Finite Group Databasebeta

← #25254747

Subgroups — #25254747

Order 11008.

472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147733C211yesmaximal, characteristic, complemented
2#19147732C211yesmaximal, characteristic, complemented
3#19136910C211yesmaximal, characteristic, complemented
4#19136909C212yesmaximal, complemented
5#19136906C212yesmaximal, complemented
6#19136903C212yesmaximal, complemented
7#19136902C211yesmaximal, characteristic, complemented
8C2×#14582734C211yesmaximal, characteristic, complemented
9D32×D43C212yesmaximal, complemented
10#19136890C211yesmaximal, characteristic, complemented
11C43×#2263C211yesmaximal, characteristic, complemented
12#14583701—21no—
13#14583700—21no—
14#14583336—22no—
15#14583335—21no—
16#14583334—21no—
17#14583333—22no—
18#14583332C2212yescomplemented
19#14583331C2211yescharacteristic, complemented
20#14583328C2212yescomplemented
21C2×D688C2211yescharacteristic, complemented
22D16×D43C2212yescomplemented
23D16×D43C2212yescomplemented
24#14583315C2211yescharacteristic
25#14582739C2211yescharacteristic, complemented
26#14582738C2212yescomplemented
27#14582737C2211yescharacteristic, complemented
28#14582736C2211yescharacteristic, complemented
29D1376C2212yescomplemented
30#14582734C2211yescharacteristic, complemented
31#14582734C2212yescomplemented
32#14582734C2212yescomplemented
33#14582732C2212yescomplemented
34C2×C43⋊C32C2211yescharacteristic, complemented
35C32×D43C2212yescomplemented
36C43×#508C2211yescharacteristic, complemented
37C2×D16×C43C2211yescharacteristic, complemented
38C43×SD64C2212yescomplemented
39C43×D32C2212yescomplemented
40C43×M64C2211yescharacteristic, complemented
41#13063371—41no—
42#13063370—41no—
43#13063352—42no—
44#13063351—41no—
45#13063350—41no—
46#13063349—42no—
47#13063348—22no—
48#13063347—21no—
49#13063344—22no—
50C2×D344—21no—
51D8×D43—22no—
52D8×D43—22no—
53#13063331D411yescharacteristic
54Dic344C2311yescharacteristic
55#13063270—21no—
56#13063269—22no—
57#13063268—22no—
58D688—21no—
59D688C2311yescharacteristic
60D688C2312yes—
61#13063266—22no—
62#13063266—22no—
63#13063265D411yescharacteristic
64#13063264D412yes—
65C16×D43C2312yes—
66C43⋊C32C2311yescharacteristic
67C43⋊C32C2311yescharacteristic
68#135×C43—21no—
69C2×D8×C43—21no—
70Q32×C43C2311yescharacteristic
71SD32×C43—21no—
72D16×C43—21no—
73D16×C43C2312yes—
74D16×C43C2311yescharacteristic
75C2×C16×C43C2311yescharacteristic
76C32×C43C2312yes—
77#41×C43—41no—
78C2×D4×C43—41no—
79C2×C22⋊D43—82no—
80#10621902—42no—
81#10621900—42no—
82#10621900—81no—
83D4×D43—42no—
84D4×D43—42no—
85D4×D43—82no—
86D4×D43—81no—
87#10621898—41no—
88#10621898—81no—
89#10621898D811yescharacteristic
90C2×D172—41no—
91C2×D172—81no—
92Q16×C43—21no—
93SD16×C43—41no—
94D8×C43—22no—
95D8×C43—21no—
96D8×C43—41no—
97C2×C8×C43C2×D411yescharacteristic
98#10621884—42no—
99#10621883—42no—
100#10621882—42no—
101#10621882—42no—
102#10621877D811yescharacteristic
103Dic172—21no—
104D344—21no—
105D344—22no—
106D344—41no—
107#10621873—41no—
108#10621872D812yes—
109C8×D43C2×D412yes—
110C16×C43C2×D411yescharacteristic
111C16×C43C2411yescharacteristic
112C43⋊C16C2×D412yes—
113C23×C43—81no—
114C22×D43—81no—
115C22×D43—82no—
116C22×D43—82no—
117Q8×C43—41no—
118D4×C43—41no—
119D4×C43—42no—
120D4×C43—81no—
121D4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43C2×D811yescharacteristic
124C22⋊D43—81no—
125C22⋊D43—82no—
126C22⋊D43—82no—
127C22⋊D43—82no—
128C22⋊D43D1612yes—
129C2×Dic43—82no—
130D172—41no—
131D172—42no—
132D172—82no—
133D172—81no—
134D172D1611yescharacteristic
135C4×D43—81no—
136C4×D43—82no—
137C4×D43C2×D812yes—
138Dic86—41no—
139Dic86D1611yescharacteristic
140C8×C43C2×D811yescharacteristic
