Finite Group Databasebeta

← #26004991

Subgroups — #26004991

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#19148680C212yesmaximal, complemented
2#19148627C216yesmaximal, complemented
3#19148601C212yesmaximal, complemented
4#19148556C216yesmaximal, complemented
5#19148506C213yesmaximal, complemented
6#19148471C213yesmaximal, complemented
7#19148414C211yesmaximal, characteristic, complemented
8#19148373C211yesmaximal, characteristic, complemented
9#19148330C216yesmaximal, complemented
10#19148264C212yesmaximal, complemented
11#19148221C212yesmaximal, complemented
12#19148205C216yesmaximal, complemented
13#19148190C212yesmaximal, complemented
14D4×#10621898C216yesmaximal, complemented
15#19148011C216yesmaximal, complemented
16#19147891C213yesmaximal, complemented
17C2×#14583449C213yesmaximal, complemented
18C4×#13063371C212yesmaximal, complemented
19C2×C4×#41×C43C211yesmaximal, characteristic, complemented
20C2×#13063371C2212yes—
21C22×#10621898C2216yescomplemented
22#14583634C2216yescomplemented
23#14583634C2216yescomplemented
24Q8×Dic86C2212yescomplemented
25#14583628C2212yescomplemented
26#14583622C2216yescomplemented
27#14583614C2216yescomplemented
28#14583612C22112yescomplemented
29#14583609C2216yescomplemented
30#14583606C2216yescomplemented
31#14583597C22112yescomplemented
32#14583595C22112yescomplemented
33#14583593C22112yescomplemented
34#14583573C22124yescomplemented
35#14583571C2212yescomplemented
36#14583571C2212yescomplemented
37#14583570C2216yescomplemented
38#14583570C2216yescomplemented
39#14583568C2214yescomplemented
40D4×Dic86C2216yescomplemented
41#14583560C2214yescomplemented
42#14583558C22112yescomplemented
43#14583554C2216yescomplemented
44#14583550C22112yescomplemented
45#14583545C22112yescomplemented
46#14583545C22112yescomplemented
47#14583539C22124yescomplemented
48#14583537C22112yescomplemented
49D4×D172C2216yescomplemented
50D4×D172C2216yescomplemented
51D4×C22⋊D43C22112yescomplemented
52#14583527C2216yescomplemented
53#14583521C22112yescomplemented
54#14583520C22112yescomplemented
55#14583504C22112yescomplemented
56#14583500C22112yescomplemented
57#14583482C22124yescomplemented
58#14583477C2216yescomplemented
59#14583468C2216yescomplemented
60#14583463C2216yescomplemented
61#14583456C2211yescharacteristic, complemented
62#14583456C2213yescomplemented
63#14583456C2213yescomplemented
64#14583449C2216yescomplemented
65#14583449C2216yescomplemented
66#14583449C2216yescomplemented
67#14583449C2216yescomplemented
68#14583449C2213yescomplemented
69#14583449C2213yescomplemented
70#14583449C2216yescomplemented
71#14583449C2216yescomplemented
72#14583449C2216yescomplemented
73#14583449C2213yescomplemented
74#14583446C22112yescomplemented
75C2×#13063325C2213yescomplemented
76C2×#13063322C2213yescomplemented
77#14583436C22112yescomplemented
78#14583433C2216yescomplemented
79#14583433C2216yescomplemented
80#14583433C2216yescomplemented
81#14583433C2216yescomplemented
82#14583433C2216yescomplemented
83#14583433C2216yescomplemented
84C2×#13063313C2216yescomplemented
85#14583410C2216yescomplemented
86#14583410C2216yescomplemented
87#14583410C2216yescomplemented
88#14583408C22124yescomplemented
89C2×#13063299C2216yescomplemented
90C2×#13063299C2216yescomplemented
91#14583382C2212yes—
92#14583381C2214yescomplemented
93#14583379C2216yescomplemented
94#14583373C2216yescomplemented
