Finite Group Databasebeta

← #25253250

Subgroups — #25253250

Order 11008.

812 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×D16×D43C212yesmaximal, complemented
2#19146270C212yesmaximal, complemented
3#19136678C212yesmaximal, complemented
4#19136627C212yesmaximal, complemented
5#19136505C214yesmaximal, complemented
6C4×D688C211yesmaximal, characteristic, complemented
7C16×D172C211yesmaximal, characteristic, complemented
8C43×#2246C211yesmaximal, characteristic, complemented
9C2×D8×D43C2214yescomplemented
10#14583534—22no—
11C2×D688C2211yescharacteristic
12C2×#13063266C2214yescomplemented
13D16×D43—28no—
14C2×C16×D43C2212yescomplemented
15#14583132C2214yescomplemented
16#14583091—22no—
17#14583031—24no—
18C4×D344C2212yescomplemented
19C8×D172C2211yescharacteristic
20#14582725C2211yescharacteristic, complemented
21C4⋊(C43⋊C16)C2211yescharacteristic, complemented
22#14582701C2212yescomplemented
23#14582700C2214yescomplemented
24(C2×D43)⋊C16C2212yescomplemented
25C2×D16×C43C2212yescomplemented
26C2×D16×C43C2212yescomplemented
27C43×#493C2212yescomplemented
28C4×C16×C43C2211yescharacteristic, complemented
29C2×D4×D43—24no—
30C2×D4×D43—42no—
31C2×D344C2312yes—
32C2×#10621882—24no—
33D8×D43—28no—
34D8×D43—44no—
35C2×C8×D43C2312yes—
36#13063296—24no—
37#13063296—42no—
38#13063293—44no—
39C4×D172—22no—
40C4×D172D411yescharacteristic
41D688D414yescomplemented
42#13063266—28no—
43C2×C43⋊C16C2312yes—
44C16×D43—24no—
45#13063259C2312yes—
46C4⋊(C43⋊C8)D411yescharacteristic
47#13063247—22no—
48#13063246—24no—
49(C2×D43)⋊C8D412yes—
50C2×D8×C43—22no—
51C2×D8×C43C2314yes—
52#127×C43—22no—
53D16×C43—24no—
54D16×C43—42no—
55C2×C16×C43C2311yescharacteristic
56C2×C16×C43C2311yescharacteristic
57C4×C8×C43C2311yescharacteristic
58C23×D43—44no—
59C2×D4×C43—24no—
60C2×D4×C43—42no—
61C2×D4×C43—42no—
62C2×C22⋊D43—44no—
63C2×C22⋊D43—44no—
64D4×D43—48no—
65D4×D43—84no—
66D4×D43—88no—
67C2×D172—22no—
68C2×D172D811yescharacteristic
69C2×C4×D43—42no—
70C2×C4×D43C2×D412yes—
71D8×C43—24no—
72D8×C43—24no—
73D8×C43—82no—
74C2×C8×C43C2×D411yescharacteristic
75C2×C8×C43C2411yescharacteristic
76C42×C43C2×D411yescharacteristic
77C22⋊Dic43—44no—
78#10621882—48no—
79(C2×D43)⋊C4—42no—
80(C2×D43)⋊C4D812yes—
81C4⋊Dic43—22no—
82C4⋊Dic43D811yescharacteristic
83C2×C43⋊C8C2×D412yes—
84D344—22no—
85D344C2×D414yescomplemented
86C8×D43—22no—
87C8×D43—22no—
88C16×C43—21no—
89C16×C43C2×D412yescomplemented
90C43⋊C16—22no—
91C23×C43—44no—
92C22×D43—42no—
93C22×D43—88no—
94C22×D43—88no—
95C22×D43—164no—
96C22×D43C2×D812yes—
97D4×C43—44no—
98D4×C43—44no—
99D4×C43—84no—
100D4×C43—162no—
101C2×C4×C43C2×D811yescharacteristic
102C2×C4×C43C2×D811yescharacteristic
103C2×C4×C43C22×D411yescharacteristic
104C22⋊D43—88no—
105C22⋊D43—88no—
106C2×Dic43—42no—
107C2×Dic43C2×D812yes—
108D172—24no—
109D172—42no—
110D172D1614yescomplemented
111C4×D43—22no—
112C4×D43—22no—
113C4×D43—84no—
114C8×C43—21no—
115C8×C43C22×D411yescharacteristic
116C8×C43H(5,𝔽2)11yescharacteristic
117C43⋊C8—22no—
118D4×D16—431nomaximal, Sylow
119C22×C43—84no—
120C22×C43—84no—
121C22×C43—84no—
122C22×C43C22×D811yescharacteristic
123C2×D43—22no—
124C2×D43—22no—
125C2×D43—44no—
126C2×D43—82no—
127C2×D43—82no—
128C2×D43—1616no—
129C2×D43C2×D1614yescomplemented
130C4×C43—21no—
131C4×C43C2×D1612yescomplemented
132C4×C43D4211yescharacteristic
133C4×C43#57611yescharacteristic
134Dic43—22no—
135Dic43—82no—
136C22×D16—432no—
137D4×D8—432no—
138#2246D4311yescharacteristic, complemented
139#2215—432no—
140#2206—432no—
141#2184—434no—
142C4×D16—431no—
143D4×C16—431no—
144C2×C43—164no—
145C2×C43D4×D811yescharacteristic
146C2×C43C22×D1611yescharacteristic
147C2×C43#341511yescharacteristic
148D43—24no—
149D43—84no—
150C22×D8—434no—
151D42—862no—
152C2×D16—434no—
