Finite Group Databasebeta

← #20243805

Subgroups — #20243805

Order 6016.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic, complemented
2#15689635C211yesmaximal, characteristic
3#15689105C211yesmaximal, characteristic, complemented
4#15689086C211yesmaximal, characteristic, complemented
5#15689086C211yesmaximal, characteristic, complemented
6#15688893C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×C4×D47C2211yescharacteristic
10#13094032—22no—
11#13094030—22no—
12C2×#10625329C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14M16×D47—22no—
15#13094008C412yes—
16#13094004—21no—
17#13093999—21no—
18#13093994C412yes—
19C4×D188—22no—
20#13093942—21no—
21#13093940—21no—
22(C2×D47)⋊C8—22no—
23(C2×D47)⋊C8—22no—
24C2×M16×C47C2211yescharacteristic
25C2×M16×C47C2211yescharacteristic
26#117×C47C2211yescharacteristic
27C23×D47C2×C411yescharacteristic
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47C2×C412yes—
30C22×Dic47C2×C411yescharacteristic
31#10625350—21no—
32#10625350—21no—
33#10625350—21no—
34#10625350—21no—
35C2×D188—22no—
36C2×D188D411yescharacteristic
37C2×C4×D47—21no—
38C2×C4×D47—21no—
39C2×C4×D47—21no—
40C2×C4×D47—21no—
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×C4×D47D412yes—
44C2×Dic94D411yescharacteristic
45M16×C47—21no—
46M16×C47—21no—
47M16×C47—21no—
48M16×C47—21no—
49C2×C8×C47—21no—
50C2×C8×C47D412yescomplemented
51C4⋊C4×C47—21no—
52C22⋊C4×C47C2×C412yes—
53C42×C47—21no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—22no—
57#10625329—21no—
58#10625329—21no—
59#10625329—21no—
60#10625329—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8D412yescomplemented
63#10625324—24no—
64C8×D47—24no—
65C23×C47C22×C411yescharacteristic
66C22×D47—21no—
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—42no—
70C22×D47C22⋊C412yes—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C22⋊D47—22no—
79C22⋊D47—22no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47C22⋊C412yes—
84D188—21no—
85D188—21no—
86D188—44no—
87C4×D47—22no—
88C4×D47—22no—
89C4×D47—41no—
90C4×D47—41no—
91C4×D47—41no—
92C4×D47—41no—
93Dic94—21no—
94Dic94—21no—
95C8×C47—22no—
96C8×C47—41no—
97C47⋊C8—22no—
98C47⋊C8—41no—
99C22×C47—41no—
100C22×C47C2×C22⋊C411yescharacteristic
101C22×C47C4×D411yescharacteristic
102C22×C47C4×D411yescharacteristic
103C2×D47—22no—
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—41no—
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—42no—
112C4×C47—42no—
113C4×C47#12011yescharacteristic
114C4×C47#12111yescharacteristic
115C4×C47#12111yescharacteristic
116C4×C47#12311yescharacteristic
117Dic47—22no—
118Dic47—41no—
119#1891—471nomaximal, Sylow
120C2×C47—21no—
121C2×C47—21no—
122C2×C47—21no—
123C2×C47#38611yescharacteristic
124D47—42no—
125D47—42no—
126#568—471no—
127#525—471no—
128#413—471no—
129#407—471no—
130#407—471no—
131#344—471no—
132#344D4711yescharacteristic, complemented
133C47#189111yescharacteristic, complemented, Sylow
134C2×#41—471no—
135C23×C4—471no—
136#131—942no—
137#131—942no—
138C2×M16—471no—
139C2×M16—471no—
140C2×M16—942no—
141C2×M16C2×D4711yescharacteristic
142C2×M16C2×D4711yescharacteristic
143#123—472no—
144C22⋊Q8—941no—
145#121—941no—
146#120—472no—
147C4×D4—942no—
148#117C2×D4711yescharacteristic
149#101—941no—
150#100—941no—
151C22⋊C8—942no—
152C22⋊C8—942no—
153C24—471no—
154#41—941no—
155#41—941no—
156#41—941no—
157#41—941no—
158C2×Q8—471no—
159C2×D4—472no—
160C2×D4—471no—
161C2×D4—942no—
162C22×C4—472no—
163C22×C4—471no—
164C22×C4—941no—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4—941no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4C22×D4711yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—944no—
176M16—941no—
177M16—941no—
178M16—941no—
179M16—941no—
180C2×C8—21no—
181C2×C8—472no—
182C2×C8—944no—
183C2×C8—941no—
184C2×C8D18812yescomplemented
185C4⋊C4—21no—
186C4⋊C4—942no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C22⋊C4C4×D4712yes—
190C42—21no—
191C23—472no—
192C23—941no—
193C23—941no—
194C23—941no—
195C23—1882no—
196C23C2×C4×D4711yescharacteristic
197Q8—941no—
198Q8—941no—
199D4—942no—
200D4—942no—
201D4—941no—
202D4—941no—
203D4—1884no—
204C2×C4—22no—
205C2×C4—472no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—1881no—
212C2×C4—1881no—
213C2×C4—1881no—
214C2×C4—1881no—
215C2×C4C2×D18811yescharacteristic
216C2×C4#1062535011yescharacteristic
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4D4×D4711yescharacteristic
220C2×C4#1062535411yescharacteristic
221C8—22no—
222C8—41no—
223C8—942no—
224C8—1881no—
225C22—41no—
226C22—942no—
227C22—942no—
228C22—942no—
229C22—942no—
230C22—1882no—
231C22—1881no—
232C22—1881no—
233C22—1881no—
234C22—1881no—
235C22C22⋊C4×D4711yescharacteristic
236C22#1309398611yescharacteristic
237C22C4×D18811yescharacteristic
238C4—42no—
239C4—942no—
240C4—1881no—
241C4#1309399411yescharacteristic
242C4#1309399711yescharacteristic
243C4#1309399911yescharacteristic
244C4#1309400911yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—1882no—
249C2—1882no—
250C2#1568900111yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1891
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #15689889C2semidirect
3. #15689105C2semidirect
4. #15689086C2semidirect
5. #15689086C2semidirect
6. #15688893C2semidirect
7. C47×#344C2semidirect
50. C2×C8×C47D4semidirect
62. C2×C47⋊C8D4semidirect
132. #344D47semidirect
133. C47#1891semidirect
184. C2×C8D188semidirect