Finite Group Databasebeta

← #25096734

Subgroups — #25096734

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147794C211yesmaximal, characteristic
2#19143231C211yesmaximal, characteristic, complemented
3#19137090C211yesmaximal, characteristic, complemented
4#19134693C212yesmaximal, complemented
5#19134614C212yesmaximal, complemented
6#19134613C212yesmaximal, complemented
7#19134537C212yesmaximal
8#19134406C211yesmaximal, characteristic, complemented
9C4×#13063251C211yesmaximal, characteristic, complemented
10C4×#13063252C211yesmaximal, characteristic, complemented
11C43×#1759C211yesmaximal, characteristic, complemented
12C2×#41×D43C2211yescharacteristic
13#14583381C412yescomplemented
14#14583378—22no—
15#14583378C412yescomplemented
16#14583375C412yescomplemented
17#14583371—22no—
18#14583371C412yescomplemented
19#41×Dic43C2211yescharacteristic
20C4×#10621898—21no—
21C4×#10621898C2211yescharacteristic
22#14583367—21no—
23#14583367C2211yescharacteristic
24C2×#13063282—21no—
25C2×#13063282C2211yescharacteristic
26#117×D43—21no—
27#117×D43C2211yescharacteristic
28#14582961—21no—
29#14582961—21no—
30#14582958—21no—
31#14582958—21no—
32#14582922C2212yescomplemented
33C2×#13063253C2212yes—
34C2×#13063252C2212yes—
35C2×#13063251C2212yes—
36#14582862C2212yes—
37C4×#10621877C2211yescharacteristic, complemented
38#14582788—22no—
39#14582781—22no—
40C4×Dic43⋊C4C2212yescomplemented
41C4×(C2×D43)⋊C4C2212yes—
42C42×Dic43C2211yescharacteristic, complemented
43#14582660C2212yescomplemented
44#14582659C2212yescomplemented
45#14582658C2212yescomplemented
46C4×#41×C43C2211yescharacteristic
47C2×#104×C43C2212yes—
48C4×M16×C43C2211yescharacteristic, complemented
49C43×#376C2211yescharacteristic, complemented
50C43×#339C2212yescomplemented
51C2×#10621902C2×C411yescharacteristic
52C2×#10621898—21no—
53C2×#10621898C2311yescharacteristic
54C2×#10621900—21no—
55C2×#10621900C2×C411yescharacteristic
56#41×D43—24no—
57#41×D43—24no—
58C2×Q8×D43C2×C411yescharacteristic
59C2×D4×D43—21no—
60C2×D4×D43C2×C411yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C2×#10621877C2312yes—
64Q8×Dic43C2×C412yes—
65C4×Dic86—22no—
66C4×Dic86C2×C412yes—
67#13063290—22no—
68#13063290C2×C412yes—
69C4×D172—22no—
70C4×D172C2×C412yes—
71D4×Dic43—22no—
72D4×Dic43C2×C412yes—
73#13063287—22no—
74#13063287C2×C412yes—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78(C22⋊D43)⋊C4—22no—
79(C22⋊D43)⋊C4—22no—
80(C22⋊D43)⋊C4—22no—
81#13063284—21no—
82#13063284C2311yescharacteristic
83#13063283—22no—
84#13063283C2×C412yes—
85#13063282—21no—
86#13063282—21no—
87#13063282—22no—
88#13063282—22no—
89#13063282—21no—
90#13063282C2×C412yes—
91#13063282C2×C412yes—
92#13063282D411yescharacteristic
93#13063282D411yescharacteristic
94#13063282D411yescharacteristic
95#13063282D411yescharacteristic
96#13063281—21no—
97#13063281—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4D412yes—
101C4⋊C4×D43—22no—
102C4⋊C4×D43C2×C412yes—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4D412yes—
106C22⋊C4×D43—21no—
107C22⋊C4×D43—22no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43C2312yes—
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—21no—
113C42×D43—21no—
114C42×D43—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117#13063253—24no—
118#13063252—24no—
119#13063251—24no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C2×#41×C43C2311yescharacteristic
127C2×M16×C43C2312yes—
128C4×Q8×C43C2×C412yes—
129C4×D4×C43—22no—
130C4×D4×C43C2×C412yes—
131#117×C43—21no—
132#117×C43C2311yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2312yes—
