Finite Group Databasebeta

← #25253436

Subgroups — #25253436

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146282C211yesmaximal, characteristic
2#19136829C211yesmaximal, characteristic, complemented
3#19136792C211yesmaximal, characteristic, complemented
4#19136786C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136684C211yesmaximal, characteristic, complemented
8#19136657C211yesmaximal, characteristic, complemented
9#19136533C211yesmaximal, characteristic, complemented
10#19136523C211yesmaximal, characteristic, complemented
11C4×#13063268C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136300C211yesmaximal, characteristic, complemented
14C2×#14582699C211yesmaximal, characteristic, complemented
15C43×#3336C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583545—21no—
19C2×#13063271C2211yescharacteristic, complemented
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
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#14582726C2211yescharacteristic, complemented
33#14582724C2211yescharacteristic, complemented
34C4⋊(C43⋊C16)C2211yescharacteristic, complemented
35#14582703C2211yescharacteristic, complemented
36#14582702C2211yescharacteristic, complemented
37#14582702C2211yescharacteristic, complemented
38#14582702C2211yescharacteristic, 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×#552—21no—
49C43×#499C2211yescharacteristic, complemented
50C43×#485—21no—
51C43×#483—21no—
52C43×#479—21no—
53C43×#467C2211yescharacteristic
54C43×#467C2211yescharacteristic, complemented
55C4×Q16×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#13063271—41no—
80#13063268—22no—
81#13063268—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×Q16×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#126×C43—41no—
96#125×C43—21no—
97#125×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×D4×C43D411yescharacteristic
103#117×C43—21no—
104#117×C43—41no—
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#103×C43—21no—
114#103×C43—21no—
115#103×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C2×Q8×C43—21no—
121C2×D4×C43D811yescharacteristic
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127#10621898—42no—
128#10621898—81no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—41no—
132C2×D172—42no—
133C2×D172—81no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×Dic86—21no—
137Q16×C43—21no—
138Q16×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2411yescharacteristic
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43—41no—
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×C43D811yescharacteristic
161C22⋊C4×C43D811yescharacteristic
162C42×C43—41no—
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×C43C2×D811yescharacteristic
186C23×C43C2×D811yescharacteristic
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—82no—
190C22×D43—82no—
191C22×D43—161no—
192Q8×C43—41no—
193Q8×C43—41no—
194D4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—82no—
204C2×C4×C43C2×D811yescharacteristic
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C22⋊D43—82no—
210C22⋊D43—161no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213D172—22no—
214D172—41no—
215D172—41no—
216D172—41no—
217D172—82no—
218C4×D43—82no—
219C4×D43—161no—
220Dic86—41no—
221Dic86—41no—
222C8×C43—21no—
223C8×C43—21no—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43H(5,𝔽2)11yescharacteristic
227#33863—431nomaximal, Sylow
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43#50812yes—
234C22×C43C22×D811yescharacteristic
235C2×D43—42no—
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—164no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—81no—
247C4×C43—81no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43#54611yescharacteristic
251C4×C43#57711yescharacteristic
252Dic43—81no—
253Dic43—81no—
254#3336D4311yescharacteristic, complemented
255#3280—431no—
256#2242—431no—
257#2235—431no—
258#2234—431no—
259#2228—431no—
260#2217—431no—
261#2216—431no—
262#2211—431no—
263#2189—431no—
264#2187—431no—
265C4×SD32—431no—
266D4×C16—431no—
267#2138—431no—
268C2×#357—431no—
269C2×C43—22no—
270C2×C43—41no—
271C2×C43#329411yescharacteristic
272C2×C43C2×#50811yescharacteristic
273C2×C43#341611yescharacteristic
274D43—82no—
275D43—161no—
276C2×#135—431no—
277C22×D8—431no—
278#552—21no—
279#546—861no—
280C2×Q32—431no—
281C2×SD32—431no—
282C2×SD32—431no—
283C22×C16—431no—
284C22×C16—431no—
285#499C2×D4311yescharacteristic, complemented
286#495—431no—
287#485—21no—
288#483—21no—
289#479—21no—
290#467—431no—
291#467C2×D4311yescharacteristic
292#467C2×D4311yescharacteristic, complemented
293#466—431no—
294#463—861no—
295#450—861no—
296#449—861no—
297C4×Q16C2×D4311yescharacteristic, complemented
298C4×D8—431no—
299C8×D4C2×D4311yescharacteristic
300#427C2×D4311yescharacteristic, complemented
301C2×#107C2×D4311yescharacteristic
302#367—431no—
303#367—431no—
304#366—431no—
305C4⋊C16—431no—
306#358—431no—
307#358—431no—
308#358—431no—
309#358—431no—
310#357—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357—431no—
