Finite Group Databasebeta

← #20241855

Subgroups — #20241855

Order 6016.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689670C211yesmaximal, characteristic
2#15689179C211yesmaximal, characteristic, complemented
3#15689174C211yesmaximal, characteristic, complemented
4#15688852C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9#13094023C411yescharacteristic
10#13094020C411yescharacteristic
11#13094010—21no—
12#13093999C411yescharacteristic
13#13093997—21no—
14#13093995C411yescharacteristic
15C4×D188C2211yescharacteristic
16C4×C22⋊D47—21no—
17C42×D47C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22#13093934—21no—
23C4×C47⋊C8C2211yescharacteristic
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic
26C4×C8×C47C2211yescharacteristic
27C2×D4×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C2×C22⋊D47—21no—
30C2×C22⋊D47—21no—
31C2×C22⋊D47—21no—
32#10625350—42no—
33#10625350—42no—
34C2×D188—21no—
35C2×D188C2×C411yescharacteristic
36C2×C4×D47—21no—
37C2×C4×D47C2×C411yescharacteristic
38C2×C4×D47D411yescharacteristic
39C2×C4×D47D411yescharacteristic
40C2×Dic94—21no—
41C2×C8×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47C2×C411yescharacteristic
44C22⋊C4×C47—21no—
45C42×C47C2311yescharacteristic
46C22⋊Dic47—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47C2×C411yescharacteristic
50Dic47⋊C4—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47—21no—
57C22×D47—21no—
58C22×D47C22⋊C411yescharacteristic
59D4×C47—21no—
60D4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C22⋊D47—42no—
68C22⋊D47—42no—
69C22⋊D47—42no—
70C2×Dic47—21no—
71C2×Dic47C22⋊C411yescharacteristic
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74D188—21no—
75D188—21no—
76D188—42no—
77C4×D47—21no—
78C4×D47—21no—
79C4×D47—21no—
80C4×D47—21no—
81C4×D47—41no—
82C4×D47—41no—
83C4×D47—41no—
84Dic94—42no—
85C8×C47—41no—
86C8×C47—41no—
87C47⋊C8—41no—
88C47⋊C8—41no—
89C22×C47—41no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47C2×C22⋊C411yescharacteristic
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—41no—
97C2×D47—41no—
98C2×D47—41no—
99C4×C47—21no—
100C4×C47—41no—
101C4×C47#13111yescharacteristic
102C4×C47#13111yescharacteristic
103C4×C47AGL(1,ℤ/8)11yescharacteristic
104C4×C47AGL(1,ℤ/8)11yescharacteristic
105Dic47—21no—
106Dic47—21no—
107Dic47—21no—
108Dic47—41no—
109#1496—471nomaximal, Sylow
110C2×C47—81no—
111C2×C47#40811yescharacteristic
112C2×C47#41811yescharacteristic
113C2×C47#42111yescharacteristic
114D47—41no—
115D47—81no—
116#532—471no—
117#432—471no—
118#431—471no—
119D4⋊C8—471no—
120D4⋊C8—471no—
121D4⋊C8—471no—
122D4⋊C8D4711yescharacteristic, complemented
123C47#149611yescharacteristic, complemented, Sylow
124C2×#41—941no—
125C4⋊Q8—471no—
126#127—471no—
127#124—941no—
128#121—471no—
129#121—471no—
130#121—941no—
131C4×D4—471no—
132C4×D4—941no—
133C4×D4C2×D4711yescharacteristic
134C2×C42—471no—
135C4⋊C8—471no—
136C4⋊C8—941no—
137C4⋊C8C2×D4711yescharacteristic
138C22⋊C8—941no—
139C22⋊C8—941no—
140#97—941no—
141C4×C8—471no—
142C4×C8C2×D4711yescharacteristic
143#41—1882no—
144#41—1882no—
145C2×Q8—941no—
146C2×D4—471no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C2×D4—941no—
151C2×D4C4×D4711yescharacteristic
152C22×C4—21no—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—941no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—941no—
160C2×C8—941no—
161C4⋊C4—471no—
162C4⋊C4—941no—
163C4⋊C4C4×D4711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C42—471no—
169C42—471no—
170C42—471no—
171C42C22×D4711yescharacteristic
172C23—21no—
173C23—471no—
174C23—941no—
175Q8—1882no—
176D4—21no—
177D4—21no—
178D4—941no—
179D4—941no—
180D4—1882no—
181D4—1882no—
182D4—1882no—
183D4—1882no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—471no—
188C2×C4—471no—
189C2×C4—471no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4C2×C4×D4711yescharacteristic
199C2×C4D4×D4711yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C8—41no—
202C8—41no—
203C8—1881no—
204C8—1881no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—941no—
209C22—941no—
210C22—941no—
211C22—1881no—
212C22—1881no—
213C22—1881no—
214C22C22⋊C4×D4711yescharacteristic
215C4—21no—
216C4—41no—
217C4—941no—
218C4—941no—
219C4—941no—
220C4—1881no—
221C4#1309403011yescharacteristic
222C4#1309403211yescharacteristic
223C4#1309404811yescharacteristic
224C4#1309405111yescharacteristic
225C2—81no—
226C2—3761no—
227C2—1881no—
228C2#1568908811yescharacteristic
229C2#1568912611yescharacteristic
230C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1496
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689179C2semidirect
3. #15689174C2semidirect
4. #15688852C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×D4⋊C8C2semidirect
122. D4⋊C8D47semidirect
123. C47#1496semidirect