Finite Group Databasebeta

← #23749643

Subgroups — #23749643

Order 9536.

154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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×#14558736C211yesmaximal, characteristic
2C2×#14558720C211yesmaximal, characteristic, complemented
3#18011839C214yesmaximal, complemented
4#117×C149C211yesmaximal, characteristic, complemented
5#14558736—21no—
6#14558736—21no—
7#14558736C412yescomplemented
8#14558736C2212yes—
9C2×Dic298C411yescharacteristic, complemented
10C2×D596C411yescharacteristic, complemented
11C2×C22⋊D149—21no—
12C2×C4×D149—21no—
13#14558720—21no—
14#14558720C2212yescomplemented
15C2×#11924746—21no—
16C22×C4×C149C2211yescharacteristic
17C4⋊C4×C149—21no—
18C22⋊C4×C149—21no—
19C42×C149C2212yescomplemented
20C22×D149—21no—
21Dic298—21no—
22Dic298C2×C412yes—
23D596—21no—
24D596C2×C412yes—
25C22⋊D149—22no—
26C22⋊D149—22no—
27C2×Dic149—21no—
28C4×D149—22no—
29C4×D149—22no—
30#11924746—22no—
31C23×C149D411yescharacteristic
32C2×C4×C149—22no—
33C2×C4×C149C2×C411yescharacteristic
34C2×C4×C149C2×C411yescharacteristic
35C2×C4×C149D411yescharacteristic
36C2×C4×C149D411yescharacteristic
37C2×C4×C149D411yescharacteristic
38C2×C4×C149C2311yescharacteristic
39C22×C149—41no—
40C22×C149C22⋊C411yescharacteristic
41C22×C149C22⋊C411yescharacteristic
42C22×C149C2×D411yescharacteristic
43C2×D149—22no—
44C2×D149—42no—
45C4×C149—42no—
46C4×C149C22⋊C411yescharacteristic
47C4×C149C22⋊C411yescharacteristic
48C4×C149C22×C411yescharacteristic
49C4×C149C2×D411yescharacteristic
50Dic149—22no—
51C2×C149—21no—
52C2×C149—21no—
53C2×C149—21no—
54C2×C149C2×C22⋊C411yescharacteristic
55D149—42no—
56C149#42111yescharacteristic, complemented, Sylow
57#421—1491nomaximal, Sylow
58C2×#41—1491no—
59C2×M16—1491no—
60#117D14911yescharacteristic, complemented
61#104—1494no—
62#41—2981no—
63#41—2981no—
64#41—1492no—
65#41—1492no—
66C2×Q8—1491no—
67C2×D4—2981no—
68C2×D4—1491no—
69C22×C4—2981no—
70C22×C4C2×D14911yescharacteristic
71M16—2981no—
72M16—1492no—
73C2×C8—2981no—
74C4⋊C4—21no—
75C22⋊C4—21no—
76C42C2×D14912yescomplemented
77C23—2981no—
78C23C22⋊D14911yescharacteristic
79Q8—2981no—
80Q8—1492no—
81D4—2982no—
82D4—2982no—
83D4—2981no—
84D4—1492no—
85C2×C4—22no—
86C2×C4—2981no—
87C2×C4—2982no—
88C2×C4—2982no—
89C2×C4C4×D14911yescharacteristic
90C2×C4C4×D14911yescharacteristic
91C2×C4C22⋊D14911yescharacteristic
92C2×C4D59611yescharacteristic
93C2×C4D59611yescharacteristic
94C2×C4C22×D14911yescharacteristic
95C8—2982no—
96C22—41no—
97C22—2982no—
98C22—5962no—
99C22#1455871311yescharacteristic
100C22#1455871311yescharacteristic
101C22C2×C22⋊D14911yescharacteristic
102C4—42no—
103C4—2982no—
104C4#1455871311yescharacteristic
105C4#1455871311yescharacteristic
106C4C2×C4×D14911yescharacteristic
107C4C2×D59611yescharacteristic
108C2—21no—
109C2—21no—
110C2—21no—
111C2—5962no—
112C2C2×#1455871311yescharacteristic
subgroupG/H
centerC4C2×D596
commutatorC4×C149C22×C4
FrattiniC2×C4C22×D149
Fitting#117×C149C2
socleC2×C149C2×C22⋊C4
prime radicalC2×#14558736C2
cosocleC2×C4×C149C23
hypercenter#117D149
hypocenterC149#421
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#14558720C2semidirect
3. #18011839C2semidirect
4. #117×C149C2semidirect
7. #14558736C4semidirect
9. C2×Dic298C4semidirect
10. C2×D596C4semidirect
14. #14558720C22semidirect
19. C42×C149C22semidirect
56. C149#421semidirect
60. #117D149semidirect
76. C42C2×D149semidirect