Finite Group Databasebeta

← C2×#20268534 #27209265

Subgroups — C2×#20268534 #27209265

Order 13184.

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#20268534C2116yesmaximal, direct product factor
2C2×#15693008C213yesmaximal, complemented
3C2×#15693007C216yesmaximal, complemented
4C2×#15692990C212yesmaximal, complemented
5C2×#15692989C213yesmaximal, complemented
6C2×#120×C103C211yesmaximal, characteristic, complemented
7C24×D103C2211yescharacteristic, complemented
8C22×Dic206C2213yescomplemented
9C22×C22⋊D103C2216yes—
10#15693008C22124yescomplemented
11#15693007C22148yescomplemented
12#15692990C22116yescomplemented
13#15692989C22124yescomplemented
14C2×C22⋊Dic103C2216yescomplemented
15C2×C22⋊Dic103C2213yescomplemented
16C2×(C2×D103)⋊C4C2216yescomplemented
17C2×C4×Dic103C2213yescomplemented
18C25×C103C2211yescharacteristic, complemented
19C22×D4×C103C2213yes—
20#120×C103C2218yescomplemented
21C2×C22⋊C4×C103C2213yescomplemented
22C23×D103—46no—
23C23×D103C2312yes—
24C23×D103C2314yescomplemented
25C2×Dic206—46no—
26C2×Dic206C23112yescomplemented
27C2×C22⋊D103—412no—
28C2×C22⋊D103C23124yes—
29C22×Dic103C2316yes—
30C22⋊Dic103C23112yescomplemented
31C22⋊Dic103C23124yescomplemented
32(C2×D103)⋊C4C23124yescomplemented
33C4×Dic103C23112yescomplemented
34C24×C103—46no—
35C24×C103C2313yes—
36C24×C103C2311yescharacteristic
37C24×C103C2314yescomplemented
38C2×D4×C103—46no—
39C2×D4×C103C23112yes—
40C22×C4×C103C2313yes—
41C22⋊C4×C103C23112yescomplemented
42C23×C103—26no—
43C23×C103—26no—
44C23×C103—212no—
45C23×C103—412no—
46C23×C103—416no—
47C23×C103C2416yes—
48C23×C103C2412yes—
49C23×C103C2411yescharacteristic
50C22×D103—212no—
51C22×D103—412no—
52C22×D103—416no—
53C22×D103C2414yes—
54D4×C103—412no—
55C2×C4×C103—26no—
56C2×C4×C103C2416yes—
57C22⋊D103—424no—
58C2×Dic103—212no—
59C2×Dic103C24112yes—
60Dic206—412no—
61C22×C103—212no—
62C22×C103—26no—
63C22×C103—26no—
64C22×C103—416no—
65C22×C103—44no—
66C22×C103—412no—
67C22×C103H(5,𝔽2)16yes—
68C22×C103C2511yescharacteristic
69C2×D103—212no—
70C2×D103—416no—
71C2×D103—48no—
72C4×C103—26no—
73Dic103—212no—
74C2×C103—42no—
75C2×C103—46no—
76C2×C103H(3,𝔽4)14yescomplemented
77C2×C103C2×H(5,𝔽2)13yes—
78D103—44no—
79C2×H(3,𝔽4)—1031nomaximal, Sylow
80C103C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
81H(3,𝔽4)—10316no—
82C2×#124—1033no—
83C2×#124—1036no—
84C2×#120—1032no—
85C2×#120—1033no—
86C2×#120D10311yescharacteristic, complemented
87C25—1031no—
88C25C2×D10311yescharacteristic, complemented
89C22×Q8—1033no—
90C22×D4—1036no—
91C22×D4C2×D10313yes—
92#124—10324no—
93#124—10348no—
94#120—10316no—
95#120—10324no—
96#120C2×D10318yescomplemented
97C2×C22⋊C4—1033no—
98C2×C22⋊C4—1036no—
99C2×C22⋊C4—1036no—
100C2×C22⋊C4C2×D10313yescomplemented
101C2×C42—1033no—
102C24—46no—
103C24—1034no—
104C24—1032no—
105C24—4126no—
106C24C22×D10311yescharacteristic
107C24C22×D10313yes—
108C24C22×D10314yescomplemented
109C2×Q8—10312no—
110C2×Q8—4126no—
111C2×D4—46no—
112C2×D4—10324no—
113C2×D4—41212no—
114C2×D4C22×D103112yes—
115C22×C4—1036no—
116C22×C4C22×D10313yes—
117C22⋊C4—10312no—
118C22⋊C4—10324no—
119C22⋊C4—10324no—
120C22⋊C4C22×D103112yescomplemented
121C42—10312no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—1034no—
128C23—41212no—
129C23—41216no—
130C23—20612no—
131C23C23×D10312yes—
132C23C23×D10316yes—
133C23C23×D10311yescharacteristic
134Q8—41212no—
135D4—412no—
136D4—41224no—
137C2×C4—26no—
138C2×C4—10312no—
139C2×C4—20612no—
140C2×C4C23×D10316yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—41216no—
148C22—4128no—
149C22—20612no—
150C22#1569306616yes—
151C22C24×D10311yescharacteristic
152C4—26no—
153C4—20612no—
154C2—46no—
155C2—42no—
156C2—4124no—
157C2#2026853414yesdirect product factor
158C2C2×#1569306613yes—
subgroupG/H
centerC23C23×D103
commutator, cosocleC22×C103C25
FrattiniC22C24×D103
FittingC2×#120×C103C2
socleC23×C103C24
hypercenterC2×#120D103
hypocenterC103C2×H(3,𝔽4)
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #20268534C2direct (N × H)
2. C2×#15693008C2semidirect
3. C2×#15693007C2semidirect
4. C2×#15692990C2semidirect
5. C2×#15692989C2semidirect
6. C2×#120×C103C2semidirect
7. C24×D103C22semidirect
8. C22×Dic206C22semidirect
10. #15693008C22semidirect
11. #15693007C22semidirect
12. #15692990C22semidirect
13. #15692989C22semidirect
14. C2×C22⋊Dic103C22semidirect
15. C2×C22⋊Dic103C22semidirect
16. C2×(C2×D103)⋊C4C22semidirect
17. C2×C4×Dic103C22semidirect
18. C25×C103C22semidirect
20. #120×C103C22semidirect
21. C2×C22⋊C4×C103C22semidirect
24. C23×D103C23semidirect
26. C2×Dic206C23semidirect
30. C22⋊Dic103C23semidirect
31. C22⋊Dic103C23semidirect
32. (C2×D103)⋊C4C23semidirect
33. C4×Dic103C23semidirect
37. C24×C103C23semidirect
41. C22⋊C4×C103C23semidirect
76. C2×C103H(3,𝔽4)semidirect
80. C103C2×H(3,𝔽4)semidirect
86. C2×#120D103semidirect
88. C25C2×D103semidirect
96. #120C2×D103semidirect
100. C2×C22⋊C4C2×D103semidirect
108. C24C22×D103semidirect
120. C22⋊C4C22×D103semidirect
157. C2#20268534direct (N × H)

Maximal subgroups

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

subgroupindex
#202685342
C2×#156930082
C2×#156930072
C2×#156929902
C2×#156929892
C2×#120×C1032
C2×H(3,𝔽4)103