Finite Group Databasebeta

← #25253451

Subgroups — #25253451

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146282C211yesmaximal, characteristic, complemented
2#19136829C211yesmaximal, characteristic, complemented
3#19136797C211yesmaximal, characteristic, complemented
4#19136786C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136689C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136506C211yesmaximal, characteristic, complemented
11C4×#13063266C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136300C211yesmaximal, characteristic, complemented
14C2×#14582699C211yesmaximal, characteristic, complemented
15C43×#3339C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583545—21no—
19C2×#13063269C2211yescharacteristic, complemented
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23C22×C43⋊C16C2211yescharacteristic, complemented
24#14583283C2211yescharacteristic
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583115—21no—
28#14583052—21no—
29#14583046—21no—
30C4×D344C2211yescharacteristic
31#14582726C2211yescharacteristic, complemented
32#14582724C2211yescharacteristic, complemented
33#14582724C2211yescharacteristic, complemented
34C4⋊(C43⋊C16)C2211yescharacteristic, complemented
35#14582702C2211yescharacteristic, complemented
36#14582702C2211yescharacteristic, complemented
37#14582702C2211yescharacteristic, complemented
38#14582700C2211yescharacteristic, complemented
39#14582699C2211yescharacteristic
40#14582699C2211yescharacteristic
41#14582699C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic, complemented
47C4×C43⋊C16C2211yescharacteristic, complemented
48C43×#553—21no—
49C43×#499C2211yescharacteristic, complemented
50C43×#482—21no—
51C43×#481—21no—
52C43×#478—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic, complemented
55C4×D8×C43C2211yescharacteristic, complemented
56C8×D4×C43C2211yescharacteristic
57C43×#427C2211yescharacteristic, complemented
58C2×#107×C43C2211yescharacteristic
59C2×#10621898—21no—
60C22×D172—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621873—21no—
65C2×#10621873—21no—
66C2×D344—22no—
67C2×D344—21no—
68C2×D344—41no—
69C2×D344C2311yescharacteristic
70C2×D344C2311yescharacteristic
71#13063313—21no—
72#13063310—41no—
73#13063304—21no—
74#13063299—21no—
75#13063298—41no—
76#13063293—41no—
77C4×D172—21no—
78C22⋊C4×D43—41no—
79#13063269—41no—
80#13063266—22no—
81#13063266—41no—
82C2×C43⋊C16—41no—
83C2×C43⋊C16—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063247—21no—
91#13063247—21no—
92C2×D8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#126×C43—41no—
96#125×C43—21no—
97#123×C43—41no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101C4×D4×C43—21no—
102C4×D4×C43—41no—
103C4×D4×C43D411yescharacteristic
104#117×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113#102×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C2×D4×C43—41no—
123C2×D4×C43D811yescharacteristic
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130#10621898—42no—
131#10621898—81no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—41no—
135C2×D172—42no—
136C2×D172—81no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×Dic86—21no—
140D8×C43—21no—
141D8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2×D411yescharacteristic
149C2×C8×C43C2411yescharacteristic
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43—41no—
156C4⋊C4×C43D811yescharacteristic
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—41no—
160C22⋊C4×C43—41no—
161C22⋊C4×C43D811yescharacteristic
162C22⋊C4×C43D811yescharacteristic
163C42×C43—41no—
164C42×C43C2×D411yescharacteristic
165C22⋊Dic43—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—41no—
169(C2×D43)⋊C4—41no—
