Finite Group Databasebeta

← C2×#15690872 #20261723

Subgroups — C2×#15690872 #20261723

Order 6208.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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×#13095519C211yesmaximal, characteristic, complemented
2C2×C4⋊#87604C211yesmaximal, characteristic, complemented
3#15690872C214yesmaximal, direct product factor
4C2×D4×D97C211yesmaximal, characteristic
5C22×#87604—21no—
6#13095519—21no—
7#13095519C2212yescomplemented
8C2×#11715897—21no—
9C4⋊#87604—21no—
10C4⋊#87604C2212yescomplemented
11C23×D97—21no—
12C2×D388C411yescharacteristic, complemented
13C2×C22⋊D97—21no—
14D4×D97—21no—
15D4×D97—21no—
16D4×D97C412yescomplemented
17D4×D97C2212yes—
18C2×C4×D97C2211yescharacteristic
19C2×D4×C97C411yescharacteristic, complemented
20C23×C97—21no—
21C22×D97—21no—
22C22×D97—22no—
23C22×D97—22no—
24C22×D97—42no—
25C22×D97—42no—
26C22×D97D411yescharacteristic
27C2×#87604—22no—
28C2×#87604—42no—
29D4×C97—21no—
30D4×C97C2×C412yescomplemented
31C2×C4×C97C2×C411yescharacteristic
32C22⋊D97—22no—
33C22⋊D97—22no—
34C2×Dic97D411yescharacteristic
35D388—21no—
36D388C2×C412yescomplemented
37C4×D97C2×C411yescharacteristic
38C4×D97D411yescharacteristic
39C4×D97D411yescharacteristic
40C4×D97C2311yescharacteristic
41#11715897—22no—
42C22×C97—22no—
43C22×C97—42no—
44C22×C97C22⋊C411yescharacteristic
45C2×D97—22no—
46C2×D97—42no—
47C2×D97—44no—
48C2×D97—42no—
49C2×D97—42no—
50C2×D97C22⋊C411yescharacteristic
51C2×D97D812yes—
52C2×D97SD1612yes—
53C2×D97C2×D411yescharacteristic
54#87604—42no—
55C4×C97C22⋊C411yescharacteristic
56C4×C97C22×C411yescharacteristic
57Dic97C22⋊C411yescharacteristic
58Dic97C2×D411yescharacteristic
59C2×C97—42no—
60C2×C97#10212yescomplemented
61C2×C97C2×C22⋊C411yescharacteristic
62D97—42no—
63D97#10212yescomplemented
64D97C2×D811yescharacteristic
65D97C2×SD1611yescharacteristic
66C97C2×#10211yescharacteristic, complemented, Sylow
67C2×#102—971nomaximal, Sylow
68C22×D4—971no—
69C22×C8—971no—
70C2×C4⋊C4—971no—
71#102—974no—
72C24—1941no—
73C2×D4—972no—
74C2×D4—972no—
75C2×D4—971no—
76C2×D4—1941no—
77C2×D4—1941no—
78C2×D4—1941no—
79C2×D4#8760411yescharacteristic, complemented
80C22×C4—971no—
81C22×C4—1941no—
82C2×C8—972no—
83C2×C8—1941no—
84C2×C8—1941no—
85C4⋊C4—972no—
86C4⋊C4—1941no—
87C23—21no—
88C23—971no—
89C23—3882no—
90C23—3882no—
91C23—1942no—
92C23—1942no—
93C23—1941no—
94D4—21no—
95D4—972no—
96D4—1942no—
97D4—1942no—
98D4—1941no—
99D4C2×#8760412yescomplemented
100C2×C4—971no—
101C2×C4—971no—
102C2×C4—971no—
103C2×C4—971no—
104C2×C4—971no—
105C2×C4—3882no—
106C2×C4—1942no—
107C2×C4C2×#8760411yescharacteristic
108C8—1942no—
109C22—22no—
110C22—42no—
111C22—972no—
112C22—972no—
113C22—971no—
114C22—971no—
115C22—3882no—
116C22—3884no—
117C22—3882no—
118C22—3882no—
119C22—1942no—
120C22C22⋊#8760411yescharacteristic
121C4—971no—
122C4—971no—
123C4—3882no—
124C4C22⋊#8760411yescharacteristic
125C4C22×#8760411yescharacteristic
126C2—42no—
127C2—971no—
128C2—972no—
129C2—971no—
130C2—3882no—
131C2#1569087212yesdirect product factor
132C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×D4×C97C4
socleC22×C97C22⋊C4
hypercenterC2×D4#87604
hypocenterC97C2×#102
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13095519C2semidirect
2. C2×C4⋊#87604C2semidirect
3. #15690872C2direct (N × H)
7. #13095519C22semidirect
10. C4⋊#87604C22semidirect
12. C2×D388C4semidirect
16. D4×D97C4semidirect
19. C2×D4×C97C4semidirect
30. D4×C97C2×C4semidirect
36. D388C2×C4semidirect
60. C2×C97#102semidirect
63. D97#102semidirect
66. C97C2×#102semidirect
79. C2×D4#87604semidirect
99. D4C2×#87604semidirect
131. C2#15690872direct (N × H)