Finite Group Databasebeta

← #20243742

Subgroups — #20243742

Order 6016.

374 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10625325C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3C2×#13093949C211yesmaximal, characteristic, complemented
4C2×#13093946C211yesmaximal, characteristic
5#15689025C211yesmaximal, characteristic
6#15688886C211yesmaximal, characteristic, complemented
7C47×#336C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×D188C2211yescharacteristic
10C2×#10625325—22no—
11C2×#10625325—22no—
12C2×#10625325C414yescomplemented
13C4×Dic94—22no—
14C4×Dic94—22no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—21no—
18C2×(C2×D47)⋊C4—21no—
19C2×(C2×D47)⋊C4—21no—
20C2×C4×Dic47—21no—
21#13093949—22no—
22#13093946—22no—
23C22×C8×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C42×C47C2211yescharacteristic
26C23×D47—21no—
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188C2×C412yes—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94C2×C412yes—
43C2×Dic94D412yes—
44C2×Dic94D412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47—21no—
50C2×C8×C47C2×C412yes—
51C42×C47—21no—
52C42×C47—21no—
53(C2×D47)⋊C4—42no—
54(C2×D47)⋊C4—42no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47D412yes—
59Dic47⋊C4—24no—
60C4×Dic47—24no—
61#10625325—28no—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
67C22×D47—41no—
68C22×D47—41no—
69C22×D47—41no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47SD1612yescomplemented
76C2×C4×C47C22×C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—41no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91D188—22no—
92D188—22no—
93D188—41no—
94D188—41no—
95Dic94—22no—
96Dic94—22no—
97Dic94—22no—
98Dic94C22⋊C414yescomplemented
99C8×C47—22no—
100C8×C47—41no—
101C22×C47C4×D411yescharacteristic
102C22×C47#12011yescharacteristic
103C22×C47#12111yescharacteristic
104C22×C47C2×SD1611yescharacteristic
105C22×C47#13511yescharacteristic
106C22×C47AGL(1,ℤ/8)11yescharacteristic
107C22×C47#13711yescharacteristic
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—81no—
112C2×D47—81no—
113C2×D47—81no—
114C2×D47—81no—
115C4×C47—22no—
116C4×C47—41no—
117C4×C47C2×C22⋊C411yescharacteristic
118C4×C47C4×D411yescharacteristic
119C4×C47#12111yescharacteristic
120C4×C47#12311yescharacteristic
121Dic47—24no—
122Dic47—42no—
123Dic47—81no—
124#1880—471nomaximal, Sylow
125C2×C47#38611yescharacteristic
126C2×C47C4×SD1611yescharacteristic
127C2×C47#44011yescharacteristic
128C2×C47#44811yescharacteristic
129C2×C47#44911yescharacteristic
130C2×C47#46011yescharacteristic
131C2×C47#46411yescharacteristic
132D47—82no—
133C22×SD16—471no—
134C2×C4×Q8—471no—
135C2×#103—471no—
136C2×#102—471no—
137#390—471no—
138#340—471no—
139#336D4711yescharacteristic, complemented
140C47#188011yescharacteristic, complemented, Sylow
141C22×Q8—471no—
142C22×D4—471no—
143C2×SD16—474no—
144C2×SD16—942no—
145C2×SD16—942no—
146C22×C8C2×D4711yescharacteristic
147C22×C8C2×D4711yescharacteristic
148C4×Q8—942no—
149C4×Q8—942no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—471no—
152C2×C4⋊C4—941no—
153C2×C22⋊C4—941no—
154C2×C22⋊C4—941no—
155C2×C42—941no—
156C2×C42C2×D4711yescharacteristic
157#103—942no—
158#102—942no—
159C24—941no—
160C2×Q8—472no—
161C2×Q8—472no—
162C2×Q8—472no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×D4—472no—
167C2×D4—941no—
168C2×D4—941no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—941no—
172C22×C4—941no—
173C22×C4—941no—
174C22×C4—941no—
175C22×C4D18811yescharacteristic
176C22×C4D18811yescharacteristic
177C22×C4C22×D4711yescharacteristic
178SD16—948no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8C4×D4712yes—
185C4⋊C4—472no—
186C4⋊C4—944no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C22⋊C4—1882no—
191C22⋊C4—1882no—
192C42—21no—
193C42—21no—
194C42—944no—
195C23—942no—
196C23—1881no—
197C23—1881no—
198C23—1881no—
199C23—1881no—
200C23—1881no—
201C23—1881no—
202C23C2×D18811yescharacteristic
203Q8—474no—
204Q8—942no—
205Q8—942no—
206Q8—942no—
207D4—942no—
208D4—942no—
209D4—1881no—
210D4—1881no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—1881no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4—1881no—
225C2×C4#1062532512yescomplemented
226C2×C4C2×C4×D4711yescharacteristic
227C2×C4#1062535011yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4#1062535411yescharacteristic
232C8—22no—
233C8—41no—
234C22—3761no—
235C22—3761no—
236C22—3761no—
237C22—3761no—
238C22—1882no—
239C22—1882no—
240C22—1882no—
241C22C4×D18811yescharacteristic
242C22#1309399411yescharacteristic
243C22#1309399911yescharacteristic
244C22C2×#1062532511yescharacteristic
245C22#1309404611yescharacteristic
246C22#1309405211yescharacteristic
247C22#1309405711yescharacteristic
248C4—22no—
249C4—41no—
250C4—944no—
251C4—3761no—
252C4—1882no—
253C4C22⋊C4×D4711yescharacteristic
254C4#1309398611yescharacteristic
255C4#1309399711yescharacteristic
256C4#1309400911yescharacteristic
257C2—3762no—
258C2#1568900111yescharacteristic
259C2C4×#1062532511yescharacteristic
260C2#1568922511yescharacteristic
261C2#1568926411yescharacteristic
262C2#1568927011yescharacteristic
263C2#1568932411yescharacteristic
264C2#1568934611yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#1880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
3. C2×#13093949C2semidirect
6. #15688886C2semidirect
7. C47×#336C2semidirect
12. C2×#10625325C4semidirect
75. C2×C4×C47SD16semidirect
98. Dic94C22⋊C4semidirect
139. #336D47semidirect
140. C47#1880semidirect
225. C2×C4#10625325semidirect