Finite Group Databasebeta

← C2×#23750368 #34058812

Subgroups — C2×#23750368 #34058812

Order 19072.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#23750368C2116yesmaximal, direct product factor
2C2×#18011898C213yesmaximal, complemented
3C2×#18011897C216yesmaximal, complemented
4C2×#18011880C212yesmaximal, complemented
5C2×#18011879C213yesmaximal, complemented
6C2×#120×C149C211yesmaximal, characteristic, complemented
7C24×D149C2211yescharacteristic, complemented
8C22×Dic298C2213yescomplemented
9C22×C22⋊D149C2216yes—
10#18011898C22124yescomplemented
11#18011897C22148yescomplemented
12#18011880C22116yescomplemented
13#18011879C22124yescomplemented
14C2×C22⋊Dic149C2213yescomplemented
15C2×C22⋊Dic149C2216yescomplemented
16C2×#14558713C2216yescomplemented
17C2×C4×Dic149C2213yescomplemented
18C25×C149C2211yescharacteristic, complemented
19C22×D4×C149C2213yes—
20#120×C149C2218yescomplemented
21C2×C22⋊C4×C149C2213yescomplemented
22C23×D149—46no—
23C23×D149C2312yes—
24C23×D149C2314yescomplemented
25C2×Dic298—46no—
26C2×Dic298C23112yescomplemented
27C2×C22⋊D149—412no—
28C2×C22⋊D149C23124yes—
29C22×Dic149C2316yes—
30C22⋊Dic149C23112yescomplemented
31C22⋊Dic149C23124yescomplemented
32#14558713C23124yescomplemented
33C4×Dic149C23112yescomplemented
34C24×C149—46no—
35C24×C149C2313yes—
36C24×C149C2311yescharacteristic
37C24×C149C2314yescomplemented
38C2×D4×C149—46no—
39C2×D4×C149C23112yes—
40C22×C4×C149C2313yes—
41C22⋊C4×C149C23112yescomplemented
42C22×D149—212no—
43C22×D149—412no—
44C22×D149—416no—
45C22×D149C2414yes—
46Dic298—412no—
47C22⋊D149—424no—
48C2×Dic149—212no—
49C2×Dic149C24112yes—
50C23×C149—212no—
51C23×C149—26no—
52C23×C149—26no—
53C23×C149—412no—
54C23×C149—416no—
55C23×C149C2416yes—
56C23×C149C2412yes—
57C23×C149C2411yescharacteristic
58D4×C149—412no—
59C2×C4×C149—26no—
60C2×C4×C149C2416yes—
61C22×C149—26no—
62C22×C149—26no—
63C22×C149—212no—
64C22×C149—416no—
65C22×C149—412no—
66C22×C149—44no—
67C22×C149H(5,𝔽2)16yes—
68C22×C149C2511yescharacteristic
69C2×D149—212no—
70C2×D149—416no—
71C2×D149—48no—
72C4×C149—26no—
73Dic149—212no—
74C2×C149—42no—
75C2×C149—46no—
76C2×C149H(3,𝔽4)14yescomplemented
77C2×C149C2×H(5,𝔽2)13yes—
78D149—44no—
79C149C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—1491nomaximal, Sylow
81H(3,𝔽4)—14916no—
82C2×#124—1493no—
83C2×#124—1496no—
84C2×#120—1492no—
85C2×#120—1493no—
86C2×#120D14911yescharacteristic, complemented
87C25—1491no—
88C25C2×D14911yescharacteristic, complemented
89C22×Q8—1493no—
90C22×D4—1496no—
91C22×D4C2×D14913yes—
92#124—14924no—
93#124—14948no—
94#120—14916no—
95#120—14924no—
96#120C2×D14918yescomplemented
97C2×C22⋊C4—1493no—
98C2×C22⋊C4—1496no—
99C2×C22⋊C4—1496no—
100C2×C22⋊C4C2×D14913yescomplemented
101C2×C42—1493no—
102C24—46no—
103C24—5966no—
104C24—1492no—
105C24—1494no—
106C24C22×D14911yescharacteristic
107C24C22×D14913yes—
108C24C22×D14914yescomplemented
109C2×Q8—5966no—
110C2×Q8—14912no—
111C2×D4—46no—
112C2×D4—59612no—
113C2×D4—14924no—
114C2×D4C22×D149112yes—
115C22×C4—1496no—
116C22×C4C22×D14913yes—
117C22⋊C4—14912no—
118C22⋊C4—14924no—
119C22⋊C4—14924no—
120C22⋊C4C22×D149112yescomplemented
121C42—14912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—29812no—
128C23—59612no—
129C23—59616no—
130C23—1494no—
131C23C23×D14912yes—
132C23C23×D14916yes—
133C23C23×D14911yescharacteristic
134Q8—59612no—
135D4—412no—
136D4—59624no—
137C2×C4—26no—
138C2×C4—29812no—
139C2×C4—14912no—
140C2×C4C23×D14916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—29812no—
148C22—59616no—
149C22—5968no—
150C22#1801195616yes—
151C22C24×D14911yescharacteristic
152C4—26no—
153C4—29812no—
154C2—46no—
155C2—42no—
156C2—5964no—
157C2#2375036814yesdirect product factor
158C2C2×#1801195613yes—
subgroupG/H
centerC23C23×D149
commutator, cosocleC22×C149C25
FrattiniC22C24×D149
FittingC2×#120×C149C2
socleC23×C149C24
hypercenterC2×#120D149
hypocenterC149C2×H(3,𝔽4)
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #23750368C2direct (N × H)
2. C2×#18011898C2semidirect
3. C2×#18011897C2semidirect
4. C2×#18011880C2semidirect
5. C2×#18011879C2semidirect
6. C2×#120×C149C2semidirect
7. C24×D149C22semidirect
8. C22×Dic298C22semidirect
10. #18011898C22semidirect
11. #18011897C22semidirect
12. #18011880C22semidirect
13. #18011879C22semidirect
14. C2×C22⋊Dic149C22semidirect
15. C2×C22⋊Dic149C22semidirect
16. C2×#14558713C22semidirect
17. C2×C4×Dic149C22semidirect
18. C25×C149C22semidirect
20. #120×C149C22semidirect
21. C2×C22⋊C4×C149C22semidirect
24. C23×D149C23semidirect
26. C2×Dic298C23semidirect
30. C22⋊Dic149C23semidirect
31. C22⋊Dic149C23semidirect
32. #14558713C23semidirect
33. C4×Dic149C23semidirect
37. C24×C149C23semidirect
41. C22⋊C4×C149C23semidirect
76. C2×C149H(3,𝔽4)semidirect
79. C149C2×H(3,𝔽4)semidirect
86. C2×#120D149semidirect
88. C25C2×D149semidirect
96. #120C2×D149semidirect
100. C2×C22⋊C4C2×D149semidirect
108. C24C22×D149semidirect
120. C22⋊C4C22×D149semidirect
157. C2#23750368direct (N × H)

Maximal subgroups

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

subgroupindex
#237503682
C2×#180118982
C2×#180118972
C2×#180118802
C2×#180118792
C2×#120×C1492
C2×H(3,𝔽4)149