Finite Group Databasebeta

← #20260996

Subgroups — #20260996

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#15690840C211yesmaximal, characteristic, complemented
2C2×#13095499C211yesmaximal, characteristic, complemented
3#15690817C211yesmaximal, characteristic, complemented
4#15690745C211yesmaximal, characteristic, complemented
5#15690728C211yesmaximal, characteristic, complemented
6#15690727C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9#13095501—21no—
10#13095499—21no—
11#13095499—21no—
12#13095499—21no—
13#13095495—21no—
14#13095495C2211yescharacteristic
15#13095495C2211yescharacteristic
16C2×#11715895—21no—
17C2×#11715895C2211yescharacteristic
18#41×C97C2211yescharacteristic
19C2×D4×C97C2211yescharacteristic
20SD16×C97—21no—
21D8×C97—21no—
22M16×C97C2211yescharacteristic
23C23×C97—21no—
24Q8×C97D411yescharacteristic
25D4×C97—21no—
26D4×C97—21no—
27D4×C97—21no—
28D4×C97D411yescharacteristic
29C2×C4×C97—21no—
30C2×C4×C97C2311yescharacteristic
31C2×Dic97—21no—
32Dic194—21no—
33Dic194—21no—
34C8×C97—21no—
35#11715895—21no—
36#11715895—21no—
37#11715895D411yescharacteristic
38#11715895D411yescharacteristic
39C22×C97—21no—
40C22×C97—41no—
41C22×C97—81no—
42C22×C97#4111yescharacteristic
43C4×C97—21no—
44C4×C97C2×D411yescharacteristic
45C4×C97C2×D411yescharacteristic
46Dic97—41no—
47C2×C97—21no—
48C2×C97—41no—
49C2×C97—81no—
50C2×C97#12111yescharacteristic
51C97#47111yescharacteristic, complemented, Sylow
52#471—971nomaximal, Sylow
53#137—971no—
54AGL(1,ℤ/8)D9711yescharacteristic
55C2×SD16—971no—
56#131—971no—
57#108—971no—
58#101—971no—
59#100—971no—
60#41C2×D9711yescharacteristic
61C2×Q8—971no—
62C2×D4C2×D9711yescharacteristic
63Q16—1941no—
64SD16—21no—
65SD16—1941no—
66SD16—1941no—
67SD16—1941no—
68D8—21no—
69M16—971no—
70M16—971no—
71M16—1941no—
72M16C2×D9711yescharacteristic
73C2×C8—971no—
74C2×C8—1941no—
75C23—21no—
76Q8—1941no—
77Q8—1941no—
78Q8C22⋊D9711yescharacteristic
79D4—21no—
80D4—21no—
81D4—21no—
82D4C22⋊D9711yescharacteristic
83C2×C4—21no—
84C2×C4—1941no—
85C2×C4C22×D9711yescharacteristic
86C8—21no—
87C8—971no—
88C8—971no—
89C8—1941no—
90C8—1941no—
91C22—21no—
92C22—41no—
93C22—81no—
94C22#1309551011yescharacteristic
95C4—21no—
96C4—3881no—
97C4D4×D9711yescharacteristic
98C4C2×C22⋊D9711yescharacteristic
99C2—21no—
100C2—41no—
101C2—81no—
102C2#1569078211yescharacteristic
subgroupG/H
centerC2#15690782
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingAGL(1,ℤ/8)×C97C2
socleC2×C97#121
hypercenterAGL(1,ℤ/8)D97
hypocenterC97#471
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15690840C2semidirect
2. C2×#13095499C2semidirect
3. #15690817C2semidirect
4. #15690745C2semidirect
5. #15690728C2semidirect
6. #15690727C2semidirect
51. C97#471semidirect