Finite Group Databasebeta

← #20254854

Subgroups — #20254854

Order 6016.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689746C212yesmaximal, complemented
2#15689412C212yesmaximal, complemented
3#15689406C212yesmaximal, complemented
4#15689376C211yesmaximal, characteristic
5#15689354C212yesmaximal, complemented
6#15689347C212yesmaximal, complemented
7#15689341C212yesmaximal, complemented
8#15689151C211yesmaximal, characteristic, complemented
9C47×#470C211yesmaximal, characteristic, complemented
10C2×#10625336C2212yes—
11C2×D376C2211yescharacteristic
12C22×C47⋊C8C2211yescharacteristic
13#13094023C2212yes—
14#13094019—22no—
15#13094013C2212yes—
16#13094010—22no—
17#13094006—22no—
18#13094004—22no—
19#13093998C2212yes—
20Q8×Dic47C2212yes—
21#13093986C2212yes—
22#13093983C2211yescharacteristic
23#13093956C2211yescharacteristic
24#13093955C2212yes—
25Dic47⋊C8C2212yes—
26Dic47⋊C8C2212yes—
27#13093948C2212yes—
28#13093946C2212yes—
29#13093944C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#106×C47C2211yescharacteristic
34#103×C47C2212yes—
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—22no—
38C2×D188C2312yes—
39C2×C4×D47—22no—
40C2×Dic94—22no—
41Q16×C47—41no—
42M16×C47—41no—
43C2×C8×C47C2311yescharacteristic
44C2×C8×C47C2311yescharacteristic
45C4⋊C4×C47—22no—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—22no—
48C22⋊Dic47D411yescharacteristic
49C22⋊Dic47D411yescharacteristic
50#10625336—42no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47D412yes—
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C4×Dic47C2312yes—
61C2×C47⋊C8—41no—
62C2×C47⋊C8C2312yes—
63D376—41no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66Q8×C47—22no—
67Q8×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2411yescharacteristic
74C22⋊D47—82no—
75C2×Dic47—22no—
76C2×Dic47C2×D412yes—
77C2×Dic47C2×D412yes—
78D188—22no—
79D188—22no—
80C4×D47—82no—
81Dic94—82no—
82C8×C47—21no—
83C8×C47—21no—
84C47⋊C8—22no—
85C22×C47—21no—
86C22×C47—22no—
87C22×C47C22×D411yescharacteristic
88C2×D47—42no—
89C2×D47—42no—
90C2×D47—42no—
91C4×C47—21no—
92C4×C47—42no—
93C4×C47—42no—
94C4×C47H(5,𝔽2)11yescharacteristic
95C4×C472−1+411yescharacteristic
96Dic47—22no—
97Dic47—22no—
98Dic47—42no—
99#3263—471nomaximal, Sylow
100C2×C47—41no—
101C2×C47#53711yescharacteristic
102C2×C47#57712yes—
103D47—82no—
104#542—472no—
105#476—472no—
106#475—472no—
107#470D4711yescharacteristic, complemented
108#469—471no—
109#465—472no—
110#464—472no—
111#463—472no—
112#424—471no—
113C47#326311yescharacteristic, complemented, Sylow
114C2×Q16C2×D4711yescharacteristic
115C2×SD16—472no—
116C2×D8—471no—
117C2×M16C2×D4711yescharacteristic
118C22×C8—471no—
119C4⋊Q8—472no—
120#126—942no—
121#124—472no—
122#124—942no—
123#123—942no—
124C22⋊Q8—942no—
125C22⋊Q8C2×D4712yes—
126#121—472no—
127C4×Q8—472no—
128C4×D4—472no—
129#117—471no—
130#106—471no—
131#106—472no—
132#106C2×D4711yescharacteristic
133C4⋊C8—472no—
134C4⋊C8—472no—
135#103—472no—
136#103C2×D4712yes—
137#102—472no—
138#102—472no—
139C2×Q8—942no—
140C2×Q8C22×D4712yes—
141C2×D4—472no—
142C2×D4—942no—
143C22×C4—942no—
144C22×C4C22×D4711yescharacteristic
145Q16—41no—
146SD16—1882no—
147D8—1881no—
148M16—41no—
149C2×C8—472no—
150C2×C8—1881no—
151C2×C8C22×D4711yescharacteristic
152C2×C8C22×D4711yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—472no—
155C4⋊C4—472no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4C22×D4712yes—
159C22⋊C4—22no—
160C22⋊C4—471no—
161C22⋊C4—471no—
162C22⋊C4—942no—
163C22⋊C4—942no—
164C22⋊C4—942no—
165C22⋊C4—942no—
166C42—472no—
167C42—942no—
168C23—942no—
169C23D4×D4711yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—3762no—
173D4—942no—
174D4—942no—
175D4—3762no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—472no—
181C2×C4—472no—
182C2×C4—942no—
183C2×C4—3762no—
184C2×C4D4×D4711yescharacteristic
185C2×C4C23×D4711yescharacteristic
186C8—21no—
187C8—21no—
188C8—942no—
189C22—22no—
190C22—21no—
191C22—1882no—
192C22—1882no—
193C22—1882no—
194C22C2×D4×D4711yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—942no—
199C4—942no—
200C4—1882no—
201C4#1309406911yescharacteristic
202C4#1309407111yescharacteristic
203C2—41no—
204C2—3762no—
205C2#1568970011yescharacteristic
206C2#1568993212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3263
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689412C2semidirect
3. #15689406C2semidirect
5. #15689354C2semidirect
6. #15689347C2semidirect
7. #15689341C2semidirect
8. #15689151C2semidirect
9. C47×#470C2semidirect
107. #470D47semidirect
113. C47#3263semidirect