141C8×C43C22×D411yescharacteristic
142C43⋊C8C2×D812yes—
143#33982—431nomaximal, Sylow
144C22×C43—81no—
145C22×C43—82no—
146C22×C43—321no—
147C22×C43C2×D1611yescharacteristic
148C2×D43—82no—
149C2×D43—81no—
150C2×D43—322no—
151C2×D43—322no—
152C2×D43—321no—
153C2×D43C2×D1612yes—
154C4×C43—81no—
155C4×C43C2×D1611yescharacteristic
156C4×C43C22×D811yescharacteristic
157Dic43—81no—
158Dic43C2×D1612yes—
159#3415—431no—
160#3415—431no—
161#2263—432no—
162#2263—432no—
163#2263—431no—
164#2263D4311yescharacteristic, complemented
165#2262—431no—
166#2262—432no—
167C2×D32—431no—
168C2×D32—432no—
169#2258—431no—
170C2×C43—21no—
171C2×C43—161no—
172C2×C43—162no—
173C2×C43C22×D1611yescharacteristic
174D43—22no—
175D43—162no—
176D43—161no—
177#576—861no—
178#576—861no—
179#509—862no—
180#509—862no—
181#509—861no—
182#509—861no—
183#508—432no—
184#508—432no—
185#508—431no—
186#508C2×D4311yescharacteristic, complemented
187C2×D16—432no—
188C2×D16—432no—
189C2×D16—431no—
190C2×D16C2×D4311yescharacteristic, complemented
191#504—431no—
192Q64—431no—
193SD64—431no—
194SD64—431no—
195SD64—432no—
196SD64C2×D4312yescomplemented
197D32—432no—
198D32—431no—
199D32—432no—
200D32—432no—
201D32C2×D4312yescomplemented
202M64—432no—
203M64C2×D4311yescharacteristic, complemented
204C2×C32—431no—
205C2×C32—432no—
206C43#3398211yescharacteristic, complemented, Sylow
207H(5,𝔽2)—1721no—
208H(5,𝔽2)—1721no—
209AGL(1,ℤ/8)—1722no—
210AGL(1,ℤ/8)—1722no—
211AGL(1,ℤ/8)—1721no—
212AGL(1,ℤ/8)—1721no—
213#135—21no—
214#135—862no—
215#135—862no—
216#135—861no—
217C2×D8—21no—
218C2×D8—862no—
219C2×D8—862no—
220C2×D8—861no—
221#131—431no—
222Q32—431no—
223Q32C22×D4311yescharacteristic
224SD32—21no—
225SD32—862no—
226SD32—862no—
227SD32—861no—
228D16—21no—
229D16—431no—
230D16—432no—
231D16—862no—
232D16—862no—
233D16—861no—
234D16C22×D4312yes—
235D16C22×D4311yescharacteristic
236M32—431no—
237M32—432no—
238C2×C16—432no—
239C2×C16C22×D4311yescharacteristic
240C32—431no—
241C32—431no—
242C32C22×D4312yes—
243#41—41no—
244#41—431no—
245#41—3441no—
246#41—3441no—
247#41—1722no—
248#41—1722no—
249#41—1721no—
250C2×D4—41no—
251C2×D4—3441no—
252C2×D4—3442no—
253C2×D4—3441no—
254C2×D4—3442no—
255C2×D4—1722no—
256C2×D4—1722no—
257C2×D4—1721no—
258Q16—21no—
259Q16—861no—
260SD16—41no—
261SD16—1722no—
262SD16—1722no—
263SD16—1721no—
264D8—22no—
265D8—21no—
266D8—41no—
267D8—861no—
268D8—862no—
269D8—1722no—
270D8—1722no—
271D8—1721no—
272M16—431no—
273M16—432no—
274C2×C8—432no—
275C2×C8D4×D4311yescharacteristic
276C16—432no—
277C16D4×D4311yescharacteristic
278C16C23×D4311yescharacteristic
279C23—81no—
280C23—3442no—
281C23—3442no—
282C23—3441no—
283Q8—41no—
284Q8—431no—
285Q8—1721no—
286D4—42no—
287D4—41no—
288D4—81no—
289D4—81no—
290D4—432no—
291D4—431no—
292D4—3442no—
293D4—3442no—
294D4—3442no—
295D4—3442no—
296D4—3441no—
297D4—3441no—
298D4—1721no—
299D4—1722no—
300C2×C4—81no—
301C2×C4—432no—
302C2×C4—3442no—
303C2×C4—3442no—
304C2×C4—3441no—
305C2×C4D8×D4311yescharacteristic
306C8—432no—
307C8D8×D4311yescharacteristic
308C8C2×D4×D4311yescharacteristic
309C22—81no—
310C22—82no—
311C22—321no—
312C22—432no—
313C22—3442no—
314C22—3441no—
315C22—13761no—
316C22—13762no—
317C22—13762no—
318C22D16×D4311yescharacteristic
319C4—81no—
320C4—432no—
321C4—3441no—
322C4D16×D4311yescharacteristic
323C4C2×D8×D4311yescharacteristic
324C2—21no—
325C2—162no—
326C2—161no—
327C2—862no—
328C2—6882no—
329C2—6881no—
330C2C2×D16×D4311yescharacteristic
subgroupG/H
centerC2C2×D16×D43
commutator, cosocleC16×C43C24
FrattiniC16C23×D43
FittingC43×#2263C2
socleC2×C43C22×D16
hypercenter#2263D43
hypocenterC43#33982
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2263

