Finite Group Databasebeta

← #20260884

Subgroups — #20260884

Order 6208.

188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4×D97C211yesmaximal, characteristic
2C2×#13095498C211yesmaximal, characteristic, complemented
3#15690786C211yesmaximal, characteristic, complemented
4#15690732C211yesmaximal, characteristic, complemented
5#15690731C211yesmaximal, characteristic, complemented
6#15690722C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8C23×D97—21no—
9C2×D388C2211yescharacteristic
10C2×C22⋊D97—21no—
11D4×D97—22no—
12D4×D97—22no—
13C2×C4×D97C2211yescharacteristic
14#13095498—22no—
15C2×#11715895C2211yescharacteristic, complemented
16C4⋊Dic97C2211yescharacteristic, complemented
17#13095490—21no—
18#13095488—21no—
19C2×Q8×C97C2211yescharacteristic, complemented
20C2×D4×C97C2211yescharacteristic
21SD16×C97—22no—
22C2×C8×C97C2211yescharacteristic, complemented
23C23×C97—21no—
24C22×D97—24no—
25C22×D97—21no—
26C22×D97—42no—
27C22×D97—42no—
28C22×D97D411yescharacteristic
29Q8×C97—21no—
30Q8×C97—21no—
31D4×C97—21no—
32D4×C97D412yes—
33C2×C4×C97—21no—
34C2×C4×C97C2311yescharacteristic
35C22⋊D97—24no—
36C2×Dic97—21no—
37C2×Dic97D411yescharacteristic
38D388—21no—
39D388D412yes—
40C4×D97—21no—
41C4×D97—21no—
42C8×C97—21no—
43#11715895—21no—
44C22×C97—22no—
45C22×C97—41no—
46C22×C97—41no—
47C22×C97C2×D411yescharacteristic
48C2×D97—21no—
49C2×D97—21no—
50C2×D97—22no—
51C2×D97—48no—
52C2×D97—41no—
53C2×D97—41no—
54C2×D97SD1612yescomplemented
55C4×C97—41no—
56C4×C97C2×D411yescharacteristic
57C4×C97C2×D411yescharacteristic
58Dic97—21no—
59Dic97—41no—
60C2×C97—42no—
61C2×C97#12011yescharacteristic
62C2×C97C2×SD1611yescharacteristic
63C2×C97AGL(1,ℤ/8)11yescharacteristic
64D97—22no—
65D97—42no—
66C97#45011yescharacteristic, complemented, Sylow
67#450—971nomaximal, Sylow
68C22×D4—971no—
69C2×SD16—971no—
70C2×SD16D9711yescharacteristic, complemented
71C22⋊Q8—971no—
72#102—971no—
73#102—971no—
74C22⋊C8—971no—
75C24—1941no—
76C2×Q8C2×D9711yescharacteristic, complemented
77C2×D4—971no—
78C2×D4—1941no—
79C2×D4—1942no—
80C2×D4—1942no—
81C2×D4C2×D9711yescharacteristic
82C22×C4—971no—
83SD16—22no—
84SD16—1942no—
85C2×C8—971no—
86C2×C8C2×D9711yescharacteristic, complemented
87C4⋊C4—971no—
88C4⋊C4—1941no—
89C22⋊C4—1941no—
90C23—21no—
91C23—971no—
92C23—3882no—
93C23—3882no—
94C23—1944no—
95C23—1941no—
96Q8—21no—
97Q8—21no—
98D4—21no—
99D4—972no—
100D4—1944no—
101D4—1941no—
102D4C22⋊D9712yes—
103C2×C4—21no—
104C2×C4—971no—
105C2×C4—1941no—
106C2×C4—1941no—
107C2×C4—1941no—
108C2×C4C22×D9711yescharacteristic
109C8—21no—
110C8—1941no—
111C22—22no—
112C22—41no—
113C22—41no—
114C22—972no—
115C22—3888no—
116C22—3881no—
117C22—3881no—
118C22—1942no—
119C22—1941no—
120C22—1941no—
121C22D4×D9711yescharacteristic
122C4—41no—
123C4—3881no—
124C4—1941no—
125C4D4×D9711yescharacteristic
126C4C2×C22⋊D9711yescharacteristic
127C2—42no—
128C2—3882no—
129C2—1942no—
130C2#1569077811yescharacteristic
131C2SD16×D9711yescharacteristic
132C2#1569083711yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#450
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#13095498C2semidirect
3. #15690786C2semidirect
4. #15690732C2semidirect
5. #15690731C2semidirect
6. #15690722C2semidirect
7. C2×SD16×C97C2semidirect
15. C2×#11715895C22semidirect
16. C4⋊Dic97C22semidirect
19. C2×Q8×C97C22semidirect
22. C2×C8×C97C22semidirect
54. C2×D97SD16semidirect
66. C97#450semidirect
70. C2×SD16D97semidirect
76. C2×Q8C2×D97semidirect
86. C2×C8C2×D97semidirect