Finite Group Databasebeta

← #20267786

Subgroups — #20267786

Order 6592.

158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#13110106C211yesmaximal, characteristic
2C2×C8×D103C211yesmaximal, characteristic, complemented
3#15692979C211yesmaximal, characteristic, complemented
4#15692945C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8#13110106—22no—
9#13110106C414yescomplemented
10C2×D412—21no—
11C2×D412C2211yescharacteristic
12C2×C4×D103—21no—
13C2×C4×D103C2211yescharacteristic
14C2×C103⋊C8C2211yescharacteristic
15C8×D103—22no—
16C4⋊Dic103C2211yescharacteristic
17(C2×D103)⋊C4—21no—
18C4×Dic103—21no—
19C2×Q8×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic
21C4⋊C4×C103C2211yescharacteristic
22C22×D103—21no—
23C22×D103D411yescharacteristic
24Q8×C103—21no—
25Q8×C103C2×C412yes—
26C2×C4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30C2×Dic103D411yescharacteristic
31D412—24no—
32D412—21no—
33D412C2×C412yes—
34C4×D103—24no—
35C4×D103C2×C412yes—
36C4×D103D412yes—
37C8×C103—21no—
38C103⋊C8—21no—
39C22×C103C2×D411yescharacteristic
40C2×D103—21no—
41C2×D103—21no—
42C2×D103—22no—
43C2×D103—41no—
44C2×D103—41no—
45C2×D103C22⋊C412yes—
46C4×C103—22no—
47C4×C103—41no—
48C4×C103C22×C411yescharacteristic
49C4×C103C2×D411yescharacteristic
50Dic103—41no—
51Dic103C22⋊C412yes—
52C2×C103C2×C22⋊C411yescharacteristic
53C2×C103#13511yescharacteristic
54C2×C103#13511yescharacteristic
55D103—22no—
56D103—42no—
57C103#41611yescharacteristic, complemented, Sylow
58#416—1031nomaximal, Sylow
59C2×#41—1031no—
60C22×C8—1031no—
61#117—1031no—
62#103—1031no—
63#103D10311yescharacteristic, complemented
64#102—1031no—
65#102—1031no—
66#41—1034no—
67#41—2062no—
68C2×Q8C2×D10311yescharacteristic
69C2×D4—1031no—
70C2×D4—2061no—
71C22×C4—1031no—
72C22×C4—2061no—
73C2×C8—1031no—
74C2×C8—2062no—
75C2×C8C2×D10311yescharacteristic
76C4⋊C4—1031no—
77C4⋊C4C2×D10311yescharacteristic
78C22⋊C4—2061no—
79C42—2061no—
80C23—1031no—
81C23—2061no—
82Q8—21no—
83Q8C4×D10312yes—
84D4—1032no—
85D4—2064no—
86D4—2061no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—1031no—
90C2×C4—1032no—
91C2×C4—1032no—
92C2×C4—2064no—
93C2×C4—2061no—
94C2×C4C22×D10311yescharacteristic
95C8—21no—
96C8—2061no—
97C22—1032no—
98C22—4121no—
99C22—4121no—
100C22—2062no—
101C22—2061no—
102C22—2061no—
103C22D4×D10311yescharacteristic
104C4—22no—
105C4—41no—
106C4—1032no—
107C4—4121no—
108C4C2×C4×D10311yescharacteristic
109C4D4×D10311yescharacteristic
110C2—4122no—
111C2—2062no—
112C2C22⋊C4×D10311yescharacteristic
113C2#1569304211yescharacteristic
114C2#1569304411yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#416
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×C8×D103C2semidirect
3. #15692979C2semidirect
4. #15692945C2semidirect
5. #15692943C2semidirect
6. #15692941C2semidirect
7. #103×C103C2semidirect
9. #13110106C4semidirect
57. C103#416semidirect
63. #103D103semidirect