Finite Group Databasebeta

← #20243835

Subgroups — #20243835

Order 6016.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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
1#15689635C211yesmaximal, characteristic
2C2×#13093981C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic, complemented
4C2×#13093950C211yesmaximal, characteristic, complemented
5#15689086C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×C4×D47C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094008—21no—
12#13094004C412yescomplemented
13#13093999C412yescomplemented
14#13093994—21no—
15C4×D188—22no—
16#13093981—22no—
17#13093981—22no—
18C2×Dic47⋊C4—21no—
19C2×(C2×D47)⋊C4—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093952—22no—
22#13093950—22no—
23(C2×D47)⋊C8—22no—
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37C2×D188—22no—
38C2×D188C2×C411yescharacteristic
39C2×C4×D47—21no—
40C2×C4×D47—21no—
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×C4×D47—21no—
44C2×C4×D47C2×C412yes—
45C2×C4×D47D412yes—
46C2×Dic94C2×C411yescharacteristic
47M16×C47—21no—
48M16×C47—21no—
49C2×C8×C47—21no—
50C4⋊C4×C47C2×C412yes—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53C42×C47—21no—
54C42×C47D412yescomplemented
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59Dic47⋊C4—24no—
60C4×Dic47—21no—
61C4×Dic47D412yescomplemented
62#10625329—21no—
63#10625329—21no—
64C2×C47⋊C8—21no—
65C23×C47C2×D411yescharacteristic
66C22×D47—21no—
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—42no—
70C22×D47C22⋊C412yes—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—42no—
74C2×C4×C47C22×C411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C22⋊D47—41no—
81C22⋊D47—41no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—42no—
87C2×Dic47C22⋊C412yes—
88D188—21no—
89D188—21no—
90D188—44no—
91C4×D47—22no—
92C4×D47—22no—
93C4×D47—22no—
94C4×D47—22no—
95C4×D47—41no—
96C4×D47—41no—
97Dic94—21no—
98Dic94—21no—
99C8×C47—41no—
100C47⋊C8—41no—
101C22×C47—22no—
102C22×C47C2×C22⋊C411yescharacteristic
103C22×C47#12011yescharacteristic
104C22×C47#12311yescharacteristic
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—41no—
111C2×D47—42no—
112C4×C47—42no—
113C4×C47—42no—
114C4×C47C4×D411yescharacteristic
115C4×C47C4×D411yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12111yescharacteristic
118Dic47—22no—
119Dic47—42no—
120Dic47—41no—
121#1897—471nomaximal, Sylow
122C2×C47—21no—
123C2×C47—21no—
124C2×C47#38611yescharacteristic
125C2×C47#42112yes—
126D47—42no—
127D47—81no—
128#525—471no—
129C2×#117—471no—
130C2×#104—471no—
131C2×#104—471no—
132#407—471no—
133#339—471no—
134#339D4711yescharacteristic, complemented
135C47#189711yescharacteristic, complemented, Sylow
136C2×#41—471no—
137C23×C4—471no—
138C2×M16—471no—
139C2×M16C2×D4711yescharacteristic
140#123—941no—
141C22⋊Q8—472no—
142#121—472no—
143#120—941no—
144C4×D4—942no—
145#117—942no—
146#117—942no—
147#117C2×D4711yescharacteristic
148C2×C4⋊C4—941no—
149C2×C22⋊C4—941no—
150C2×C42—471no—
151C2×C42C2×D4711yescharacteristic
152#104—942no—
153#104—942no—
154C22⋊C8—942no—
155C24—471no—
156#41—941no—
157#41—941no—
158#41—941no—
159#41—941no—
160C2×Q8—471no—
161C2×D4—471no—
162C2×D4—942no—
163C2×D4—941no—
164C22×C4—21no—
165C22×C4—471no—
166C22×C4—472no—
167C22×C4—472no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4—941no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4C22×D4711yescharacteristic
175M16—21no—
176M16—21no—
177M16—941no—
178M16—941no—
179C2×C8—21no—
180C2×C8—941no—
181C4⋊C4—942no—
182C4⋊C4—944no—
183C4⋊C4C4×D4712yes—
184C22⋊C4—21no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C22⋊C4—944no—
188C42—21no—
189C42—21no—
190C42—472no—
191C42—941no—
192C42D18812yescomplemented
193C23—472no—
194C23—941no—
195C23—941no—
196C23—941no—
197C23—1882no—
198C23D4×D4711yescharacteristic
199Q8—941no—
200Q8—941no—
201D4—941no—
202D4—941no—
203D4—1884no—
204D4—1881no—
205D4—1881no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—472no—
210C2×C4—941no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—1882no—
219C2×C4—1881no—
220C2×C4—1881no—
221C2×C4C2×C4×D4711yescharacteristic
222C2×C4C2×D18811yescharacteristic
223C2×C4#1062535011yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4#1062535411yescharacteristic
227C8—41no—
228C8—1881no—
229C22—22no—
230C22—942no—
231C22—942no—
232C22—942no—
233C22—1882no—
234C22—1882no—
235C22—1881no—
236C22—1882no—
237C22C22⋊C4×D4711yescharacteristic
238C22#1309399411yescharacteristic
239C22#1309400911yescharacteristic
240C4—42no—
241C4—42no—
242C4—942no—
243C4—1882no—
244C4—1881no—
245C4#1309398611yescharacteristic
246C4C4×D18811yescharacteristic
247C4#1309399711yescharacteristic
248C4#1309399911yescharacteristic
249C2—21no—
250C2—21no—
251C2—3761no—
252C2—1882no—
253C2#1568900111yescharacteristic
254C2#1568913812yes—
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1897
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×#13093981C2semidirect
3. C2×#13093952C2semidirect
4. C2×#13093950C2semidirect
5. #15689086C2semidirect
6. #15688882C2semidirect
7. C47×#339C2semidirect
12. #13094004C4semidirect
13. #13093999C4semidirect
54. C42×C47D4semidirect
61. C4×Dic47D4semidirect
134. #339D47semidirect
135. C47#1897semidirect
192. C42D188semidirect