Finite Group Databasebeta

← #18004969

Subgroups — #18004969

Order 4736.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#14558089C211yesmaximal, characteristic, complemented
2#127×D37C211yesmaximal, characteristic
3#14557899C211yesmaximal, characteristic, complemented
4#14557898C211yesmaximal, characteristic, complemented
5#14557897C211yesmaximal, characteristic, complemented
6#14557878C214yesmaximal, complemented
7#14557536C214yesmaximal, complemented
8#14557485C211yesmaximal, characteristic, complemented
9C37×#490C211yesmaximal, characteristic, complemented
10C2×D4×D37—22no—
11C2×D4×D37C2212yes—
12C2×#10596929C2212yes—
13#11924535C2212yescomplemented
14#11924533C2211yescharacteristic
15#11924532—22no—
16#11924532C2212yes—
17#11924528C2211yescharacteristic, complemented
18#11924514—22no—
19#11924501—22no—
20#11924494C2212yes—
21C42×D37C2211yescharacteristic
22#11924458C2214yescomplemented
23#11924457C2214yescomplemented
24#11924456C2214yescomplemented
25#11924447C2211yescharacteristic, complemented
26C8×Dic37C2212yescomplemented
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×D37D412yes—
41C2×C4×D37C2311yescharacteristic
42C2×Dic74—22no—
43C2×C8×C37C2312yes—
44C4⋊C4×C37—22no—
45C4⋊C4×C37C2312yes—
46C42×C37C2311yescharacteristic
47#10596938—22no—
48C4⋊Dic37C2312yes—
49#10596936—22no—
50#10596936—22no—
51C4×Dic37—22no—
52C4×Dic37D412yes—
53C4×Dic37C2311yescharacteristic
54C2×#64436C2312yes—
55#10596929—24no—
56C23×C37—22no—
57C22×D37—22no—
58C22×D37—48no—
59C22×D37—44no—
60C22×D37C2×D411yescharacteristic
61D4×C37—24no—
62D4×C37—44no—
63C2×C4×C37—22no—
64C2×C4×C37C2×D412yes—
65C2×C4×C37C2411yescharacteristic
66C22⋊D37—44no—
67C22⋊D37—48no—
68C2×Dic37—22no—
69C2×Dic37C2×D411yescharacteristic
70C2×Dic37C2×D412yes—
71D148—24no—
72D148—44no—
73C4×D37—24no—
74C4×D37#4114yes—
75Dic74—44no—
76C8×C37—22no—
77#64436—22no—
78C22×C37—42no—
79C22×C37—44no—
80C22×C37C22×D411yescharacteristic
81C2×D37—22no—
82C2×D37—42no—
83C2×D37—44no—
84C2×D37—88no—
85C2×D37#12412yes—
86C4×C37—22no—
87C4×C37—42no—
88C4×C37C2×#4112yes—
89Dic37—42no—
90Dic37#12412yes—
91Dic37AGL(1,ℤ/8)14yes—
92#3138—371nomaximal, Sylow
93C2×C37—82no—
94C2×C37C2×#12411yescharacteristic
95C2×C37C2×AGL(1,ℤ/8)12yes—
96D37—22no—
97D37—82no—
98#533—371no—
99C2×#127—371no—
100#490—371no—
101#490—371no—
102#490—371no—
103#490D3711yescharacteristic, complemented
104#486—374no—
105#418—374no—
106C4×M16—371no—
107C37#313811yescharacteristic, complemented, Sylow
108C22×D4—372no—
109C22×D4—742no—
110C2×M16—372no—
111C4⋊Q8—372no—
112#127—372no—
113#127—371no—
114#127—742no—
115#127C2×D3711yescharacteristic
116#125—371no—
117#125C2×D3711yescharacteristic, complemented
118C22⋊Q8—742no—
119C4×Q8—742no—
120#117—372no—
121C2×C42—371no—
122#102—374no—
123#102—374no—
124#102—374no—
125#102C2×D3714yescomplemented
126#97—371no—
127#97C2×D3711yescharacteristic, complemented
128C4×C8—372no—
129C24—742no—
130C2×Q8—742no—
131C2×D4—22no—
132C2×D4—372no—
133C2×D4—748no—
134C2×D4—744no—
135C2×D4—742no—
136C2×D4—742no—
137C2×D4—1488no—
138C2×D4C22×D3712yes—
139C22×C4—371no—
140C22×C4—372no—
141M16—744no—
142C2×C8—372no—
143C2×C8C22×D3712yes—
144C4⋊C4—22no—
145C4⋊C4—372no—
146C4⋊C4—742no—
147C4⋊C4—742no—
148C4⋊C4C22×D3712yes—
149C22⋊C4—742no—
150C42—372no—
151C42—371no—
152C42—742no—
153C42C22×D3711yescharacteristic
154C23—22no—
155C23—371no—
156C23—742no—
157C23—1484no—
158C23—1488no—
159Q8—1484no—
160D4—24no—
161D4—44no—
162D4—744no—
163D4—1484no—
164D4—1484no—
165D4—1488no—
166C2×C4—22no—
167C2×C4—371no—
168C2×C4—372no—
169C2×C4—374no—
170C2×C4—744no—
171C2×C4—742no—
172C2×C4D4×D3712yes—
173C2×C4C23×D3711yescharacteristic
174C8—22no—
175C8—742no—
176C22—42no—
177C22—44no—
178C22—372no—
179C22—2968no—
180C22—742no—
181C22—1482no—
182C22—1484no—
183C22C2×D4×D3711yescharacteristic
184C4—22no—
185C4—42no—
186C4—372no—
187C4—374no—
188C4—1482no—
189C4#41×D3712yes—
190C2—82no—
191C2—2962no—
192C2—742no—
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
hypocenterC37#3138
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
1. #14558089C2semidirect
3. #14557899C2semidirect
4. #14557898C2semidirect
5. #14557897C2semidirect
6. #14557878C2semidirect
7. #14557536C2semidirect
8. #14557485C2semidirect
9. C37×#490C2semidirect
13. #11924535C22semidirect
17. #11924528C22semidirect
22. #11924458C22semidirect
23. #11924457C22semidirect
24. #11924456C22semidirect
25. #11924447C22semidirect
26. C8×Dic37C22semidirect
28. #125×C37C22semidirect
29. #102×C37C22semidirect
30. #97×C37C22semidirect
103. #490D37semidirect
107. C37#3138semidirect
117. #125C2×D37semidirect
125. #102C2×D37semidirect
127. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580892
#127×D372
#145578992
#145578982
#145578972
#145578782
#145575362
#145574852
C37×#4902
#313837