95#14583371C22112yescomplemented
96C4×#10621902C2214yescomplemented
97C4×#10621898C2216yescomplemented
98C4×#10621898C2216yescomplemented
99C4×#10621898C2216yescomplemented
100C2×C4×D172C2216yescomplemented
101C2×C4×D172C2216yescomplemented
102C4×D4×D43C22112yescomplemented
103C22×#41×C43C2211yescharacteristic
104C4×#41×C43C2211yescharacteristic
105C4×#41×C43C2211yescharacteristic
106C4×#41×C43C2213yescomplemented
107C4×#41×C43C2211yescharacteristic, complemented
108C4×#41×C43C2213yescomplemented
109C4×#41×C43C2213yescomplemented
110C4×#41×C43C2211yescharacteristic, complemented
111C4×#41×C43C2213yescomplemented
112C2×C4×Q8×C43C2211yescharacteristic, complemented
113C2×C4×Q8×C43C2211yescharacteristic, complemented
114C2×C4×D4×C43C2213yescomplemented
115C2×C4×D4×C43C2213yescomplemented
116C2×#117×C43C2213yescomplemented
117C22×C42×C43C2213yescomplemented
118#13063371—216no—
119C2×#10621902C2314yes—
120C2×#10621898—424no—
121C2×#10621898C2316yes—
122C2×#10621898C2316yes—
123C2×#10621898C23112yes—
124C2×#10621898C2316yes—
125C2×#10621898C23112yes—
126C2×#10621898C23112yes—
127C22×Dic86C2316yes—
128C22×D172C2316yes—
129C22×D172C2316yes—
130C22×D172C2316yes—
131C22×C22⋊D43C23112yes—
132C2×D4×D43C23112yes—
133C22×C4×D43C23112yes—
134#13063325C2316yes—
135#13063325C2316yes—
136#13063325C2313yes—
137#13063325C2316yes—
138#13063325C2311yescharacteristic
139#13063325C2311yescharacteristic
140#13063324C23112yes—
141#13063322C2316yes—
142#13063322C2316yes—
143#13063322C2313yes—
144#13063322C2316yes—
145#13063321C23112yes—
146#13063320C23124yes—
147#13063319C23112yes—
148#13063319C23112yes—
149#13063317C2316yes—
150#13063317C2312yes—
151#13063317C2316yes—
152#13063316C23112yes—
153#13063314C23112yes—
154#13063313C23112yes—
155#13063313C23112yes—
156#13063313C2316yes—
157#13063313C2316yes—
158#13063313C23112yes—
159#13063313C2316yes—
160#13063311C23124yes—
161#13063310C23124yes—
162#13063310C23124yes—
163#13063308C23112yes—
164#13063308C23112yes—
165#13063308C23112yes—
166#13063307C23124yes—
167#13063304C2316yes—
168#13063304C2316yes—
169#13063304C2316yes—
170#13063304C2312yes—
171#13063304C2312yes—
172#13063304C2316yes—
173#13063303C23124yes—
174#13063302C23124yes—
175#13063301C23112yes—
176#13063300C23112yes—
177#13063300C23112yes—
178#13063299C2316yes—
179#13063299C23112yes—
180#13063299C23112yes—
181#13063299C2316yes—
182#13063299C23112yes—
183#13063299C2316yes—
184#13063299C23112yes—
185#13063299C2316yes—
186#13063299C2316yes—
187#13063299C23112yes—
188#13063299C23112yes—
189#13063299C2316yes—
190#13063298C23124yes—
191#13063298C23124yes—
192#13063297C23124yes—
193#13063296C23112yes—
194#13063295C23124yes—
195#13063294C23112yes—
196#13063293C23124yes—
197Q8×Dic43C2314yes—
198C4×Dic86C2316yes—
199C4×Dic86C2316yes—
200C4×Dic86C2316yes—
201C4×Dic86C2312yes—
202C4×Dic86C2312yes—
203C4×Dic86C2316yes—
204C4×D172C2316yes—
205C4×D172C2316yes—
206C4×D172C23112yes—
207C4×D172C23112yes—
208C4×D172C23112yes—
209C4×D172C2316yes—
210C4×D172C2316yes—
211C4×D172C23112yes—
212C4×D172C23112yes—
213C4×D172C23112yes—
214C4×D172C2316yes—
215C4×D172C2316yes—
216D4×Dic43C23112yes—
217#13063287C23112yes—
218#13063287C23112yes—
219C4×C22⋊D43C23112yes—
220C4×C22⋊D43C23112yes—
221C4×C22⋊D43C23112yes—
222C4×C22⋊D43C23112yes—
223C4×C22⋊D43C23112yes—
224C4×C22⋊D43C23112yes—
225(C22⋊D43)⋊C4C23124yes—
226#13063284C2316yes—
227#13063284C2312yes—
