Finite Group Databasebeta

← #25096731

Subgroups — #25096731

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#19147796C211yesmaximal, characteristic
2#19143230C211yesmaximal, characteristic, complemented
3#19137091C211yesmaximal, characteristic, complemented
4#19134694C211yesmaximal, characteristic, complemented
5#19134614C212yesmaximal, complemented
6#19134614C212yesmaximal, complemented
7#19134540C211yesmaximal, characteristic
8#19134538C211yesmaximal, characteristic
9#19134404C212yesmaximal, complemented
10#19134399C212yesmaximal, complemented
11C43×#1826C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13#14583380C412yescomplemented
14#14583380C412yescomplemented
15#14583379—21no—
16#14583379—21no—
17#14583376C412yescomplemented
18#14583373C412yescomplemented
19#14583372—21no—
20#14583372—21no—
21C4×#10621898—22no—
22#14583367C2212yes—
23#14583367C2212yes—
24C2×#13063284C2211yescharacteristic
25#117×D43—22no—
26#14582957—22no—
27#14582957—22no—
28#14582922C2212yescomplemented
29C2×#13063253C2212yes—
30C2×#13063253C2212yes—
31C2×#13063251C2212yes—
32C2×#13063251C2212yes—
33#14582863C2211yescharacteristic
34M16×Dic43C2212yescomplemented
35#14582793—21no—
36#14582787—21no—
37#14582784—21no—
38#14582782—21no—
39C4×Dic43⋊C4C2211yescharacteristic, complemented
40C4×Dic43⋊C4C2211yescharacteristic, complemented
41C4×C22⋊Dic43C2211yescharacteristic
42#14582745C2211yescharacteristic, complemented
43C42×Dic43C2211yescharacteristic, complemented
44#14582658C2212yescomplemented
45#14582658C2212yescomplemented
46C2×#117×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C4×C22⋊C4×C43C2211yescharacteristic
49C43×#339C2212yescomplemented
50C43×#339C2212yescomplemented
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898—24no—
54C2×#10621898—24no—
55C2×#10621898C2×C412yes—
56C2×#10621898C2312yes—
57C22×Dic86C2×C411yescharacteristic
58C22×D172C2×C411yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43—21no—
61C2×#10621877C2312yes—
62C4×Dic86—22no—
63C4×Dic86—22no—
64#13063290C2×C412yes—
65#13063290C2×C412yes—
66#13063290C2×C412yes—
67#13063290C2×C412yes—
68C4×D172—22no—
69C4×D172—22no—
70#13063287C2×C412yes—
71#13063287C2×C412yes—
72#13063287C2×C412yes—
73#13063287C2×C412yes—
74C4×C22⋊D43—22no—
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(C22⋊D43)⋊C4—22no—
82#13063284C2×C412yes—
83#13063284C2×C412yes—
84#13063284D412yes—
85#13063284D412yes—
86#13063283—22no—
87#13063283—22no—
88#13063282—22no—
89#13063282—22no—
90#13063281—22no—
91#13063281—22no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43D411yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—22no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43D411yescharacteristic
100C2×C22⋊Dic43D411yescharacteristic
101C22⋊C4×D43—22no—
102C22⋊C4×D43—22no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C42×D43—22no—
110C42×D43—22no—
111Dic43⋊C8—24no—
112#13063253—24no—
113#13063253—24no—
114#13063251—24no—
115#13063251—24no—
116C22⋊(C43⋊C8)—21no—
117C22⋊(C43⋊C8)—21no—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43C2312yes—
127#117×C43—21no—
128#117×C43—21no—
129#117×C43C2×C412yes—
130#117×C43C2312yes—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—24no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166#10621898—24no—
167#10621898—24no—
168#10621898—28no—
169#10621898—22no—
170#10621898—22no—
171#10621898—24no—
172#10621898—24no—
173#10621898#4114yes—
174#10621898#4114yes—
175C2×D172—21no—
176C2×D172—24no—
177C2×D172C22×C412yes—
178C2×C4×D43—28no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×Dic86—21no—
186C2×Dic86—24no—
187C2×Dic86C22×C412yes—
