Finite Group Databasebeta

← #15686537

Subgroups — #15686537

Order 2944.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#13093219C211yesmaximal, characteristic, complemented
2#13093218C211yesmaximal, characteristic, complemented
3#13092855C211yesmaximal, characteristic, complemented
4#13092854C212yesmaximal, complemented
5#13092851C212yesmaximal, complemented
6#13092848C212yesmaximal, complemented
7#13092847C211yesmaximal, characteristic, complemented
8C2×#10625008C211yesmaximal, characteristic, complemented
9D16×D23C212yesmaximal, complemented
10#13092835C211yesmaximal, characteristic, complemented
11C23×#509C211yesmaximal, characteristic, complemented
12#10625160—21no—
13#10625155—21no—
14C23×#135C2211yescharacteristic, complemented
15C2×D8×C23C2211yescharacteristic, complemented
16#10625120—21no—
17#10625103—21no—
18#10625090C2212yescomplemented
19#10625085—22no—
20#10625083C2212yescomplemented
21#10625082—22no—
22D8×D23C2212yescomplemented
23D8×D23C2212yescomplemented
24#10625075C2211yescharacteristic, complemented
25C2×D184C2211yescharacteristic, complemented
26#10625072C2211yescharacteristic
27C23×SD32C2212yescomplemented
28C23×D16C2212yescomplemented
29C23×M32C2211yescharacteristic, complemented
30#10625011C2211yescharacteristic, complemented
31#10625010C2211yescharacteristic, complemented
32#10625009C2211yescharacteristic, complemented
33#10625008C2211yescharacteristic, complemented
34#10625008C2212yescomplemented
35#10625008C2212yescomplemented
36C2×C23⋊C16C2211yescharacteristic, complemented
37#10624982C2212yescomplemented
38D368C2212yescomplemented
39#10624980C2212yescomplemented
40C16×D23C2212yescomplemented
41#41×C23—21no—
42C2×D4×C23—21no—
43C2×C22⋊D23—42no—
44#67292—22no—
45#67290—22no—
46#67290—41no—
47D4×D23—22no—
48D4×D23—22no—
49D4×D23—42no—
50D4×D23—41no—
51#67288—21no—
52#67288—41no—
53#67288D411yescharacteristic
54C2×D92—21no—
55C2×D92—41no—
56Q16×C23C2311yescharacteristic
57SD16×C23—21no—
58D8×C23—21no—
59D8×C23C2311yescharacteristic
60D8×C23C2312yes—
61C2×C8×C23C2311yescharacteristic
62#67274—22no—
63#67273—22no—
64#67272—22no—
65#67272—22no—
66#67267D411yescharacteristic
67Dic92C2311yescharacteristic
68D184—21no—
69D184C2312yes—
70D184C2311yescharacteristic
71#67263—21no—
72#67262D412yes—
73C8×D23C2312yes—
74C16×C23C2312yes—
75C23⋊C16C2311yescharacteristic
76C23⋊C16C2311yescharacteristic
77C23×C23—41no—
78C22×D23—41no—
79C22×D23—42no—
80C22×D23—42no—
81Q8×C23—21no—
82D4×C23—21no—
83D4×C23—22no—
84D4×C23—41no—
85D4×C23—41no—
86C2×C4×C23—41no—
87C2×C4×C23C2×D411yescharacteristic
88C22⋊D23—41no—
89C22⋊D23—42no—
90C22⋊D23—42no—
91C22⋊D23—42no—
92C22⋊D23D812yes—
93C2×Dic23—42no—
94D92—21no—
95D92—22no—
96D92—42no—
97D92—41no—
98D92D811yescharacteristic
99C4×D23—41no—
100C4×D23—42no—
101C4×D23C2×D412yes—
102Dic46—21no—
103Dic46D811yescharacteristic
104C8×C23C2×D411yescharacteristic
105C8×C23C2411yescharacteristic
106C23⋊C8C2×D412yes—
107#3415—231nomaximal, Sylow
108C22×C23—42no—
109C22×C23—41no—
110C22×C23—161no—
111C22×C23C2×D811yescharacteristic
112C2×D23—42no—
113C2×D23—41no—
114C2×D23—162no—
115C2×D23—162no—
116C2×D23—161no—
117C2×D23C2×D812yes—
118C4×C23—41no—
119C4×C23C2×D811yescharacteristic
120C4×C23C22×D411yescharacteristic
121Dic23—41no—
122Dic23C2×D812yes—
123#576—231no—
124#576—231no—
125#509—232no—
126#509—232no—
127#509—231no—
128#509D2311yescharacteristic, complemented
129#508—231no—
130#508—232no—
131C2×D16—231no—
132C2×D16—232no—
133#504—231no—
134C2×C23—21no—
135C2×C23—81no—
136C2×C23—82no—
137C2×C23C22×D811yescharacteristic
