Finite Group Databasebeta

← #20243830

Subgroups — #20243830

Order 6016.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D47C211yesmaximal, 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×D47—21no—
10C22×C4×D47C2211yescharacteristic
11C2×#10625329C2211yescharacteristic
12#13094008—21no—
13#13094004C412yescomplemented
14#13093999C412yescomplemented
15#13093994—21no—
16C4×D188—22no—
17C2×C4×Dic47—21no—
18C2×C4×Dic47C2211yescharacteristic
19C42×D47—22no—
20C42×D47—22no—
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, complemented
39C2×C4×D47—24no—
40C2×C4×D47—28no—
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×C4×D47—21no—
44C2×C4×D47—21no—
45C2×C4×D47—21no—
46C2×C4×D47C2×C412yes—
47C2×C4×D47D412yes—
48C2×Dic94C2×C411yescharacteristic, complemented
49M16×C47—21no—
50M16×C47—21no—
51C2×C8×C47—21no—
52C4⋊C4×C47C2×C412yescomplemented
53C22⋊C4×C47—21no—
54C42×C47—21no—
55C42×C47—21no—
56C42×C47D412yescomplemented
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—22no—
60C4×Dic47—24no—
61C4×Dic47—21no—
62C4×Dic47D412yescomplemented
63#10625329—21no—
64#10625329—21no—
65C2×C47⋊C8—21no—
66C23×C47C2×D411yescharacteristic
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—24no—
70C22×D47—21no—
71C22×D47C22⋊C412yes—
72C2×C4×C47—24no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C22⋊D47—41no—
82C22⋊D47—41no—
83C2×Dic47—24no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47C22⋊C412yes—
89D188—21no—
90D188—21no—
91D188—44no—
92C4×D47—216no—
93C4×D47—22no—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—22no—
97C4×D47—41no—
98C4×D47—41no—
99Dic94—21no—
100Dic94—21no—
101C8×C47—41no—
102C47⋊C8—41no—
103C22×C47—22no—
104C22×C47C2×C22⋊C411yescharacteristic
105C22×C47#12011yescharacteristic
106C22×C47#12311yescharacteristic
107C2×D47—24no—
108C2×D47—24no—
109C2×D47—22no—
110C2×D47—22no—
111C2×D47—41no—
112C2×D47—42no—
113C2×D47#10414yescomplemented
114C4×C47—24no—
115C4×C47—42no—
116C4×C47C4×D411yescharacteristic
117C4×C47C4×D411yescharacteristic
118C4×C47#12111yescharacteristic
119C4×C47#12111yescharacteristic
120Dic47—24no—
121Dic47—22no—
122Dic47—41no—
123#1896—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47#38611yescharacteristic
127C2×C47C2×#10412yes—
128D47—24no—
129D47—81no—
130#525—471no—
131C22×C42—471no—
132C2×#104—471no—
133C2×#104—471no—
134#407—471no—
135#339—471no—
136#339D4711yescharacteristic, complemented
137C47#189611yescharacteristic, complemented, Sylow
138C2×#41—471no—
139C23×C4—471no—
140C23×C4—941no—
141C2×M16—471no—
142C2×M16C2×D4711yescharacteristic
143#123—941no—
144C22⋊Q8—472no—
145#121—472no—
146#120—941no—
147C4×D4—942no—
148#117C2×D4711yescharacteristic
149C2×C42—471no—
150C2×C42—942no—
151C2×C42—941no—
152C2×C42—942no—
153C2×C42C2×D4711yescharacteristic
154#104—942no—
155#104—942no—
156C22⋊C8—942no—
157C24—471no—
158#41—941no—
159#41—941no—
160#41—941no—
161#41—941no—
162C2×Q8—471no—
163C2×D4—471no—
164C2×D4—942no—
165C2×D4—941no—
166C22×C4—21no—
167C22×C4—471no—
168C22×C4—472no—
169C22×C4—472no—
170C22×C4—944no—
171C22×C4—948no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4—941no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4—941no—
178C22×C4C22×D4711yescharacteristic
179M16—21no—
180M16—21no—
181M16—941no—
182M16—941no—
183C2×C8—21no—
184C2×C8—941no—
185C4⋊C4—942no—
186C4⋊C4C4×D4712yescomplemented
187C22⋊C4—21no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C42—21no—
191C42—21no—
192C42—472no—
193C42—944no—
194C42—941no—
195C42D18812yescomplemented
196C23—472no—
197C23—944no—
198C23—941no—
199C23—941no—
200C23—941no—
201C23D4×D4711yescharacteristic
202Q8—941no—
203Q8—941no—
204D4—941no—
205D4—941no—
206D4—1884no—
207D4—1881no—
208D4—1881no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—472no—
213C2×C4—9416no—
214C2×C4—944no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—1881no—
224C2×C4—1881no—
225C2×C4C2×C4×D4711yescharacteristic
226C2×C4C2×D18811yescharacteristic
227C2×C4#1062535011yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4#1062535411yescharacteristic
231C8—41no—
232C8—1881no—
233C22—22no—
234C22—474no—
235C22—944no—
236C22—944no—
237C22—942no—
238C22—942no—
239C22—1881no—
240C22—1882no—
241C22C22⋊C4×D4711yescharacteristic
242C22#1309399411yescharacteristic
243C22#1309400911yescharacteristic
244C4—24no—
245C4—42no—
246C4—944no—
247C4—942no—
248C4—1881no—
249C4#1309398611yescharacteristic
250C4C4×D18811yescharacteristic
251C4#1309399711yescharacteristic
252C4#1309399911yescharacteristic
253C2—21no—
254C2—21no—
255C2—944no—
256C2—3761no—
257C2#1568900111yescharacteristic
258C2#104×D4712yes—
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1896
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×C42×D47C2semidirect
3. C2×#13093952C2semidirect
4. C2×#13093950C2semidirect
5. #15689086C2semidirect
6. #15688882C2semidirect
7. C47×#339C2semidirect
13. #13094004C4semidirect
14. #13093999C4semidirect
38. C2×D188C2×C4semidirect
48. C2×Dic94C2×C4semidirect
52. C4⋊C4×C47C2×C4semidirect
56. C42×C47D4semidirect
62. C4×Dic47D4semidirect
113. C2×D47#104semidirect
136. #339D47semidirect
137. C47#1896semidirect
186. C4⋊C4C4×D47semidirect
195. C42D188semidirect