Finite Group Databasebeta

← #20252271

Subgroups — #20252271

Order 6016.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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
2#15689604C212yesmaximal, complemented
3#15689234C212yesmaximal, complemented
4#15689229C212yesmaximal, complemented
5#15689210C214yesmaximal, complemented
6#15689122C212yesmaximal, complemented
7#15689078C211yesmaximal, characteristic, complemented
8C2×#106×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10#13094046C418yescomplemented
11C2×Dic188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13093989C2214yes—
16#13093986C2214yes—
17C4×C22⋊D47—24no—
18#13093983C2211yescharacteristic
19#13093982—22no—
20C4⋊C4×D47—22no—
21#13093947C2214yes—
22#13093944C2214yes—
23#13093934C2212yes—
24C8×Dic47C2212yes—
25C22×C8×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2212yes—
27#106×C47C2212yes—
28#106×C47C2212yes—
29C22×C4×C47—22no—
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×C47C2×C414yescomplemented
39C2×C8×C47C2311yescharacteristic
40C2×C8×C47C2311yescharacteristic
41C4⋊C4×C47—22no—
42C4⋊C4×C47C2314yes—
43C22⋊Dic47D412yes—
44(C2×D47)⋊C4—24no—
45C4⋊Dic47D412yes—
46Dic47⋊C4—24no—
47C4×Dic47—24no—
48C4×Dic47C2312yes—
49#10625329—22no—
50C2×C47⋊C8C2312yes—
51Dic188C2×C414yescomplemented
52D376C2×C414yescomplemented
53#10625325C2×C418yescomplemented
54C23×C47C2×D411yescharacteristic
55C22×D47—22no—
56C2×C4×C47—24no—
57C2×C4×C47—82no—
58C2×C4×C47C22×C412yes—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47#4112yes—
61C2×C4×C47C2411yescharacteristic
62C22⋊D47—28no—
63C2×Dic47—22no—
64C2×Dic47C2×D414yes—
65D188—22no—
66D188C22×C414yes—
67C4×D47—28no—
68C4×D47—84no—
69Dic94—22no—
70Dic94C22×C414yes—
71C8×C47C22×C412yes—
72C8×C47C22×C412yes—
73C47⋊C8—22no—
74C22×C47—22no—
75C22×C47C4×D412yes—
76C22×C47C22×D411yescharacteristic
77C2×D47—24no—
78C2×D47—42no—
79C2×D47—42no—
80C4×C47—44no—
81C4×C47C4×D412yes—
82C4×C47C23×C411yescharacteristic
83C4×C47C2×#4111yescharacteristic
84Dic47—24no—
85Dic47—24no—
86#2952—471nomaximal, Sylow
87C2×C47—22no—
88C2×C47C2×C4×D411yescharacteristic
89C2×C47#57712yes—
90D47—44no—
91C2×#135—471no—
92#520—472no—
93#442—472no—
94#441—472no—
95C4×SD16—474no—
96C2×#106D4711yescharacteristic, complemented
97#417—472no—
98#405—471no—
99C47#295211yescharacteristic, complemented, Sylow
100C2×#41—472no—
101#135—478no—
102C2×Q16—471no—
103C2×SD16—472no—
104C2×D8—471no—
105C2×M16—471no—
106C22×C8C2×D4711yescharacteristic
107C4×Q8—474no—
108C4×D4—474no—
109C4×D4—944no—
110#117—471no—
111#117—942no—
112C2×C4⋊C4—942no—
113C2×C4⋊C4C2×D4712yes—
114#106C2×D4712yes—
115#106C2×D4712yes—
116#103—474no—
117#102—474no—
118#97—472no—
119C4×C8—472no—
120#41—478no—
121#41—944no—
122C2×Q8—472no—
123C2×D4—472no—
124C2×D4—942no—
125C22×C4—22no—
126C22×C4—944no—
127C22×C4—942no—
128C22×C4C22×D4711yescharacteristic
129Q16—474no—
130SD16—478no—
131D8—474no—
132M16—942no—
133C2×C8—472no—
134C2×C8C4×D4714yescomplemented
135C2×C8C22×D4711yescharacteristic
136C2×C8C22×D4711yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—472no—
139C4⋊C4—944no—
140C4⋊C4C22×D4714yes—
141C22⋊C4—472no—
142C22⋊C4—944no—
143C42—472no—
144C42—944no—
145C23—942no—
146C23D4×D4711yescharacteristic
147Q8—474no—
148Q8—942no—
149D4—474no—
150D4—948no—
151D4—942no—
152C2×C4—24no—
153C2×C4—82no—
154C2×C4—474no—
155C2×C4—942no—
156C2×C4—948no—
157C2×C4—3764no—
158C2×C4C2×C4×D4712yes—
159C2×C4D4×D4711yescharacteristic
160C2×C4#1062535412yes—
161C2×C4C23×D4711yescharacteristic
162C8—942no—
163C8C2×C4×D4712yes—
164C8C2×C4×D4712yes—
165C22—22no—
166C22—944no—
167C22—1882no—
168C22—1882no—
169C22#1309398612yes—
170C22C2×D4×D4711yescharacteristic
171C4—44no—
172C4—944no—
173C4—944no—
174C4#1309398612yes—
175C4C22×C4×D4711yescharacteristic
176C4C2×#1062535411yescharacteristic
177C2—22no—
178C2—1884no—
179C2C2×#1309398611yescharacteristic
180C2#1568992912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#2952
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #15689604C2semidirect
3. #15689234C2semidirect
4. #15689229C2semidirect
5. #15689210C2semidirect
6. #15689122C2semidirect
7. #15689078C2semidirect
8. C2×#106×C47C2semidirect
10. #13094046C4semidirect
33. #10625350C2×C4semidirect
38. C2×C8×C47C2×C4semidirect
51. Dic188C2×C4semidirect
52. D376C2×C4semidirect
53. #10625325C2×C4semidirect
96. C2×#106D47semidirect
99. C47#2952semidirect
134. C2×C8C4×D47semidirect