Finite Group Databasebeta

← #20267972

Subgroups — #20267972

Order 6592.

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

normal subgroups only

This group has 142 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#15693068C211yesmaximal, characteristic
2#15693052C211yesmaximal, characteristic, complemented
3#15693019C211yesmaximal, characteristic, complemented
4#15692948C211yesmaximal, characteristic, complemented
5#15692947C211yesmaximal, characteristic, complemented
6#15692939C211yesmaximal, characteristic, complemented
7#137×C103C211yesmaximal, characteristic, complemented
8#13110105—21no—
9#13110105C2211yescharacteristic
10#13110104—21no—
11#13110104—22no—
12C2×Dic206—21no—
13C2×Dic206C2211yescharacteristic
14Q8×D103—21no—
15#13110095—21no—
16#13110092—21no—
17#13110089C2211yescharacteristic
18Dic103⋊C4—22no—
19C4×Dic103C2211yescharacteristic
20#41×C103C2211yescharacteristic
21C2×Q8×C103C2211yescharacteristic
22Q16×C103—21no—
23SD16×C103—21no—
24M16×C103C2211yescharacteristic
25Q8×C103—21no—
26Q8×C103—21no—
27Q8×C103D411yescharacteristic
28D4×C103—21no—
29D4×C103D411yescharacteristic
30C2×C4×C103—21no—
31C2×C4×C103—21no—
32C2×C4×C103C2311yescharacteristic
33C22⋊D103—22no—
34C22⋊D103—21no—
35C2×Dic103—22no—
36C2×Dic103—21no—
37C2×Dic103D412yes—
38D412D411yescharacteristic
39C4×D103—22no—
40C4×D103—21no—
41Dic206—22no—
42Dic206—21no—
43Dic206—21no—
44Dic206D411yescharacteristic
45C8×C103—21no—
46C103⋊C8—21no—
47C22×C103—21no—
48C22×C103C2×D411yescharacteristic
49C2×D103—21no—
50C4×C103—21no—
51C4×C103—41no—
52C4×C103C2×D411yescharacteristic
53C4×C103C2×D411yescharacteristic
54Dic103—22no—
55Dic103—22no—
56Dic103—21no—
57C2×C103—21no—
58C2×C103—41no—
59C2×C103#12011yescharacteristic
60D103—41no—
61C103#45611yescharacteristic, complemented, Sylow
62#456—1031nomaximal, Sylow
632−1+4—1031no—
64#137—1031no—
65#137D10311yescharacteristic, complemented
66C4⋊Q8—1031no—
67#104—1031no—
68#104—1031no—
69#101—1031no—
70#41—1031no—
71#41—2061no—
72#41—2062no—
73#41—2061no—
74#41C2×D10311yescharacteristic
75C2×Q8—1031no—
76C2×Q8—2061no—
77C2×Q8—2061no—
78C2×Q8C2×D10311yescharacteristic
79Q16—21no—
80Q16—2061no—
81SD16—21no—
82SD16—2061no—
83M16—1031no—
84M16C2×D10311yescharacteristic
85C4⋊C4—2062no—
86C42—1031no—
87Q8—21no—
88Q8—21no—
89Q8—1031no—
90Q8—2062no—
91Q8—2061no—
92Q8—2061no—
93Q8C22⋊D10311yescharacteristic
94D4—21no—
95D4—1031no—
96D4—2062no—
97D4—2061no—
98D4C22⋊D10311yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—1032no—
102C2×C4—2062no—
103C2×C4—2062no—
104C2×C4—2061no—
105C2×C4—2061no—
106C2×C4C22×D10311yescharacteristic
107C8—21no—
108C8—2061no—
109C22—21no—
110C22—2061no—
111C22D4×D10311yescharacteristic
112C4—21no—
113C4—41no—
114C4—2062no—
115C4—2062no—
116C4—2061no—
117C4D4×D10311yescharacteristic
118C4C2×C22⋊D10311yescharacteristic
119C2—21no—
120C2—41no—
121C2—4121no—
122C2#1569298911yescharacteristic
subgroupG/H
centerC2#15692989
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#137×C103C2
socleC2×C103#120
hypercenter#137D103
hypocenterC103#456
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #15693052C2semidirect
3. #15693019C2semidirect
4. #15692948C2semidirect
5. #15692947C2semidirect
6. #15692939C2semidirect
7. #137×C103C2semidirect
61. C103#456semidirect
65. #137D103semidirect