C23C24×D4313yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—866no—
943Q8—864no—
944Q8C2×#1062190214yescomplemented
945D4—8624no—
946D4—8624no—
947D4—8612no—
948D4—8624no—
949D4—8612no—
950D4—866no—
951D4—8612no—
952D4—8612no—
953D4—17212no—
954D4—17224no—
955D4—17212no—
956D4—17212no—
957D4C2×#10621902112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—431no—
962C2×C4—434no—
963C2×C4—431no—
964C2×C4—431no—
965C2×C4—433no—
966C2×C4—433no—
967C2×C4—434no—
968C2×C4—433no—
969C2×C4—866no—
970C2×C4—8624no—
971C2×C4—866no—
972C2×C4—866no—
973C2×C4—866no—
974C2×C4—862no—
975C2×C4—866no—
976C2×C4—866no—
977C2×C4—866no—
978C2×C4—8624no—
979C2×C4—866no—
980C2×C4—862no—
981C2×C4—866no—
982C2×C4—17224no—
983C2×C4—1723no—
984C2×C4—1723no—
985C2×C4—17212no—
986C2×C4—1723no—
987C2×C4C2×#10621902112yescomplemented
988C2×C4C24×D4313yes—
989C2×C4C24×D4313yes—
990C2×C4C24×D4314yes—
991C2×C4C24×D43112yes—
992C2×C4C24×D4311yescharacteristic
993C2×C4C24×D4313yes—
994C2×C4C24×D4311yescharacteristic
995C2×C4C24×D4311yescharacteristic
996C22—23no—
997C22—23no—
998C22—432no—
999C22—861no—
1000C22—861no—
1001C22—863no—
1002C22—8612no—
1003C22—863no—
1004C22—8612no—
1005C22—863no—
1006C22—8612no—
1007C22—34424no—
1008C22—17212no—
1009C22C22×#1062190216yes—
1010C22C25×D4311yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—432no—
1016C4—861no—
1017C4—864no—
1018C4—863no—
1019C4—863no—
1020C4—861no—
1021C4—863no—
1022C4C22×#1062190216yes—
1023C4C22×#1062190212yes—
1024C4H(5,𝔽2)×D4312yes—
1025C4#1458373612yes—
1026C2—26no—
1027C2—862no—
1028C2—17212no—
1029C2—1723no—
1030C2C23×#1062190211yescharacteristic
1031C2C2×H(5,𝔽2)×D4311yescharacteristic
1032C2C2×#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3503C2
hypercenter#3503D43
hypocenterC43#62800
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #19148681C2semidirect
2. #19148628C2semidirect
3. #19148602C2semidirect
4. #19148557C2semidirect
5. #19148508C2semidirect
6. #19148472C2semidirect
7. #19148373C2semidirect
8. #19148333C2semidirect
9. #19148265C2semidirect
10. #19148222C2semidirect
11. #19148206C2semidirect
12. #19148195C2semidirect
13. D4×#10621902C2semidirect
14. #19148018C2semidirect
15. #19147892C2semidirect
16. C2×#14583450C2semidirect
17. #19147801C2semidirect
18. C4×#41×D43C2semidirect
19. C43×#3503C2semidirect
21. C22×#10621902C22semidirect
23. #14583634C22semidirect
24. #14583634C22semidirect
25. #14583623C22semidirect
26. #14583615C22semidirect
27. #14583615C22semidirect
28. #14583610C22semidirect
29. #14583602C22semidirect
30. #14583602C22semidirect
31. #14583597C22semidirect
32. #14583576C22semidirect
33. #14583571C22semidirect
34. #14583571C22semidirect
35. #14583571C22semidirect
36. #14583571C22semidirect
37. #14583571C22semidirect
38. #14583561C22semidirect
39. #14583560C22semidirect
40. #14583552C22semidirect
41. #14583552C22semidirect
42. #14583544C22semidirect
43. #14583540C22semidirect
44. #14583540C22semidirect
45. #14583540C22semidirect
46. D4×D172C22semidirect
47. D4×D172C22semidirect
48. D4×D172C22semidirect
49. #14583523C22semidirect
50. #14583523C22semidirect
51. #14583505C22semidirect
52. #14583505C22semidirect
53. #14583489C22semidirect
54. #14583480C22semidirect
55. #14583468C22semidirect
56. #14583468C22semidirect
57. #14583454C22semidirect
58. #14583454C22semidirect
59. #14583450C22semidirect
60. #14583450C22semidirect
61. #14583450C22semidirect
62. #14583450C22semidirect
63. #14583450C22semidirect
64. #14583450C22semidirect
65. #14583450C22semidirect
66. #14583450C22semidirect
67. #14583450C22semidirect
68. #14583450C22semidirect
69. #14583449C22semidirect
70. C2×#13063322C22semidirect
71. #14583436C22semidirect
72. #14583436C22semidirect
73. #14583435C22semidirect
74. #14583435C22semidirect
75. #14583434C22semidirect
76. #14583434C22semidirect
77. #14583434C22semidirect
78. C2×#13063314C22semidirect
79. #14583412C22semidirect
80. #14583412C22semidirect
81. #14583412C22semidirect
82. #14583411C22semidirect
83. C2×#13063300C22semidirect
84. C2×#13063300C22semidirect
85. #14583381C22semidirect
86. #14583380C22semidirect
87. #14583373C22semidirect
88. #14583371C22semidirect
90. C4×#10621902C22semidirect
91. C4×#10621902C22semidirect
92. C4×#10621902C22semidirect
93. C4×#10621902C22semidirect
94. C4×#10621902C22semidirect
95. C4×#10621898C22semidirect
96. #14583367C22semidirect
97. #14583367C22semidirect
98. C4×#10621900C22semidirect
99. C4×#10621900C22semidirect
100. C4×Q8×D43C22semidirect
101. C4×Q8×D43C22semidirect
102. C2×#13063287C22semidirect
103. C2×#13063287C22semidirect
104. C4×D4×D43C22semidirect
105. C4×D4×D43C22semidirect
106. C4×D4×D43C22semidirect
107. #117×D43C22semidirect
108. C2×C42×D43C22semidirect
109. Q82×C43C22semidirect
110. C43×#557C22semidirect
111. C43×#554C22semidirect
112. D4×Q8×C43C22semidirect
113. C43×#544C22semidirect
114. C43×#533C22semidirect
115. C2×C4⋊Q8×C43C22semidirect
293. #41×C43#41semidirect
425. Q8×C43C2×#41semidirect
426. D4×C43C2×#41semidirect
430. C2×C4×C43C2×#41semidirect
476. C4×D43H(5,𝔽2)semidirect
516. #3503D43semidirect
541. Q82C2×D43semidirect
542. #557C2×D43semidirect
547. #554C2×D43semidirect
557. D4×Q8C2×D43semidirect
569. #544C2×D43semidirect
580. #533C2×D43semidirect
592. C2×C4⋊Q8C2×D43semidirect
634. C43#62800semidirect
820. #41#10621902semidirect
944. Q8C2×#10621902semidirect
957. D4C2×#10621902semidirect
987. C2×C4C2×#10621902semidirect

Maximal subgroups

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

subgroupindex
#191486812
#191486282
#191486022
#191485572
#191485082
#191484722
#191483732
#191483332
#191482652
#191482222
#191482062
#191481952
D4×#106219022
#191480182
#191478922
C2×#145834502
#191478012
C4×#41×D432
C43×#35032
#6280043