Finite Group Databasebeta

← C2×#14558276 #18008717

Subgroups — C2×#14558276 #18008717

Order 4736.

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#14558276C2116yesmaximal, direct product factor
2C2×#11924523C213yesmaximal, complemented
3C2×#11924522C216yesmaximal, complemented
4C2×#11924505C212yesmaximal, complemented
5C2×#11924504C213yesmaximal, complemented
6C2×#120×C37C211yesmaximal, characteristic, complemented
7C24×D37C2211yescharacteristic, complemented
8C22×Dic74C2213yescomplemented
9C22×C22⋊D37C2216yes—
10#11924523C22124yescomplemented
11#11924522C22148yescomplemented
12#11924505C22116yescomplemented
13#11924504C22124yescomplemented
14C2×C22⋊Dic37C2213yescomplemented
15C2×C22⋊Dic37C2216yescomplemented
16C2×#10596938C2216yescomplemented
17C2×C4×Dic37C2213yescomplemented
18C25×C37C2211yescharacteristic, complemented
19C22×D4×C37C2213yes—
20#120×C37C2218yescomplemented
21C2×C22⋊C4×C37C2213yescomplemented
22C24×C37—46no—
23C24×C37C2311yescharacteristic
24C24×C37C2313yes—
25C24×C37C2314yescomplemented
26C23×D37—46no—
27C23×D37C2312yes—
28C23×D37C2314yescomplemented
29C2×D4×C37—46no—
30C2×D4×C37C23112yes—
31C22×C4×C37C2313yes—
32C2×C22⋊D37—412no—
33C2×C22⋊D37C23124yes—
34C22×Dic37C2316yes—
35C2×Dic74—46no—
36C2×Dic74C23112yescomplemented
37C22⋊C4×C37C23112yescomplemented
38C22⋊Dic37C23112yescomplemented
39C22⋊Dic37C23124yescomplemented
40#10596938C23124yescomplemented
41C4×Dic37C23112yescomplemented
42C23×C37—212no—
43C23×C37—26no—
44C23×C37—26no—
45C23×C37—412no—
46C23×C37—416no—
47C23×C37C2412yes—
48C23×C37C2416yes—
49C23×C37C2411yescharacteristic
50C22×D37—212no—
51C22×D37—412no—
52C22×D37—416no—
53C22×D37C2414yes—
54D4×C37—412no—
55C2×C4×C37—26no—
56C2×C4×C37C2416yes—
57C22⋊D37—424no—
58C2×Dic37—212no—
59C2×Dic37C24112yes—
60Dic74—412no—
61C22×C37—212no—
62C22×C37—26no—
63C22×C37—26no—
64C22×C37—416no—
65C22×C37—44no—
66C22×C37—412no—
67C22×C37H(5,𝔽2)16yes—
68C22×C37C2511yescharacteristic
69C2×D37—212no—
70C2×D37—416no—
71C2×D37—48no—
72C4×C37—26no—
73Dic37—212no—
74C2×H(3,𝔽4)—371nomaximal, Sylow
75C2×C37—42no—
76C2×C37—46no—
77C2×C37H(3,𝔽4)14yescomplemented
78C2×C37C2×H(5,𝔽2)13yes—
79D37—44no—
80H(3,𝔽4)—3716no—
81C2×#124—373no—
82C2×#124—376no—
83C2×#120—372no—
84C2×#120—373no—
85C2×#120D3711yescharacteristic, complemented
86C37C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
87C25—371no—
88C25C2×D3711yescharacteristic, complemented
89C22×Q8—373no—
90C22×D4—376no—
91C22×D4C2×D3713yes—
92#124—3724no—
93#124—3748no—
94#120—3716no—
95#120—3724no—
96#120C2×D3718yescomplemented
97C2×C22⋊C4—373no—
98C2×C22⋊C4—376no—
99C2×C22⋊C4—376no—
100C2×C22⋊C4C2×D3713yescomplemented
101C2×C42—373no—
102C24—46no—
103C24—372no—
104C24—374no—
105C24—1486no—
106C24C22×D3711yescharacteristic
107C24C22×D3713yes—
108C24C22×D3714yescomplemented
109C2×Q8—3712no—
110C2×Q8—1486no—
111C2×D4—46no—
112C2×D4—3724no—
113C2×D4—14812no—
114C2×D4C22×D37112yes—
115C22×C4—376no—
116C22×C4C22×D3713yes—
117C22⋊C4—3712no—
118C22⋊C4—3724no—
119C22⋊C4—3724no—
120C22⋊C4C22×D37112yescomplemented
121C42—3712no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—374no—
128C23—7412no—
129C23—14812no—
130C23—14816no—
131C23C23×D3712yes—
132C23C23×D3716yes—
133C23C23×D3711yescharacteristic
134Q8—14812no—
135D4—412no—
136D4—14824no—
137C2×C4—26no—
138C2×C4—3712no—
139C2×C4—7412no—
140C2×C4C23×D3716yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—7412no—
148C22—14816no—
149C22—1488no—
150C22#1192458116yes—
151C22C24×D3711yescharacteristic
152C4—26no—
153C4—7412no—
154C2—46no—
155C2—42no—
156C2—1484no—
157C2#1455827614yesdirect product factor
158C2C2×#1192458113yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#120×C37C2
socleC23×C37C24
hypercenterC2×#120D37
hypocenterC37C2×H(3,𝔽4)
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #14558276C2direct (N × H)
2. C2×#11924523C2semidirect
3. C2×#11924522C2semidirect
4. C2×#11924505C2semidirect
5. C2×#11924504C2semidirect
6. C2×#120×C37C2semidirect
7. C24×D37C22semidirect
8. C22×Dic74C22semidirect
10. #11924523C22semidirect
11. #11924522C22semidirect
12. #11924505C22semidirect
13. #11924504C22semidirect
14. C2×C22⋊Dic37C22semidirect
15. C2×C22⋊Dic37C22semidirect
16. C2×#10596938C22semidirect
17. C2×C4×Dic37C22semidirect
18. C25×C37C22semidirect
20. #120×C37C22semidirect
21. C2×C22⋊C4×C37C22semidirect
25. C24×C37C23semidirect
28. C23×D37C23semidirect
36. C2×Dic74C23semidirect
37. C22⋊C4×C37C23semidirect
38. C22⋊Dic37C23semidirect
39. C22⋊Dic37C23semidirect
40. #10596938C23semidirect
41. C4×Dic37C23semidirect
77. C2×C37H(3,𝔽4)semidirect
85. C2×#120D37semidirect
86. C37C2×H(3,𝔽4)semidirect
88. C25C2×D37semidirect
96. #120C2×D37semidirect
100. C2×C22⋊C4C2×D37semidirect
108. C24C22×D37semidirect
120. C22⋊C4C22×D37semidirect
157. C2#14558276direct (N × H)

Maximal subgroups

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

subgroupindex
#145582762
C2×#119245232
C2×#119245222
C2×#119245052
C2×#119245042
C2×#120×C372
C2×H(3,𝔽4)37