Finite Group Databasebeta

← #20268065

Subgroups — #20268065

Order 6592.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#15693054C211yesmaximal, characteristic
2#15693052C211yesmaximal, characteristic
3C2×#13110095C211yesmaximal, characteristic, complemented
4#15693029C211yesmaximal, characteristic
5#15692956C211yesmaximal, characteristic, complemented
6#15692939C211yesmaximal, characteristic, complemented
7#101×C103C211yesmaximal, characteristic, complemented
8#13110105C2211yescharacteristic
9C2×Dic206C2211yescharacteristic
10Dic412—21no—
11#13110095—21no—
12#13110095—21no—
13#13110095—21no—
14#13110094—21no—
15#13110092—21no—
16#13110089C2211yescharacteristic
17#13110088—21no—
18C2×C103⋊C8C2211yescharacteristic
19C8×D103—21no—
20C2×Q8×C103C2211yescharacteristic
21M16×C103C2211yescharacteristic
22M16×C103C2211yescharacteristic
23Q8×C103—21no—
24Q8×C103—21no—
25C2×C4×C103—21no—
26C2×C4×C103C2311yescharacteristic
27C22⋊D103—21no—
28C2×Dic103—21no—
29D412D411yescharacteristic
30C4×D103—21no—
31Dic206—21no—
32Dic206—21no—
33Dic206D411yescharacteristic
34C8×C103—21no—
35C8×C103—21no—
36C103⋊C8—21no—
37C103⋊C8D411yescharacteristic
38C103⋊C8D411yescharacteristic
39C22×C103#4111yescharacteristic
40C2×D103—21no—
41C4×C103—41no—
42C4×C103C2×D411yescharacteristic
43C4×C103C2×D411yescharacteristic
44Dic103—21no—
45Dic103—41no—
46C2×C103—21no—
47C2×C103#12111yescharacteristic
48D103—41no—
49C103#47311yescharacteristic, complemented, Sylow
50#473—1031nomaximal, Sylow
51#137—1031no—
52#137—1031no—
53C2×Q16—1031no—
54#131—1031no—
55#108—1031no—
56#101—1031no—
57#101D10311yescharacteristic, complemented
58#41—1031no—
59C2×Q8—1031no—
60C2×Q8C2×D10311yescharacteristic
61Q16—2061no—
62Q16—2061no—
63Q16—2061no—
64Q16—2061no—
65SD16—2061no—
66SD16—2061no—
67M16—1031no—
68M16—2061no—
69M16C2×D10311yescharacteristic
70M16C2×D10311yescharacteristic
71C2×C8—1031no—
72C2×C8—2061no—
73Q8—21no—
74Q8—21no—
75Q8—1031no—
76Q8—2061no—
77Q8—2061no—
78D4—1031no—
79D4—2061no—
80C2×C4—21no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4C22×D10311yescharacteristic
84C8—21no—
85C8—21no—
86C8—1031no—
87C8—1031no—
88C8—2061no—
89C22—2061no—
90C22#1311010511yescharacteristic
91C4—41no—
92C4—4121no—
93C4—2061no—
94C4D4×D10311yescharacteristic
95C4D4×D10311yescharacteristic
96C2—21no—
97C2—4121no—
98C2#1569299411yescharacteristic
subgroupG/H
centerC2#15692994
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#101×C103C2
socleC2×C103#121
hypercenter#101D103
hypocenterC103#473
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#13110095C2semidirect
5. #15692956C2semidirect
6. #15692939C2semidirect
7. #101×C103C2semidirect
49. C103#473semidirect
57. #101D103semidirect