Finite Group Databasebeta

← #25102537

Subgroups — #25102537

Order 11008.

1370 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583072C211yesmaximal, characteristic
2C4×#13063350C212yesmaximal, complemented
3#19137302C211yesmaximal, characteristic, complemented
4#19134998C211yesmaximal, characteristic, complemented
5#19134971C212yesmaximal, complemented
6#19134821C212yesmaximal, complemented
7#19134810C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic, complemented
9#19134405C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×2−1+4×C43C211yesmaximal, characteristic, complemented
12C2×#13063350C2212yes—
13C2×#13063314C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583072C418yescomplemented
16#14583009—22no—
17#14582997—22no—
18C4×#10621884—22no—
19C4×#10621882—22no—
20#14582942C2212yes—
21C2×#13063252C2212yes—
22C2×#13063252C2212yes—
23#14582903C2212yes—
24#14582900C2212yes—
25C2×#13063244C2211yescharacteristic
26C2×#13063244C2211yescharacteristic
27C4×#10621877C2212yes—
28#14582806C2211yescharacteristic
29#14582800C2211yescharacteristic
30#14582790—22no—
31#14582770—22no—
32#14582768C2211yescharacteristic
33#14582745C2211yescharacteristic
34#14582668C2212yes—
35#14582658C2212yes—
36#14582658C2212yes—
37C2×2−1+4×C43C2211yescharacteristic
38C43×#520—22no—
39C43×#520—22no—
40C43×#520C2212yes—
41C43×#519—22no—
42C43×#519C2211yescharacteristic
43C4×#41×C43—22no—
44C4×#41×C43—22no—
45C4×#41×C43C2212yes—
46C2×C4×Q8×C43—22no—
47C2×C4×Q8×C43C2211yescharacteristic
48C22×D172C2311yescharacteristic
49C22×C4×D43—21no—
50#13063350—24no—
51#13063350C2×C418yescomplemented
52C2×#10621884—22no—
53C2×#10621882—22no—
54C2×#10621877C2312yes—
55C2×#10621877C2312yes—
56#13063314—22no—
57#13063314C2×C414yescomplemented
58C4×D172—22no—
59C4×D172—22no—
60C2×C4⋊Dic43C2311yescharacteristic
61C2×Dic43⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—21no—
64C2×(C2×D43)⋊C4—22no—
65C2×C4×Dic43C2311yescharacteristic
66C2×C4×Dic43C2311yescharacteristic
67#13063258—22no—
68#13063256—22no—
69#13063252—24no—
70#13063252C2×C418yescomplemented
71#13063249—22no—
72#13063246—22no—
73#13063245—22no—
74#13063245—22no—
75#13063244—22no—
76#13063244C2×C414yescomplemented
77#13063236—22no—
78C4×C43⋊C8—22no—
79C43⋊#95—21no—
80C43⋊#95—22no—
81C43⋊#95—21no—
822−1+4×C43—24no—
832−1+4×C43—22no—
842−1+4×C43C2×C414yescomplemented
85C2×#41×C43—22no—
86C2×#41×C43—22no—
87C2×#41×C43C2312yes—
88C22×Q8×C43—22no—
89C22×Q8×C43C2311yescharacteristic
90C4×Q8×C43—22no—
91C4×Q8×C43—24no—
92C4×Q8×C43—22no—
93C4×Q8×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43D412yes—
99C4×Q8×C43D412yes—
100C4×D4×C43—22no—
101C4×D4×C43—24no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—24no—
106C4×D4×C43—22no—
107C4×D4×C43D412yes—
108C4×D4×C43D412yes—
109#117×C43—24no—
110#117×C43—24no—
111#117×C43—22no—
112#117×C43—22no—
113#117×C43—22no—
114#117×C43C2312yes—
115C2×C4⋊C4×C43—24no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43D412yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—24no—
120C2×C42×C43—22no—
121C2×C42×C43D412yes—
122C2×C42×C43C2311yescharacteristic
123C23×D43—21no—
124#41×C43—28no—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—28no—
128#41×C43—22no—
129#41×C43—22no—
130#41×C43C22×C414yes—
131#41×C43#4114yes—
132C2×Q8×C43—22no—
133C2×Q8×C43—28no—
134C2×Q8×C43—28no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43C22×C412yes—
138C2×Q8×C43C2×D412yes—
139C2×Q8×C43#4112yes—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43C2×D412yes—
143C22×C4×C43—24no—
144C22×C4×C43—22no—
145C22×C4×C43—24no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×D172—21no—
157C2×D172—22no—
158C2×D172—22no—
159C2×D172C22×C412yes—
160C2×C4×D43—42no—
161C2×C4×D43—82no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43C2×D412yes—
