Finite Group Databasebeta

← #15686539

Subgroups — #15686539

Order 2944.

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

normal subgroups only

This group has 360 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#13093230C211yesmaximal, characteristic, complemented
2#13093218C211yesmaximal, characteristic, complemented
3#13092858C211yesmaximal, characteristic, complemented
4#13092856C212yesmaximal, complemented
5#13092854C212yesmaximal, complemented
6#13092853C211yesmaximal, characteristic, complemented
7#13092849C211yesmaximal, characteristic, complemented
8#13092848C212yesmaximal, complemented
9SD32×D23C212yesmaximal, complemented
10#13092833C211yesmaximal, characteristic, complemented
11C2×C23×SD32C211yesmaximal, characteristic, complemented
12#10625158—21no—
13#10625155—21no—
14C2×Q16×C23C2211yescharacteristic, complemented
15C2×D8×C23C2211yescharacteristic
16#10625113—21no—
17#10625103—21no—
18#10625090C2212yescomplemented
19#10625089—22no—
20Q16×D23C2212yescomplemented
21#10625083C2212yes—
22#10625082—22no—
23D8×D23C2212yes—
24#10625075C2211yescharacteristic
25#10625075C2211yescharacteristic, complemented
26#10625072C2211yescharacteristic
27C23×SD32C2212yescomplemented
28C23×SD32C2212yescomplemented
29C2×C16×C23C2211yescharacteristic, complemented
30#10625011C2212yescomplemented
31#10625010C2212yescomplemented
32#10625009C2212yescomplemented
33#10625008C2212yescomplemented
34#10624994C2211yescharacteristic, complemented
35Dic184C2211yescharacteristic, complemented
36#10624982C2211yescharacteristic, complemented
37#10624982C2211yescharacteristic, complemented
38D368C2211yescharacteristic, complemented
39#10624980C2212yescomplemented
40C16×D23C2212yescomplemented
41C2×Q8×C23—21no—
42C2×D4×C23—21no—
43C2×C22⋊D23—42no—
44#67292—22no—
45#67292—41no—
46Q8×D23—22no—
47Q8×D23—41no—
48#67290—22no—
49#67290—41no—
50D4×D23—22no—
51D4×D23—41no—
52#67288—21no—
53#67288—21no—
54#67288—42no—
55#67288D411yescharacteristic
56Q16×C23—21no—
57Q16×C23C2312yes—
58D8×C23—21no—
59D8×C23C2312yes—
60C2×C8×C23C2311yescharacteristic
61#67275—22no—
62#67274—22no—
63#67273—22no—
64#67272—22no—
65#67267D411yescharacteristic
66Dic92C2311yescharacteristic
67Dic92C2311yescharacteristic
68D184C2311yescharacteristic
69D184C2311yescharacteristic
70#67263—21no—
71#67263—21no—
72#67262D412yes—
73C8×D23C2312yes—
74C16×C23C2311yescharacteristic
75C16×C23C2311yescharacteristic
76C23⋊C16C2312yes—
77C23×C23—41no—
78C22×D23—42no—
79Q8×C23—22no—
80Q8×C23—41no—
81D4×C23—22no—
82D4×C23—41no—
83C2×C4×C23—41no—
84C2×C4×C23C2×D411yescharacteristic
85C22⋊D23—41no—
86C22⋊D23—41no—
87C22⋊D23—42no—
88C22⋊D23—42no—
89C22⋊D23D812yes—
90C2×Dic23—42no—
91D92—21no—
92D92—21no—
93D92—42no—
94D92D811yescharacteristic
95C4×D23—42no—
96C4×D23—41no—
97C4×D23—41no—
98C4×D23—42no—
99C4×D23C2×D412yes—
100Dic46—21no—
101Dic46—21no—
102Dic46—42no—
103Dic46D811yescharacteristic
104C8×C23C2×D411yescharacteristic
105C8×C23C2411yescharacteristic
106C23⋊C8C2×D412yes—
107#3416—231nomaximal, Sylow
108C22×C23—42no—
109C22×C23—161no—
110C22×C23C2×D811yescharacteristic
111C2×D23—41no—
112C2×D23—41no—
113C2×D23—162no—
114C2×D23C2×D812yes—
115C4×C23—42no—
116C4×C23C2×D811yescharacteristic
117C4×C23C22×D411yescharacteristic
118Dic23—41no—
119Dic23—41no—
120Dic23C2×D812yes—
121#578—231no—
122#576—231no—
123#510—231no—
124#510—232no—
125#509—231no—
126#509—232no—
127#508—232no—
128#508—231no—
129C2×SD32—232no—
130C2×SD32D2311yescharacteristic, complemented