170C4⋊Dic43—21no—
171Dic43⋊C4—41no—
172Dic172—21no—
173Dic172—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—42no—
178D344#4112yes—
179#10621873—42no—
180#10621873—81no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—82no—
191C22×D43—82no—
192C22×D43—161no—
193D4×C43—22no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—82no—
197D4×C43—161no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—161no—
206C2×C4×C43—161no—
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C22⋊D43—82no—
213C22⋊D43—161no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216D172—22no—
217D172—41no—
218D172—41no—
219D172—41no—
220D172—82no—
221C4×D43—82no—
222C4×D43—161no—
223Dic86—41no—
224Dic86—41no—
225C8×C43—21no—
226C8×C43—21no—
227C8×C43—21no—
228C8×C43C2×#4111yescharacteristic
229C8×C43H(5,𝔽2)11yescharacteristic
230#33864—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#50812yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—42no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—164no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43—81no—
255C4×C43#54611yescharacteristic
256C4×C43#57711yescharacteristic
257Dic43—81no—
258Dic43—81no—
259#3339D4311yescharacteristic, complemented
260#3280—431no—
261#2242—431no—
262#2236—431no—
263#2234—431no—
264#2228—431no—
265#2217—431no—
266#2215—431no—
267#2210—431no—
268#2186—431no—
269#2184—431no—
270C4×D16—431no—
271D4×C16—431no—
272#2138—431no—
273C2×#357—431no—
274C2×C43—22no—
275C2×C43—41no—
276C2×C43—161no—
277C2×C43#329411yescharacteristic
278C2×C43C2×#50811yescharacteristic
279C2×C43#341511yescharacteristic
280D43—82no—
281D43—161no—
282C2×#135—431no—
283C22×D8—431no—
284#553—21no—
285#546—861no—
286C2×SD32—431no—
287C2×D16—431no—
288C2×D16—431no—
289C22×C16—431no—
290C22×C16—431no—
291#499C2×D4311yescharacteristic, complemented
292#495—431no—
293#482—21no—
294#481—21no—
295#478—21no—
296#467—431no—
297#466—431no—
298#466C2×D4311yescharacteristic
299#466C2×D4311yescharacteristic, complemented
300#463—861no—
301#450—861no—
302#449—861no—
303C4×D8—431no—
304C4×D8C2×D4311yescharacteristic, complemented
305C8×D4C2×D4311yescharacteristic
306#427C2×D4311yescharacteristic, complemented
307C2×#107C2×D4311yescharacteristic
308#367—431no—
309#366—431no—
310#366—431no—
311C4⋊C16—431no—
312#358—431no—
313#358—431no—
314#358—431no—
315#357—431no—
316#357—431no—
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322C22⋊C16—431no—
323C22⋊C16—431no—
324C4×C16—431no—
325C43#3386411yescharacteristic, complemented, Sylow
326C2×#41—861no—
327C22×D4—861no—
328#135—862no—
329#135—1721no—
330C2×Q16—431no—
331C2×SD16—861no—
332C2×SD16—861no—
333C2×D8—431no—
334C2×D8—431no—
335C2×D8—862no—
336C2×D8—861no—
337C2×D8—1721no—
338C2×D8C22×D4311yescharacteristic
339C22×C8C22×D4311yescharacteristic
340C22×C8C22×D4311yescharacteristic
341#126—41no—
342#125—21no—
343#124—861no—
344#123—41no—
345#123—1721no—
346C22⋊Q8—861no—
347#121—21no—
348#121—21no—
349#121—41no—
350#121—861no—
351#121—1721no—
352#120—1721no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4—861no—
356C4×D4C22⋊D4311yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359C2×C22⋊C4—1721no—
360SD32—1721no—
361D16—862no—
362D16—1721no—
363C2×C16—431no—
364C2×C16—431no—
365C2×C16—431no—
366C2×C16—431no—
367C2×C16—1721no—
368C2×C16—1721no—
369#107—21no—
370#107—431no—
371#107C22×D4311yescharacteristic
372#107C22×D4311yescharacteristic
373#107C22×D4311yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8C22⋊D4311yescharacteristic
377#103—861no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—861no—
382#102—861no—
383C22⋊C8C22⋊D4311yescharacteristic
384C22⋊C8C22⋊D4311yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C24—1721no—
