Finite Group Databasebeta

← C2×#31827302 #49136070

Subgroups — C2×#31827302 #49136070

Order 36224.

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#31827302C2132yesmaximal, direct product factor
2C2×#22583658C215yesmaximal, complemented
3C2×#22583656C2110yesmaximal, complemented
4C22×#17985393C215yesmaximal, complemented
5C2×#41×D283C2110yesmaximal, complemented
6C2×2−1+4×C283C211yesmaximal, characteristic, complemented
7#22583658C22180yescomplemented
8#22583656C221160yescomplemented
9C2×#17985393C22110yescomplemented
10C2×#17985393C22120yescomplemented
11C2×#17985393C22180yescomplemented
12C2×#17985392C22130yescomplemented
13C2×#17985391C22110yescomplemented
14#41×D283C221160yescomplemented
15C2×Q8×D283C22110yescomplemented
16C22×D1132C22115yescomplemented
17C2×D4×D283C22130yescomplemented
18C22×C4×D283C22115yescomplemented
192−1+4×C283C22116yescomplemented
20C2×#41×C283C22110yescomplemented
21C22×Q8×C283C2215yescomplemented
22C23×D283C23115yes—
23#17985393C23180yescomplemented
24#17985393C231160yescomplemented
25#17985392C231240yescomplemented
26#17985391C23180yescomplemented
27C2×Dic566C23110yes—
28Q8×D283C23180yescomplemented
29C2×D1132C23130yes—
30C2×D1132C231120yescomplemented
31C2×C22⋊D283C23120yes—
32D4×D283C231240yescomplemented
33C22×Dic283C2315yes—
34C2×C4×D283C23110yes—
35C2×C4×D283C23130yes—
36C2×C4×D283C231120yescomplemented
37#41×C283C23180yescomplemented
38C2×Q8×C283C23110yes—
39C2×Q8×C283C23140yescomplemented
40C2×D4×C283C23110yes—
41C22×C4×C283C23115yes—
42C22×D283—430no—
43C22×D283C24110yes—
44C22×D283C24160yes—
45Dic566C24140yes—
46D1132C241120yes—
47C22⋊D283C24180yes—
48C2×Dic283C2411yescharacteristic
49C2×Dic283C2415yes—
50C2×Dic283C24120yes—
51C4×D283C24140yes—
52C4×D283C241120yes—
53C23×C283C2415yes—
54Q8×C283C24140yes—
55D4×C283C24140yes—
56C2×C4×C283C24110yes—
57C2×C4×C283C24160yes—
58C22×C283—210no—
59C22×C283C25110yes—
60C22×C283C2511yescharacteristic
61C2×D283—220no—
62C2×D283—460no—
63C2×D283C25120yes—
64C4×C283C25120yes—
65Dic283C2512yes—
66Dic283C25110yes—
67C2×C283—210no—
68C2×C283#58512yescomplemented
69C2×C283C2611yescharacteristic
70D283—220no—
71C283C2×#58511yescharacteristic, complemented, Sylow
72C2×#585—2831nomaximal, Sylow
73#585—28332no—
74C2×2−1+4—2835no—
75C2×2−1+4D28311yescharacteristic, complemented
76C2×H(5,𝔽2)—28310no—
77C22×#41—28310no—
78C22×#41—2835no—
792−1+4—28380no—
802−1+4C2×D283116yescomplemented
81H(5,𝔽2)—283160no—
82C2×#41—283160no—
83C2×#41—28310no—
84C2×#41—28320no—
85C2×#41—28380no—
86C2×#41—28310no—
87C2×#41—28330no—
88C2×#41C2×D283110yescomplemented
89C22×Q8—28310no—
90C22×Q8C2×D28315yescomplemented
91C22×D4—28330no—
92C22×D4—28315no—
93C23×C4—28315no—
94C24—28315no—
95#41—28380no—
96#41—283160no—
97#41—28380no—
98#41—283240no—
99#41C22×D283180yescomplemented
100C2×Q8—28380no—
101C2×Q8—28310no—
102C2×Q8C22×D283110yes—
103C2×Q8C22×D283140yescomplemented
104C2×D4—28320no—
105C2×D4—283240no—
106C2×D4—28330no—
107C2×D4—283120no—
108C2×D4C22×D283110yes—
109C22×C4—2835no—
110C22×C4—28310no—
111C22×C4—28330no—
112C22×C4—283120no—
113C22×C4C22×D283115yes—
114C23—28310no—
115C23—28360no—
116C23—113230no—
117C23C23×D28315yes—
118Q8—28340no—
119Q8C23×D283140yes—
120D4—28380no—
121D4—283120no—
122D4C23×D283140yes—
123C2×C4—28320no—
124C2×C4—2831no—
125C2×C4—2835no—
126C2×C4—28340no—
127C2×C4—283120no—
128C2×C4C23×D283160yes—
129C2×C4C23×D283110yes—
130C22—210no—
131C22—28320no—
132C22—56620no—
133C22—113260no—
134C22C24×D283110yes—
135C22C24×D28311yescharacteristic
136C4—2832no—
137C4—28310no—
138C4C24×D283120yes—
139C2—210no—
140C2—56620no—
141C2#3182730212yesdirect product factor
142C2C25×D28311yescharacteristic
subgroupG/H
centerC22C24×D283
commutator, cosocleC2×C283C26
FrattiniC2C25×D283
FittingC2×2−1+4×C283C2
socleC22×C283C25
hypercenterC2×2−1+4D283
hypocenterC283C2×#585
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #31827302C2direct (N × H)
2. C2×#22583658C2semidirect
3. C2×#22583656C2semidirect
4. C22×#17985393C2semidirect
5. C2×#41×D283C2semidirect
6. C2×2−1+4×C283C2semidirect
7. #22583658C22semidirect
8. #22583656C22semidirect
9. C2×#17985393C22semidirect
10. C2×#17985393C22semidirect
11. C2×#17985393C22semidirect
12. C2×#17985392C22semidirect
13. C2×#17985391C22semidirect
14. #41×D283C22semidirect
15. C2×Q8×D283C22semidirect
16. C22×D1132C22semidirect
17. C2×D4×D283C22semidirect
18. C22×C4×D283C22semidirect
19. 2−1+4×C283C22semidirect
20. C2×#41×C283C22semidirect
21. C22×Q8×C283C22semidirect
23. #17985393C23semidirect
24. #17985393C23semidirect
25. #17985392C23semidirect
26. #17985391C23semidirect
28. Q8×D283C23semidirect
30. C2×D1132C23semidirect
32. D4×D283C23semidirect
36. C2×C4×D283C23semidirect
37. #41×C283C23semidirect
39. C2×Q8×C283C23semidirect
68. C2×C283#585semidirect
71. C283C2×#585semidirect
75. C2×2−1+4D283semidirect
80. 2−1+4C2×D283semidirect
88. C2×#41C2×D283semidirect
90. C22×Q8C2×D283semidirect
99. #41C22×D283semidirect
103. C2×Q8C22×D283semidirect
141. C2#31827302direct (N × H)

Maximal subgroups

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

subgroupindex
#318273022
C2×#225836582
C2×#225836562
C22×#179853932
C2×#41×D2832
C2×2−1+4×C2832
C2×#585283