Finite Group Databasebeta

← #20249159

Subgroups — #20249159

Order 6016.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094004C211yesmaximal, characteristic
3C2×#13094000C211yesmaximal, characteristic
4C2×#13093981C211yesmaximal, characteristic
5#15689057C214yesmaximal, complemented
6#15689052C214yesmaximal
7#15689029C211yesmaximal, characteristic, complemented
8#15688988C211yesmaximal, characteristic, complemented
9C47×#391C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×C4×D47C2211yescharacteristic
12#13094022—24no—
13#13094004—24no—
14#13094000—24no—
15#13093981—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2214yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2214yes—
26C47⋊#95C2214yes—
27C22×Q8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2214yes—
31C23×D47C2311yescharacteristic
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×Dic47C2312yes—
42C22×Dic47C2311yescharacteristic
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47D414yes—
46C2×Dic94—22no—
47C2×Dic94—22no—
48C2×Dic94—22no—
49C4⋊C4×C47—22no—
50C42×C47—22no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53(C2×D47)⋊C4—24no—
54C4⋊Dic47—22no—
55C4⋊Dic47—24no—
56Dic47⋊C4—24no—
57Dic47⋊C4—24no—
58Dic47⋊C4—28no—
59C4×Dic47D414yes—
60C23×C47C2411yescharacteristic
61C22×D47—21no—
62C22×D47—21no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47C2×D412yes—
66Q8×C47—44no—
67C2×C4×C47—22no—
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×C47C2×D412yes—
76C2×C4×C47C2×D412yes—
77C2×C4×C47#4112yes—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47C2×D414yes—
88C2×Dic47C2×D412yes—
89C4×D47—28no—
90Dic94—44no—
91C22×C47C22×D411yescharacteristic
92C22×C47C22×D411yescharacteristic
93C22×C47C2×#4111yescharacteristic
94C22×C472−1+412yes—
95C22×C472−1+412yes—
96C2×D47—22no—
97C2×D47—22no—
98C2×D47—22no—
99C2×D47—42no—
100C2×D47—42no—
101C4×C47—42no—
102C4×C47—42no—
103C4×C47—42no—
104C4×C47#12114yes—
105Dic47—22no—
106Dic47—24no—
107Dic47—42no—
108Dic47—42no—
109#2621—471nomaximal, Sylow
110C2×C47C2×#12111yescharacteristic
111C2×C47#53611yescharacteristic
112C2×C47#53612yes—
113C2×C47#53611yescharacteristic
114C2×C47#54112yes—
115D47—42no—
116C2×C4⋊Q8—471no—
117C2×C22⋊Q8—471no—
118C2×C22⋊Q8—471no—
119C2×#117—471no—
120#398—474no—
121#397—474no—
122#391—471no—
123#391D4711yescharacteristic, complemented
124#382—471no—
125C47#262111yescharacteristic, complemented, Sylow
126C22×Q8—471no—
127C22×Q8C2×D4711yescharacteristic
128C23×C4—471no—
129C4⋊Q8—944no—
130C22⋊Q8—944no—
131C22⋊Q8—944no—
132#117—944no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4—474no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—472no—
140C2×C22⋊C4—472no—
141C2×C22⋊C4—472no—
142C2×C42—471no—
143C2×C42C2×D4711yescharacteristic
144#95—474no—
145#95—474no—
146#95C2×D4714yes—
147C24—471no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—942no—
152C2×Q8—942no—
153C2×Q8—942no—
154C22×C4—472no—
155C22×C4—471no—
156C22×C4—474no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4—942no—
160C22×C4—942no—
161C22×C4C22×D4712yes—
162C22×C4C22×D4712yes—
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—944no—
167C4⋊C4—944no—
168C4⋊C4—948no—
169C4⋊C4—944no—
170C4⋊C4—942no—
171C22⋊C4—944no—
172C22⋊C4—944no—
173C22⋊C4—944no—
174C42—22no—
175C42—474no—
176C23—472no—
177C23—941no—
178C23—941no—
179C23—942no—
180C23—942no—
181C23C23×D4711yescharacteristic
182Q8—44no—
183Q8—1884no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—474no—
193C2×C4—472no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—948no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—944no—
204C2×C4#1062535012yes—
205C2×C4D4×D4712yes—
206C2×C4D4×D4712yes—
207C22—942no—
208C22—942no—
209C22—942no—
210C22—1882no—
211C22—1882no—
212C22C2×D4×D4711yescharacteristic
213C22C2×D4×D4711yescharacteristic
214C22C2×#1062535011yescharacteristic
215C22#1309407112yes—
216C22#1309407212yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—942no—
221C4—944no—
222C4—1882no—
223C4—1882no—
224C4#1309399714yes—
225C2—1882no—
226C2C2×#1309399711yescharacteristic
227C2#1568969311yescharacteristic
228C2#1568969612yes—
229C2#1568969811yescharacteristic
230C2#1568973112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2621
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. #15689057C2semidirect
7. #15689029C2semidirect
8. #15688988C2semidirect
9. C47×#391C2semidirect
123. #391D47semidirect
125. C47#2621semidirect