Finite Group Databasebeta

← C2×#20299341 #28404695

Subgroups — C2×#20299341 #28404695

Order 14464.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#20299341C2116yesmaximal, direct product factor
2C2×#16813609C213yesmaximal, complemented
3C2×#16813608C216yesmaximal, complemented
4C2×#16813591C212yesmaximal, complemented
5C2×#16813590C213yesmaximal, complemented
6C2×#120×C113C211yesmaximal, characteristic, complemented
7C24×D113C2211yescharacteristic, complemented
8C22×Dic226C2213yescomplemented
9C22×C22⋊D113C2216yes—
10#16813609C22124yescomplemented
11#16813608C22148yescomplemented
12#16813591C22116yescomplemented
13#16813590C22124yescomplemented
14C2×C22⋊Dic113C2213yescomplemented
15C2×C22⋊Dic113C2216yescomplemented
16C2×#14268624C2216yescomplemented
17C2×C4×Dic113C2213yescomplemented
18C25×C113C2211yescharacteristic, complemented
19C22×D4×C113C2213yes—
20#120×C113C2218yescomplemented
21C2×C22⋊C4×C113C2213yescomplemented
22C23×D113—46no—
23C23×D113C2312yes—
24C23×D113C2314yescomplemented
25C2×Dic226—46no—
26C2×Dic226C23112yescomplemented
27C2×C22⋊D113—412no—
28C2×C22⋊D113C23124yes—
29C22×Dic113C2316yes—
30C22⋊Dic113C23112yescomplemented
31C22⋊Dic113C23124yescomplemented
32#14268624C23124yescomplemented
33C4×Dic113C23112yescomplemented
34C24×C113—46no—
35C24×C113C2311yescharacteristic
36C24×C113C2313yes—
37C24×C113C2314yescomplemented
38C2×D4×C113—46no—
39C2×D4×C113C23112yes—
40C22×C4×C113C2313yes—
41C22⋊C4×C113C23112yescomplemented
42C23×C113—26no—
43C23×C113—26no—
44C23×C113—212no—
45C23×C113—412no—
46C23×C113—416no—
47C23×C113C2416yes—
48C23×C113C2412yes—
49C23×C113C2411yescharacteristic
50C22×D113—212no—
51C22×D113—412no—
52C22×D113—416no—
53C22×D113C2414yes—
54D4×C113—412no—
55C2×C4×C113—26no—
56C2×C4×C113C2416yes—
57C22⋊D113—424no—
58C2×Dic113—212no—
59C2×Dic113C24112yes—
60Dic226—412no—
61C22×C113—212no—
62C22×C113—26no—
63C22×C113—26no—
64C22×C113—416no—
65C22×C113—44no—
66C22×C113—412no—
67C22×C113H(5,𝔽2)16yes—
68C22×C113C2511yescharacteristic
69C2×D113—212no—
70C2×D113—416no—
71C2×D113—48no—
72C4×C113—26no—
73Dic113—212no—
74C2×C113—42no—
75C2×C113—46no—
76C2×C113H(3,𝔽4)14yescomplemented
77C2×C113C2×H(5,𝔽2)13yes—
78D113—44no—
79C2×H(3,𝔽4)—1131nomaximal, Sylow
80C113C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
81H(3,𝔽4)—11316no—
82C2×#124—1133no—
83C2×#124—1136no—
84C2×#120—1132no—
85C2×#120—1133no—
86C2×#120D11311yescharacteristic, complemented
87C25—1131no—
88C25C2×D11311yescharacteristic, complemented
89C22×Q8—1133no—
90C22×D4—1136no—
91C22×D4C2×D11313yes—
92#124—11324no—
93#124—11348no—
94#120—11316no—
95#120—11324no—
96#120C2×D11318yescomplemented
97C2×C22⋊C4—1133no—
98C2×C22⋊C4—1136no—
99C2×C22⋊C4—1136no—
100C2×C22⋊C4C2×D11313yescomplemented
101C2×C42—1133no—
102C24—46no—
103C24—1134no—
104C24—1132no—
105C24—4526no—
106C24C22×D11311yescharacteristic
107C24C22×D11313yes—
108C24C22×D11314yescomplemented
109C2×Q8—11312no—
110C2×Q8—4526no—
111C2×D4—46no—
112C2×D4—11324no—
113C2×D4—45212no—
114C2×D4C22×D113112yes—
115C22×C4—1136no—
116C22×C4C22×D11313yes—
117C22⋊C4—11312no—
118C22⋊C4—11324no—
119C22⋊C4—11324no—
120C22⋊C4C22×D113112yescomplemented
121C42—11312no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—1134no—
128C23—45212no—
129C23—45216no—
130C23—22612no—
131C23C23×D11312yes—
132C23C23×D11316yes—
133C23C23×D11311yescharacteristic
134Q8—45212no—
135D4—412no—
136D4—45224no—
137C2×C4—26no—
138C2×C4—11312no—
139C2×C4—22612no—
140C2×C4C23×D11316yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—45216no—
148C22—4528no—
149C22—22612no—
150C22#1681366716yes—
151C22C24×D11311yescharacteristic
152C4—26no—
153C4—22612no—
154C2—46no—
155C2—42no—
156C2—4524no—
157C2#2029934114yesdirect product factor
158C2C2×#1681366713yes—
subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#120×C113C2
socleC23×C113C24
hypercenterC2×#120D113
hypocenterC113C2×H(3,𝔽4)
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #20299341C2direct (N × H)
2. C2×#16813609C2semidirect
3. C2×#16813608C2semidirect
4. C2×#16813591C2semidirect
5. C2×#16813590C2semidirect
6. C2×#120×C113C2semidirect
7. C24×D113C22semidirect
8. C22×Dic226C22semidirect
10. #16813609C22semidirect
11. #16813608C22semidirect
12. #16813591C22semidirect
13. #16813590C22semidirect
14. C2×C22⋊Dic113C22semidirect
15. C2×C22⋊Dic113C22semidirect
16. C2×#14268624C22semidirect
17. C2×C4×Dic113C22semidirect
18. C25×C113C22semidirect
20. #120×C113C22semidirect
21. C2×C22⋊C4×C113C22semidirect
24. C23×D113C23semidirect
26. C2×Dic226C23semidirect
30. C22⋊Dic113C23semidirect
31. C22⋊Dic113C23semidirect
32. #14268624C23semidirect
33. C4×Dic113C23semidirect
37. C24×C113C23semidirect
41. C22⋊C4×C113C23semidirect
76. C2×C113H(3,𝔽4)semidirect
80. C113C2×H(3,𝔽4)semidirect
86. C2×#120D113semidirect
88. C25C2×D113semidirect
96. #120C2×D113semidirect
100. C2×C22⋊C4C2×D113semidirect
108. C24C22×D113semidirect
120. C22⋊C4C22×D113semidirect
157. C2#20299341direct (N × H)

Maximal subgroups

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

subgroupindex
#202993412
C2×#168136092
C2×#168136082
C2×#168135912
C2×#168135902
C2×#120×C1132
C2×H(3,𝔽4)113