Finite Group Databasebeta

← #28403714

Subgroups — #28403714

Order 14464.

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#20299400C211yesmaximal, characteristic, complemented
2#20299399C211yesmaximal, characteristic, complemented
3#20299036C211yesmaximal, characteristic, complemented
4#20299035C212yesmaximal, complemented
5#20299032C212yesmaximal, complemented
6#20299029C212yesmaximal, complemented
7#20299028C211yesmaximal, characteristic, complemented
8C2×#16813563C211yesmaximal, characteristic, complemented
9D16×D113C212yesmaximal, complemented
10#20299016C211yesmaximal, characteristic, complemented
11#509×C113C211yesmaximal, characteristic, complemented
12#16813668—21no—
13#16813667—21no—
14#16813649—22no—
15#16813648—21no—
16#16813647—21no—
17#16813646—22no—
18#16813645C2212yescomplemented
19#16813644C2211yescharacteristic, complemented
20#16813641C2212yescomplemented
21C2×D904C2211yescharacteristic, complemented
22D8×D113C2212yescomplemented
23D8×D113C2212yescomplemented
24#16813628C2211yescharacteristic
25#16813568C2211yescharacteristic, complemented
26#16813567C2212yescomplemented
27#16813566C2211yescharacteristic, complemented
28#16813565C2211yescharacteristic, complemented
29D1808C2212yescomplemented
30#16813563C2211yescharacteristic, complemented
31#16813563C2212yescomplemented
32#16813563C2212yescomplemented
33#16813561C2212yescomplemented
34C2×#14268622C2211yescharacteristic, complemented
35C16×D113C2212yescomplemented
36#135×C113C2211yescharacteristic, complemented
37C2×D8×C113C2211yescharacteristic, complemented
38SD32×C113C2212yescomplemented
39D16×C113C2212yescomplemented
40M32×C113C2211yescharacteristic, complemented
41#14268648—22no—
42#14268647—21no—
43#14268647—41no—
44#14268647D411yescharacteristic
45#14268646—22no—
46#14268646—41no—
47C2×D452—21no—
48C2×D452—41no—
49C2×C22⋊D113—42no—
50D4×D113—22no—
51D4×D113—22no—
52D4×D113—42no—
53D4×D113—41no—
54Dic452C2311yescharacteristic
55#14268636—21no—
56#14268635—22no—
57#14268634—22no—
58D904—21no—
59D904C2311yescharacteristic
60D904C2312yes—
61#14268632—22no—
62#14268632—22no—
63#14268631D411yescharacteristic
64#14268630D412yes—
65C8×D113C2312yes—
66#14268622C2311yescharacteristic
67#14268622C2311yescharacteristic
68#41×C113—21no—
69C2×D4×C113—21no—
70Q16×C113C2311yescharacteristic
71SD16×C113—21no—
72D8×C113—21no—
73D8×C113C2311yescharacteristic
74D8×C113C2312yes—
75C2×C8×C113C2311yescharacteristic
76C16×C113C2312yes—
77C23×C113—41no—
78C22×D113—41no—
79C22×D113—42no—
80C22×D113—42no—
81Q8×C113—21no—
82D4×C113—22no—
83D4×C113—21no—
84D4×C113—41no—
85D4×C113—41no—
86C2×C4×C113—41no—
87C2×C4×C113C2×D411yescharacteristic
88C22⋊D113—41no—
89C22⋊D113—42no—
90C22⋊D113—42no—
91C22⋊D113—42no—
92C22⋊D113D812yes—
93C2×Dic113—42no—
94D452—21no—
95D452—22no—
96D452—42no—
97D452—41no—
98D452D811yescharacteristic
99C4×D113—41no—
100C4×D113—42no—
101C4×D113C2×D412yes—
102Dic226—21no—
103Dic226D811yescharacteristic
104C8×C113C2×D411yescharacteristic
105C8×C113C2411yescharacteristic
106#11744751C2×D412yes—
107C22×C113—42no—
108C22×C113—41no—
109C22×C113—161no—
110C22×C113C2×D811yescharacteristic
111C2×D113—42no—
112C2×D113—41no—
113C2×D113—162no—
114C2×D113—162no—
115C2×D113—161no—
116C2×D113C2×D812yes—
117C4×C113—41no—
118C4×C113C2×D811yescharacteristic
119C4×C113C22×D411yescharacteristic
120Dic113—41no—
121Dic113C2×D812yes—
122C2×C113—21no—
123C2×C113—81no—
124C2×C113—82no—
125C2×C113C22×D811yescharacteristic
126D113—22no—
127D113—82no—
128D113—81no—
129#3415—1131nomaximal, Sylow
130C113#341511yescharacteristic, complemented, Sylow
131#576—1131no—
132#576—1131no—
133#509—1132no—
134#509—1132no—
135#509—1131no—
