Finite Group Databasebeta

← C2×#23758016 #34114257

Subgroups — C2×#23758016 #34114257

Order 20096.

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#23758016C2116yesmaximal, direct product factor
2C2×#19097758C213yesmaximal, complemented
3C2×#19097757C216yesmaximal, complemented
4C2×#19097740C212yesmaximal, complemented
5C2×#19097739C213yesmaximal, complemented
6C2×#120×C157C211yesmaximal, characteristic, complemented
7C24×D157C2211yescharacteristic, complemented
8C22×Dic314C2213yescomplemented
9C22×C22⋊D157C2216yes—
10#19097758C22124yescomplemented
11#19097757C22148yescomplemented
12#19097740C22116yescomplemented
13#19097739C22124yescomplemented
14C2×C22⋊Dic157C2213yescomplemented
15C2×C22⋊Dic157C2216yescomplemented
16C2×#14578931C2216yescomplemented
17C2×C4×Dic157C2213yescomplemented
18C25×C157C2211yescharacteristic, complemented
19C22×D4×C157C2213yes—
20#120×C157C2218yescomplemented
21C2×C22⋊C4×C157C2213yescomplemented
22C23×D157—46no—
23C23×D157C2312yes—
24C23×D157C2314yescomplemented
25C2×Dic314—46no—
26C2×Dic314C23112yescomplemented
27C2×C22⋊D157—412no—
28C2×C22⋊D157C23124yes—
29C22×Dic157C2316yes—
30C22⋊Dic157C23112yescomplemented
31C22⋊Dic157C23124yescomplemented
32#14578931C23124yescomplemented
33C4×Dic157C23112yescomplemented
34C24×C157—46no—
35C24×C157C2313yes—
36C24×C157C2311yescharacteristic
37C24×C157C2314yescomplemented
38C2×D4×C157—46no—
39C2×D4×C157C23112yes—
40C22×C4×C157C2313yes—
41C22⋊C4×C157C23112yescomplemented
42C22×D157—212no—
43C22×D157—412no—
44C22×D157—416no—
45C22×D157C2414yes—
46Dic314—412no—
47C22⋊D157—424no—
48C2×Dic157—212no—
49C2×Dic157C24112yes—
50C23×C157—212no—
51C23×C157—26no—
52C23×C157—26no—
53C23×C157—412no—
54C23×C157—416no—
55C23×C157C2416yes—
56C23×C157C2412yes—
57C23×C157C2411yescharacteristic
58D4×C157—412no—
59C2×C4×C157—26no—
60C2×C4×C157C2416yes—
61C22×C157—26no—
62C22×C157—26no—
63C22×C157—212no—
64C22×C157—416no—
65C22×C157—412no—
66C22×C157—44no—
67C22×C157H(5,𝔽2)16yes—
68C22×C157C2511yescharacteristic
69C2×D157—212no—
70C2×D157—416no—
71C2×D157—48no—
72C4×C157—26no—
73Dic157—212no—
74C2×C157—42no—
75C2×C157—46no—
76C2×C157H(3,𝔽4)14yescomplemented
77C2×C157C2×H(5,𝔽2)13yes—
78D157—44no—
79C157C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—1571nomaximal, Sylow
81H(3,𝔽4)—15716no—
82C2×#124—1573no—
83C2×#124—1576no—
84C2×#120—1572no—
85C2×#120—1573no—
86C2×#120D15711yescharacteristic, complemented
87C25—1571no—
88C25C2×D15711yescharacteristic, complemented
89C22×Q8—1573no—
90C22×D4—1576no—
91C22×D4C2×D15713yes—
92#124—15724no—
93#124—15748no—
94#120—15716no—
95#120—15724no—
96#120C2×D15718yescomplemented
97C2×C22⋊C4—1573no—
98C2×C22⋊C4—1576no—
99C2×C22⋊C4—1576no—
100C2×C22⋊C4C2×D15713yescomplemented
101C2×C42—1573no—
102C24—46no—
103C24—6286no—
104C24—1572no—
105C24—1574no—
106C24C22×D15711yescharacteristic
107C24C22×D15713yes—
108C24C22×D15714yescomplemented
109C2×Q8—6286no—
110C2×Q8—15712no—
111C2×D4—46no—
112C2×D4—62812no—
113C2×D4—15724no—
114C2×D4C22×D157112yes—
115C22×C4—1576no—
116C22×C4C22×D15713yes—
117C22⋊C4—15712no—
118C22⋊C4—15724no—
119C22⋊C4—15724no—
120C22⋊C4C22×D157112yescomplemented
121C42—15712no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—31412no—
128C23—62812no—
129C23—62816no—
130C23—1574no—
131C23C23×D15712yes—
132C23C23×D15716yes—
133C23C23×D15711yescharacteristic
134Q8—62812no—
135D4—412no—
136D4—62824no—
137C2×C4—26no—
138C2×C4—31412no—
139C2×C4—15712no—
140C2×C4C23×D15716yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—31412no—
148C22—62816no—
149C22—6288no—
150C22#1909781616yes—
151C22C24×D15711yescharacteristic
152C4—26no—
153C4—31412no—
154C2—46no—
155C2—42no—
156C2—6284no—
157C2#2375801614yesdirect product factor
158C2C2×#1909781613yes—
subgroupG/H
centerC23C23×D157
commutator, cosocleC22×C157C25
FrattiniC22C24×D157
FittingC2×#120×C157C2
socleC23×C157C24
hypercenterC2×#120D157
hypocenterC157C2×H(3,𝔽4)
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #23758016C2direct (N × H)
2. C2×#19097758C2semidirect
3. C2×#19097757C2semidirect
4. C2×#19097740C2semidirect
5. C2×#19097739C2semidirect
6. C2×#120×C157C2semidirect
7. C24×D157C22semidirect
8. C22×Dic314C22semidirect
10. #19097758C22semidirect
11. #19097757C22semidirect
12. #19097740C22semidirect
13. #19097739C22semidirect
14. C2×C22⋊Dic157C22semidirect
15. C2×C22⋊Dic157C22semidirect
16. C2×#14578931C22semidirect
17. C2×C4×Dic157C22semidirect
18. C25×C157C22semidirect
20. #120×C157C22semidirect
21. C2×C22⋊C4×C157C22semidirect
24. C23×D157C23semidirect
26. C2×Dic314C23semidirect
30. C22⋊Dic157C23semidirect
31. C22⋊Dic157C23semidirect
32. #14578931C23semidirect
33. C4×Dic157C23semidirect
37. C24×C157C23semidirect
41. C22⋊C4×C157C23semidirect
76. C2×C157H(3,𝔽4)semidirect
79. C157C2×H(3,𝔽4)semidirect
86. C2×#120D157semidirect
88. C25C2×D157semidirect
96. #120C2×D157semidirect
100. C2×C22⋊C4C2×D157semidirect
108. C24C22×D157semidirect
120. C22⋊C4C22×D157semidirect
157. C2#23758016direct (N × H)

Maximal subgroups

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

subgroupindex
#237580162
C2×#190977582
C2×#190977572
C2×#190977402
C2×#190977392
C2×#120×C1572
C2×H(3,𝔽4)157