Finite Group Databasebeta

← #20247842

Subgroups — #20247842

Order 6016.

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

normal subgroups only

This group has 484 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×#13093983C211yesmaximal, characteristic
2#15689051C214yesmaximal
3#15689030C211yesmaximal, characteristic, complemented
4#15689030C211yesmaximal, characteristic, complemented
5#15689004C214yesmaximal, complemented
6#15688992C211yesmaximal, characteristic, complemented
7#15688988C211yesmaximal, characteristic, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic
9C2×C22⋊Q8×C47C211yesmaximal, characteristic
10#13093983—24no—
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2214yes—
14C2×C22⋊Dic47C2212yes—
15C2×C22⋊Dic47C2212yes—
16C2×C4×Dic47C2211yescharacteristic
17C2×C4×Dic47C2211yescharacteristic
18C2×C4×Dic47C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2214yes—
21C47⋊#95C2214yes—
22C47⋊#95C2214yes—
23C22×Q8×C47C2211yescharacteristic
24C23×C4×C47C2211yescharacteristic
25C22⋊Q8×C47—24no—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2212yes—
29C24×C47C2311yescharacteristic
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47—22no—
33C22×C4×C47—22no—
34C22×C4×C47—22no—
35C22×C4×C47D414yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—24no—
46C22⋊C4×C47—24no—
47C22⋊Dic47—24no—
48C22⋊Dic47—24no—
49C4⋊Dic47—22no—
50C4⋊Dic47—22no—
51Dic47⋊C4—28no—
52C4×Dic47—24no—
53C4×Dic47—22no—
54C4×Dic47—22no—
55C23×C47—22no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—22no—
59C23×C47C2×D412yes—
60C23×C47C2411yescharacteristic
61Q8×C47—44no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—28no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47#4112yes—
73C2×C4×C47#4112yes—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—24no—
80C2×Dic47—22no—
81C2×Dic47—24no—
82C2×Dic47—22no—
83C2×Dic47#4114yes—
84C22×C47—22no—
85C22×C47—22no—
86C22×C47—22no—
87C22×C47—42no—
88C22×C47—42no—
89C22×C47C22×D411yescharacteristic
90C22×C47C2×#4112yes—
91C22×C47C2×#4111yescharacteristic
92C22×C47C2×#4111yescharacteristic
93C22×C472−1+412yes—
94C4×C47—22no—
95C4×C47—42no—
96C4×C47—42no—
97C4×C47#12314yes—
98Dic47—24no—
99Dic47—42no—
100Dic47—42no—
101Dic47—42no—
102#2499—471nomaximal, Sylow
103C2×C47—42no—
104C2×C47C2×#12311yescharacteristic
105C2×C47#53211yescharacteristic
106C2×C47#53611yescharacteristic
107C2×C47#55212yes—
108C2×C47#55612yes—
109C2×C22⋊Q8D4711yescharacteristic
110C2×#117—471no—
111#397—474no—
112#391—471no—
113#391—471no—
114#387—474no—
115#384—471no—
116#382—471no—
117C4×C22⋊C4—471no—
118C47#249911yescharacteristic, complemented, Sylow
119C22×Q8C2×D4711yescharacteristic
120C23×C4C2×D4711yescharacteristic
121C22⋊Q8—24no—
122#117—944no—
123C2×C4⋊C4—471no—
124C2×C4⋊C4—471no—
125C2×C4⋊C4—474no—
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C4⋊C4C2×D4712yes—
128C2×C22⋊C4—472no—
129C2×C22⋊C4—472no—
130C2×C22⋊C4C2×D4712yes—
131C2×C42—472no—
132C2×C42—471no—
133C2×C42—471no—
134#95—472no—
135#95—474no—
136#95—474no—
137#95—474no—
138C24C22×D4711yescharacteristic
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4C22⋊D4714yes—
149C22×C4C22×D4712yes—
150C22×C4C22×D4712yes—
151C22×C4C22×D4711yescharacteristic
152C22×C4C22×D4711yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—24no—
155C4⋊C4—948no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C22⋊C4—24no—
159C22⋊C4—944no—
160C22⋊C4—944no—
161C42—942no—
162C42—942no—
163C42—944no—
164C23—22no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23C2×C22⋊D4712yes—
169C23C23×D4711yescharacteristic
170Q8—44no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—28no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—474no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—944no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—944no—
189C2×C4#1062535212yes—
190C2×C4#1062535212yes—
191C2×C4C2×C22⋊D4712yes—
192C2×C4C2×C22⋊D4712yes—
193C22—22no—
194C22—22no—
195C22—22no—
196C22—42no—
197C22—42no—
198C22C22×C22⋊D4711yescharacteristic
199C22#41×D4712yes—
200C22C2×#1062535211yescharacteristic
201C22C2×#1062535211yescharacteristic
202C22#1309407212yes—
203C4—22no—
204C4—42no—
205C4—42no—
206C4—944no—
207C4—1882no—
208C4—1882no—
209C4—1882no—
210C4#1309400514yes—
211C2—42no—
212C2C2×#1309400511yescharacteristic
213C2#1568966911yescharacteristic
214C2#1568969711yescharacteristic
215C2#1568980712yes—
216C2#1568984412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2499
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #15689030C2semidirect
4. #15689030C2semidirect
5. #15689004C2semidirect
6. #15688992C2semidirect
7. #15688988C2semidirect
118. C47#2499semidirect