Finite Group Databasebeta

← C2×#15690786 #20261230

Subgroups — C2×#15690786 #20261230

Order 6208.

322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C22×C4×D97C211yesmaximal, characteristic
2#15690786C218yesmaximal, direct product factor
3C2×C4⋊Dic97C211yesmaximal, characteristic, complemented
4C2×#13095490C212yesmaximal, complemented
5C2×#13095488C212yesmaximal
6C22×Q8×C97C211yesmaximal, characteristic, complemented
7C23×D97C2211yescharacteristic
8C22×Dic97C2212yes—
9C22×Dic97C2211yescharacteristic
10C2×C4×D97—24no—
11C2×C4×D97C2214yes—
12C4⋊Dic97C2214yescomplemented
13#13095490C2218yescomplemented
14#13095488C2218yes—
15C2×Q8×C97—24no—
16C2×Q8×C97C2214yescomplemented
17C22×C4×C97C2212yes—
18C22×C4×C97C2211yescharacteristic
19C23×C97C2311yescharacteristic
20C22×D97—22no—
21C22×D97—22no—
22C22×D97Q814yescomplemented
23C22×D97C2312yes—
24Q8×C97—28no—
25C2×C4×C97—24no—
26C2×C4×C97D414yes—
27C2×C4×C97C2314yes—
28C2×C4×C97C2312yes—
29C2×Dic97—22no—
30C2×Dic97—24no—
31C2×Dic97C2314yes—
32C2×Dic97C2312yes—
33C4×D97—28no—
34C22×C97C2×D412yes—
35C22×C97C2×Q812yes—
36C22×C97#4112yes—
37C22×C97C2411yescharacteristic
38C2×D97—28no—
39C2×D97—22no—
40C2×D97—22no—
41C2×D97C2×Q814yescomplemented
42C4×C97—24no—
43C4×C97C2×D414yes—
44Dic97—22no—
45Dic97—24no—
46C2×C97C22⋊Q814yescomplemented
47C2×C97C22×D411yescharacteristic
48C2×C97C22×Q811yescharacteristic
49C2×C97C2×#4111yescharacteristic
50D97—24no—
51C97C2×C22⋊Q811yescharacteristic, complemented, Sylow
52C2×C22⋊Q8—971nomaximal, Sylow
53C22×Q8D9711yescharacteristic, complemented
54C23×C4—971no—
55C22⋊Q8—978no—
56C2×C4⋊C4—972no—
57C2×C4⋊C4—971no—
58C2×C22⋊C4—972no—
59C24—971no—
60C2×Q8—24no—
61C2×Q8C2×D9714yescomplemented
62C22×C4—972no—
63C22×C4—971no—
64C22×C4—974no—
65C22×C4—1944no—
66C22×C4C2×D9712yes—
67C22×C4C2×D9711yescharacteristic
68C4⋊C4—978no—
69C4⋊C4—974no—
70C22⋊C4—978no—
71C23—974no—
72C23—972no—
73C23—1942no—
74C23—1942no—
75C23C22×D9711yescharacteristic
76Q8—28no—
77C2×C4—24no—
78C2×C4—974no—
79C2×C4—972no—
80C2×C4—1942no—
81C2×C4—1944no—
82C2×C4—1948no—
83C2×C4C22⋊D9714yes—
84C2×C4C22×D9714yes—
85C2×C4C22×D9712yes—
86C22—974no—
87C22—1948no—
88C22—1942no—
89C22—1942no—
90C22C2×C22⋊D9712yes—
91C22Q8×D9712yes—
92C22#1309551212yes—
93C22C23×D9711yescharacteristic
94C4—24no—
95C4—1942no—
96C4—1944no—
97C4C2×C22⋊D9714yes—
98C2—1944no—
99C2#1569078614yesdirect product factor
100C2C22×C22⋊D9711yescharacteristic
101C2C2×Q8×D9711yescharacteristic
102C2C2×#1309551211yescharacteristic
subgroupG/H
centerC23C22×D97
commutatorC22×C97C24
FrattiniC22C23×D97
FittingC22×Q8×C97C2
socleC23×C97C23
hypercenterC22×Q8D97
hypocenterC97C2×C22⋊Q8
LCSG ▷ C22×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #15690786C2direct (N × H)
3. C2×C4⋊Dic97C2semidirect
4. C2×#13095490C2semidirect
6. C22×Q8×C97C2semidirect
12. C4⋊Dic97C22semidirect
13. #13095490C22semidirect
16. C2×Q8×C97C22semidirect
22. C22×D97Q8semidirect
41. C2×D97C2×Q8semidirect
46. C2×C97C22⋊Q8semidirect
51. C97C2×C22⋊Q8semidirect
53. C22×Q8D97semidirect
61. C2×Q8C2×D97semidirect
99. C2#15690786direct (N × H)