138D23—22no—
139D23—82no—
140D23—81no—
141H(5,𝔽2)—461no—
142H(5,𝔽2)—461no—
143AGL(1,ℤ/8)—462no—
144AGL(1,ℤ/8)—462no—
145AGL(1,ℤ/8)—461no—
146AGL(1,ℤ/8)—461no—
147#135—232no—
148#135—232no—
149#135—231no—
150#135C2×D2311yescharacteristic, complemented
151C2×D8—232no—
152C2×D8—232no—
153C2×D8—231no—
154C2×D8C2×D2311yescharacteristic, complemented
155#131—231no—
156Q32—231no—
157SD32—231no—
158SD32—231no—
159SD32—232no—
160SD32C2×D2312yescomplemented
161D16—232no—
162D16—231no—
163D16—232no—
164D16—232no—
165D16C2×D2312yescomplemented
166M32—232no—
167M32C2×D2311yescharacteristic, complemented
168C2×C16—231no—
169C2×C16—232no—
170C23#341511yescharacteristic, complemented, Sylow
171#41—21no—
172#41—231no—
173#41—462no—
174#41—462no—
175#41—461no—
176#41—921no—
177#41—921no—
178C2×D4—21no—
179C2×D4—462no—
180C2×D4—462no—
181C2×D4—461no—
182C2×D4—921no—
183C2×D4—922no—
184C2×D4—921no—
185C2×D4—922no—
186Q16—231no—
187Q16C22×D2311yescharacteristic
188SD16—21no—
189SD16—462no—
190SD16—462no—
191SD16—461no—
192D8—21no—
193D8—232no—
194D8—231no—
195D8—462no—
196D8—462no—
197D8—461no—
198D8C22×D2312yes—
199D8C22×D2311yescharacteristic
200M16—231no—
201M16—232no—
202C2×C8—232no—
203C2×C8C22×D2311yescharacteristic
204C16—231no—
205C16—231no—
206C16C22×D2312yes—
207C23—41no—
208C23—922no—
209C23—922no—
210C23—921no—
211Q8—21no—
212Q8—231no—
213Q8—461no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—232no—
219D4—231no—
220D4—461no—
221D4—462no—
222D4—922no—
223D4—922no—
224D4—922no—
225D4—922no—
226D4—921no—
227D4—921no—
228C2×C4—41no—
229C2×C4—232no—
230C2×C4—922no—
231C2×C4—922no—
232C2×C4—921no—
233C2×C4D4×D2311yescharacteristic
234C8—232no—
235C8D4×D2311yescharacteristic
236C8C23×D2311yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—232no—
241C22—922no—
242C22—921no—
243C22—3681no—
244C22—3682no—
245C22—3682no—
246C22D8×D2311yescharacteristic
247C4—41no—
248C4—232no—
249C4—921no—
250C4D8×D2311yescharacteristic
251C4C2×D4×D2311yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—462no—
256C2—1842no—
257C2—1841no—
258C2C2×D8×D2311yescharacteristic
subgroupG/H
centerC2C2×D8×D23
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC23×#509C2
socleC2×C23C22×D8
hypercenter#509D23
hypocenterC23#3415
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #13093219C2semidirect
2. #13093218C2semidirect
3. #13092855C2semidirect
4. #13092854C2semidirect
5. #13092851C2semidirect
6. #13092848C2semidirect
7. #13092847C2semidirect
8. C2×#10625008C2semidirect
9. D16×D23C2semidirect
10. #13092835C2semidirect
11. C23×#509C2semidirect
14. C23×#135C22semidirect
15. C2×D8×C23C22semidirect
18. #10625090C22semidirect
20. #10625083C22semidirect
22. D8×D23C22semidirect
23. D8×D23C22semidirect
24. #10625075C22semidirect
25. C2×D184C22semidirect
27. C23×SD32C22semidirect
28. C23×D16C22semidirect
29. C23×M32C22semidirect
30. #10625011C22semidirect
31. #10625010C22semidirect
32. #10625009C22semidirect
33. #10625008C22semidirect
34. #10625008C22semidirect
35. #10625008C22semidirect
36. C2×C23⋊C16C22semidirect
37. #10624982C22semidirect
38. D368C22semidirect
39. #10624980C22semidirect
40. C16×D23C22semidirect
128. #509D23semidirect
150. #135C2×D23semidirect
154. C2×D8C2×D23semidirect
160. SD32C2×D23semidirect
165. D16C2×D23semidirect
167. M32C2×D23semidirect
170. C23#3415semidirect

Maximal subgroups

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

subgroupindex
#130932192
#130932182
#130928552
#130928542
#130928512
#130928482
#130928472
C2×#106250082
D16×D232
#130928352
C23×#5092
#341523