Finite Group Databasebeta

← #20253783

Subgroups — #20253783

Order 6016.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689674C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic, complemented
3#15689484C214yesmaximal, complemented
4#15689473C211yesmaximal, characteristic, complemented
5#15689471C211yesmaximal, characteristic, complemented
6#15689470C211yesmaximal, characteristic, complemented
7#15689123C214yesmaximal, complemented
8C4×#10625324C211yesmaximal, characteristic, complemented
9C47×#487C211yesmaximal, characteristic, complemented
10C2×#10625354C2212yes—
11C2×Q8×D47—21no—
12C2×#10625324C2212yes—
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094022—21no—
17#13094021C2211yescharacteristic
18#13094013C2212yes—
19#13093999—21no—
20#13093999—21no—
21#13093986—21no—
22#13093986—21no—
23C4⋊C4×D47—21no—
24C4⋊C4×D47C2212yes—
25C42×D47C2211yescharacteristic
26#13093948C2214yes—
27#13093946C2214yes—
28#13093944C2214yes—
29#13093934C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#103×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47C2312yes—
37#10625354—28no—
38Q8×D47—44no—
39C2×D188—22no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47D411yescharacteristic
46C2×C4×D47D411yescharacteristic
47C2×C4×D47C2311yescharacteristic
48C2×Dic94—21no—
49C2×Dic94—22no—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C42×C47C2311yescharacteristic
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2312yes—
66#10625324—24no—
67C22×D47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—24no—
70Q8×C47—42no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D411yescharacteristic
80D188—24no—
81D188—44no—
82D188—42no—
83D188—42no—
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—44no—
87C4×D47—44no—
88C4×D47#4114yes—
89Dic94—44no—
90Dic94—42no—
91C8×C47—22no—
92C47⋊C8—22no—
93C22×C47C22×D411yescharacteristic
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47#12412yes—
100C4×C47—42no—
101C4×C47—42no—
102C4×C47AGL(1,ℤ/8)12yes—
103C4×C47#13712yes—
104C4×C47C2×#4112yes—
105Dic47—21no—
106Dic47—21no—
107Dic47—42no—
108Dic47#12412yes—
109#3141—471nomaximal, Sylow
110C2×C47C2×#12411yescharacteristic
111C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C47C2×#13711yescharacteristic
113D47—22no—
114D47—82no—
115#532—471no—
116C2×C4⋊Q8—471no—
117#489—474no—
118#487—471no—
119#487D4711yescharacteristic, complemented
120#486—471no—
121#486—471no—
122#417—474no—
123C4×M16—471no—
124C47#314111yescharacteristic, complemented, Sylow
125C2×#41—472no—
126C22×Q8—941no—
127C2×M16—472no—
128C4⋊Q8—472no—
129C4⋊Q8—471no—
130C4⋊Q8—941no—
131C4⋊Q8—941no—
132C4⋊Q8C2×D4711yescharacteristic
133C4⋊Q8C2×D4711yescharacteristic
134#127—471no—
135#124—472no—
136#121—941no—
137#121—941no—
138C4×D4—941no—
139C4×D4—941no—
140C2×C4⋊C4—472no—
141C2×C4⋊C4—941no—
142C2×C42—471no—
143#103—474no—
144#103C2×D4714yes—
145#102—474no—
146#102—474no—
147#97—472no—
148C4×C8—471no—
149C4×C8C2×D4711yescharacteristic
150#41—948no—
151C2×Q8—21no—
152C2×Q8—942no—
153C2×Q8—941no—
154C2×Q8—1884no—
155C2×Q8C22×D4712yes—
156C2×D4—472no—
157C2×D4—942no—
158C2×D4—941no—
159C2×D4—941no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—942no—
164C22×C4—942no—
165M16—944no—
166C2×C8—472no—
167C2×C8C22×D4712yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—941no—
175C4⋊C4C22×D4712yes—
176C22⋊C4—942no—
177C22⋊C4—942no—
178C42—471no—
179C42—471no—
180C42—471no—
181C42C22×D4711yescharacteristic
182C23—471no—
183C23—942no—
184Q8—24no—
185Q8—42no—
186Q8—1884no—
187Q8—1882no—
188D4—944no—
189D4—1884no—
190D4—1882no—
191D4—1882no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—471no—
195C2×C4—474no—
196C2×C4—471no—
197C2×C4—471no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—1884no—
202C2×C4—1884no—
203C2×C4D4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4C23×D4711yescharacteristic
206C8—22no—
207C8—942no—
208C22—472no—
209C22—941no—
210C22—941no—
211C22—1882no—
212C22—1882no—
213C22—1882no—
214C22C2×D4×D4711yescharacteristic
215C4—42no—
216C4—42no—
217C4—472no—
218C4—941no—
219C4—941no—
220C4—1882no—
221C4#1309405112yes—
222C4#1309405612yes—
223C4#41×D4712yes—
224C2—942no—
225C2—3762no—
226C2#124×D4711yescharacteristic
227C2C2×#1309405111yescharacteristic
228C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3141
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D47C2semidirect
3. #15689484C2semidirect
4. #15689473C2semidirect
5. #15689471C2semidirect
6. #15689470C2semidirect
7. #15689123C2semidirect
8. C4×#10625324C2semidirect
9. C47×#487C2semidirect
119. #487D47semidirect
124. C47#3141semidirect