170C4⋊C4×C43C2×D412yes—
171C22⋊C4×C43—24no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C42×C43—24no—
176C42×C43—24no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43—22no—
181C42×C43—22no—
182C42×C43C2×D412yes—
183C42×C43C2×D412yes—
184#10621884—28no—
185#10621882—28no—
186(C2×D43)⋊C4—28no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—82no—
190C4⋊Dic43—22no—
191Dic43⋊C4—82no—
192C4×Dic43—21no—
193C4×Dic43—22no—
194C4×Dic43C22×C412yes—
195#10621877—22no—
196#10621877—22no—
197#10621877—22no—
198#10621877C22×C414yes—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43—22no—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—41no—
207C22×D43—41no—
208Q8×C43—28no—
209Q8×C43—24no—
210Q8×C43—22no—
211Q8×C43—24no—
212Q8×C43C4×D414yes—
213D4×C43—28no—
214D4×C43—24no—
215D4×C43—24no—
216D4×C43—22no—
217D4×C43C4×D414yes—
218C2×C4×C43—216no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—44no—
230C2×C4×C43—42no—
231C2×C4×C43—82no—
232C2×C4×C43—84no—
233C2×C4×C43C4×D414yes—
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#12012yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D412yes—
239C2×C4×C43C2×#4112yes—
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—22no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249D172—24no—
250D172—42no—
251C4×D43—84no—
252C43⋊C8—24no—
253C43⋊C8—42no—
254#21475—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—24no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C2×C4×D411yescharacteristic
261C22×C43C2×#12011yescharacteristic
262C22×C43#52511yescharacteristic
263C2×D43—44no—
264C2×D43—42no—
265C2×D43—82no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—22no—
271C4×C43—24no—
272C4×C43—24no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43C2×C4×D412yes—
277C4×C43#52512yes—
278Dic43—42no—
279Dic43—81no—
280Dic43—81no—
281C4×2−1+4D4311yescharacteristic, complemented
282C2×#454—431no—
283C4×AGL(1,ℤ/8)—432no—
284#2326—431no—
285#1888—431no—
286#1883—432no—
287#1859—432no—
288#1857—431no—
289#1793—431no—
290#1759—432no—
291C4×#101—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—44no—
295C2×C43C4×#12011yescharacteristic
296C2×C43#302011yescharacteristic
297C2×C43#302111yescharacteristic
298D43—82no—
299C2×2−1+4C2×D4311yescharacteristic
300C2×AGL(1,ℤ/8)—432no—
301C2×#124—431no—
302#520—22no—
303#520—22no—
304#520C2×D4312yes—
305#519—22no—
306#519C2×D4311yescharacteristic
307C4×#41—22no—
308C4×#41—22no—
309C4×#41C2×D4312yes—
310C2×C4×Q8—22no—
311C2×C4×Q8C2×D4311yescharacteristic
312C2×C4×D4—431no—
313#454—438no—
314#442—862no—
315#440—862no—
316C4×SD16—862no—
317C4×D8—862no—
318#428—432no—
319C2×#104—432no—
320C2×#104—432no—
321#418—432no—
322#417—432no—
323C2×#101—431no—
324C2×#101—431no—
325C4×M16—432no—
326#391—431no—
327#390—431no—
328#388—862no—
329#385—862no—
330#384—431no—
331#376—431no—
332#343—432no—
333#339—432no—
334#339—432no—
335C43#2147511yescharacteristic, complemented, Sylow
3362−1+4—24no—
3372−1+4—22no—
3382−1+4C4×D4314yescomplemented
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C22×D4312yes—
342C22×Q8—22no—
343C22×Q8C22×D4311yescharacteristic
344C22×D4—431no—
345C23×C4—861no—
346AGL(1,ℤ/8)—438no—
347AGL(1,ℤ/8)—864no—
348C2×SD16—862no—
349C2×D8—862no—
350C2×M16—432no—
351C2×M16—432no—
352#124—434no—
353#124—862no—
354C4×Q8—22no—
355C4×Q8—24no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8C22⋊D4312yes—
363C4×Q8C22⋊D4312yes—
364C4×D4—22no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—862no—
372C4×D4—862no—
373C4×D4C22⋊D4312yes—
374C4×D4C22⋊D4312yes—
375#117—24no—
376#117—24no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117C22×D4312yes—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4C22⋊D4312yes—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—861no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42C22⋊D4312yes—
