Finite Group Databasebeta

← #20260995

Subgroups — #20260995

Order 6208.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#15690841C211yesmaximal, characteristic, complemented
2#15690836C211yesmaximal, characteristic
3#15690816C211yesmaximal, characteristic, complemented
4#15690746C211yesmaximal, characteristic, complemented
5#15690729C211yesmaximal, characteristic, complemented
6#15690727C211yesmaximal, characteristic, complemented
7C2×SD16×C97C211yesmaximal, characteristic, complemented
8#13095511C2211yescharacteristic
9#13095501—21no—
10#13095499—21no—
11#13095498—21no—
12#13095496—21no—
13#13095495C2211yescharacteristic
14#13095495C2211yescharacteristic
15#13095495C2211yescharacteristic
16#13095494—21no—
17C8×D97—21no—
18C2×Q8×C97C2211yescharacteristic
19C2×D4×C97C2211yescharacteristic
20SD16×C97—21no—
21SD16×C97—21no—
22C2×C8×C97C2211yescharacteristic
23C23×C97—21no—
24Q8×C97—21no—
25Q8×C97—21no—
26D4×C97—21no—
27D4×C97—21no—
28C2×C4×C97—21no—
29C2×C4×C97C2311yescharacteristic
30C22⋊D97—21no—
31D388D411yescharacteristic
32C4×D97—21no—
33Dic194D411yescharacteristic
34C8×C97D411yescharacteristic
35C8×C97D411yescharacteristic
36#11715895—21no—
37#11715895—21no—
38#11715895—21no—
39C22×C97—41no—
40C22×C97—81no—
41C22×C97#4111yescharacteristic
42C2×D97—21no—
43C4×C97—41no—
44C4×C97C2×D411yescharacteristic
45C4×C97C2×D411yescharacteristic
46Dic97—21no—
47C2×C97—21no—
48C2×C97—81no—
49C2×C97#12111yescharacteristic
50D97—41no—
51C97#47111yescharacteristic, complemented, Sylow
52#471—971nomaximal, Sylow
53#137—971no—
54AGL(1,ℤ/8)—971no—
55C2×SD16D9711yescharacteristic, complemented
56#131—971no—
57#108—971no—
58#101—971no—
59#100—971no—
60#41—971no—
61C2×Q8C2×D9711yescharacteristic
62C2×D4C2×D9711yescharacteristic
63Q16—1941no—
64SD16—21no—
65SD16—21no—
66SD16—1941no—
67SD16—1941no—
68D8—1941no—
69M16—971no—
70M16—971no—
71M16—971no—
72M16—1941no—
73C2×C8—1941no—
74C2×C8C2×D9711yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8—971no—
79D4—21no—
80D4—21no—
81D4—971no—
82D4—1941no—
83C2×C4—21no—
84C2×C4—1941no—
85C2×C4C22×D9711yescharacteristic
86C8—1941no—
87C8—1941no—
88C8—1941no—
89C8C22⋊D9711yescharacteristic
90C8C22⋊D9711yescharacteristic
91C22—41no—
92C22—81no—
93C22—1941no—
94C22#1309551011yescharacteristic
95C4—41no—
96C4—1941no—
97C4D4×D9711yescharacteristic
98C4C2×C22⋊D9711yescharacteristic
99C2—21no—
100C2—81no—
101C2—3881no—
102C2#1569078111yescharacteristic
subgroupG/H
centerC2#15690781
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingC2×SD16×C97C2
socleC2×C97#121
hypercenterC2×SD16D97
hypocenterC97#471
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #15690841C2semidirect
3. #15690816C2semidirect
4. #15690746C2semidirect
5. #15690729C2semidirect
6. #15690727C2semidirect
7. C2×SD16×C97C2semidirect
51. C97#471semidirect
55. C2×SD16D97semidirect