Finite Group Databasebeta

← #25096729

Subgroups — #25096729

Order 11008.

1258 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147798C211yesmaximal, characteristic
2#19143230C211yesmaximal, characteristic, complemented
3#19137091C211yesmaximal, characteristic, complemented
4#19134695C211yesmaximal, characteristic, complemented
5#19134692C211yesmaximal, characteristic, complemented
6#19134613C212yesmaximal, complemented
7#19134613C212yesmaximal, complemented
8#19134539C211yesmaximal, characteristic
9#19134407C212yesmaximal, complemented
10#104×Dic43C212yesmaximal, complemented
11C43×#1789C211yesmaximal, characteristic
12#14583382—21no—
13#14583382—21no—
14#14583382C412yescomplemented
15#14583382C412yescomplemented
16#14583377C412yescomplemented
17#14583374—21no—
18#14583374—21no—
19#14583374C412yescomplemented
20#41×Dic43—22no—
21#41×Dic43C2212yes—
22#41×Dic43C2212yes—
23C2×#13063284—22no—
24C2×#13063284C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26#14582957—22no—
27#14582957—22no—
28#14582922C2212yescomplemented
29C2×#13063252C2212yes—
30C2×#13063252C2212yes—
31#14582863C2211yescharacteristic
32M16×Dic43C2212yescomplemented
33#14582793—21no—
34#14582787—21no—
35#14582784—21no—
36#14582782—21no—
37C4×Dic43⋊C4C2211yescharacteristic, complemented
38C4×Dic43⋊C4C2211yescharacteristic, complemented
39C4×C22⋊Dic43C2211yescharacteristic
40#14582745C2211yescharacteristic, complemented
41C42×Dic43C2211yescharacteristic, complemented
42#14582660C2212yescomplemented
43#14582660C2212yescomplemented
44#14582659C2212yescomplemented
45#14582659C2212yescomplemented
46C22×#41×C43C2211yescharacteristic
47C2×#104×C43C2212yes—
48C2×#104×C43C2212yes—
49C43×#407C2211yescharacteristic
50C4×C22⋊C4×C43C2211yescharacteristic
51C2×#10621877C2312yes—
52Q8×Dic43—22no—
53Q8×Dic43—22no—
54Q8×Dic43C2×C412yes—
55Q8×Dic43C2×C412yes—
56Q8×Dic43C2×C412yes—
57Q8×Dic43C2×C412yes—
58D4×Dic43—22no—
59D4×Dic43—22no—
60D4×Dic43—22no—
61D4×Dic43—22no—
62D4×Dic43—22no—
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43C2×C412yes—
69D4×Dic43C2×C412yes—
70D4×Dic43C2×C412yes—
71D4×Dic43C2×C412yes—
72#13063284—21no—
73#13063284—21no—
74#13063284—22no—
75#13063284—22no—
76#13063284—22no—
77#13063284—22no—
78#13063284—22no—
79#13063284—22no—
80#13063284C2×C412yes—
81#13063284C2×C412yes—
82#13063284C2×C412yes—
83#13063284D412yes—
84#13063284D412yes—
85#13063284C2312yes—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43C2×C411yescharacteristic
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43D411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43D411yescharacteristic
99C2×C22⋊Dic43D411yescharacteristic
100C2×C4×Dic43—21no—
101C2×C4×Dic43—22no—
102C2×C4×Dic43—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—24no—
110#13063252—24no—
111#13063252—24no—
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114#13063235—22no—
115C8×Dic43—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C2×#41×C43—24no—
122C2×#41×C43—24no—
123C2×#41×C43—21no—
124C2×#41×C43—21no—
125C2×#41×C43C2×C412yes—
126C2×#41×C43C2312yes—
127C22×Q8×C43C2×C411yescharacteristic
128C22×D4×C43—21no—
129C22×D4×C43C2×C411yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43C2312yes—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#104×C43—24no—
137#104×C43—24no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143#41×C43—24no—
144#41×C43—24no—
145#41×C43—28no—
146#41×C43—24no—
147#41×C43—24no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43#4114yes—
151#41×C43#4114yes—
152C2×Q8×C43—24no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22×C412yes—
155C2×D4×C43—24no—
156C2×D4×C43—24no—
157C2×D4×C43—24no—
158C2×D4×C43—21no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43C22×C412yes—
162C22×C4×C43—28no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188M16×C43—22no—
189M16×C43—22no—
190C2×C8×C43—22no—
191C22⋊C4×C43—42no—
192C42×C43—22no—
193C42×C43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—42no—
201C22⋊Dic43C22⋊C412yes—
202C22⋊Dic43C22⋊C412yes—
203C22⋊Dic43C22⋊C412yes—