153C2×D16—431no—
154C2×D16—868no—
155C2×D16C2×D4312yescomplemented
156C2×D16C2×D4312yescomplemented
157C22×C16—432no—
158#493C2×D4312yescomplemented
159#466—434no—
160#459—862no—
161#447—864no—
162C4×D8—432no—
163C8×D4—431no—
164#366—431no—
165C4⋊C16—431no—
166#357—434no—
167#357—432no—
168C22⋊C16—432no—
169C4×C16C2×D4311yescharacteristic, complemented
170C43D4×D1611yescharacteristic, complemented, Sylow
171C22×D4—864no—
172C22×D4—1722no—
173C2×D8—22no—
174C2×D8—432no—
175C2×D8—864no—
176C2×D8—868no—
177C2×D8—1724no—
178C2×D8C22×D4314yes—
179C22×C8—432no—
180#127—22no—
181#121—864no—
182#121—1722no—
183#120—1724no—
184C4×D4—431no—
185C4×D4—862no—
186D16—24no—
187D16—42no—
188D16—434no—
189D16—868no—
190C2×C16—432no—
191C2×C16—864no—
192C2×C16C22×D4311yescharacteristic
193C2×C16C22×D4311yescharacteristic
194#107—432no—
195C4⋊C8—431no—
196#102—864no—
197#102—862no—
198C22⋊C8—432no—
199C4×C8C22×D4311yescharacteristic
200C24—1724no—
201C2×D4—24no—
202C2×D4—42no—
203C2×D4—42no—
204C2×D4—431no—
205C2×D4—862no—
206C2×D4—3444no—
207C2×D4—3448no—
208C2×D4—1724no—
209C2×D4—1728no—
210C2×D4—1724no—
211C22×C4—432no—
212C22×C4—1722no—
213D8—24no—
214D8—24no—
215D8—82no—
216D8—434no—
217D8—862no—
218D8—1728no—
219C2×C8—432no—
220C2×C8—862no—
221C2×C8—862no—
222C2×C8D4×D4311yescharacteristic
223C2×C8C23×D4311yescharacteristic
224C4⋊C4—431no—
225C4⋊C4—862no—
226C22⋊C4—432no—
227C22⋊C4—1724no—
228C22⋊C4—1722no—
229C42D4×D4311yescharacteristic
230C16—21no—
231C16—862no—
232C16D4×D4312yescomplemented
233C23—44no—
234C23—432no—
235C23—3448no—
236C23—3448no—
237C23—1722no—
238C23—6884no—
239D4—44no—
240D4—44no—
241D4—84no—
242D4—162no—
243D4—434no—
244D4—864no—
245D4—3448no—
246D4—3448no—
247D4—1722no—
248C2×C4—432no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—3444no—
252C2×C4—1722no—
253C2×C4D8×D4311yescharacteristic
254C2×C4D8×D4311yescharacteristic
255C2×C4C2×D4×D4311yescharacteristic
256C8—21no—
257C8—862no—
258C8C2×D4×D4311yescharacteristic
259C8#1306337011yescharacteristic
260C22—84no—
261C22—84no—
262C22—84no—
263C22—434no—
264C22—862no—
265C22—862no—
266C22—3442no—
267C22—3442no—
268C22—1724no—
269C22—68816no—
270C22C2×D8×D4311yescharacteristic
271C4—21no—
272C4—862no—
273C4—3442no—
274C4D16×D4312yescomplemented
275C4#1458353411yescharacteristic
276C4#1458370011yescharacteristic
277C2—164no—
278C2—864no—
279C2—3444no—
280C2#1914627011yescharacteristic
281C2C2×D16×D4311yescharacteristic
282C2#1914773211yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2246C2
socleC22×C43C22×D8
hypercenter#2246D43
hypocenterC43D4×D16
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. C2×D16×D43C2semidirect
2. #19146270C2semidirect
3. #19136678C2semidirect
4. #19136627C2semidirect
5. #19136505C2semidirect
6. C4×D688C2semidirect
7. C16×D172C2semidirect
8. C43×#2246C2semidirect
9. C2×D8×D43C22semidirect
12. C2×#13063266C22semidirect
14. C2×C16×D43C22semidirect
15. #14583132C22semidirect
18. C4×D344C22semidirect
20. #14582725C22semidirect
21. C4⋊(C43⋊C16)C22semidirect
22. #14582701C22semidirect
23. #14582700C22semidirect
24. (C2×D43)⋊C16C22semidirect
25. C2×D16×C43C22semidirect
26. C2×D16×C43C22semidirect
27. C43×#493C22semidirect
28. C4×C16×C43C22semidirect
41. D688D4semidirect
85. D344C2×D4semidirect
89. C16×C43C2×D4semidirect
110. D172D16semidirect
129. C2×D43C2×D16semidirect
131. C4×C43C2×D16semidirect
138. #2246D43semidirect
155. C2×D16C2×D43semidirect
156. C2×D16C2×D43semidirect
158. #493C2×D43semidirect
169. C4×C16C2×D43semidirect
170. C43D4×D16semidirect
232. C16D4×D43semidirect
274. C4D16×D43semidirect

Maximal subgroups

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

subgroupindex
C2×D16×D432
#191462702
#191366782
#191366272
#191365052
C4×D6882
C16×D1722
C43×#22462
D4×D1643