Finite Group Databasebeta

← C2×#15690873 #20261724

Subgroups — C2×#15690873 #20261724

Order 6208.

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

normal subgroups only

This group has 162 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
2C2×C4⋊#87604C211yesmaximal, characteristic
3#15690873C214yesmaximal, direct product factor
4C2×Q8×D97C211yesmaximal, characteristic
5C22×#87604—21no—
6#13095519—21no—
7#13095519C2212yes—
8C2×#11715897—21no—
9C4⋊#87604—21no—
10C4⋊#87604C2212yes—
11C2×Dic194—21no—
12C2×Dic194C411yescharacteristic, complemented
13Q8×D97—21no—
14Q8×D97—21no—
15Q8×D97C412yescomplemented
16Q8×D97C2212yes—
17C2×C4×D97—21no—
18C2×C4×D97C2211yescharacteristic
19C2×Q8×C97C411yescharacteristic, complemented
20C22×D97D411yescharacteristic
21C2×#87604—22no—
22C2×#87604—42no—
23Q8×C97—21no—
24Q8×C97C2×C412yescomplemented
25C2×C4×C97—21no—
26C2×C4×C97C2×C411yescharacteristic
27C2×Dic97—21no—
28C2×Dic97D411yescharacteristic
29C4×D97—22no—
30C4×D97—22no—
31C4×D97C2×C411yescharacteristic
32C4×D97D411yescharacteristic
33C4×D97D411yescharacteristic
34C4×D97C2311yescharacteristic
35Dic194—21no—
36Dic194—22no—
37Dic194—22no—
38Dic194C2×C412yescomplemented
39#11715897—22no—
40C22×C97C22⋊C411yescharacteristic
41C2×D97C22⋊C411yescharacteristic
42C2×D97SD1612yes—
43C2×D97Q1612yes—
44C2×D97C2×D411yescharacteristic
45#87604—42no—
46C4×C97—22no—
47C4×C97C22⋊C411yescharacteristic
48C4×C97C22×C411yescharacteristic
49Dic97—22no—
50Dic97C22⋊C411yescharacteristic
51Dic97C2×D411yescharacteristic
52C2×C97#10312yescomplemented
53C2×C97C2×C22⋊C411yescharacteristic
54D97#10312yescomplemented
55D97C2×SD1611yescharacteristic
56D97C2×Q1611yescharacteristic
57C97C2×#10311yescharacteristic, complemented, Sylow
58C2×#103—971nomaximal, Sylow
59C22×Q8—971no—
60C22×C8—971no—
61C2×C4⋊C4—971no—
62#103—974no—
63C2×Q8—972no—
64C2×Q8—972no—
65C2×Q8—971no—
66C2×Q8—1941no—
67C2×Q8—1941no—
68C2×Q8—1941no—
69C2×Q8#8760411yescharacteristic, complemented
70C22×C4—971no—
71C22×C4—1941no—
72C22×C4—1941no—
73C2×C8—972no—
74C2×C8—1941no—
75C2×C8—1941no—
76C4⋊C4—972no—
77C4⋊C4—1941no—
78C23—971no—
79Q8—21no—
80Q8—972no—
81Q8—1942no—
82Q8—1942no—
83Q8—1941no—
84Q8C2×#8760412yescomplemented
85C2×C4—21no—
86C2×C4—971no—
87C2×C4—971no—
88C2×C4—971no—
89C2×C4—971no—
90C2×C4—971no—
91C2×C4—3882no—
92C2×C4—1942no—
93C2×C4—1942no—
94C2×C4—1942no—
95C2×C4—1941no—
96C2×C4C2×#8760411yescharacteristic
97C8—1942no—
98C22—972no—
99C22—972no—
100C22—971no—
101C22—971no—
102C22C22⋊#8760411yescharacteristic
103C4—22no—
104C4—971no—
105C4—971no—
106C4—3882no—
107C4—1942no—
108C4C22⋊#8760411yescharacteristic
109C4C22×#8760411yescharacteristic
110C2—971no—
111C2—972no—
112C2—971no—
113C2#1569087312yesdirect product factor
114C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C22⋊#87604
commutatorC4×C97C22×C4
FrattiniC4C22×#87604
FittingC2×Q8×C97C4
socleC22×C97C22⋊C4
hypercenterC2×Q8#87604
hypocenterC97C2×#103
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. #15690873C2direct (N × H)
12. C2×Dic194C4semidirect
15. Q8×D97C4semidirect
19. C2×Q8×C97C4semidirect
24. Q8×C97C2×C4semidirect
38. Dic194C2×C4semidirect
52. C2×C97#103semidirect
54. D97#103semidirect
57. C97C2×#103semidirect
69. C2×Q8#87604semidirect
84. Q8C2×#87604semidirect
113. C2#15690873direct (N × H)