Finite Group Databasebeta

← #20248385

Subgroups — #20248385

Order 6016.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094013C211yesmaximal, characteristic
3C2×#13094012C211yesmaximal, characteristic
4C2×#13093986C211yesmaximal, characteristic
5#15689052C214yesmaximal, complemented
6#15689028C211yesmaximal, characteristic, complemented
7#15688982C214yesmaximal, complemented
8C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
9C47×#391C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094022—24no—
14#13094013—24no—
15#13094012—24no—
16#13093986—24no—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2214yes—
27C22×Q8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2214yes—
31C23×D47C2312yes—
32C2×Q8×C47—22no—
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2311yescharacteristic
43C2×D188—22no—
44C2×D188—22no—
45C2×D188D414yes—
46C2×C4×D47—24no—
47C2×C4×D47—28no—
48C2×Dic94—22no—
49C2×Dic94—22no—
50C2×Dic94—22no—
51C4⋊C4×C47—22no—
52C42×C47—22no—
53(C2×D47)⋊C4—28no—
54(C2×D47)⋊C4—28no—
55(C2×D47)⋊C4—24no—
56Dic47⋊C4—24no—
57Dic47⋊C4—24no—
58Dic47⋊C4—24no—
59C4×Dic47—22no—
60C4×Dic47D414yes—
61C23×C47C2411yescharacteristic
62C22×D47—22no—
63C22×D47—24no—
64C22×D47—22no—
65C22×D47—24no—
66C22×D47C2×D414yes—
67Q8×C47—44no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—24no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47#4112yes—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88C2×Dic47#4114yes—
89D188—28no—
90C4×D47—48no—
91Dic94—44no—
92C22×C47C22×D411yescharacteristic
93C22×C47C22×D411yescharacteristic
94C22×C47C2×#4112yes—
95C22×C47C2×#4111yescharacteristic
96C22×C472−1+412yes—
97C2×D47—24no—
98C2×D47—28no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—44no—
102C4×C47—42no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47#12114yes—
106Dic47—22no—
107Dic47—42no—
108Dic47—42no—
109Dic47#12414yescomplemented
110#2547—471nomaximal, Sylow
111C2×C47C2×#12111yescharacteristic
112C2×C47C2×#12411yescharacteristic
113C2×C47#53611yescharacteristic
114C2×C47#54712yes—
115C2×C47#55612yes—
116D47—44no—
117C2×C4⋊Q8—471no—
118C2×#124—471no—
119C2×#124—471no—
120C2×C4×D4—471no—
121#397—474no—
122#391—471no—
123#391D4711yescharacteristic, complemented
124#380—474no—
125C4×C4⋊C4—471no—
126C47#254711yescharacteristic, complemented, Sylow
127C22×Q8—471no—
128C22×Q8C2×D4711yescharacteristic
129C22×D4—471no—
130C23×C4—472no—
131C4⋊Q8—944no—
132#124—944no—
133#124—944no—
134C4×D4—944no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—472no—
140C2×C22⋊C4—474no—
141C2×C22⋊C4—474no—
142C2×C42—471no—
143C2×C42—471no—
144C2×C42C2×D4711yescharacteristic
145#95—472no—
146#95—474no—
147#95C2×D4714yes—
148C24—472no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—942no—
153C2×Q8—942no—
154C2×Q8—942no—
155C2×D4—474no—
156C2×D4—942no—
157C2×D4—942no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—472no—
161C22×C4—472no—
162C22×C4—944no—
163C22×C4—948no—
164C22×C4C22×D4712yes—
165C22×C4C22×D4712yes—
166C22×C4C22×D4712yes—
167C22×C4C22×D4711yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—944no—
170C4⋊C4—944no—
171C4⋊C4—944no—
172C22⋊C4—944no—
173C22⋊C4—948no—
174C22⋊C4—948no—
175C42—22no—
176C42—474no—
177C42—942no—
178C23—474no—
179C23—942no—
180C23—944no—
181C23—942no—
182C23—944no—
183C23C23×D4711yescharacteristic
184Q8—44no—
185Q8—1884no—
186D4—948no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—472no—
196C2×C4—474no—
197C2×C4—472no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—1888no—
206C2×C4#1062535012yes—
207C2×C4D4×D4712yes—
208C2×C4D4×D4712yes—
209C22—948no—
210C22—944no—
211C22—1884no—
212C22—1882no—
213C22—1882no—
214C22C2×D4×D4711yescharacteristic
215C22C2×D4×D4711yescharacteristic
216C22#41×D4712yes—
217C22C2×#1062535011yescharacteristic
218C22#1309407212yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—474no—
223C4—942no—
224C4—1882no—
225C4—1882no—
226C4#1309399714yes—
227C2—1884no—
228C2C2×#1309399711yescharacteristic
229C2#124×D4711yescharacteristic
230C2#1568969811yescharacteristic
231C2#1568977512yes—
232C2#1568984512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2547
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
5. #15689052C2semidirect
6. #15689028C2semidirect
7. #15688982C2semidirect
8. C4×Dic47⋊C4C2semidirect
9. C47×#391C2semidirect
109. Dic47#124semidirect
123. #391D47semidirect
126. C47#2547semidirect