Finite Group Databasebeta

← #23750615

Subgroups — #23750615

Order 9536.

158 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 50 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×D149⋊C8C211yesmaximal, characteristic, complemented
2#18011990C211yesmaximal, characteristic, complemented
3#18011974C212yesmaximal, complemented
4#18011973C212yesmaximal, complemented
5#41×D149C211yesmaximal, characteristic
6D149⋊C8—21no—
7D149⋊C8C2212yes—
8C2×#11924753—21no—
9C4⋊#10597010C2212yes—
10C22⋊#10597010—21no—
11C4×#10597010—21no—
12#14558737C411yescharacteristic, complemented
13#14558736—21no—
14#14558736C411yescharacteristic, complemented
15#14558735—21no—
16#14558735C411yescharacteristic, complemented
17Q8×D149C2211yescharacteristic
18D4×D149—21no—
19D4×D149C2211yescharacteristic
20C2×C4×D149—21no—
21C2×C4×D149C2211yescharacteristic
22#41×C149C411yescharacteristic, complemented
23C2×#10597010—22no—
24#11924753—22no—
25C22×D149—21no—
26C22×D149D411yescharacteristic
27Dic298—21no—
28Dic298C2×C411yescharacteristic
29D596—21no—
30D596C2×C411yescharacteristic
31C22⋊D149—21no—
32C22⋊D149—21no—
33C22⋊D149—21no—
34C2×Dic149—21no—
35C2×Dic149D411yescharacteristic
36C4×D149—21no—
37C4×D149—21no—
38C4×D149—21no—
39C4×D149C2×C411yescharacteristic
40C4×D149D411yescharacteristic
41C4×D149D411yescharacteristic
42C4×D149C2311yescharacteristic
43Q8×C149C2×C411yescharacteristic
44D4×C149—21no—
45D4×C149C2×C411yescharacteristic
46C2×C4×C149—21no—
47C2×C4×C149C2×C411yescharacteristic
48C22×C149—21no—
49C22×C149C22⋊C411yescharacteristic
50C2×D149—22no—
51C2×D149—21no—
52C2×D149—42no—
53C2×D149C22⋊C411yescharacteristic
54C2×D149C2×D411yescharacteristic
55#10597010—42no—
56C4×C149—21no—
57C4×C149C22⋊C411yescharacteristic
58C4×C149C22×C411yescharacteristic
59Dic149—21no—
60Dic149C22⋊C411yescharacteristic
61Dic149C2×D411yescharacteristic
62C2×C149—21no—
63C2×C149—41no—
64C2×C149C2×C22⋊C411yescharacteristic
65D149—21no—
66D149—41no—
67D149#13512yes—
68C149#41611yescharacteristic, complemented, Sylow
69#416—1491nomaximal, Sylow
70C2×#41—1491no—
71C22×C8—1491no—
72#117—1491no—
73#103—1492no—
74#102—1492no—
75#41—2981no—
76#41—2981no—
77#41—1491no—
78#41—1491no—
79#41—1491no—
80#41#1059701011yescharacteristic, complemented
81C2×Q8—1491no—
82C2×D4—2981no—
83C2×D4—1491no—
84C22×C4—2981no—
85C22×C4—1491no—
86C2×C8—2981no—
87C2×C8—2981no—
88C2×C8—1492no—
89C4⋊C4—1492no—
90C22⋊C4—2981no—
91C42—2981no—
92C23—2981no—
93C23—1491no—
94Q8—2981no—
95Q8—1491no—
96Q8C2×#1059701011yescharacteristic
97D4—21no—
98D4—2981no—
99D4—2981no—
100D4—2981no—
101D4—2981no—
102D4—1491no—
103D4C2×#1059701011yescharacteristic
104C2×C4—21no—
105C2×C4—2981no—
106C2×C4—2981no—
107C2×C4—2981no—
108C2×C4—2981no—
109C2×C4—2982no—
110C2×C4—1491no—
111C2×C4—1491no—
112C2×C4—1491no—
113C2×C4—1491no—
114C2×C4—1491no—
115C2×C4C2×#1059701011yescharacteristic
116C8—2982no—
117C22—21no—
118C22—2982no—
119C22—2981no—
120C22—5962no—
121C22—1491no—
122C22—1491no—
123C22C22⋊#1059701011yescharacteristic
124C4—21no—
125C4—2981no—
126C4—5962no—
127C4—1491no—
128C4—1491no—
129C4C22⋊#1059701011yescharacteristic
130C4C22×#1059701011yescharacteristic
131C2—21no—
132C2—41no—
133C2—2981no—
134C2—5961no—
135C2—1492no—
136C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC4C22⋊#10597010
commutatorC4×C149C22×C4
FrattiniC4C22×#10597010
Fitting#41×C149C4
socleC2×C149C2×C22⋊C4
prime radical#41×D149C2
cosocleC4×D149C23
hypercenter#41#10597010
hypocenterC149#416
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C2×D149⋊C8C2semidirect
2. #18011990C2semidirect
3. #18011974C2semidirect
4. #18011973C2semidirect
12. #14558737C4semidirect
14. #14558736C4semidirect
16. #14558735C4semidirect
22. #41×C149C4semidirect
68. C149#416semidirect
80. #41#10597010semidirect