204C22⋊Dic43C22⋊C412yes—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—22no—
208C4⋊Dic43—22no—
209C4⋊Dic43—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43C22⋊C412yes—
212C4⋊Dic43C22⋊C412yes—
213C4⋊Dic43C22⋊C412yes—
214C4⋊Dic43C22⋊C412yes—
215C4⋊Dic43C22×C412yes—
216C4⋊Dic43C22×C412yes—
217Dic43⋊C4—42no—
218Dic43⋊C4—42no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43—22no—
227C4×Dic43—42no—
228C4×Dic43—42no—
229C4×Dic43C22×C412yes—
230C4×Dic43C22×C412yes—
231C4×Dic43C2×D412yes—
232C4×Dic43C2×D412yes—
233#10621877—22no—
234#10621877—22no—
235C2×C43⋊C8—22no—
236C23×C43—24no—
237C23×C43—22no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—81no—
243C23×C43—81no—
244C23×C43C2×C22⋊C411yescharacteristic
245C23×C43C2×C22⋊C411yescharacteristic
246C23×C43C22×D411yescharacteristic
247Q8×C43—24no—
248Q8×C43—22no—
249Q8×C43#11714yes—
250D4×C43—28no—
251D4×C43—24no—
252D4×C43—24no—
253D4×C43—24no—
254D4×C43—22no—
255D4×C43#11714yes—
256C2×C4×C43—24no—
257C2×C4×C43—28no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—24no—
265C2×C4×C43—24no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43C2×C22⋊C411yescharacteristic
274C2×C4×C43C2×C22⋊C411yescharacteristic
275C2×C4×C43C23×C411yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C2×#4112yes—
278C2×C4×C43C2×#4112yes—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—82no—
292C2×Dic43—82no—
293C2×Dic43—82no—
294C2×Dic43—82no—
295C2×Dic43—81no—
296C2×Dic43—81no—
297C2×Dic43C2×C22⋊C412yes—
298C2×Dic43C2×C22⋊C412yes—
299C2×Dic43C2×C22⋊C412yes—
300C2×Dic43C2×C22⋊C412yes—
301C8×C43—42no—
302C43⋊C8—42no—
303#20749—431nomaximal, Sylow
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—24no—
312C22×C43—21no—
313C22×C43—42no—
314C22×C43—42no—
315C22×C43—81no—
316C22×C43—81no—
317C22×C43—84no—
318C22×C43C22×C22⋊C411yescharacteristic
319C22×C43#52511yescharacteristic
320C22×C43#52511yescharacteristic
321C4×C43—21no—
322C4×C43—24no—
323C4×C43—21no—
324C4×C43—42no—
325C4×C43—81no—
326C4×C43C2×#11712yes—
327C4×C43#52512yes—
328Dic43—22no—
329Dic43—22no—
330Dic43—22no—
331Dic43—22no—
332Dic43—42no—
333Dic43—42no—
334Dic43—42no—
335Dic43—81no—
336#3428—431no—
337#2921—431no—
338#2298—431no—
339#1826—431no—
340#1826—431no—
341#1806—432no—
342#1806—432no—
343#1789—431no—
344#1789D4311yescharacteristic
345#1759—432no—
346C4×#104—432no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—41no—
350C2×C43—41no—
351C2×C43—44no—
352C2×C43#228011yescharacteristic
353C2×C43#290111yescharacteristic
354C2×C43#290111yescharacteristic
355C22×#41C2×D4311yescharacteristic
356#520—432no—
357#520—432no—
358#520—861no—
359#520—861no—
360#519—432no—
361#518—432no—
362#518—861no—
363#518—861no—
364C4×#41—432no—
365C4×#41—432no—
366C4×#41—862no—
367C2×#117—431no—
368C2×#117—431no—
369C2×#117—862no—
370#433—862no—
371#433—862no—
372#423—432no—
373C2×#104—432no—
374C2×#104—432no—
375C2×#104C2×D4312yes—
376C2×#104C2×D4312yes—
377#407—431no—
378#407C2×D4311yescharacteristic
379C4×M16—432no—
380#388—861no—
381#388—861no—
382#387—861no—
383#387—861no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C22⋊C4—431no—
387C4×C22⋊C4C2×D4311yescharacteristic
388#376—431no—
389C43—431no—
390#339—432no—
391#339—432no—
392#339—432no—
393#339—432no—
394C43#2074911yescharacteristic, complemented, Sylow
395C2×#41—24no—
396C2×#41—24no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41C4×D4312yes—
400C2×#41C22×D4312yes—
401C22×Q8C4×D4311yescharacteristic
402C22×D4—21no—
403C22×D4C4×D4311yescharacteristic
404C23×C4—21no—
405C23×C4C22×D4311yescharacteristic
406C2×M16—432no—
407C2×M16C22×D4312yes—
408C4×Q8—432no—
409C4×Q8—432no—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—862no—
413C4×Q8—862no—
414C4×D4—432no—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428#117—432no—
429#117—432no—
430#117—432no—
431#117—432no—
432#117—432no—
433#117—432no—
434#117—862no—
435#117—862no—
436#117—862no—
437#117—862no—
438#117—862no—
439#117—862no—
440#117—861no—
441#117—861no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—862no—
