Finite Group Databasebeta

← #14580579

Subgroups — #14580579

Order 2624.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C2×#10620272C211yesmaximal, characteristic, complemented
2#13050140C211yesmaximal, characteristic, complemented
3#13050135C211yesmaximal, characteristic
4#13050098C211yesmaximal, characteristic, complemented
5#13050088C211yesmaximal, characteristic, complemented
6#13050085C211yesmaximal, characteristic, complemented
7C2×SD16×C41C211yesmaximal, characteristic, complemented
8C2×Q8×C41C2211yescharacteristic
9C2×D4×C41C2211yescharacteristic
10C2×C22⋊D41—21no—
11C2×C4×D41C2211yescharacteristic
12SD16×C41—22no—
13C2×C8×C41C2211yescharacteristic
14C22⋊Dic41—21no—
15#10620281—21no—
16C4⋊Dic41C2211yescharacteristic
17C4⋊Dic41C2211yescharacteristic
18#10620279—21no—
19C2×#66491C2211yescharacteristic
20#10620272—22no—
21C23×C41—21no—
22C22×D41D411yescharacteristic
23Q8×C41—21no—
24Q8×C41—21no—
25D4×C41—21no—
26D4×C41—21no—
27C2×C4×C41—21no—
28C2×C4×C41C2311yescharacteristic
29C22⋊D41—42no—
30C2×Dic41—21no—
31C2×Dic41—21no—
32C2×Dic41D411yescharacteristic
33C4×D41—21no—
34C4×D41—21no—
35C8×C41D412yescomplemented
36#66491—21no—
37C22×C41—41no—
38C22×C41—41no—
39C22×C41—41no—
40C22×C41C2×D411yescharacteristic
41C2×D41—21no—
42C2×D41—21no—
43C2×D41—21no—
44C4×C41—41no—
45C4×C41C2×D411yescharacteristic
46C4×C41#4111yescharacteristic
47Dic41—21no—
48Dic41—41no—
49Dic41—41no—
50C2×C41—81no—
51C2×C41#12111yescharacteristic
52C2×C41AGL(1,ℤ/8)11yescharacteristic
53C2×C41#13711yescharacteristic
54D41—41no—
55#468—411nomaximal, Sylow
56C41#46811yescharacteristic, complemented, Sylow
57C2×SD16D4111yescharacteristic, complemented
58C2×M16—411no—
59C22⋊Q8—411no—
60#121—411no—
61#107—411no—
62#103—411no—
63#102—411no—
64C2×Q8C2×D4111yescharacteristic
65C2×D4—821no—
66C2×D4C2×D4111yescharacteristic
67C22×C4—411no—
68SD16—22no—
69M16—822no—
70C2×C8—411no—
71C2×C8C2×D4111yescharacteristic
72C4⋊C4—411no—
73C4⋊C4—411no—
74C4⋊C4—821no—
75C22⋊C4—821no—
76C22⋊C4—821no—
77C23—21no—
78C23—411no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—1642no—
84C2×C4—21no—
85C2×C4—411no—
86C2×C4—821no—
87C2×C4—821no—
88C2×C4—821no—
89C2×C4—821no—
90C2×C4C22×D4111yescharacteristic
91C8—821no—
92C8C22⋊D4112yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—821no—
97C22—821no—
98C22—821no—
99C22D4×D4111yescharacteristic
100C4—41no—
101C4—821no—
102C4—1641no—
103C4—1641no—
104C4#1062030811yescharacteristic
105C4C2×C22⋊D4111yescharacteristic
106C2—81no—
107C2—1641no—
108C2#1305013511yescharacteristic
109C2#1305019111yescharacteristic
110C2#1305019311yescharacteristic
subgroupG/H
centerC22D4×D41
commutator, cosocleC2×C4×C41C23
FrattiniC2×C4C22×D41
FittingC2×SD16×C41C2
socleC22×C41C2×D4
prime radical#13050135C2
hypercenterC2×SD16D41
hypocenterC41#468
LCSG ▷ C2×C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10620272C2semidirect
2. #13050140C2semidirect
4. #13050098C2semidirect
5. #13050088C2semidirect
6. #13050085C2semidirect
7. C2×SD16×C41C2semidirect
35. C8×C41D4semidirect
56. C41#468semidirect
57. C2×SD16D41semidirect
92. C8C22⋊D41semidirect

Maximal subgroups

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

subgroupindex
C2×#106202722
#130501402
#130501352
#130500982
#130500882
#130500852
C2×SD16×C412
#46841