Finite Group Databasebeta

← C2×#18011973 #23750613

Subgroups — C2×#18011973 #23750613

Order 9536.

202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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
2C2×C4⋊#10597010C211yesmaximal, characteristic, complemented
3#18011973C214yesmaximal, direct product factor
4C2×D4×D149C211yesmaximal, characteristic
5C22×#10597010—21no—
6D149⋊C8—21no—
7D149⋊C8C2212yescomplemented
8C2×#11924753—21no—
9C4⋊#10597010—21no—
10C4⋊#10597010C2212yescomplemented
11C23×D149—21no—
12C2×D596C411yescharacteristic, complemented
13C2×C22⋊D149—21no—
14D4×D149—21no—
15D4×D149—21no—
16D4×D149C412yescomplemented
17D4×D149C2212yes—
18C2×C4×D149C2211yescharacteristic
19C2×D4×C149C411yescharacteristic, complemented
20C2×#10597010—22no—
21C2×#10597010—42no—
22#11924753—22no—
23C22×D149—21no—
24C22×D149—22no—
25C22×D149—22no—
26C22×D149—42no—
27C22×D149—42no—
28C22×D149D411yescharacteristic
29D596—21no—
30D596C2×C412yescomplemented
31C22⋊D149—22no—
32C22⋊D149—22no—
33C2×Dic149D411yescharacteristic
34C4×D149C2×C411yescharacteristic
35C4×D149D411yescharacteristic
36C4×D149D411yescharacteristic
37C4×D149C2311yescharacteristic
38C23×C149—21no—
39D4×C149—21no—
40D4×C149C2×C412yescomplemented
41C2×C4×C149C2×C411yescharacteristic
42C22×C149—22no—
43C22×C149—42no—
44C22×C149C22⋊C411yescharacteristic
45C2×D149—22no—
46C2×D149—42no—
47C2×D149—44no—
48C2×D149—42no—
49C2×D149—42no—
50C2×D149C22⋊C411yescharacteristic
51C2×D149D812yes—
52C2×D149SD1612yes—
53C2×D149C2×D411yescharacteristic
54#10597010—42no—
55C4×C149C22⋊C411yescharacteristic
56C4×C149C22×C411yescharacteristic
57Dic149C22⋊C411yescharacteristic
58Dic149C2×D411yescharacteristic
59C2×C149—42no—
60C2×C149#10212yescomplemented
61C2×C149C2×C22⋊C411yescharacteristic
62D149—42no—
63D149#10212yescomplemented
64D149C2×D811yescharacteristic
65D149C2×SD1611yescharacteristic
66C149C2×#10211yescharacteristic, complemented, Sylow
67C2×#102—1491nomaximal, Sylow
68C22×D4—1491no—
69C22×C8—1491no—
70C2×C4⋊C4—1491no—
71#102—1494no—
72C24—2981no—
73C2×D4—2981no—
74C2×D4—2981no—
75C2×D4—2981no—
76C2×D4—1492no—
77C2×D4—1492no—
78C2×D4—1491no—
79C2×D4#1059701011yescharacteristic, complemented
80C22×C4—2981no—
81C22×C4—1491no—
82C2×C8—2981no—
83C2×C8—2981no—
84C2×C8—1492no—
85C4⋊C4—2981no—
86C4⋊C4—1492no—
87C23—21no—
88C23—2982no—
89C23—2982no—
90C23—2981no—
91C23—5962no—
92C23—5962no—
93C23—1491no—
94D4—21no—
95D4—2982no—
96D4—2982no—
97D4—2981no—
98D4—1492no—
99D4C2×#1059701012yescomplemented
100C2×C4—2982no—
101C2×C4—5962no—
102C2×C4—1491no—
103C2×C4—1491no—
104C2×C4—1491no—
105C2×C4—1491no—
106C2×C4—1491no—
107C2×C4C2×#1059701011yescharacteristic
108C8—2982no—
109C22—22no—
110C22—42no—
111C22—2982no—
112C22—5962no—
113C22—5964no—
114C22—5962no—
115C22—5962no—
116C22—1492no—
117C22—1492no—
118C22—1491no—
119C22—1491no—
120C22C22⋊#1059701011yescharacteristic
121C4—5962no—
122C4—1491no—
123C4—1491no—
124C4C22⋊#1059701011yescharacteristic
125C4C22×#1059701011yescharacteristic
126C2—42no—
127C2—5962no—
128C2—1491no—
129C2—1492no—
130C2—1491no—
131C2#1801197312yesdirect product factor
132C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC22C22⋊#10597010
commutatorC4×C149C22×C4
FrattiniC4C22×#10597010
FittingC2×D4×C149C4
socleC22×C149C22⋊C4
prime radicalC2×D4×D149C2
cosocleC4×D149C23
hypercenterC2×D4#10597010
hypocenterC149C2×#102
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D149⋊C8C2semidirect
2. C2×C4⋊#10597010C2semidirect
3. #18011973C2direct (N × H)
7. D149⋊C8C22semidirect
10. C4⋊#10597010C22semidirect
12. C2×D596C4semidirect
16. D4×D149C4semidirect
19. C2×D4×C149C4semidirect
30. D596C2×C4semidirect
40. D4×C149C2×C4semidirect
60. C2×C149#102semidirect
63. D149#102semidirect
66. C149C2×#102semidirect
79. C2×D4#10597010semidirect
99. D4C2×#10597010semidirect
131. C2#18011973direct (N × H)