Finite Group Databasebeta

← C2×#15690738 #20260749

Subgroups — C2×#15690738 #20260749

Order 6208.

170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×#13095511C211yesmaximal, characteristic
2C2×#13095495C211yesmaximal, characteristic, complemented
3#15690738C214yesmaximal, direct product factor
4C2×C42×C97C211yesmaximal, characteristic, complemented
5#13095511—21no—
6#13095511—21no—
7#13095511C412yescomplemented
8#13095511C2212yes—
9C2×Dic194C411yescharacteristic, complemented
10C2×D388C411yescharacteristic, complemented
11C2×C22⋊D97—21no—
12C2×C4×D97—21no—
13#13095495—21no—
14#13095495C2212yescomplemented
15C2×#11715895—21no—
16C22×C4×C97—21no—
17C22×C4×C97C2211yescharacteristic
18C42×C97—21no—
19C42×C97C2212yescomplemented
20C23×C97D411yescharacteristic
21C22×D97—21no—
22C2×C4×C97—24no—
23C2×C4×C97—22no—
24C2×C4×C97C2×C411yescharacteristic
25C2×C4×C97C2×C411yescharacteristic
26C2×C4×C97D411yescharacteristic
27C2×C4×C97D411yescharacteristic
28C2×C4×C97D411yescharacteristic
29C2×C4×C97C2311yescharacteristic
30C22⋊D97—22no—
31C22⋊D97—22no—
32C2×Dic97—21no—
33D388—21no—
34D388C2×C412yescomplemented
35C4×D97—22no—
36C4×D97—22no—
37Dic194—21no—
38Dic194C2×C412yescomplemented
39#11715895—22no—
40C22×C97—22no—
41C22×C97C22⋊C411yescharacteristic
42C22×C97C22⋊C411yescharacteristic
43C22×C97C2×D411yescharacteristic
44C2×D97—22no—
45C2×D97—42no—
46C4×C97—24no—
47C4×C97C22⋊C411yescharacteristic
48C4×C97C22⋊C411yescharacteristic
49C4×C97C22×C411yescharacteristic
50C4×C97C2×D411yescharacteristic
51Dic97—22no—
52C2×C97—21no—
53C2×C97—21no—
54C2×C97#10412yescomplemented
55C2×C97C2×C22⋊C411yescharacteristic
56D97—42no—
57C97C2×#10411yescharacteristic, complemented, Sylow
58C2×#104—971nomaximal, Sylow
59C2×#41—971no—
60C2×M16—971no—
61C2×C42D9711yescharacteristic, complemented
62#104—974no—
63#41—972no—
64#41—972no—
65#41—1941no—
66#41—1941no—
67C2×Q8—971no—
68C2×D4—971no—
69C2×D4—1941no—
70C22×C4—21no—
71C22×C4—1941no—
72C22×C4C2×D9711yescharacteristic
73M16—972no—
74M16—1941no—
75C2×C8—1941no—
76C42—21no—
77C42C2×D9712yescomplemented
78C23—1941no—
79C23C22⋊D9711yescharacteristic
80Q8—972no—
81Q8—1941no—
82D4—972no—
83D4—1942no—
84D4—1942no—
85D4—1941no—
86C2×C4—24no—
87C2×C4—22no—
88C2×C4—1941no—
89C2×C4—1942no—
90C2×C4—1942no—
91C2×C4C4×D9711yescharacteristic
92C2×C4C4×D9711yescharacteristic
93C2×C4D38811yescharacteristic
94C2×C4D38811yescharacteristic
95C2×C4C22⋊D9711yescharacteristic
96C2×C4C22×D9711yescharacteristic
97C8—1942no—
98C22—22no—
99C22—3882no—
100C22—1942no—
101C22#1309548811yescharacteristic
102C22#1309548811yescharacteristic
103C22C2×C22⋊D9711yescharacteristic
104C4—24no—
105C4—1942no—
106C4#1309548811yescharacteristic
107C4#1309548811yescharacteristic
108C4C2×C4×D9711yescharacteristic
109C4C2×D38811yescharacteristic
110C2—21no—
111C2—21no—
112C2—3882no—
113C2#1569073812yesdirect product factor
114C2C2×#1309548811yescharacteristic
subgroupG/H
centerC2×C4D388
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×C42×C97C2
socleC22×C97C22⋊C4
hypercenterC2×C42D97
hypocenterC97C2×#104
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#13095495C2semidirect
3. #15690738C2direct (N × H)
4. C2×C42×C97C2semidirect
7. #13095511C4semidirect
9. C2×Dic194C4semidirect
10. C2×D388C4semidirect
14. #13095495C22semidirect
19. C42×C97C22semidirect
34. D388C2×C4semidirect
38. Dic194C2×C4semidirect
54. C2×C97#104semidirect
57. C97C2×#104semidirect
61. C2×C42D97semidirect
77. C42C2×D97semidirect
113. C2#15690738direct (N × H)