Finite Group Databasebeta

← #25254257

Subgroups — #25254257

Order 11008.

486 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147583C211yesmaximal, characteristic, complemented
2#19147462C211yesmaximal, characteristic, complemented
3#19136828C211yesmaximal, characteristic, complemented
4#19136827C211yesmaximal, characteristic, complemented
5#19136821C211yesmaximal, characteristic, complemented
6#19136762C211yesmaximal, characteristic, complemented
7#19136759C211yesmaximal, characteristic, complemented
8#19136741C211yesmaximal, characteristic, complemented
9#19136652C211yesmaximal, characteristic
10#19136650C211yesmaximal, characteristic
11#19136638C211yesmaximal, characteristic, complemented
12C16×Dic86C211yesmaximal, characteristic, complemented
13#19136450C211yesmaximal, characteristic, complemented
14#19136439C211yesmaximal, characteristic
15C4×SD32×C43C211yesmaximal, characteristic, complemented
16#14583621—21no—
17#14583608—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583284C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583277C2211yescharacteristic
26#14583201—21no—
27#14583199—21no—
28#14583187—21no—
29#14583124—21no—
30#14583121—21no—
31#14583103—21no—
32C8×Dic86C2211yescharacteristic
33#14582993C2211yescharacteristic
34D8×Dic43C2211yescharacteristic
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582726C2211yescharacteristic
38#14582724C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40Dic43⋊C16C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582702C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582699C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C43×#367C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621885—21no—
61C2×#10621873—21no—
62C2×#10621884—21no—
63C2×D344C2311yescharacteristic
64#13063324—21no—
65#13063323—21no—
66#13063320—41no—
67#13063319—41no—
68#13063317—21no—
69#13063316—21no—
70#13063314—21no—
71#13063313—21no—
72#13063304—41no—
73#13063303—41no—
74#13063302—41no—
75#13063302—41no—
76C4×Dic86D411yescharacteristic
77#13063290—21no—
78D4×Dic43—21no—
79D4×Dic43—21no—
80#13063287—21no—
81#13063282—41no—
82C2×Dic43⋊C4—41no—
83#13063269—22no—
84#13063266—22no—
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063257—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)D411yescharacteristic
93Dic43⋊C8D411yescharacteristic
94Dic43⋊C8D411yescharacteristic
95#13063248—21no—
96#13063246—21no—
97#13063246—21no—
98#13063245—21no—
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C2×Q16×C43C2311yescharacteristic
102C2×D8×C43C2311yescharacteristic
103C4×Q8×C43—21no—
104C4×D4×C43—21no—
105SD32×C43—22no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#103×C43—21no—
111#102×C43—21no—
112C4×C8×C43C2311yescharacteristic
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C22×C4×C43—41no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C2×D172—21no—
119C2×C4×D43—41no—
120C2×Dic86—21no—
121C2×Dic86—41no—
122C2×Dic86D811yescharacteristic
123Q16×C43—21no—
124Q16×C43—21no—
125D8×C43—21no—
126D8×C43#4112yes—
127C2×C8×C43C2×D411yescharacteristic
128C2×C8×C43C2411yescharacteristic
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C42×C43—41no—
134C42×C43C2×D411yescharacteristic
135C22⋊Dic43—41no—
136C22⋊Dic43—41no—
137#10621885—81no—
138#10621884—81no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—41no—
147C4⋊Dic43D811yescharacteristic
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4D811yescharacteristic
156Dic43⋊C4D811yescharacteristic
157C4×Dic43—41no—
158C4×Dic43C2×D411yescharacteristic
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162Dic172—21no—
163Dic172—21no—
164D344—21no—
165D344—21no—
166#10621873—81no—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C22×D43—41no—
173Q8×C43—41no—
174Q8×C43—41no—
175D4×C43—22no—
176D4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—161no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43C22×D411yescharacteristic
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—82no—
188C2×Dic43—161no—
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193D172—41no—
194D172—41no—
195C4×D43—82no—
196Dic86—22no—
197Dic86—41no—
198Dic86—41no—
199Dic86—161no—
200C8×C43—21no—
201C8×C43C2×#4111yescharacteristic
202C8×C432−1+411yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33927—431nomaximal, Sylow
206C22×C43—42no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43C22×D811yescharacteristic
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43#54811yescharacteristic
219C4×C43#57711yescharacteristic
220Dic43—21no—
221Dic43—21no—
222Dic43—21no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43#50812yes—
227#3393—431no—
228#3380—431no—
229#2242—431no—
230#2242—431no—
