Finite Group Databasebeta

← #20243899

Subgroups — #20243899

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×#13094050C211yesmaximal, characteristic
2C2×#13094030C211yesmaximal, characteristic, complemented
3#15689122C211yesmaximal, characteristic, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5#15688892C211yesmaximal, characteristic, complemented
6#15688888C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094050—22no—
10#13094050C414yescomplemented
11C2×#10625335—21no—
12C2×#10625334—21no—
13#13094030—22no—
14#13094030—22no—
15C2×#10625329C2211yescharacteristic
16C2×#10625329C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C2×#10625324—21no—
19C2×C8×D47—21no—
20#13093947—21no—
21#13093944—21no—
22#13093941—22no—
23C22×D4×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26#102×C47—21no—
27#102×C47—21no—
28C24×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47C2×C412yes—
35C22×C4×C47—21no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—21no—
38#10625350—21no—
39#10625350—21no—
40#10625350C2×C412yes—
41#10625350D412yes—
42C2×D188D411yescharacteristic
43C2×C4×D47—21no—
44C2×Dic94D411yescharacteristic
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47D411yescharacteristic
48C2×C8×C47D411yescharacteristic
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51#10625335—24no—
52#10625334—24no—
53#10625329—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329—21no—
57#10625329C2×C412yes—
58#10625329D412yes—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62#10625324—24no—
63C8×D47—24no—
64C23×C47—22no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—81no—
68C23×C47—81no—
69C23×C47#4111yescharacteristic
70C22×D47—21no—
71D4×C47—22no—
72D4×C47—22no—
73D4×C47—41no—
74D4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—81no—
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C22⋊D47—22no—
84C22⋊D47—22no—
85C2×Dic47—21no—
86D188—21no—
87D188C22⋊C412yes—
88C4×D47—22no—
89C4×D47—22no—
90Dic94—21no—
91Dic94C22⋊C412yes—
92C8×C47—21no—
93C8×C47—21no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C47⋊C8—41no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—42no—
100C22×C47—82no—
101C22×C47—82no—
102C22×C47—81no—
103C22×C47—81no—
104C22×C47C4×D411yescharacteristic
105C22×C47#12111yescharacteristic
106C22×C47#12311yescharacteristic
107C2×D47—22no—
108C2×D47—41no—
109C2×D47—41no—
110C4×C47—81no—
111C4×C47C2×C22⋊C411yescharacteristic
112C4×C47C4×D411yescharacteristic
113C4×C47#12011yescharacteristic
114C4×C47#12111yescharacteristic
115Dic47—22no—
116#1907—471nomaximal, Sylow
117C2×C47—21no—
118C2×C47—21no—
119C2×C47—82no—
120C2×C47#38611yescharacteristic
121C2×C47#47111yescharacteristic
122C2×C47#47211yescharacteristic
123D47—42no—
124C2×AGL(1,ℤ/8)—471no—
125C2×#131—471no—
126#417—471no—
127C2×#102D4711yescharacteristic, complemented
128C2×#100—471no—
129#343—471no—
130#341—471no—
131C47#190711yescharacteristic, complemented, Sylow
132C2×#41—471no—
133C22×D4C2×D4711yescharacteristic
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—471no—
142C2×M16—471no—
143C2×M16—941no—
144C22×C8—941no—
145C22×C8C2×D4711yescharacteristic
146C2×C4⋊C4C2×D4711yescharacteristic
147#103—941no—
148#102—21no—
149#102—21no—
150#102—941no—
151#100—942no—
152C24—21no—
153#41—472no—
154#41—472no—
155#41—941no—
156#41—941no—
157C2×Q8—471no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—471no—
164C2×D4—941no—
165C2×D4C4×D4712yes—
166C22×C4—21no—
167C22×C4—941no—
168C22×C4C22×D4711yescharacteristic
169SD16—944no—
170D8—944no—
171M16—472no—
172M16—472no—
173M16—944no—
174M16—941no—
175M16—941no—
176M16—941no—
177M16—941no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—944no—
181C2×C8—941no—
182C2×C8—941no—
183C2×C8—941no—
184C2×C8C22⋊D4711yescharacteristic
185C2×C8C22⋊D4711yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—21no—
188C23—22no—
189C23—41no—
190C23—41no—
191C23—81no—
192C23—81no—
193C23—941no—
194C23#1062535211yescharacteristic
195Q8—472no—
196Q8—941no—
197D4—22no—
198D4—22no—
199D4—41no—
200D4—41no—
201D4—472no—
202D4—942no—
203D4—942no—
204D4—941no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—941no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4C2×C4×D4711yescharacteristic
211C2×C4#1062535011yescharacteristic
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4D4×D4711yescharacteristic
215C2×C4C2×C22⋊D4711yescharacteristic
216C8—21no—
217C8—21no—
218C8—942no—
219C8—942no—
220C8—1881no—
221C22—21no—
222C22—21no—
223C22—42no—
224C22—82no—
225C22—82no—
226C22—81no—
227C22—81no—
228C22—942no—
229C22—1881no—
230C22—1881no—
231C22(C22⋊D47)⋊C411yescharacteristic
232C22#1309399511yescharacteristic
233C22#1309400611yescharacteristic
234C4—81no—
235C4—942no—
236C4C22⋊C4×D4711yescharacteristic
237C4C4×C22⋊D4711yescharacteristic
238C4#1309399211yescharacteristic
239C4#1309399711yescharacteristic
240C2—21no—
241C2—21no—
242C2—82no—
243C2—1882no—
244C2#1568899911yescharacteristic
245C2#1568938311yescharacteristic
246C2#1568939011yescharacteristic
subgroupG/H
centerC22#13093995
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC22×C47#121
hypercenterC2×#102D47
hypocenterC47#1907
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13094030C2semidirect
3. #15689122C2semidirect
4. C2×#13093941C2semidirect
5. #15688892C2semidirect
6. #15688888C2semidirect
7. C2×#102×C47C2semidirect
10. #13094050C4semidirect
127. C2×#102D47semidirect
131. C47#1907semidirect