Finite Group Databasebeta

← #20253761

Subgroups — #20253761

Order 6016.

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#15689679C211yesmaximal, characteristic, complemented
2#127×D47C211yesmaximal, characteristic
3#15689489C211yesmaximal, characteristic, complemented
4#15689488C211yesmaximal, characteristic, complemented
5#15689487C211yesmaximal, characteristic, complemented
6#15689468C214yesmaximal, complemented
7#15689126C214yesmaximal, complemented
8#15689075C211yesmaximal, characteristic, complemented
9C47×#490C211yesmaximal, characteristic, complemented
10C2×D4×D47—22no—
11C2×D4×D47C2212yes—
12C2×#10625324C2212yes—
13#13094023C2212yescomplemented
14#13094021C2211yescharacteristic
15#13094020—22no—
16#13094020C2212yes—
17#13094016C2211yescharacteristic, complemented
18#13094002—22no—
19#13093989—22no—
20#13093982C2212yes—
21C42×D47C2211yescharacteristic
22#13093946C2214yescomplemented
23#13093945C2214yescomplemented
24#13093944C2214yescomplemented
25#13093935C2211yescharacteristic, complemented
26C8×Dic47C2212yescomplemented
27#127×C47C2211yescharacteristic
28#125×C47C2211yescharacteristic, complemented
29#102×C47C2214yescomplemented
30#97×C47C2211yescharacteristic, complemented
31C23×D47—22no—
32C2×D4×C47—22no—
33C2×D4×C47C2312yes—
34C2×C22⋊D47—22no—
35C2×C22⋊D47—24no—
36D4×D47—28no—
37D4×D47—48no—
38C2×D188—22no—
39C2×D188C2312yes—
40C2×C4×D47D412yes—
41C2×C4×D47C2311yescharacteristic
42C2×Dic94—22no—
43C2×C8×C47C2312yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47C2312yes—
46C42×C47C2311yescharacteristic
47(C2×D47)⋊C4—22no—
48C4⋊Dic47C2312yes—
49Dic47⋊C4—22no—
50Dic47⋊C4—22no—
51C4×Dic47—22no—
52C4×Dic47D412yes—
53C4×Dic47C2311yescharacteristic
54C2×C47⋊C8C2312yes—
55#10625324—24no—
56C23×C47—22no—
57C22×D47—22no—
58C22×D47—48no—
59C22×D47—44no—
60C22×D47C2×D411yescharacteristic
61D4×C47—24no—
62D4×C47—44no—
63C2×C4×C47—22no—
64C2×C4×C47C2×D412yes—
65C2×C4×C47C2411yescharacteristic
66C22⋊D47—44no—
67C22⋊D47—48no—
68C2×Dic47—22no—
69C2×Dic47C2×D411yescharacteristic
70C2×Dic47C2×D412yes—
71D188—24no—
72D188—44no—
73C4×D47—24no—
74C4×D47#4114yes—
75Dic94—44no—
76C8×C47—22no—
77C47⋊C8—22no—
78C22×C47—42no—
79C22×C47—44no—
80C22×C47C22×D411yescharacteristic
81C2×D47—22no—
82C2×D47—42no—
83C2×D47—44no—
84C2×D47—88no—
85C2×D47#12412yes—
86C4×C47—22no—
87C4×C47—42no—
88C4×C47C2×#4112yes—
89Dic47—42no—
90Dic47#12412yes—
91Dic47AGL(1,ℤ/8)14yes—
92#3138—471nomaximal, Sylow
93C2×C47—82no—
94C2×C47C2×#12411yescharacteristic
95C2×C47C2×AGL(1,ℤ/8)12yes—
96D47—22no—
97D47—82no—
98#533—471no—
99C2×#127—471no—
100#490—471no—
101#490—471no—
102#490—471no—
103#490D4711yescharacteristic, complemented
104#486—474no—
105#418—474no—
106C4×M16—471no—
107C47#313811yescharacteristic, complemented, Sylow
108C22×D4—472no—
109C22×D4—942no—
110C2×M16—472no—
111C4⋊Q8—472no—
112#127—472no—
113#127—471no—
114#127—942no—
115#127C2×D4711yescharacteristic
116#125—471no—
117#125C2×D4711yescharacteristic, complemented
118C22⋊Q8—942no—
119C4×Q8—942no—
120#117—472no—
121C2×C42—471no—
122#102—474no—
123#102—474no—
124#102—474no—
125#102C2×D4714yescomplemented
126#97—471no—
127#97C2×D4711yescharacteristic, complemented
128C4×C8—472no—
129C24—942no—
130C2×Q8—942no—
131C2×D4—22no—
132C2×D4—472no—
133C2×D4—948no—
134C2×D4—944no—
135C2×D4—942no—
136C2×D4—942no—
137C2×D4—1888no—
138C2×D4C22×D4712yes—
139C22×C4—471no—
140C22×C4—472no—
141M16—944no—
142C2×C8—472no—
143C2×C8C22×D4712yes—
144C4⋊C4—22no—
145C4⋊C4—472no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4C22×D4712yes—
149C22⋊C4—942no—
150C42—472no—
151C42—471no—
152C42—942no—
153C42C22×D4711yescharacteristic
154C23—22no—
155C23—471no—
156C23—942no—
157C23—1884no—
158C23—1888no—
159Q8—1884no—
160D4—24no—
161D4—44no—
162D4—944no—
163D4—1884no—
164D4—1884no—
165D4—1888no—
166C2×C4—22no—
167C2×C4—471no—
168C2×C4—472no—
169C2×C4—474no—
170C2×C4—944no—
171C2×C4—942no—
172C2×C4D4×D4712yes—
173C2×C4C23×D4711yescharacteristic
174C8—22no—
175C8—942no—
176C22—42no—
177C22—44no—
178C22—472no—
179C22—942no—
180C22—3768no—
181C22—1882no—
182C22—1884no—
183C22C2×D4×D4711yescharacteristic
184C4—22no—
185C4—42no—
186C4—472no—
187C4—474no—
188C4—1882no—
189C4#41×D4712yes—
190C2—82no—
191C2—942no—
192C2—3762no—
193C2#124×D4711yescharacteristic
194C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#490C2
socleC22×C47C22×D4
hypercenter#490D47
hypocenterC47#3138
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #15689679C2semidirect
3. #15689489C2semidirect
4. #15689488C2semidirect
5. #15689487C2semidirect
6. #15689468C2semidirect
7. #15689126C2semidirect
8. #15689075C2semidirect
9. C47×#490C2semidirect
13. #13094023C22semidirect
17. #13094016C22semidirect
22. #13093946C22semidirect
23. #13093945C22semidirect
24. #13093944C22semidirect
25. #13093935C22semidirect
26. C8×Dic47C22semidirect
28. #125×C47C22semidirect
29. #102×C47C22semidirect
30. #97×C47C22semidirect
103. #490D47semidirect
107. C47#3138semidirect
117. #125C2×D47semidirect
125. #102C2×D47semidirect
127. #97C2×D47semidirect