228#13063284C2316yes—
229#13063283C23112yes—
230#13063282C23112yes—
231#13063282C23112yes—
232#13063282C23112yes—
233C2×C4⋊Dic43C2316yes—
234C2×C4⋊Dic43C2316yes—
235C4⋊C4×D43C23112yes—
236C2×(C2×D43)⋊C4C23112yes—
237C2×(C2×D43)⋊C4C23112yes—
238C22⋊C4×D43C23124yes—
239C42×D43C23112yes—
240C2×#41×C43—28no—
241C2×#41×C43C2311yescharacteristic
242C2×#41×C43C2313yes—
243C2×#41×C43C2313yes—
244C2×#41×C43C2311yescharacteristic
245C22×Q8×C43C2311yescharacteristic
246C22×D4×C43C2313yes—
247C23×C4×C43C2313yes—
248C23×C4×C43C2313yes—
249C23×C4×C43C2313yes—
250C4×Q8×C43C2311yescharacteristic
251C4×Q8×C43C2311yescharacteristic
252C4×Q8×C43C2311yescharacteristic
253C4×Q8×C43C2311yescharacteristic
254C4×Q8×C43C2313yes—
255C4×Q8×C43C2313yes—
256C4×Q8×C43C2313yes—
257C4×Q8×C43C2313yes—
258C4×D4×C43C2313yes—
259C4×D4×C43C2316yes—
260C4×D4×C43C2313yes—
261C4×D4×C43C2313yes—
262C4×D4×C43C2313yes—
263C4×D4×C43C2313yes—
264C4×D4×C43C2313yes—
265C4×D4×C43C2316yes—
266C4×D4×C43C2316yes—
267C4×D4×C43C2313yes—
268C4×D4×C43C2316yes—
269C4×D4×C43C2313yes—
270#117×C43C2313yes—
271#117×C43C2313yes—
272#117×C43C2316yes—
273#117×C43C2313yes—
274#117×C43C2313yes—
275#117×C43C2316yes—
276C2×C4⋊C4×C43C2313yes—
277C2×C4⋊C4×C43C2313yes—
278C2×C22⋊C4×C43C2316yes—
279C2×C42×C43C2311yescharacteristic
280C2×C42×C43C2313yes—
281C2×C42×C43C2313yes—
282C2×C42×C43C2313yes—
283C2×C42×C43C2313yes—
284C2×C42×C43C2313yes—
285C2×C42×C43C2313yes—
286C2×C42×C43C2313yes—
287C2×C42×C43C2313yes—
288C2×C42×C43C2313yes—
289C2×C42×C43C2313yes—
290C2×C42×C43C2313yes—
291C24×C43C2413yes—
292C23×D43C24112yes—
293#41×C43—24no—
294#41×C43—212no—
295#41×C43—212no—
296#41×C43#4118yescomplemented
297C2×Q8×C43—24no—
298C2×Q8×C43C2413yes—
299C2×Q8×C43C2411yescharacteristic
300C2×D4×C43—212no—
301C2×D4×C43C2416yes—
302C2×D4×C43C2413yes—
303C2×D4×C43C2413yes—
304C22×C4×C43—212no—
305C22×C4×C43—212no—
306C22×C4×C43—46no—
307C22×C4×C43C2411yescharacteristic
308C22×C4×C43C2411yescharacteristic
309C22×C4×C43C2413yes—
310C22×C4×C43C2413yes—
311C22×C4×C43C2413yes—
312C22×C4×C43C2413yes—
313C22×C4×C43C2413yes—
314C22×C4×C43C2413yes—
315C22×C4×C43C2413yes—
316C22×C4×C43C2413yes—
317C22×C4×C43C2413yes—
318C22×C4×C43C2413yes—
319C22×C4×C43C2413yes—
320C22×C4×C43C2413yes—
321C22×C4×C43C2413yes—
322C22×C4×C43C2413yes—
323C22×C4×C43C2413yes—
324C22×C4×C43C2411yescharacteristic
325C2×C22⋊D43—424no—
326C2×C22⋊D43C24112yes—
327C2×C22⋊D43C24112yes—
328C2×C22⋊D43C24112yes—
329C2×C22⋊D43C24124yes—
330C22×Dic43C24112yes—
331#10621902—216no—
332D4×D43—248no—
333#10621898—224no—
334#10621898—224no—
335#10621898—424no—
336#10621898—412no—
337#10621898—424no—
338#10621898—424no—
339C2×D172—224no—
340C2×D172—412no—
341C2×D172—412no—
342C2×D172C24112yes—
343C2×D172C2416yes—
344C2×D172C2416yes—
345C2×D172C2416yes—
346C2×D172C24112yes—
347C2×D172C24112yes—
348C2×C4×D43—424no—
349C2×C4×D43C24112yes—
350C2×C4×D43C24112yes—
351C2×C4×D43C24112yes—
352C2×C4×D43C24124yes—
353C2×Dic86—412no—
354C2×Dic86C2412yes—
355C2×Dic86C2412yes—
356C2×Dic86C2416yes—
357C2×Dic86C24112yes—
358C4⋊C4×C43C2413yes—
359C4⋊C4×C43C2413yes—
360C4⋊C4×C43C2413yes—
361C4⋊C4×C43C2413yes—
362C4⋊C4×C43C2416yes—
363C4⋊C4×C43C2416yes—
364C22⋊C4×C43C2416yes—
365C22⋊C4×C43C2416yes—
366C22⋊C4×C43C2416yes—
367C22⋊C4×C43C2416yes—
368C42×C43C2411yescharacteristic
369C42×C43C2411yescharacteristic
370C42×C43C2411yescharacteristic
371C42×C43C2411yescharacteristic
