Finite Group Databasebeta

← #28402368

Subgroups — #28402368

Order 14464.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#20299410C212yesmaximal, complemented
2#20299405C212yesmaximal, complemented
3#20298971C211yesmaximal, characteristic, complemented
4#20298862C212yesmaximal, complemented
5#20298861C212yesmaximal, complemented
6#20298782C212yesmaximal, complemented
7#20298767C212yesmaximal, complemented
8#20298716C211yesmaximal, characteristic, complemented
9#443×C113C211yesmaximal, characteristic, complemented
10#16813669C2212yes—
11#16813668C2212yescomplemented
12#16813655—22no—
13#16813655C2212yescomplemented
14#16813654—22no—
15#16813652C2212yescomplemented
16#16813650—22no—
17#16813650C2212yes—
18#16813647C2212yes—
19#16813646—22no—
20#16813644—22no—
21#16813644C2211yescharacteristic
22#16813643—22no—
23C2×#14268636—22no—
24C2×#14268636C2212yescomplemented
25C2×#14268636C2212yescomplemented
26SD16×D113—22no—
27#16813628C2212yescomplemented
28#16813622C2211yescharacteristic, complemented
29#16813619C2211yescharacteristic
30#16813558C2211yescharacteristic, complemented
31#16813550C2212yescomplemented
32#16813540C2212yescomplemented
33#16813538C2212yescomplemented
34#135×C113C2211yescharacteristic
35#131×C113C2212yescomplemented
36#108×C113C2211yescharacteristic, complemented
37#104×C113C2212yescomplemented
38C4×C8×C113C2211yescharacteristic, complemented
39#14268648—22no—
40#14268647—22no—
41#14268647—22no—
42#14268647C2312yes—
43#14268646—22no—
44#14268646—42no—
45C2×Dic226—22no—
46C2×Dic226C2312yes—
47Q8×D113—22no—
48C2×D452—22no—
49C2×D452—41no—
50C2×D452C2312yes—
51D4×D113—22no—
52D4×D113—42no—
53Dic452—22no—
54Dic452D411yescharacteristic, complemented
55#14268637—22no—
56#14268636—22no—
57#14268636—22no—
58#14268636—22no—
59#14268636—22no—
60#14268636—22no—
61#14268636—22no—
62#14268636D412yescomplemented
63#14268635—22no—
64#14268634—22no—
65D904—22no—
66D904D411yescharacteristic, complemented
67#14268632—22no—
68#14268631C2312yes—
69#14268630—22no—
70C8×D113—22no—
71C4⋊Dic113—41no—
72#41×C113C2312yes—
73Q16×C113D411yescharacteristic, complemented
74SD16×C113D412yescomplemented
75D8×C113D411yescharacteristic, complemented
76M16×C113—22no—
77M16×C113C2312yes—
78C2×C8×C113—22no—
79C2×C8×C113C2311yescharacteristic
80C2×C8×C113C2311yescharacteristic
81C42×C113C2311yescharacteristic
82C22×D113—22no—
83C22×D113—42no—
84Q8×C113C2×D412yes—
85D4×C113—22no—
86D4×C113C2×D412yes—
87C2×C4×C113—21no—
88C2×C4×C113—22no—
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—22no—
91C22⋊D113—42no—
92C22⋊D113—42no—
93C2×Dic113—22no—
94C2×Dic113—42no—
95D452—22no—
96D452—22no—
97D452—42no—
98D452—82no—
99D452C2×D412yes—
100C4×D113—22no—
101C4×D113—42no—
102C4×D113—42no—
103Dic226—22no—
104Dic226—22no—
105Dic226—42no—
106Dic226C2×D412yes—
107C8×C113—22no—
108C8×C113C2×D411yescharacteristic
109C8×C113C2×D411yescharacteristic
110C8×C113C2×D411yescharacteristic
111C8×C113C2×D411yescharacteristic
112#11744751—22no—
113C22×C113—22no—
114C22×C113H(5,𝔽2)11yescharacteristic
115C2×D113—22no—
116C2×D113—42no—
117C2×D113—82no—
118C2×D113—162no—
119C4×C113—22no—
120C4×C113—22no—
121C4×C113C22×D411yescharacteristic
122C4×C113C22×D411yescharacteristic
123Dic113—22no—
124Dic113—42no—
125C2×C113—21no—
126C2×C113—42no—
127C2×C113D4211yescharacteristic
128D113—42no—
129D113—82no—
130#3291—1131nomaximal, Sylow
131C113#329111yescharacteristic, complemented, Sylow
132#577—1132no—
133#577—1132no—
134#492—1131no—
135#471—1132no—
136#471—1132no—
137#456—1132no—
138#453—1132no—
139#443—1131no—
140#443D11311yescharacteristic, complemented
1412−1+4—1132no—
142H(5,𝔽2)—1132no—
143#137—1132no—
144#137—1132no—
