Finite Group Databasebeta

← #20260869

Subgroups — #20260869

Order 6208.

198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13095496C212yesmaximal, complemented
2#15690784C211yesmaximal, characteristic, complemented
3#15690731C212yesmaximal, complemented
4C22⋊#11715895C211yesmaximal, characteristic, complemented
5C22×D4×C97C211yesmaximal, characteristic, complemented
6C2×D388C2211yescharacteristic, complemented
7C2×C22⋊D97—21no—
8#13095496—24no—
9C2×#11715895C2212yescomplemented
10C4⋊Dic97C2211yescharacteristic, complemented
11#13095488—21no—
12C24×C97—21no—
13C2×D4×C97—24no—
14C2×D4×C97—21no—
15C2×D4×C97C2212yes—
16C22×C4×C97C2211yescharacteristic
17C23×C97—24no—
18C23×C97—22no—
19C23×C97—42no—
20C23×C97—42no—
21C23×C97D411yescharacteristic
22C22×D97—21no—
23D4×C97—24no—
24D4×C97—22no—
25D4×C97D414yescomplemented
26C2×C4×C97—22no—
27C2×C4×C97D411yescharacteristic
28C2×C4×C97C2311yescharacteristic
29C22⋊D97—42no—
30C2×Dic97—21no—
31D388—22no—
32#11715895—22no—
33C22×C97—21no—
34C22×C97—21no—
35C22×C97—24no—
36C22×C97—48no—
37C22×C97—42no—
38C22×C97—42no—
39C22×C97D812yescomplemented
40C22×C97C2×D411yescharacteristic
41C2×D97—41no—
42C2×D97—41no—
43C2×D97—41no—
44C4×C97—21no—
45C4×C97C2×D412yes—
46Dic97—41no—
47C2×C97—22no—
48C2×C97—44no—
49C2×C97#12011yescharacteristic
50C2×C97C2×D811yescharacteristic
51C2×C97AGL(1,ℤ/8)11yescharacteristic
52D97—81no—
53C97#44711yescharacteristic, complemented, Sylow
54#447—971nomaximal, Sylow
55C22×D4D9711yescharacteristic, complemented
56C2×D8—972no—
57#121—971no—
58#102—972no—
59C22⋊C8—971no—
60C24—21no—
61C2×D4—24no—
62C2×D4—21no—
63C2×D4—971no—
64C2×D4—1941no—
65C2×D4C2×D9712yes—
66C22×C4C2×D9711yescharacteristic
67D8—1944no—
68C2×C8—972no—
69C4⋊C4—971no—
70C22⋊C4—1941no—
71C23—24no—
72C23—22no—
73C23—42no—
74C23—42no—
75C23—1941no—
76C23C22⋊D9711yescharacteristic
77D4—24no—
78D4—22no—
79D4—3882no—
80D4—1942no—
81D4C22⋊D9714yescomplemented
82C2×C4—22no—
83C2×C4—1941no—
84C2×C4C22⋊D9711yescharacteristic
85C2×C4C22×D9711yescharacteristic
86C8—1942no—
87C22—21no—
88C22—21no—
89C22—24no—
90C22—48no—
91C22—42no—
92C22—42no—
93C22—3881no—
94C22—3881no—
95C22—3881no—
96C22#1309549612yescomplemented
97C22C2×C22⋊D9711yescharacteristic
98C4—21no—
99C4—3881no—
100C4C2×C22⋊D9712yes—
101C2—22no—
102C2—44no—
103C2—7761no—
104C2#1569077911yescharacteristic
105C2C2×#1309549611yescharacteristic
106C2#1569083611yescharacteristic
subgroupG/H
centerC22C2×C22⋊D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC22×D4×C97C2
socleC22×C97C2×D4
hypercenterC22×D4D97
hypocenterC97#447
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13095496C2semidirect
2. #15690784C2semidirect
3. #15690731C2semidirect
4. C22⋊#11715895C2semidirect
5. C22×D4×C97C2semidirect
6. C2×D388C22semidirect
9. C2×#11715895C22semidirect
10. C4⋊Dic97C22semidirect
25. D4×C97D4semidirect
39. C22×C97D8semidirect
53. C97#447semidirect
55. C22×D4D97semidirect
81. D4C22⋊D97semidirect
96. C22#13095496semidirect