Finite Group Databasebeta

← #20241777

Subgroups — #20241777

Order 6016.

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

normal subgroups only

This group has 312 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
1C4×D4×D47C211yesmaximal, characteristic
2#15689175C211yesmaximal, 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×D4×D47C411yescharacteristic
9C22×C4×D47—21no—
10C4×D188C2211yescharacteristic
11D4×Dic47C411yescharacteristic
12#13093986C411yescharacteristic
13C4×C22⋊D47—21no—
14(C22⋊D47)⋊C4—21no—
15C4⋊C4×D47C411yescharacteristic
16C22⋊C4×D47—21no—
17C42×D47C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic, complemented
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22C4×C47⋊C8C2211yescharacteristic, complemented
23C8×Dic47—21no—
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic, complemented
26C4×C8×C47C2211yescharacteristic, complemented
27C23×D47—21no—
28C2×D4×C47C2×C411yescharacteristic
29C22×C4×C47—21no—
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32D4×D47—22no—
33D4×D47C814yescomplemented
34C2×D188C2×C411yescharacteristic
35C2×C4×D47—21no—
36C2×C4×D47—21no—
37C2×C4×D47—21no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C4×D47C2×C411yescharacteristic
41C2×C4×D47D411yescharacteristic
42C2×C4×D47D411yescharacteristic
43C2×C8×C47—21no—
44C2×C8×C47—21no—
45C4⋊C4×C47C2×C411yescharacteristic
46C22⋊C4×C47—21no—
47C42×C47C2311yescharacteristic
48C22⋊Dic47—21no—
49(C2×D47)⋊C4—21no—
50(C2×D47)⋊C4—21no—
51C4⋊Dic47C2×C411yescharacteristic
52Dic47⋊C4—21no—
53C4×Dic47C2×C411yescharacteristic
54C4×Dic47D411yescharacteristic
55C4×Dic47D411yescharacteristic
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C22×D47—21no—
60C22×D47—24no—
61C22×D47—42no—
62C22×D47—42no—
63C22×D47C22⋊C411yescharacteristic
64D4×C47—21no—
65D4×C47C2×C812yes—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C22⋊D47—24no—
73C2×Dic47—21no—
74C2×Dic47—42no—
75C2×Dic47C22⋊C411yescharacteristic
76C2×Dic47C22⋊C411yescharacteristic
77C2×Dic47C22⋊C411yescharacteristic
78D188—21no—
79D188C2×C812yes—
80C4×D47—21no—
81C4×D47—21no—
82C4×D47—41no—
83C4×D47—42no—
84C4×D47—42no—
85C4×D47—41no—
86C4×D47—41no—
87C4×D47C2×C812yes—
88C4×D47M1612yes—
89C8×C47—41no—
90C8×C47—41no—
91C47⋊C8—41no—
92C47⋊C8—41no—
93C22×C47—22no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47C2×C22⋊C411yescharacteristic
97C2×D47—21no—
98C2×D47—21no—
99C2×D47—22no—
100C2×D47—48no—
101C2×D47—41no—
102C2×D47—41no—
103C2×D47C22⋊C812yes—
104C4×C47—21no—
105C4×C47—41no—
106C4×C47C22×C811yescharacteristic
107C4×C47C2×M1611yescharacteristic
108C4×C47AGL(1,ℤ/8)11yescharacteristic
109C4×C47AGL(1,ℤ/8)11yescharacteristic
110Dic47—21no—
111Dic47—21no—
112Dic47—41no—
113Dic47C22⋊C812yes—
114#1478—471nomaximal, Sylow
115C2×C47—42no—
116C2×C47C2×C22⋊C811yescharacteristic
117C2×C47#41811yescharacteristic
118C2×C47#42111yescharacteristic
119D47—22no—
120D47—42no—
121C2×C4×D4—471no—
122#431—471no—
123#431—471no—
124D4⋊C8—471no—
125D4⋊C8—471no—
126D4⋊C8—471no—
127D4⋊C8D4711yescharacteristic, complemented
128C47#147811yescharacteristic, complemented, Sylow
129C22×D4—471no—
130C23×C4—941no—
131C4×D4—471no—
132C4×D4—471no—
133C4×D4—471no—
134C4×D4—941no—
135C4×D4—941no—
136C4×D4C2×D4711yescharacteristic
137C2×C4⋊C4—471no—
138C2×C22⋊C4—941no—
139C2×C42—471no—
140C4⋊C8—471no—
141C4⋊C8—941no—
142C4⋊C8C2×D4711yescharacteristic, complemented
143C22⋊C8—941no—
144C22⋊C8—941no—
145C4×C8—471no—
146C4×C8—941no—
147C4×C8C2×D4711yescharacteristic, complemented
148C24—941no—
149C2×D4—474no—
150C2×D4—471no—
151C2×D4—942no—
152C2×D4—941no—
153C2×D4C4×D4711yescharacteristic
154C22×C4—21no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—941no—
159C22×C4—941no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4—1882no—
163C22×C4—1882no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—941no—
167C2×C8—941no—
168C4⋊C4—471no—
169C4⋊C4—941no—
170C4⋊C4C4×D4711yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C22⋊C4—941no—
175C42—471no—
176C42—471no—
177C42—471no—
178C42C22×D4711yescharacteristic
179C23—21no—
180C23—471no—
181C23—944no—
182C23—941no—
183C23—1882no—
184C23—1882no—
185D4—21no—
186D4—472no—
187D4—944no—
188D4—941no—
189D4C8×D4712yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—471no—
194C2×C4—472no—
195C2×C4—472no—
196C2×C4—471no—
197C2×C4—471no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—1881no—
202C2×C4—1882no—
203C2×C4—1882no—
204C2×C4—1882no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4C2×C4×D4711yescharacteristic
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C8—41no—
211C8—41no—
212C8—1881no—
213C8—1881no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—472no—
218C22—941no—
219C22—941no—
220C22—942no—
221C22—1888no—
222C22—1881no—
223C22—1881no—
224C22C22⋊C4×D4711yescharacteristic
225C4—21no—
226C4—41no—
227C4—472no—
228C4—941no—
229C4—941no—
230C4—1881no—
231C4C2×C8×D4711yescharacteristic
232C4M16×D4711yescharacteristic
233C4#1309404811yescharacteristic
234C4#1309405111yescharacteristic
235C2—42no—
236C2—942no—
237C2—1882no—
238C2C22⋊C8×D4711yescharacteristic
239C2#1568912611yescharacteristic
240C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC4×C47C22×C8
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1478
LCSG ▷ 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. #15689175C2semidirect
3. #15689174C2semidirect
4. #15688852C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×D4⋊C8C2semidirect
18. C4⋊(C47⋊C8)C22semidirect
22. C4×C47⋊C8C22semidirect
25. C4⋊C8×C47C22semidirect
26. C4×C8×C47C22semidirect
33. D4×D47C8semidirect
127. D4⋊C8D47semidirect
128. C47#1478semidirect
142. C4⋊C8C2×D47semidirect
147. C4×C8C2×D47semidirect