372C42×C43C2413yes—
373C42×C43C2413yes—
374C42×C43C2413yes—
375C42×C43C2413yes—
376C42×C43C2413yes—
377C42×C43C2413yes—
378C42×C43C2413yes—
379C42×C43C2413yes—
380C42×C43C2413yes—
381C42×C43C2413yes—
382C42×C43C2413yes—
383C42×C43C2413yes—
384C22⋊Dic43C24112yes—
385C22⋊Dic43C2414yes—
386C22⋊Dic43C24112yes—
387(C2×D43)⋊C4C24112yes—
388(C2×D43)⋊C4C24124yes—
389(C2×D43)⋊C4C24112yes—
390(C2×D43)⋊C4C24112yes—
391(C2×D43)⋊C4C24124yes—
392(C2×D43)⋊C4C24112yes—
393(C2×D43)⋊C4C24112yes—
394(C2×D43)⋊C4C24112yes—
395C4⋊Dic43C24112yes—
396C4⋊Dic43C2416yes—
397C4⋊Dic43C2416yes—
398C4⋊Dic43C24112yes—
399C4⋊Dic43C2412yes—
400C4⋊Dic43C2412yes—
401C4⋊Dic43C2412yes—
402C4⋊Dic43C2412yes—
403Dic43⋊C4C24112yes—
404Dic43⋊C4C2414yes—
405Dic43⋊C4C2414yes—
406Dic43⋊C4C24112yes—
407Dic43⋊C4C24112yes—
408Dic43⋊C4C24112yes—
409C4×Dic43C2414yes—
410C4×Dic43C24112yes—
411C4×Dic43C24112yes—
412C23×C43—26no—
413C23×C43—26no—
414C23×C43—43no—
415C23×C43C2513yes—
416C23×C43C2513yes—
417C23×C43C2511yescharacteristic
418C22×D43—224no—
419C22×D43—412no—
420C22×D43—412no—
421C22×D43C25112yes—
422Q8×C43—26no—
423Q8×C43C2×#4114yescomplemented
424D4×C43—212no—
425D4×C43—26no—
426D4×C43C2×#41112yescomplemented
427C2×C4×C43—26no—
428C2×C4×C43—26no—
429C2×C4×C43—22no—
430C2×C4×C43—26no—
431C2×C4×C43—26no—
432C2×C4×C43—26no—
433C2×C4×C43—26no—
434C2×C4×C43—26no—
435C2×C4×C43—26no—
436C2×C4×C43—26no—
437C2×C4×C43—26no—
438C2×C4×C43—26no—
439C2×C4×C43—22no—
440C2×C4×C43—43no—
441C2×C4×C43—43no—
442C2×C4×C43—43no—
443C2×C4×C43C2×#41112yescomplemented
444C2×C4×C43H(5,𝔽2)14yescomplemented
445C2×C4×C43C2513yes—
446C2×C4×C43C2513yes—
447C2×C4×C43C2511yescharacteristic
448C2×C4×C43C2511yescharacteristic
449C2×C4×C43C2513yes—
450C2×C4×C43C2513yes—
451C2×C4×C43C2513yes—
452C2×C4×C43C2513yes—
453C2×C4×C43C2511yescharacteristic
454C2×C4×C43C2511yescharacteristic
455C2×C4×C43C2511yescharacteristic
456C2×C4×C43C2511yescharacteristic
457C22⋊D43—224no—
458C22⋊D43—224no—
459C22⋊D43—424no—
460C22⋊D43—412no—
461C2×Dic43—412no—
462C2×Dic43C2514yes—
463C2×Dic43C2514yes—
464C2×Dic43C25112yes—
465D172—212no—
466D172—224no—
467D172—212no—
468D172—212no—
469D172—412no—
470D172—412no—
471C4×D43—224no—
472C4×D43—224no—
473C4×D43—424no—
474C4×D43—412no—
475Dic86—24no—
476Dic86—212no—
477Dic86—24no—
478Dic86—412no—
479#62800—431nomaximal, Sylow
480C22×C43—21no—
481C22×C43—23no—
482C22×C43—23no—
483C22×C43—21no—
484C22×C43—23no—
485C22×C43—23no—
486C22×C43—23no—
487C22×C43—412no—
488C22×C43C22×#4116yes—
489C22×C43C2×H(5,𝔽2)12yes—
490C22×C43C2611yescharacteristic
491C2×D43—212no—
492C2×D43—212no—
493C2×D43—212no—
494C2×D43—824no—
495C4×C43—21no—
496C4×C43—23no—
497C4×C43—23no—
498C4×C43—23no—
499C4×C43—23no—
500C4×C43—23no—
501C4×C43—21no—
502C4×C43C22×#4112yes—
503C4×C43C22×#4116yes—
504C4×C43C2×H(5,𝔽2)12yes—
505C4×C43C2×H(5,𝔽2)12yes—
506C4×C43#58512yes—
507Dic43—24no—
508Dic43—212no—
509Dic43—24no—
510#3522—432no—
511#3519—436no—
512#3517—432no—
513#3514—436no—
514#3511—433no—
515#3508—433no—
516#3503—431no—
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×#41D4311yescharacteristic, complemented
529C2×C43—26no—
530C2×C43—22no—
531C2×C43—43no—
532C2×C43C23×#4111yescharacteristic
533C2×C43C22×H(5,𝔽2)11yescharacteristic
534C2×C43C2×#58511yescharacteristic
535D43—412no—
536C2×H(5,𝔽2)—432no—
537C22×#41—436no—
538C22×#41C2×D4311yescharacteristic
539#559—436no—