188M16×C43—22no—
189M16×C43—22no—
190C2×C8×C43—22no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43C22×C412yes—
194C4⋊C4×C43C22×C412yes—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—42no—
198C42×C43—22no—
199C42×C43—22no—
200C42×C43—22no—
201C42×C43—22no—
202C22⋊Dic43—42no—
203C22⋊Dic43C22⋊C412yes—
204C22⋊Dic43C22⋊C412yes—
205C22⋊Dic43C22⋊C412yes—
206C22⋊Dic43C22⋊C412yes—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210(C2×D43)⋊C4—22no—
211C4⋊Dic43C22⋊C412yes—
212C4⋊Dic43C22⋊C412yes—
213C4⋊Dic43C22⋊C412yes—
214C4⋊Dic43C22⋊C412yes—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4—42no—
220Dic43⋊C4—42no—
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—21no—
237C23×C43—21no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43C2×C22⋊C411yescharacteristic
241C23×C43C2×C22⋊C411yescharacteristic
242C23×C43C22×D411yescharacteristic
243C22×D43—22no—
244C22×D43—24no—
245C22×D43—81no—
246C22×D43—81no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—81no—
262C2×C4×C43—81no—
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C23×C411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4112yes—
268C2×C4×C43C2×#4112yes—
269C22⋊D43—28no—
270C22⋊D43—24no—
271C22⋊D43—24no—
272C2×Dic43—24no—
273C2×Dic43—22no—
274C2×Dic43—22no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43C2×C22⋊C412yes—
285C2×Dic43C2×C22⋊C412yes—
286C2×Dic43C2×C22⋊C412yes—
287C2×Dic43C2×C22⋊C412yes—
288D172—24no—
289D172—22no—
290D172#11714yes—
291C4×D43—28no—
292C4×D43—24no—
293C4×D43—24no—
294C4×D43—82no—
295C4×D43—82no—
296C4×D43—82no—
297C4×D43—82no—
298Dic86—24no—
299Dic86—22no—
300Dic86#11714yes—
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—21no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43C22×C22⋊C411yescharacteristic
315C22×C43#52511yescharacteristic
316C22×C43#52511yescharacteristic
317C2×D43—24no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—84no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—81no—
327C4×C43C2×#11712yes—
328C4×C43#52512yes—
329Dic43—22no—
330Dic43—22no—
331Dic43—22no—
332Dic43—22no—
333Dic43—24no—
334Dic43—42no—
335Dic43—81no—
336#3428—431no—
337#2921—431no—
338#2298—431no—
339#1826—431no—
340#1826D4311yescharacteristic, complemented
341#1806—432no—
342#1806—432no—
343#1789—431no—
344#1789—431no—
345#1759—432no—
346C4×#104—432no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—41no—
350C2×C43—41no—
351C2×C43#228011yescharacteristic
352C2×C43#290111yescharacteristic
353C2×C43#290111yescharacteristic
354D43—44no—
355C22×#41—431no—
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—862no—
369C2×#117C2×D4311yescharacteristic
370#433—862no—
371#433—862no—
372#423—432no—
373C2×#104—432no—
374C2×#104—432no—
375C2×#104—432no—
376C2×#104—432no—
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#339C2×D4312yescomplemented
393#339C2×D4312yescomplemented
394C43#2074911yescharacteristic, complemented, Sylow
395C2×#41—432no—
396C2×#41—432no—
397C2×#41—864no—
398C2×#41—864no—
399C2×#41—861no—
400C2×#41—861no—
401C22×Q8—431no—
402C22×D4—431no—
403C22×D4—861no—
404C23×C4—861no—
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—21no—
429#117—21no—
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#117C4×D4312yes—
441#117C22×D4312yes—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—862no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4—861no—
448C2×C4⋊C4C4×D4311yescharacteristic
449C2×C4⋊C4C4×D4311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—862no—
455C2×C22⋊C4—862no—
456C2×C22⋊C4—861no—
457C2×C42—21no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—862no—
