Finite Group Databasebeta

← #20260938

Subgroups — #20260938

Order 6208.

120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13095499C211yesmaximal, characteristic
2#15690808C211yesmaximal, characteristic, complemented
3D4×Dic97C211yesmaximal, characteristic
4#15690739C211yesmaximal, characteristic, complemented
5#15690735C211yesmaximal, characteristic, complemented
6#15690734C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9C22×Dic97—21no—
10#13095499—22no—
11C2×#11715895C2211yescharacteristic
12C4⋊Dic97C2211yescharacteristic
13#13095490—21no—
14#13095490—21no—
15C22⋊Dic97—21no—
16C4×Dic97C2211yescharacteristic
17C2×Q8×C97C2211yescharacteristic
18C2×D4×C97C2211yescharacteristic
19SD16×C97—22no—
20C2×C8×C97C2211yescharacteristic
21C23×C97—21no—
22Q8×C97—21no—
23Q8×C97—21no—
24D4×C97—21no—
25D4×C97D412yes—
26C2×C4×C97—21no—
27C2×C4×C97C2311yescharacteristic
28C2×Dic97—21no—
29C2×Dic97—21no—
30C2×Dic97—42no—
31C2×Dic97D411yescharacteristic
32C2×Dic97D411yescharacteristic
33Dic194—21no—
34Dic194—21no—
35C8×C97—21no—
36#11715895—21no—
37C22×C97—22no—
38C22×C97—41no—
39C22×C97—41no—
40C22×C97C2×D411yescharacteristic
41C4×C97—41no—
42C4×C97C2×D411yescharacteristic
43C4×C97#4111yescharacteristic
44Dic97—21no—
45Dic97—41no—
46Dic97—41no—
47Dic97SD1612yescomplemented
48C2×C97—42no—
49C2×C97#12111yescharacteristic
50C2×C97C2×SD1611yescharacteristic
51C2×C97#13711yescharacteristic
52C97#46111yescharacteristic, complemented, Sylow
53#461—971nomaximal, Sylow
54C2×SD16—971no—
55C2×SD16D9711yescharacteristic
56C4⋊Q8—971no—
57C4×D4—971no—
58C4⋊C8—971no—
59#103—971no—
60#103—971no—
61C2×Q8—971no—
62C2×Q8C2×D9711yescharacteristic
63C2×D4C2×D9711yescharacteristic
64C22×C4—1941no—
65SD16—22no—
66SD16—1942no—
67C2×C8—971no—
68C2×C8C2×D9711yescharacteristic
69C4⋊C4—971no—
70C4⋊C4—1941no—
71C4⋊C4—1941no—
72C22⋊C4—1941no—
73C42—971no—
74C23—21no—
75Q8—21no—
76Q8—21no—
77Q8—1941no—
78Q8—1941no—
79D4—21no—
80D4C22⋊D9712yes—
81C2×C4—21no—
82C2×C4—971no—
83C2×C4—971no—
84C2×C4—3882no—
85C2×C4—1941no—
86C2×C4—1941no—
87C2×C4C22×D9711yescharacteristic
88C8—21no—
89C8—1941no—
90C22—22no—
91C22—41no—
92C22—41no—
93C22D4×D9711yescharacteristic
94C4—41no—
95C4—972no—
96C4—3881no—
97C4—3881no—
98C4—1941no—
99C4C2×C22⋊D9711yescharacteristic
100C4#1309551011yescharacteristic
101C2—42no—
102C2#1569078211yescharacteristic
103C2SD16×D9711yescharacteristic
104C2#1569083911yescharacteristic
subgroupG/H
centerC22D4×D97
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC22×C97C2×D4
hypercenterC2×SD16D97
hypocenterC97#461
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. #15690808C2semidirect
4. #15690739C2semidirect
5. #15690735C2semidirect
6. #15690734C2semidirect
47. Dic97SD16semidirect
52. C97#461semidirect