Finite Group Databasebeta

← #28402183

Subgroups — #28402183

Order 14464.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#16813649C212yesmaximal, complemented
2#20299241C212yesmaximal, complemented
3#20298841C212yesmaximal, complemented
4#20298810C212yesmaximal, complemented
5#20298759C212yesmaximal, complemented
6#20298730C212yesmaximal, complemented
7C4×D904C211yesmaximal, characteristic, complemented
8#20298677C211yesmaximal, characteristic, complemented
9#495×C113C211yesmaximal, characteristic, complemented
10C2×#14268648C2212yes—
11C2×D4×D113C2212yescomplemented
12#16813649—28no—
13C2×#14268634C2212yescomplemented
14C2×D904C2211yescharacteristic
15C2×#14268632C2212yes—
16C2×#14268630C2212yescomplemented
17#16813604—22no—
18#16813598C2212yescomplemented
19#16813595—22no—
20#16813593C2212yes—
21#16813592—22no—
22C4×D452C2211yescharacteristic
23C4×D452C2212yescomplemented
24C22⋊C4×D113—22no—
25#16813556C2211yescharacteristic, complemented
26C4⋊#11744751C2211yescharacteristic, complemented
27#16813546C2212yescomplemented
28#16813544C2212yescomplemented
29#16813543C2212yescomplemented
30#16813534C2212yescomplemented
31C2×Q16×C113C2211yescharacteristic, complemented
32C2×SD16×C113C2212yescomplemented
33C2×D8×C113C2211yescharacteristic
34#124×C113C2212yescomplemented
35C4×C8×C113C2211yescharacteristic, complemented
36C23×D113—22no—
37#14268648—24no—
38#14268648—42no—
39C2×D452—22no—
40C2×D452D411yescharacteristic
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43C2×C22⋊D113—22no—
44D4×D113—24no—
45D4×D113—42no—
46C2×C4×D113—22no—
47C2×C4×D113—22no—
48C2×C4×D113C2312yes—
49#14268634—24no—
50D904D414yescomplemented
51#14268632—24no—
52#14268630—24no—
53C2×#11744751C2312yes—
54C4⋊Dic113D411yescharacteristic
55C4⋊Dic113C2312yes—
56#14268626—22no—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624—22no—
60#14268624D412yes—
61C2×Q8×C113C2312yes—
62C2×D4×C113C2312yes—
63Q16×C113—41no—
64SD16×C113—24no—
65D8×C113—41no—
66C2×C8×C113C2311yescharacteristic
67C2×C8×C113C2311yescharacteristic
68C22⋊C4×C113—22no—
69C22⋊C4×C113—22no—
70C42×C113C2311yescharacteristic
71C23×C113—22no—
72C22×D113—22no—
73C22×D113—44no—
74C22×D113—44no—
75C22×D113—82no—
76C22×D113C2×D412yes—
77Q8×C113—22no—
78Q8×C113—22no—
79D4×C113—22no—
80D4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2411yescharacteristic
85C22⋊D113—44no—
86C22⋊D113—82no—
87C2×Dic113—22no—
88C2×Dic113C2×D412yes—
89D452—22no—
90D452—41no—
91D452—44no—
92D452C2×D414yes—
93C4×D113—22no—
94C4×D113—22no—
95C4×D113—44no—
96C4×D113—82no—
97C8×C113—21no—
98C8×C113C2×D412yes—
99#11744751—22no—
100C22×C113—42no—
101C22×C113—42no—
102C22×C113—42no—
103C22×C113C22×D411yescharacteristic
104C2×D113—22no—
105C2×D113—24no—
106C2×D113—22no—
107C2×D113—22no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—88no—
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—42no—
114C4×C113C22×D411yescharacteristic
115C4×C113H(5,𝔽2)11yescharacteristic
116Dic113—22no—
117Dic113—42no—
118C2×C113—82no—
119C2×C113D4211yescharacteristic
120C2×C113#57511yescharacteristic
121C2×C113#57611yescharacteristic
122D113—42no—
123D113—44no—
124#3273—1131nomaximal, Sylow
125C113#327311yescharacteristic, complemented, Sylow
126C2×AGL(1,ℤ/8)—1132no—
127#546—1132no—
128#495D11311yescharacteristic, complemented
129#468—1132no—
130#463—1132no—
