Finite Group Databasebeta

← #28401439

Subgroups — #28401439

Order 14464.

442 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299162C212yesmaximal, complemented
2#20298923C214yesmaximal, complemented
3#20298851C212yesmaximal, complemented
4#20298834C212yesmaximal, complemented
5#20298734C214yesmaximal, complemented
6#408×C113C211yesmaximal, characteristic, complemented
7C22×D452C2212yescomplemented
8C2×D904C2212yes—
9C2×D904C2212yes—
10#16813618—22no—
11#16813611—22no—
12#16813596C2214yes—
13#16813596C2214yescomplemented
14#16813590—22no—
15#16813590—22no—
16#16813581C2212yescomplemented
17#16813556C2212yescomplemented
18#16813554C2212yescomplemented
19#16813544C2214yescomplemented
20#16813544C2214yescomplemented
21C2×#41×C113C2211yescharacteristic
22C2×M16×C113C2211yescharacteristic, complemented
23C22×C8×C113C2211yescharacteristic, complemented
24C22⋊C8×C113C2214yescomplemented
25C23×D113—22no—
26C2×D452—22no—
27C2×D452—42no—
28C2×D452—42no—
29C2×D452C2314yes—
30C2×C22⋊D113—24no—
31C2×C22⋊D113—24no—
32D904—42no—
33D904—42no—
34C4⋊Dic113C2314yes—
35C22⋊Dic113—22no—
36#14268624—24no—
37#14268624—24no—
38C4×Dic113—22no—
39#41×C113—41no—
40#41×C113—41no—
41C2×Q8×C113D411yescharacteristic
42C2×D4×C113D411yescharacteristic
43C2×D4×C113D412yes—
44C22×C4×C113C2312yes—
45C22×C4×C113C2311yescharacteristic
46M16×C113—41no—
47C2×C8×C113—41no—
48C2×C8×C113C2312yes—
49C2×C8×C113C2312yes—
50C23×C113C2×D412yes—
51C23×C113C2×D411yescharacteristic
52C22×D113—24no—
53C22×D113—44no—
54C22×D113—84no—
55Q8×C113—41no—
56D4×C113—42no—
57D4×C113—41no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—22no—
61C2×C4×C113—22no—
62C2×C4×C113C2×D412yes—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2411yescharacteristic
65C22⋊D113—84no—
66C22⋊D113—84no—
67C2×Dic113—24no—
68D452—24no—
69D452—24no—
70D452—44no—
71C8×C113—22no—
72C8×C113—22no—
73C22×C113—22no—
74C22×C113—21no—
75C22×C113—22no—
76C22×C113—24no—
77C22×C113C22×D411yescharacteristic
78C2×D113—44no—
79C2×D113—44no—
80C2×D113—44no—
81C2×D113—88no—
82C4×C113—22no—
83C4×C113—21no—
84C4×C113H(5,𝔽2)11yescharacteristic
85C4×C113H(5,𝔽2)11yescharacteristic
86Dic113—44no—
87C2×C113—42no—
88C2×C113—41no—
89C2×C113#53411yescharacteristic
90C2×C113#57612yes—
91D113—84no—
92#3199—1131nomaximal, Sylow
93C113#319911yescharacteristic, complemented, Sylow
94#535—1132no—
95#482—1134no—
96#469—1132no—
97#466—1132no—
98#447—1134no—
99#408D11311yescharacteristic, complemented
100C2×#41C2×D11311yescharacteristic
101C22×D4—1132no—
102C2×D8—1132no—
103C2×D8—1132no—
104C2×M16C2×D11311yescharacteristic, complemented
105C22×C8C2×D11311yescharacteristic, complemented
106#127—2262no—
107#124—2262no—
108#121—1134no—
109#121—1134no—
110#120—2262no—
111#120—2262no—
112#117—1132no—
113#107—1132no—
114#106—1132no—
115#102—1134no—
116#102—1134no—
117C22⋊C8C2×D11314yescomplemented
118C24—2262no—
119#41—41no—
120#41—41no—
121C2×Q8D45211yescharacteristic
122C2×D4—1134no—
123C2×D4—4522no—
124C2×D4—4522no—
125C2×D4—2264no—
126C2×D4—2264no—
127C2×D4—2262no—
128C2×D4D45211yescharacteristic
129C2×D4D45212yes—
130C22×C4C22×D11312yes—
131C22×C4C22×D11311yescharacteristic
132D8—4522no—
133D8—4522no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D11312yes—
137C2×C8C22×D11312yes—
138C4⋊C4—1134no—
139C22⋊C4—2262no—
140C22⋊C4—2264no—
141C22⋊C4—2264no—
142C42—2262no—
143C23—9044no—
144C23—4524no—
145C23—2264no—
146C23C2×D45212yes—
147C23C2×D45211yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—9044no—
152D4—9044no—
153D4—4524no—
154D4—2264no—
155D4—2264no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—2264no—
161C2×C4C2×D45212yes—
162C2×C4C2×D45211yescharacteristic
163C2×C4C23×D11311yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—9048no—
171C22—4524no—
172C22—4524no—
173C22—4524no—
174C22C22×D45211yescharacteristic
175C4—22no—
176C4—21no—
177C4—4524no—
178C4#1681366711yescharacteristic
179C4#1681366711yescharacteristic
180C2—42no—
181C2—41no—
182C2—9044no—
183C2#2029916011yescharacteristic
184C2#2029940312yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#408×C113C2
socleC22×C113C22×D4
hypercenter#408D113
hypocenterC113#3199
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #20299162C2semidirect
2. #20298923C2semidirect
3. #20298851C2semidirect
4. #20298834C2semidirect
5. #20298734C2semidirect
6. #408×C113C2semidirect
7. C22×D452C22semidirect
13. #16813596C22semidirect
16. #16813581C22semidirect
17. #16813556C22semidirect
18. #16813554C22semidirect
19. #16813544C22semidirect
20. #16813544C22semidirect
22. C2×M16×C113C22semidirect
23. C22×C8×C113C22semidirect
24. C22⋊C8×C113C22semidirect
93. C113#3199semidirect
99. #408D113semidirect
104. C2×M16C2×D113semidirect
105. C22×C8C2×D113semidirect
117. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202989232
#202988512
#202988342
#202987342
#408×C1132
#3199113