Finite Group Databasebeta

← #20260885

Subgroups — #20260885

Order 6208.

188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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×D388C211yesmaximal, characteristic
2C2×#13095498C212yesmaximal, complemented
3#15690730C212yesmaximal, complemented
4C22⋊#11715895C211yesmaximal, characteristic, complemented
5C22⋊Q8×C97C211yesmaximal, characteristic, complemented
6C23×D97—21no—
7C2×D388—21no—
8C2×D388—24no—
9C2×D388C2212yes—
10#13095498—24no—
11C2×#11715895C2212yescomplemented
12C2×Q8×C97C2211yescharacteristic, complemented
13C22×C4×C97C2211yescharacteristic
14C4⋊C4×C97—21no—
15C4⋊C4×C97C2211yescharacteristic, complemented
16C22⋊C4×C97—21no—
17C23×C97D411yescharacteristic
18C22×D97—24no—
19C22×D97—22no—
20C22×D97—42no—
21C22×D97—42no—
22Q8×C97—22no—
23C2×C4×C97—22no—
24C2×C4×C97—21no—
25C2×C4×C97—21no—
26C2×C4×C97D411yescharacteristic
27C2×C4×C97C2311yescharacteristic
28D388—24no—
29D388—22no—
30D388D414yes—
31#11715895—22no—
32C22×C97—21no—
33C22×C97—21no—
34C22×C97SD1612yescomplemented
35C22×C97C2×D411yescharacteristic
36C2×D97—24no—
37C2×D97—48no—
38C2×D97—42no—
39C2×D97—42no—
40C4×C97—21no—
41C4×C97—41no—
42C4×C97—41no—
43C4×C97C2×D412yes—
44C2×C97—22no—
45C2×C97#12011yescharacteristic
46C2×C97C2×SD1611yescharacteristic
47C2×C97AGL(1,ℤ/8)11yescharacteristic
48D97—44no—
49C97#45011yescharacteristic, complemented, Sylow
50#450—971nomaximal, Sylow
51C22×D4—971no—
52C2×SD16—972no—
53C22⋊Q8D9711yescharacteristic, complemented
54#102—972no—
55C22⋊C8—971no—
56C24—1941no—
57C2×Q8C2×D9711yescharacteristic, complemented
58C2×D4—972no—
59C2×D4—1944no—
60C2×D4—1941no—
61C22×C4C2×D9711yescharacteristic
62SD16—1944no—
63C2×C8—972no—
64C4⋊C4—21no—
65C4⋊C4C2×D9711yescharacteristic, complemented
66C22⋊C4—21no—
67C23—3882no—
68C23—3882no—
69C23—1944no—
70C23—1942no—
71C23C22⋊D9711yescharacteristic
72Q8—22no—
73D4—974no—
74D4—1944no—
75D4—1942no—
76C2×C4—22no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4C22⋊D9711yescharacteristic
80C2×C4C22×D9711yescharacteristic
81C8—1942no—
82C22—21no—
83C22—21no—
84C22—3888no—
85C22—3882no—
86C22—3882no—
87C22—1944no—
88C22#1309549812yescomplemented
89C22C2×C22⋊D9711yescharacteristic
90C4—21no—
91C4—41no—
92C4—41no—
93C4D4×D9712yes—
94C2—22no—
95C2—3884no—
96C2#1569077811yescharacteristic
97C2C2×#1309549811yescharacteristic
98C2#1569083511yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22⋊Q8×C97C2
socleC22×C97C2×D4
hypercenterC22⋊Q8D97
hypocenterC97#450
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13095498C2semidirect
3. #15690730C2semidirect
4. C22⋊#11715895C2semidirect
5. C22⋊Q8×C97C2semidirect
11. C2×#11715895C22semidirect
12. C2×Q8×C97C22semidirect
15. C4⋊C4×C97C22semidirect
34. C22×C97SD16semidirect
49. C97#450semidirect
53. C22⋊Q8D97semidirect
57. C2×Q8C2×D97semidirect
65. C4⋊C4C2×D97semidirect
88. C22#13095498semidirect