131#452—1132no—
132#447—1132no—
133C4×D8—1131no—
134#436—1131no—
135C2×#41—1132no—
136C22×D4—1132no—
137AGL(1,ℤ/8)—2268no—
138C2×Q16C2×D11311yescharacteristic, complemented
139C2×SD16—1132no—
140C2×SD16C2×D11312yescomplemented
141C2×D8—1132no—
142C2×D8—1131no—
143C2×D8C2×D11311yescharacteristic
144C2×M16—1132no—
145#124C2×D11312yescomplemented
146#123—2262no—
147C22⋊Q8—1132no—
148#121—1132no—
149#121—2262no—
150#120—2262no—
151C4×D4—1131no—
152C4×D4—1132no—
153C2×C22⋊C4—2262no—
154#107—1131no—
155C4⋊C8—1131no—
156#103—1132no—
157#102—1132no—
158#102—1132no—
159C22⋊C8—1132no—
160C4×C8C2×D11311yescharacteristic, complemented
161C24—2262no—
162#41—4522no—
163#41—2264no—
164C2×Q8C22×D11312yes—
165C2×D4—1131no—
166C2×D4—1132no—
167C2×D4—4522no—
168C2×D4—2262no—
169C2×D4—2262no—
170C2×D4—2264no—
171C2×D4—2262no—
172C2×D4C22×D11312yes—
173C22×C4—1132no—
174C22×C4—2262no—
175C22×C4—2262no—
176Q16—41no—
177SD16—24no—
178SD16—2264no—
179D8—41no—
180D8—1134no—
181D8—2264no—
182M16—2264no—
183C2×C8—1132no—
184C2×C8C22×D11311yescharacteristic
185C2×C8C22×D11311yescharacteristic
186C4⋊C4—1131no—
187C4⋊C4—1132no—
188C4⋊C4—2262no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—1132no—
192C22⋊C4—2262no—
193C22⋊C4—2262no—
194C22⋊C4—2262no—
195C42C22×D11311yescharacteristic
196C23—22no—
197C23—1132no—
198C23—9042no—
199C23—4524no—
200C23—4524no—
201C23—2262no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—1134no—
207D4—9042no—
208D4—4521no—
209D4—4524no—
210D4—4524no—
211D4—2262no—
212C2×C4—22no—
213C2×C4—1132no—
214C2×C4—9042no—
215C2×C4—4524no—
216C2×C4—2262no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4D4×D11311yescharacteristic
220C2×C4D4×D11311yescharacteristic
221C2×C4C23×D11311yescharacteristic
222C8—21no—
223C8—2262no—
224C8D4×D11312yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—9048no—
229C22—4522no—
230C22—4522no—
231C22—2262no—
232C22—2262no—
233C22—2264no—
234C22—2262no—
235C22C2×D4×D11311yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—4522no—
240C4—2262no—
241C4C2×D4×D11311yescharacteristic
242C4#1681366711yescharacteristic
243C2—82no—
244C2—4522no—
245C2—4524no—
246C2#2029923311yescharacteristic
247C2#2029939511yescharacteristic
248C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#495×C113C2
socleC22×C113C22×D4
hypercenter#495D113
hypocenterC113#3273
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. #20299241C2semidirect
3. #20298841C2semidirect
4. #20298810C2semidirect
5. #20298759C2semidirect
6. #20298730C2semidirect
7. C4×D904C2semidirect
8. #20298677C2semidirect
9. #495×C113C2semidirect
11. C2×D4×D113C22semidirect
13. C2×#14268634C22semidirect
16. C2×#14268630C22semidirect
18. #16813598C22semidirect
23. C4×D452C22semidirect
25. #16813556C22semidirect
26. C4⋊#11744751C22semidirect
27. #16813546C22semidirect
28. #16813544C22semidirect
29. #16813543C22semidirect
30. #16813534C22semidirect
31. C2×Q16×C113C22semidirect
32. C2×SD16×C113C22semidirect
34. #124×C113C22semidirect
35. C4×C8×C113C22semidirect
50. D904D4semidirect
125. C113#3273semidirect
128. #495D113semidirect
138. C2×Q16C2×D113semidirect
140. C2×SD16C2×D113semidirect
145. #124C2×D113semidirect
160. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#202992412
#202988412
#202988102
#202987592
#202987302
C4×D9042
#202986772
#495×C1132
#3273113