Finite Group Databasebeta

← #25251272

Subgroups — #25251272

Order 11008.

542 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#499×D43C211yesmaximal, characteristic, complemented
2C4×#13063344C211yesmaximal, characteristic
3#19136762C211yesmaximal, characteristic, complemented
4#19136760C211yesmaximal, characteristic, complemented
5#19136758C211yesmaximal, characteristic, complemented
6#19136756C211yesmaximal, characteristic, complemented
7#19136754C211yesmaximal, characteristic, complemented
8#19136752C211yesmaximal, characteristic, complemented
9#19136750C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic, complemented
11#19136380C211yesmaximal, characteristic, complemented
12#19136349C211yesmaximal, characteristic, complemented
13#19136304C211yesmaximal, characteristic
14#19136304C211yesmaximal, characteristic
15C43×#2228C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17#125×D43—21no—
18C4×#10621900—21no—
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583300C2211yescharacteristic
24#14583299—21no—
25#14583298—21no—
26C4×Dic172C2211yescharacteristic
27#14582993C2211yescharacteristic
28#14582990—21no—
29C4×#10621883—21no—
30D8×Dic43C2211yescharacteristic
31#14582936C2211yescharacteristic
32#107×D43C2211yescharacteristic
33#107×D43C2211yescharacteristic
34#106×D43—21no—
35#14582892—21no—
36C4×C8×D43C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582724C2211yescharacteristic
42#14582724C2211yescharacteristic
43C4⋊(C43⋊C16)C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46#14582704C2211yescharacteristic
47#14582704C2211yescharacteristic
48#14582702C2211yescharacteristic
49#14582702C2211yescharacteristic
50#14582700C2211yescharacteristic
51#14582700C2211yescharacteristic
52C43×#499C2211yescharacteristic
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×C4⋊C16C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—21no—
60#13063344—22no—
61#13063344Q814yes—
62C2×Dic172C2311yescharacteristic
63C2×#10621883—21no—
64C2×C8×D43D411yescharacteristic
65C2×C8×D43C2311yescharacteristic
66#13063317—21no—
67#13063316—21no—
68#13063316—21no—
69#13063315—41no—
70#13063315—41no—
71C4×Dic86—21no—
72#13063290—21no—
73D4×Dic43—21no—
74C4×C22⋊D43—41no—
75(C22⋊D43)⋊C4—41no—
76#13063283—21no—
77#13063281—41no—
78C4⋊C4×D43—21no—
79C4⋊C4×D43—21no—
80C4⋊C4×D43—41no—
81C4⋊C4×D43—41no—
82C2×C4×Dic43—41no—
83C42×D43D411yescharacteristic
84#13063264—22no—
85#13063264—22no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063257—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063250—21no—
98#13063248—21no—
99#13063246—21no—
100C4×C43⋊C8D411yescharacteristic
101C8×Dic43D411yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×D8×C43C2311yescharacteristic
104#125×C43—21no—
105C4×D4×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#106×C43—21no—
112#102×C43—21no—
113C4×C8×C43C2311yescharacteristic
114C2×D4×C43—21no—
115C22×C4×C43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119#10621900—24no—
120#10621900—42no—
121C2×C4×D43—41no—
122C2×C4×D43—41no—
123C2×C4×D43D811yescharacteristic
124C2×C4×D43D811yescharacteristic
125C2×C4×D43C2×D411yescharacteristic
126C2×Dic86—21no—
127D8×C43—21no—
128D8×C43C2×Q812yes—
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2411yescharacteristic
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C42×C43C2×D411yescharacteristic
