Finite Group Databasebeta

← #25254752

Subgroups — #25254752

Order 11008.

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

normal subgroups only

This group has 462 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#19147744C211yesmaximal, characteristic, complemented
2#19147733C211yesmaximal, characteristic, complemented
3#19136914C212yesmaximal, complemented
4#19136910C211yesmaximal, characteristic, complemented
5#19136909C212yesmaximal, complemented
6#19136905C212yesmaximal, complemented
7#19136902C211yesmaximal, characteristic, complemented
8C2×#14582736C211yesmaximal, characteristic, complemented
9SD64×D43C212yesmaximal, complemented
10#19136890C211yesmaximal, characteristic, complemented
11C43×#2264C211yesmaximal, characteristic, complemented
12#14583712—21no—
13#14583701—21no—
14#14583341—22no—
15#14583340—21no—
16#14583336—22no—
17#14583334—21no—
18#14583332C2212yes—
19#14583332C2212yescomplemented
20#14583331C2211yescharacteristic, complemented
21Q32×D43C2212yescomplemented
22C2×D688C2211yescharacteristic
23D16×D43C2212yes—
24#14583315C2211yescharacteristic
25#14582739C2211yescharacteristic, complemented
26#14582738C2212yescomplemented
27#14582737C2211yescharacteristic, complemented
28#14582736C2212yescomplemented
29#14582736C2212yescomplemented
30#14582736C2211yescharacteristic, complemented
31D1376C2212yescomplemented
32#14582734C2211yescharacteristic, complemented
33#14582732C2212yescomplemented
34C2×C43⋊C32C2211yescharacteristic, complemented
35C32×D43C2212yescomplemented
36C43×#508C2211yescharacteristic
37C2×Q32×C43C2211yescharacteristic, complemented
38C43×Q64C2212yescomplemented
39C43×SD64C2212yescomplemented
40C43×M64C2211yescharacteristic, complemented
41#13063373—41no—
42#13063371—41no—
43#13063357—42no—
44#13063356—41no—
45#13063352—42no—
46#13063350—41no—
47#13063348—22no—
48#13063348—22no—
49#13063347—21no—
50Q16×D43—22no—
51C2×D344—21no—
52D8×D43—22no—
53#13063331D411yescharacteristic
54Dic344C2311yescharacteristic
55#13063271—22no—
56#13063270—21no—
57#13063268—22no—
58#13063268—22no—
59D688—21no—
60D688C2312yes—
61D688C2311yescharacteristic
62#13063266—22no—
63#13063265D411yescharacteristic
64#13063264D412yes—
65C16×D43C2312yes—
66C43⋊C32C2311yescharacteristic
67C43⋊C32C2311yescharacteristic
68#135×C43—21no—
69C2×Q16×C43—21no—
70Q32×C43—21no—
71Q32×C43C2312yes—
72Q32×C43C2311yescharacteristic
73SD32×C43—21no—
74D16×C43C2311yescharacteristic
75C2×C16×C43C2311yescharacteristic
76C32×C43C2312yes—
77#41×C43—41no—
78C2×Q8×C43—41no—
79#10621902—42no—
80#10621902—42no—
81#10621902—81no—
82Q8×D43—42no—
83Q8×D43—81no—
84D4×D43—42no—
85D4×D43—82no—
86#10621898—41no—
87#10621898—82no—
88#10621898—81no—
89#10621898D811yescharacteristic
90C2×D172—41no—
91C2×D172—81no—
92Q16×C43—21no—
93Q16×C43—22no—
94Q16×C43—41no—
95SD16×C43—41no—
96D8×C43—21no—
97C2×C8×C43C2×D411yescharacteristic
98#10621885—42no—
99#10621884—42no—
100#10621884—42no—
101#10621882—42no—
102#10621877D811yescharacteristic
103Dic172—21no—
104D344—22no—
105D344—21no—
106D344—41no—
107#10621873—41no—
108#10621872D812yes—
109C8×D43C2×D412yes—
110C16×C43C2×D411yescharacteristic
111C16×C43C2411yescharacteristic
112C43⋊C16C2×D412yes—
113C22×D43—81no—
114C22×D43—82no—
115Q8×C43—41no—
116Q8×C43—42no—
117Q8×C43—81no—
118D4×C43—41no—
119D4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43C2×D811yescharacteristic
123C22⋊D43—81no—
124C22⋊D43—82no—
125C22⋊D43D1612yes—
126D172—41no—
127D172—42no—
128D172—82no—
129D172—82no—
130D172—81no—
131D172D1611yescharacteristic
132C4×D43—82no—
133C4×D43—81no—
134C4×D43—82no—
135C4×D43—82no—
136C4×D43C2×D812yes—
137Dic86—41no—
138Dic86—82no—