395C2×C42C22×D4311yescharacteristic
396#107—862no—
397#106—862no—
398#104—438no—
399#104—864no—
400#103—862no—
401#102—862no—
402#102—862no—
403#102—862no—
404#101—434no—
405#101—862no—
406#97—862no—
407C4×C8—862no—
408#95—861no—
409#95—861no—
410#95—862no—
411C24—861no—
412#41—28no—
413#41—28no—
414#41—28no—
415#41—28no—
416#41—22no—
417#41—22no—
418#41C2×C4×D4314yes—
419#41#1062189814yes—
420C2×Q8—22no—
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8C2×C4×D4312yes—
426C2×Q8#1062189812yes—
427C2×Q8C2×C22⋊D4312yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—432no—
431C2×D4—862no—
432C2×D4—862no—
433C2×D4—861no—
434C2×D4C2×C22⋊D4312yes—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—3442no—
444C22×C4—1722no—
445C22×C4C2×C22⋊D4312yes—
446C22×C4C2×C22⋊D4312yes—
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450SD16—868no—
451D8—868no—
452M16—434no—
453M16—862no—
454M16—862no—
455M16—862no—
456C2×C8—862no—
457C2×C8—862no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—862no—
466C4⋊C4—3442no—
467C4⋊C4C2×C22⋊D4312yes—
468C4⋊C4C2×C22⋊D4312yes—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—868no—
474C22⋊C4—3442no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—24no—
478C42—24no—
479C42—22no—
480C42—22no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42—432no—
485C42—861no—
486C42—862no—
487C42C2×C22⋊D4312yes—
488C42C2×C22⋊D4312yes—
489C23—22no—
490C23—862no—
491C23—1722no—
492C23—1722no—
493C23—1721no—
494C23—1721no—
495C23C22×C22⋊D4311yescharacteristic
496Q8—28no—
497Q8—24no—
498Q8—24no—
499Q8—22no—
500Q8C4×C22⋊D4314yes—
501D4—28no—
502D4—24no—
503D4—24no—
504D4—22no—
505D4—864no—
506D4—1722no—
507D4C4×C22⋊D4314yes—
508C2×C4—216no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—84no—
523C2×C4—862no—
524C2×C4—3444no—
525C2×C4—1721no—
526C2×C4—1722no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4C4×C22⋊D4314yes—
533C2×C4#1306329411yescharacteristic
534C2×C4#1306329411yescharacteristic
535C2×C4#1306329412yes—
536C2×C4C22×C4×D4311yescharacteristic
537C2×C4C22×C22⋊D4312yes—
538C2×C4C2×#1062189812yes—
539C2×C4C2×#1062189811yescharacteristic
540C8—864no—
541C8—1722no—
542C22—21no—
543C22—21no—
544C22—24no—
545C22—42no—
546C22—42no—
547C22—3442no—
548C22—3441no—
549C22—3441no—
550C22—1724no—
551C22—1722no—
552C22C2×C4×C22⋊D4311yescharacteristic
553C22C2×#1306329411yescharacteristic
554C22#1458341011yescharacteristic
555C4—21no—
556C4—21no—
557C4—22no—
558C4—24no—
559C4—24no—
560C4—42no—
561C4—42no—
562C4—42no—
563C4—3441no—
564C4—3441no—
565C4—1722no—
566C4C2×C4×C22⋊D4312yes—
567C4#1458341012yes—
568C2—21no—
569C2—21no—
570C2—44no—
571C2—3442no—
572C2C4×#1306329411yescharacteristic
573C2#1914395911yescharacteristic
574C2#1914396711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×2−1+4×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583072C2
cosocleC22×C4×C43C24
hypercenterC4×2−1+4D43
hypocenterC43#21475
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#13063350C2semidirect
3. #19137302C2semidirect
4. #19134998C2semidirect
5. #19134971C2semidirect
6. #19134821C2semidirect
7. #19134810C2semidirect
8. #19134554C2semidirect
9. #19134405C2semidirect
10. C4×#13063244C2semidirect
11. C4×2−1+4×C43C2semidirect
15. #14583072C4semidirect
51. #13063350C2×C4semidirect
57. #13063314C2×C4semidirect
70. #13063252C2×C4semidirect
76. #13063244C2×C4semidirect
84. 2−1+4×C43C2×C4semidirect
281. C4×2−1+4D43semidirect
335. C43#21475semidirect
338. 2−1+4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830722
C4×#130633502
#191373022
#191349982
#191349712
#191348212
#191348102
#191345542
#191344052
C4×#130632442
C4×2−1+4×C432
#2147543