540#559—436no—
541Q82—432no—
542#557—432no—
543#556—436no—
544#555—436no—
545#555—4312no—
546#554—436no—
547#554—436no—
548#553—4312no—
549#553—4312no—
550#553—4312no—
551#551—4324no—
552#550—434no—
553#550—432no—
554#550—432no—
555#550—436no—
556#550—436no—
557D4×Q8—436no—
558#548—434no—
559#548—4312no—
560#547—436no—
561#547—4312no—
562#546—4312no—
563#546—4312no—
564#546—4312no—
565#546—4324no—
566D42—4312no—
567D42—436no—
568D42—436no—
569#544—436no—
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#533—433no—
581#532—4312no—
582#532—433no—
583#532—436no—
584#532—436no—
585#532—436no—
586#532—436no—
587#532—436no—
588#532—436no—
589#532—436no—
590#532—433no—
591#532—433no—
592C2×C4⋊Q8—433no—
593C2×#127—433no—
594#529—4312no—
595#529—436no—
596#529—436no—
597#529—436no—
598#529—436no—
599#529—436no—
600#529—436no—
601C2×#124—436no—
602#525—436no—
603#525—436no—
604#525—436no—
605#525—4324no—
606C2×#121—436no—
607C2×#121—436no—
608#520—432no—
609#520—434no—
610#520—436no—
611#518—4312no—
612#518—436no—
613C4×#41—434no—
614C4×#41—436no—
615C4×#41—436no—
616C4×#41—436no—
617C4×#41C2×D4311yescharacteristic
618C4×#41C2×D4311yescharacteristic
619C4×#41C2×D4313yescomplemented
620C4×#41C2×D4313yescomplemented
621C4×#41C2×D4311yescharacteristic, complemented
622C4×#41C2×D4313yescomplemented
623C4×#41C2×D4313yescomplemented
624C4×#41C2×D4311yescharacteristic, complemented
625C2×C4×Q8C2×D4311yescharacteristic, complemented
626C2×C4×Q8C2×D4311yescharacteristic, complemented
627C2×C4×D4—4312no—
628C2×C4×D4—436no—
629C2×C4×D4—436no—
630C2×C4×D4C2×D4313yescomplemented
631C2×C4×D4C2×D4313yescomplemented
632C2×#117C2×D4313yescomplemented
633C22×C42C2×D4313yescomplemented
634C43#6280011yescharacteristic, complemented, Sylow
635H(5,𝔽2)—8616no—
636C2×#41—28no—
637C2×#41—434no—
638C2×#41—436no—
639C2×#41—436no—
640C2×#41—436no—
641C2×#41—4312no—
642C2×#41—4312no—
643C2×#41—4312no—
644C2×#41—17224no—
645C2×#41C22×D4313yes—
646C2×#41C22×D4313yes—
647C2×#41C22×D4311yescharacteristic
648C2×#41C22×D4311yescharacteristic
649C22×Q8—436no—
650C22×Q8C22×D4311yescharacteristic
651C22×D4—4312no—
652C22×D4—4312no—
653C22×D4—436no—
654C22×D4—436no—
655C22×D4—436no—
656C22×D4C22×D4313yes—
657C23×C4—4312no—
658C23×C4C22×D4313yes—
659C23×C4C22×D4313yes—
660C23×C4C22×D4313yes—
661C4⋊Q8—4312no—
662C4⋊Q8—433no—
663C4⋊Q8—436no—
664C4⋊Q8—436no—
665C4⋊Q8—436no—
666C4⋊Q8—431no—
667C4⋊Q8—431no—
668#127—4312no—
669#127—433no—
670#127—436no—
671#127—436no—
672#127—436no—
673#126—4324no—
674#126—4312no—
675#126—4312no—
676#125—4312no—
677#125—432no—
678#125—436no—
679#125—436no—
680#124—4312no—
681#124—4324no—
682#124—436no—
683#124—4312no—
684#124—4312no—
685#124—4312no—
686#124—436no—
687#124—436no—
688#123—4312no—
689#123—4312no—
690#123—4312no—
691#123—4324no—
692#123—4324no—
693#123—4324no—
694C22⋊Q8—4312no—
695C22⋊Q8—432no—
696C22⋊Q8—432no—
697C22⋊Q8—436no—
698C22⋊Q8—436no—
699C22⋊Q8—436no—
700C22⋊Q8—436no—
701C22⋊Q8—4324no—
702C22⋊Q8—4324no—
703#121—4324no—
704#121—4312no—
705#121—436no—
706#121—436no—
707#121—4312no—
708#121—4312no—
709#121—4312no—
710#121—4312no—
711#121—4312no—
712#121—4312no—
713#121—436no—
714#121—436no—
715#121—436no—
716#121—436no—
717#121—4312no—
718#121—4312no—
719#121—4324no—
720#121—4324no—
721#120—4312no—
722#120—4324no—
723#120—4324no—
724C4×Q8—434no—
725C4×Q8—432no—
726C4×Q8—432no—
727C4×Q8—436no—
728C4×Q8—436no—