315#357—431no—
316C22⋊C16—431no—
317C22⋊C16—431no—
318C4×C16—431no—
319C43#3386311yescharacteristic, complemented, Sylow
320C2×#41—861no—
321C22×D4—861no—
322#135—862no—
323#135—1721no—
324C2×Q16—431no—
325C2×Q16C22×D4311yescharacteristic
326C2×SD16—861no—
327C2×SD16—861no—
328C2×D8—431no—
329C2×D8—431no—
330C2×D8—862no—
331C2×D8—861no—
332C2×D8—1721no—
333C22×C8C22×D4311yescharacteristic
334C22×C8C22×D4311yescharacteristic
335#126—41no—
336#125—21no—
337#125—41no—
338#124—861no—
339#123—41no—
340#123—1721no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—861no—
344#121—861no—
345#121—1721no—
346#120—1721no—
347C4×Q8—21no—
348C4×D4—861no—
349C4×D4C22⋊D4311yescharacteristic
350#117—21no—
351#117—41no—
352C2×C4⋊C4—21no—
353C2×C22⋊C4—1721no—
354Q32—1721no—
355SD32—862no—
356SD32—1721no—
357C2×C16—431no—
358C2×C16—431no—
359C2×C16—431no—
360C2×C16—431no—
361C2×C16—1721no—
362C2×C16—1721no—
363#107—21no—
364#107—431no—
365#107C22×D4311yescharacteristic
366#107C22×D4311yescharacteristic
367#107C22×D4311yescharacteristic
368#106—21no—
369#106—21no—
370C4⋊C8C22⋊D4311yescharacteristic
371#103—21no—
372#103—21no—
373#103—21no—
374#103—861no—
375#102—861no—
376#102—861no—
377C22⋊C8C22⋊D4311yescharacteristic
378C22⋊C8C22⋊D4311yescharacteristic
379C4×C8C22×D4311yescharacteristic
380C24—1721no—
381#41—3441no—
382#41—1722no—
383C2×Q8—21no—
384C2×Q8—861no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—3441no—
388C2×D4—1722no—
389C2×D4—1721no—
390C2×D4—1721no—
391C2×D4—1721no—
392C2×D4#1062188211yescharacteristic
393C22×C4—41no—
394C22×C4—1721no—
395C22×C4—1721no—
396C22×C4C2×C22⋊D4311yescharacteristic
397C22×C4C2×C22⋊D4311yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—861no—
401Q16—861no—
402SD16—3441no—
403SD16—1722no—
404D8—432no—
405D8—861no—
406D8—861no—
407D8—861no—
408D8—1722no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×C22⋊D4311yescharacteristic
414C2×C8C2×C22⋊D4311yescharacteristic
415C2×C8C2×C22⋊D4311yescharacteristic
416C2×C8C23×D4311yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—861no—
427C4⋊C4—1721no—
428C4⋊C4#1062188211yescharacteristic
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4#1062188211yescharacteristic
438C22⋊C4#1062188211yescharacteristic
439C42—41no—
440C42—41no—
441C42C2×C22⋊D4311yescharacteristic
442C16—861no—
443C16—861no—
444C16—861no—
445C16—861no—
446C23—3442no—
447C23—3442no—
448C23—1721no—
449C23—1721no—
450C23—6881no—
451C23C2×#1062188211yescharacteristic
452C23C2×#1062188211yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—1721no—
456Q8—1721no—
457D4—22no—
458D4—862no—
459D4—3442no—
460D4—3442no—
461D4—1721no—
462D4—1721no—
463D4—1721no—
464D4—6881no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—3442no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—6881no—
478C2×C4C2×#1062188211yescharacteristic
479C2×C4C2×#1062188211yescharacteristic
480C2×C4C2×#1062188211yescharacteristic
481C2×C4C2×#1062188211yescharacteristic
482C2×C4C22×C22⋊D4311yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8#41×D4311yescharacteristic
487C8#1306337111yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—3441no—
494C22—3441no—
495C22—3441no—
496C22—3441no—
497C22—3441no—
498C22—1722no—
499C22—6884no—
500C22#1458332912yes—
501C22C22×#1062188211yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—3441no—
511C4—3441no—
512C4#1458353711yescharacteristic
513C4#1458370711yescharacteristic
514C2—22no—
515C2—41no—
516C2—3442no—
517C2—6881no—
518C2#1914640211yescharacteristic
519C2C2×#1458332911yescharacteristic
520C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3336C2
socleC22×C43C22×D8
prime radical#19146282C2
hypercenter#3336D43
hypocenterC43#33863
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #19136829C2semidirect
3. #19136792C2semidirect
4. #19136786C2semidirect
5. #19136749C2semidirect
6. #19136693C2semidirect
7. #19136684C2semidirect
8. #19136657C2semidirect
9. #19136533C2semidirect
10. #19136523C2semidirect
11. C4×#13063268C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136300C2semidirect
14. C2×#14582699C2semidirect
15. C43×#3336C2semidirect
19. C2×#13063271C22semidirect
23. C22×C43⋊C16C22semidirect
31. #14582726C22semidirect
32. #14582726C22semidirect
33. #14582724C22semidirect
34. C4⋊(C43⋊C16)C22semidirect
35. #14582703C22semidirect
36. #14582702C22semidirect
37. #14582702C22semidirect
38. #14582702C22semidirect
46. C22⋊(C43⋊C16)C22semidirect
47. C4×C43⋊C16C22semidirect
49. C43×#499C22semidirect
54. C43×#467C22semidirect
55. C4×Q16×C43C22semidirect
57. C43×#427C22semidirect
254. #3336D43semidirect
285. #499C2×D43semidirect
292. #467C2×D43semidirect
297. C4×Q16C2×D43semidirect
300. #427C2×D43semidirect
319. C43#33863semidirect

Maximal subgroups

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

subgroupindex
#191462822
#191368292
#191367922
#191367862
#191367492
#191366932
#191366842
#191366572
#191365332
#191365232
C4×#130632682
D4×C43⋊C162
#191363002
C2×#145826992
C43×#33362
#3386343