463C2×C42—862no—
464C2×C42—861no—
465C2×C42—861no—
466C2×C42C22×D4311yescharacteristic
467C2×C42C22×D4311yescharacteristic
468C4⋊C8—864no—
469#104—864no—
470#104—864no—
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—861no—
486C24D4×D4311yescharacteristic
487#41—434no—
488#41—434no—
489#41—864no—
490#41—864no—
491#41—864no—
492#41—864no—
493#41—868no—
494#41—862no—
495#41—862no—
496C2×Q8—432no—
497C2×Q8—864no—
498C2×Q8—861no—
499C2×D4—432no—
500C2×D4—864no—
501C2×D4—864no—
502C2×D4—864no—
503C2×D4—862no—
504C2×D4—862no—
505C2×D4—861no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—868no—
521C22×C4—861no—
522C22×C4—862no—
523C22×C4—862no—
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—21no—
539C4⋊C4—21no—
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—1722no—
549C4⋊C4—1722no—
550C4⋊C4C2×C4×D4312yes—
551C4⋊C4C2×C4×D4312yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—42no—
555C22⋊C4—432no—
556C22⋊C4—432no—
557C22⋊C4—432no—
558C22⋊C4—432no—
559C22⋊C4—862no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—1722no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—22no—
568C42—432no—
569C42—432no—
570C42—432no—
571C42—432no—
572C42—862no—
573C42—862no—
574C42—862no—
575C42—862no—
576C42—862no—
577C42—862no—
578C42—1722no—
579C42—1722no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—864no—
585C23—862no—
586C23—3441no—
587C23—3441no—
588C23C22⋊C4×D4311yescharacteristic
589C23C22⋊C4×D4311yescharacteristic
590C23C2×D4×D4311yescharacteristic
591Q8—434no—
592Q8—864no—
593Q8—862no—
594D4—434no—
595D4—864no—
596D4—868no—
597D4—864no—
598D4—864no—
599D4—862no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—432no—
617C2×C4—432no—
618C2×C4—432no—
619C2×C4—432no—
620C2×C4—868no—
621C2×C4—864no—
622C2×C4—862no—
623C2×C4—864no—
624C2×C4—864no—
625C2×C4—862no—
626C2×C4—3442no—
627C2×C4—3442no—
628C2×C4—3442no—
629C2×C4—3442no—
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×C4#41×D4312yes—
644C2×C4#41×D4312yes—
645C8—42no—
646C8—1722no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—81no—
656C22—81no—
657C22—864no—
658C22—3444no—
659C22—1722no—
660C22—1722no—
661C22C2×C22⋊C4×D4311yescharacteristic
662C22#1458340711yescharacteristic
663C22#1458340711yescharacteristic
664C4—21no—
665C4—21no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—81no—
670C4—864no—
671C4—862no—
672C4—862no—
673C4—862no—
674C4—862no—
675C4—3441no—
676C4—1722no—
677C4#117×D4312yes—
678C4#1458340712yes—
679C2—21no—
680C2—21no—
681C2—41no—
682C2—41no—
683C2—1724no—
684C2#1913697511yescharacteristic
685C2#1914313911yescharacteristic
686C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43#20749
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
2. #19143230C2semidirect
3. #19137091C2semidirect
4. #19134694C2semidirect
5. #19134614C2semidirect
6. #19134614C2semidirect
9. #19134404C2semidirect
10. #19134399C2semidirect
11. C43×#1826C2semidirect
13. #14583380C4semidirect
14. #14583380C4semidirect
17. #14583376C4semidirect
18. #14583373C4semidirect
28. #14582922C22semidirect
34. M16×Dic43C22semidirect
39. C4×Dic43⋊C4C22semidirect
40. C4×Dic43⋊C4C22semidirect
42. #14582745C22semidirect
43. C42×Dic43C22semidirect
44. #14582658C22semidirect
45. #14582658C22semidirect
49. C43×#339C22semidirect
50. C43×#339C22semidirect
340. #1826D43semidirect
392. #339C2×D43semidirect
393. #339C2×D43semidirect
394. C43#20749semidirect

Maximal subgroups

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

subgroupindex
#191477962
#191432302
#191370912
#191346942
#191346142
#191345402
#191345382
#191344042
#191343992
C43×#18262
#2074943