Complements

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

NH ≅ G/Ntype
1. #19147733C2semidirect
2. #19147732C2semidirect
3. #19136910C2semidirect
4. #19136909C2semidirect
5. #19136906C2semidirect
6. #19136903C2semidirect
7. #19136902C2semidirect
8. C2×#14582734C2semidirect
9. D32×D43C2semidirect
10. #19136890C2semidirect
11. C43×#2263C2semidirect
18. #14583332C22semidirect
19. #14583331C22semidirect
20. #14583328C22semidirect
21. C2×D688C22semidirect
22. D16×D43C22semidirect
23. D16×D43C22semidirect
25. #14582739C22semidirect
26. #14582738C22semidirect
27. #14582737C22semidirect
28. #14582736C22semidirect
29. D1376C22semidirect
30. #14582734C22semidirect
31. #14582734C22semidirect
32. #14582734C22semidirect
33. #14582732C22semidirect
34. C2×C43⋊C32C22semidirect
35. C32×D43C22semidirect
36. C43×#508C22semidirect
37. C2×D16×C43C22semidirect
38. C43×SD64C22semidirect
39. C43×D32C22semidirect
40. C43×M64C22semidirect
164. #2263D43semidirect
186. #508C2×D43semidirect
190. C2×D16C2×D43semidirect
196. SD64C2×D43semidirect
201. D32C2×D43semidirect
203. M64C2×D43semidirect
206. C43#33982semidirect

Maximal subgroups

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

subgroupindex
#191477332
#191477322
#191369102
#191369092
#191369062
#191369032
#191369022
C2×#145827342
D32×D432
#191368902
C43×#22632
#3398243