Finite Group Databasebeta

← #28388726

Subgroups — #28388726

Order 14464.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#20298770C211yesmaximal, characteristic
2#20298393C211yesmaximal, characteristic, complemented
3#329×C113C211yesmaximal, characteristic, complemented
4#16813670C411yescharacteristic, complemented
5#16813648—21no—
6#16813550—21no—
7#16813541C411yescharacteristic, complemented
8#16813537—21no—
9#124×C113C2211yescharacteristic
10#97×C113—21no—
11#14268648—41no—
12#14268647—21no—
13#14268647—41no—
14Q8×D113—41no—
15#14268635—41no—
16#14268632—41no—
17#14268631—21no—
18C22⋊Dic113—41no—
19C2×Q8×C113C2×C411yescharacteristic
20C2×D4×C113D411yescharacteristic
21C2×C8×C113—41no—
22C22⋊C4×C113—41no—
23C42×C113D411yescharacteristic
24C23×C113—21no—
25Q8×C113—41no—
26D4×C113—41no—
27C2×C4×C113—21no—
28C2×C4×C113—21no—
29C2×C4×C113C22⋊C411yescharacteristic
30C22⋊D113—41no—
31C2×Dic113—81no—
32D452—21no—
33D452—41no—
34C4×D113—41no—
35C4×D113—42no—
36Dic226—21no—
37Dic226—41no—
38C8×C113—42no—
39#11744751—41no—
40C22×C113—41no—
41C22×C113—81no—
42C22×C113#9911yescharacteristic
43C2×D113—41no—
44C4×C113—21no—
45C4×C113—41no—
46C4×C113—41no—
47Dic113—41no—
48Dic113—161no—
49C2×C113—21no—
50C2×C113—81no—
51C2×C113AΣL(1,𝔽16)11yescharacteristic
52D113—81no—
53#1404—1131nomaximal, Sylow
54C113#140411yescharacteristic, complemented, Sylow
55#454—1131no—
56#354—1131no—
57#329D11311yescharacteristic, complemented
582−1+4—1131no—
59AGL(1,ℤ/8)—2261no—
60#124C2×D11311yescharacteristic
61#104—2261no—
62#101—1131no—
63#99—2261no—
64#97—21no—
65#41—4521no—
66#41—4521no—
67#41—2261no—
68C2×Q8—4521no—
69C2×Q8C4×D11311yescharacteristic
70C2×D4D45211yescharacteristic
71SD16—4521no—
72D8—4521no—
73M16—2261no—
74C2×C8—41no—
75C22⋊C4—41no—
76C22⋊C4—4521no—
77C42C22⋊D11311yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—4521no—
81Q8—2261no—
82D4—41no—
83D4—4521no—
84D4—4521no—
85D4—2261no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—9041no—
89C2×C4—4521no—
90C2×C4—4522no—
91C2×C4#1426862411yescharacteristic
92C8—42no—
93C8—4521no—
94C22—41no—
95C22—81no—
96C22—4521no—
97C22#1681353611yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—18081no—
102C4—4521no—
103C2—21no—
104C2—81no—
105C2—9041no—
106C2#2029838611yescharacteristic
subgroupG/H
centerC2#20298386
commutatorC2×Q8×C113C2×C4
Frattini#124C2×D113
Fitting#329×C113C2
socleC2×C113AΣL(1,𝔽16)
prime radical#20298770C2
cosocle#124×C113C22
hypercenter#329D113
hypocenterC113#1404
LCSG ▷ C2×Q8×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20298393C2semidirect
3. #329×C113C2semidirect
4. #16813670C4semidirect
7. #16813541C4semidirect
54. C113#1404semidirect
57. #329D113semidirect

Maximal subgroups

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

subgroupindex
#202987702
#202983932
#329×C1132
#1404113