Finite Group Databasebeta

← #14580484

Subgroups — #14580484

Order 2624.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#10620310C211yesmaximal, characteristic, complemented
2C2×#10620284C211yesmaximal, characteristic, complemented
3C2×D328C211yesmaximal, characteristic, complemented
4#13050139C211yesmaximal, characteristic, complemented
5#13050084C211yesmaximal, characteristic, complemented
6#13050076C211yesmaximal, characteristic, complemented
7#103×C41C211yesmaximal, characteristic, complemented
8C2×Q8×C41C2211yescharacteristic
9#10620310—22no—
10#10620310—22no—
11C2×D164—21no—
12C2×D164—21no—
13C2×D164C2211yescharacteristic
14C2×D164C2211yescharacteristic
15C2×C4×D41—21no—
16C2×C4×D41C2211yescharacteristic
17C2×C8×C41C2211yescharacteristic
18C4⋊C4×C41C2211yescharacteristic
19#10620284—22no—
20#10620281—21no—
21C2×#66491C2211yescharacteristic
22D328—22no—
23C22×D41—21no—
24C22×D41—21no—
25C22×D41D411yescharacteristic
26Q8×C41—21no—
27Q8×C41D412yescomplemented
28C2×C4×C41—21no—
29C2×C4×C41—21no—
30C2×C4×C41C2311yescharacteristic
31C2×Dic41D411yescharacteristic
32D164—24no—
33D164—21no—
34D164—21no—
35D164—21no—
36D164—42no—
37D164D412yescomplemented
38C4×D41—24no—
39C4×D41—21no—
40C4×D41—21no—
41C8×C41—21no—
42#66491—21no—
43C22×C41C2×D411yescharacteristic
44C2×D41—21no—
45C2×D41—22no—
46C2×D41—21no—
47C2×D41—21no—
48C2×D41—41no—
49C2×D41—41no—
50C2×D41—41no—
51C2×D41—41no—
52C2×D41—41no—
53C4×C41—22no—
54C4×C41—41no—
55C4×C41C2×D411yescharacteristic
56C4×C41C2×D411yescharacteristic
57Dic41—21no—
58C2×C41#12011yescharacteristic
59C2×C41#13511yescharacteristic
60C2×C41AGL(1,ℤ/8)11yescharacteristic
61D41—41no—
62D41—42no—
63D41—81no—
64#449—411nomaximal, Sylow
65C41#44911yescharacteristic, complemented, Sylow
66C2×#41—411no—
67C2×SD16—411no—
68C2×D8—411no—
69#121—411no—
70#103D4111yescharacteristic, complemented
71#102—411no—
72C22⋊C8—411no—
73#41—822no—
74#41—822no—
75C2×Q8C2×D4111yescharacteristic
76C2×D4—411no—
77C2×D4—411no—
78C2×D4—821no—
79C2×D4—821no—
80C22×C4—411no—
81C22×C4—821no—
82SD16—822no—
83D8—822no—
84C2×C8—411no—
85C2×C8C2×D4111yescharacteristic
86C4⋊C4C2×D4111yescharacteristic
87C22⋊C4—821no—
88C23—411no—
89C23—821no—
90C23—821no—
91Q8—21no—
92Q8D16412yescomplemented
93D4—412no—
94D4—824no—
95D4—821no—
96D4—821no—
97D4—821no—
98D4—1642no—
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—411no—
102C2×C4—824no—
103C2×C4—821no—
104C2×C4—821no—
105C2×C4C22×D4111yescharacteristic
106C8—21no—
107C8—821no—
108C22—822no—
109C22—821no—
110C22—821no—
111C22—821no—
112C22—1641no—
113C22—1641no—
114C22—1641no—
115C22—1641no—
116C22—1641no—
117C22D4×D4111yescharacteristic
118C4—22no—
119C4—41no—
120C4—821no—
121C4C2×D16411yescharacteristic
122C4D4×D4111yescharacteristic
123C2—3281no—
124C2—1641no—
125C2—1642no—
126C2#1305013411yescharacteristic
127C2#1305018711yescharacteristic
128C2#1305019111yescharacteristic
subgroupG/H
centerC22D4×D41
commutator, cosocleC2×C4×C41C23
FrattiniC2×C4C22×D41
Fitting#103×C41C2
socleC22×C41C2×D4
hypercenter#103D41
hypocenterC41#449
LCSG ▷ C2×C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#10620310C2semidirect
2. C2×#10620284C2semidirect
3. C2×D328C2semidirect
4. #13050139C2semidirect
5. #13050084C2semidirect
6. #13050076C2semidirect
7. #103×C41C2semidirect
27. Q8×C41D4semidirect
37. D164D4semidirect
65. C41#449semidirect
70. #103D41semidirect
92. Q8D164semidirect

Maximal subgroups

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

subgroupindex
C2×#106203102
C2×#106202842
C2×D3282
#130501392
#130500842
#130500762
#103×C412
#44941