387#41—3441no—
388#41—1722no—
389C2×Q8—861no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—861no—
394C2×D4—861no—
395C2×D4—3441no—
396C2×D4—1722no—
397C2×D4—1721no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4#1062188211yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4C2×C22⋊D4311yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407Q16—861no—
408Q16—861no—
409SD16—3441no—
410SD16—1722no—
411D8—21no—
412D8—21no—
413D8—432no—
414D8—861no—
415D8—861no—
416D8—861no—
417D8—1722no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×C22⋊D4311yescharacteristic
423C2×C8C2×C22⋊D4311yescharacteristic
424C2×C8C2×C22⋊D4311yescharacteristic
425C2×C8C23×D4311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—861no—
433C4⋊C4—1721no—
434C4⋊C4#1062188211yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4#1062188211yescharacteristic
445C22⋊C4#1062188211yescharacteristic
446C42—41no—
447C42C2×C22⋊D4311yescharacteristic
448C16—861no—
449C16—861no—
450C16—861no—
451C16—861no—
452C23—41no—
453C23—3442no—
454C23—3442no—
455C23—1721no—
456C23—1721no—
457C23—6881no—
458C23C2×#1062188211yescharacteristic
459C23C2×#1062188211yescharacteristic
460Q8—1721no—
461Q8—1721no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—161no—
467D4—862no—
468D4—3442no—
469D4—3442no—
470D4—1721no—
471D4—1721no—
472D4—1721no—
473D4—6881no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—161no—
482C2×C4—161no—
483C2×C4—3442no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—6881no—
487C2×C4C2×#1062188211yescharacteristic
488C2×C4C2×#1062188211yescharacteristic
489C2×C4C2×#1062188211yescharacteristic
490C2×C4C2×#1062188211yescharacteristic
491C2×C4C22×C22⋊D4311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D4311yescharacteristic
496C8#1306337111yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22—3441no—
509C22—3441no—
510C22—1722no—
511C22—6884no—
512C22#1458332912yes—
513C22C22×#1062188211yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—3441no—
522C4—3441no—
523C4#1458353711yescharacteristic
524C4#1458370711yescharacteristic
525C2—22no—
526C2—41no—
527C2—161no—
528C2—3442no—
529C2—6881no—
530C2#1914640211yescharacteristic
531C2C2×#1458332911yescharacteristic
532C2#1914773411yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3339C2
socleC22×C43C22×D8
hypercenter#3339D43
hypocenterC43#33864
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #19146282C2semidirect
2. #19136829C2semidirect
3. #19136797C2semidirect
4. #19136786C2semidirect
5. #19136749C2semidirect
6. #19136689C2semidirect
7. #19136679C2semidirect
8. #19136650C2semidirect
9. #19136516C2semidirect
10. #19136506C2semidirect
11. C4×#13063266C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136300C2semidirect
14. C2×#14582699C2semidirect
15. C43×#3339C2semidirect
19. C2×#13063269C22semidirect
23. C22×C43⋊C16C22semidirect
31. #14582726C22semidirect
32. #14582724C22semidirect
33. #14582724C22semidirect
34. C4⋊(C43⋊C16)C22semidirect
35. #14582702C22semidirect
36. #14582702C22semidirect
37. #14582702C22semidirect
38. #14582700C22semidirect
46. C22⋊(C43⋊C16)C22semidirect
47. C4×C43⋊C16C22semidirect
49. C43×#499C22semidirect
54. C43×#466C22semidirect
55. C4×D8×C43C22semidirect
57. C43×#427C22semidirect
259. #3339D43semidirect
291. #499C2×D43semidirect
299. #466C2×D43semidirect
304. C4×D8C2×D43semidirect
306. #427C2×D43semidirect
325. C43#33864semidirect

Maximal subgroups

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

subgroupindex
#191462822
#191368292
#191367972
#191367862
#191367492
#191366892
#191366792
#191366502
#191365162
#191365062
C4×#130632662
D4×C43⋊C162
#191363002
C2×#145826992
C43×#33392
#3386443