Finite Group Databasebeta

← #20260717

Subgroups — #20260717

Order 6208.

150 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 59 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×#13095511C211yesmaximal, characteristic
2C2×#13095495C211yesmaximal, characteristic, complemented
3#15690728C212yesmaximal, complemented
4#15690726C212yesmaximal, complemented
5C2×M16×C97C211yesmaximal, characteristic, complemented
6#13095511—21no—
7#13095511—21no—
8#13095511—21no—
9#13095511—21no—
10C2×Dic194C2211yescharacteristic
11C2×D388C2211yescharacteristic
12C2×C22⋊D97C412yes—
13C2×C4×D97C412yes—
14#13095495—21no—
15#13095495C2212yes—
16C2×#11715895—21no—
17C22×C4×C97C2211yescharacteristic
18M16×C97—21no—
19M16×C97C2212yes—
20C2×C8×C97—21no—
21C23×C97C2×C411yescharacteristic
22C22×D97C2×C412yes—
23C2×C4×C97C2×C411yescharacteristic
24C2×C4×C97D411yescharacteristic
25C2×C4×C97D411yescharacteristic
26C2×C4×C97D411yescharacteristic
27C2×C4×C97D411yescharacteristic
28C2×C4×C97C2311yescharacteristic
29C22⋊D97—22no—
30C22⋊D97—22no—
31C2×Dic97C2×C412yes—
32D388—21no—
33D388—21no—
34C4×D97—22no—
35C4×D97—22no—
36Dic194—21no—
37Dic194—21no—
38C8×C97—22no—
39#11715895—22no—
40C22×C97—41no—
41C22×C97C22⋊C411yescharacteristic
42C22×C97C22⋊C411yescharacteristic
43C22×C97C22×C411yescharacteristic
44C2×D97—22no—
45C2×D97—42no—
46C4×C97C22⋊C411yescharacteristic
47C4×C97C22⋊C411yescharacteristic
48C4×C97C2×D411yescharacteristic
49C4×C97C2×D411yescharacteristic
50Dic97—22no—
51C2×C97—21no—
52C2×C97—21no—
53C2×C97—21no—
54C2×C97C2×C22⋊C411yescharacteristic
55D97—42no—
56C97#41311yescharacteristic, complemented, Sylow
57#413—971nomaximal, Sylow
58C2×#41—971no—
59C2×M16—971no—
60C2×M16D9711yescharacteristic, complemented
61#101—972no—
62#100—972no—
63#41—1941no—
64#41—1941no—
65#41—1941no—
66#41—1941no—
67C2×Q8—971no—
68C2×D4—972no—
69C2×D4—971no—
70C22×C4—972no—
71C22×C4C2×D9711yescharacteristic
72M16—21no—
73M16—972no—
74M16—1941no—
75M16C2×D9712yes—
76C2×C8—21no—
77C2×C8—1941no—
78C23—972no—
79C23C4×D9711yescharacteristic
80Q8—1941no—
81Q8—1941no—
82D4—1942no—
83D4—1942no—
84D4—1941no—
85D4—1941no—
86C2×C4—972no—
87C2×C4—1942no—
88C2×C4—1942no—
89C2×C4C4×D9711yescharacteristic
90C2×C4D38811yescharacteristic
91C2×C4D38811yescharacteristic
92C2×C4C22⋊D9711yescharacteristic
93C2×C4C22⋊D9711yescharacteristic
94C2×C4C22×D9711yescharacteristic
95C8—22no—
96C8—1942no—
97C22—41no—
98C22—3882no—
99C22—1942no—
100C22#1309548811yescharacteristic
101C22#1309548811yescharacteristic
102C22C2×C4×D9711yescharacteristic
103C4—1942no—
104C4#1309548811yescharacteristic
105C4#1309548811yescharacteristic
106C4C2×C22⋊D9711yescharacteristic
107C4C2×D38811yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—3882no—
112C2C2×#1309548811yescharacteristic
subgroupG/H
centerC4#13095488
commutatorC22×C97C22×C4
FrattiniC2×C4C22×D97
FittingC2×M16×C97C2
socleC2×C97C2×C22⋊C4
hypercenterC2×M16D97
hypocenterC97#413
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#13095495C2semidirect
3. #15690728C2semidirect
4. #15690726C2semidirect
5. C2×M16×C97C2semidirect
56. C97#413semidirect
60. C2×M16D97semidirect