Finite Group Databasebeta

← #25252163

Subgroups — #25252163

Order 11008.

554 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145169C211yesmaximal, characteristic, complemented
2#19145160C211yesmaximal, characteristic, complemented
3#19136880C211yesmaximal, characteristic, complemented
4#19136858C211yesmaximal, characteristic, complemented
5#19136835C211yesmaximal, characteristic, complemented
6#19136830C211yesmaximal, characteristic, complemented
7#19136708C211yesmaximal, characteristic, complemented
8#19136706C211yesmaximal, characteristic, complemented
9#19136696C211yesmaximal, characteristic, complemented
10#19136450C211yesmaximal, characteristic, complemented
11#19136446C211yesmaximal, characteristic, complemented
12D16×Dic43C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14M32×Dic43C211yesmaximal, characteristic, complemented
15C43×#2218C211yesmaximal, characteristic, complemented
16#14583444—21no—
17#14583430—21no—
18C2×#13063270C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583300C2211yescharacteristic
24#14583282C2211yescharacteristic
25#14583274C2211yescharacteristic
26#14583252—21no—
27#14583244—21no—
28#14583140C2211yescharacteristic
29#14583135C2211yescharacteristic
30#14583133—21no—
31#14583126—21no—
32#14582993C2211yescharacteristic
33#14582990—21no—
34D8×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582979—21no—
38C2×C8×Dic43C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582702C2211yescharacteristic
44#14582701C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582674C2211yescharacteristic
49#14582674C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×D16×C43C2211yescharacteristic
53C2×M32×C43C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—41no—
60C2×Dic172C2311yescharacteristic
61C2×#10621883—21no—
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64C22×C43⋊C8D411yescharacteristic
65#13063324—21no—
66#13063321—21no—
67#13063318—41no—
68#13063316—21no—
69#13063312—21no—
70#13063311—41no—
71#13063306—41no—
72#13063304—21no—
73#13063299—21no—
74#13063297—41no—
75#13063290—21no—
76D4×Dic43—21no—
77D4×Dic43—21no—
78D4×Dic43—41no—
79#13063287—21no—
80(C22⋊D43)⋊C4—41no—
81#13063281—41no—
82C2×C4×Dic43D411yescharacteristic
83#13063270—22no—
84#13063269—22no—
85#13063266—22no—
86#13063265—22no—
87C2×C43⋊C16C2311yescharacteristic
88C2×C43⋊C16C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063256—21no—
93#13063250—21no—
94#13063248—21no—
95#13063247—21no—
96#13063246—21no—
97#13063246—21no—
98#13063245—21no—
99C8×Dic43D411yescharacteristic
100C8×Dic43D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×D8×C43C2311yescharacteristic
104C2×D8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106#121×C43—21no—
107#121×C43—21no—
108D16×C43—22no—
109M32×C43—22no—
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#102×C43—21no—
115#102×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C22×Dic43—41no—
125C22×Dic43—41no—
126C22×Dic43D811yescharacteristic
127C22×Dic43D811yescharacteristic
128#10621900—84no—
129C2×D172—21no—
130C2×C4×D43—41no—
131C2×Dic86—21no—
132C2×Dic86—41no—
133D8×C43—21no—
134D8×C43—21no—
135D8×C43—21no—
136D8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2411yescharacteristic
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149C22⋊Dic43—41no—
150#10621883—42no—
151#10621882—42no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161C4×Dic43—41no—
162C4×Dic43D811yescharacteristic
163C4×Dic43D811yescharacteristic
164C4×Dic43C2×D411yescharacteristic
165C4×Dic43C2×D411yescharacteristic
166C2×C43⋊C8—22no—
167C2×C43⋊C8C2×D411yescharacteristic
168C2×C43⋊C8C2×D411yescharacteristic
169Dic172—21no—
170Dic172—21no—
171D344—21no—
172D344—21no—
173C16×C43—21no—
174C16×C43#4112yescomplemented
175C43⋊C16—21no—
176C43⋊C16#4112yescomplemented
177C23×C43—41no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180C22×D43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—82no—
186D4×C43—82no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C22×D411yescharacteristic
193C22⋊D43—82no—
194C22⋊D43—82no—
195C22⋊D43—82no—
196C2×Dic43—22no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—82no—
202C2×Dic43—82no—
203C2×Dic43C2×D811yescharacteristic
204C2×Dic43C2×D811yescharacteristic
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207D172—41no—
208D172—41no—
209C4×D43—82no—
210Dic86—41no—
211Dic86—41no—
212Dic86—82no—
213C8×C43—21no—
214C8×C43C2×#4111yescharacteristic
215C8×C43C2×#4111yescharacteristic
216C43⋊C8—21no—
217C43⋊C8#13512yes—
218#33737—431nomaximal, Sylow
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—81no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43C22×D811yescharacteristic
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C4×C43—21no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43#53211yescharacteristic
236C4×C43C2×#13511yescharacteristic
237Dic43—21no—
238Dic43—21no—
239Dic43—21no—
240Dic43—81no—
241Dic43—81no—
242Dic43—81no—
243Dic43#50912yes—
244#3169—431no—
245#3168—431no—
