Finite Group Databasebeta

← C2×#31827208 #49135382

Subgroups — C2×#31827208 #49135382

Order 36224.

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#31827208C2116yesmaximal, direct product factor
2C2×#22583597C213yesmaximal, complemented
3C2×#22583596C216yesmaximal, complemented
4C2×#22583579C212yesmaximal, complemented
5C2×#22583578C213yesmaximal, complemented
6C2×#120×C283C211yesmaximal, characteristic, complemented
7C24×D283C2211yescharacteristic, complemented
8C22×Dic566C2213yescomplemented
9C22×C22⋊D283C2216yes—
10#22583597C22124yescomplemented
11#22583596C22148yescomplemented
12#22583579C22116yescomplemented
13#22583578C22124yescomplemented
14C2×C22⋊Dic283C2213yescomplemented
15C2×C22⋊Dic283C2216yescomplemented
16C2×(C2×D283)⋊C4C2216yescomplemented
17C2×C4×Dic283C2213yescomplemented
18C25×C283C2211yescharacteristic, complemented
19C22×D4×C283C2213yes—
20#120×C283C2218yescomplemented
21C2×C22⋊C4×C283C2213yescomplemented
22C23×D283—46no—
23C23×D283C2312yes—
24C23×D283C2314yescomplemented
25C2×Dic566—46no—
26C2×Dic566C23112yescomplemented
27C2×C22⋊D283—412no—
28C2×C22⋊D283C23124yes—
29C22×Dic283C2316yes—
30C22⋊Dic283C23112yescomplemented
31C22⋊Dic283C23124yescomplemented
32(C2×D283)⋊C4C23124yescomplemented
33C4×Dic283C23112yescomplemented
34C24×C283—46no—
35C24×C283C2311yescharacteristic
36C24×C283C2313yes—
37C24×C283C2314yescomplemented
38C2×D4×C283—46no—
39C2×D4×C283C23112yes—
40C22×C4×C283C2313yes—
41C22⋊C4×C283C23112yescomplemented
42C22×D283—212no—
43C22×D283—412no—
44C22×D283—416no—
45C22×D283C2414yes—
46Dic566—412no—
47C22⋊D283—424no—
48C2×Dic283—212no—
49C2×Dic283C24112yes—
50C23×C283—26no—
51C23×C283—26no—
52C23×C283—212no—
53C23×C283—412no—
54C23×C283—416no—
55C23×C283C2416yes—
56C23×C283C2412yes—
57C23×C283C2411yescharacteristic
58D4×C283—412no—
59C2×C4×C283—26no—
60C2×C4×C283C2416yes—
61C22×C283—26no—
62C22×C283—26no—
63C22×C283—212no—
64C22×C283—416no—
65C22×C283—412no—
66C22×C283—44no—
67C22×C283H(5,𝔽2)16yes—
68C22×C283C2511yescharacteristic
69C2×D283—212no—
70C2×D283—416no—
71C2×D283—48no—
72C4×C283—26no—
73Dic283—212no—
74C2×C283—42no—
75C2×C283—46no—
76C2×C283H(3,𝔽4)14yescomplemented
77C2×C283C2×H(5,𝔽2)13yes—
78D283—44no—
79C283C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—2831nomaximal, Sylow
81H(3,𝔽4)—28316no—
82C2×#124—2833no—
83C2×#124—2836no—
84C2×#120—2832no—
85C2×#120—2833no—
86C2×#120D28311yescharacteristic, complemented
87C25—2831no—
88C25C2×D28311yescharacteristic, complemented
89C22×Q8—2833no—
90C22×D4—2836no—
91C22×D4C2×D28313yes—
92#124—28324no—
93#124—28348no—
94#120—28316no—
95#120—28324no—
96#120C2×D28318yescomplemented
97C2×C22⋊C4—2833no—
98C2×C22⋊C4—2836no—
99C2×C22⋊C4—2836no—
100C2×C22⋊C4C2×D28313yescomplemented
101C2×C42—2833no—
102C24—46no—
103C24—2832no—
104C24—2834no—
105C24—11326no—
106C24C22×D28311yescharacteristic
107C24C22×D28313yes—
108C24C22×D28314yescomplemented
109C2×Q8—28312no—
110C2×Q8—11326no—
111C2×D4—46no—
112C2×D4—28324no—
113C2×D4—113212no—
114C2×D4C22×D283112yes—
115C22×C4—2836no—
116C22×C4C22×D28313yes—
117C22⋊C4—28312no—
118C22⋊C4—28324no—
119C22⋊C4—28324no—
120C22⋊C4C22×D283112yescomplemented
121C42—28312no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—2834no—
128C23—56612no—
129C23—113212no—
130C23—113216no—
131C23C23×D28312yes—
132C23C23×D28316yes—
133C23C23×D28311yescharacteristic
134Q8—113212no—
135D4—412no—
136D4—113224no—
137C2×C4—26no—
138C2×C4—28312no—
139C2×C4—56612no—
140C2×C4C23×D28316yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—56612no—
148C22—113216no—
149C22—11328no—
150C22#2258365516yes—
151C22C24×D28311yescharacteristic
152C4—26no—
153C4—56612no—
154C2—46no—
155C2—42no—
156C2—11324no—
157C2#3182720814yesdirect product factor
158C2C2×#2258365513yes—
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#120×C283C2
socleC23×C283C24
hypercenterC2×#120D283
hypocenterC283C2×H(3,𝔽4)
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #31827208C2direct (N × H)
2. C2×#22583597C2semidirect
3. C2×#22583596C2semidirect
4. C2×#22583579C2semidirect
5. C2×#22583578C2semidirect
6. C2×#120×C283C2semidirect
7. C24×D283C22semidirect
8. C22×Dic566C22semidirect
10. #22583597C22semidirect
11. #22583596C22semidirect
12. #22583579C22semidirect
13. #22583578C22semidirect
14. C2×C22⋊Dic283C22semidirect
15. C2×C22⋊Dic283C22semidirect
16. C2×(C2×D283)⋊C4C22semidirect
17. C2×C4×Dic283C22semidirect
18. C25×C283C22semidirect
20. #120×C283C22semidirect
21. C2×C22⋊C4×C283C22semidirect
24. C23×D283C23semidirect
26. C2×Dic566C23semidirect
30. C22⋊Dic283C23semidirect
31. C22⋊Dic283C23semidirect
32. (C2×D283)⋊C4C23semidirect
33. C4×Dic283C23semidirect
37. C24×C283C23semidirect
41. C22⋊C4×C283C23semidirect
76. C2×C283H(3,𝔽4)semidirect
79. C283C2×H(3,𝔽4)semidirect
86. C2×#120D283semidirect
88. C25C2×D283semidirect
96. #120C2×D283semidirect
100. C2×C22⋊C4C2×D283semidirect
108. C24C22×D283semidirect
120. C22⋊C4C22×D283semidirect
157. C2#31827208direct (N × H)

Maximal subgroups

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

subgroupindex
#318272082
C2×#225835972
C2×#225835962
C2×#225835792
C2×#225835782
C2×#120×C2832
C2×H(3,𝔽4)283