Finite Group Databasebeta

← #20243895

Subgroups — #20243895

Order 6016.

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

normal subgroups only

This group has 332 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
1C2×#13094052C211yesmaximal, characteristic
2C2×#13094030C211yesmaximal, characteristic, complemented
3#15689125C211yesmaximal, characteristic, complemented
4C2×#13093946C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688891C211yesmaximal, characteristic, complemented
7C47×#341C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×D188C2211yescharacteristic
10#13094052—22no—
11#13094052C414yescomplemented
12C2×#10625325—21no—
13C2×D376—21no—
14#13094030—22no—
15#13094030—22no—
16C2×#10625329C2211yescharacteristic
17C2×#10625324—21no—
18C2×C8×D47—21no—
19C2×C4⋊Dic47C2211yescharacteristic
20#13093949—21no—
21#13093946—21no—
22#13093946—21no—
23#13093946—21no—
24#13093940—22no—
25C2×M16×C47C2211yescharacteristic
26C2×M16×C47C2211yescharacteristic
27C22×C8×C47C2211yescharacteristic
28C23×D47—21no—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32#10625350—21no—
33#10625350—21no—
34#10625350C2×C412yes—
35#10625350D412yes—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188C2×C412yes—
42C2×D188D411yescharacteristic
43C2×C4×D47—21no—
44C2×Dic94D411yescharacteristic
45M16×C47—21no—
46M16×C47—21no—
47M16×C47—21no—
48M16×C47C2×C412yes—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47D411yescharacteristic
54C2×C8×C47D411yescharacteristic
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57#10625329—21no—
58#10625329D412yes—
59C2×C47⋊C8—21no—
60D376—24no—
61#10625325—24no—
62#10625324—24no—
63C8×D47—24no—
64C23×C47#4111yescharacteristic
65C22×D47—21no—
66C22×D47—22no—
67C22×D47—41no—
68C22×D47—41no—
69C22×D47—81no—
70C22×D47—81no—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C22⋊D47—22no—
78C22⋊D47—22no—
79C2×Dic47—21no—
80C2×Dic47—41no—
81C2×Dic47—81no—
82D188—22no—
83D188—22no—
84D188—21no—
85D188—41no—
86D188—41no—
87D188C22⋊C412yes—
88C4×D47—22no—
89C4×D47—22no—
90Dic94—21no—
91Dic94C22⋊C412yes—
92C8×C47—22no—
93C8×C47—21no—
94C8×C47—21no—
95C8×C47—41no—
96C47⋊C8—22no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47C4×D411yescharacteristic
100C22×C47#12111yescharacteristic
101C22×C47#12311yescharacteristic
102C2×D47—22no—
103C2×D47—41no—
104C2×D47—41no—
105C2×D47—42no—
106C2×D47—82no—
107C2×D47—81no—
108C2×D47—81no—
109C2×D47—82no—
110C4×C47C2×C22⋊C411yescharacteristic
111C4×C47C4×D411yescharacteristic
112C4×C47#12011yescharacteristic
113C4×C47#12111yescharacteristic
114Dic47—22no—
115Dic47—81no—
116#1907—471nomaximal, Sylow
117C2×C47—21no—
118C2×C47—21no—
119C2×C47#38611yescharacteristic
120C2×C47#47111yescharacteristic
121C2×C47#47211yescharacteristic
122D47—42no—
123D47—82no—
124C2×AGL(1,ℤ/8)—471no—
125C2×#131—471no—
126#417—471no—
127C2×#102—471no—
128C2×#100—471no—
129#343—471no—
130#341D4711yescharacteristic, complemented
131C47#190711yescharacteristic, complemented, Sylow
132C2×#41—471no—
133C22×D4—471no—
134AGL(1,ℤ/8)—474no—
135AGL(1,ℤ/8)—942no—
136C2×SD16—941no—
137C2×D8—941no—
138#131—942no—
139#131—942no—
140C2×M16—471no—
141C2×M16—941no—
142C2×M16C2×D4711yescharacteristic
143C2×M16C2×D4711yescharacteristic
144C22×C8—941no—
145C22×C8C2×D4711yescharacteristic
146C2×C4⋊C4—471no—
147#103—941no—
148#102—941no—
149#102—941no—
150#102—941no—
151#100—942no—
152C24—941no—
153#41—472no—
154#41—472no—
155#41—941no—
156#41—941no—
157C2×Q8—471no—
158C2×D4—472no—
159C2×D4—471no—
160C2×D4—941no—
161C2×D4—941no—
162C2×D4—941no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4—941no—
166C22×C4—941no—
167C22×C4—941no—
168C22×C4C22×D4711yescharacteristic
169SD16—944no—
170D8—944no—
171M16—21no—
172M16—21no—
173M16—21no—
174M16—472no—
175M16—944no—
176M16—941no—
177M16C4×D4712yes—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—944no—
183C2×C8—941no—
184C2×C8D18811yescharacteristic
185C2×C8D18811yescharacteristic
186C4⋊C4—941no—
187C4⋊C4—941no—
188C23—941no—
189C23—942no—
190C23—3761no—
191C23—3761no—
192C23—1881no—
193C23—1881no—
194C23#1062535411yescharacteristic
195Q8—472no—
196Q8—941no—
197D4—472no—
198D4—942no—
199D4—942no—
200D4—942no—
201D4—942no—
202D4—941no—
203D4—1881no—
204D4—1881no—
205C2×C4—941no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—3761no—
209C2×C4—1881no—
210C2×C4C2×C4×D4711yescharacteristic
211C2×C4C2×D18811yescharacteristic
212C2×C4#1062535011yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4D4×D4711yescharacteristic
215C2×C4D4×D4711yescharacteristic
216C8—22no—
217C8—21no—
218C8—21no—
219C8—41no—
220C8—942no—
221C22—21no—
222C22—21no—
223C22—942no—
224C22—3762no—
225C22—3762no—
226C22—3761no—
227C22—3761no—
228C22—1882no—
229C22—1881no—
230C22—1881no—
231C22#1309398611yescharacteristic
232C22#1309399911yescharacteristic
233C22#1309400911yescharacteristic
234C4—942no—
235C4—3761no—
236C4C22⋊C4×D4711yescharacteristic
237C4C4×D18811yescharacteristic
238C4#1309399411yescharacteristic
239C4#1309399711yescharacteristic
240C2—21no—
241C2—21no—
242C2—3762no—
243C2—1882no—
244C2#1568900111yescharacteristic
245C2#1568938711yescharacteristic
246C2#1568939411yescharacteristic
subgroupG/H
centerC22#13093999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#341C2
socleC22×C47#121
hypercenter#341D47
hypocenterC47#1907
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
2. C2×#13094030C2semidirect
3. #15689125C2semidirect
4. C2×#13093946C2semidirect
5. C2×#13093940C2semidirect
6. #15688891C2semidirect
7. C47×#341C2semidirect
11. #13094052C4semidirect
130. #341D47semidirect
131. C47#1907semidirect