Finite Group Databasebeta

← C2×#23752955 #34083231

Subgroups — C2×#23752955 #34083231

Order 19328.

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#23752955C2116yesmaximal, direct product factor
2C2×#18012726C213yesmaximal, complemented
3C2×#18012725C216yesmaximal, complemented
4C2×#18012708C212yesmaximal, complemented
5C2×#18012707C213yesmaximal, complemented
6C2×#120×C151C211yesmaximal, characteristic, complemented
7C24×D151C2211yescharacteristic, complemented
8C22×Dic302C2213yescomplemented
9C22×C22⋊D151C2216yes—
10#18012726C22124yescomplemented
11#18012725C22148yescomplemented
12#18012708C22116yescomplemented
13#18012707C22124yescomplemented
14C2×C22⋊Dic151C2216yescomplemented
15C2×C22⋊Dic151C2213yescomplemented
16C2×(C2×D151)⋊C4C2216yescomplemented
17C2×C4×Dic151C2213yescomplemented
18C25×C151C2211yescharacteristic, complemented
19C22×D4×C151C2213yes—
20#120×C151C2218yescomplemented
21C2×C22⋊C4×C151C2213yescomplemented
22C23×D151—46no—
23C23×D151C2312yes—
24C23×D151C2314yescomplemented
25C2×Dic302—46no—
26C2×Dic302C23112yescomplemented
27C2×C22⋊D151—412no—
28C2×C22⋊D151C23124yes—
29C22×Dic151C2316yes—
30C22⋊Dic151C23112yescomplemented
31C22⋊Dic151C23124yescomplemented
32(C2×D151)⋊C4C23124yescomplemented
33C4×Dic151C23112yescomplemented
34C24×C151—46no—
35C24×C151C2311yescharacteristic
36C24×C151C2313yes—
37C24×C151C2314yescomplemented
38C2×D4×C151—46no—
39C2×D4×C151C23112yes—
40C22×C4×C151C2313yes—
41C22⋊C4×C151C23112yescomplemented
42C22×D151—212no—
43C22×D151—412no—
44C22×D151—416no—
45C22×D151C2414yes—
46Dic302—412no—
47C22⋊D151—424no—
48C2×Dic151—212no—
49C2×Dic151C24112yes—
50C23×C151—212no—
51C23×C151—26no—
52C23×C151—26no—
53C23×C151—412no—
54C23×C151—416no—
55C23×C151C2416yes—
56C23×C151C2412yes—
57C23×C151C2411yescharacteristic
58D4×C151—412no—
59C2×C4×C151—26no—
60C2×C4×C151C2416yes—
61C22×C151—26no—
62C22×C151—26no—
63C22×C151—212no—
64C22×C151—416no—
65C22×C151—412no—
66C22×C151—44no—
67C22×C151H(5,𝔽2)16yes—
68C22×C151C2511yescharacteristic
69C2×D151—212no—
70C2×D151—416no—
71C2×D151—48no—
72C4×C151—26no—
73Dic151—212no—
74C2×C151—42no—
75C2×C151—46no—
76C2×C151H(3,𝔽4)14yescomplemented
77C2×C151C2×H(5,𝔽2)13yes—
78D151—44no—
79C151C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—1511nomaximal, Sylow
81H(3,𝔽4)—15116no—
82C2×#124—1513no—
83C2×#124—1516no—
84C2×#120—1512no—
85C2×#120—1513no—
86C2×#120D15111yescharacteristic, complemented
87C25—1511no—
88C25C2×D15111yescharacteristic, complemented
89C22×Q8—1513no—
90C22×D4—1516no—
91C22×D4C2×D15113yes—
92#124—15124no—
93#124—15148no—
94#120—15116no—
95#120—15124no—
96#120C2×D15118yescomplemented
97C2×C22⋊C4—1513no—
98C2×C22⋊C4—1516no—
99C2×C22⋊C4—1516no—
100C2×C22⋊C4C2×D15113yescomplemented
101C2×C42—1513no—
102C24—46no—
103C24—6046no—
104C24—1512no—
105C24—1514no—
106C24C22×D15111yescharacteristic
107C24C22×D15113yes—
108C24C22×D15114yescomplemented
109C2×Q8—6046no—
110C2×Q8—15112no—
111C2×D4—46no—
112C2×D4—60412no—
113C2×D4—15124no—
114C2×D4C22×D151112yes—
115C22×C4—1516no—
116C22×C4C22×D15113yes—
117C22⋊C4—15112no—
118C22⋊C4—15124no—
119C22⋊C4—15124no—
120C22⋊C4C22×D151112yescomplemented
121C42—15112no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—30212no—
128C23—60412no—
129C23—60416no—
130C23—1514no—
131C23C23×D15112yes—
132C23C23×D15116yes—
133C23C23×D15111yescharacteristic
134Q8—60412no—
135D4—412no—
136D4—60424no—
137C2×C4—26no—
138C2×C4—30212no—
139C2×C4—15112no—
140C2×C4C23×D15116yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—30212no—
148C22—60416no—
149C22—6048no—
150C22#1801278416yes—
151C22C24×D15111yescharacteristic
152C4—26no—
153C4—30212no—
154C2—46no—
155C2—42no—
156C2—6044no—
157C2#2375295514yesdirect product factor
158C2C2×#1801278413yes—
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#120×C151C2
socleC23×C151C24
hypercenterC2×#120D151
hypocenterC151C2×H(3,𝔽4)
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #23752955C2direct (N × H)
2. C2×#18012726C2semidirect
3. C2×#18012725C2semidirect
4. C2×#18012708C2semidirect
5. C2×#18012707C2semidirect
6. C2×#120×C151C2semidirect
7. C24×D151C22semidirect
8. C22×Dic302C22semidirect
10. #18012726C22semidirect
11. #18012725C22semidirect
12. #18012708C22semidirect
13. #18012707C22semidirect
14. C2×C22⋊Dic151C22semidirect
15. C2×C22⋊Dic151C22semidirect
16. C2×(C2×D151)⋊C4C22semidirect
17. C2×C4×Dic151C22semidirect
18. C25×C151C22semidirect
20. #120×C151C22semidirect
21. C2×C22⋊C4×C151C22semidirect
24. C23×D151C23semidirect
26. C2×Dic302C23semidirect
30. C22⋊Dic151C23semidirect
31. C22⋊Dic151C23semidirect
32. (C2×D151)⋊C4C23semidirect
33. C4×Dic151C23semidirect
37. C24×C151C23semidirect
41. C22⋊C4×C151C23semidirect
76. C2×C151H(3,𝔽4)semidirect
79. C151C2×H(3,𝔽4)semidirect
86. C2×#120D151semidirect
88. C25C2×D151semidirect
96. #120C2×D151semidirect
100. C2×C22⋊C4C2×D151semidirect
108. C24C22×D151semidirect
120. C22⋊C4C22×D151semidirect
157. C2#23752955direct (N × H)

Maximal subgroups

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

subgroupindex
#237529552
C2×#180127262
C2×#180127252
C2×#180127082
C2×#180127072
C2×#120×C1512
C2×H(3,𝔽4)151