Finite Group Databasebeta

← #20243758

Subgroups — #20243758

Order 6016.

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

normal subgroups only

This group has 334 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×#13094057C211yesmaximal, characteristic
2#15689603C211yesmaximal, characteristic
3C2×#13093952C211yesmaximal, characteristic
4#15689131C211yesmaximal, characteristic, complemented
5#15689029C211yesmaximal, characteristic, complemented
6#15688891C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10#13094057—22no—
11#13094057C414yescomplemented
12C2×Dic188—21no—
13C2×#10625325—21no—
14C2×#10625329C2211yescharacteristic
15C4×Dic94—21no—
16C4×D188—21no—
17(C22⋊D47)⋊C4—22no—
18#13093982—21no—
19C2×C4⋊Dic47C2211yescharacteristic
20C4⋊C4×D47—21no—
21#13093952—22no—
22#13093947—21no—
23#13093947—21no—
24C47⋊#95—22no—
25C2×M16×C47C2211yescharacteristic
26#117×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32C22×Dic47D412yes—
33#10625350—21no—
34#10625350—21no—
35#10625350C2×C412yes—
36#10625350D412yes—
37C2×D188D411yescharacteristic
38C2×C4×D47—21no—
39C2×C4×D47—22no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94C2×C412yescomplemented
46C2×Dic94D411yescharacteristic
47M16×C47—21no—
48M16×C47C2×C412yescomplemented
49C2×C8×C47—21no—
50C4⋊C4×C47D411yescharacteristic
51C4⋊C4×C47D411yescharacteristic
52C22⋊C4×C47—21no—
53C42×C47—21no—
54C42×C47—21no—
55C42×C47—21no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61#10625329—21no—
62#10625329—21no—
63C2×C47⋊C8—21no—
64Dic188—24no—
65#10625325—24no—
66C23×C47C2×D411yescharacteristic
67C22×D47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C22⋊D47—22no—
80C22⋊D47—22no—
81C2×Dic47—21no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—42no—
87D188—21no—
88D188C22⋊C412yes—
89C4×D47—22no—
90C4×D47—22no—
91C4×D47—82no—
92Dic94—21no—
93Dic94—22no—
94Dic94—22no—
95Dic94—41no—
96Dic94—41no—
97Dic94C22⋊C412yes—
98C8×C47—22no—
99C47⋊C8—41no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47C4×D411yescharacteristic
103C22×C47#12011yescharacteristic
104C22×C47#12111yescharacteristic
105C2×D47—22no—
106C2×D47—41no—
107C2×D47—41no—
108C4×C47—42no—
109C4×C47—41no—
110C4×C47—41no—
111C4×C47C2×C22⋊C411yescharacteristic
112C4×C47C4×D411yescharacteristic
113C4×C47#12111yescharacteristic
114C4×C47#12311yescharacteristic
115Dic47—22no—
116Dic47—42no—
117Dic47—42no—
118#1882—471nomaximal, Sylow
119C2×C47—21no—
120C2×C47—21no—
121C2×C47#38611yescharacteristic
122C2×C47#45511yescharacteristic
123C2×C47#45611yescharacteristic
124D47—42no—
125C2×#137—471no—
126#520—471no—
127C2×#104—471no—
128#419—471no—
129#391—471no—
130#343—471no—
131#339D4711yescharacteristic, complemented
132C47#188211yescharacteristic, complemented, Sylow
133C2×#41—471no—
134C22×Q8—471no—
135#137—474no—
136#137—942no—
137C2×Q16—941no—
138C2×SD16—941no—
139C2×M16—471no—
140C2×M16C2×D4711yescharacteristic
141C4×Q8—941no—
142C4×D4—941no—
143C4×D4—942no—
144#117—941no—
145#117C2×D4711yescharacteristic
146C2×C4⋊C4—471no—
147C2×C4⋊C4—941no—
148C2×C42C2×D4711yescharacteristic
149#104—942no—
150#103—941no—
151#103—941no—
152#95—942no—
153#41—472no—
154#41—472no—
155#41—941no—
156#41—941no—
157C2×Q8—472no—
158C2×Q8—471no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×Q8—941no—
163C2×Q8—941no—
164C2×D4—471no—
165C2×D4—941no—
166C22×C4—21no—
167C22×C4—472no—
168C22×C4—942no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4C22×D4711yescharacteristic
172Q16—944no—
173SD16—944no—
174M16—21no—
175M16—941no—
176M16—941no—
177M16C4×D4712yescomplemented
178C2×C8—21no—
179C2×C8—941no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4D18811yescharacteristic
184C4⋊C4D18811yescharacteristic
185C22⋊C4—21no—
186C22⋊C4—942no—
187C42—21no—
188C42—21no—
189C42—21no—
190C42—942no—
191C23—941no—
192C23D4×D4711yescharacteristic
193Q8—472no—
194Q8—941no—
195Q8—942no—
196Q8—942no—
197Q8—1881no—
198Q8—1881no—
199D4—472no—
200D4—942no—
201D4—942no—
202D4—941no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—941no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—3762no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1882no—
217C2×C4C2×C4×D4711yescharacteristic
218C2×C4C2×D18811yescharacteristic
219C2×C4#1062535011yescharacteristic
220C2×C4D4×D4711yescharacteristic
221C2×C4D4×D4711yescharacteristic
222C2×C4#1062535411yescharacteristic
223C8—22no—
224C8—1881no—
225C22—21no—
226C22—21no—
227C22—942no—
228C22—1881no—
229C22—1881no—
230C22#1309398611yescharacteristic
231C22#1309399411yescharacteristic
232C22#1309399711yescharacteristic
233C4—42no—
234C4—41no—
235C4—41no—
236C4—942no—
237C4—1882no—
238C4—1882no—
239C4C22⋊C4×D4711yescharacteristic
240C4C4×D18811yescharacteristic
241C4#1309399911yescharacteristic
242C4#1309400911yescharacteristic
243C2—21no—
244C2—21no—
245C2—1882no—
246C2#1568900111yescharacteristic
247C2#1568930211yescharacteristic
248C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#1882
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #15689131C2semidirect
5. #15689029C2semidirect
6. #15688891C2semidirect
7. C47×#339C2semidirect
11. #13094057C4semidirect
45. C2×Dic94C2×C4semidirect
48. M16×C47C2×C4semidirect
131. #339D47semidirect
132. C47#1882semidirect
177. M16C4×D47semidirect