139Dic86D1611yescharacteristic
140C8×C43C2×D811yescharacteristic
141C8×C43C22×D411yescharacteristic
142C43⋊C8C2×D812yes—
143#33983—431nomaximal, Sylow
144C22×C43—81no—
145C22×C43C2×D1611yescharacteristic
146C2×D43—82no—
147C2×D43—81no—
148C2×D43—322no—
149C2×D43—321no—
150C2×D43C2×D1612yes—
151C4×C43—82no—
152C4×C43—81no—
153C4×C43C2×D1611yescharacteristic
154C4×C43C22×D811yescharacteristic
155Dic43—81no—
156Dic43C2×D1612yes—
157#3417—431no—
158#3415—431no—
159#2264—432no—
160#2264D4311yescharacteristic, complemented
161#2263—432no—
162#2263—431no—
163#2262—431no—
164#2262—432no—
165C2×SD64—431no—
166C2×SD64—432no—
167#2258—431no—
168C2×C43—21no—
169C2×C43—161no—
170C2×C43C22×D1611yescharacteristic
171D43—22no—
172D43—161no—
173D43—162no—
174#578—861no—
175#576—861no—
176#510—862no—
177#510—861no—
178#509—862no—
179#509—861no—
180#508—432no—
181#508—432no—
182#508—431no—
183#508C2×D4311yescharacteristic
184C2×Q32—432no—
185C2×Q32C2×D4311yescharacteristic, complemented
186C2×D16—432no—
187C2×D16—431no—
188#504—431no—
189Q64—431no—
190Q64C2×D4312yescomplemented
191SD64—432no—
192SD64—432no—
193SD64—431no—
194SD64—431no—
195SD64—432no—
196SD64C2×D4312yescomplemented
197D32—431no—
198D32—432no—
199M64—432no—
200M64C2×D4311yescharacteristic, complemented
201C2×C32—431no—
202C2×C32—432no—
203C43#3398311yescharacteristic, complemented, Sylow
2042−1+4—1721no—
205H(5,𝔽2)—1721no—
206#137—1722no—
207#137—1721no—
208AGL(1,ℤ/8)—1722no—
209AGL(1,ℤ/8)—1721no—
210#135—21no—
211#135—862no—
212#135—862no—
213#135—861no—
214C2×Q16—21no—
215C2×Q16—862no—
216C2×D8—862no—
217C2×D8—861no—
218#131—431no—
219Q32—21no—
220Q32—431no—
221Q32—862no—
222Q32C22×D4312yes—
223Q32C22×D4311yescharacteristic
224SD32—21no—
225SD32—862no—
226SD32—862no—
227SD32—861no—
228D16—431no—
229D16—432no—
230D16—862no—
231D16—861no—
232D16C22×D4311yescharacteristic
233M32—431no—
234M32—432no—
235C2×C16—432no—
236C2×C16C22×D4311yescharacteristic
237C32—431no—
238C32—431no—
239C32C22×D4312yes—
240#41—41no—
241#41—431no—
242#41—3442no—
243#41—3441no—
244#41—3441no—
245#41—1722no—
246#41—1722no—
247#41—1721no—
248C2×Q8—41no—
249C2×Q8—3441no—
250C2×Q8—1722no—
251C2×D4—3441no—
252C2×D4—3442no—
253C2×D4—1722no—
254C2×D4—1721no—
255Q16—21no—
256Q16—22no—
257Q16—41no—
258Q16—861no—
259Q16—1722no—
260SD16—41no—
261SD16—1722no—
262SD16—1722no—
263SD16—1721no—
264D8—21no—
265D8—862no—
266D8—861no—
267D8—1722no—
268D8—1721no—
269M16—431no—
270M16—432no—
271C2×C8—432no—
272C2×C8D4×D4311yescharacteristic
273C16—432no—
274C16D4×D4311yescharacteristic
275C16C23×D4311yescharacteristic
276C23—3442no—
277C23—3441no—
278Q8—41no—
279Q8—42no—
280Q8—81no—
281Q8—431no—
282Q8—3442no—
283Q8—1721no—
284D4—41no—
285D4—81no—
286D4—432no—
287D4—431no—
288D4—3442no—
289D4—3442no—
290D4—3442no—
291D4—3441no—
292D4—3441no—
293D4—1722no—
294D4—1721no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—432no—
298C2×C4—3442no—
299C2×C4—3442no—
300C2×C4—3442no—
301C2×C4—3441no—
302C2×C4D8×D4311yescharacteristic
303C8—432no—
304C8D8×D4311yescharacteristic
305C8C2×D4×D4311yescharacteristic
306C22—81no—
307C22—432no—
308C22—3441no—
309C22—3442no—
310C22—13761no—
311C22—13762no—
312C22D16×D4311yescharacteristic
313C4—81no—
314C4—82no—
315C4—432no—
316C4—3441no—
317C4D16×D4311yescharacteristic
318C4C2×D8×D4311yescharacteristic
319C2—21no—
320C2—161no—
321C2—862no—
322C2—6882no—
323C2—6881no—
324C2C2×D16×D4311yescharacteristic
subgroupG/H
centerC2C2×D16×D43
commutator, cosocleC16×C43C24
FrattiniC16C23×D43
FittingC43×#2264C2
socleC2×C43C22×D16
hypercenter#2264D43
hypocenterC43#33983
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #2264

