Finite Group Databasebeta

← #25252174

Subgroups — #25252174

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145176C211yesmaximal, characteristic, complemented
2#19145166C211yesmaximal, characteristic
3#19136880C211yesmaximal, characteristic, complemented
4#19136863C211yesmaximal, characteristic, complemented
5#19136839C211yesmaximal, characteristic, complemented
6#19136833C211yesmaximal, characteristic, complemented
7#19136710C211yesmaximal, characteristic
8#19136708C211yesmaximal, characteristic
9#19136701C211yesmaximal, characteristic, complemented
10Q32×Dic43C211yesmaximal, characteristic, complemented
11#19136451C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136444C211yesmaximal, characteristic, complemented
14M32×Dic43C211yesmaximal, characteristic, complemented
15C43×#2219C211yesmaximal, characteristic, complemented
16#14583451—21no—
17#14583435—21no—
18C2×#13063271C2211yescharacteristic
19C2×#13063270C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583300C2211yescharacteristic
24#14583284C2211yescharacteristic
25#14583277C2211yescharacteristic
26#14583255—21no—
27#14583248—21no—
28#14583140C2211yescharacteristic
29#14583138—21no—
30#14583135C2211yescharacteristic
31#14583130—21no—
32Q16×Dic43C2211yescharacteristic
33Q16×Dic43C2211yescharacteristic
34#14582993C2211yescharacteristic
35#14582991—21no—
36#14582984—21no—
37#14582981C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582702C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582674C2211yescharacteristic
49#14582674C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×Q32×C43C2211yescharacteristic
53C2×M32×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#358C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C2×#10621884—21no—
62C2×D344C2311yescharacteristic
63C22×C43⋊C8D411yescharacteristic
64#13063324—21no—
65#13063323—21no—
66#13063320—41no—
67#13063316—21no—
68#13063315—41no—
69#13063314—21no—
70#13063309—41no—
71#13063304—21no—
72#13063302—41no—
73#13063299—21no—
74Q8×Dic43—21no—
75Q8×Dic43—21no—
76#13063290—21no—
77#13063290—41no—
78#13063287—21no—
79(C22⋊D43)⋊C4—41no—
80#13063283—41no—
81#13063281—41no—
82C2×C4×Dic43D411yescharacteristic
83#13063271—22no—
84#13063270—22no—
85#13063268—22no—
86#13063265—22no—
87C2×C43⋊C16C2311yescharacteristic
88C2×C43⋊C16C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063256—21no—
93#13063250—21no—
94#13063249—21no—
95#13063249—21no—
96#13063248—21no—
97#13063247—21no—
98#13063245—21no—
99C8×Dic43D411yescharacteristic
100C8×Dic43D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×Q16×C43C2311yescharacteristic
104C2×Q16×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22⋊Q8×C43—21no—
107C22⋊Q8×C43—21no—
108Q32×C43—22no—
109M32×C43—22no—
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#103×C43—21no—
115#103×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C2×C22⋊D43—41no—
120C22×Dic43D811yescharacteristic
121C22×Dic43D811yescharacteristic
122C2×D172—21no—
123C2×C4×D43—41no—
124C2×Dic86—21no—
125C2×Dic86—41no—
126Q16×C43—21no—
127Q16×C43—21no—
128Q16×C43—21no—
129Q16×C43—21no—
130C2×C8×C43—21no—
131C2×C8×C43—21no—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2411yescharacteristic
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C22⋊C4×C43—41no—
140C22⋊Dic43—41no—
141#10621885—42no—
142#10621884—42no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158C4×Dic43—41no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43D811yescharacteristic
162C4×Dic43D811yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164C4×Dic43C2×D411yescharacteristic
165C2×C43⋊C8—22no—
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168Dic172—21no—
169Dic172—21no—
170D344—21no—
171D344—21no—
172C16×C43—21no—
173C16×C43#4112yes—
174C43⋊C16—21no—
175C43⋊C16#4112yes—
176C23×C43C2×D811yescharacteristic
177C22×D43—41no—
178Q8×C43—41no—
179Q8×C43—41no—
180Q8×C43—41no—
181Q8×C43—41no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C22⋊D43—82no—
191C2×Dic43—22no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43C2×D811yescharacteristic
197C2×Dic43C2×D811yescharacteristic
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200D172—41no—
201D172—41no—
202C4×D43—82no—
203Dic86—41no—
204Dic86—41no—
205Dic86—82no—
206C8×C43—21no—
207C8×C43C2×#4111yescharacteristic
208C8×C43C2×#4111yescharacteristic
209C43⋊C8—21no—
210C43⋊C8#13512yes—
211#33738—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43C22×D811yescharacteristic
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—81no—
219C4×C43—21no—
220C4×C43—81no—
221C4×C43—81no—
222C4×C43—81no—
223C4×C43—81no—
224C4×C43#53211yescharacteristic
225C4×C43C2×#13511yescharacteristic
226Dic43—21no—
227Dic43—21no—
228Dic43—21no—
229Dic43—81no—
230Dic43—81no—
231Dic43—81no—
232Dic43#51012yes—
233#3170—431no—
234#3168—431no—
235#2255—431no—
236#2251—431no—