135C2×C42×C43C2311yescharacteristic
136#104×C43—24no—
137#97×C43—21no—
138C4×C8×C43—21no—
139#95×C43—22no—
140C23×D43—21no—
141C23×D43C2×D411yescharacteristic
142#41×C43—22no—
143#41×C43#4114yes—
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C22×Dic43—21no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D412yes—
160#10621902—22no—
161#10621902—22no—
162Q8×D43—22no—
163Q8×D43—22no—
164#10621900—28no—
165#10621900—22no—
166#10621900—22no—
167D4×D43—28no—
168D4×D43—22no—
169D4×D43—22no—
170#10621898—28no—
171#10621898—22no—
172#10621898#4114yes—
173C2×D172—21no—
174C2×D172C22×C411yescharacteristic
175C2×C4×D43—28no—
176C2×C4×D43—21no—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—21no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—21no—
183C2×C4×D43—22no—
184C2×C4×D43C22×C411yescharacteristic
185C2×C4×D43C22×C411yescharacteristic
186C2×C4×D43C2×D411yescharacteristic
187C2×C4×D43C2×D411yescharacteristic
188C2×Dic86—21no—
189C2×Dic86C22×C411yescharacteristic
190M16×C43—22no—
191M16×C43—22no—
192C2×C8×C43—22no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43C22×C412yes—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—21no—
197C42×C43—22no—
198C42×C43—21no—
199C42×C43—22no—
200C42×C43—22no—
201C42×C43C22×C412yes—
202C42×C43C2×D411yescharacteristic
203C42×C43C2×D411yescharacteristic
204C22⋊Dic43—22no—
205C22⋊Dic43—21no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—44no—
210(C2×D43)⋊C4C22⋊C412yes—
211(C2×D43)⋊C4C22⋊C412yes—
212(C2×D43)⋊C4C22⋊C412yes—
213(C2×D43)⋊C4C22⋊C412yes—
214C4⋊Dic43—22no—
215C4⋊Dic43C22×C412yes—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—44no—
220Dic43⋊C4C22⋊C412yes—
221Dic43⋊C4C22⋊C412yes—
222Dic43⋊C4C22⋊C412yes—
223Dic43⋊C4C22⋊C412yes—
224C4×Dic43—22no—
225C4×Dic43—21no—
226C4×Dic43—22no—
227C4×Dic43—22no—
228C4×Dic43—22no—
229C4×Dic43—22no—
230C4×Dic43—22no—
231C4×Dic43—44no—
232C4×Dic43C22×C412yes—
233C4×Dic43C2×D411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235#10621877—22no—
236#10621877—22no—
237C2×C43⋊C8—22no—
238C23×C43—21no—
239C23×C43C22×D411yescharacteristic
240C22×D43—21no—
241C22×D43—24no—
242C22×D43—22no—
243C22×D43—42no—
244C22×D43—82no—
245C22×D43C2×C22⋊C411yescharacteristic
246C22×D43C2×C22⋊C411yescharacteristic
247Q8×C43—21no—
248Q8×C43#11712yes—
249D4×C43—24no—
250D4×C43—21no—
251D4×C43#11712yes—
252C2×C4×C43—21no—
253C2×C4×C43—24no—
254C2×C4×C43—22no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—82no—
260C2×C4×C43C2×C22⋊C412yes—
261C2×C4×C43C2×C22⋊C412yes—
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4112yes—
265C2×C4×C43C2×#4112yes—
266C22⋊D43—24no—
267C22⋊D43—24no—
268C22⋊D43—24no—
269C2×Dic43—24no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—24no—
273C2×Dic43—22no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—82no—
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C412yes—
280C2×Dic43C2×C22⋊C412yes—
281C2×Dic43C2×C22⋊C411yescharacteristic
282D172—24no—
283D172—21no—
284D172#11712yes—
285C4×D43—24no—
286C4×D43—24no—
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—21no—
290C4×D43—21no—
291C4×D43—22no—
292C4×D43—24no—
293C4×D43—22no—
294C4×D43—82no—
295C4×D43—82no—
296C4×D43—82no—
297Dic86—24no—
298Dic86—21no—
299Dic86#11712yes—
300C8×C43—42no—
301C43⋊C8—42no—
302#20749—431nomaximal, Sylow
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—42no—
306C22×C43C22×C22⋊C411yescharacteristic
307C22×C43#52512yes—
308C2×D43—22no—
309C2×D43—22no—
310C2×D43—21no—
311C2×D43—22no—
312C2×D43—21no—
313C2×D43—42no—
314C2×D43—82no—
