Finite Group Databasebeta

← #25082007

Subgroups — #25082007

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144071C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic, complemented
3#19143703C211yesmaximal, characteristic, complemented
4#19134036C212yesmaximal, complemented
5#19134029C212yesmaximal, complemented
6#19133952C212yesmaximal, complemented
7#19133947C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582643C211yesmaximal, characteristic, complemented
11C43×#3205C211yesmaximal, characteristic, complemented
12C2×#13063351—21no—
13C2×#13063345—21no—
14C4×#10621898C2211yescharacteristic
15#14583118—21no—
16#14583111—21no—
17#14583106C2211yescharacteristic, complemented
18#14583101C2211yescharacteristic, complemented
19#14583096—21no—
20#14583096C2212yes—
21#14583096C2211yescharacteristic, complemented
22#14583091—21no—
23#14583091C2212yes—
24#14583091C2211yescharacteristic, complemented
25C8×Dic86C2212yescomplemented
26C8×D172C2212yescomplemented
27(C22⋊D43)⋊C8—22no—
28#14582951—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582904—21no—
34#14582895—21no—
35#14582652C2212yescomplemented
36#14582652C2212yescomplemented
37#14582645C2212yescomplemented
38#14582643C2212yes—
39#14582643C2212yes—
40#14582643C2212yescomplemented
41C43×#532C2211yescharacteristic
42C2×#127×C43C2211yescharacteristic
43C43×#493C2212yes—
44C43×#486C2212yes—
45C43×#459—21no—
46C43×#459—21no—
47C43×#447—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063351—44no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621883—22no—
54C2×#10621883—21no—
55C2×#10621884—21no—
56C2×#10621882—22no—
57C2×#10621882—21no—
58C2×#10621877—21no—
59C22×C43⋊C8—21no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62C4×Dic86D411yescharacteristic
63C4×Dic86C2311yescharacteristic
64C4×D172D411yescharacteristic
65C4×D172C2311yescharacteristic
66C4×C22⋊D43—21no—
67C4×C22⋊D43—21no—
68#13063284D411yescharacteristic
69#13063282—21no—
70C42×D43—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)C2312yes—
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2311yescharacteristic
77C4⋊(C43⋊C8)C2312yes—
78Dic43⋊C8—22no—
79#13063249—21no—
80#13063249—21no—
81#13063246—22no—
82#13063246—22no—
83#13063246—21no—
84#13063246—21no—
85(C2×D43)⋊C8—22no—
86C8×Dic43—22no—
87C2×#41×C43—21no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C2×D8×C43—22no—
92C2×D8×C43—22no—
93C4⋊Q8×C43C2311yescharacteristic
94#127×C43—21no—
95#127×C43—21no—
96#127×C43—21no—
97#127×C43C2312yes—
98#127×C43C2311yescharacteristic
99#124×C43—21no—
100#121×C43—21no—
101#121×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43D411yescharacteristic
107#102×C43—22no—
108#102×C43—22no—
109C22⋊C8×C43D412yes—
110C4×C8×C43C2312yes—
111C24×C43—41no—
112#41×C43—42no—
113#41×C43—42no—
114C2×Q8×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×D4×C43—42no—
126C2×D4×C43—42no—
127C2×D4×C43—81no—
128C2×D4×C43—81no—
129C2×D4×C43—82no—
130C22×C4×C43—41no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C2×C22⋊D43—21no—
135#10621898—22no—
136#10621898D814yescomplemented
137C2×D172C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×Dic86C2×D411yescharacteristic
142D8×C43—82no—
143D8×C43—82no—
144C2×C8×C43C2×D412yes—
145C2×C8×C43C2×D412yes—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154C22⋊Dic43—21no—
155#10621885—42no—
156#10621884—42no—
157#10621883—42no—
158#10621883—44no—
159#10621882—42no—
160#10621882—44no—
161(C2×D43)⋊C4—21no—
162(C2×D43)⋊C4—21no—
163C4⋊Dic43C2×D411yescharacteristic
164C4⋊Dic43C2×D411yescharacteristic
165Dic43⋊C4—21no—
166Dic43⋊C4—21no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169C4×Dic43—21no—