237#2245—431no—
238#2243—431no—
239#2220—431no—
240#2220—431no—
241#2219—431no—
242#2219D4311yescharacteristic, complemented
243C4×Q32—431no—
244C4×Q32—431no—
245C4×SD32—431no—
246C4×SD32—431no—
247C4×M32—431no—
248C2×C43—41no—
249C2×C43#316911yescharacteristic
250C2×C43C2×#51011yescharacteristic
251C2×C43#341411yescharacteristic
252D43—161no—
253#533—861no—
254#529—861no—
255C2×Q32—431no—
256C2×Q32C2×D4311yescharacteristic
257C2×SD32—431no—
258C2×SD32—431no—
259C2×M32—431no—
260C2×M32C2×D4311yescharacteristic
261#500—431no—
262#499—431no—
263#495—431no—
264#494—431no—
265#488—861no—
266#487—861no—
267#467—431no—
268#467—861no—
269#467C2×D4311yescharacteristic
270#467C2×D4311yescharacteristic
271#466—431no—
272#465—861no—
273C4×Q16—431no—
274C4×Q16—431no—
275C4×Q16—431no—
276C4×Q16—861no—
277C4×SD16—861no—
278C4×D8—431no—
279C2×C4×C8—431no—
280#367—431no—
281#367C2×D4311yescharacteristic
282#366—431no—
283#366—431no—
284#358—431no—
285#358—431no—
286#358—431no—
287#358—431no—
288#358C2×D4311yescharacteristic
289#358C2×D4311yescharacteristic
290#357—431no—
291#357—431no—
292#346—431no—
293#346—431no—
294C4×C16—431no—
295C4×C16—431no—
296C43#3373811yescharacteristic, complemented, Sylow
297C2×Q16—431no—
298C2×Q16—861no—
299C2×Q16C22×D4311yescharacteristic
300C2×Q16C22×D4311yescharacteristic
301C2×SD16—861no—
302C2×D8—431no—
303C22×C8—431no—
304C22×C8C22×D4311yescharacteristic
305C4⋊Q8—861no—
306C4⋊Q8—861no—
307#126—1721no—
308#125—861no—
309#125—1721no—
310#124—861no—
311#123—1721no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—861no—
315C22⋊Q8—1721no—
316#121—861no—
317C4×Q8—861no—
318C4×Q8—861no—
319C4×Q8—861no—
320C4×Q8—1721no—
321C4×D4—861no—
322C4×D4—1721no—
323#117—1721no—
324#117—1721no—
325C2×C42—431no—
326Q32—22no—
327Q32—862no—
328SD32—862no—
329SD32—862no—
330M32—22no—
331M32—862no—
332C2×C16—431no—
333C2×C16—431no—
334C2×C16C22×D4311yescharacteristic
335C2×C16C22×D4311yescharacteristic
336#107—431no—
337#107—431no—
338#107—861no—
339#107C22×D4311yescharacteristic
340#107C22×D4311yescharacteristic
341#106—861no—
342#103—21no—
343#103—21no—
344#103—861no—
345#103—861no—
346#103—861no—
347#103—861no—
348#102—861no—
349#102—861no—
350C4×C8—431no—
351C4×C8—431no—
352C4×C8—431no—
353C4×C8—431no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—861no—
357C2×Q8—1721no—
358C2×D4—861no—
359C2×D4—1721no—
360C22×C4—431no—
361C22×C4—431no—
362C22×C4—1721no—
363C22×C4D4×D4311yescharacteristic
364Q16—21no—
365Q16—21no—
366Q16—21no—
367Q16—21no—
368Q16—861no—
369Q16—861no—
370Q16—1722no—
371SD16—1722no—
372D8—861no—
373D8—861no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—431no—
377C2×C8—431no—
378C2×C8—862no—
379C2×C8D4×D4311yescharacteristic
380C2×C8C23×D4311yescharacteristic
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C4⋊C4—1721no—
390C4⋊C4—1721no—
391C4⋊C4—1721no—
392C4⋊C4—1721no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—1721no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C42—431no—
404C42—431no—
405C42—431no—
406C42—431no—
407C42—1721no—
408C42—1721no—
409C42—1721no—
410C16—21no—
411C16—432no—
412C16—861no—
413C16#1062190012yes—
414C23—1721no—
415C23D8×D4311yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—3442no—
421Q8—1721no—
422Q8—1721no—
423D4—3442no—
424D4—1721no—
425D4—1721no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—431no—
433C2×C4—431no—
434C2×C4—431no—
435C2×C4—431no—
436C2×C4—862no—
437C2×C4—3442no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4D8×D4311yescharacteristic
443C2×C4C2×D4×D4311yescharacteristic
444C8—21no—
445C8—432no—
446C8—861no—
447C8#41×D4311yescharacteristic
448C8C2×#1062190011yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22C2×D8×D4311yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—432no—
462C4—861no—
463C4—861no—
464C4—861no—
465C4—3441no—
466C4—3441no—
467C4—3441no—
468C4#1458344411yescharacteristic
469C4#135×D4311yescharacteristic
470C2—41no—
471C2—6881no—
472C2#1914516911yescharacteristic
473C2#510×D4311yescharacteristic
474C2#1914773011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2219C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#2219D43
hypocenterC43#33738
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
1. #19145176C2semidirect
3. #19136880C2semidirect
4. #19136863C2semidirect
5. #19136839C2semidirect
6. #19136833C2semidirect
9. #19136701C2semidirect
10. Q32×Dic43C2semidirect
11. #19136451C2semidirect
12. #19136446C2semidirect
13. #19136444C2semidirect
14. M32×Dic43C2semidirect
15. C43×#2219C2semidirect
242. #2219D43semidirect
296. C43#33738semidirect

Maximal subgroups

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

subgroupindex
#191451762
#191451662
#191368802
#191368632
#191368392
#191368332
#191367102
#191367082
#191367012
Q32×Dic432
#191364512
#191364462
#191364442
M32×Dic432
C43×#22192
#3373843