Finite Group Databasebeta

← #20267951

Subgroups — #20267951

Order 6592.

152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13110105C211yesmaximal, characteristic
2C2×#13110095C211yesmaximal, characteristic, complemented
3C2×#13110092C211yesmaximal, characteristic, complemented
4#15692944C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7C22⋊Q8×C103C211yesmaximal, characteristic, complemented
8#13110105—22no—
9#13110105—22no—
10C2×Dic206C2211yescharacteristic
11C2×D412C2211yescharacteristic
12C2×C22⋊D103—21no—
13C2×C4×D103—21no—
14#13110095—22no—
15#13110092—22no—
16C2×C103⋊C8C2211yescharacteristic
17C2×C103⋊C8C2211yescharacteristic
18C2×Q8×C103C2211yescharacteristic
19C22×C4×C103C2211yescharacteristic
20C4⋊C4×C103—21no—
21C4⋊C4×C103C2211yescharacteristic
22C22⋊C4×C103—21no—
23C23×C103D411yescharacteristic
24C22×D103—21no—
25Q8×C103—21no—
26Q8×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103—21no—
30C2×C4×C103—21no—
31C2×C4×C103D411yescharacteristic
32C2×C4×C103C2311yescharacteristic
33C22⋊D103—24no—
34C2×Dic103—21no—
35D412—21no—
36D412D412yes—
37C4×D103—24no—
38Dic206—21no—
39Dic206D412yes—
40C103⋊C8—21no—
41C103⋊C8—21no—
42C22×C103—21no—
43C22×C103—21no—
44C22×C103—21no—
45C22×C103C2×D411yescharacteristic
46C2×D103—22no—
47C2×D103—41no—
48C2×D103—41no—
49C4×C103—21no—
50C4×C103—41no—
51C4×C103—41no—
52C4×C103C2×D411yescharacteristic
53C4×C103C2×D411yescharacteristic
54Dic103—22no—
55C2×C103—41no—
56C2×C103#12011yescharacteristic
57C2×C103#13511yescharacteristic
58C2×C103#13711yescharacteristic
59D103—42no—
60C103#45211yescharacteristic, complemented, Sylow
61#452—1031nomaximal, Sylow
62C2×#41—1031no—
63C2×Q16—1031no—
64C2×SD16—1031no—
65C22⋊Q8D10311yescharacteristic, complemented
66#103—1031no—
67#102—1031no—
68C22⋊C8—1031no—
69#41—2062no—
70#41—2062no—
71C2×Q8—1031no—
72C2×Q8C2×D10311yescharacteristic
73C2×D4—1031no—
74C2×D4—2061no—
75C22×C4—2061no—
76C22×C4C2×D10311yescharacteristic
77Q16—2062no—
78SD16—2062no—
79C2×C8—1031no—
80C2×C8—1031no—
81C4⋊C4—21no—
82C4⋊C4C2×D10311yescharacteristic
83C22⋊C4—21no—
84C23—2061no—
85C23C22⋊D10311yescharacteristic
86Q8—21no—
87Q8—21no—
88Q8—1032no—
89Q8—2061no—
90D4—1032no—
91D4—2064no—
92D4—2061no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—2064no—
98C2×C4—2061no—
99C2×C4C22⋊D10311yescharacteristic
100C2×C4C22×D10311yescharacteristic
101C8—2061no—
102C8—2061no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—4121no—
107C22—4121no—
108C22—2062no—
109C22C2×C22⋊D10311yescharacteristic
110C4—21no—
111C4—41no—
112C4—41no—
113C4—2062no—
114C4D4×D10311yescharacteristic
115C4D4×D10311yescharacteristic
116C2—41no—
117C2—4122no—
118C2#1569298911yescharacteristic
119C2#1569304111yescharacteristic
120C2#1569305211yescharacteristic
subgroupG/H
centerC22C2×C22⋊D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC22⋊Q8×C103C2
socleC22×C103C2×D4
hypercenterC22⋊Q8D103
hypocenterC103#452
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13110095C2semidirect
3. C2×#13110092C2semidirect
4. #15692944C2semidirect
5. #15692941C2semidirect
6. C22⋊(C103⋊C8)C2semidirect
7. C22⋊Q8×C103C2semidirect
60. C103#452semidirect
65. C22⋊Q8D103semidirect