315C2×D43—84no—
316C4×C43—22no—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43—42no—
320C4×C43—82no—
321C4×C43C2×#11711yescharacteristic
322C4×C43C2×#11711yescharacteristic
323C4×C43#52512yes—
324Dic43—22no—
325Dic43—22no—
326Dic43—21no—
327Dic43—22no—
328Dic43—21no—
329Dic43—44no—
330Dic43—42no—
331#3428—431no—
332#2921—431no—
333#2298—431no—
334#1826—432no—
335#1806—432no—
336#1806—432no—
337#1789—432no—
338#1759—431no—
339#1759D4311yescharacteristic, complemented
340C4×#104—431no—
341C4×#104—431no—
342C2×C43—22no—
343C2×C43—42no—
344C2×C43#228011yescharacteristic
345C2×C43#290112yes—
346D43—41no—
347D43—41no—
348D43—42no—
349C22×#41—431no—
350#520—432no—
351#520—432no—
352#520—862no—
353#519—432no—
354#518—432no—
355#518—862no—
356C4×#41—431no—
357C4×#41—431no—
358C4×#41—431no—
359C4×#41—861no—
360C4×#41—861no—
361C4×#41C2×D4311yescharacteristic
362C2×#117—431no—
363C2×#117—431no—
364C2×#117—861no—
365C2×#117—861no—
366#433—861no—
367#433—861no—
368#433—861no—
369#433—861no—
370#423—432no—
371C2×#104—432no—
372C2×#104—432no—
373C2×#104—432no—
374C2×#104C2×D4312yes—
375#407—432no—
376C4×M16—431no—
377C4×M16C2×D4311yescharacteristic, complemented
378#388—862no—
379#387—862no—
380C4×C4⋊C4—432no—
381C4×C22⋊C4—432no—
382#376C2×D4311yescharacteristic, complemented
383C43—431no—
384#339—432no—
385#339—432no—
386#339—432no—
387#339C2×D4312yescomplemented
388C43#2074911yescharacteristic, complemented, Sylow
389C2×#41—431no—
390C2×#41—431no—
391C2×#41—431no—
392C2×#41—861no—
393C2×#41—861no—
394C2×#41—864no—
395C2×#41—864no—
396C2×#41C22×D4311yescharacteristic
397C22×Q8—431no—
398C22×D4—431no—
399C22×D4—861no—
400C23×C4—431no—
401C23×C4—861no—
402C2×M16—432no—
403C2×M16C22×D4312yes—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—432no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8C4×D4312yes—
410C4×D4—22no—
411C4×D4—432no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—862no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4C4×D4312yes—
424#117—21no—
425#117—432no—
426#117—432no—
427#117—431no—
428#117—431no—
429#117—431no—
430#117—431no—
431#117—431no—
432#117—432no—
433#117—861no—
434#117—862no—
435#117—862no—
436#117—861no—
437#117—861no—
438#117—862no—
439#117—861no—
440#117—862no—
441#117—861no—
442#117C22×D4311yescharacteristic
443C2×C4⋊C4—432no—
444C2×C4⋊C4—432no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—862no—
448C2×C22⋊C4—432no—
449C2×C22⋊C4—862no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—862no—
452C2×C22⋊C4—862no—
453C2×C42—21no—
454C2×C42—431no—
455C2×C42—432no—
456C2×C42—861no—
457C2×C42—861no—
458C2×C42—861no—
459C2×C42—861no—
460C2×C42—862no—
461C2×C42C22×D4312yes—
462C2×C42C22×D4311yescharacteristic
463C4⋊C8—862no—
464C4⋊C8—862no—
465#104—24no—
466#104—864no—
467#104—864no—
468#104—864no—
469C22⋊C8—862no—
470C22⋊C8—862no—
471#97—21no—
472#97—861no—
473C4×C8—21no—
474C4×C8—861no—
475#95—22no—
476#95—862no—
477#95—862no—
478C24—431no—
479C24—861no—
480#41—22no—
481#41—434no—
482#41—868no—
483#41—862no—
484#41—868no—
485#41—862no—
486#41—862no—
487#41—862no—
488#41—862no—
489#41#1062189814yes—
490C2×Q8—431no—
491C2×Q8—861no—
492C2×Q8—862no—
493C2×Q8—862no—
494C2×Q8C2×C4×D4311yescharacteristic
495C2×D4—21no—
496C2×D4—431no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—862no—
500C2×D4—868no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—862no—
504C2×D4C2×C4×D4311yescharacteristic
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—431no—
509C22×C4—432no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—862no—
