Finite Group Databasebeta

← #490×D37 #18004928

Subgroups — #490×D37 #18004928

Order 4736.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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#127×D37C211yesmaximal, characteristic
2#125×D37C211yesmaximal, characteristic, complemented
3#14557899C211yesmaximal, characteristic, complemented
4#14557898C211yesmaximal, characteristic, complemented
5#14557897C211yesmaximal, characteristic, complemented
6#14557896C214yesmaximal, complemented
7#102×D37C214yesmaximal, complemented
8#97×D37C211yesmaximal, characteristic, complemented
9C37×#490C211yesmaximal, characteristic, complemented
10C2×D4×D37—22no—
11C2×D4×D37C2212yes—
12C2×C8×D37C2212yes—
13#11924533C2211yescharacteristic
14#11924532—22no—
15#11924532C2212yes—
16#11924528C2211yescharacteristic, complemented
17#11924527C2212yescomplemented
18#11924526—22no—
19C4⋊C4×D37—22no—
20C4⋊C4×D37C2212yes—
21C42×D37C2211yescharacteristic
22#11924458C2214yescomplemented
23#11924457C2214yescomplemented
24#11924456C2214yescomplemented
25#11924447C2211yescharacteristic, complemented
26#11924446C2212yescomplemented
27#127×C37C2211yescharacteristic
28#125×C37C2211yescharacteristic, complemented
29#102×C37C2214yescomplemented
30#97×C37C2211yescharacteristic, complemented
31C23×D37—22no—
32C2×D4×C37—22no—
33C2×D4×C37C2312yes—
34C2×C22⋊D37—22no—
35C2×C22⋊D37—24no—
36D4×D37—28no—
37D4×D37—48no—
38C2×D148—22no—
39C2×D148C2312yes—
40C2×C4×D37—22no—
41C2×C4×D37D412yes—
42C2×C4×D37C2311yescharacteristic
43C2×C8×C37C2312yes—
44C4⋊C4×C37—22no—
45C4⋊C4×C37C2312yes—
46C42×C37C2311yescharacteristic
47C4⋊Dic37—22no—
48C4⋊Dic37C2312yes—
49#10596936—22no—
50#10596936—22no—
51#10596936—22no—
52C4×Dic37D412yes—
53C4×Dic37C2311yescharacteristic
54C2×#64436C2312yes—
55C8×D37—24no—
56C23×C37—22no—
57C22×D37—22no—
58C22×D37—44no—
59C22×D37—48no—
60C22×D37C2×D411yescharacteristic
61D4×C37—24no—
62D4×C37—44no—
63C2×C4×C37—22no—
64C2×C4×C37C2×D412yes—
65C2×C4×C37C2411yescharacteristic
66C22⋊D37—48no—
67C22⋊D37—44no—
68C2×Dic37—22no—
69C2×Dic37C2×D412yes—
70C2×Dic37C2×D411yescharacteristic
71D148—24no—
72D148—44no—
73C4×D37—24no—
74C4×D37—44no—
75C4×D37#4114yes—
76C8×C37—22no—
77#64436—22no—
78C22×C37—42no—
79C22×C37—44no—
80C22×C37C22×D411yescharacteristic
81C2×D37—42no—
82C2×D37—44no—
83C2×D37—88no—
84C2×D37#12412yes—
85C2×D37AGL(1,ℤ/8)14yes—
86C4×C37—22no—
87C4×C37—42no—
88C4×C37C2×#4112yes—
89Dic37—22no—
90Dic37—42no—
91Dic37#12412yes—
92C2×#490—371nomaximal, Sylow
93C2×C37—82no—
94C2×C37C2×#12411yescharacteristic
95C2×C37C2×AGL(1,ℤ/8)12yes—
96D37—82no—
97D37#49014yesdirect product factor
98C2×#127—371no—
99C2×#125—371no—
100#490—371no—
101#490—371no—
102#490—374no—
103#490—371no—
104#490D3711yescharacteristic, direct product factor
105C2×#102—374no—
106C2×#97—371no—
107C37C2×#49011yescharacteristic, complemented, Sylow
108C22×D4—372no—
109C22×D4—742no—
110C22×C8—372no—
111#127—372no—
112#127—371no—
113#127—742no—
114#127C2×D3711yescharacteristic
115#125—372no—
116#125—371no—
117#125—742no—
118#125C2×D3711yescharacteristic, complemented
119C2×C4⋊C4—372no—
120C2×C4⋊C4—742no—
121C2×C42—371no—
122#102—374no—
123#102—374no—
124#102—374no—
125#102C2×D3714yescomplemented
126#97—372no—
127#97—371no—
128#97C2×D3711yescharacteristic, complemented
129C24—742no—
130C2×D4—22no—
131C2×D4—372no—
132C2×D4—748no—
133C2×D4—744no—
134C2×D4—742no—
135C2×D4—742no—
136C2×D4—1488no—
137C2×D4C22×D3712yes—
138C22×C4—371no—
139C22×C4—372no—
140C22×C4—742no—
141C2×C8—372no—
142C2×C8—744no—
143C2×C8C22×D3712yes—
144C4⋊C4—22no—
145C4⋊C4—372no—
146C4⋊C4—742no—
147C4⋊C4—742no—
148C4⋊C4—742no—
149C4⋊C4—742no—
150C4⋊C4C22×D3712yes—
151C42—372no—
152C42—371no—
153C42C22×D3711yescharacteristic
154C23—22no—
155C23—371no—
156C23—742no—
157C23—1484no—
158C23—1488no—
159D4—24no—
160D4—44no—
161D4—744no—
162D4—1484no—
163D4—1484no—
164D4—1488no—
165C2×C4—22no—
166C2×C4—371no—
167C2×C4—374no—
168C2×C4—372no—
169C2×C4—744no—
170C2×C4—742no—
171C2×C4—1484no—
172C2×C4D4×D3712yes—
173C2×C4C23×D3711yescharacteristic
174C8—22no—
175C8—742no—
176C22—42no—
177C22—44no—
178C22—372no—
179C22—374no—
180C22—2968no—
181C22—1482no—
182C22—1484no—
183C22C2×D4×D3711yescharacteristic
184C4—22no—
185C4—42no—
186C4—372no—
187C4—742no—
188C4—1482no—
189C4#41×D3712yes—
190C2—82no—
191C2—374no—
192C2—2962no—
193C2#124×D3711yescharacteristic
194C2AGL(1,ℤ/8)×D3712yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#490C2
socleC22×C37C22×D4
prime radical#127×D37C2
hypercenter#490D37
hypocenterC37C2×#490
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D37C2semidirect
3. #14557899C2semidirect
4. #14557898C2semidirect
5. #14557897C2semidirect
6. #14557896C2semidirect
7. #102×D37C2semidirect
8. #97×D37C2semidirect
9. C37×#490C2semidirect
16. #11924528C22semidirect
17. #11924527C22semidirect
22. #11924458C22semidirect
23. #11924457C22semidirect
24. #11924456C22semidirect
25. #11924447C22semidirect
26. #11924446C22semidirect
28. #125×C37C22semidirect
29. #102×C37C22semidirect
30. #97×C37C22semidirect
97. D37#490direct (N × H)
104. #490D37direct (N × H)
107. C37C2×#490semidirect
118. #125C2×D37semidirect
125. #102C2×D37semidirect
128. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#127×D372
#125×D372
#145578992
#145578982
#145578972
#145578962
#102×D372
#97×D372
C37×#4902
C2×#49037