729C4×Q8—436no—
730C4×Q8—436no—
731C4×Q8C22×D4311yescharacteristic
732C4×Q8C22×D4311yescharacteristic
733C4×Q8C22×D4311yescharacteristic
734C4×Q8C22×D4311yescharacteristic
735C4×Q8C22×D4313yes—
736C4×Q8C22×D4313yes—
737C4×Q8C22×D4313yes—
738C4×Q8C22×D4313yes—
739C4×D4—4312no—
740C4×D4—4312no—
741C4×D4—4312no—
742C4×D4—4312no—
743C4×D4—4312no—
744C4×D4—4312no—
745C4×D4—4312no—
746C4×D4—4312no—
747C4×D4—4312no—
748C4×D4—4324no—
749C4×D4—4312no—
750C4×D4—436no—
751C4×D4—436no—
752C4×D4—4312no—
753C4×D4—4312no—
754C4×D4—4312no—
755C4×D4—4312no—
756C4×D4—4312no—
757C4×D4—436no—
758C4×D4—436no—
759C4×D4—436no—
760C4×D4—436no—
761C4×D4C22×D4313yes—
762C4×D4C22×D4313yes—
763C4×D4C22×D4313yes—
764C4×D4C22×D4313yes—
765C4×D4C22×D4316yes—
766C4×D4C22×D4313yes—
767C4×D4C22×D4316yes—
768C4×D4C22×D4313yes—
769C4×D4C22×D4316yes—
770C4×D4C22×D4316yes—
771C4×D4C22×D4313yes—
772C4×D4C22×D4313yes—
773#117—432no—
774#117—436no—
775#117—436no—
776#117—4312no—
777#117—4312no—
778#117—4312no—
779#117—4312no—
780#117C22×D4313yes—
781#117C22×D4313yes—
782#117C22×D4316yes—
783#117C22×D4316yes—
784#117C22×D4313yes—
785#117C22×D4313yes—
786C2×C4⋊C4—436no—
787C2×C4⋊C4—436no—
788C2×C4⋊C4—4312no—
789C2×C4⋊C4C22×D4313yes—
790C2×C4⋊C4C22×D4313yes—
791C2×C22⋊C4—4312no—
792C2×C22⋊C4—4312no—
793C2×C22⋊C4—4324no—
794C2×C22⋊C4C22×D4316yes—
795C2×C42—4312no—
796C2×C42C22×D4313yes—
797C2×C42C22×D4313yes—
798C2×C42C22×D4313yes—
799C2×C42C22×D4313yes—
800C2×C42C22×D4313yes—
801C2×C42C22×D4313yes—
802C2×C42C22×D4313yes—
803C2×C42C22×D4313yes—
804C2×C42C22×D4313yes—
805C2×C42C22×D4313yes—
806C2×C42C22×D4313yes—
807C2×C42C22×D4311yescharacteristic
808C24—4312no—
809C24C23×D4313yes—
810#41—24no—
811#41—212no—
812#41—212no—
813#41—8616no—
814#41—8624no—
815#41—8624no—
816#41—17224no—
817#41—17224no—
818#41—17224no—
819#41—17212no—
820#41#1062189818yescomplemented
821C2×Q8—24no—
822C2×Q8—432no—
823C2×Q8—432no—
824C2×Q8—436no—
825C2×Q8—4312no—
826C2×Q8—17212no—
827C2×Q8C23×D4313yes—
828C2×Q8C23×D4311yescharacteristic
829C2×D4—212no—
830C2×D4—4312no—
831C2×D4—4312no—
832C2×D4—4312no—
833C2×D4—4324no—
834C2×D4—4312no—
835C2×D4—436no—
836C2×D4—436no—
837C2×D4—436no—
838C2×D4—4312no—
839C2×D4—4312no—
840C2×D4—8648no—
841C2×D4—8624no—
842C2×D4—17212no—
843C2×D4—17212no—
844C2×D4—17224no—
845C2×D4C23×D4316yes—
846C2×D4C23×D4313yes—
847C2×D4C23×D4313yes—
848C22×C4—212no—
849C22×C4—212no—
850C22×C4—46no—
851C22×C4—4312no—
852C22×C4—4312no—
853C22×C4—4312no—
854C22×C4—4312no—
855C22×C4—4324no—
856C22×C4—17224no—
857C22×C4C23×D4311yescharacteristic
858C22×C4C23×D4311yescharacteristic
859C22×C4C23×D4313yes—
860C22×C4C23×D4313yes—
861C22×C4C23×D4313yes—
862C22×C4C23×D4313yes—
863C22×C4C23×D4313yes—
864C22×C4C23×D4313yes—
865C22×C4C23×D4313yes—
866C22×C4C23×D4313yes—
867C22×C4C23×D4313yes—
868C22×C4C23×D4313yes—
869C22×C4C23×D4313yes—
870C22×C4C23×D4313yes—
871C22×C4C23×D4313yes—
872C22×C4C23×D4313yes—
873C22×C4C23×D4313yes—
874C22×C4C23×D4311yescharacteristic
875C4⋊C4—4312no—
876C4⋊C4—436no—
877C4⋊C4—436no—
878C4⋊C4—4312no—
879C4⋊C4—4312no—
880C4⋊C4—432no—
881C4⋊C4—432no—
882C4⋊C4—434no—
883C4⋊C4—434no—
884C4⋊C4—432no—
885C4⋊C4—432no—
886C4⋊C4—4312no—
887C4⋊C4—4312no—
888C4⋊C4—4312no—
889C4⋊C4C23×D4313yes—
890C4⋊C4C23×D4313yes—
891C4⋊C4C23×D4313yes—
892C4⋊C4C23×D4313yes—
893C4⋊C4C23×D4316yes—
894C4⋊C4C23×D4316yes—
895C22⋊C4—4312no—
896C22⋊C4—434no—
897C22⋊C4—4312no—