246#2255—431no—
247#2250—431no—
248#2244—431no—
249#2243—431no—
250#2220—431no—
251#2220—431no—
252#2218—431no—
253#2218D4311yescharacteristic, complemented
254C4×SD32—431no—
255C4×SD32—431no—
256C4×D16—431no—
257C4×D16—431no—
258C4×M32—431no—
259C2×C43—41no—
260C2×C43—161no—
261C2×C43—161no—
262C2×C43#316911yescharacteristic
263C2×C43C2×#50911yescharacteristic
264C2×C43#341411yescharacteristic
265D43—161no—
266#532—861no—
267#529—861no—
268C2×SD32—431no—
269C2×SD32—431no—
270C2×D16—431no—
271C2×D16C2×D4311yescharacteristic
272C2×M32—431no—
273C2×M32C2×D4311yescharacteristic
274#500—431no—
275#499—431no—
276#495—431no—
277#493—431no—
278#488—861no—
279#486—861no—
280#467—431no—
281#466—431no—
282#466—861no—
283#466C2×D4311yescharacteristic
284#466C2×D4311yescharacteristic
285#465—861no—
286C4×Q16—431no—
287C4×SD16—861no—
288C4×D8—431no—
289C4×D8—431no—
290C4×D8—431no—
291C4×D8—861no—
292C2×C4×C8—431no—
293#367—431no—
294#367C2×D4311yescharacteristic
295#366—431no—
296#366—431no—
297#358—431no—
298#358—431no—
299#357—431no—
300#357—431no—
301#357—431no—
302#357—431no—
303#357C2×D4311yescharacteristic
304#357C2×D4311yescharacteristic
305#346—431no—
306#346—431no—
307C4×C16—431no—
308C4×C16—431no—
309C43#3373711yescharacteristic, complemented, Sylow
310C2×#41—1721no—
311C2×Q16—431no—
312C2×SD16—861no—
313C2×D8—431no—
314C2×D8—861no—
315C2×D8C22×D4311yescharacteristic
316C2×D8C22×D4311yescharacteristic
317C22×C8—431no—
318C22×C8C22×D4311yescharacteristic
319C4⋊Q8—861no—
320#127—861no—
321#126—1721no—
322#125—861no—
323#124—861no—
324#124—1721no—
325#123—1721no—
326C22⋊Q8—861no—
327#121—21no—
328#121—21no—
329#121—861no—
330#121—1721no—
331C4×Q8—861no—
332C4×D4—861no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—1721no—
336C4×D4—1721no—
337#117—1721no—
338C2×C42—431no—
339SD32—862no—
340SD32—862no—
341D16—22no—
342D16—862no—
343M32—22no—
344M32—862no—
345C2×C16—431no—
346C2×C16—431no—
347C2×C16C22×D4311yescharacteristic
348C2×C16C22×D4311yescharacteristic
349#107—431no—
350#107—431no—
351#107—861no—
352#107C22×D4311yescharacteristic
353#107C22×D4311yescharacteristic
354#106—861no—
355#103—861no—
356#103—861no—
357#102—21no—
358#102—21no—
359#102—861no—
360#102—861no—
361#102—861no—
362#102—861no—
363C4×C8—431no—
364C4×C8—431no—
365C4×C8—431no—
366C4×C8—431no—
367#41—3444no—
368C2×Q8—861no—
369C2×Q8—1721no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—861no—
375C2×D4—1721no—
376C2×D4—1721no—
377C2×D4—1721no—
378C22×C4—431no—
379C22×C4—431no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4D4×D4311yescharacteristic
384Q16—861no—
385Q16—861no—
386SD16—1722no—
387D8—21no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—861no—
392D8—861no—
393D8—1722no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—862no—
399C2×C8D4×D4311yescharacteristic
400C2×C8C23×D4311yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C42—431no—
420C42—431no—
421C42—431no—
422C42—431no—
423C42—1721no—
424C16—21no—
425C16—432no—
426C16—861no—
427C16#1062190012yescomplemented
428C23—41no—
429C23—41no—
430C23—1721no—
431C23D8×D4311yescharacteristic
432Q8—3442no—
433Q8—1721no—
434Q8—1721no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—82no—
440D4—82no—
441D4—3442no—
442D4—3442no—
443D4—3442no—
444D4—1721no—
445D4—1721no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—431no—
451C2×C4—431no—
452C2×C4—431no—
453C2×C4—431no—
454C2×C4—862no—
455C2×C4—3442no—
456C2×C4—3442no—
457C2×C4—3442no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4D8×D4311yescharacteristic
463C2×C4C2×D4×D4311yescharacteristic
464C8—21no—
465C8—432no—
466C8—861no—
467C8#41×D4311yescharacteristic
468C8C2×#1062190011yescharacteristic
469C22—21no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22C2×D8×D4311yescharacteristic
482C4—21no—
483C4—81no—
484C4—81no—
485C4—432no—
486C4—861no—
487C4—861no—
488C4—861no—
489C4—3441no—
490C4—3441no—
491C4—3441no—
492C4#1458344411yescharacteristic
493C4#135×D4311yescharacteristic
494C2—41no—
495C2—161no—
496C2—161no—
497C2—6881no—
498C2#1914516911yescharacteristic
499C2#509×D4311yescharacteristic
500C2#1914772711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2218C2
socleC22×C43C22×D8
hypercenter#2218D43
hypocenterC43#33737
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #19145169C2semidirect
2. #19145160C2semidirect
3. #19136880C2semidirect
4. #19136858C2semidirect
5. #19136835C2semidirect
6. #19136830C2semidirect
7. #19136708C2semidirect
8. #19136706C2semidirect
9. #19136696C2semidirect
10. #19136450C2semidirect
11. #19136446C2semidirect
12. D16×Dic43C2semidirect
13. #19136439C2semidirect
14. M32×Dic43C2semidirect
15. C43×#2218C2semidirect
174. C16×C43#41semidirect
176. C43⋊C16#41semidirect
253. #2218D43semidirect
309. C43#33737semidirect
427. C16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191451692
#191451602
#191368802
#191368582
#191368352
#191368302
#191367082
#191367062
#191366962
#191364502
#191364462
D16×Dic432
#191364392
M32×Dic432
C43×#22182
#3373743