516C22×C4—861no—
517C22×C4—868no—
518C22×C4—862no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4D4×D4312yes—
527C22×C4C23×D4311yescharacteristic
528M16—22no—
529M16—22no—
530M16—862no—
531M16—862no—
532C2×C8—22no—
533C2×C8—862no—
534C4⋊C4—22no—
535C4⋊C4—432no—
536C4⋊C4—432no—
537C4⋊C4—432no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—862no—
543C4⋊C4—862no—
544C4⋊C4—1724no—
545C4⋊C4C2×C4×D4312yes—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—432no—
549C22⋊C4—432no—
550C22⋊C4—432no—
551C22⋊C4—432no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—861no—
556C22⋊C4—862no—
557C22⋊C4—1724no—
558C42—22no—
559C42—21no—
560C42—22no—
561C42—22no—
562C42—432no—
563C42—431no—
564C42—431no—
565C42—862no—
566C42—862no—
567C42—862no—
568C42—862no—
569C42—861no—
570C42—862no—
571C42—862no—
572C42—1724no—
573C42C2×C4×D4312yes—
574C42D4×D4311yescharacteristic
575C42D4×D4311yescharacteristic
576C23—21no—
577C23—431no—
578C23—431no—
579C23—864no—
580C23—862no—
581C23—861no—
582C23—3442no—
583C23—1722no—
584C23C2×D4×D4311yescharacteristic
585Q8—21no—
586Q8—432no—
587Q8—864no—
588Q8—861no—
589Q8#1306328212yes—
590D4—24no—
591D4—21no—
592D4—432no—
593D4—864no—
594D4—864no—
595D4—864no—
596D4—864no—
597D4—861no—
598D4#1306328212yes—
599C2×C4—21no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—82no—
607C2×C4—432no—
608C2×C4—432no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—864no—
612C2×C4—864no—
613C2×C4—864no—
614C2×C4—861no—
615C2×C4—862no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—864no—
623C2×C4—864no—
624C2×C4—862no—
625C2×C4—3442no—
626C2×C4—3442no—
627C2×C4—3442no—
628C2×C4—3442no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4C22⋊C4×D4312yes—
633C2×C4C22⋊C4×D4312yes—
634C2×C4C22×C4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4#41×D4312yes—
637C2×C4C2×#1062189812yes—
638C8—42no—
639C8—1722no—
640C22—22no—
641C22—22no—
642C22—42no—
643C22—861no—
644C22—862no—
645C22—861no—
646C22—862no—
647C22—862no—
648C22—3442no—
649C22—3444no—
650C22—1722no—
651C22C2×C22⋊C4×D4311yescharacteristic
652C22#1458340812yes—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—82no—
658C4—861no—
659C4—861no—
660C4—862no—
661C4—862no—
662C4—862no—
663C4—1724no—
664C4—1722no—
665C4#117×D4311yescharacteristic
666C4C2×#1306328211yescharacteristic
667C4#1458340812yes—
668C2—22no—
669C2—42no—
670C2—1721no—
671C2—1721no—
672C2—1722no—
673C2#1913697611yescharacteristic
674C2#1914314112yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#20749
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #19143231C2semidirect
3. #19137090C2semidirect
4. #19134693C2semidirect
5. #19134614C2semidirect
6. #19134613C2semidirect
8. #19134406C2semidirect
9. C4×#13063251C2semidirect
10. C4×#13063252C2semidirect
11. C43×#1759C2semidirect
13. #14583381C4semidirect
15. #14583378C4semidirect
16. #14583375C4semidirect
18. #14583371C4semidirect
32. #14582922C22semidirect
37. C4×#10621877C22semidirect
40. C4×Dic43⋊C4C22semidirect
42. C42×Dic43C22semidirect
43. #14582660C22semidirect
44. #14582659C22semidirect
45. #14582658C22semidirect
48. C4×M16×C43C22semidirect
49. C43×#376C22semidirect
50. C43×#339C22semidirect
339. #1759D43semidirect
377. C4×M16C2×D43semidirect
382. #376C2×D43semidirect
387. #339C2×D43semidirect
388. C43#20749semidirect

Maximal subgroups

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

subgroupindex
#191477942
#191432312
#191370902
#191346932
#191346142
#191346132
#191345372
#191344062
C4×#130632512
C4×#130632522
C43×#17592
#2074943