Finite Group Databasebeta

← #20241837

Subgroups — #20241837

Order 6016.

276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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#15689145C211yesmaximal, characteristic, complemented
3C4×C8×D47C211yesmaximal, characteristic, complemented
4#15688852C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625350—21no—
9C2×#10625324—21no—
10C2×C8×D47—21no—
11#13094023C411yescharacteristic
12#13094020C411yescharacteristic
13#13094010—21no—
14#13093999C411yescharacteristic
15#13093997—21no—
16#13093995C411yescharacteristic
17C4×D188C2211yescharacteristic
18C4×C22⋊D47—21no—
19C42×D47C2211yescharacteristic
20C4⋊(C47⋊C8)C2211yescharacteristic
21Dic47⋊C8—21no—
22C4×C47⋊C8C2211yescharacteristic
23C8×Dic47—21no—
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—
56#10625324—42no—
57C8×D47—24no—
58C23×C47—21no—
59C22×D47—21no—
60C22×D47C22⋊C411yescharacteristic
61D4×C47—21no—
62D4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C22⋊D47—42no—
70C22⋊D47—42no—
71C22⋊D47—42no—
72C2×Dic47—21no—
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C2×Dic47C22⋊C411yescharacteristic
76D188—21no—
77D188—21no—
78D188—42no—
79C4×D47—21no—
80C4×D47—21no—
81C4×D47—22no—
82C4×D47—41no—
83C4×D47—41no—
84C4×D47D812yes—
85C4×D47SD1612yes—
86Dic94—42no—
87C8×C47—22no—
88C8×C47—41no—
89C47⋊C8—22no—
90C47⋊C8—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47—41no—
94C22×C47C2×C22⋊C411yescharacteristic
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—41no—
98C2×D47—41no—
99C2×D47—41no—
100C2×D47#10212yes—
101C4×C47—21no—
102C4×C47—41no—
103C4×C47#13111yescharacteristic
104C4×C47#13111yescharacteristic
105C4×C47C2×D811yescharacteristic
106C4×C47C2×SD1611yescharacteristic
107Dic47—21no—
108Dic47—41no—
109Dic47#10212yes—
110Dic47#10412yes—
111#1492—471nomaximal, Sylow
112C2×C47—81no—
113C2×C47#40811yescharacteristic
114C2×C47C2×#10211yescharacteristic
115C2×C47C2×#10411yescharacteristic
116D47—22no—
117D47—81no—
118#532—471no—
119#423—471no—
120C2×C4×C8—471no—
121D4⋊C8—471no—
122D4⋊C8—471no—
123D4⋊C8—471no—
124D4⋊C8D4711yescharacteristic, complemented
125C47#149211yescharacteristic, complemented, Sylow
126C2×#41—941no—
127C2×M16—941no—
128C22×C8—941no—
129C4⋊Q8—471no—
130#127—471no—
131#124—941no—
132#121—471no—
133#121—471no—
134#121—941no—
135C4×D4—471no—
136C4×D4—941no—
137C4×D4C2×D4711yescharacteristic
138C2×C42—471no—
139C4⋊C8—471no—
140C4⋊C8—941no—
141C4⋊C8C2×D4711yescharacteristic
142C4×C8—471no—
143C4×C8—941no—
144C4×C8C2×D4711yescharacteristic
145#41—1882no—
146#41—1882no—
147C2×Q8—941no—
148C2×D4—471no—
149C2×D4—941no—
150C2×D4—941no—
151C2×D4—941no—
152C2×D4—941no—
153C2×D4C4×D4711yescharacteristic
154C22×C4—21no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—941no—
159M16—1882no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—944no—
163C2×C8—941no—
164C2×C8—941no—
165C4⋊C4—471no—
166C4⋊C4—941no—
167C4⋊C4C4×D4711yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—941no—
170C22⋊C4—941no—
171C22⋊C4—941no—
172C42—471no—
173C42—471no—
174C42—471no—
175C42C22×D4711yescharacteristic
176C23—21no—
177C23—471no—
178C23—941no—
179Q8—1882no—
180D4—21no—
181D4—21no—
182D4—941no—
183D4—941no—
184D4—1882no—
185D4—1882no—
186D4—1882no—
187D4—1882no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—471no—
192C2×C4—471no—
193C2×C4—472no—
194C2×C4—472no—
195C2×C4—471no—
196C2×C4—942no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4C2×C4×D4711yescharacteristic
203C2×C4D4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C8—22no—
206C8—41no—
207C8—942no—
208C8—1881no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—472no—
213C22—941no—
214C22—941no—
215C22—1881no—
216C22—1881no—
217C22—1881no—
218C22C22⋊C4×D4711yescharacteristic
219C4—21no—
220C4—41no—
221C4—472no—
222C4—472no—
223C4—941no—
224C4—1881no—
225C4#1309403011yescharacteristic
226C4#1309403211yescharacteristic
227C4D8×D4711yescharacteristic
228C4SD16×D4711yescharacteristic
229C2—81no—
230C2—942no—
231C2—3761no—
232C2#1568908811yescharacteristic
233C2#102×D4711yescharacteristic
234C2#104×D4711yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1492
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. #15689145C2semidirect
3. C4×C8×D47C2semidirect
4. #15688852C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×D4⋊C8C2semidirect
124. D4⋊C8D47semidirect
125. C47#1492semidirect