Finite Group Databasebeta

← #20251762

Subgroups — #20251762

Order 6016.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13094013C211yesmaximal, characteristic
3#15689030C211yesmaximal, characteristic, complemented
4#15689025C211yesmaximal, characteristic
5#15689024C211yesmaximal, characteristic
6#15689015C214yesmaximal, complemented
7#15689012C214yesmaximal, complemented
8C42×Dic47C211yesmaximal, characteristic, complemented
9C47×#391C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11#13094015—24no—
12#13094013—24no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2214yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×C4×Dic47C2212yes—
21C2×C4×Dic47C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2214yes—
25C22×Q8×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2214yes—
29C23×D47C2312yes—
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47—22no—
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2311yescharacteristic
39C22×Dic47C2311yescharacteristic
40C22×Dic47C2312yes—
41C2×D188—22no—
42C2×D188—22no—
43C2×D188—22no—
44C4⋊C4×C47—22no—
45C42×C47—22no—
46(C2×D47)⋊C4—28no—
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4—28no—
50C4⋊Dic47—22no—
51C4⋊Dic47—24no—
52Dic47⋊C4—24no—
53C4×Dic47—22no—
54C4×Dic47—24no—
55C4×Dic47—24no—
56C4×Dic47D414yes—
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—24no—
60C22×D47—24no—
61C22×D47—22no—
62C22×D47—22no—
63Q8×C47—44no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—24no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D412yes—
72C2×C4×C47#4112yes—
73C2×C4×C47#4112yes—
74C2×C4×C47#4114yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—24no—
81C2×Dic47C2×D412yes—
82C2×Dic47C2×D412yes—
83C2×Dic47#4114yes—
84D188—44no—
85C22×C47C22×D411yescharacteristic
86C22×C47C2×#4112yes—
87C22×C47C2×#4111yescharacteristic
88C22×C47C2×#4111yescharacteristic
89C22×C47C2×#4112yes—
90C2×D47—42no—
91C2×D47—44no—
92C2×D47—44no—
93C2×D47—42no—
94C2×D47—42no—
95C4×C47—24no—
96C4×C47—42no—
97C4×C47—42no—
98C4×C47#12414yes—
99Dic47—24no—
100Dic47—22no—
101Dic47—22no—
102Dic47—42no—
103#2861—471nomaximal, Sylow
104C2×C47C2×#12411yescharacteristic
105C2×C47#52912yes—
106C2×C47#52912yes—
107C2×C47#53211yescharacteristic
108C2×C47#53211yescharacteristic
109D47—82no—
110C2×#125—471no—
111C2×#124—471no—
112#391—471no—
113#391D4711yescharacteristic, complemented
114#390—471no—
115#390—471no—
116#388—474no—
117#388—474no—
118C43—471no—
119C47#286111yescharacteristic, complemented, Sylow
120C22×Q8C2×D4711yescharacteristic
121C22×D4—471no—
122#125—944no—
123#124—944no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C22⋊C4—472no—
129C2×C22⋊C4—472no—
130C2×C22⋊C4—474no—
131C2×C22⋊C4—474no—
132C2×C42—471no—
133C2×C42—472no—
134C2×C42—472no—
135C2×C42—471no—
136C2×C42C2×D4711yescharacteristic
137#95—474no—
138#95C2×D4714yes—
139C24—472no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—942no—
144C2×D4—942no—
145C2×D4—942no—
146C22×C4—472no—
147C22×C4—471no—
148C22×C4—471no—
149C22×C4—472no—
150C22×C4C22×D4712yes—
151C22×C4C22×D4712yes—
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—944no—
156C4⋊C4—944no—
157C4⋊C4—942no—
158C22⋊C4—948no—
159C22⋊C4—944no—
160C22⋊C4—944no—
161C22⋊C4—948no—
162C42—22no—
163C42—474no—
164C42—944no—
165C42—942no—
166C42—944no—
167C23—942no—
168C23—944no—
169C23—942no—
170C23—942no—
171C23—944no—
172C23C23×D4711yescharacteristic
173Q8—44no—
174D4—1884no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—472no—
183C2×C4—472no—
184C2×C4—474no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—944no—
191C2×C4#1062535012yes—
192C2×C4D4×D4712yes—
193C2×C4#1062535212yes—
194C2×C4#1062535414yes—
195C22—1882no—
196C22—1884no—
197C22—1884no—
198C22—1882no—
199C22—1882no—
200C22C2×D4×D4711yescharacteristic
201C22#41×D4712yes—
202C22C2×#1062535211yescharacteristic
203C22C2×#1062535011yescharacteristic
204C22C2×#1062535412yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—944no—
209C4—942no—
210C4—942no—
211C4—1882no—
212C4#1309401014yes—
213C2—3762no—
214C2C2×#1309401011yescharacteristic
215C2#1568965912yes—
216C2#1568966012yes—
217C2#1568967211yescharacteristic
218C2#1568967411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2861
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
3. #15689030C2semidirect
6. #15689015C2semidirect
7. #15689012C2semidirect
8. C42×Dic47C2semidirect
9. C47×#391C2semidirect
113. #391D47semidirect
119. C47#2861semidirect