Finite Group Databasebeta

← #490×D113 #28400906

Subgroups — #490×D113 #28400906

Order 14464.

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

normal subgroups only

This group has 488 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#127×D113C211yesmaximal, characteristic
2#125×D113C211yesmaximal, characteristic, complemented
3#20298964C211yesmaximal, characteristic, complemented
4#20298963C211yesmaximal, characteristic, complemented
5#20298962C211yesmaximal, characteristic, complemented
6#20298961C214yesmaximal, complemented
7#102×D113C214yesmaximal, complemented
8#97×D113C211yesmaximal, characteristic, complemented
9#490×C113C211yesmaximal, characteristic, complemented
10C2×D4×D113—22no—
11C2×D4×D113C2212yes—
12C2×C8×D113C2212yes—
13#16813619C2211yescharacteristic
14#16813618—22no—
15#16813618C2212yes—
16#16813614C2211yescharacteristic, complemented
17#16813613C2212yescomplemented
18#16813612—22no—
19C4⋊C4×D113—22no—
20C4⋊C4×D113C2212yes—
21C42×D113C2211yescharacteristic
22#16813544C2214yescomplemented
23#16813543C2214yescomplemented
24#16813542C2214yescomplemented
25#16813533C2211yescharacteristic, complemented
26#16813532C2212yescomplemented
27#127×C113C2211yescharacteristic
28#125×C113C2211yescharacteristic, complemented
29#102×C113C2214yescomplemented
30#97×C113C2211yescharacteristic, complemented
31C23×D113—22no—
32C2×D452—22no—
33C2×D452C2312yes—
34C2×C22⋊D113—22no—
35C2×C22⋊D113—24no—
36D4×D113—28no—
37D4×D113—48no—
38C2×C4×D113—22no—
39C2×C4×D113D412yes—
40C2×C4×D113C2311yescharacteristic
41C2×#11744751C2312yes—
42C8×D113—24no—
43C4⋊Dic113—22no—
44C4⋊Dic113C2312yes—
45#14268626—22no—
46#14268626—22no—
47#14268626—22no—
48C4×Dic113D412yes—
49C4×Dic113C2311yescharacteristic
50C2×D4×C113—22no—
51C2×D4×C113C2312yes—
52C2×C8×C113C2312yes—
53C4⋊C4×C113—22no—
54C4⋊C4×C113C2312yes—
55C42×C113C2311yescharacteristic
56C23×C113—22no—
57C22×D113—22no—
58C22×D113—44no—
59C22×D113—48no—
60C22×D113C2×D411yescharacteristic
61D4×C113—24no—
62D4×C113—44no—
63C2×C4×C113—22no—
64C2×C4×C113C2×D412yes—
65C2×C4×C113C2411yescharacteristic
66C22⋊D113—48no—
67C22⋊D113—44no—
68C2×Dic113—22no—
69C2×Dic113C2×D412yes—
70C2×Dic113C2×D411yescharacteristic
71D452—24no—
72D452—44no—
73C4×D113—24no—
74C4×D113—44no—
75C4×D113#4114yes—
76C8×C113—22no—
77#11744751—22no—
78C22×C113—42no—
79C22×C113—44no—
80C22×C113C22×D411yescharacteristic
81C2×D113—42no—
82C2×D113—44no—
83C2×D113—88no—
84C2×D113#12412yes—
85C2×D113AGL(1,ℤ/8)14yes—
86C4×C113—22no—
87C4×C113—42no—
88C4×C113C2×#4112yes—
89Dic113—22no—
90Dic113—42no—
91Dic113#12412yes—
92C2×C113—82no—
93C2×C113C2×#12411yescharacteristic
94C2×C113C2×AGL(1,ℤ/8)12yes—
95D113—82no—
96D113#49014yesdirect product factor
97C2×#490—1131nomaximal, Sylow
98C113C2×#49011yescharacteristic, complemented, Sylow
99C2×#127—1131no—
100C2×#125—1131no—
101#490—1131no—
102#490—1131no—
103#490—1134no—
104#490—1131no—
105#490D11311yescharacteristic, direct product factor
106C2×#102—1134no—
107C2×#97—1131no—
108C22×D4—1132no—
109C22×D4—2262no—
110C22×C8—1132no—
111#127—1132no—
112#127—1131no—
113#127—2262no—
114#127C2×D11311yescharacteristic
115#125—1132no—
116#125—1131no—
117#125—2262no—
118#125C2×D11311yescharacteristic, complemented
119C2×C4⋊C4—1132no—
120C2×C4⋊C4—2262no—
121C2×C42—1131no—
122#102—1134no—
123#102—1134no—
124#102—1134no—
125#102C2×D11314yescomplemented
126#97—1132no—
127#97—1131no—
128#97C2×D11311yescharacteristic, complemented
129C24—2262no—
130C2×D4—22no—
131C2×D4—1132no—
132C2×D4—4528no—
133C2×D4—2268no—
134C2×D4—2264no—
135C2×D4—2262no—
136C2×D4—2262no—
137C2×D4C22×D11312yes—
138C22×C4—1131no—
139C22×C4—1132no—
140C22×C4—2262no—
141C2×C8—1132no—
142C2×C8—2264no—
143C2×C8C22×D11312yes—
144C4⋊C4—22no—
145C4⋊C4—1132no—
146C4⋊C4—2262no—
147C4⋊C4—2262no—
148C4⋊C4—2262no—
149C4⋊C4—2262no—
150C4⋊C4C22×D11312yes—
151C42—1132no—
152C42—1131no—
153C42C22×D11311yescharacteristic
154C23—22no—
155C23—1131no—
156C23—4528no—
157C23—4524no—
158C23—2262no—
159D4—24no—
160D4—44no—
161D4—4524no—
162D4—4524no—
163D4—4528no—
164D4—2264no—
165C2×C4—22no—
166C2×C4—1131no—
167C2×C4—1134no—
168C2×C4—1132no—
169C2×C4—4524no—
170C2×C4—2264no—
171C2×C4—2262no—
172C2×C4D4×D11312yes—
173C2×C4C23×D11311yescharacteristic
174C8—22no—
175C8—2262no—
176C22—42no—
177C22—44no—
178C22—1132no—
179C22—1134no—
180C22—9048no—
181C22—4522no—
182C22—4524no—
183C22C2×D4×D11311yescharacteristic
184C4—22no—
185C4—42no—
186C4—1132no—
187C4—4522no—
188C4—2262no—
189C4#41×D11312yes—
190C2—82no—
191C2—1134no—
192C2—9042no—
193C2#124×D11311yescharacteristic
194C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#490×C113C2
socleC22×C113C22×D4
prime radical#127×D113C2
hypercenter#490D113
hypocenterC113C2×#490
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D113C2semidirect
3. #20298964C2semidirect
4. #20298963C2semidirect
5. #20298962C2semidirect
6. #20298961C2semidirect
7. #102×D113C2semidirect
8. #97×D113C2semidirect
9. #490×C113C2semidirect
16. #16813614C22semidirect
17. #16813613C22semidirect
22. #16813544C22semidirect
23. #16813543C22semidirect
24. #16813542C22semidirect
25. #16813533C22semidirect
26. #16813532C22semidirect
28. #125×C113C22semidirect
29. #102×C113C22semidirect
30. #97×C113C22semidirect
96. D113#490direct (N × H)
98. C113C2×#490semidirect
105. #490D113direct (N × H)
118. #125C2×D113semidirect
125. #102C2×D113semidirect
128. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#127×D1132
#125×D1132
#202989642
#202989632
#202989622
#202989612
#102×D1132
#97×D1132
#490×C1132
C2×#490113