136#509D11311yescharacteristic, complemented
137#508—1131no—
138#508—1132no—
139C2×D16—1131no—
140C2×D16—1132no—
141#504—1131no—
142H(5,𝔽2)—2261no—
143H(5,𝔽2)—2261no—
144AGL(1,ℤ/8)—2262no—
145AGL(1,ℤ/8)—2262no—
146AGL(1,ℤ/8)—2261no—
147AGL(1,ℤ/8)—2261no—
148#135—1132no—
149#135—1132no—
150#135—1131no—
151#135C2×D11311yescharacteristic, complemented
152C2×D8—1132no—
153C2×D8—1132no—
154C2×D8—1131no—
155C2×D8C2×D11311yescharacteristic, complemented
156#131—1131no—
157Q32—1131no—
158SD32—1131no—
159SD32—1131no—
160SD32—1132no—
161SD32C2×D11312yescomplemented
162D16—1132no—
163D16—1131no—
164D16—1132no—
165D16—1132no—
166D16C2×D11312yescomplemented
167M32—1132no—
168M32C2×D11311yescharacteristic, complemented
169C2×C16—1131no—
170C2×C16—1132no—
171#41—21no—
172#41—1131no—
173#41—4521no—
174#41—4521no—
175#41—2262no—
176#41—2262no—
177#41—2261no—
178C2×D4—21no—
179C2×D4—4521no—
180C2×D4—4522no—
181C2×D4—4521no—
182C2×D4—4522no—
183C2×D4—2262no—
184C2×D4—2262no—
185C2×D4—2261no—
186Q16—1131no—
187Q16C22×D11311yescharacteristic
188SD16—21no—
189SD16—2262no—
190SD16—2262no—
191SD16—2261no—
192D8—21no—
193D8—1132no—
194D8—1131no—
195D8—2262no—
196D8—2262no—
197D8—2261no—
198D8C22×D11312yes—
199D8C22×D11311yescharacteristic
200M16—1131no—
201M16—1132no—
202C2×C8—1132no—
203C2×C8C22×D11311yescharacteristic
204C16—1131no—
205C16—1131no—
206C16C22×D11312yes—
207C23—41no—
208C23—4522no—
209C23—4522no—
210C23—4521no—
211Q8—21no—
212Q8—1131no—
213Q8—2261no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—1132no—
219D4—1131no—
220D4—4522no—
221D4—4522no—
222D4—4522no—
223D4—4522no—
224D4—4521no—
225D4—4521no—
226D4—2261no—
227D4—2262no—
228C2×C4—41no—
229C2×C4—1132no—
230C2×C4—4522no—
231C2×C4—4522no—
232C2×C4—4521no—
233C2×C4D4×D11311yescharacteristic
234C8—1132no—
235C8D4×D11311yescharacteristic
236C8C23×D11311yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—18081no—
241C22—18082no—
242C22—18082no—
243C22—1132no—
244C22—4522no—
245C22—4521no—
246C22D8×D11311yescharacteristic
247C4—41no—
248C4—1132no—
249C4—4521no—
250C4D8×D11311yescharacteristic
251C4C2×D4×D11311yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—9042no—
256C2—9041no—
257C2—2262no—
258C2C2×D8×D11311yescharacteristic
subgroupG/H
centerC2C2×D8×D113
commutator, cosocleC8×C113C24
FrattiniC8C23×D113
Fitting#509×C113C2
socleC2×C113C22×D8
hypercenter#509D113
hypocenterC113#3415
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #20299400C2semidirect
2. #20299399C2semidirect
3. #20299036C2semidirect
4. #20299035C2semidirect
5. #20299032C2semidirect
6. #20299029C2semidirect
7. #20299028C2semidirect
8. C2×#16813563C2semidirect
9. D16×D113C2semidirect
10. #20299016C2semidirect
11. #509×C113C2semidirect
18. #16813645C22semidirect
19. #16813644C22semidirect
20. #16813641C22semidirect
21. C2×D904C22semidirect
22. D8×D113C22semidirect
23. D8×D113C22semidirect
25. #16813568C22semidirect
26. #16813567C22semidirect
27. #16813566C22semidirect
28. #16813565C22semidirect
29. D1808C22semidirect
30. #16813563C22semidirect
31. #16813563C22semidirect
32. #16813563C22semidirect
33. #16813561C22semidirect
34. C2×#14268622C22semidirect
35. C16×D113C22semidirect
36. #135×C113C22semidirect
37. C2×D8×C113C22semidirect
38. SD32×C113C22semidirect
39. D16×C113C22semidirect
40. M32×C113C22semidirect
130. C113#3415semidirect
136. #509D113semidirect
151. #135C2×D113semidirect
155. C2×D8C2×D113semidirect
161. SD32C2×D113semidirect
166. D16C2×D113semidirect
168. M32C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994002
#202993992
#202990362
#202990352
#202990322
#202990292
#202990282
C2×#168135632
D16×D1132
#202990162
#509×C1132
#3415113