Complements

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

NH ≅ G/Ntype
1. #19147744C2semidirect
2. #19147733C2semidirect
3. #19136914C2semidirect
4. #19136910C2semidirect
5. #19136909C2semidirect
6. #19136905C2semidirect
7. #19136902C2semidirect
8. C2×#14582736C2semidirect
9. SD64×D43C2semidirect
10. #19136890C2semidirect
11. C43×#2264C2semidirect
19. #14583332C22semidirect
20. #14583331C22semidirect
21. Q32×D43C22semidirect
25. #14582739C22semidirect
26. #14582738C22semidirect
27. #14582737C22semidirect
28. #14582736C22semidirect
29. #14582736C22semidirect
30. #14582736C22semidirect
31. D1376C22semidirect
32. #14582734C22semidirect
33. #14582732C22semidirect
34. C2×C43⋊C32C22semidirect
35. C32×D43C22semidirect
37. C2×Q32×C43C22semidirect
38. C43×Q64C22semidirect
39. C43×SD64C22semidirect
40. C43×M64C22semidirect
160. #2264D43semidirect
185. C2×Q32C2×D43semidirect
190. Q64C2×D43semidirect
196. SD64C2×D43semidirect
200. M64C2×D43semidirect
203. C43#33983semidirect

Maximal subgroups

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

subgroupindex
#191477442
#191477332
#191369142
#191369102
#191369092
#191369052
#191369022
C2×#145827362
SD64×D432
#191368902
C43×#22642
#3398343