Finite Group Databasebeta

← #20253483

Subgroups — #20253483

Order 6016.

444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D188C211yesmaximal, characteristic
2#15689456C212yesmaximal, complemented
3#15689400C212yesmaximal, complemented
4#15689325C212yesmaximal, complemented
5#15689273C212yesmaximal
6#15689221C214yesmaximal, complemented
7#15689180C211yesmaximal, characteristic, complemented
8C47×#533C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C4×D47—21no—
11C2×#10625336C2214yes—
12C4×D188—21no—
13C4×D188—21no—
14C4×D188C2212yes—
15C4×D188C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4—21no—
18#13093957C2214yescomplemented
19C4⋊(C47⋊C8)C2212yescomplemented
20#13093948C2214yescomplemented
21#13093944C2214yes—
22C22⋊(C47⋊C8)C2212yes—
23#13093935C2212yescomplemented
24C4⋊Q8×C47C2211yescharacteristic, complemented
25C4⋊Q8×C47C2211yescharacteristic, complemented
26#125×C47—21no—
27C22⋊Q8×C47—21no—
28C22⋊Q8×C47C2212yes—
29C4×Q8×C47—21no—
30C4×Q8×C47C2212yescomplemented
31#117×C47—21no—
32C2×C42×C47C2211yescharacteristic
33C23×D47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47C2312yes—
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C2×D188—21no—
41C2×D188—24no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47—44no—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47C2312yes—
52C22⋊C4×C47—22no—
53C42×C47—22no—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58#10625336—28no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63C2×C47⋊C8C2314yes—
64C23×C47C2×D411yescharacteristic
65C22×D47—24no—
66C22×D47—22no—
67C22×D47—42no—
68C22×D47—42no—
69Q8×C47—24no—
70Q8×C47—42no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—42no—
84D188—24no—
85D188—22no—
86D188#4114yes—
87C4×D47—44no—
88C4×D47—44no—
89C47⋊C8—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#13712yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—24no—
95C2×D47—48no—
96C2×D47—42no—
97C2×D47—42no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47—42no—
104C4×C47AGL(1,ℤ/8)12yes—
105C4×C47C2×#4112yes—
106Dic47—42no—
107#3110—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#52511yescharacteristic
110C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—44no—
113#533D4711yescharacteristic, complemented
114C2×C4×D4—471no—
115#484—472no—
116#474—472no—
117#461—472no—
118#450—472no—
119#440—474no—
120#432—471no—
121C47#311011yescharacteristic, complemented, Sylow
122C22×D4—471no—
123C23×C4—941no—
124C2×SD16—474no—
125C4⋊Q8C2×D4711yescharacteristic, complemented
126C4⋊Q8C2×D4711yescharacteristic, complemented
127#125—21no—
128C22⋊Q8—21no—
129C22⋊Q8C2×D4712yes—
130C4×Q8—21no—
131C4×Q8C2×D4712yescomplemented
132C4×D4—472no—
133C4×D4—472no—
134C4×D4—941no—
135C4×D4—941no—
136#117—21no—
137C2×C4⋊C4—471no—
138C2×C22⋊C4—941no—
139C2×C42C2×D4711yescharacteristic
140#107—474no—
141C4⋊C8—472no—
142#103—474no—
143#102—474no—
144C22⋊C8—472no—
145#97—472no—
146C24—941no—
147C2×Q8—21no—
148C2×Q8C22×D4712yes—
149C2×D4—472no—
150C2×D4—944no—
151C2×D4—941no—
152C22×C4—941no—
153C22×C4—942no—
154C22×C4—942no—
155C22×C4—1884no—
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22⋊D4711yescharacteristic
158C22×C4C22×D4711yescharacteristic
159SD16—948no—
160C2×C8—474no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—472no—
167C4⋊C4—941no—
168C4⋊C4C22×D4712yes—
169C22⋊C4—22no—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C42—22no—
173C42C22⋊D4711yescharacteristic
174C42C22⋊D4711yescharacteristic
175C42C22×D4711yescharacteristic
176C42C22×D4711yescharacteristic
177C23—944no—
178C23—942no—
179C23—1882no—
180C23—1882no—
181C23C2×C22⋊D4711yescharacteristic
182Q8—24no—
183Q8—42no—
184D4—474no—
185D4—944no—
186D4—942no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—942no—
193C2×C4—1884no—
194C2×C4—1882no—
195C2×C4—1884no—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C2×C4C2×C22⋊D4711yescharacteristic
200C2×C4C2×C22⋊D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—944no—
203C22—21no—
204C22—21no—
205C22—944no—
206C22—1888no—
207C22—1882no—
208C22—1882no—
209C22#1309405512yes—
210C22C22×C22⋊D4711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—1882no—
218C4#1309404912yes—
219C4#41×D4712yes—
220C2—22no—
221C2—1884no—
222C2#1568963011yescharacteristic
223C2C2×#1309404911yescharacteristic
224C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3110
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #15689456C2semidirect
3. #15689400C2semidirect
4. #15689325C2semidirect
6. #15689221C2semidirect
7. #15689180C2semidirect
8. C47×#533C2semidirect
18. #13093957C22semidirect
19. C4⋊(C47⋊C8)C22semidirect
20. #13093948C22semidirect
23. #13093935C22semidirect
24. C4⋊Q8×C47C22semidirect
25. C4⋊Q8×C47C22semidirect
30. C4×Q8×C47C22semidirect
113. #533D47semidirect
121. C47#3110semidirect
125. C4⋊Q8C2×D47semidirect
126. C4⋊Q8C2×D47semidirect
131. C4×Q8C2×D47semidirect