Finite Group Databasebeta

← C2×#126×D149 #34057945

Subgroups — C2×#126×D149 #34057945

Order 19072.

1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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
1C2×#18011906C213yesmaximal, complemented
2C2×#18011905C211yesmaximal, characteristic, complemented
3C2×#18011904C213yesmaximal, complemented
4#126×D149C2116yesmaximal, direct product factor
5C2×C4⋊C4×D149C213yesmaximal, complemented
6C2×C22⋊C4×D149C213yesmaximal
7C2×C42×D149C211yesmaximal, characteristic, complemented
8C2×#126×C149C211yesmaximal, characteristic, complemented
9C24×D149C2211yescharacteristic
10C22×C4×D149C2213yes—
11C22×C4×D149C2213yes—
12#18011906C22124yescomplemented
13#18011905C2218yescomplemented
14#18011904C22124yescomplemented
15C2×C4⋊Dic149C2213yescomplemented
16C2×#14558715C2213yescomplemented
17C2×#14558715C2213yescomplemented
18C4⋊C4×D149C22124yescomplemented
19C2×C22⋊Dic149C2213yes—
20C2×#14558713C2213yes—
21C2×#14558713C2213yes—
22C22⋊C4×D149C22124yes—
23C2×C4×Dic149C2213yescomplemented
24C42×D149C2218yescomplemented
25#126×C149C2218yescomplemented
26C2×C4⋊C4×C149C2213yescomplemented
27C2×C22⋊C4×C149C2213yes—
28C2×C42×C149C2211yescharacteristic, complemented
29C23×D149—212no—
30C23×D149C2314yes—
31C23×D149C2311yescharacteristic
32C23×D149C2311yescharacteristic
33C22×Dic149C2313yes—
34C22×Dic149C2313yes—
35C2×C4×D149—212no—
36C2×C4×D149—212no—
37C2×C4×D149C23112yes—
38C2×C4×D149C23112yes—
39C4⋊Dic149C23112yescomplemented
40#14558715C23112yescomplemented
41#14558715C23112yescomplemented
42C22⋊Dic149C23112yes—
43#14558713C23112yes—
44#14558713C23112yes—
45C4×Dic149C23112yescomplemented
46C24×C149C2311yescharacteristic
47C22×C4×C149C2313yes—
48C22×C4×C149C2313yes—
49C4⋊C4×C149C23112yescomplemented
50C22⋊C4×C149C23112yes—
51C42×C149C2314yescomplemented
52C22×D149—26no—
53C22×D149—224no—
54C22×D149—416no—
55C22×D149#41112yes—
56C22×D149C2412yes—
57C22×D149C2412yes—
58C2×Dic149—26no—
59C2×Dic149—26no—
60C2×Dic149C2416yes—
61C2×Dic149C2416yes—
62C4×D149—224no—
63C4×D149—224no—
64C23×C149—26no—
65C23×C149C2412yes—
66C23×C149C2411yescharacteristic
67C2×C4×C149—26no—
68C2×C4×C149—26no—
69C2×C4×C149C2416yes—
70C2×C4×C149C2416yes—
71C22×C149—26no—
72C22×C149—44no—
73C22×C149C2×#4116yes—
74C22×C149C2511yescharacteristic
75C2×D149—26no—
76C2×D149—44no—
77C2×D149—416no—
78C2×D149#126116yesdirect product factor
79C2×D149C2×#41112yes—
80C4×C149—26no—
81C4×C149—26no—
82Dic149—26no—
83Dic149—26no—
84C2×C149—42no—
85C2×C149C2×#12614yescomplemented
86C2×C149C22×#4113yes—
87D149—42no—
88D149C2×#12618yesdirect product factor
89C149C22×#12611yescharacteristic, complemented, Sylow
90C22×#126—1491nomaximal, Sylow
91C2×#126—14916no—
92C2×#126—1493no—
93C2×#126—1493no—
94C2×#126—1491no—
95C2×#126D14911yescharacteristic, direct product factor
96C22×C4⋊C4—1493no—
97C22×C22⋊C4—1493no—
98C22×C42—1491no—
99C25—1491no—
100C23×C4—1493no—
101C23×C4—1493no—
