Finite Group Databasebeta

← C2×#31771442 #46825694

Subgroups — C2×#31771442 #46825694

Order 34432.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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#31771442C2132yesmaximal, direct product factor
2C2×#22575501C215yesmaximal, complemented
3C2×#22575499C2110yesmaximal, complemented
4C22×#16864403C215yesmaximal, complemented
5C2×#41×D269C2110yesmaximal, complemented
6C2×2−1+4×C269C211yesmaximal, characteristic, complemented
7#22575501C22180yescomplemented
8#22575499C221160yescomplemented
9C2×#16864403C22110yescomplemented
10C2×#16864403C22120yescomplemented
11C2×#16864403C22180yescomplemented
12C2×#16864402C22130yescomplemented
13C2×#16864401C22110yescomplemented
14#41×D269C221160yescomplemented
15C2×Q8×D269C22110yescomplemented
16C22×D1076C22115yescomplemented
17C2×D4×D269C22130yescomplemented
18C22×C4×D269C22115yescomplemented
192−1+4×C269C22116yescomplemented
20C2×#41×C269C22110yescomplemented
21C22×Q8×C269C2215yescomplemented
22C23×D269C23115yes—
23#16864403C23180yescomplemented
24#16864403C231160yescomplemented
25#16864402C231240yescomplemented
26#16864401C23180yescomplemented
27C2×Dic538C23110yes—
28Q8×D269C23180yescomplemented
29C2×D1076C23130yes—
30C2×D1076C231120yescomplemented
31C2×C22⋊D269C23120yes—
32D4×D269C231240yescomplemented
33C22×Dic269C2315yes—
34C2×C4×D269C23110yes—
35C2×C4×D269C23130yes—
36C2×C4×D269C231120yescomplemented
37#41×C269C23180yescomplemented
38C2×Q8×C269C23110yes—
39C2×Q8×C269C23140yescomplemented
40C2×D4×C269C23110yes—
41C22×C4×C269C23115yes—
42C22×D269—430no—
43C22×D269C24110yes—
44C22×D269C24160yes—
45Dic538C24140yes—
46D1076C241120yes—
47C22⋊D269C24180yes—
48C2×Dic269C2411yescharacteristic
49C2×Dic269C2415yes—
50C2×Dic269C24120yes—
51C4×D269C24140yes—
52C4×D269C241120yes—
53C23×C269C2415yes—
54Q8×C269C24140yes—
55D4×C269C24140yes—
56C2×C4×C269C24110yes—
57C2×C4×C269C24160yes—
58C22×C269—210no—
59C22×C269C25110yes—
60C22×C269C2511yescharacteristic
61C2×D269—220no—
62C2×D269—460no—
63C2×D269C25120yes—
64C4×C269C25120yes—
65Dic269C2512yes—
66Dic269C25110yes—
67C2×C269—210no—
68C2×C269#58512yescomplemented
69C2×C269C2611yescharacteristic
70D269—220no—
71C269C2×#58511yescharacteristic, complemented, Sylow
72C2×#585—2691nomaximal, Sylow
73#585—26932no—
74C2×2−1+4—2695no—
75C2×2−1+4D26911yescharacteristic, complemented
76C2×H(5,𝔽2)—26910no—
77C22×#41—26910no—
78C22×#41—2695no—
792−1+4—26980no—
802−1+4C2×D269116yescomplemented
81H(5,𝔽2)—269160no—
82C2×#41—269160no—
83C2×#41—26910no—
84C2×#41—26920no—
85C2×#41—26980no—
86C2×#41—26910no—
87C2×#41—26930no—
88C2×#41C2×D269110yescomplemented
89C22×Q8—26910no—
90C22×Q8C2×D26915yescomplemented
91C22×D4—26930no—
92C22×D4—26915no—
93C23×C4—26915no—
94C24—26915no—
95#41—26980no—
96#41—269160no—
97#41—26980no—
98#41—269240no—
99#41C22×D269180yescomplemented
100C2×Q8—26980no—
101C2×Q8—26910no—
102C2×Q8C22×D269110yes—
103C2×Q8C22×D269140yescomplemented
104C2×D4—26920no—
105C2×D4—269240no—
106C2×D4—26930no—
107C2×D4—269120no—
108C2×D4C22×D269110yes—
109C22×C4—2695no—
110C22×C4—26910no—
111C22×C4—26930no—
112C22×C4—269120no—
113C22×C4C22×D269115yes—
114C23—26910no—
115C23—26960no—
116C23—107630no—
117C23C23×D26915yes—
118Q8—26940no—
119Q8C23×D269140yes—
120D4—26980no—
121D4—269120no—
122D4C23×D269140yes—
123C2×C4—26920no—
124C2×C4—2691no—
125C2×C4—2695no—
126C2×C4—26940no—
127C2×C4—269120no—
128C2×C4C23×D269160yes—
129C2×C4C23×D269110yes—
130C22—210no—
131C22—26920no—
132C22—53820no—
133C22—107660no—
134C22C24×D269110yes—
135C22C24×D26911yescharacteristic
136C4—2692no—
137C4—26910no—
138C4C24×D269120yes—
139C2—210no—
140C2—53820no—
141C2#3177144212yesdirect product factor
142C2C25×D26911yescharacteristic
subgroupG/H
centerC22C24×D269
commutator, cosocleC2×C269C26
FrattiniC2C25×D269
FittingC2×2−1+4×C269C2
socleC22×C269C25
hypercenterC2×2−1+4D269
hypocenterC269C2×#585
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #31771442C2direct (N × H)
2. C2×#22575501C2semidirect
3. C2×#22575499C2semidirect
4. C22×#16864403C2semidirect
5. C2×#41×D269C2semidirect
6. C2×2−1+4×C269C2semidirect
7. #22575501C22semidirect
8. #22575499C22semidirect
9. C2×#16864403C22semidirect
10. C2×#16864403C22semidirect
11. C2×#16864403C22semidirect
12. C2×#16864402C22semidirect
13. C2×#16864401C22semidirect
14. #41×D269C22semidirect
15. C2×Q8×D269C22semidirect
16. C22×D1076C22semidirect
17. C2×D4×D269C22semidirect
18. C22×C4×D269C22semidirect
19. 2−1+4×C269C22semidirect
20. C2×#41×C269C22semidirect
21. C22×Q8×C269C22semidirect
23. #16864403C23semidirect
24. #16864403C23semidirect
25. #16864402C23semidirect
26. #16864401C23semidirect
28. Q8×D269C23semidirect
30. C2×D1076C23semidirect
32. D4×D269C23semidirect
36. C2×C4×D269C23semidirect
37. #41×C269C23semidirect
39. C2×Q8×C269C23semidirect
68. C2×C269#585semidirect
71. C269C2×#585semidirect
75. C2×2−1+4D269semidirect
80. 2−1+4C2×D269semidirect
88. C2×#41C2×D269semidirect
90. C22×Q8C2×D269semidirect
99. #41C22×D269semidirect
103. C2×Q8C22×D269semidirect
141. C2#31771442direct (N × H)

Maximal subgroups

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

subgroupindex
#317714422
C2×#225755012
C2×#225754992
C22×#168644032
C2×#41×D2692
C2×2−1+4×C2692
C2×#585269