898C22⋊C4—4312no—
899C22⋊C4—4324no—
900C22⋊C4—4312no—
901C22⋊C4—4312no—
902C22⋊C4—4324no—
903C22⋊C4—4312no—
904C22⋊C4—4312no—
905C22⋊C4—4312no—
906C22⋊C4C23×D4316yes—
907C22⋊C4C23×D4316yes—
908C22⋊C4C23×D4316yes—
909C22⋊C4C23×D4316yes—
910C42—4312no—
911C42—4312no—
912C42—434no—
913C42C23×D4311yescharacteristic
914C42C23×D4311yescharacteristic
915C42C23×D4313yes—
916C42C23×D4313yes—
917C42C23×D4313yes—
918C42C23×D4313yes—
919C42C23×D4313yes—
920C42C23×D4313yes—
921C42C23×D4313yes—
922C42C23×D4313yes—
923C42C23×D4313yes—
924C42C23×D4313yes—
925C42C23×D4313yes—
926C42C23×D4311yescharacteristic
927C42C23×D4311yescharacteristic
928C42C23×D4313yes—
929C23—26no—
930C23—26no—
931C23—43no—
932C23—4312no—
933C23—8624no—
934C23—17212no—
935C23—17212no—
936C23C24×D4313yes—
937C23C24×D4313yes—
938C23C24×D4311yescharacteristic
939Q8—26no—
940Q8—864no—
941Q8—8612no—
942Q8—864no—
943Q8—17212no—
944Q8C2×#1062189814yescomplemented
945D4—212no—
946D4—26no—
947D4—8624no—
948D4—8624no—
949D4—8612no—
950D4—8624no—
951D4—8612no—
952D4—8612no—
953D4—17212no—
954D4—17212no—
955D4—17224no—
956D4—17212no—
957D4C2×#10621898112yescomplemented
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—434no—
975C2×C4—434no—
976C2×C4—4312no—
977C2×C4—8624no—
978C2×C4—8624no—
979C2×C4—17224no—
980C2×C4—17212no—
981C2×C4—17212no—
982C2×C4C2×#10621898112yescomplemented
983C2×C4#1306337114yescomplemented
984C2×C4C24×D4313yes—
985C2×C4C24×D4311yescharacteristic
986C2×C4C24×D4311yescharacteristic
987C2×C4C24×D4313yes—
988C2×C4C24×D4313yes—
989C2×C4C24×D4313yes—
990C2×C4C24×D4313yes—
991C2×C4C24×D4313yes—
992C2×C4C24×D4311yescharacteristic
993C2×C4C24×D4311yescharacteristic
994C2×C4C24×D4311yescharacteristic
995C2×C4C24×D4311yescharacteristic
996C22—21no—
997C22—23no—
998C22—21no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—23no—
1003C22—412no—
1004C22—8612no—
1005C22—8612no—
1006C22—8612no—
1007C22—34424no—
1008C22C22×#1062189816yes—
1009C22C2×#1306337112yes—
1010C22C25×D4311yescharacteristic
1011C4—21no—
1012C4—23no—
1013C4—23no—
1014C4—23no—
1015C4—21no—
1016C4—23no—
1017C4—23no—
1018C4—864no—
1019C4—8612no—
1020C4—864no—
1021C4C22×#1062189812yes—
1022C4C22×#1062189816yes—
1023C4C2×#1306337112yes—
1024C4C2×#1306337112yes—
1025C4#1458373512yes—
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—17212no—
1030C2C23×#1062189811yescharacteristic
1031C2C22×#1306337111yescharacteristic
1032C2C2×#1458373511yescharacteristic
subgroupG/H
centerC2×C4C24×D43
commutator, socle, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C4×#41×C43C2
hypercenterC2×C4×#41D43
hypocenterC43#62800
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #19148680C2semidirect
2. #19148627C2semidirect
3. #19148601C2semidirect
4. #19148556C2semidirect
5. #19148506C2semidirect
6. #19148471C2semidirect
7. #19148414C2semidirect
8. #19148373C2semidirect
9. #19148330C2semidirect
10. #19148264C2semidirect
11. #19148221C2semidirect
12. #19148205C2semidirect
13. #19148190C2semidirect
14. D4×#10621898C2semidirect
15. #19148011C2semidirect
16. #19147891C2semidirect
17. C2×#14583449C2semidirect
18. C4×#13063371C2semidirect
19. C2×C4×#41×C43C2semidirect
21. C22×#10621898C22semidirect
22. #14583634C22semidirect
23. #14583634C22semidirect
24. Q8×Dic86C22semidirect
25. #14583628C22semidirect
26. #14583622C22semidirect
27. #14583614C22semidirect
28. #14583612C22semidirect
