Finite Group Databasebeta

← #20243329

Subgroups — #20243329

Order 6016.

612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13093949C212yesmaximal, complemented
3C2×#13093946C212yesmaximal, complemented
4#15688983C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
6C2×#10625350—22no—
7C2×#10625350—24no—
8C2×#10625350—24no—
9C2×#10625350C414yescomplemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C22⋊D47—21no—
13C22×C4×D47—21no—
14C2×C4⋊Dic47C2212yes—
15C2×C22⋊Dic47—21no—
16#13093949—24no—
17#13093946—24no—
18C47⋊#95—21no—
19C23×C4×C47C2211yescharacteristic
20C22×C8×C47C2212yes—
21C22⋊C8×C47—22no—
22C24×C47D411yescharacteristic
23C23×D47—21no—
24C22×C4×C47—22no—
25C22×C4×C47—22no—
26C22×C4×C47C2×C412yes—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D412yes—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—28no—
31C2×C22⋊D47—24no—
32C22×Dic47—21no—
33C22×Dic47—22no—
34#10625350—216no—
35#10625350—28no—
36#10625350—28no—
37C2×D188—22no—
38C2×D188—21no—
39C2×D188C2×C412yes—
40C2×D188D414yes—
41C2×C4×D47—28no—
42C2×C4×D47—24no—
43C2×Dic94—22no—
44C2×Dic94—21no—
45C2×Dic94C2×C412yes—
46C2×Dic94D414yes—
47C2×C8×C47—22no—
48C2×C8×C47—22no—
49C2×C8×C47—22no—
50C22⋊Dic47—42no—
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47—21no—
57C23×C47C22⋊C412yes—
58C23×C47C2×D411yescharacteristic
59C22×D47—22no—
60C22×D47—24no—
61C22×D47—42no—
62C22×D47—41no—
63C22×D47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47C22⋊C412yes—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×D411yescharacteristic
73C22⋊D47—216no—
74C2×Dic47—22no—
75C2×Dic47—24no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79D188—22no—
80D188—24no—
81D188C22⋊C414yescomplemented
82C4×D47—216no—
83Dic94—22no—
84Dic94—24no—
85Dic94C22⋊C414yescomplemented
86C8×C47—42no—
87C22×C47—22no—
88C22×C47—22no—
89C22×C47—22no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47#12012yes—
94C22×C47#13512yes—
95C22×C47AGL(1,ℤ/8)11yescharacteristic
96C22×C47#13711yescharacteristic
97C2×D47—24no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—44no—
101C2×D47—44no—
102C4×C47—22no—
103C4×C47C2×C22⋊C411yescharacteristic
104C4×C47C2×C22⋊C411yescharacteristic
105C4×C47#12012yes—
106Dic47—24no—
107Dic47—82no—
108#1788—471nomaximal, Sylow
109C2×C47—42no—
110C2×C47#37911yescharacteristic
111C2×C47#41611yescharacteristic
112C2×C47#41711yescharacteristic
113C2×C47#44912yes—
114C2×C47#45212yes—
115D47—44no—
116C22×#41—471no—
117C2×#103—472no—
118C2×#102—472no—
119C2×C22⋊C8D4711yescharacteristic, complemented
120#380—471no—
121C47#178811yescharacteristic, complemented, Sylow
122C2×#41—474no—
123C2×#41—944no—
124C2×#41—944no—
125C2×#41—942no—
126C22×Q8—471no—
127C22×D4—471no—
128C22×D4—941no—
129C23×C4—941no—
130C23×C4C2×D4711yescharacteristic
131C22×C8C2×D4712yes—
132C2×C4⋊C4—472no—
133C2×C22⋊C4—941no—
134#103—944no—
135#102—944no—
136C22⋊C8—22no—
137#95—941no—
138C24—941no—
139C24D18811yescharacteristic
140#41—948no—
141#41—948no—
142#41—9416no—
143C2×Q8—472no—
144C2×Q8—474no—
145C2×Q8—942no—
146C2×Q8—941no—
147C2×D4—472no—
148C2×D4—474no—
149C2×D4—948no—
150C2×D4—944no—
151C2×D4—942no—
152C2×D4—941no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—948no—
156C22×C4—941no—
157C22×C4—944no—
158C22×C4—942no—
159C22×C4C4×D4712yes—
160C22×C4D18811yescharacteristic
161C22×C4C22⋊D4712yes—
162C22×C4C22×D4711yescharacteristic
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—22no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C22⋊C4—1882no—
169C23—22no—
170C23—22no—
171C23—21no—
172C23—21no—
173C23—942no—
174C23—944no—
175C23—1882no—
176C23—1881no—
177C23—1881no—
178C23(C2×D47)⋊C412yes—
179C23C2×D18811yescharacteristic
180Q8—474no—
181Q8—942no—
182Q8—944no—
183D4—474no—
184D4—9416no—
185D4—942no—
186D4—944no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—9416no—
192C2×C4—942no—
193C2×C4—944no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4(C2×D47)⋊C412yes—
198C2×C4C2×C4×D4711yescharacteristic
199C2×C4D4×D4712yes—
200C2×C4D4×D4712yes—
201C2×C4C2×C22⋊D4711yescharacteristic
202C8—42no—
203C22—22no—
204C22—22no—
205C22—22no—
206C22—42no—
207C22—42no—
208C22—944no—
209C22—1884no—
210C22—1884no—
211C22—1882no—
212C22—1882no—
213C22C2×(C2×D47)⋊C411yescharacteristic
214C22#1309399412yes—
215C22#1309404612yes—
216C22#1309405211yescharacteristic
217C22#1309405711yescharacteristic
218C4—22no—
219C4—944no—
220C4—3762no—
221C4C22⋊C4×D4711yescharacteristic
222C4C22⋊C4×D4711yescharacteristic
223C4#1309399212yes—
224C2—42no—
225C2—1884no—
226C2#1568897811yescharacteristic
227C2#1568912011yescharacteristic
228C2#1568912511yescharacteristic
229C2#1568927012yes—
230C2#1568928712yes—
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#1788
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13093949C2semidirect
3. C2×#13093946C2semidirect
4. #15688983C2semidirect
5. C2×C22⋊C8×C47C2semidirect
9. C2×#10625350C4semidirect
81. D188C22⋊C4semidirect
85. Dic94C22⋊C4semidirect
119. C2×C22⋊C8D47semidirect
121. C47#1788semidirect