102#126—14924no—
103#126—14924no—
104#126—1498no—
105#126C2×D14918yesdirect product factor
106C2×C4⋊C4—1493no—
107C2×C4⋊C4—1493no—
108C2×C4⋊C4—1493no—
109C2×C4⋊C4—14924no—
110C2×C4⋊C4C2×D14913yescomplemented
111C2×C22⋊C4—1493no—
112C2×C22⋊C4—1493no—
113C2×C22⋊C4—1493no—
114C2×C22⋊C4—14924no—
115C2×C22⋊C4C2×D14913yes—
116C2×C42—1493no—
117C2×C42—1498no—
118C2×C42C2×D14911yescharacteristic, complemented
119C24—29812no—
120C24—1494no—
121C24—1491no—
122C24—1491no—
123C24C22×D14911yescharacteristic
124C22×C4—29812no—
125C22×C4—29812no—
126C22×C4—1493no—
127C22×C4—1493no—
128C22×C4—14912no—
129C22×C4—14912no—
130C22×C4C22×D14913yes—
131C22×C4C22×D14913yes—
132C4⋊C4—14912no—
133C4⋊C4—14912no—
134C4⋊C4—14912no—
135C4⋊C4C22×D149112yescomplemented
136C22⋊C4—14912no—
137C22⋊C4—14912no—
138C22⋊C4—14912no—
139C22⋊C4C22×D149112yes—
140C42—14912no—
141C42C22×D14914yescomplemented
142C23—26no—
143C23—29824no—
144C23—2986no—
145C23—59616no—
146C23—1492no—
147C23—14912no—
148C23—1492no—
149C23C23×D14912yes—
150C23C23×D14911yescharacteristic
151C2×C4—26no—
152C2×C4—26no—
153C2×C4—29824no—
154C2×C4—29824no—
155C2×C4—2986no—
156C2×C4—2986no—
157C2×C4—1496no—
158C2×C4—1496no—
159C2×C4C23×D14916yes—
160C2×C4C23×D14916yes—
161C22—26no—
162C22—44no—
163C22—2986no—
164C22—59616no—
165C22—5964no—
166C22—14916no—
167C22—14912no—
168C22#41×D14916yes—
169C22C24×D14911yescharacteristic
170C4—26no—
171C4—26no—
172C4—2986no—
173C4—2986no—
174C2—42no—
175C2—5962no—
176C2—1498no—
177C2#126×D14914yesdirect product factor
178C2C2×#41×D14913yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#126×C149C2
socleC23×C149C24
prime radicalC24×D149C22
hypercenterC2×#126D149
hypocenterC149C22×#126
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#18011906C2semidirect
2. C2×#18011905C2semidirect
3. C2×#18011904C2semidirect
4. #126×D149C2direct (N × H)
5. C2×C4⋊C4×D149C2semidirect
7. C2×C42×D149C2semidirect
8. C2×#126×C149C2semidirect
12. #18011906C22semidirect
13. #18011905C22semidirect
14. #18011904C22semidirect
15. C2×C4⋊Dic149C22semidirect
16. C2×#14558715C22semidirect
17. C2×#14558715C22semidirect
18. C4⋊C4×D149C22semidirect
23. C2×C4×Dic149C22semidirect
24. C42×D149C22semidirect
25. #126×C149C22semidirect
26. C2×C4⋊C4×C149C22semidirect
28. C2×C42×C149C22semidirect
39. C4⋊Dic149C23semidirect
40. #14558715C23semidirect
41. #14558715C23semidirect
45. C4×Dic149C23semidirect
49. C4⋊C4×C149C23semidirect
51. C42×C149C23semidirect
78. C2×D149#126direct (N × H)
85. C2×C149C2×#126semidirect
88. D149C2×#126direct (N × H)
89. C149C22×#126semidirect
95. C2×#126D149direct (N × H)
105. #126C2×D149direct (N × H)
110. C2×C4⋊C4C2×D149semidirect
118. C2×C42C2×D149semidirect
135. C4⋊C4C22×D149semidirect
141. C42C22×D149semidirect
177. C2#126×D149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119062
C2×#180119052
C2×#180119042
#126×D1492
C2×C4⋊C4×D1492
C2×C22⋊C4×D1492
C2×C42×D1492
C2×#126×C1492
C22×#126149