Finite Group Databasebeta

← C2×#127×D149 #34057961

Subgroups — C2×#127×D149 #34057961

Order 19072.

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×D149C216yesmaximal, complemented
2C2×#18011908C211yesmaximal, characteristic, complemented
3C2×#18011907C216yesmaximal, complemented
4#127×D149C2116yesmaximal, direct product factor
5C2×C42×D149C211yesmaximal, characteristic, complemented
6C2×#127×C149C211yesmaximal, characteristic, complemented
7C24×D149C2214yes—
8C22×D596C2216yescomplemented
9C22×C22⋊D149C22112yescomplemented
10C2×D4×D149—248no—
11C2×D4×D149C22148yescomplemented
12C22×C4×D149C2213yes—
13#18011908C2218yescomplemented
14#18011907C22148yescomplemented
15C2×C4×Dic149C2213yescomplemented
16C42×D149C2218yescomplemented
17C22×D4×C149C2216yescomplemented
18#127×C149C2218yescomplemented
19C2×C42×C149C2211yescharacteristic, complemented
20C23×D149—248no—
21C23×D149C23116yes—
22C23×D149C2314yes—
23C23×D149C2311yescharacteristic
24C2×D596—224no—
25C2×D596C23124yescomplemented
26C2×C22⋊D149—248no—
27C2×C22⋊D149C23148yescomplemented
28D4×D149—2192no—
29C22×Dic149C2313yes—
30C2×C4×D149D4124yescomplemented
31C2×C4×D149C23112yes—
32C4×Dic149C23112yescomplemented
33C24×C149C2314yes—
34C2×D4×C149—224no—
35C2×D4×C149C23124yescomplemented
36C22×C4×C149C2313yes—
37C42×C149C2314yescomplemented
38C22×D149—224no—
39C22×D149—296no—
40C22×D149—464no—
41C22×D149C2×D4112yes—
42C22×D149C2418yes—
43C22×D149C2412yes—
44D596—248no—
45C22⋊D149—296no—
46C2×Dic149C2×D4112yescomplemented
47C2×Dic149C2416yes—
48C4×D149C2×D4148yescomplemented
49C23×C149—224no—
50C23×C149C2418yes—
51C23×C149C2411yescharacteristic
52D4×C149—248no—
53C2×C4×C149C2×D4112yescomplemented
54C2×C4×C149C2416yes—
55C22×C149—224no—
56C22×C149—416no—
57C22×C149C22×D416yes—
58C22×C149C2511yescharacteristic
59C2×D149—224no—
60C2×D149—416no—
61C2×D149—464no—
62C2×D149#127116yesdirect product factor
63C2×D149C22×D4112yes—
64C4×C149C22×D4112yescomplemented
65Dic149C22×D4112yescomplemented
66C2×C149—48no—
67C2×C149C2×#12714yescomplemented
68C2×C149C23×D413yes—
69D149—48no—
70D149C2×#12718yesdirect product factor
71C149C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—1491nomaximal, Sylow
73C23×D4—1496no—
74C2×#127—1496no—
75C2×#127—14916no—
76C2×#127—1491no—
77C2×#127D14911yescharacteristic, direct product factor
78C22×C42—1491no—
79C25—1494no—
80C22×D4—29848no—
81C22×D4—14912no—
82C22×D4—14948no—
83C22×D4—1496no—
84C22×D4C2×D14916yescomplemented
85C23×C4—1493no—
86#127—14948no—
87#127—1498no—
88#127C2×D14918yesdirect product factor
89C2×C42—1493no—
90C2×C42—1498no—
91C2×C42C2×D14911yescharacteristic, complemented
92C24—29848no—
93C24—14916no—
94C24—1494no—
95C24—1491no—
96C24C22×D14914yes—
97C2×D4—224no—
98C2×D4—298192no—
99C2×D4—29848no—
100C2×D4—29824no—
101C2×D4—14948no—
102C2×D4—14924no—
103C2×D4C22×D149124yescomplemented
104C22×C4—1493no—
105C22×C4—14924no—
106C22×C4—14912no—
107C22×C4C22×D14913yes—
108C42—14912no—
109C42C22×D14914yescomplemented
110C23—224no—
111C23—29896no—
112C23—29824no—
113C23—59664no—
114C23—1498no—
115C23—14912no—
116C23—1492no—
117C23C23×D14918yes—
118C23C23×D14911yescharacteristic
119D4—248no—
120D4—29896no—
121D4—29848no—
122C2×C4—14912no—
123C2×C4—1496no—
124C2×C4—14948no—
125C2×C4D4×D149112yescomplemented
126C2×C4C23×D14916yes—
127C22—224no—
128C22—416no—
129C22—29824no—
130C22—59664no—
131C22—59616no—
132C22—14916no—
133C22—14912no—
134C22C2×D4×D14916yes—
135C22C24×D14911yescharacteristic
136C4—14912no—
137C4C2×D4×D149112yescomplemented
138C2—48no—
139C2—5968no—
140C2—1498no—
141C2#127×D14914yesdirect product factor
142C2C22×D4×D14913yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#127×C149C2
socleC23×C149C24
hypercenterC2×#127D149
hypocenterC149C22×#127
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D149C2semidirect
2. C2×#18011908C2semidirect
3. C2×#18011907C2semidirect
4. #127×D149C2direct (N × H)
5. C2×C42×D149C2semidirect
6. C2×#127×C149C2semidirect
8. C22×D596C22semidirect
9. C22×C22⋊D149C22semidirect
11. C2×D4×D149C22semidirect
13. #18011908C22semidirect
14. #18011907C22semidirect
15. C2×C4×Dic149C22semidirect
16. C42×D149C22semidirect
17. C22×D4×C149C22semidirect
18. #127×C149C22semidirect
19. C2×C42×C149C22semidirect
25. C2×D596C23semidirect
27. C2×C22⋊D149C23semidirect
30. C2×C4×D149D4semidirect
32. C4×Dic149C23semidirect
35. C2×D4×C149C23semidirect
37. C42×C149C23semidirect
46. C2×Dic149C2×D4semidirect
48. C4×D149C2×D4semidirect
53. C2×C4×C149C2×D4semidirect
62. C2×D149#127direct (N × H)
64. C4×C149C22×D4semidirect
65. Dic149C22×D4semidirect
67. C2×C149C2×#127semidirect
70. D149C2×#127direct (N × H)
71. C149C22×#127semidirect
77. C2×#127D149direct (N × H)
84. C22×D4C2×D149semidirect
88. #127C2×D149direct (N × H)
91. C2×C42C2×D149semidirect
103. C2×D4C22×D149semidirect
109. C42C22×D149semidirect
125. C2×C4D4×D149semidirect
137. C4C2×D4×D149semidirect
141. C2#127×D149direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1492
C2×#180119082
C2×#180119072
#127×D1492
C2×C42×D1492
C2×#127×C1492
C22×#127149