Finite Group Databasebeta

← #20253790

Subgroups — #20253790

Order 6016.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689674C211yesmaximal, characteristic
2#125×D47C211yesmaximal, characteristic, complemented
3#15689491C211yesmaximal, characteristic, complemented
4#15689489C211yesmaximal, characteristic, complemented
5#15689488C211yesmaximal, characteristic, complemented
6#15689479C214yesmaximal, complemented
7#15689123C214yesmaximal, complemented
8#15689075C211yesmaximal, characteristic, complemented
9C47×#491C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×#10625324C2212yes—
12#13094021C2211yescharacteristic
13#13094016C2211yescharacteristic
14#13094015C2212yes—
15#13094014—22no—
16#13094013C2212yes—
17#13093999—22no—
18#13093986—22no—
19C4⋊C4×D47—22no—
20C4⋊C4×D47C2212yes—
21C42×D47C2211yescharacteristic
22#13093948C2214yes—
23#13093946C2214yes—
24#13093944C2214yes—
25#13093935C2211yescharacteristic
26C8×Dic47C2212yes—
27C4⋊Q8×C47C2211yescharacteristic
28#125×C47C2211yescharacteristic
29#103×C47C2214yes—
30#97×C47C2211yescharacteristic
31C2×Q8×C47C2312yes—
32#10625354—28no—
33C2×D188—22no—
34C2×D188—22no—
35C2×D188C2312yes—
36C2×C4×D47—22no—
37C2×C4×D47—22no—
38C2×C4×D47D412yes—
39C2×C4×D47C2311yescharacteristic
40C2×C8×C47C2312yes—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—22no—
43C4⋊C4×C47C2312yes—
44C42×C47C2311yescharacteristic
45(C2×D47)⋊C4—24no—
46C4⋊Dic47—22no—
47C4⋊Dic47C2312yes—
48Dic47⋊C4—22no—
49Dic47⋊C4—22no—
50Dic47⋊C4—22no—
51C4×Dic47D412yes—
52C4×Dic47C2311yescharacteristic
53C2×C47⋊C8C2312yes—
54#10625324—24no—
55C22×D47—22no—
56C22×D47C2×D411yescharacteristic
57Q8×C47—24no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2411yescharacteristic
62C2×Dic47—22no—
63C2×Dic47C2×D412yes—
64C2×Dic47C2×D411yescharacteristic
65D188—24no—
66D188—44no—
67D188—44no—
68C4×D47—42no—
69C4×D47—44no—
70C4×D47—44no—
71C4×D47#4114yes—
72C8×C47—22no—
73C47⋊C8—22no—
74C22×C47C22×D411yescharacteristic
75C2×D47—22no—
76C2×D47—42no—
77C2×D47—44no—
78C2×D47#12412yes—
79C4×C47—22no—
80C4×C47—42no—
81C4×C47—42no—
82C4×C47C2×#4112yes—
83Dic47—22no—
84Dic47—42no—
85Dic47#12412yes—
86#3142—471nomaximal, Sylow
87C2×C47C2×#12411yescharacteristic
88C2×C47#57512yes—
89D47—22no—
90D47—82no—
91#532—471no—
92C2×#125—471no—
93#491—471no—
94#491D4711yescharacteristic, complemented
95#490—471no—
96#490—471no—
97#488—474no—
98#417—474no—
99C4×M16—471no—
100C47#314211yescharacteristic, complemented, Sylow
101C2×#41—472no—
102C2×M16—472no—
103C4⋊Q8C2×D4711yescharacteristic
104#127—471no—
105#125—472no—
106#125—471no—
107#125—942no—
108#125C2×D4711yescharacteristic
109#124—472no—
110#121—942no—
111C4×D4—942no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—942no—
114C2×C42—471no—
115#103—474no—
116#103C2×D4714yes—
117#102—474no—
118#102—474no—
119#97—471no—
120#97C2×D4711yescharacteristic
121C4×C8—472no—
122#41—948no—
123C2×Q8C22×D4712yes—
124C2×D4—472no—
125C2×D4—942no—
126C2×D4—942no—
127C22×C4—471no—
128C22×C4—472no—
129C22×C4—942no—
130C22×C4—942no—
131M16—944no—
132C2×C8—472no—
133C2×C8C22×D4712yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—472no—
137C4⋊C4—942no—
138C4⋊C4—942no—
139C4⋊C4—942no—
140C4⋊C4—942no—
141C4⋊C4C22×D4712yes—
142C22⋊C4—944no—
143C42—472no—
144C42—471no—
145C42C22×D4711yescharacteristic
146C23—471no—
147C23—942no—
148Q8—24no—
149D4—944no—
150D4—1884no—
151D4—1884no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—471no—
155C2×C4—474no—
156C2×C4—472no—
157C2×C4—942no—
158C2×C4—1882no—
159C2×C4—1884no—
160C2×C4—1884no—
161C2×C4D4×D4712yes—
162C2×C4C23×D4711yescharacteristic
163C8—22no—
164C8—942no—
165C22—472no—
166C22—942no—
167C22—1882no—
168C22—1884no—
169C22C2×D4×D4711yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—472no—
174C4—942no—
175C4—1882no—
176C4#41×D4712yes—
177C2—942no—
178C2—3762no—
179C2#124×D4711yescharacteristic
180C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#491C2
socleC22×C47C22×D4
hypercenter#491D47
hypocenterC47#3142
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #125×D47C2semidirect
3. #15689491C2semidirect
4. #15689489C2semidirect
5. #15689488C2semidirect
6. #15689479C2semidirect
7. #15689123C2semidirect
8. #15689075C2semidirect
9. C47×#491C2semidirect
94. #491D47semidirect
100. C47#3142semidirect