Finite Group Databasebeta

← #20246725

Subgroups — #20246725

Order 6016.

864 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×#10625350C211yesmaximal, characteristic
2C2×#13094008C212yesmaximal, complemented
3C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
4#15689044C212yesmaximal, complemented
5#15689041C212yesmaximal, complemented
6#15689000C212yesmaximal, complemented
7#15688997C214yesmaximal, complemented
8C47×#381C211yesmaximal, characteristic, complemented
9C2×#10625350—24no—
10C2×#10625350—28no—
11C22×Dic94C2211yescharacteristic
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2212yes—
14C23×Dic47C2211yescharacteristic
15C23×Dic47C2211yescharacteristic
16C22×C4×D47C2212yes—
17#13094008—28no—
18C2×C4⋊Dic47C2214yes—
19C2×Dic47⋊C4—24no—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2214yes—
23C2×(C2×D47)⋊C4C2214yes—
24C47⋊#95C2214yes—
25C23×C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2212yes—
27#95×C47C2212yes—
28#95×C47C2212yes—
29C24×C47C2311yescharacteristic
30C23×D47C2312yes—
31C22×C4×C47—24no—
32C22×C4×C47D414yes—
33C22×C4×C47C2314yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—24no—
37C2×C22⋊D47—24no—
38C2×C22⋊D47D418yes—
39C22×Dic47—22no—
40C22×Dic47—24no—
41C22×Dic47—22no—
42C22×Dic47—24no—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46#10625350—232no—
47C2×D188—24no—
48C2×D188—22no—
49C2×C4×D47—24no—
50C2×C4×D47—24no—
51C2×C4×D47—24no—
52C2×Dic94—22no—
53C2×Dic94—24no—
54C22⋊C4×C47—24no—
55(C2×D47)⋊C4—28no—
56(C2×D47)⋊C4—28no—
57C4⋊Dic47—28no—
58Dic47⋊C4—24no—
59Dic47⋊C4—24no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47C2×D412yes—
63C23×C47C2×D414yes—
64C23×C47C2411yescharacteristic
65C22×D47—22no—
66C22×D47—22no—
67C22×D47—24no—
68C22×D47—24no—
69C22×D47C2×D414yes—
70C2×C4×C47—28no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—24no—
74C2×C4×C47—24no—
75C2×C4×C47—24no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C22⋊D47—216no—
79C2×Dic47—28no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—24no—
86C2×Dic47—44no—
87C2×Dic47C2×D414yes—
88C2×Dic47#4114yescomplemented
89D188—28no—
90C4×D47—216no—
91Dic94—28no—
92C22×C47—22no—
93C22×C47—22no—
94C22×C47—28no—
95C22×C47#12014yes—
96C22×C47C22×D412yes—
97C22×C47C22×D411yescharacteristic
98C22×C47C2×#4112yes—
99C22×C472−1+412yes—
100C2×D47—24no—
101C2×D47—28no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—44no—
105C4×C47—22no—
106C4×C47—22no—
107C4×C47—44no—
108Dic47—24no—
109Dic47—24no—
110Dic47—42no—
111#2406—471nomaximal, Sylow
112C2×C47—24no—
113C2×C47C2×#12011yescharacteristic
114C2×C47#52511yescharacteristic
115C2×C47#53611yescharacteristic
116C2×C47#54714yes—
117D47—44no—
118C22×#41—471no—
119C2×#123—472no—
120C22×C4⋊C4—471no—
121#395—472no—
122#394—472no—
123#386—472no—
124#385—474no—
125#381D4711yescharacteristic, complemented
126C47#240611yescharacteristic, complemented, Sylow
127C2×#41—948no—
128C2×#41—944no—
129C22×Q8—471no—
130C22×D4—472no—
131C22×D4—471no—
132C23×C4—471no—
133C23×C4—471no—
134C23×C4—472no—
135C23×C4C2×D4711yescharacteristic
136#123—948no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—474no—
140C2×C4⋊C4—944no—
141C2×C22⋊C4—474no—
142C2×C22⋊C4—474no—
143C2×C22⋊C4C2×D4712yes—
144#95—474no—
145#95C2×D4712yes—
146#95C2×D4712yes—
147C24—472no—
148C24C22×D4711yescharacteristic
149#41—9432no—
150C2×Q8—944no—
151C2×Q8—942no—
152C2×D4—478no—
153C2×D4—944no—
154C2×D4—944no—
155C2×D4—944no—
156C2×D4—942no—
157C22×C4—24no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4—472no—
161C22×C4—944no—
162C22×C4—944no—
163C22×C4—944no—
164C22×C4—942no—
165C22×C4—944no—
166C22×C4—942no—
167C22×C4—944no—
168C22×C4D18814yes—
169C22×C4C22×D4714yes—
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4711yescharacteristic
172C4⋊C4—948no—
173C4⋊C4—944no—
174C4⋊C4—944no—
175C22⋊C4—24no—
176C22⋊C4—948no—
177C22⋊C4—948no—
178C23—22no—
179C23—22no—
180C23—474no—
181C23—942no—
182C23—942no—
183C23—944no—
184C23—944no—
185C23C2×D18812yes—
186C23D4×D4714yes—
187C23C23×D4711yescharacteristic
188Q8—948no—
189D4—948no—
190D4—9416no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—474no—
198C2×C4—474no—
199C2×C4—9416no—
200C2×C4—948no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—944no—
206C2×C4—942no—
207C2×C4—1884no—
208C2×C4C2×D18812yes—
209C2×C4C2×D18812yes—
210C22—28no—
211C22—22no—
212C22—22no—
213C22—948no—
214C22—944no—
215C22—1884no—
216C22—1882no—
217C22—1882no—
218C22#1309399414yes—
219C22C2×D4×D4712yes—
220C22C22×D18811yescharacteristic
221C22#41×D4712yes—
222C22#1309407112yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—944no—
227C4—944no—
228C4—1882no—
229C2—24no—
230C2—1884no—
231C2C2×#1309399411yescharacteristic
232C2#1568963511yescharacteristic
233C2#1568969911yescharacteristic
234C2#1568977114yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#381C2
hypercenter#381D47
hypocenterC47#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#13094008C2semidirect
3. C22×Dic47⋊C4C2semidirect
4. #15689044C2semidirect
5. #15689041C2semidirect
6. #15689000C2semidirect
7. #15688997C2semidirect
8. C47×#381C2semidirect
88. C2×Dic47#41semidirect
125. #381D47semidirect
126. C47#2406semidirect