Finite Group Databasebeta

← C2×#127×D139 #31819674

Subgroups — C2×#127×D139 #31819674

Order 17792.

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×D139C216yesmaximal, complemented
2C2×#17984839C211yesmaximal, characteristic, complemented
3C2×#17984838C216yesmaximal, complemented
4#127×D139C2116yesmaximal, direct product factor
5C2×C42×D139C211yesmaximal, characteristic, complemented
6C2×#127×C139C211yesmaximal, characteristic, complemented
7C24×D139C2214yes—
8C22×D556C2216yescomplemented
9C22×C22⋊D139C22112yescomplemented
10C2×D4×D139—248no—
11C2×D4×D139C22148yescomplemented
12C22×C4×D139C2213yes—
13#17984839C2218yescomplemented
14#17984838C22148yescomplemented
15C2×C4×Dic139C2213yescomplemented
16C42×D139C2218yescomplemented
17C22×D4×C139C2216yescomplemented
18#127×C139C2218yescomplemented
19C2×C42×C139C2211yescharacteristic, complemented
20C23×D139—248no—
21C23×D139C23116yes—
22C23×D139C2314yes—
23C23×D139C2311yescharacteristic
24C2×D556—224no—
25C2×D556C23124yescomplemented
26C2×C22⋊D139—248no—
27C2×C22⋊D139C23148yescomplemented
28D4×D139—2192no—
29C22×Dic139C2313yes—
30C2×C4×D139D4124yescomplemented
31C2×C4×D139C23112yes—
32C4×Dic139C23112yescomplemented
33C24×C139C2314yes—
34C2×D4×C139—224no—
35C2×D4×C139C23124yescomplemented
36C22×C4×C139C2313yes—
37C42×C139C2314yescomplemented
38C22×D139—224no—
39C22×D139—296no—
40C22×D139—464no—
41C22×D139C2×D4112yes—
42C22×D139C2418yes—
43C22×D139C2412yes—
44D556—248no—
45C22⋊D139—296no—
46C2×Dic139C2×D4112yescomplemented
47C2×Dic139C2416yes—
48C4×D139C2×D4148yescomplemented
49C23×C139—224no—
50C23×C139C2418yes—
51C23×C139C2411yescharacteristic
52D4×C139—248no—
53C2×C4×C139C2×D4112yescomplemented
54C2×C4×C139C2416yes—
55C22×C139—224no—
56C22×C139—416no—
57C22×C139C22×D416yes—
58C22×C139C2511yescharacteristic
59C2×D139—224no—
60C2×D139—416no—
61C2×D139—464no—
62C2×D139#127116yesdirect product factor
63C2×D139C22×D4112yes—
64C4×C139C22×D4112yescomplemented
65Dic139C22×D4112yescomplemented
66C2×C139—48no—
67C2×C139C2×#12714yescomplemented
68C2×C139C23×D413yes—
69D139—48no—
70D139C2×#12718yesdirect product factor
71C139C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—1391nomaximal, Sylow
73C23×D4—1396no—
74C2×#127—1396no—
75C2×#127—13916no—
76C2×#127—1391no—
77C2×#127D13911yescharacteristic, direct product factor
78C22×C42—1391no—
79C25—1394no—
80C22×D4—27848no—
81C22×D4—13912no—
82C22×D4—13948no—
83C22×D4—1396no—
84C22×D4C2×D13916yescomplemented
85C23×C4—1393no—
86#127—13948no—
87#127—1398no—
88#127C2×D13918yesdirect product factor
89C2×C42—1393no—
90C2×C42—1398no—
91C2×C42C2×D13911yescharacteristic, complemented
92C24—27848no—
93C24—13916no—
94C24—1394no—
95C24—1391no—
96C24C22×D13914yes—
97C2×D4—224no—
98C2×D4—278192no—
99C2×D4—27848no—
100C2×D4—27824no—
101C2×D4—13948no—
102C2×D4—13924no—
103C2×D4C22×D139124yescomplemented
104C22×C4—1393no—
105C22×C4—13924no—
106C22×C4—13912no—
107C22×C4C22×D13913yes—
108C42—13912no—
109C42C22×D13914yescomplemented
110C23—224no—
111C23—27896no—
112C23—27824no—
113C23—55664no—
114C23—1398no—
115C23—13912no—
116C23—1392no—
117C23C23×D13918yes—
118C23C23×D13911yescharacteristic
119D4—248no—
120D4—27896no—
121D4—27848no—
122C2×C4—13912no—
123C2×C4—1396no—
124C2×C4—13948no—
125C2×C4D4×D139112yescomplemented
126C2×C4C23×D13916yes—
127C22—224no—
128C22—416no—
129C22—27824no—
130C22—55664no—
131C22—55616no—
132C22—13912no—
133C22—13916no—
134C22C2×D4×D13916yes—
135C22C24×D13911yescharacteristic
136C4—13912no—
137C4C2×D4×D139112yescomplemented
138C2—48no—
139C2—5568no—
140C2—1398no—
141C2#127×D13914yesdirect product factor
142C2C22×D4×D13913yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#127×C139C2
socleC23×C139C24
hypercenterC2×#127D139
hypocenterC139C22×#127
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D139C2semidirect
2. C2×#17984839C2semidirect
3. C2×#17984838C2semidirect
4. #127×D139C2direct (N × H)
5. C2×C42×D139C2semidirect
6. C2×#127×C139C2semidirect
8. C22×D556C22semidirect
9. C22×C22⋊D139C22semidirect
11. C2×D4×D139C22semidirect
13. #17984839C22semidirect
14. #17984838C22semidirect
15. C2×C4×Dic139C22semidirect
16. C42×D139C22semidirect
17. C22×D4×C139C22semidirect
18. #127×C139C22semidirect
19. C2×C42×C139C22semidirect
25. C2×D556C23semidirect
27. C2×C22⋊D139C23semidirect
30. C2×C4×D139D4semidirect
32. C4×Dic139C23semidirect
35. C2×D4×C139C23semidirect
37. C42×C139C23semidirect
46. C2×Dic139C2×D4semidirect
48. C4×D139C2×D4semidirect
53. C2×C4×C139C2×D4semidirect
62. C2×D139#127direct (N × H)
64. C4×C139C22×D4semidirect
65. Dic139C22×D4semidirect
67. C2×C139C2×#127semidirect
70. D139C2×#127direct (N × H)
71. C139C22×#127semidirect
77. C2×#127D139direct (N × H)
84. C22×D4C2×D139semidirect
88. #127C2×D139direct (N × H)
91. C2×C42C2×D139semidirect
103. C2×D4C22×D139semidirect
109. C42C22×D139semidirect
125. C2×C4D4×D139semidirect
137. C4C2×D4×D139semidirect
141. C2#127×D139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1392
C2×#179848392
C2×#179848382
#127×D1392
C2×C42×D1392
C2×#127×C1392
C22×#127139