Finite Group Databasebeta

← #23750616

Subgroups — #23750616

Order 9536.

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

normal subgroups only

This group has 162 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
1D149⋊M16C211yesmaximal, characteristic, complemented
2C2×C4⋊#10597010C211yesmaximal, characteristic, complemented
3#18011974C212yesmaximal, complemented
4#18011973C212yesmaximal, complemented
5#41×D149C211yesmaximal, characteristic
6C22×#10597010—21no—
7#14558746—21no—
8#14558745—21no—
9D149⋊C8C2212yes—
10C4⋊#10597010—21no—
11C4⋊#10597010C2212yes—
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—
24C2×#10597010—42no—
25#11924753—22no—
26C22×D149—21no—
27C22×D149D411yescharacteristic
28Dic298—21no—
29Dic298C2×C411yescharacteristic, complemented
30D596—21no—
31D596C2×C411yescharacteristic, complemented
32C22⋊D149—21no—
33C22⋊D149—21no—
34C22⋊D149—21no—
35C2×Dic149—21no—
36C2×Dic149D411yescharacteristic
37C4×D149—21no—
38C4×D149—21no—
39C4×D149—21no—
40C4×D149C2×C411yescharacteristic
41C4×D149D411yescharacteristic
42C4×D149D411yescharacteristic
43C4×D149C2311yescharacteristic
44Q8×C149C2×C411yescharacteristic, complemented
45D4×C149—21no—
46D4×C149C2×C411yescharacteristic, complemented
47C2×C4×C149—21no—
48C2×C4×C149C2×C411yescharacteristic
49C22×C149—21no—
50C22×C149C22⋊C411yescharacteristic
51C2×D149—21no—
52C2×D149—21no—
53C2×D149—21no—
54C2×D149—41no—
55C2×D149—41no—
56C2×D149C22⋊C411yescharacteristic
57C2×D149C2×D411yescharacteristic
58#10597010—42no—
59C4×C149—21no—
60C4×C149C22⋊C411yescharacteristic
61C4×C149C22×C411yescharacteristic
62Dic149—21no—
63Dic149C22⋊C411yescharacteristic
64Dic149C2×D411yescharacteristic
65C2×C149—21no—
66C2×C149—41no—
67C2×C149C2×C22⋊C411yescharacteristic
68D149—21no—
69D149—41no—
70D149AGL(1,ℤ/8)11yescharacteristic
71D149#13711yescharacteristic
72C149#41711yescharacteristic, complemented, Sylow
73#417—1491nomaximal, Sylow
74C2×#41—1491no—
75C2×M16—1491no—
76C2×C4⋊C4—1491no—
77#103—1492no—
78#102—1492no—
79#41—2981no—
80#41—2981no—
81#41—1491no—
82#41—1491no—
83#41—1491no—
84#41#1059701011yescharacteristic, complemented
85C2×Q8—1491no—
86C2×D4—2981no—
87C2×D4—1491no—
88C22×C4—2981no—
89C22×C4—2981no—
90C22×C4—1491no—
91M16—2981no—
92M16—2981no—
93C2×C8—1492no—
94C4⋊C4—2981no—
95C4⋊C4—1492no—
96C23—2981no—
97C23—1491no—
98Q8—2981no—
99Q8—1491no—
100Q8C2×#1059701011yescharacteristic, complemented
101D4—21no—
102D4—2981no—
103D4—2981no—
104D4—2981no—
105D4—2981no—
106D4—1491no—
107D4C2×#1059701011yescharacteristic, complemented
108C2×C4—21no—
109C2×C4—2981no—
110C2×C4—2981no—
111C2×C4—2981no—
112C2×C4—2981no—
113C2×C4—2982no—
114C2×C4—5962no—
115C2×C4—1491no—
116C2×C4—1491no—
117C2×C4—1491no—
118C2×C4—1491no—
119C2×C4—1491no—
120C2×C4C2×#1059701011yescharacteristic
121C8—2982no—
122C22—21no—
123C22—2981no—
124C22—2981no—
125C22—2981no—
126C22—5961no—
127C22—5961no—
128C22—1491no—
129C22—1491no—
130C22C22⋊#1059701011yescharacteristic
131C4—21no—
132C4—2981no—
133C4—5962no—
134C4—1491no—
135C4—1491no—
136C4C22⋊#1059701011yescharacteristic
137C4C22×#1059701011yescharacteristic
138C2—21no—
139C2—41no—
140C2—2981no—
141C2—5961no—
142C2—1491no—
143C2—1491no—
144C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10597010
commutatorC4×C149C22×C4
FrattiniC4C22×#10597010
Fitting#41×C149C4
socleC2×C149C2×C22⋊C4
prime radical#41×D149C2
cosocleC4×D149C23
hypercenter#41#10597010
hypocenterC149#417
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. D149⋊M16C2semidirect
2. C2×C4⋊#10597010C2semidirect
3. #18011974C2semidirect
4. #18011973C2semidirect
12. #14558737C4semidirect
14. #14558736C4semidirect
16. #14558735C4semidirect
22. #41×C149C4semidirect
29. Dic298C2×C4semidirect
31. D596C2×C4semidirect
44. Q8×C149C2×C4semidirect
46. D4×C149C2×C4semidirect
72. C149#417semidirect
84. #41#10597010semidirect
100. Q8C2×#10597010semidirect
107. D4C2×#10597010semidirect