138C22⋊Dic43—41no—
139#10621883—24no—
140(C2×D43)⋊C4—41no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—41no—
145C4⋊Dic43—41no—
146Dic43⋊C4—41no—
147Dic43⋊C4—41no—
148Dic43⋊C4—41no—
149Dic43⋊C4—41no—
150Dic43⋊C4—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154C4×Dic43—41no—
155C4×Dic43—41no—
156C4×Dic43—41no—
157C4×Dic43D811yescharacteristic
158C4×Dic43D811yescharacteristic
159C4×Dic43C2×D411yescharacteristic
160C2×C43⋊C8C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162Dic172—21no—
163Dic172C2×Q812yes—
164C8×D43—22no—
165C8×D43C2×Q812yes—
166C8×D43#4112yes—
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C22×D43C2×D811yescharacteristic
173D4×C43—22no—
174D4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—82no—
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43C22×D411yescharacteristic
182C22⋊D43—44no—
183C2×Dic43—41no—
184C2×Dic43—44no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—82no—
189C2×Dic43C2×D811yescharacteristic
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C4×D43—41no—
193C4×D43—41no—
194C4×D43—82no—
195C4×D43—82no—
196C4×D43C22⋊Q812yes—
197C4×D43#13712yes—
198Dic86—22no—
199Dic86—41no—
200C8×C43—21no—
201C8×C43C22×Q811yescharacteristic
202C8×C43C2×#4111yescharacteristic
203C43⋊C8—21no—
204C43⋊C8C22⋊Q812yes—
205#33630—431nomaximal, Sylow
206C22×C43—42no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43C22×D811yescharacteristic
210C2×D43—21no—
211C2×D43—21no—
212C2×D43#47412yes—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—81no—
216C4×C43—81no—
217C4×C43—81no—
218C4×C43C2×C22⋊Q811yescharacteristic
219C4×C43C2×#13711yescharacteristic
220Dic43—21no—
221Dic43—21no—
222Dic43—42no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43#47412yes—
227C2×#499—431no—
228C4×#135—431no—
229#2229—431no—
230#2229—431no—
231#2229—431no—
232#2229—431no—
233#2228—431no—
234#2228—431no—
235#2228—431no—
236#2228D4311yescharacteristic, complemented
237#2159—431no—
238#2159—431no—
239#2150—431no—
240#2139—431no—
241#2139—431no—
242C2×C43—82no—
243C2×C43C2×#47411yescharacteristic
244C2×C43#341411yescharacteristic
245C2×C43#341411yescharacteristic
246D43—22no—
247C2×#135—431no—
248C2×#125—861no—
249C4×#41—861no—
250C2×M32—431no—
251C2×M32—431no—
252#499—431no—
253#499—431no—
254#499—431no—
255#499—861no—
256#499—861no—
257#499C2×D4311yescharacteristic
258C4×Q16—431no—
259C4×Q16—431no—
260C4×SD16—861no—
261C4×SD16—861no—
262C4×D8—431no—
263C4×D8C2×D4311yescharacteristic
264#427—431no—
265C2×#107—431no—
266C2×#107—431no—
267C2×#106—861no—
268#416—861no—
269C2×C4×C8—431no—
270#367—431no—
271#367—431no—
272#367—431no—
273#367C2×D4311yescharacteristic
274#366—431no—
275#366—431no—
276#366—431no—
277#366C2×D4311yescharacteristic
278C4⋊C16—431no—
279C4⋊C16—431no—
280C4⋊C16—431no—
281C4⋊C16C2×D4311yescharacteristic
282#358—431no—
283#358—431no—
284#358—431no—
285#358—431no—
286#357—431no—
287#357—431no—
288#357C2×D4311yescharacteristic
289#357C2×D4311yescharacteristic
290C43#3363011yescharacteristic, complemented, Sylow
291C2×#41—861no—
292#135—434no—
293#135—862no—
294C2×Q16—431no—
295C2×SD16—861no—
296C2×D8C22×D4311yescharacteristic
297C22×C8—431no—
298C22×C8—431no—
299#125—21no—
300#125—861no—
301#125—861no—
302#125—861no—
303#125—1721no—
304#125—1721no—
305C4×Q8—861no—
306C4×Q8—861no—
307C4×D4—21no—