170#10621877—42no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—42no—
176C2×C43⋊C8—81no—
177C8×D43—82no—
178C23×C43—41no—
179C23×C43—42no—
180C23×C43—82no—
181C23×C43—82no—
182C23×C43—82no—
183C23×C43#12111yescharacteristic
184C22×D43—21no—
185Q8×C43—41no—
186Q8×C43—41no—
187D4×C43—42no—
188D4×C43—41no—
189D4×C43—42no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—42no—
193D4×C43—41no—
194D4×C43—42no—
195D4×C43—81no—
196D4×C43—82no—
197D4×C43—82no—
198D4×C43—82no—
199D4×C43—82no—
200D4×C43—82no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—82no—
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43#12111yescharacteristic
209C2×C4×C43C2×D812yes—
210C2×C4×C43#13512yes—
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C22⋊D43—24no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218D172—21no—
219D172C2×D812yes—
220C4×D43—24no—
221C4×D43—41no—
222C4×D43—41no—
223C4×D43—81no—
224Dic86—21no—
225Dic86C2×D812yes—
226C8×C43—22no—
227C8×C43—22no—
228C43⋊C8—41no—
229C43⋊C8—41no—
230C43⋊C8—42no—
231C43⋊C8—42no—
232#19410—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—82no—
236C22×C43—81no—
237C22×C43—82no—
238C22×C43—81no—
239C22×C43—82no—
240C22×C43—81no—
241C22×C43—164no—
242C22×C43#46612yes—
243C22×C43C2×#12111yescharacteristic
244C2×D43—22no—
245C2×D43—41no—
246C2×D43—41no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—81no—
251C4×C43#46612yes—
252C4×C43C22×D811yescharacteristic
253C4×C43C2×#13511yescharacteristic
254C4×C43#57611yescharacteristic
255C4×C43#57711yescharacteristic
256Dic43—22no—
257Dic43—41no—
258Dic43—41no—
259#3205D4311yescharacteristic, complemented
260#3038—431no—
261#3035—431no—
262#2988—431no—
263#1682—432no—
264#1681—432no—
265#1668—432no—
266#1667—432no—
267#1571—431no—
268#1547—431no—
269C2×#331—431no—
270C2×C43—22no—
271C2×C43—161no—
272C2×C43—162no—
273C2×C43#304511yescharacteristic
274C2×C43C2×#46611yescharacteristic
275C2×C43#306811yescharacteristic
276D43—42no—
277C2×AGL(1,ℤ/8)—861no—
278C2×#135—861no—
279#532C2×D4311yescharacteristic
280C2×#127C2×D4311yescharacteristic
281C4×#41—431no—
282#493C2×D4312yes—
283#486C2×D4312yes—
284#464—861no—
285#463—861no—
286#462—431no—
287#461—431no—
288#460—432no—
289#460—431no—
290#460—861no—
291#459—21no—
292#459—21no—
293#459—432no—
294#459—431no—
295#459—861no—
296#447—22no—
297C8×Q8—432no—
298C8×D4—432no—
299C8×D4—862no—
300#431—861no—
301#431C2×D4311yescharacteristic
302#423—431no—
303C2×C4⋊C8—431no—
304C2×C4⋊C8—431no—
305C2×C4⋊C8—861no—
306#418—861no—
307#416—861no—
308#335—432no—
309#335—432no—
310#332—432no—
311#331—432no—
312#331—432no—
313#331—432no—
314C43#1941011yescharacteristic, complemented, Sylow
315C2×#41—21no—
316C2×#41—431no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320AGL(1,ℤ/8)—1724no—
321#135—1724no—
322C2×Q16—861no—
323C2×SD16—861no—
324C2×SD16—862no—
325C2×SD16—861no—
326C2×D8—22no—
327C2×D8—22no—
328C2×D8—861no—
329C2×D8—862no—
330C2×M16—861no—
331C22×C8—861no—
332C22×C8—861no—
333C22×C8—862no—
334C4⋊Q8C22×D4311yescharacteristic
335#127—21no—
336#127—21no—
337#127—21no—
338#127C22×D4312yes—
339#127C22×D4311yescharacteristic
340#124—21no—
341#121—21no—
342#121—21no—
343C4×Q8—431no—
344C4×Q8—431no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—431no—
348C4×D4—431no—
349C4×D4—861no—
350C4×D4—861no—
351#117—431no—
352#117—861no—
353C2×C42—861no—
354C2×C42C22×D4311yescharacteristic
355C4⋊C8—432no—
356C4⋊C8—431no—
357C4⋊C8—431no—
358C4⋊C8—432no—
359C4⋊C8—862no—
360C4⋊C8—861no—
361C4⋊C8—861no—
362C4⋊C8—861no—
363C4⋊C8C22⋊D4311yescharacteristic
364C4⋊C8C22⋊D4311yescharacteristic
365#103—861no—
366#103—861no—
367#102—22no—
368#102—22no—
369#102—861no—
370#102—861no—
