Finite Group Databasebeta

← C2×#127×D19 #14576905

Subgroups — C2×#127×D19 #14576905

Order 2432.

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×D19C216yesmaximal, complemented
2C2×#10597320C211yesmaximal, characteristic, complemented
3C2×#10597386C216yesmaximal, complemented
4#127×D19C2116yesmaximal, direct product factor
5C2×C42×D19C211yesmaximal, characteristic, complemented
6C2×C19×#127C211yesmaximal, characteristic, complemented
7C24×D19C2214yes—
8C22×D4×C19C2216yescomplemented
9C22×C22⋊D19C22112yescomplemented
10C2×D4×D19—248no—
11C2×D4×D19C22148yescomplemented
12C22×D76C2216yescomplemented
13C22×C4×D19C2213yes—
14C19×#127C2218yescomplemented
15C2×C42×C19C2211yescharacteristic, complemented
16#10597386C22148yescomplemented
17C2×C4×Dic19C2213yescomplemented
18#10597320C2218yescomplemented
19C42×D19C2218yescomplemented
20C24×C19C2314yes—
21C23×D19—248no—
22C23×D19C2314yes—
23C23×D19C23116yes—
24C23×D19C2311yescharacteristic
25C2×D4×C19—224no—
26C2×D4×C19C23124yescomplemented
27C22×C4×C19C2313yes—
28C2×C22⋊D19—248no—
29C2×C22⋊D19C23148yescomplemented
30C22×Dic19C2313yes—
31D4×D19—2192no—
32C2×D76—224no—
33C2×D76C23124yescomplemented
34C2×C4×D19D4124yescomplemented
35C2×C4×D19C23112yes—
36C42×C19C2314yescomplemented
37C4×Dic19C23112yescomplemented
38C23×C19—224no—
39C23×C19C2418yes—
40C23×C19C2411yescharacteristic
41C22×D19—224no—
42C22×D19—296no—
43C22×D19—464no—
44C22×D19C2×D4112yes—
45C22×D19C2418yes—
46C22×D19C2412yes—
47D4×C19—248no—
48C2×C4×C19C2×D4112yescomplemented
49C2×C4×C19C2416yes—
50C22⋊D19—296no—
51C2×Dic19C2×D4112yescomplemented
52C2×Dic19C2416yes—
53D76—248no—
54C4×D19C2×D4148yescomplemented
55C22×#127—191nomaximal, Sylow
56C22×C19—224no—
57C22×C19—416no—
58C22×C19C22×D416yes—
59C22×C19C2511yescharacteristic
60C2×D19—224no—
61C2×D19—416no—
62C2×D19—464no—
63C2×D19#127116yesdirect product factor
64C2×D19C22×D4112yes—
65C4×C19C22×D4112yescomplemented
66Dic19C22×D4112yescomplemented
67C23×D4—196no—
68C2×#127—196no—
69C2×#127—1916no—
70C2×#127—191no—
71C2×#127D1911yescharacteristic, direct product factor
72C22×C42—191no—
73C2×C19—48no—
74C2×C19C2×#12714yescomplemented
75C2×C19C23×D413yes—
76D19—48no—
77D19C2×#12718yesdirect product factor
78C25—194no—
79C22×D4—1912no—
80C22×D4—1948no—
81C22×D4—196no—
82C22×D4—3848no—
83C22×D4C2×D1916yescomplemented
84C23×C4—193no—
85#127—1948no—
86#127—198no—
87#127C2×D1918yesdirect product factor
88C2×C42—193no—
89C2×C42—198no—
90C2×C42C2×D1911yescharacteristic, complemented
91C19C22×#12711yescharacteristic, complemented, Sylow
92C24—191no—
93C24—1916no—
94C24—194no—
95C24—3848no—
96C24C22×D1914yes—
97C2×D4—224no—
98C2×D4—1948no—
99C2×D4—1924no—
100C2×D4—38192no—
101C2×D4—3848no—
102C2×D4—3824no—
103C2×D4C22×D19124yescomplemented
104C22×C4—193no—
105C22×C4—1924no—
106C22×C4—1912no—
107C22×C4C22×D1913yes—
108C42—1912no—
109C42C22×D1914yescomplemented
110C23—224no—
111C23—1912no—
112C23—192no—
113C23—198no—
114C23—3896no—
115C23—3824no—
116C23—7664no—
117C23C23×D1918yes—
118C23C23×D1911yescharacteristic
119D4—248no—
120D4—3896no—
121D4—3848no—
122C2×C4—1912no—
123C2×C4—196no—
124C2×C4—1948no—
125C2×C4D4×D19112yescomplemented
126C2×C4C23×D1916yes—
127C22—224no—
128C22—416no—
129C22—1916no—
130C22—1912no—
131C22—3824no—
132C22—7664no—
133C22—7616no—
134C22C2×D4×D1916yes—
135C22C24×D1911yescharacteristic
136C4—1912no—
137C4C2×D4×D19112yescomplemented
138C2—48no—
139C2—198no—
140C2—768no—
141C2#127×D1914yesdirect product factor
142C2C22×D4×D1913yes—
subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C19×#127C2
socleC23×C19C24
hypercenterC2×#127D19
hypocenterC19C22×#127
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D19C2semidirect
2. C2×#10597320C2semidirect
3. C2×#10597386C2semidirect
4. #127×D19C2direct (N × H)
5. C2×C42×D19C2semidirect
6. C2×C19×#127C2semidirect
8. C22×D4×C19C22semidirect
9. C22×C22⋊D19C22semidirect
11. C2×D4×D19C22semidirect
12. C22×D76C22semidirect
14. C19×#127C22semidirect
15. C2×C42×C19C22semidirect
16. #10597386C22semidirect
17. C2×C4×Dic19C22semidirect
18. #10597320C22semidirect
19. C42×D19C22semidirect
26. C2×D4×C19C23semidirect
29. C2×C22⋊D19C23semidirect
33. C2×D76C23semidirect
34. C2×C4×D19D4semidirect
36. C42×C19C23semidirect
37. C4×Dic19C23semidirect
48. C2×C4×C19C2×D4semidirect
51. C2×Dic19C2×D4semidirect
54. C4×D19C2×D4semidirect
63. C2×D19#127direct (N × H)
65. C4×C19C22×D4semidirect
66. Dic19C22×D4semidirect
71. C2×#127D19direct (N × H)
74. C2×C19C2×#127semidirect
77. D19C2×#127direct (N × H)
83. C22×D4C2×D19semidirect
87. #127C2×D19direct (N × H)
90. C2×C42C2×D19semidirect
91. C19C22×#127semidirect
103. C2×D4C22×D19semidirect
109. C42C22×D19semidirect
125. C2×C4D4×D19semidirect
137. C4C2×D4×D19semidirect
141. C2#127×D19direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D192
C2×#105973202
C2×#105973862
#127×D192
C2×C42×D192
C2×C19×#1272
C22×#12719