Finite Group Databasebeta

← C2×#127×D151 #34082380

Subgroups — C2×#127×D151 #34082380

Order 19328.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C22×D4×D151C216yesmaximal, complemented
2C2×#18012736C211yesmaximal, characteristic, complemented
3C2×#18012735C216yesmaximal, complemented
4#127×D151C2116yesmaximal, direct product factor
5C2×C42×D151C211yesmaximal, characteristic, complemented
6C2×#127×C151C211yesmaximal, characteristic, complemented
7C24×D151C2214yes—
8C22×D604C2216yescomplemented
9C22×C22⋊D151C22112yescomplemented
10C2×D4×D151—248no—
11C2×D4×D151C22148yescomplemented
12C22×C4×D151C2213yes—
13#18012736C2218yescomplemented
14#18012735C22148yescomplemented
15C2×C4×Dic151C2213yescomplemented
16C42×D151C2218yescomplemented
17C22×D4×C151C2216yescomplemented
18#127×C151C2218yescomplemented
19C2×C42×C151C2211yescharacteristic, complemented
20C23×D151—248no—
21C23×D151C23116yes—
22C23×D151C2314yes—
23C23×D151C2311yescharacteristic
24C2×D604—224no—
25C2×D604C23124yescomplemented
26C2×C22⋊D151—248no—
27C2×C22⋊D151C23148yescomplemented
28D4×D151—2192no—
29C22×Dic151C2313yes—
30C2×C4×D151D4124yescomplemented
31C2×C4×D151C23112yes—
32C4×Dic151C23112yescomplemented
33C24×C151C2314yes—
34C2×D4×C151—224no—
35C2×D4×C151C23124yescomplemented
36C22×C4×C151C2313yes—
37C42×C151C2314yescomplemented
38C22×D151—224no—
39C22×D151—296no—
40C22×D151—464no—
41C22×D151C2×D4112yes—
42C22×D151C2418yes—
43C22×D151C2412yes—
44D604—248no—
45C22⋊D151—296no—
46C2×Dic151C2×D4112yescomplemented
47C2×Dic151C2416yes—
48C4×D151C2×D4148yescomplemented
49C23×C151—224no—
50C23×C151C2418yes—
51C23×C151C2411yescharacteristic
52D4×C151—248no—
53C2×C4×C151C2×D4112yescomplemented
54C2×C4×C151C2416yes—
55C22×C151—224no—
56C22×C151—416no—
57C22×C151C22×D416yes—
58C22×C151C2511yescharacteristic
59C2×D151—224no—
60C2×D151—416no—
61C2×D151—464no—
62C2×D151#127116yesdirect product factor
63C2×D151C22×D4112yes—
64C4×C151C22×D4112yescomplemented
65Dic151C22×D4112yescomplemented
66C2×C151—48no—
67C2×C151C2×#12714yescomplemented
68C2×C151C23×D413yes—
69D151—48no—
70D151C2×#12718yesdirect product factor
71C151C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—1511nomaximal, Sylow
73C23×D4—1516no—
74C2×#127—1516no—
75C2×#127—15116no—
76C2×#127—1511no—
77C2×#127D15111yescharacteristic, direct product factor
78C22×C42—1511no—
79C25—1514no—
80C22×D4—30248no—
81C22×D4—15112no—
82C22×D4—15148no—
83C22×D4—1516no—
84C22×D4C2×D15116yescomplemented
85C23×C4—1513no—
86#127—15148no—
87#127—1518no—
88#127C2×D15118yesdirect product factor
89C2×C42—1513no—
90C2×C42—1518no—
91C2×C42C2×D15111yescharacteristic, complemented
92C24—30248no—
93C24—15116no—
94C24—1514no—
95C24—1511no—
96C24C22×D15114yes—
97C2×D4—224no—
98C2×D4—302192no—
99C2×D4—30248no—
100C2×D4—30224no—
101C2×D4—15148no—
102C2×D4—15124no—
103C2×D4C22×D151124yescomplemented
104C22×C4—1513no—
105C22×C4—15124no—
106C22×C4—15112no—
107C22×C4C22×D15113yes—
108C42—15112no—
109C42C22×D15114yescomplemented
110C23—224no—
111C23—30296no—
112C23—30224no—
113C23—60464no—
114C23—1518no—
115C23—15112no—
116C23—1512no—
117C23C23×D15118yes—
118C23C23×D15111yescharacteristic
119D4—248no—
120D4—30296no—
121D4—30248no—
122C2×C4—15112no—
123C2×C4—1516no—
124C2×C4—15148no—
125C2×C4D4×D151112yescomplemented
126C2×C4C23×D15116yes—
127C22—224no—
128C22—416no—
129C22—30224no—
130C22—60464no—
131C22—60416no—
132C22—15116no—
133C22—15112no—
134C22C2×D4×D15116yes—
135C22C24×D15111yescharacteristic
136C4—15112no—
137C4C2×D4×D151112yescomplemented
138C2—48no—
139C2—6048no—
140C2—1518no—
141C2#127×D15114yesdirect product factor
142C2C22×D4×D15113yes—
subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#127×C151C2
socleC23×C151C24
hypercenterC2×#127D151
hypocenterC151C22×#127
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D151C2semidirect
2. C2×#18012736C2semidirect
3. C2×#18012735C2semidirect
4. #127×D151C2direct (N × H)
5. C2×C42×D151C2semidirect
6. C2×#127×C151C2semidirect
8. C22×D604C22semidirect
9. C22×C22⋊D151C22semidirect
11. C2×D4×D151C22semidirect
13. #18012736C22semidirect
14. #18012735C22semidirect
15. C2×C4×Dic151C22semidirect
16. C42×D151C22semidirect
17. C22×D4×C151C22semidirect
18. #127×C151C22semidirect
19. C2×C42×C151C22semidirect
25. C2×D604C23semidirect
27. C2×C22⋊D151C23semidirect
30. C2×C4×D151D4semidirect
32. C4×Dic151C23semidirect
35. C2×D4×C151C23semidirect
37. C42×C151C23semidirect
46. C2×Dic151C2×D4semidirect
48. C4×D151C2×D4semidirect
53. C2×C4×C151C2×D4semidirect
62. C2×D151#127direct (N × H)
64. C4×C151C22×D4semidirect
65. Dic151C22×D4semidirect
67. C2×C151C2×#127semidirect
70. D151C2×#127direct (N × H)
71. C151C22×#127semidirect
77. C2×#127D151direct (N × H)
84. C22×D4C2×D151semidirect
88. #127C2×D151direct (N × H)
91. C2×C42C2×D151semidirect
103. C2×D4C22×D151semidirect
109. C42C22×D151semidirect
125. C2×C4D4×D151semidirect
137. C4C2×D4×D151semidirect
141. C2#127×D151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1512
C2×#180127362
C2×#180127352
#127×D1512
C2×C42×D1512
C2×#127×C1512
C22×#127151