Finite Group Databasebeta

← C2×#31771410 #46825638

Subgroups — C2×#31771410 #46825638

Order 34432.

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×#22575499C212yesmaximal, complemented
2#31771410C2116yesmaximal, direct product factor
3C2×#22575481C216yesmaximal, complemented
4C2×#22575475C213yesmaximal, complemented
5C22×D2152C213yesmaximal, complemented
6C2×#131×C269C211yesmaximal, characteristic, complemented
7#22575499—28no—
8#22575499C22116yescomplemented
9C2×#16864403—22no—
10C2×#16864402C2216yescomplemented
11C22×D1076C2216yescomplemented
12C2×D4×D269—26no—
13#22575481C22148yescomplemented
14#22575475C22124yescomplemented
15C2×Dic1076C2211yescharacteristic, complemented
16C2×#16864391C2216yescomplemented
17C2×D2152C2216yescomplemented
18C2×D2152C2213yescomplemented
19C2×D2152C22124yescomplemented
20C2×#41×C269C2211yescharacteristic
21#131×C269C2218yescomplemented
22C2×M16×C269C2213yescomplemented
23C22×C8×C269C2213yescomplemented
24C23×D269—26no—
25#16864403—216no—
26#16864402—212no—
27#16864402C23124yescomplemented
28C2×Dic538C2312yes—
29C2×D1076—26no—
30C2×D1076—212no—
31C2×D1076C2316yes—
32C2×D1076C23124yescomplemented
33C2×C22⋊D269—26no—
34D4×D269—248no—
35C2×C4×D269—26no—
36Dic1076C2314yescomplemented
37#16864391C23124yescomplemented
38D2152C23112yescomplemented
39D2152C23124yescomplemented
40#41×C269D414yes—
41#41×C269C2314yes—
42C2×Q8×C269D411yescharacteristic
43C2×D4×C269D413yes—
44C22×C4×C269C2313yes—
45M16×C269C23112yescomplemented
46C2×C8×C269C2311yescharacteristic
47C2×C8×C269C2313yes—
48C2×C8×C269C23112yescomplemented
49C22×D269—26no—
50C22×D269—224no—
51C22×D269—812no—
52Dic538—22no—
53Dic538C2414yes—
54D1076—224no—
55D1076—26no—
56D1076C24112yes—
57C22⋊D269—224no—
58C2×Dic269—22no—
59C4×D269—224no—
60C23×C269C2×D413yes—
61Q8×C269C2×D414yes—
62D4×C269C2×D4112yes—
63C2×C4×C269C2×D413yes—
64C2×C4×C269C2×D416yes—
65C2×C4×C269C2411yescharacteristic
66C2×C4×C269C2416yes—
67C8×C269C2412yes—
68C8×C269C2416yes—
69C22×C269—26no—
70C22×C269C22×D416yes—
71C22×C269C22×D411yescharacteristic
72C2×D269—212no—
73C2×D269—412no—
74C2×D269—824no—
75C4×C269C22×D411yescharacteristic
76C4×C269C22×D416yes—
77C4×C269C2511yescharacteristic
78Dic269—24no—
79C2×C269—26no—
80C2×C269#57612yescomplemented
81C2×C269C23×D411yescharacteristic
82D269—412no—
83C269C2×#57611yescharacteristic, complemented, Sylow
84C2×#576—2691nomaximal, Sylow
85C2×H(5,𝔽2)—2692no—
86#576—26916no—
87C2×AGL(1,ℤ/8)—2696no—
88C2×#135—2693no—
89C22×D8—2693no—
90C2×#131D26911yescharacteristic, complemented
91H(5,𝔽2)—26916no—
92H(5,𝔽2)—5388no—
93C2×#41—2696no—
94C2×#41—5382no—
95C2×#41C2×D26911yescharacteristic
96C22×D4—2696no—
97C22×D4—5386no—
98AGL(1,ℤ/8)—26948no—
99#135—26924no—
100C2×Q16—2691no—
101C2×SD16—2696no—
102C2×D8—2693no—
103C2×D8—2696no—
104C2×D8—26924no—
105#131C2×D26918yescomplemented
106C2×M16C2×D26913yescomplemented
107C22×C8C2×D26913yescomplemented
108C24—5386no—
109#41—26924no—
110#41—53816no—
111#41—53812no—
112#41D107614yes—
113#41C22×D26914yes—
114C2×Q8—2692no—
115C2×Q8D107611yescharacteristic
116C2×D4—2696no—
117C2×D4—26924no—
118C2×D4—5386no—
119C2×D4—53848no—
120C2×D4—5386no—
121C2×D4—53812no—
122C2×D4D107613yes—
123C22×C4—5386no—
124C22×C4C22×D26913yes—
125Q16—2694no—
126SD16—26924no—
127D8—26912no—
128D8—26924no—
129M16C22×D269112yescomplemented
130C2×C8C22×D26911yescharacteristic
131C2×C8C22×D26913yes—
132C2×C8C22×D269112yescomplemented
133C23—5386no—
134C23—53824no—
135C23—215212no—
136C23C2×D107613yes—
137Q8—2694no—
138Q8—5382no—
139Q8C2×D107614yes—
140D4—26912no—
141D4—53824no—
142D4—53824no—
143D4—5386no—
144D4C2×D1076112yes—
145C2×C4—5382no—
146C2×C4—53824no—
147C2×C4C2×D107616yes—
148C2×C4C2×D107613yes—
149C2×C4C23×D26916yes—
150C2×C4C23×D26911yescharacteristic
151C8C23×D26912yes—
152C8C23×D26916yes—
153C22—26no—
154C22—53812no—
155C22—107612no—
156C22—215224no—
157C22C22×D107616yes—
158C22C22×D107611yescharacteristic
159C4—5384no—
160C4C22×D107616yes—
161C4C22×D107611yescharacteristic
162C4C24×D26911yescharacteristic
163C2—26no—
164C2—107612no—
165C2#3177141012yesdirect product factor
166C2C23×D107611yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC2×#131×C269C2
socleC22×C269C22×D4
hypercenterC2×#131D269
hypocenterC269C2×#576
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#22575499C2semidirect
2. #31771410C2direct (N × H)
3. C2×#22575481C2semidirect
4. C2×#22575475C2semidirect
5. C22×D2152C2semidirect
6. C2×#131×C269C2semidirect
8. #22575499C22semidirect
10. C2×#16864402C22semidirect
11. C22×D1076C22semidirect
13. #22575481C22semidirect
14. #22575475C22semidirect
15. C2×Dic1076C22semidirect
16. C2×#16864391C22semidirect
17. C2×D2152C22semidirect
18. C2×D2152C22semidirect
19. C2×D2152C22semidirect
21. #131×C269C22semidirect
22. C2×M16×C269C22semidirect
23. C22×C8×C269C22semidirect
27. #16864402C23semidirect
32. C2×D1076C23semidirect
36. Dic1076C23semidirect
37. #16864391C23semidirect
38. D2152C23semidirect
39. D2152C23semidirect
45. M16×C269C23semidirect
48. C2×C8×C269C23semidirect
80. C2×C269#576semidirect
83. C269C2×#576semidirect
90. C2×#131D269semidirect
105. #131C2×D269semidirect
106. C2×M16C2×D269semidirect
107. C22×C8C2×D269semidirect
129. M16C22×D269semidirect
132. C2×C8C22×D269semidirect
165. C2#31771410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225754992
#317714102
C2×#225754812
C2×#225754752
C22×D21522
C2×#131×C2692
C2×#576269