Finite Group Databasebeta

← #14580604

Subgroups — #14580604

Order 2624.

108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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#13050189C211yesmaximal, characteristic, complemented
2C2×#10620282C211yesmaximal, characteristic, complemented
3#13050171C211yesmaximal, characteristic, complemented
4#13050099C211yesmaximal, characteristic, complemented
5#13050081C211yesmaximal, characteristic, complemented
6#13050080C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C41C211yesmaximal, characteristic, complemented
8#41×C41C2211yescharacteristic
9C2×D4×C41C2211yescharacteristic
10C2×D164C2211yescharacteristic
11SD16×C41—21no—
12D8×C41—21no—
13M16×C41C2211yescharacteristic
14#10620284—21no—
15#10620282—21no—
16#10620282—21no—
17#10620282—21no—
18#10620277—21no—
19#10620277C2211yescharacteristic
20#10620277C2211yescharacteristic
21C2×#66491—21no—
22C2×#66491C2211yescharacteristic
23C23×C41—21no—
24C22×D41—21no—
25Q8×C41D411yescharacteristic
26D4×C41—21no—
27D4×C41—21no—
28D4×C41—21no—
29D4×C41D411yescharacteristic
30C2×C4×C41—21no—
31C2×C4×C41C2311yescharacteristic
32D164—21no—
33D164—21no—
34C8×C41—21no—
35#66491—21no—
36#66491—21no—
37#66491D411yescharacteristic
38#66491D411yescharacteristic
39C22×C41—21no—
40C22×C41—41no—
41C22×C41—81no—
42C22×C41#4111yescharacteristic
43C2×D41—41no—
44C2×D41—81no—
45C4×C41—21no—
46C4×C41C2×D411yescharacteristic
47C4×C41C2×D411yescharacteristic
48C2×C41—21no—
49C2×C41—41no—
50C2×C41—81no—
51C2×C41#12111yescharacteristic
52D41—81no—
53#472—411nomaximal, Sylow
54C41#47211yescharacteristic, complemented, Sylow
55AGL(1,ℤ/8)—411no—
56AGL(1,ℤ/8)D4111yescharacteristic, complemented
57C2×D8—411no—
58#131—411no—
59#108—411no—
60#100—411no—
61#100—411no—
62#41C2×D4111yescharacteristic
63C2×D4—411no—
64C2×D4C2×D4111yescharacteristic
65SD16—21no—
66SD16—821no—
67D8—21no—
68D8—821no—
69D8—821no—
70D8—821no—
71M16—411no—
72M16—411no—
73M16—821no—
74M16C2×D4111yescharacteristic
75C2×C8—411no—
76C2×C8—821no—
77C23—21no—
78C23—821no—
79Q8C22⋊D4111yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—821no—
84D4—821no—
85D4C22⋊D4111yescharacteristic
86C2×C4—21no—
87C2×C4C22×D4111yescharacteristic
88C8—21no—
89C8—411no—
90C8—411no—
91C8—821no—
92C8—821no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—3281no—
97C22—1641no—
98C22#1062030811yescharacteristic
99C4—21no—
100C4D4×D4111yescharacteristic
101C4C2×C22⋊D4111yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—3281no—
106C2#1305013611yescharacteristic
subgroupG/H
centerC2#13050136
commutator, cosocleC2×C4×C41C23
FrattiniC2×C4C22×D41
FittingAGL(1,ℤ/8)×C41C2
socleC2×C41#121
hypercenterAGL(1,ℤ/8)D41
hypocenterC41#472
LCSG ▷ C2×C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13050189C2semidirect
2. C2×#10620282C2semidirect
3. #13050171C2semidirect
4. #13050099C2semidirect
5. #13050081C2semidirect
6. #13050080C2semidirect
7. AGL(1,ℤ/8)×C41C2semidirect
54. C41#472semidirect
56. AGL(1,ℤ/8)D41semidirect

Maximal subgroups

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

subgroupindex
#130501892
C2×#106202822
#130501712
#130500992
#130500812
#130500802
AGL(1,ℤ/8)×C412
#47241