Finite Group Databasebeta

← #28403717

Subgroups — #28403717

Order 14464.

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#20299412C211yesmaximal, characteristic, complemented
2#20299400C211yesmaximal, characteristic, complemented
3#20299040C212yesmaximal, complemented
4#20299038C211yesmaximal, characteristic, complemented
5#20299033C211yesmaximal, characteristic, complemented
6#20299032C212yesmaximal, complemented
7#20299029C212yesmaximal, complemented
8C2×#16813567C211yesmaximal, characteristic, complemented
9SD32×D113C212yesmaximal, complemented
10#20299014C211yesmaximal, characteristic, complemented
11#508×C113C211yesmaximal, characteristic, complemented
12#16813669—21no—
13#16813668—21no—
14#16813652—21no—
15#16813651—22no—
16#16813649—22no—
17#16813647—21no—
18#16813645C2212yes—
19#16813641C2212yescomplemented
20C2×Dic452C2211yescharacteristic, complemented
21Q16×D113C2212yescomplemented
22C2×D904C2211yescharacteristic
23D8×D113C2212yes—
24#16813628C2211yescharacteristic
25#16813568C2212yescomplemented
26#16813567C2212yescomplemented
27#16813567C2212yescomplemented
28#16813566C2212yescomplemented
29#16813565C2212yescomplemented
30#16813563C2212yescomplemented
31#16813562C2211yescharacteristic, complemented
32#16813561C2212yescomplemented
33C16×D113C2212yescomplemented
34#135×C113C2211yescharacteristic
35#135×C113C2211yescharacteristic, complemented
36Q32×C113C2211yescharacteristic, complemented
37SD32×C113C2211yescharacteristic, complemented
38SD32×C113C2211yescharacteristic, complemented
39D16×C113C2211yescharacteristic, complemented
40C2×C16×C113C2211yescharacteristic, complemented
41#14268648—22no—
42#14268647—41no—
43#14268647—41no—
44#14268647D411yescharacteristic
45#14268646—22no—
46#14268646—42no—
47C2×Dic226—21no—
48C2×Dic226—41no—
49Q8×D113—22no—
50C2×D452—21no—
51C2×D452—41no—
52D4×D113—22no—
53D4×D113—42no—
54Dic452—21no—
55Dic452C2312yes—
56#14268637—22no—
57#14268635—22no—
58#14268634—22no—
59D904—21no—
60D904C2312yes—
61#14268632—22no—
62#14268631D411yescharacteristic
63#14268630D412yes—
64C8×D113C2312yes—
65#14268622C2312yes—
66#41×C113—21no—
67#41×C113—21no—
68Q16×C113C2311yescharacteristic
69Q16×C113C2311yescharacteristic
70SD16×C113—21no—
71SD16×C113—21no—
72D8×C113C2311yescharacteristic
73D8×C113C2311yescharacteristic
74C2×C8×C113C2311yescharacteristic
75C16×C113C2311yescharacteristic
76C16×C113C2311yescharacteristic
77C22×D113—41no—
78C22×D113—42no—
79Q8×C113—21no—
80Q8×C113—21no—
81D4×C113—21no—
82D4×C113—21no—
83D4×C113—41no—
84D4×C113—41no—
85C2×C4×C113—41no—
86C2×C4×C113—41no—
87C2×C4×C113C2×D411yescharacteristic
88C22⋊D113—42no—
89C22⋊D113—42no—
90C22⋊D113D812yes—
91C2×Dic113—41no—
92C2×Dic113—42no—
93D452—22no—
94D452—42no—
95D452—41no—
96D452D811yescharacteristic
97C4×D113—42no—
98C4×D113—42no—
99C4×D113C2×D412yes—
100Dic226—22no—
101Dic226—41no—
102Dic226—42no—
103Dic226D811yescharacteristic
104C8×C113C2×D411yescharacteristic
105C8×C113C2411yescharacteristic
106#11744751C2×D412yes—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113C2×D811yescharacteristic
110C2×D113—42no—
111C2×D113—162no—
112C2×D113—161no—
113C2×D113C2×D812yes—
114C4×C113—41no—
115C4×C113—41no—
116C4×C113C2×D811yescharacteristic
117C4×C113C22×D411yescharacteristic
118Dic113—42no—
119Dic113C2×D812yes—
120C2×C113—21no—
121C2×C113—81no—
122C2×C113—81no—
123C2×C113C22×D811yescharacteristic
124D113—22no—
125D113—82no—
126#3416—1131nomaximal, Sylow
127C113#341611yescharacteristic, complemented, Sylow
128#578—1131no—
129#576—1131no—
130#510—1131no—
131#510—1132no—
132#509—1131no—
133#509—1132no—
134#508—1132no—
