Finite Group Databasebeta

← #28389658

Subgroups — #28389658

Order 14464.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299314C211yesmaximal, characteristic, complemented
2#20298972C211yesmaximal, characteristic, complemented
3#20298794C212yesmaximal, complemented
4#20298325C212yesmaximal, complemented
5#333×C113C211yesmaximal, characteristic, complemented
6C2×#14268634—22no—
7C2×D904—22no—
8#16813619C2211yescharacteristic
9#16813611—22no—
10#16813597—22no—
11C4×D452C2212yes—
12#16813580—22no—
13#16813544—22no—
14C4×#11744751C2211yescharacteristic
15C4⋊Q8×C113C2211yescharacteristic
16C4⋊C8×C113C2212yes—
17C2×D452—22no—
18C2×D452—21no—
19C2×D452—22no—
20C2×D452D412yes—
21C2×C4×D113—22no—
22#14268634—44no—
23D904—44no—
24C2×#11744751—21no—
25C4⋊Dic113D412yes—
26#14268624—24no—
27#14268624—22no—
28C4×Dic113—22no—
29C2×Q8×C113D412yes—
30C2×C8×C113—22no—
31C4⋊C4×C113—22no—
32C42×C113C2311yescharacteristic
33C22×D113—22no—
34C22×D113—41no—
35Q8×C113—42no—
36C2×C4×C113—22no—
37C2×C4×C113C2×D412yes—
38C2×C4×C113C2×D411yescharacteristic
39C2×Dic113—22no—
40D452—22no—
41D452—22no—
42D452—42no—
43D452—42no—
44D452—42no—
45D452—82no—
46C4×D113—42no—
47C4×D113—42no—
48C8×C113—42no—
49#11744751—22no—
50C22×C113#12011yescharacteristic
51C2×D113—42no—
52C2×D113—42no—
53C2×D113—42no—
54C2×D113—82no—
55C2×D113—81no—
56C4×C113—21no—
57C4×C113—42no—
58C4×C113#13512yes—
59C4×C113AGL(1,ℤ/8)12yes—
60Dic113—42no—
61C2×C113#44912yes—
62C2×C113#45311yescharacteristic
63D113—82no—
64D113—161no—
65#1624—1131nomaximal, Sylow
66C113#162411yescharacteristic, complemented, Sylow
67#555—1131no—
68#492—1131no—
69#459—1132no—
70#333D11311yescharacteristic, complemented
71D4⋊C8—1132no—
72C2×SD16—2262no—
73C2×D8—2262no—
74C4⋊Q8C2×D11311yescharacteristic
75#127—1131no—
76#124—2262no—
77#121—2262no—
78C4×D4—1132no—
79#117—2262no—
80C4⋊C8C2×D11312yes—
81#102—2262no—
82C4×C8—1131no—
83C2×Q8D45212yes—
84C2×D4—1132no—
85C2×D4—2262no—
86C2×D4—2262no—
87C2×D4—2261no—
88C22×C4—2262no—
89SD16—4524no—
90D8—4524no—
91C2×C8—22no—
92C2×C8—2261no—
93C4⋊C4—22no—
94C4⋊C4—1132no—
95C22⋊C4—2264no—
96C22⋊C4—2262no—
97C42—2262no—
98C42C22×D11311yescharacteristic
99C23—4521no—
100C23—2262no—
101Q8—42no—
102D4—9042no—
103D4—4522no—
104D4—4522no—
105D4—4522no—
106D4—2262no—
107D4—2262no—
108C2×C4—22no—
109C2×C4—4522no—
110C2×C4—4522no—
111C2×C4—2262no—
112C2×C4D4×D11312yes—
113C2×C4C2×D45211yescharacteristic
114C8—42no—
115C8—2262no—
116C22—9041no—
117C22—9042no—
118C22—4522no—
119C22—4522no—
120C22—4522no—
121C22#1681359211yescharacteristic
122C4—21no—
123C4—42no—
124C4—4522no—
125C4#1681364512yes—
126C4#1681364912yes—
127C2—18081no—
128C2—9042no—
129C2#2029874612yes—
130C2#2029876811yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#333×C113C2
socleC22×C113#120
hypercenter#333D113
hypocenterC113#1624
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #20299314C2semidirect
2. #20298972C2semidirect
3. #20298794C2semidirect
4. #20298325C2semidirect
5. #333×C113C2semidirect
66. C113#1624semidirect
70. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202993142
#202989722
#202987942
#202983252
#333×C1132
#1624113