Finite Group Databasebeta

← C2×#20299435 #28405383

Subgroups — C2×#20299435 #28405383

Order 14464.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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#20299435C2132yesmaximal, direct product factor
2C2×#16813670C215yesmaximal, complemented
3C2×#16813668C2110yesmaximal, complemented
4C22×#14268648C215yesmaximal, complemented
5C2×#41×D113C2110yesmaximal, complemented
6C2×2−1+4×C113C211yesmaximal, characteristic, complemented
7#16813670C22180yescomplemented
8#16813668C221160yescomplemented
9C2×#14268648C22110yescomplemented
10C2×#14268648C22120yescomplemented
11C2×#14268648C22180yescomplemented
12C2×#14268647C22130yescomplemented
13C2×#14268646C22110yescomplemented
14#41×D113C221160yescomplemented
15C2×Q8×D113C22110yescomplemented
16C22×D452C22115yescomplemented
17C2×D4×D113C22130yescomplemented
18C22×C4×D113C22115yescomplemented
192−1+4×C113C22116yescomplemented
20C2×#41×C113C22110yescomplemented
21C22×Q8×C113C2215yescomplemented
22C23×D113C23115yes—
23#14268648C23180yescomplemented
24#14268648C231160yescomplemented
25#14268647C231240yescomplemented
26#14268646C23180yescomplemented
27C2×Dic226C23110yes—
28Q8×D113C23180yescomplemented
29C2×D452C23130yes—
30C2×D452C231120yescomplemented
31C2×C22⋊D113C23120yes—
32D4×D113C231240yescomplemented
33C22×Dic113C2315yes—
34C2×C4×D113C23110yes—
35C2×C4×D113C23130yes—
36C2×C4×D113C231120yescomplemented
37#41×C113C23180yescomplemented
38C2×Q8×C113C23110yes—
39C2×Q8×C113C23140yescomplemented
40C2×D4×C113C23110yes—
41C22×C4×C113C23115yes—
42C23×C113C2415yes—
43C22×D113—430no—
44C22×D113C24110yes—
45C22×D113C24160yes—
46Q8×C113C24140yes—
47D4×C113C24140yes—
48C2×C4×C113C24110yes—
49C2×C4×C113C24160yes—
50C22⋊D113C24180yes—
51C2×Dic113C2411yescharacteristic
52C2×Dic113C2415yes—
53C2×Dic113C24120yes—
54D452C241120yes—
55C4×D113C24140yes—
56C4×D113C241120yes—
57Dic226C24140yes—
58C22×C113—210no—
59C22×C113C25110yes—
60C22×C113C2511yescharacteristic
61C2×D113—220no—
62C2×D113—460no—
63C2×D113C25120yes—
64C4×C113C25120yes—
65Dic113C25110yes—
66Dic113C2512yes—
67C2×C113—210no—
68C2×C113#58512yescomplemented
69C2×C113C2611yescharacteristic
70D113—220no—
71C2×#585—1131nomaximal, Sylow
72C113C2×#58511yescharacteristic, complemented, Sylow
73#585—11332no—
74C2×2−1+4—1135no—
75C2×2−1+4D11311yescharacteristic, complemented
76C2×H(5,𝔽2)—11310no—
77C22×#41—11310no—
78C22×#41—1135no—
792−1+4—11380no—
802−1+4C2×D113116yescomplemented
81H(5,𝔽2)—113160no—
82C2×#41—113160no—
83C2×#41—11310no—
84C2×#41—11320no—
85C2×#41—11380no—
86C2×#41—11310no—
87C2×#41—11330no—
88C2×#41C2×D113110yescomplemented
89C22×Q8—11310no—
90C22×Q8C2×D11315yescomplemented
91C22×D4—11330no—
92C22×D4—11315no—
93C23×C4—11315no—
94C24—11315no—
95#41—11380no—
96#41—113160no—
97#41—11380no—
98#41—113240no—
99#41C22×D113180yescomplemented
100C2×Q8—11380no—
101C2×Q8—11310no—
102C2×Q8C22×D113110yes—
103C2×Q8C22×D113140yescomplemented
104C2×D4—11320no—
105C2×D4—113240no—
106C2×D4—11330no—
107C2×D4—113120no—
108C2×D4C22×D113110yes—
109C22×C4—1135no—
110C22×C4—11310no—
111C22×C4—11330no—
112C22×C4—113120no—
113C22×C4C22×D113115yes—
114C23—11360no—
115C23—11310no—
116C23—45230no—
117C23C23×D11315yes—
118Q8—11340no—
119Q8C23×D113140yes—
120D4—11380no—
121D4—113120no—
122D4C23×D113140yes—
123C2×C4—11320no—
124C2×C4—1131no—
125C2×C4—1135no—
126C2×C4—11340no—
127C2×C4—113120no—
128C2×C4C23×D113160yes—
129C2×C4C23×D113110yes—
130C22—210no—
131C22—11320no—
132C22—45260no—
133C22—22620no—
134C22C24×D113110yes—
135C22C24×D11311yescharacteristic
136C4—1132no—
137C4—11310no—
138C4C24×D113120yes—
139C2—210no—
140C2—22620no—
141C2#2029943512yesdirect product factor
142C2C25×D11311yescharacteristic
subgroupG/H
centerC22C24×D113
commutator, cosocleC2×C113C26
FrattiniC2C25×D113
FittingC2×2−1+4×C113C2
socleC22×C113C25
hypercenterC2×2−1+4D113
hypocenterC113C2×#585
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20299435C2direct (N × H)
2. C2×#16813670C2semidirect
3. C2×#16813668C2semidirect
4. C22×#14268648C2semidirect
5. C2×#41×D113C2semidirect
6. C2×2−1+4×C113C2semidirect
7. #16813670C22semidirect
8. #16813668C22semidirect
9. C2×#14268648C22semidirect
10. C2×#14268648C22semidirect
11. C2×#14268648C22semidirect
12. C2×#14268647C22semidirect
13. C2×#14268646C22semidirect
14. #41×D113C22semidirect
15. C2×Q8×D113C22semidirect
16. C22×D452C22semidirect
17. C2×D4×D113C22semidirect
18. C22×C4×D113C22semidirect
19. 2−1+4×C113C22semidirect
20. C2×#41×C113C22semidirect
21. C22×Q8×C113C22semidirect
23. #14268648C23semidirect
24. #14268648C23semidirect
25. #14268647C23semidirect
26. #14268646C23semidirect
28. Q8×D113C23semidirect
30. C2×D452C23semidirect
32. D4×D113C23semidirect
36. C2×C4×D113C23semidirect
37. #41×C113C23semidirect
39. C2×Q8×C113C23semidirect
68. C2×C113#585semidirect
72. C113C2×#585semidirect
75. C2×2−1+4D113semidirect
80. 2−1+4C2×D113semidirect
88. C2×#41C2×D113semidirect
90. C22×Q8C2×D113semidirect
99. #41C22×D113semidirect
103. C2×Q8C22×D113semidirect
141. C2#20299435direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202994352
C2×#168136702
C2×#168136682
C22×#142686482
C2×#41×D1132
C2×2−1+4×C1132
C2×#585113