Finite Group Databasebeta

← #28392475

Subgroups — #28392475

Order 14464.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#20299034C211yesmaximal, characteristic
2#20298719C211yesmaximal, characteristic, complemented
3#20298710C211yesmaximal, characteristic, complemented
4#20298422C211yesmaximal, characteristic, complemented
5#20298409C211yesmaximal, characteristic, complemented
6#20298375C211yesmaximal, characteristic, complemented
7#361×C113C211yesmaximal, characteristic, complemented
8#16813644C2211yescharacteristic
9#16813630—21no—
10D4×Dic113—21no—
11#16813566C412yescomplemented
12#16813563C412yescomplemented
13#16813562C2211yescharacteristic
14#16813554C2211yescharacteristic
15#16813548—21no—
16#16813543—21no—
17#16813532C2211yescharacteristic
18C2×D8×C113C2211yescharacteristic
19M32×C113C2211yescharacteristic
20#108×C113C2211yescharacteristic
21#14268647—21no—
22C22×Dic113—41no—
23Dic452C2×C411yescharacteristic, complemented
24#14268636—21no—
25D904C2×C411yescharacteristic, complemented
26#14268630—41no—
27C2×#11744751D411yescharacteristic
28C8×D113—41no—
29C4⋊Dic113—21no—
30C22⋊Dic113—41no—
31C4×Dic113D411yescharacteristic
32#14268622C2×C412yescomplemented
33C2×D4×C113—21no—
34D8×C113—21no—
35D8×C113C2×C412yes—
36M16×C113—21no—
37C2×C8×C113C2311yescharacteristic
38C16×C113—21no—
39C23×C113—41no—
40D4×C113—22no—
41D4×C113—41no—
42C2×C4×C113C2×D411yescharacteristic
43C22⋊D113—41no—
44C2×Dic113—21no—
45C2×Dic113—41no—
46C2×Dic113—82no—
47D452—21no—
48C4×D113—41no—
49Dic226—21no—
50C8×C113—41no—
51C8×C113C22×C411yescharacteristic
52C8×C113#4111yescharacteristic
53#11744751—21no—
54C22×C113—42no—
55C22×C113—81no—
56C22×C113—81no—
57C22×C113AGL(1,ℤ/8)11yescharacteristic
58C2×D113—41no—
59C4×C113C4×D411yescharacteristic
60C4×C113AGL(1,ℤ/8)11yescharacteristic
61Dic113—41no—
62Dic113—41no—
63Dic113—81no—
64C2×C113—21no—
65C2×C113—82no—
66C2×C113#44211yescharacteristic
67D113—81no—
68AGL(1,ℤ/16)—1131nomaximal, Sylow
69C113AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
70#509—1131no—
71#444—1131no—
72#442—1131no—
73#365—1131no—
74#361D11311yescharacteristic, complemented
75#360—1131no—
76#347—1131no—
77#135—1131no—
78C2×D8C2×D11311yescharacteristic
79#131—2261no—
80C4×D4—2261no—
81SD32—1132no—
82D16—1132no—
83M32—1131no—
84M32C2×D11311yescharacteristic
85#108C2×D11311yescharacteristic
86#106—1131no—
87#104—2261no—
88#102—2261no—
89#97—1131no—
90#41—2261no—
91C2×D4—21no—
92C22×C4—4521no—
93Q16—1131no—
94SD16—2261no—
95D8—21no—
96D8—1131no—
97D8C4×D11312yes—
98M16—21no—
99M16—4521no—
100C2×C8—1131no—
101C2×C8—4521no—
102C2×C8C22×D11311yescharacteristic
103C4⋊C4—2261no—
104C22⋊C4—4521no—
105C42—1131no—
106C16—21no—
107C16—1132no—
108C23—41no—
109Q8—2261no—
110D4—22no—
111D4—41no—
112D4—4521no—
113D4—2261no—
114C2×C4—9042no—
115C2×C4—4521no—
116C2×C4—4521no—
117C2×C4—2261no—
118C2×C4D4×D11311yescharacteristic
119C8—41no—
120C8—2261no—
121C8C2×C4×D11311yescharacteristic
122C8#1426864611yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—4521no—
127C22#1681364911yescharacteristic
128C4—9041no—
129C4—4521no—
130C4—4521no—
131C4#1681358211yescharacteristic
132C4#1681364611yescharacteristic
133C2—21no—
134C2—82no—
135C2—9041no—
136C2#2029870711yescharacteristic
subgroupG/H
centerC2#20298707
commutatorC8×C113C22×C4
FrattiniC2×C8C22×D113
Fitting#361×C113C2
socleC2×C113#442
prime radical#20299034C2
cosocleC2×C8×C113C23
hypercenter#361D113
hypocenterC113AGL(1,ℤ/16)
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #20298719C2semidirect
3. #20298710C2semidirect
4. #20298422C2semidirect
5. #20298409C2semidirect
6. #20298375C2semidirect
7. #361×C113C2semidirect
11. #16813566C4semidirect
12. #16813563C4semidirect
23. Dic452C2×C4semidirect
25. D904C2×C4semidirect
32. #14268622C2×C4semidirect
69. C113AGL(1,ℤ/16)semidirect
74. #361D113semidirect

Maximal subgroups

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

subgroupindex
#202990342
#202987192
#202987102
#202984222
#202984092
#202983752
#361×C1132
AGL(1,ℤ/16)113