231#2241—431no—
232#2229—431no—
233#2229—431no—
234#2226—431no—
235#2210—431no—
236#2210—431no—
237#2208—431no—
238Q8×C16—431no—
239C4×SD32—431no—
240C4×SD32D4311yescharacteristic, complemented
241C4×D16—431no—
242C2×C43—82no—
243C2×C43#335811yescharacteristic
244C2×C43C2×#50811yescharacteristic
245C2×C43#341611yescharacteristic
246D43—161no—
247#556—861no—
248#554—861no—
249C2×SD32—431no—
250C2×SD32C2×D4311yescharacteristic
251C2×D16—431no—
252#500—431no—
253#499—431no—
254#499—431no—
255#495—431no—
256#495—431no—
257#494—431no—
258#478—861no—
259#478—861no—
260#476—861no—
261#464—861no—
262#464—861no—
263#461—861no—
264C8×Q8—431no—
265C4×Q16—431no—
266C4×Q16C2×D4311yescharacteristic
267C4×D8—431no—
268C4×D8—431no—
269C4×D8—431no—
270C4×D8C2×D4311yescharacteristic
271#367—431no—
272#367C2×D4311yescharacteristic
273#366—431no—
274C4⋊C16—431no—
275C4⋊C16—431no—
276C4⋊C16—431no—
277#358—431no—
278#358—431no—
279#358—431no—
280#358—431no—
281#358—431no—
282#358C2×D4311yescharacteristic
283#357—431no—
284#357—431no—
285#357—431no—
286#357C2×D4311yescharacteristic
287C4×C16—431no—
288C4×C16—431no—
289C4×C16C2×D4311yescharacteristic
290C43#3392711yescharacteristic, complemented, Sylow
291C2×Q16—431no—
292C2×Q16—861no—
293C2×Q16C22×D4311yescharacteristic
294C2×SD16—861no—
295C2×SD16—861no—
296C2×D8—431no—
297C2×D8C22×D4311yescharacteristic
298C4⋊Q8—861no—
299C4⋊Q8—861no—
300#126—1721no—
301#126—1721no—
302#125—861no—
303#125—861no—
304#124—861no—
305#124—861no—
306C22⋊Q8—1721no—
307C22⋊Q8—1721no—
308C22⋊Q8—1721no—
309C22⋊Q8—1721no—
310C4×Q8—21no—
311C4×Q8—431no—
312C4×Q8—861no—
313C4×D4—21no—
314C4×D4—861no—
315C4×D4—861no—
316C4×D4—861no—
317#117—1721no—
318C2×C4⋊C4—1721no—
319SD32—22no—
320SD32—862no—
321D16—862no—
322C2×C16—431no—
323C2×C16—431no—
324C2×C16C22×D4311yescharacteristic
325C2×C16C22×D4311yescharacteristic
326#107—431no—
327#107—431no—
328#107—861no—
329#107C22×D4311yescharacteristic
330#107C22×D4311yescharacteristic
331#106—861no—
332#106—861no—
333C4⋊C8—431no—
334C4⋊C8—431no—
335C4⋊C8—431no—
336#103—21no—
337#103—861no—
338#102—21no—
339#102—861no—
340#102—861no—
341#102—861no—
342C4×C8—431no—
343C4×C8—431no—
344C4×C8C22×D4311yescharacteristic
345C2×Q8—21no—
346C2×Q8—431no—
347C2×Q8—861no—
348C2×Q8—1721no—
349C2×D4—21no—
350C2×D4—861no—
351C22×C4—41no—
352C22×C4—1721no—
353C22×C4—1721no—
354C22×C4—1721no—
355Q16—21no—
356Q16—21no—
357Q16—861no—
358Q16—861no—
359Q16—3441no—
360SD16—3441no—
361SD16—3441no—
362D8—21no—
363D8—861no—
364D8—861no—
365D8#1062189812yes—
366C2×C8—431no—
367C2×C8—431no—
368C2×C8D4×D4311yescharacteristic
369C2×C8C23×D4311yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—431no—
374C4⋊C4—431no—
375C4⋊C4—431no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C22⋊C4—41no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C42—41no—
395C42—431no—
396C42—431no—
397C42—1721no—
398C42D4×D4311yescharacteristic
399C16—21no—
400C16—21no—
401C16—861no—
402C16—861no—
403C23—41no—
404C23—1721no—
405Q8—41no—
406Q8—41no—
407Q8—862no—
408Q8—1721no—
409Q8—1721no—
410Q8—6881no—
411D4—22no—
412D4—41no—
413D4—1721no—
414D4—1721no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—161no—
419C2×C4—431no—
420C2×C4—431no—
421C2×C4—431no—
422C2×C4—431no—
423C2×C4—3442no—
424C2×C4—3442no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—6881no—
429C2×C4D8×D4311yescharacteristic
430C2×C4D8×D4311yescharacteristic
431C2×C4C2×D4×D4311yescharacteristic
432C8—21no—
433C8—861no—
434C8—861no—
435C8C2×#1062189811yescharacteristic
436C8#1306337211yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—3441no—
441C22—3441no—
442C22—3441no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—432no—
450C4—861no—
451C4—861no—
452C4—861no—
453C4—3441no—
454C4—3441no—
455C4—3441no—
456C4#1458355811yescharacteristic
457C4#1458370611yescharacteristic
458C2—82no—
459C2—6881no—
460C2#1914722811yescharacteristic
461C2#508×D4311yescharacteristic
462C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radicalC2×#13063266C22
hypercenterC4×SD32D43
hypocenterC43#33927
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #19147583C2semidirect
2. #19147462C2semidirect
3. #19136828C2semidirect
4. #19136827C2semidirect
5. #19136821C2semidirect
6. #19136762C2semidirect
7. #19136759C2semidirect
8. #19136741C2semidirect
11. #19136638C2semidirect
12. C16×Dic86C2semidirect
13. #19136450C2semidirect
15. C4×SD32×C43C2semidirect
240. C4×SD32D43semidirect
290. C43#33927semidirect

Maximal subgroups

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

subgroupindex
#191475832
#191474622
#191368282
#191368272
#191368212
#191367622
#191367592
#191367412
#191366522
#191366502
#191366382
C16×Dic862
#191364502
#191364392
C4×SD32×C432
#3392743