371#102—862no—
372#102—862no—
373C22⋊C8—862no—
374C22⋊C8C22⋊D4312yes—
375C4×C8—862no—
376C4×C8C22×D4312yes—
377C24—41no—
378#41—42no—
379#41—42no—
380#41—434no—
381#41—862no—
382C2×Q8—21no—
383C2×Q8—431no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—81no—
397C2×D4—81no—
398C2×D4—82no—
399C2×D4—431no—
400C2×D4—861no—
401C22×C4—41no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4D4×D4311yescharacteristic
406C22×C4#1062190011yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408Q16—1722no—
409SD16—1722no—
410SD16—1724no—
411SD16—1722no—
412D8—82no—
413D8—82no—
414D8—1722no—
415D8—1724no—
416M16—1722no—
417C2×C8—862no—
418C2×C8—861no—
419C2×C8—861no—
420C2×C8—862no—
421C2×C8—3442no—
422C2×C8—3441no—
423C2×C8—1722no—
424C2×C8C2×C22⋊D4312yes—
425C2×C8C2×C22⋊D4312yes—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—431no—
429C4⋊C4—431no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—861no—
435C22⋊C4—861no—
436C22⋊C4—861no—
437C42—861no—
438C42—861no—
439C42—861no—
440C42D4×D4311yescharacteristic
441C42#1062190011yescharacteristic
442C42C2×C22⋊D4311yescharacteristic
443C42C23×D4311yescharacteristic
444C23—41no—
445C23—42no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—861no—
450C23#1306329611yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—432no—
454Q8—861no—
455D4—42no—
456D4—41no—
457D4—42no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—42no—
463D4—82no—
464D4—81no—
465D4—82no—
466D4—82no—
467D4—82no—
468D4—82no—
469D4—432no—
470D4—864no—
471D4—861no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—861no—
478C2×C4—864no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—3441no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4#1306329611yescharacteristic
485C2×C4#1306329611yescharacteristic
486C2×C4#1306329611yescharacteristic
487C2×C4D8×D4312yes—
488C2×C4#1306334412yes—
489C2×C4C2×D4×D4311yescharacteristic
490C2×C4C22×C22⋊D4311yescharacteristic
491C2×C4C2×#1062190011yescharacteristic
492C8—22no—
493C8—22no—
494C8—1721no—
495C8—1721no—
496C8—1722no—
497C8—1722no—
498C22—21no—
499C22—21no—
500C22—82no—
501C22—81no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—82no—
506C22—164no—
507C22—862no—
508C22—1721no—
509C22—1721no—
510C22#1458313212yes—
511C22C2×#1306329611yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—81no—
516C4—862no—
517C4—1721no—
518C4—1721no—
519C4#1458313212yes—
520C4C2×D8×D4311yescharacteristic
521C4C2×#1306334411yescharacteristic
522C4#1458370211yescharacteristic
523C4#1458371011yescharacteristic
524C2—22no—
525C2—162no—
526C2—161no—
527C2—1722no—
528C2#1914413011yescharacteristic
529C2C2×#1458313211yescharacteristic
530C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3205C2
socleC22×C43C2×#121
hypercenter#3205D43
hypocenterC43#19410
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #19144071C2semidirect
2. #19144044C2semidirect
3. #19143703C2semidirect
4. #19134036C2semidirect
5. #19134029C2semidirect
6. #19133952C2semidirect
7. #19133947C2semidirect
8. #19133370C2semidirect
9. #19133272C2semidirect
10. C2×#14582643C2semidirect
11. C43×#3205C2semidirect
17. #14583106C22semidirect
18. #14583101C22semidirect
21. #14583096C22semidirect
24. #14583091C22semidirect
25. C8×Dic86C22semidirect
26. C8×D172C22semidirect
35. #14582652C22semidirect
36. #14582652C22semidirect
37. #14582645C22semidirect
40. #14582643C22semidirect
136. #10621898D8semidirect
259. #3205D43semidirect
314. C43#19410semidirect

Maximal subgroups

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

subgroupindex
#191440712
#191440442
#191437032
#191340362
#191340292
#191339522
#191339472
#191333702
#191332722
C2×#145826432
C43×#32052
#1941043