308C4×D4—861no—
309C4×D4—1721no—
310C4×D4—1721no—
311#117—861no—
312#117—1721no—
313C2×C4⋊C4—861no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4—1721no—
316C2×C4⋊C4—1721no—
317C2×C42—431no—
318C2×C42—1721no—
319M32—862no—
320M32—862no—
321C2×C16—431no—
322C2×C16—431no—
323C2×C16C22×D4311yescharacteristic
324C2×C16C22×D4311yescharacteristic
325#107—431no—
326#107—431no—
327#107—431no—
328#107—861no—
329#107—861no—
330#107C22×D4311yescharacteristic
331#107C22×D4311yescharacteristic
332#107C22×D4311yescharacteristic
333#106—21no—
334#106—861no—
335#106—861no—
336#106—861no—
337#106—861no—
338#103—861no—
339#103—861no—
340#102—21no—
341#102—861no—
342C4×C8—431no—
343C4×C8—431no—
344C4×C8—431no—
345C4×C8C22×D4311yescharacteristic
346#41—864no—
347#41—1722no—
348C2×Q8—861no—
349C2×D4—21no—
350C2×D4—1721no—
351C22×C4—41no—
352C22×C4—431no—
353C22×C4—431no—
354C22×C4—431no—
355C22×C4—1721no—
356C22×C4—1721no—
357C22×C4—1721no—
358C22×C4—1721no—
359Q16—432no—
360Q16—861no—
361SD16—864no—
362D8—21no—
363D8Q8×D4312yes—
364C2×C8—431no—
365C2×C8—432no—
366C2×C8—432no—
367C2×C8—431no—
368C2×C8—862no—
369C2×C8D4×D4311yescharacteristic
370C2×C8C23×D4311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—861no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C22⋊C4—41no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—431no—
393C42—431no—
394C42—431no—
395C42—1721no—
396C42—1721no—
397C42—1721no—
398C42D4×D4311yescharacteristic
399C16—21no—
400C16—21no—
401C16—861no—
402C16—861no—
403C23—41no—
404C23—431no—
405Q8—862no—
406Q8—1721no—
407D4—22no—
408D4—41no—
409D4—1724no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—431no—
415C2×C4—432no—
416C2×C4—432no—
417C2×C4—431no—
418C2×C4—431no—
419C2×C4—3442no—
420C2×C4—3442no—
421C2×C4—3442no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4—1724no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4—1721no—
429C2×C4D8×D4311yescharacteristic
430C2×C4D8×D4311yescharacteristic
431C2×C4C2×D4×D4311yescharacteristic
432C8—21no—
433C8—432no—
434C8—861no—
435C8C2×Q8×D4311yescharacteristic
436C8#41×D4311yescharacteristic
437C22—42no—
438C22—81no—
439C22—81no—
440C22—432no—
441C22—861no—
442C22—861no—
443C22C2×D8×D4311yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—432no—
450C4—861no—
451C4—861no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4—1722no—
456C4C22⋊Q8×D4311yescharacteristic
457C4#137×D4311yescharacteristic
458C2—82no—
459C2—862no—
460C2#474×D4311yescharacteristic
461C2#1914772711yescharacteristic
462C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2228C2
socleC22×C43C22×D8
prime radicalC2×#13063344C22
hypercenter#2228D43
hypocenterC43#33630
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #499×D43C2semidirect
3. #19136762C2semidirect
4. #19136760C2semidirect
5. #19136758C2semidirect
6. #19136756C2semidirect
7. #19136754C2semidirect
8. #19136752C2semidirect
9. #19136750C2semidirect
10. #19136382C2semidirect
11. #19136380C2semidirect
12. #19136349C2semidirect
15. C43×#2228C2semidirect
236. #2228D43semidirect
290. C43#33630semidirect

Maximal subgroups

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

subgroupindex
#499×D432
C4×#130633442
#191367622
#191367602
#191367582
#191367562
#191367542
#191367522
#191367502
#191363822
#191363802
#191363492
#191363042
C43×#22282
#3363043