Finite Group Databasebeta

← #28402367

Subgroups — #28402367

Order 14464.

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

normal subgroups only

This group has 460 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#20299404C214yesmaximal, complemented
2#20298858C214yesmaximal, complemented
3#20298780C212yesmaximal, complemented
4#20298765C212yesmaximal, complemented
5#20298716C212yesmaximal, complemented
6#492×C113C211yesmaximal, characteristic, complemented
7#16813670C2212yes—
8#16813667C2212yescomplemented
9#16813653C2214yescomplemented
10#16813651—24no—
11#16813649—24no—
12#16813648C2214yes—
13#16813644C2212yes—
14#16813643—24no—
15SD16×D113—24no—
16#16813628C2214yescomplemented
17#16813558C2212yescomplemented
18#16813550C2214yescomplemented
19#16813541C2212yescomplemented
20#16813539C2212yescomplemented
21C2×SD16×C113C2214yescomplemented
22C4⋊Q8×C113C2211yescharacteristic, complemented
23#127×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic, complemented
25#14268648—24no—
26#14268647—42no—
27#14268647C2314yes—
28#14268646—24no—
29Q8×D113—24no—
30C2×C22⋊D113—42no—
31D4×D113—24no—
32Dic452D412yescomplemented
33#14268637—24no—
34#14268636D414yescomplemented
35#14268635—24no—
36#14268634—24no—
37D904D412yescomplemented
38#14268632—24no—
39#14268631C2314yes—
40#14268630—24no—
41C8×D113—24no—
42C2×Q8×C113C2312yes—
43C2×D4×C113—41no—
44C2×D4×C113C2312yes—
45SD16×C113—24no—
46SD16×C113—24no—
47C2×C8×C113C2312yes—
48C4⋊C4×C113—41no—
49C42×C113C2311yescharacteristic
50C23×C113—22no—
51C22×D113—42no—
52Q8×C113—24no—
53D4×C113—24no—
54D4×C113—82no—
55C2×C4×C113—21no—
56C2×C4×C113—22no—
57C2×C4×C113C2411yescharacteristic
58C22⋊D113—24no—
59C22⋊D113—44no—
60C2×Dic113—42no—
61D452—42no—
62D452C2×D414yes—
63C4×D113—24no—
64C4×D113—44no—
65Dic226—42no—
66Dic226C2×D414yes—
67C8×C113C2×D412yes—
68C8×C113C2×D412yes—
69#11744751—24no—
70C22×C113—42no—
71C22×C113—82no—
72C22×C113H(5,𝔽2)11yescharacteristic
73C2×D113—24no—
74C2×D113—162no—
75C4×C113—22no—
76C4×C113—42no—
77C4×C113C22×D412yes—
78Dic113—24no—
79C2×C113—21no—
80C2×C113—82no—
81C2×C113D4211yescharacteristic
82D113—44no—
83#3291—1131nomaximal, Sylow
84C113#329111yescharacteristic, complemented, Sylow
85#577—1134no—
86#492D11311yescharacteristic, complemented
87#471—1134no—
88#456—1132no—
89#453—1132no—
90#443—1132no—
912−1+4—1132no—
92H(5,𝔽2)—1132no—
93#137—1134no—
94#137—2264no—
95AGL(1,ℤ/8)—1134no—
96AGL(1,ℤ/8)—2264no—
97#135—1132no—
98#135—2264no—
99C2×SD16—2264no—
100C2×SD16C2×D11314yescomplemented
101#131—1134no—
102C4⋊Q8C2×D11311yescharacteristic, complemented
103#127C2×D11311yescharacteristic
104#108—1132no—
105#104—1134no—
106#101—1132no—
107#100—1132no—
108C4×C8C2×D11311yescharacteristic, complemented
109#41—1134no—
110#41—4522no—
111#41—2264no—
112#41—2264no—
113C2×Q8—2264no—
114C2×Q8C22×D11312yes—
115C2×D4—41no—
116C2×D4—4522no—
117C2×D4—2264no—
118C2×D4C22×D11312yes—
119Q16—1132no—
120Q16—2264no—
121SD16—24no—
122SD16—24no—
123SD16—1134no—
124SD16—2264no—
125SD16—2264no—
126D8—1132no—
127D8—2264no—
128M16—1134no—
129M16—2264no—
130C2×C8—2264no—
131C2×C8C22×D11312yes—
132C4⋊C4—41no—
133C42C22×D11311yescharacteristic
134C23—22no—
135C23—4522no—
136Q8—24no—
137Q8—1134no—
138Q8—4522no—
139D4—24no—
140D4—82no—
141D4—1134no—
142D4—4522no—
143D4—4524no—
144D4—2264no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—4524no—
148C2×C4—4522no—
149C2×C4—2264no—
150C2×C4C23×D11311yescharacteristic
151C8—2264no—
152C8D4×D11312yes—
153C8D4×D11312yes—
154C22—42no—
155C22—82no—
156C22—18082no—
157C22—2264no—
158C22#1681366711yescharacteristic
159C4—22no—
160C4—42no—
161C4—2264no—
162C4C2×D4×D11312yes—
163C2—21no—
164C2—82no—
165C2—4524no—
166C2#2029923311yescharacteristic
subgroupG/H
centerC2#20299233
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#492×C113C2
socleC2×C113D42
hypercenter#492D113
hypocenterC113#3291
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #20299404C2semidirect
2. #20298858C2semidirect
3. #20298780C2semidirect
4. #20298765C2semidirect
5. #20298716C2semidirect
6. #492×C113C2semidirect
8. #16813667C22semidirect
9. #16813653C22semidirect
16. #16813628C22semidirect
17. #16813558C22semidirect
18. #16813550C22semidirect
19. #16813541C22semidirect
20. #16813539C22semidirect
21. C2×SD16×C113C22semidirect
22. C4⋊Q8×C113C22semidirect
24. C4×C8×C113C22semidirect
32. Dic452D4semidirect
34. #14268636D4semidirect
37. D904D4semidirect
84. C113#3291semidirect
86. #492D113semidirect
100. C2×SD16C2×D113semidirect
102. C4⋊Q8C2×D113semidirect
108. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994042
#202988582
#202987802
#202987652
#202987162
#492×C1132
#3291113