Finite Group Databasebeta

← #20252190

Subgroups — #20252190

Order 6016.

492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C2×#13094046C211yesmaximal, characteristic
2C4×#10625350C212yesmaximal, complemented
3#15689236C212yesmaximal, complemented
4#15689231C212yesmaximal, complemented
5#15689225C214yesmaximal, complemented
6#15689161C211yesmaximal, characteristic, complemented
7#15689120C212yesmaximal, complemented
8C2×#97×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10#13094046C418yescomplemented
11C2×Dic188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×D376C2211yescharacteristic
14C4×Dic94C2214yes—
15C4×D188C2214yes—
16C4×C22⋊D47—24no—
17#13093983C2212yes—
18#13093981—22no—
19C42×D47—22no—
20#13093958C2212yes—
21#13093956C2212yes—
22#13093949C2214yes—
23#13093946C2214yes—
24C22×C8×C47C2211yescharacteristic
25C22×C8×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27#97×C47C2212yes—
28#97×C47C2212yes—
29C22×C4×C47D412yes—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—22no—
32#10625350—24no—
33#10625350C2×C418yescomplemented
34C2×D188C2312yes—
35C2×C4×D47—22no—
36C2×C4×D47—24no—
37C2×Dic94C2312yes—
38C2×C8×C47—22no—
39C2×C8×C47C2×C414yescomplemented
40C2×C8×C47C2312yes—
41C2×C8×C47C2311yescharacteristic
42C2×C8×C47C2311yescharacteristic
43C42×C47D412yes—
44C42×C47C2312yes—
45C22⋊Dic47—22no—
46(C2×D47)⋊C4—24no—
47C4⋊Dic47C2314yes—
48Dic47⋊C4—24no—
49C4×Dic47—22no—
50C4×Dic47—24no—
51Dic188C2×C414yescomplemented
52D376C2×C414yescomplemented
53#10625325C2×C418yescomplemented
54C23×C47C2×D411yescharacteristic
55C22×D47—22no—
56C2×C4×C47—42no—
57C2×C4×C47C22×C412yes—
58C2×C4×C47C2×D414yes—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47#4112yes—
61C2×C4×C47C2411yescharacteristic
62C22⋊D47—28no—
63C2×Dic47—22no—
64C2×Dic47—24no—
65D188—22no—
66D188C22×C414yes—
67C4×D47—28no—
68C4×D47—48no—
69Dic94—22no—
70Dic94C22×C414yes—
71C8×C47—22no—
72C8×C47C22×C412yes—
73C8×C47C22×C412yes—
74C22×C47—22no—
75C22×C47C4×D412yes—
76C22×C47C22×D411yescharacteristic
77C2×D47—24no—
78C2×D47—44no—
79C4×C47—24no—
80C4×C47C4×D412yes—
81C4×C47C23×C411yescharacteristic
82C4×C47C2×#4111yescharacteristic
83Dic47—24no—
84Dic47—44no—
85#2943—471nomaximal, Sylow
86C2×C47—22no—
87C2×C47C2×C4×D411yescharacteristic
88C2×C47#57512yes—
89D47—44no—
90C2×#135—471no—
91C4×#41—472no—
92#442—472no—
93#441—472no—
94#440—474no—
95#427—471no—
96#416—472no—
97C2×#97D4711yescharacteristic, complemented
98C47#294311yescharacteristic, complemented, Sylow
99C2×#41—472no—
100#135—478no—
101C2×Q16—471no—
102C2×SD16—472no—
103C2×D8—471no—
104C22×C8C2×D4711yescharacteristic
105C22×C8C2×D4711yescharacteristic
106C4×Q8—474no—
107C4×D4—474no—
108C4×D4—944no—
109#117—472no—
110#117—942no—
111C2×C42—942no—
112C2×C42C2×D4711yescharacteristic
113#107—472no—
114#106—472no—
115#103—474no—
116#102—474no—
117#97C2×D4712yes—
118#97C2×D4712yes—
119#41—478no—
120#41—944no—
121C2×Q8—472no—
122C2×D4—472no—
123C2×D4—942no—
124C22×C4—942no—
125C22×C4—944no—
126C22×C4D18812yes—
127C22×C4C22×D4711yescharacteristic
128Q16—474no—
129SD16—478no—
130D8—474no—
131C2×C8—22no—
132C2×C8C4×D4714yescomplemented
133C2×C8C22×D4712yes—
134C2×C8C22×D4711yescharacteristic
135C2×C8C22×D4711yescharacteristic
136C4⋊C4—474no—
137C4⋊C4—944no—
138C22⋊C4—942no—
139C22⋊C4—944no—
140C42—944no—
141C42—942no—
142C42D18812yes—
143C42C22×D4712yes—
144C23—942no—
145C23C2×D18811yescharacteristic
146Q8—474no—
147Q8—942no—
148D4—474no—
149D4—948no—
150D4—942no—
151C2×C4—42no—
152C2×C4—942no—
153C2×C4—948no—
154C2×C4—944no—
155C2×C4—1888no—
156C2×C4C2×C4×D4712yes—
157C2×C4C2×D18814yes—
158C2×C4C2×D18811yescharacteristic
159C2×C4#1062535012yes—
160C2×C4C23×D4711yescharacteristic
161C8—22no—
162C8C2×C4×D4712yes—
163C8C2×C4×D4712yes—
164C22—22no—
165C22—944no—
166C22—1884no—
167C22C4×D18812yes—
168C22C22×D18811yescharacteristic
169C4—24no—
170C4—944no—
171C4—1884no—
172C4C4×D18812yes—
173C4C22×C4×D4711yescharacteristic
174C4C2×#1062535011yescharacteristic
175C2—22no—
176C2—1884no—
177C2C2×C4×D18811yescharacteristic
178C2#1568992312yes—
subgroupG/H
centerC2×C4C2×D188
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#97×C47C2
socleC22×C47C22×D4
hypercenterC2×#97D47
hypocenterC47#2943
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C4×#10625350C2semidirect
3. #15689236C2semidirect
4. #15689231C2semidirect
5. #15689225C2semidirect
6. #15689161C2semidirect
7. #15689120C2semidirect
8. C2×#97×C47C2semidirect
10. #13094046C4semidirect
33. #10625350C2×C4semidirect
39. C2×C8×C47C2×C4semidirect
51. Dic188C2×C4semidirect
52. D376C2×C4semidirect
53. #10625325C2×C4semidirect
97. C2×#97D47semidirect
98. C47#2943semidirect
132. C2×C8C4×D47semidirect