145#137—2262no—
146#137—2262no—
147AGL(1,ℤ/8)—1132no—
148AGL(1,ℤ/8)—1132no—
149AGL(1,ℤ/8)—2262no—
150AGL(1,ℤ/8)—2262no—
151#135—1131no—
152#135—2262no—
153#135—2262no—
154#135C2×D11311yescharacteristic
155C2×SD16—1132no—
156C2×SD16—1132no—
157C2×SD16—2262no—
158C2×SD16—2262no—
159#131—1132no—
160#131C2×D11312yescomplemented
161C4⋊Q8—1131no—
162#127—1131no—
163#108—1131no—
164#108C2×D11311yescharacteristic, complemented
165#104—1132no—
166#104C2×D11312yescomplemented
167#101—1132no—
168#100—1132no—
169C4×C8C2×D11311yescharacteristic, complemented
170#41—1132no—
171#41—4522no—
172#41—2262no—
173#41—2262no—
174#41—2262no—
175#41—2262no—
176#41C22×D11312yes—
177C2×Q8—1132no—
178C2×Q8—2262no—
179C2×Q8—2262no—
180C2×D4—1132no—
181C2×D4—4521no—
182C2×D4—4522no—
183C2×D4—2262no—
184C2×D4—2262no—
185Q16—1131no—
186Q16—2262no—
187Q16—2262no—
188Q16D45211yescharacteristic, complemented
189SD16—1132no—
190SD16—2262no—
191SD16—2262no—
192SD16—2262no—
193SD16—2262no—
194SD16—2262no—
195SD16—2262no—
196SD16—2262no—
197SD16—2262no—
198SD16D45212yescomplemented
199D8—1131no—
200D8—2262no—
201D8—2262no—
202D8D45211yescharacteristic, complemented
203M16—22no—
204M16—1132no—
205M16—2262no—
206M16C22×D11312yes—
207C2×C8—22no—
208C2×C8—2262no—
209C2×C8C22×D11311yescharacteristic
210C2×C8C22×D11311yescharacteristic
211C4⋊C4—4521no—
212C42C22×D11311yescharacteristic
213C23—4522no—
214C23—2262no—
215Q8—1132no—
216Q8—4522no—
217Q8—2262no—
218Q8—2262no—
219Q8C2×D45212yes—
220D4—22no—
221D4—1132no—
222D4—9042no—
223D4—4522no—
224D4—4522no—
225D4—4522no—
226D4—2262no—
227D4—2262no—
228D4—2262no—
229D4C2×D45212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—4522no—
233C2×C4—4522no—
234C2×C4—4522no—
235C2×C4—2262no—
236C2×C4—2262no—
237C2×C4C23×D11311yescharacteristic
238C8—22no—
239C8—2262no—
240C8D4×D11311yescharacteristic
241C8D4×D11311yescharacteristic
242C8C2×D45211yescharacteristic
243C8C2×D45211yescharacteristic
244C22—22no—
245C22—18082no—
246C22—9042no—
247C22—4522no—
248C22—2262no—
249C22#1681366811yescharacteristic
250C4—22no—
251C4—22no—
252C4—4522no—
253C4—2262no—
254C4C2×D4×D11311yescharacteristic
255C4C22×D45211yescharacteristic
256C2—21no—
257C2—42no—
258C2—9042no—
259C2—4522no—
260C2D4×D45211yescharacteristic
subgroupG/H
centerC2D4×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#443×C113C2
socleC2×C113D42
hypercenter#443D113
hypocenterC113#3291
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #20299410C2semidirect
2. #20299405C2semidirect
3. #20298971C2semidirect
4. #20298862C2semidirect
5. #20298861C2semidirect
6. #20298782C2semidirect
7. #20298767C2semidirect
8. #20298716C2semidirect
9. #443×C113C2semidirect
11. #16813668C22semidirect
13. #16813655C22semidirect
15. #16813652C22semidirect
24. C2×#14268636C22semidirect
25. C2×#14268636C22semidirect
27. #16813628C22semidirect
28. #16813622C22semidirect
30. #16813558C22semidirect
31. #16813550C22semidirect
32. #16813540C22semidirect
33. #16813538C22semidirect
35. #131×C113C22semidirect
36. #108×C113C22semidirect
37. #104×C113C22semidirect
38. C4×C8×C113C22semidirect
54. Dic452D4semidirect
62. #14268636D4semidirect
66. D904D4semidirect
73. Q16×C113D4semidirect
74. SD16×C113D4semidirect
75. D8×C113D4semidirect
131. C113#3291semidirect
140. #443D113semidirect
160. #131C2×D113semidirect
164. #108C2×D113semidirect
166. #104C2×D113semidirect
169. C4×C8C2×D113semidirect
188. Q16D452semidirect
198. SD16D452semidirect
202. D8D452semidirect

Maximal subgroups

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

subgroupindex
#202994102
#202994052
#202989712
#202988622
#202988612
#202987822
#202987672
#202987162
#443×C1132
#3291113