135#508D11311yescharacteristic, complemented
136C2×SD32—1132no—
137C2×SD32—1131no—
138#504—1131no—
1392−1+4—2261no—
140H(5,𝔽2)—2261no—
141#137—2262no—
142#137—2261no—
143AGL(1,ℤ/8)—2262no—
144AGL(1,ℤ/8)—2261no—
145#135—1132no—
146#135—1132no—
147#135C2×D11311yescharacteristic
148#135C2×D11311yescharacteristic, complemented
149C2×Q16—1132no—
150C2×Q16—1131no—
151C2×D8—1132no—
152C2×D8—1131no—
153#131—1131no—
154Q32—1132no—
155Q32C2×D11311yescharacteristic, complemented
156SD32—1132no—
157SD32—1132no—
158SD32—1132no—
159SD32—1132no—
160SD32C2×D11311yescharacteristic, complemented
161SD32C2×D11311yescharacteristic, complemented
162D16—1132no—
163D16C2×D11311yescharacteristic, complemented
164M32—1131no—
165M32—1132no—
166C2×C16—1132no—
167C2×C16C2×D11311yescharacteristic, complemented
168#41—21no—
169#41—21no—
170#41—1131no—
171#41—4521no—
172#41—4521no—
173#41—4522no—
174#41—2262no—
175#41—2262no—
176C2×Q8—4521no—
177C2×Q8—2262no—
178C2×Q8—2261no—
179C2×D4—4521no—
180C2×D4—4522no—
181C2×D4—2262no—
182C2×D4—2261no—
183Q16—1132no—
184Q16—2262no—
185Q16—2261no—
186Q16C22×D11311yescharacteristic
187Q16C22×D11311yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—2262no—
191SD16—2262no—
192D8—1132no—
193D8—2262no—
194D8—2261no—
195D8C22×D11311yescharacteristic
196D8C22×D11311yescharacteristic
197M16—1131no—
198M16—1132no—
199C2×C8—1132no—
200C2×C8C22×D11311yescharacteristic
201C16—1132no—
202C16C22×D11311yescharacteristic
203C16C22×D11311yescharacteristic
204C23—4522no—
205C23—4521no—
206Q8—21no—
207Q8—21no—
208Q8—1131no—
209Q8—4522no—
210Q8—4521no—
211Q8—2262no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—1132no—
217D4—1131no—
218D4—4522no—
219D4—4522no—
220D4—4522no—
221D4—4521no—
222D4—2262no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—1132no—
226C2×C4—4522no—
227C2×C4—4522no—
228C2×C4—4522no—
229C2×C4—4521no—
230C2×C4D4×D11311yescharacteristic
231C8—1132no—
232C8D4×D11311yescharacteristic
233C8C23×D11311yescharacteristic
234C22—41no—
235C22—41no—
236C22—18081no—
237C22—18082no—
238C22—1132no—
239C22—4522no—
240C22D8×D11311yescharacteristic
241C4—41no—
242C4—41no—
243C4—1132no—
244C4—4522no—
245C4D8×D11311yescharacteristic
246C4C2×D4×D11311yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—9042no—
251C2—2262no—
252C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#508×C113C2
socleC2×C113C22×D8
hypercenter#508D113
hypocenterC113#3416
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #20299412C2semidirect
2. #20299400C2semidirect
3. #20299040C2semidirect
4. #20299038C2semidirect
5. #20299033C2semidirect
6. #20299032C2semidirect
7. #20299029C2semidirect
8. C2×#16813567C2semidirect
9. SD32×D113C2semidirect
10. #20299014C2semidirect
11. #508×C113C2semidirect
19. #16813641C22semidirect
20. C2×Dic452C22semidirect
21. Q16×D113C22semidirect
25. #16813568C22semidirect
26. #16813567C22semidirect
27. #16813567C22semidirect
28. #16813566C22semidirect
29. #16813565C22semidirect
30. #16813563C22semidirect
31. #16813562C22semidirect
32. #16813561C22semidirect
33. C16×D113C22semidirect
35. #135×C113C22semidirect
36. Q32×C113C22semidirect
37. SD32×C113C22semidirect
38. SD32×C113C22semidirect
39. D16×C113C22semidirect
40. C2×C16×C113C22semidirect
127. C113#3416semidirect
135. #508D113semidirect
148. #135C2×D113semidirect
155. Q32C2×D113semidirect
160. SD32C2×D113semidirect
161. SD32C2×D113semidirect
163. D16C2×D113semidirect
167. C2×C16C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994122
#202994002
#202990402
#202990382
#202990332
#202990322
#202990292
C2×#168135672
SD32×D1132
#202990142
#508×C1132
#3416113