Finite Group Databasebeta

← #28389629

Subgroups — #28389629

Order 14464.

336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299233C211yesmaximal, characteristic, complemented
2#20298974C211yesmaximal, characteristic, complemented
3#20298794C212yesmaximal, complemented
4#20298325C212yesmaximal, complemented
5#331×C113C211yesmaximal, characteristic, complemented
6C2×D4×D113—22no—
7C2×D904—22no—
8C2×#14268632—22no—
9#16813619C2211yescharacteristic, complemented
10#16813593—22no—
11#16813590—22no—
12C4×D452C2212yes—
13#16813544—22no—
14C4×#11744751C2211yescharacteristic, complemented
15#127×C113C2211yescharacteristic
16C4⋊C8×C113C2212yescomplemented
17C23×D113—22no—
18C2×D452—21no—
19C2×D452—22no—
20C2×D452D412yes—
21C2×C22⋊D113—24no—
22D4×D113—44no—
23D4×D113—44no—
24C2×C4×D113—22no—
25D904—44no—
26#14268632—44no—
27C2×#11744751—21no—
28C4⋊Dic113D412yes—
29C22⋊Dic113—22no—
30#14268624—22no—
31C2×D4×C113—22no—
32C2×D4×C113D412yes—
33C2×C8×C113—22no—
34C42×C113C2311yescharacteristic
35C23×C113—22no—
36C22×D113—22no—
37C22×D113—48no—
38C22×D113—41no—
39C22×D113—82no—
40D4×C113—42no—
41D4×C113—42no—
42D4×C113—42no—
43C2×C4×C113C2×D412yes—
44C2×C4×C113C2×D411yescharacteristic
45C22⋊D113—48no—
46C2×Dic113—22no—
47D452—22no—
48D452—42no—
49D452—42no—
50D452—42no—
51D452D814yescomplemented
52C4×D113—42no—
53C4×D113—42no—
54C8×C113—42no—
55#11744751—22no—
56C22×C113—44no—
57C22×C113—42no—
58C22×C113#12011yescharacteristic
59C2×D113—24no—
60C2×D113—42no—
61C2×D113—42no—
62C2×D113—88no—
63C2×D113—82no—
64C2×D113—81no—
65C4×C113—21no—
66C4×C113C2×D812yes—
67C4×C113AGL(1,ℤ/8)12yes—
68Dic113—42no—
69C2×C113—82no—
70C2×C113#44712yes—
71C2×C113#45311yescharacteristic
72D113—44no—
73D113—161no—
74#1619—1131nomaximal, Sylow
75C113#161911yescharacteristic, complemented, Sylow
76D42—1131no—
77#493—1131no—
78#459—1132no—
79#331D11311yescharacteristic, complemented
80D4⋊C8—1132no—
81C22×D4—2262no—
82C2×D8—2262no—
83C2×D8—2262no—
84#127—1131no—
85#127C2×D11311yescharacteristic
86#121—2262no—
87#120—2262no—
88C4×D4—1132no—
89C4⋊C8C2×D11312yescomplemented
90#102—2262no—
91C4×C8—1131no—
92C24—2262no—
93C2×D4—22no—
94C2×D4—1132no—
95C2×D4—4524no—
96C2×D4—4524no—
97C2×D4—2264no—
98C2×D4—2262no—
99C2×D4—2261no—
100C2×D4D45212yes—
101C22×C4—2262no—
102D8—4524no—
103D8—4524no—
104C2×C8—22no—
105C2×C8—2261no—
106C4⋊C4—1132no—
107C22⋊C4—2262no—
108C22⋊C4—2262no—
109C42C22×D11311yescharacteristic
110C23—22no—
111C23—9042no—
112C23—4528no—
113C23—4521no—
114C23—2262no—
115D4—42no—
116D4—42no—
117D4—42no—
118D4—1134no—
119D4—4522no—
120D4—4528no—
121D4—4522no—
122D4—4522no—
123D4—2262no—
124C2×C4—4522no—
125C2×C4—4522no—
126C2×C4—2262no—
127C2×C4D4×D11312yes—
128C2×C4C2×D45211yescharacteristic
129C8—42no—
130C8—2262no—
131C22—42no—
132C22—44no—
133C22—9048no—
134C22—9041no—
135C22—9042no—
136C22—4522no—
137C22—4522no—
138C22—2264no—
139C22#1681359211yescharacteristic
140C4—21no—
141C4—4522no—
142C4D8×D11312yes—
143C4#1681364912yes—
144C2—82no—
145C2—18081no—
146C2—4524no—
147C2#2029873312yes—
148C2#2029876811yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#331×C113C2
socleC22×C113#120
hypercenter#331D113
hypocenterC113#1619
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #20299233C2semidirect
2. #20298974C2semidirect
3. #20298794C2semidirect
4. #20298325C2semidirect
5. #331×C113C2semidirect
9. #16813619C22semidirect
14. C4×#11744751C22semidirect
16. C4⋊C8×C113C22semidirect
51. D452D8semidirect
75. C113#1619semidirect
79. #331D113semidirect
89. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992332
#202989742
#202987942
#202983252
#331×C1132
#1619113