131#504—231no—
132C2×C23—21no—
133C2×C23—82no—
134C2×C23C22×D811yescharacteristic
135D23—22no—
136D23—81no—
137D23—81no—
1382−1+4—461no—
139H(5,𝔽2)—461no—
140#137—462no—
141#137—461no—
142AGL(1,ℤ/8)—462no—
143AGL(1,ℤ/8)—461no—
144#135—232no—
145#135—232no—
146#135—231no—
147#135—231no—
148C2×Q16—232no—
149C2×Q16C2×D2311yescharacteristic, complemented
150C2×D8—232no—
151C2×D8C2×D2311yescharacteristic
152#131—231no—
153Q32—232no—
154Q32—231no—
155SD32—232no—
156SD32—232no—
157SD32—231no—
158SD32—231no—
159SD32C2×D2312yescomplemented
160SD32C2×D2312yescomplemented
161D16—232no—
162D16—231no—
163M32—231no—
164M32—232no—
165C2×C16—232no—
166C2×C16C2×D2311yescharacteristic, complemented
167C23#341611yescharacteristic, complemented, Sylow
168#41—231no—
169#41—462no—
170#41—462no—
171#41—461no—
172#41—461no—
173#41—922no—
174#41—921no—
175#41—921no—
176C2×Q8—21no—
177C2×Q8—462no—
178C2×Q8—921no—
179C2×D4—21no—
180C2×D4—462no—
181C2×D4—921no—
182C2×D4—922no—
183Q16—21no—
184Q16—231no—
185Q16—231no—
186Q16—462no—
187Q16C22×D2312yes—
188SD16—462no—
189SD16—462no—
190SD16—461no—
191SD16—461no—
192D8—21no—
193D8—231no—
194D8—231no—
195D8—462no—
196D8C22×D2312yes—
197M16—231no—
198M16—232no—
199C2×C8—232no—
200C2×C8C22×D2311yescharacteristic
201C16—232no—
202C16C22×D2311yescharacteristic
203C16C22×D2311yescharacteristic
204C23—41no—
205C23—922no—
206Q8—22no—
207Q8—41no—
208Q8—231no—
209Q8—461no—
210Q8—461no—
211Q8—922no—
212D4—22no—
213D4—41no—
214D4—232no—
215D4—231no—
216D4—461no—
217D4—461no—
218D4—922no—
219D4—922no—
220D4—922no—
221D4—921no—
222D4—921no—
223C2×C4—41no—
224C2×C4—232no—
225C2×C4—922no—
226C2×C4—922no—
227C2×C4—922no—
228C2×C4—921no—
229C2×C4—921no—
230C2×C4D4×D2311yescharacteristic
231C8—232no—
232C8D4×D2311yescharacteristic
233C8C23×D2311yescharacteristic
234C22—42no—
235C22—161no—
236C22—232no—
237C22—921no—
238C22—921no—
239C22—3682no—
240C22D8×D2311yescharacteristic
241C4—42no—
242C4—232no—
243C4—921no—
244C4—921no—
245C4D8×D2311yescharacteristic
246C4C2×D4×D2311yescharacteristic
247C2—21no—
248C2—82no—
249C2—462no—
250C2—1841no—
251C2—1841no—
252C2C2×D8×D2311yescharacteristic
subgroupG/H
centerC2C2×D8×D23
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC2×C23×SD32C2
socleC2×C23C22×D8
hypercenterC2×SD32D23
hypocenterC23#3416
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #13093230C2semidirect
2. #13093218C2semidirect
3. #13092858C2semidirect
4. #13092856C2semidirect
5. #13092854C2semidirect
6. #13092853C2semidirect
7. #13092849C2semidirect
8. #13092848C2semidirect
9. SD32×D23C2semidirect
10. #13092833C2semidirect
11. C2×C23×SD32C2semidirect
14. C2×Q16×C23C22semidirect
18. #10625090C22semidirect
20. Q16×D23C22semidirect
25. #10625075C22semidirect
27. C23×SD32C22semidirect
28. C23×SD32C22semidirect
29. C2×C16×C23C22semidirect
30. #10625011C22semidirect
31. #10625010C22semidirect
32. #10625009C22semidirect
33. #10625008C22semidirect
34. #10624994C22semidirect
35. Dic184C22semidirect
36. #10624982C22semidirect
37. #10624982C22semidirect
38. D368C22semidirect
39. #10624980C22semidirect
40. C16×D23C22semidirect
130. C2×SD32D23semidirect
149. C2×Q16C2×D23semidirect
159. SD32C2×D23semidirect
160. SD32C2×D23semidirect
166. C2×C16C2×D23semidirect
167. C23#3416semidirect

Maximal subgroups

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

subgroupindex
#130932302
#130932182
#130928582
#130928562
#130928542
#130928532
#130928492
#130928482
SD32×D232
#130928332
C2×C23×SD322
#341623