Finite Group Databasebeta

← #20267957

Subgroups — #20267957

Order 6592.

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

normal subgroups only

This group has 168 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#15693067C211yesmaximal, characteristic, complemented
2#15693047C211yesmaximal, characteristic, complemented
3#15693017C211yesmaximal, characteristic, complemented
4#15692948C211yesmaximal, characteristic, complemented
5#15692947C211yesmaximal, characteristic, complemented
6#15692937C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C103C211yesmaximal, characteristic, complemented
8#13110106—21no—
9#13110105—21no—
10#13110105C2211yescharacteristic
11C2×D412—21no—
12C2×D412C2211yescharacteristic
13C2×C22⋊D103—22no—
14D4×D103—22no—
15D4×D103—21no—
16#13110093—21no—
17#13110090—21no—
18#13110089C2211yescharacteristic, complemented
19C4×Dic103C2211yescharacteristic, complemented
20#41×C103C2211yescharacteristic
21C2×D4×C103C2211yescharacteristic, complemented
22SD16×C103—21no—
23D8×C103—21no—
24M16×C103C2211yescharacteristic, complemented
25C23×C103—21no—
26C22×D103—22no—
27C22×D103D412yes—
28Q8×C103D411yescharacteristic, complemented
29D4×C103—21no—
30D4×C103—21no—
31D4×C103—21no—
32D4×C103D411yescharacteristic, complemented
33C2×C4×C103—21no—
34C2×C4×C103C2311yescharacteristic
35C22⋊D103—22no—
36C22⋊D103—21no—
37C22⋊D103—44no—
38C2×Dic103—21no—
39D412—22no—
40D412—21no—
41D412—21no—
42D412D411yescharacteristic, complemented
43C4×D103—22no—
44C4×D103—21no—
45Dic206D411yescharacteristic, complemented
46C8×C103—21no—
47C103⋊C8—21no—
48C22×C103—21no—
49C22×C103—42no—
50C22×C103—41no—
51C22×C103C2×D411yescharacteristic
52C2×D103—22no—
53C2×D103—21no—
54C2×D103—42no—
55C2×D103—82no—
56C4×C103—21no—
57C4×C103C2×D411yescharacteristic
58C4×C103C2×D411yescharacteristic
59Dic103—22no—
60Dic103—21no—
61C2×C103—21no—
62C2×C103—41no—
63C2×C103—81no—
64C2×C103#12011yescharacteristic
65D103—42no—
66D103—41no—
67C103#45311yescharacteristic, complemented, Sylow
68#453—1031nomaximal, Sylow
69H(5,𝔽2)—1031no—
70AGL(1,ℤ/8)—1031no—
71AGL(1,ℤ/8)D10311yescharacteristic, complemented
72#127—1031no—
73#104—1031no—
74#104—1031no—
75#100—1031no—
76#41—1031no—
77#41—2061no—
78#41—2061no—
79#41C2×D10311yescharacteristic
80C2×D4—1031no—
81C2×D4—2061no—
82C2×D4—2062no—
83C2×D4—2062no—
84C2×D4—2061no—
85C2×D4C2×D10311yescharacteristic, complemented
86SD16—21no—
87SD16—2061no—
88D8—21no—
89D8—2061no—
90M16—1031no—
91M16C2×D10311yescharacteristic, complemented
92C42—1031no—
93C23—21no—
94C23—1032no—
95C23—2062no—
96Q8—1031no—
97Q8C22⋊D10311yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—1031no—
102D4—4124no—
103D4—2062no—
104D4—2062no—
105D4—2061no—
106D4—2061no—
107D4—2061no—
108D4C22⋊D10311yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—2062no—
111C2×C4—2061no—
112C2×C4—2061no—
113C2×C4C22×D10311yescharacteristic
114C8—21no—
115C8—2061no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—8242no—
120C22—4122no—
121C22—2061no—
122C22—2062no—
123C22D4×D10311yescharacteristic
124C4—21no—
125C4—2062no—
126C4—2061no—
127C4D4×D10311yescharacteristic
128C4C2×C22⋊D10311yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—4121no—
133C2—4122no—
134C2#1569298911yescharacteristic
subgroupG/H
centerC2#15692989
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingAGL(1,ℤ/8)×C103C2
socleC2×C103#120
hypercenterAGL(1,ℤ/8)D103
hypocenterC103#453
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15693067C2semidirect
2. #15693047C2semidirect
3. #15693017C2semidirect
4. #15692948C2semidirect
5. #15692947C2semidirect
6. #15692937C2semidirect
7. AGL(1,ℤ/8)×C103C2semidirect
18. #13110089C22semidirect
19. C4×Dic103C22semidirect
21. C2×D4×C103C22semidirect
24. M16×C103C22semidirect
28. Q8×C103D4semidirect
32. D4×C103D4semidirect
42. D412D4semidirect
45. Dic206D4semidirect
67. C103#453semidirect
71. AGL(1,ℤ/8)D103semidirect
85. C2×D4C2×D103semidirect
91. M16C2×D103semidirect
97. Q8C22⋊D103semidirect
108. D4C22⋊D103semidirect