Finite Group Databasebeta

← C2×#14558270 #18008710

Subgroups — C2×#14558270 #18008710

Order 4736.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 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#14558270C2116yesmaximal, direct product factor
2C2×#11924530C212yesmaximal, complemented
3C2×#11924517C213yesmaximal, complemented
4C2×#11924508C216yesmaximal, complemented
5C2×#11924504C213yesmaximal, complemented
6C2×#127×C37C211yesmaximal, characteristic, complemented
7C24×D37C2211yescharacteristic
8C22×C22⋊D37C2216yes—
9C23×Dic37C2213yescomplemented
10#11924530C22116yescomplemented
11#11924517C22124yescomplemented
12#11924508C22148yescomplemented
13#11924504C22124yescomplemented
14C2×#10596936C2216yescomplemented
15C2×C22⋊Dic37C2213yes—
16C2×C22⋊Dic37C2213yescomplemented
17C2×#10596938C2216yes—
18C22×D4×C37C2213yes—
19C22×D4×C37C2213yescomplemented
20#127×C37C2218yescomplemented
21C2×C42×C37C2211yescharacteristic, complemented
22C24×C37C2311yescharacteristic
23C24×C37C2313yes—
24C23×D37—46no—
25C23×D37C2312yes—
26C23×D37C2314yes—
27C2×D4×C37—46no—
28C2×D4×C37—46no—
29C2×D4×C37C23112yes—
30C2×D4×C37C23112yescomplemented
31C22×C4×C37C2313yes—
32C2×C22⋊D37—412no—
33C2×C22⋊D37C23124yes—
34C22×Dic37—46no—
35C22×Dic37C2316yes—
36C22×Dic37C23112yescomplemented
37C42×C37C2314yescomplemented
38C22⋊Dic37C23112yes—
39C22⋊Dic37C23112yescomplemented
40#10596938C23124yes—
41#10596936C23124yescomplemented
42C23×C37—26no—
43C23×C37—212no—
44C23×C37—26no—
45C23×C37C2412yes—
46C23×C37C2416yes—
47C23×C37C2411yescharacteristic
48C22×D37—212no—
49C22×D37—412no—
50C22×D37—416no—
51C22×D37C2414yes—
52D4×C37—412no—
53D4×C37—412no—
54C2×C4×C37—26no—
55C2×C4×C37C2416yes—
56C22⋊D37—424no—
57C2×Dic37—212no—
58C2×Dic37—412no—
59C2×Dic37C24112yes—
60C22×C37—26no—
61C22×C37—212no—
62C22×C37—26no—
63C22×C37—44no—
64C22×C37—412no—
65C22×C37H(5,𝔽2)16yes—
66C22×C37C2511yescharacteristic
67C2×D37—212no—
68C2×D37—416no—
69C2×D37—48no—
70C4×C37—26no—
71Dic37—212no—
72C2×#560—371nomaximal, Sylow
73C2×C37—42no—
74C2×C37—46no—
75C2×C37#56014yescomplemented
76C2×C37C2×H(5,𝔽2)13yes—
77D37—44no—
78#560—3716no—
79C2×#127D3711yescharacteristic, complemented
80C2×#126—372no—
81C2×#123—373no—
82C2×#121—376no—
83C2×#120—373no—
84C37C2×#56011yescharacteristic, complemented, Sylow
85C25—371no—
86C22×D4—376no—
87C22×D4C2×D3713yes—
88C22×D4C2×D3713yescomplemented
89C23×C4—373no—
90#127C2×D3718yescomplemented
91#126—3716no—
92#123—3724no—
93#121—3748no—
94#120—3724no—
95C2×C4⋊C4—376no—
96C2×C22⋊C4—373no—
97C2×C22⋊C4—373no—
98C2×C22⋊C4—376no—
99C2×C42C2×D3711yescharacteristic, complemented
100C24—372no—
101C24—374no—
102C24—1486no—
103C24C22×D3711yescharacteristic
104C24C22×D3713yes—
105C2×D4—46no—
106C2×D4—46no—
107C2×D4—3724no—
108C2×D4—14812no—
109C2×D4C22×D37112yes—
110C2×D4C22×D37112yescomplemented
111C22×C4—376no—
112C22×C4—3712no—
113C22×C4—1486no—
114C22×C4C22×D3713yes—
115C4⋊C4—3724no—
116C22⋊C4—3712no—
117C22⋊C4—3712no—
118C22⋊C4—3724no—
119C42C22×D3714yescomplemented
120C23—26no—
121C23—212no—
122C23—26no—
123C23—374no—
124C23—7412no—
125C23—14812no—
126C23—14816no—
127C23C23×D3712yes—
128C23C23×D3716yes—
129C23C23×D3711yescharacteristic
130D4—412no—
131D4—412no—
132D4—14824no—
133C2×C4—26no—
134C2×C4—3712no—
135C2×C4—7412no—
136C2×C4—14812no—
137C2×C4C23×D3716yes—
138C22—26no—
139C22—212no—
140C22—26no—
141C22—44no—
142C22—412no—
143C22—7412no—
144C22—14816no—
145C22—1488no—
146C22#1192458116yes—
147C22C24×D3711yescharacteristic
148C4—26no—
149C4—7412no—
150C2—42no—
151C2—46no—
152C2—1484no—
153C2#1455827014yesdirect product factor
154C2C2×#1192458113yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×#127×C37C2
socleC23×C37C24
hypercenterC2×#127D37
hypocenterC37C2×#560
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #14558270C2direct (N × H)
2. C2×#11924530C2semidirect
3. C2×#11924517C2semidirect
4. C2×#11924508C2semidirect
5. C2×#11924504C2semidirect
6. C2×#127×C37C2semidirect
9. C23×Dic37C22semidirect
10. #11924530C22semidirect
11. #11924517C22semidirect
12. #11924508C22semidirect
13. #11924504C22semidirect
14. C2×#10596936C22semidirect
16. C2×C22⋊Dic37C22semidirect
19. C22×D4×C37C22semidirect
20. #127×C37C22semidirect
21. C2×C42×C37C22semidirect
30. C2×D4×C37C23semidirect
36. C22×Dic37C23semidirect
37. C42×C37C23semidirect
39. C22⋊Dic37C23semidirect
41. #10596936C23semidirect
75. C2×C37#560semidirect
79. C2×#127D37semidirect
84. C37C2×#560semidirect
88. C22×D4C2×D37semidirect
90. #127C2×D37semidirect
99. C2×C42C2×D37semidirect
110. C2×D4C22×D37semidirect
119. C42C22×D37semidirect
153. C2#14558270direct (N × H)

Maximal subgroups

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

subgroupindex
#145582702
C2×#119245302
C2×#119245172
C2×#119245082
C2×#119245042
C2×#127×C372
C2×#56037