447C2×C4⋊C4—862no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—862no—
454C2×C22⋊C4—862no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—862no—
462C2×C42—862no—
463C2×C42—861no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467C2×C42C22×D4311yescharacteristic
468C4⋊C8—864no—
469#104—24no—
470#104—24no—
471#104—864no—
472#104—864no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477#97—862no—
478C4×C8—862no—
479#95—21no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—21no—
486C24D4×D4311yescharacteristic
487#41—24no—
488#41—24no—
489#41—28no—
490#41—24no—
491#41—24no—
492#41—22no—
493#41—22no—
494#41#1062190014yes—
495#41#1062190014yes—
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8C2×C4×D4312yes—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—21no—
505C2×D4C2×C4×D4312yes—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4C2×C4×D4311yescharacteristic
527C22×C4C2×C4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4D4×D4311yescharacteristic
530C22×C4D4×D4311yescharacteristic
531C22×C4C23×D4311yescharacteristic
532M16—22no—
533M16—22no—
534M16—862no—
535M16—862no—
536C2×C8—22no—
537C2×C8—862no—
538C4⋊C4—432no—
539C4⋊C4—432no—
540C4⋊C4—432no—
541C4⋊C4—432no—
542C4⋊C4—432no—
543C4⋊C4—432no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—1722no—
551C4⋊C4—1722no—
552C22⋊C4—42no—
553C22⋊C4—432no—
554C22⋊C4—432no—
555C22⋊C4—432no—
556C22⋊C4—432no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—1722no—
564C42—22no—
565C42—22no—
566C42—432no—
567C42—432no—
568C42—432no—
569C42—432no—
570C42—862no—
571C42—862no—
572C42—862no—
573C42—862no—
574C42—862no—
575C42—862no—
576C42—862no—
577C42—862no—
578C42—1722no—
579C42—1722no—
580C23—24no—
581C23—22no—
582C23—21no—
583C23—21no—
584C23—41no—
585C23—41no—
586C23—81no—
587C23—81no—
588C23C22⋊C4×D4311yescharacteristic
589C23C22⋊C4×D4311yescharacteristic
590C23C2×D4×D4311yescharacteristic
591Q8—24no—
592Q8—22no—
593Q8#1306328114yes—
594D4—28no—
595D4—24no—
596D4—24no—
597D4—24no—
598D4—22no—
599D4#1306328114yes—
600C2×C4—24no—
601C2×C4—28no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—3442no—
625C2×C4—3442no—
626C2×C4—3442no—
627C2×C4—3442no—
628C2×C4—3441no—
629C2×C4—3441no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4C22⋊C4×D4311yescharacteristic
640C2×C4C22⋊C4×D4311yescharacteristic
641C2×C4C22×C4×D4311yescharacteristic
642C2×C4C2×D4×D4311yescharacteristic
643C2×C4C2×#1062190012yes—
644C2×C4C2×#1062190012yes—
645C8—42no—
646C8—1722no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—24no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—84no—
661C22C2×C22⋊C4×D4311yescharacteristic
662C22#1458340511yescharacteristic
663C22#1458340511yescharacteristic
664C4—21no—
665C4—24no—
666C4—21no—
667C4—42no—
668C4—81no—
669C4—862no—
670C4—862no—
671C4—862no—
672C4—862no—
673C4—3441no—
674C4—1722no—
675C4—1722no—
676C4—1722no—
677C4C2×#1306328112yes—
678C4#1458340512yes—
679C2—21no—
680C2—21no—
681C2—41no—
682C2—41no—
683C2—44no—
684C2#1913697311yescharacteristic
685C2#1914313911yescharacteristic
686C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1789C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1789D43
hypocenterC43#20749
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #19143230C2semidirect
3. #19137091C2semidirect
4. #19134695C2semidirect
5. #19134692C2semidirect
6. #19134613C2semidirect
7. #19134613C2semidirect
9. #19134407C2semidirect
10. #104×Dic43C2semidirect
14. #14583382C4semidirect
15. #14583382C4semidirect
16. #14583377C4semidirect
19. #14583374C4semidirect
28. #14582922C22semidirect
32. M16×Dic43C22semidirect
37. C4×Dic43⋊C4C22semidirect
38. C4×Dic43⋊C4C22semidirect
40. #14582745C22semidirect
41. C42×Dic43C22semidirect
42. #14582660C22semidirect
43. #14582660C22semidirect
44. #14582659C22semidirect
45. #14582659C22semidirect
394. C43#20749semidirect

Maximal subgroups

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

subgroupindex
#191477982
#191432302
#191370912
#191346952
#191346922
#191346132
#191345392
#191344072
#104×Dic432
C43×#17892
#2074943