Finite Group Databasebeta

← C2×#20295769 #28377153

Subgroups — C2×#20295769 #28377153

Order 13952.

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#20295769C2116yesmaximal, direct product factor
2C2×#16812686C213yesmaximal, complemented
3C2×#16812685C216yesmaximal, complemented
4C2×#16812668C212yesmaximal, complemented
5C2×#16812667C213yesmaximal, complemented
6C2×#120×C109C211yesmaximal, characteristic, complemented
7C24×D109C2211yescharacteristic, complemented
8C22×Dic218C2213yescomplemented
9C22×C22⋊D109C2216yes—
10#16812686C22124yescomplemented
11#16812685C22148yescomplemented
12#16812668C22116yescomplemented
13#16812667C22124yescomplemented
14C2×C22⋊Dic109C2213yescomplemented
15C2×C22⋊Dic109C2216yescomplemented
16C2×#13182006C2216yescomplemented
17C2×C4×Dic109C2213yescomplemented
18C25×C109C2211yescharacteristic, complemented
19C22×D4×C109C2213yes—
20#120×C109C2218yescomplemented
21C2×C22⋊C4×C109C2213yescomplemented
22C23×D109—46no—
23C23×D109C2312yes—
24C23×D109C2314yescomplemented
25C2×Dic218—46no—
26C2×Dic218C23112yescomplemented
27C2×C22⋊D109—412no—
28C2×C22⋊D109C23124yes—
29C22×Dic109C2316yes—
30C22⋊Dic109C23112yescomplemented
31C22⋊Dic109C23124yescomplemented
32#13182006C23124yescomplemented
33C4×Dic109C23112yescomplemented
34C24×C109—46no—
35C24×C109C2313yes—
36C24×C109C2311yescharacteristic
37C24×C109C2314yescomplemented
38C2×D4×C109—46no—
39C2×D4×C109C23112yes—
40C22×C4×C109C2313yes—
41C22⋊C4×C109C23112yescomplemented
42C23×C109—26no—
43C23×C109—26no—
44C23×C109—212no—
45C23×C109—412no—
46C23×C109—416no—
47C23×C109C2416yes—
48C23×C109C2412yes—
49C23×C109C2411yescharacteristic
50C22×D109—212no—
51C22×D109—412no—
52C22×D109—416no—
53C22×D109C2414yes—
54D4×C109—412no—
55C2×C4×C109—26no—
56C2×C4×C109C2416yes—
57C22⋊D109—424no—
58C2×Dic109—212no—
59C2×Dic109C24112yes—
60Dic218—412no—
61C22×C109—212no—
62C22×C109—26no—
63C22×C109—26no—
64C22×C109—416no—
65C22×C109—44no—
66C22×C109—412no—
67C22×C109H(5,𝔽2)16yes—
68C22×C109C2511yescharacteristic
69C2×D109—212no—
70C2×D109—416no—
71C2×D109—48no—
72C4×C109—26no—
73Dic109—212no—
74C2×C109—42no—
75C2×C109—46no—
76C2×C109H(3,𝔽4)14yescomplemented
77C2×C109C2×H(5,𝔽2)13yes—
78D109—44no—
79C2×H(3,𝔽4)—1091nomaximal, Sylow
80C109C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
81H(3,𝔽4)—10916no—
82C2×#124—1093no—
83C2×#124—1096no—
84C2×#120—1092no—
85C2×#120—1093no—
86C2×#120D10911yescharacteristic, complemented
87C25—1091no—
88C25C2×D10911yescharacteristic, complemented
89C22×Q8—1093no—
90C22×D4—1096no—
91C22×D4C2×D10913yes—
92#124—10924no—
93#124—10948no—
94#120—10916no—
95#120—10924no—
96#120C2×D10918yescomplemented
97C2×C22⋊C4—1093no—
98C2×C22⋊C4—1096no—
99C2×C22⋊C4—1096no—
100C2×C22⋊C4C2×D10913yescomplemented
101C2×C42—1093no—
102C24—46no—
103C24—1094no—
104C24—1092no—
105C24—4366no—
106C24C22×D10911yescharacteristic
107C24C22×D10913yes—
108C24C22×D10914yescomplemented
109C2×Q8—10912no—
110C2×Q8—4366no—
111C2×D4—46no—
112C2×D4—10924no—
113C2×D4—43612no—
114C2×D4C22×D109112yes—
115C22×C4—1096no—
116C22×C4C22×D10913yes—
117C22⋊C4—10912no—
118C22⋊C4—10924no—
119C22⋊C4—10924no—
120C22⋊C4C22×D109112yescomplemented
121C42—10912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—1094no—
128C23—43612no—
129C23—43616no—
130C23—21812no—
131C23C23×D10912yes—
132C23C23×D10916yes—
133C23C23×D10911yescharacteristic
134Q8—43612no—
135D4—412no—
136D4—43624no—
137C2×C4—26no—
138C2×C4—10912no—
139C2×C4—21812no—
140C2×C4C23×D10916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—43616no—
148C22—4368no—
149C22—21812no—
150C22#1681274416yes—
151C22C24×D10911yescharacteristic
152C4—26no—
153C4—21812no—
154C2—46no—
155C2—42no—
156C2—4364no—
157C2#2029576914yesdirect product factor
158C2C2×#1681274413yes—
subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×#120×C109C2
socleC23×C109C24
hypercenterC2×#120D109
hypocenterC109C2×H(3,𝔽4)
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #20295769C2direct (N × H)
2. C2×#16812686C2semidirect
3. C2×#16812685C2semidirect
4. C2×#16812668C2semidirect
5. C2×#16812667C2semidirect
6. C2×#120×C109C2semidirect
7. C24×D109C22semidirect
8. C22×Dic218C22semidirect
10. #16812686C22semidirect
11. #16812685C22semidirect
12. #16812668C22semidirect
13. #16812667C22semidirect
14. C2×C22⋊Dic109C22semidirect
15. C2×C22⋊Dic109C22semidirect
16. C2×#13182006C22semidirect
17. C2×C4×Dic109C22semidirect
18. C25×C109C22semidirect
20. #120×C109C22semidirect
21. C2×C22⋊C4×C109C22semidirect
24. C23×D109C23semidirect
26. C2×Dic218C23semidirect
30. C22⋊Dic109C23semidirect
31. C22⋊Dic109C23semidirect
32. #13182006C23semidirect
33. C4×Dic109C23semidirect
37. C24×C109C23semidirect
41. C22⋊C4×C109C23semidirect
76. C2×C109H(3,𝔽4)semidirect
80. C109C2×H(3,𝔽4)semidirect
86. C2×#120D109semidirect
88. C25C2×D109semidirect
96. #120C2×D109semidirect
100. C2×C22⋊C4C2×D109semidirect
108. C24C22×D109semidirect
120. C22⋊C4C22×D109semidirect
157. C2#20295769direct (N × H)

Maximal subgroups

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

subgroupindex
#202957692
C2×#168126862
C2×#168126852
C2×#168126682
C2×#168126672
C2×#120×C1092
C2×H(3,𝔽4)109