Finite Group Databasebeta

← C2×#31771348 #46825006

Subgroups — C2×#31771348 #46825006

Order 34432.

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#31771348C2116yesmaximal, direct product factor
2C2×#22575440C213yesmaximal, complemented
3C2×#22575439C216yesmaximal, complemented
4C2×#22575422C212yesmaximal, complemented
5C2×#22575421C213yesmaximal, complemented
6C2×#120×C269C211yesmaximal, characteristic, complemented
7C24×D269C2211yescharacteristic, complemented
8C22×Dic538C2213yescomplemented
9C22×C22⋊D269C2216yes—
10#22575440C22124yescomplemented
11#22575439C22148yescomplemented
12#22575422C22116yescomplemented
13#22575421C22124yescomplemented
14C2×C22⋊Dic269C2213yescomplemented
15C2×C22⋊Dic269C2216yescomplemented
16C2×#16864379C2216yescomplemented
17C2×C4×Dic269C2213yescomplemented
18C25×C269C2211yescharacteristic, complemented
19C22×D4×C269C2213yes—
20#120×C269C2218yescomplemented
21C2×C22⋊C4×C269C2213yescomplemented
22C23×D269—46no—
23C23×D269C2312yes—
24C23×D269C2314yescomplemented
25C2×Dic538—46no—
26C2×Dic538C23112yescomplemented
27C2×C22⋊D269—412no—
28C2×C22⋊D269C23124yes—
29C22×Dic269C2316yes—
30C22⋊Dic269C23112yescomplemented
31C22⋊Dic269C23124yescomplemented
32#16864379C23124yescomplemented
33C4×Dic269C23112yescomplemented
34C24×C269—46no—
35C24×C269C2311yescharacteristic
36C24×C269C2313yes—
37C24×C269C2314yescomplemented
38C2×D4×C269—46no—
39C2×D4×C269C23112yes—
40C22×C4×C269C2313yes—
41C22⋊C4×C269C23112yescomplemented
42C22×D269—212no—
43C22×D269—412no—
44C22×D269—416no—
45C22×D269C2414yes—
46Dic538—412no—
47C22⋊D269—424no—
48C2×Dic269—212no—
49C2×Dic269C24112yes—
50C23×C269—26no—
51C23×C269—26no—
52C23×C269—212no—
53C23×C269—412no—
54C23×C269—416no—
55C23×C269C2416yes—
56C23×C269C2412yes—
57C23×C269C2411yescharacteristic
58D4×C269—412no—
59C2×C4×C269—26no—
60C2×C4×C269C2416yes—
61C22×C269—26no—
62C22×C269—26no—
63C22×C269—212no—
64C22×C269—416no—
65C22×C269—412no—
66C22×C269—44no—
67C22×C269H(5,𝔽2)16yes—
68C22×C269C2511yescharacteristic
69C2×D269—212no—
70C2×D269—416no—
71C2×D269—48no—
72C4×C269—26no—
73Dic269—212no—
74C2×C269—42no—
75C2×C269—46no—
76C2×C269H(3,𝔽4)14yescomplemented
77C2×C269C2×H(5,𝔽2)13yes—
78D269—44no—
79C269C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—2691nomaximal, Sylow
81H(3,𝔽4)—26916no—
82C2×#124—2693no—
83C2×#124—2696no—
84C2×#120—2692no—
85C2×#120—2693no—
86C2×#120D26911yescharacteristic, complemented
87C25—2691no—
88C25C2×D26911yescharacteristic, complemented
89C22×Q8—2693no—
90C22×D4—2696no—
91C22×D4C2×D26913yes—
92#124—26924no—
93#124—26948no—
94#120—26916no—
95#120—26924no—
96#120C2×D26918yescomplemented
97C2×C22⋊C4—2693no—
98C2×C22⋊C4—2696no—
99C2×C22⋊C4—2696no—
100C2×C22⋊C4C2×D26913yescomplemented
101C2×C42—2693no—
102C24—46no—
103C24—2692no—
104C24—2694no—
105C24—10766no—
106C24C22×D26911yescharacteristic
107C24C22×D26913yes—
108C24C22×D26914yescomplemented
109C2×Q8—26912no—
110C2×Q8—10766no—
111C2×D4—46no—
112C2×D4—26924no—
113C2×D4—107612no—
114C2×D4C22×D269112yes—
115C22×C4—2696no—
116C22×C4C22×D26913yes—
117C22⋊C4—26912no—
118C22⋊C4—26924no—
119C22⋊C4—26924no—
120C22⋊C4C22×D269112yescomplemented
121C42—26912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—2694no—
128C23—53812no—
129C23—107612no—
130C23—107616no—
131C23C23×D26912yes—
132C23C23×D26916yes—
133C23C23×D26911yescharacteristic
134Q8—107612no—
135D4—412no—
136D4—107624no—
137C2×C4—26no—
138C2×C4—26912no—
139C2×C4—53812no—
140C2×C4C23×D26916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—53812no—
148C22—107616no—
149C22—10768no—
150C22#2257549816yes—
151C22C24×D26911yescharacteristic
152C4—26no—
153C4—53812no—
154C2—46no—
155C2—42no—
156C2—10764no—
157C2#3177134814yesdirect product factor
158C2C2×#2257549813yes—
subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC2×#120×C269C2
socleC23×C269C24
hypercenterC2×#120D269
hypocenterC269C2×H(3,𝔽4)
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #31771348C2direct (N × H)
2. C2×#22575440C2semidirect
3. C2×#22575439C2semidirect
4. C2×#22575422C2semidirect
5. C2×#22575421C2semidirect
6. C2×#120×C269C2semidirect
7. C24×D269C22semidirect
8. C22×Dic538C22semidirect
10. #22575440C22semidirect
11. #22575439C22semidirect
12. #22575422C22semidirect
13. #22575421C22semidirect
14. C2×C22⋊Dic269C22semidirect
15. C2×C22⋊Dic269C22semidirect
16. C2×#16864379C22semidirect
17. C2×C4×Dic269C22semidirect
18. C25×C269C22semidirect
20. #120×C269C22semidirect
21. C2×C22⋊C4×C269C22semidirect
24. C23×D269C23semidirect
26. C2×Dic538C23semidirect
30. C22⋊Dic269C23semidirect
31. C22⋊Dic269C23semidirect
32. #16864379C23semidirect
33. C4×Dic269C23semidirect
37. C24×C269C23semidirect
41. C22⋊C4×C269C23semidirect
76. C2×C269H(3,𝔽4)semidirect
79. C269C2×H(3,𝔽4)semidirect
86. C2×#120D269semidirect
88. C25C2×D269semidirect
96. #120C2×D269semidirect
100. C2×C22⋊C4C2×D269semidirect
108. C24C22×D269semidirect
120. C22⋊C4C22×D269semidirect
157. C2#31771348direct (N × H)

Maximal subgroups

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

subgroupindex
#317713482
C2×#225754402
C2×#225754392
C2×#225754222
C2×#225754212
C2×#120×C2692
C2×H(3,𝔽4)269