29. #14583609C22semidirect
30. #14583606C22semidirect
31. #14583597C22semidirect
32. #14583595C22semidirect
33. #14583593C22semidirect
34. #14583573C22semidirect
35. #14583571C22semidirect
36. #14583571C22semidirect
37. #14583570C22semidirect
38. #14583570C22semidirect
39. #14583568C22semidirect
40. D4×Dic86C22semidirect
41. #14583560C22semidirect
42. #14583558C22semidirect
43. #14583554C22semidirect
44. #14583550C22semidirect
45. #14583545C22semidirect
46. #14583545C22semidirect
47. #14583539C22semidirect
48. #14583537C22semidirect
49. D4×D172C22semidirect
50. D4×D172C22semidirect
51. D4×C22⋊D43C22semidirect
52. #14583527C22semidirect
53. #14583521C22semidirect
54. #14583520C22semidirect
55. #14583504C22semidirect
56. #14583500C22semidirect
57. #14583482C22semidirect
58. #14583477C22semidirect
59. #14583468C22semidirect
60. #14583463C22semidirect
61. #14583456C22semidirect
62. #14583456C22semidirect
63. #14583456C22semidirect
64. #14583449C22semidirect
65. #14583449C22semidirect
66. #14583449C22semidirect
67. #14583449C22semidirect
68. #14583449C22semidirect
69. #14583449C22semidirect
70. #14583449C22semidirect
71. #14583449C22semidirect
72. #14583449C22semidirect
73. #14583449C22semidirect
74. #14583446C22semidirect
75. C2×#13063325C22semidirect
76. C2×#13063322C22semidirect
77. #14583436C22semidirect
78. #14583433C22semidirect
79. #14583433C22semidirect
80. #14583433C22semidirect
81. #14583433C22semidirect
82. #14583433C22semidirect
83. #14583433C22semidirect
84. C2×#13063313C22semidirect
85. #14583410C22semidirect
86. #14583410C22semidirect
87. #14583410C22semidirect
88. #14583408C22semidirect
89. C2×#13063299C22semidirect
90. C2×#13063299C22semidirect
92. #14583381C22semidirect
93. #14583379C22semidirect
94. #14583373C22semidirect
95. #14583371C22semidirect
96. C4×#10621902C22semidirect
97. C4×#10621898C22semidirect
98. C4×#10621898C22semidirect
99. C4×#10621898C22semidirect
100. C2×C4×D172C22semidirect
101. C2×C4×D172C22semidirect
102. C4×D4×D43C22semidirect
106. C4×#41×C43C22semidirect
107. C4×#41×C43C22semidirect
108. C4×#41×C43C22semidirect
109. C4×#41×C43C22semidirect
110. C4×#41×C43C22semidirect
111. C4×#41×C43C22semidirect
112. C2×C4×Q8×C43C22semidirect
113. C2×C4×Q8×C43C22semidirect
114. C2×C4×D4×C43C22semidirect
115. C2×C4×D4×C43C22semidirect
116. C2×#117×C43C22semidirect
117. C22×C42×C43C22semidirect
296. #41×C43#41semidirect
423. Q8×C43C2×#41semidirect
426. D4×C43C2×#41semidirect
443. C2×C4×C43C2×#41semidirect
444. C2×C4×C43H(5,𝔽2)semidirect
528. C2×C4×#41D43semidirect
619. C4×#41C2×D43semidirect
620. C4×#41C2×D43semidirect
621. C4×#41C2×D43semidirect
622. C4×#41C2×D43semidirect
623. C4×#41C2×D43semidirect
624. C4×#41C2×D43semidirect
625. C2×C4×Q8C2×D43semidirect
626. C2×C4×Q8C2×D43semidirect
630. C2×C4×D4C2×D43semidirect
631. C2×C4×D4C2×D43semidirect
632. C2×#117C2×D43semidirect
633. C22×C42C2×D43semidirect
634. C43#62800semidirect
820. #41#10621898semidirect
944. Q8C2×#10621898semidirect
957. D4C2×#10621898semidirect
982. C2×C4C2×#10621898semidirect
983. C2×C4#13063371semidirect

Maximal subgroups

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

subgroupindex
#191486802
#191486272
#191486012
#191485562
#191485062
#191484712
#191484142
#191483732
#191483302
#191482642
#191482212
#191482052
#191481902
D4×#106218982
#191480112
#191478912
C2×#145834492
C4×#130633712
C2×C4×#41×C432
#6280043