Finite Group Databasebeta

← C2×#19152403 #26035005

Subgroups — C2×#19152403 #26035005

Order 11392.

1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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×#15668058C212yesmaximal, complemented
2#19152403C2116yesmaximal, direct product factor
3C2×#15668040C216yesmaximal, complemented
4C2×#15668034C213yesmaximal, complemented
5C22×D712C213yesmaximal, complemented
6C2×#131×C89C211yesmaximal, characteristic, complemented
7#15668058—28no—
8#15668058C22116yescomplemented
9C2×#13083575—22no—
10C2×#13083574C2216yescomplemented
11C22×D356C2216yescomplemented
12C2×D4×D89—26no—
13#15668040C22148yescomplemented
14#15668034C22124yescomplemented
15C2×Dic356C2211yescharacteristic, complemented
16C2×#13083563C2216yescomplemented
17C2×D712C2216yescomplemented
18C2×D712C2213yescomplemented
19C2×D712C22124yescomplemented
20C2×#41×C89C2211yescharacteristic
21#131×C89C2218yescomplemented
22C2×M16×C89C2213yescomplemented
23C22×C8×C89C2213yescomplemented
24C23×D89—26no—
25#13083575—216no—
26#13083574—212no—
27#13083574C23124yescomplemented
28C2×Dic178C2312yes—
29C2×D356—26no—
30C2×D356—212no—
31C2×D356C2316yes—
32C2×D356C23124yescomplemented
33C2×C22⋊D89—26no—
34D4×D89—248no—
35C2×C4×D89—26no—
36Dic356C2314yescomplemented
37#13083563C23124yescomplemented
38D712C23112yescomplemented
39D712C23124yescomplemented
40#41×C89D414yes—
41#41×C89C2314yes—
42C2×Q8×C89D411yescharacteristic
43C2×D4×C89D413yes—
44C22×C4×C89C2313yes—
45M16×C89C23112yescomplemented
46C2×C8×C89C2311yescharacteristic
47C2×C8×C89C2313yes—
48C2×C8×C89C23112yescomplemented
49C23×C89C2×D413yes—
50C22×D89—26no—
51C22×D89—224no—
52C22×D89—812no—
53Q8×C89C2×D414yes—
54D4×C89C2×D4112yes—
55C2×C4×C89C2×D413yes—
56C2×C4×C89C2×D416yes—
57C2×C4×C89C2411yescharacteristic
58C2×C4×C89C2416yes—
59C22⋊D89—224no—
60C2×Dic89—22no—
61D356—224no—
62D356—26no—
63D356C24112yes—
64C4×D89—224no—
65Dic178—22no—
66Dic178C2414yes—
67C8×C89C2412yes—
68C8×C89C2416yes—
69C22×C89—26no—
70C22×C89C22×D416yes—
71C22×C89C22×D411yescharacteristic
72C2×D89—212no—
73C2×D89—412no—
74C2×D89—824no—
75C4×C89C22×D411yescharacteristic
76C4×C89C22×D416yes—
77C4×C89C2511yescharacteristic
78Dic89—24no—
79C2×C89—26no—
80C2×C89#57612yescomplemented
81C2×C89C23×D411yescharacteristic
82D89—412no—
83C2×#576—891nomaximal, Sylow
84C89C2×#57611yescharacteristic, complemented, Sylow
85C2×H(5,𝔽2)—892no—
86#576—8916no—
87C2×AGL(1,ℤ/8)—896no—
88C2×#135—893no—
89C22×D8—893no—
90C2×#131D8911yescharacteristic, complemented
91H(5,𝔽2)—8916no—
92H(5,𝔽2)—1788no—
93C2×#41—896no—
94C2×#41—1782no—
95C2×#41C2×D8911yescharacteristic
96C22×D4—896no—
97C22×D4—1786no—
98AGL(1,ℤ/8)—8948no—
99#135—8924no—
100C2×Q16—891no—
101C2×SD16—896no—
102C2×D8—893no—
103C2×D8—896no—
104C2×D8—8924no—
105#131C2×D8918yescomplemented
106C2×M16C2×D8913yescomplemented
107C22×C8C2×D8913yescomplemented
108C24—1786no—
109#41—8924no—
110#41—17816no—
111#41—17812no—
112#41D35614yes—
113#41C22×D8914yes—
114C2×Q8—892no—
115C2×Q8D35611yescharacteristic
116C2×D4—896no—
117C2×D4—8924no—
118C2×D4—1786no—
119C2×D4—17848no—
120C2×D4—1786no—
121C2×D4—17812no—
122C2×D4D35613yes—
123C22×C4—1786no—
124C22×C4C22×D8913yes—
125Q16—894no—
126SD16—8924no—
127D8—8912no—
128D8—8924no—
129M16C22×D89112yescomplemented
130C2×C8C22×D8911yescharacteristic
131C2×C8C22×D8913yes—
132C2×C8C22×D89112yescomplemented
133C23—1786no—
134C23—17824no—
135C23—71212no—
136C23C2×D35613yes—
137Q8—894no—
138Q8—1782no—
139Q8C2×D35614yes—
140D4—8912no—
141D4—17824no—
142D4—17824no—
143D4—1786no—
144D4C2×D356112yes—
145C2×C4—1782no—
146C2×C4—17824no—
147C2×C4C2×D35616yes—
148C2×C4C2×D35613yes—
149C2×C4C23×D8916yes—
150C2×C4C23×D8911yescharacteristic
151C8C23×D8912yes—
152C8C23×D8916yes—
153C22—26no—
154C22—35612no—
155C22—17812no—
156C22—71224no—
157C22C22×D35616yes—
158C22C22×D35611yescharacteristic
159C4—1784no—
160C4C22×D35616yes—
161C4C22×D35611yescharacteristic
162C4C24×D8911yescharacteristic
163C2—26no—
164C2—35612no—
165C2#1915240312yesdirect product factor
166C2C23×D35611yescharacteristic
subgroupG/H
centerC22C22×D356
commutator, cosocleC4×C89C25
FrattiniC4C24×D89
FittingC2×#131×C89C2
socleC22×C89C22×D4
hypercenterC2×#131D89
hypocenterC89C2×#576
LCSG ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#15668058C2semidirect
2. #19152403C2direct (N × H)
3. C2×#15668040C2semidirect
4. C2×#15668034C2semidirect
5. C22×D712C2semidirect
6. C2×#131×C89C2semidirect
8. #15668058C22semidirect
10. C2×#13083574C22semidirect
11. C22×D356C22semidirect
13. #15668040C22semidirect
14. #15668034C22semidirect
15. C2×Dic356C22semidirect
16. C2×#13083563C22semidirect
17. C2×D712C22semidirect
18. C2×D712C22semidirect
19. C2×D712C22semidirect
21. #131×C89C22semidirect
22. C2×M16×C89C22semidirect
23. C22×C8×C89C22semidirect
27. #13083574C23semidirect
32. C2×D356C23semidirect
36. Dic356C23semidirect
37. #13083563C23semidirect
38. D712C23semidirect
39. D712C23semidirect
45. M16×C89C23semidirect
48. C2×C8×C89C23semidirect
80. C2×C89#576semidirect
84. C89C2×#576semidirect
90. C2×#131D89semidirect
105. #131C2×D89semidirect
106. C2×M16C2×D89semidirect
107. C22×C8C2×D89semidirect
129. M16C22×D89semidirect
132. C2×C8C22×D89semidirect
165. C2#19152403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156680582
#191524032
C2×#156680402
C2×#156680342
C22×D7122
C2×#131×C892
C2×#57689