Finite Group Databasebeta

← #20260901

Subgroups — #20260901

Order 6208.

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#15690856C211yesmaximal, characteristic, complemented
2#15690836C211yesmaximal, characteristic, complemented
3#15690806C211yesmaximal, characteristic, complemented
4#15690737C211yesmaximal, characteristic, complemented
5#15690736C211yesmaximal, characteristic, complemented
6#15690726C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C97C211yesmaximal, characteristic, complemented
8#13095512—21no—
9#13095511—21no—
10#13095511C2211yescharacteristic
11C2×D388—21no—
12C2×D388C2211yescharacteristic
13C2×C22⋊D97—22no—
14D4×D97—22no—
15D4×D97—21no—
16#13095499—21no—
17#13095496—21no—
18#13095495C2211yescharacteristic, complemented
19C4×Dic97C2211yescharacteristic, complemented
20#41×C97C2211yescharacteristic
21C2×D4×C97C2211yescharacteristic, complemented
22SD16×C97—21no—
23D8×C97—21no—
24M16×C97C2211yescharacteristic, complemented
25C23×C97—21no—
26C22×D97—22no—
27C22×D97D412yes—
28Q8×C97D411yescharacteristic, complemented
29D4×C97—21no—
30D4×C97—21no—
31D4×C97—21no—
32D4×C97D411yescharacteristic, complemented
33C2×C4×C97—21no—
34C2×C4×C97C2311yescharacteristic
35C22⋊D97—22no—
36C22⋊D97—21no—
37C22⋊D97—44no—
38C2×Dic97—21no—
39D388—22no—
40D388—21no—
41D388—21no—
42D388D411yescharacteristic, complemented
43C4×D97—22no—
44C4×D97—21no—
45Dic194D411yescharacteristic, complemented
46C8×C97—21no—
47#11715895—21no—
48C22×C97—21no—
49C22×C97—42no—
50C22×C97—41no—
51C22×C97C2×D411yescharacteristic
52C2×D97—22no—
53C2×D97—21no—
54C2×D97—42no—
55C2×D97—82no—
56C4×C97—21no—
57C4×C97C2×D411yescharacteristic
58C4×C97C2×D411yescharacteristic
59Dic97—22no—
60Dic97—21no—
61C2×C97—21no—
62C2×C97—41no—
63C2×C97—81no—
64C2×C97#12011yescharacteristic
65D97—42no—
66D97—41no—
67C97#45311yescharacteristic, complemented, Sylow
68#453—971nomaximal, Sylow
69H(5,𝔽2)—971no—
70AGL(1,ℤ/8)—971no—
71AGL(1,ℤ/8)D9711yescharacteristic, complemented
72#127—971no—
73#104—971no—
74#104—971no—
75#100—971no—
76#41—971no—
77#41—1941no—
78#41—1941no—
79#41C2×D9711yescharacteristic
80C2×D4—971no—
81C2×D4—1941no—
82C2×D4—1942no—
83C2×D4—1942no—
84C2×D4—1941no—
85C2×D4C2×D9711yescharacteristic, complemented
86SD16—21no—
87SD16—1941no—
88D8—21no—
89D8—1941no—
90M16—971no—
91M16C2×D9711yescharacteristic, complemented
92C42—971no—
93C23—21no—
94C23—972no—
95C23—1942no—
96Q8—971no—
97Q8C22⋊D9711yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—971no—
102D4—3884no—
103D4—1942no—
104D4—1942no—
105D4—1941no—
106D4—1941no—
107D4—1941no—
108D4C22⋊D9711yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—1942no—
111C2×C4—1941no—
112C2×C4—1941no—
113C2×C4C22×D9711yescharacteristic
114C8—21no—
115C8—1941no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—7762no—
120C22—3882no—
121C22—1941no—
122C22—1942no—
123C22D4×D9711yescharacteristic
124C4—21no—
125C4—1942no—
126C4—1941no—
127C4D4×D9711yescharacteristic
128C4C2×C22⋊D9711yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—3881no—
133C2—3882no—
134C2#1569077811yescharacteristic
subgroupG/H
centerC2#15690778
commutatorC2×C4×C97C23
FrattiniC2×C4C22×D97
FittingAGL(1,ℤ/8)×C97C2
socleC2×C97#120
hypercenterAGL(1,ℤ/8)D97
hypocenterC97#453
LCSG ▷ C2×C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15690856C2semidirect
2. #15690836C2semidirect
3. #15690806C2semidirect
4. #15690737C2semidirect
5. #15690736C2semidirect
6. #15690726C2semidirect
7. AGL(1,ℤ/8)×C97C2semidirect
18. #13095495C22semidirect
19. C4×Dic97C22semidirect
21. C2×D4×C97C22semidirect
24. M16×C97C22semidirect
28. Q8×C97D4semidirect
32. D4×C97D4semidirect
42. D388D4semidirect
45. Dic194D4semidirect
67. C97#453semidirect
71. AGL(1,ℤ/8)D97semidirect
85. C2×D4C2×D97semidirect
91. M16C2×D97semidirect
97. Q8C22⋊D97semidirect
108. D4C22⋊D97semidirect