Finite Group Databasebeta

← #20260914

Subgroups — #20260914

Order 6208.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#15690856C211yesmaximal, characteristic
2#15690843C211yesmaximal, characteristic, complemented
3#15690840C211yesmaximal, characteristic, complemented
4#15690798C211yesmaximal, characteristic, complemented
5#15690738C211yesmaximal, characteristic, complemented
6#15690726C211yesmaximal, characteristic, complemented
7#104×C97C211yesmaximal, characteristic, complemented
8#13095512—21no—
9#13095511—21no—
10#13095511C2211yescharacteristic
11C2×Dic194C2211yescharacteristic, complemented
12C2×D388—21no—
13C2×D388C2211yescharacteristic
14D4×D97—22no—
15D4×D97—21no—
16Dic388—21no—
17#13095501—21no—
18#13095500—21no—
19#13095499—21no—
20#13095495C2211yescharacteristic, complemented
21#13095488—22no—
22#41×C97C2211yescharacteristic
23M16×C97C2211yescharacteristic, complemented
24C42×C97C2211yescharacteristic, complemented
25C22×D97—22no—
26C22×D97D412yes—
27Q8×C97D411yescharacteristic
28D4×C97—21no—
29D4×C97D411yescharacteristic
30C2×C4×C97—21no—
31C2×C4×C97—21no—
32C2×C4×C97C2311yescharacteristic
33C22⋊D97—22no—
34C22⋊D97—21no—
35C2×Dic97—21no—
36D388—22no—
37D388—21no—
38D388—21no—
39D388D411yescharacteristic
40C4×D97—22no—
41C4×D97—21no—
42Dic194—21no—
43Dic194—21no—
44Dic194D411yescharacteristic
45C8×C97—21no—
46#11715895—21no—
47C22×C97—21no—
48C22×C97C2×D411yescharacteristic
49C2×D97—22no—
50C2×D97—21no—
51C2×D97—42no—
52C2×D97—82no—
53C4×C97—21no—
54C4×C97—41no—
55C4×C97C2×D411yescharacteristic
56C4×C97C2×D411yescharacteristic
57Dic97—21no—
58Dic97—41no—
59C2×C97—21no—
60C2×C97—41no—
61C2×C97#12011yescharacteristic
62D97—42no—
63D97—41no—
64C97#45511yescharacteristic, complemented, Sylow
65#455—971nomaximal, Sylow
66H(5,𝔽2)—971no—
67#137—971no—
68#137—971no—
69#124—971no—
70#104—971no—
71#104D9711yescharacteristic, complemented
72#100—971no—
73#41—971no—
74#41—1941no—
75#41—1941no—
76#41C2×D9711yescharacteristic
77C2×Q8—971no—
78C2×D4—971no—
79C2×D4—1941no—
80C2×D4—1942no—
81C2×D4—1941no—
82Q16—1941no—
83Q16—1941no—
84SD16—1941no—
85SD16—1941no—
86M16—971no—
87M16C2×D9711yescharacteristic, complemented
88C22⋊C4—1942no—
89C42C2×D9711yescharacteristic, complemented
90C23—972no—
91C23—1942no—
92Q8—971no—
93Q8—1941no—
94Q8—1941no—
95Q8D38811yescharacteristic
96D4—21no—
97D4—971no—
98D4—1942no—
99D4—1942no—
100D4—1941no—
101D4—1941no—
102D4—1941no—
103D4D38811yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—1942no—
107C2×C4—1941no—
108C2×C4—1941no—
109C2×C4C22×D9711yescharacteristic
110C8—21no—
111C8—1941no—
112C22—21no—
113C22—7762no—
114C22—3882no—
115C22—1941no—
116C22—1942no—
117C22D4×D9711yescharacteristic
118C4—21no—
119C4—41no—
120C4—3881no—
121C4—1941no—
122C4D4×D9711yescharacteristic
123C4C2×D38811yescharacteristic
124C2—21no—
125C2—41no—
126C2—3881no—
127C2—3882no—
128C2#1569078011yescharacteristic
subgroupG/H
centerC2#15690780
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
Fitting#104×C97C2
socleC2×C97#120
hypercenter#104D97
hypocenterC97#455
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #15690843C2semidirect
3. #15690840C2semidirect
4. #15690798C2semidirect
5. #15690738C2semidirect
6. #15690726C2semidirect
7. #104×C97C2semidirect
11. C2×Dic194C22semidirect
20. #13095495C22semidirect
23. M16×C97C22semidirect
24. C42×C97C22semidirect
64. C97#455semidirect
71. #104D97semidirect
87. M16C2×D97semidirect
89. C42C2×D97semidirect