Finite Group Databasebeta

← #20253778

Subgroups — #20253778

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#15689671C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic, complemented
3#15689481C214yesmaximal, complemented
4#15689475C211yesmaximal, characteristic, complemented
5#15689474C211yesmaximal, characteristic, complemented
6#15689469C211yesmaximal, characteristic, complemented
7#15689121C214yesmaximal, complemented
8C4×#10625324C211yesmaximal, characteristic, complemented
9C47×#486C211yesmaximal, characteristic, complemented
10C2×#10625352C2212yes—
11C2×Q8×D47—21no—
12C2×#10625324C2212yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094023—21no—
16#13094023C2212yes—
17#13094022—21no—
18#13094011C2212yes—
19#13093995—21no—
20#13093995—21no—
21D4×Dic47—21no—
22D4×Dic47—21no—
23C4⋊C4×D47—21no—
24C4⋊C4×D47C2212yes—
25C42×D47C2211yescharacteristic
26#13093949C2214yes—
27#13093947C2214yes—
28#13093945C2214yes—
29#13093934C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32#127×C47C2211yescharacteristic
33#102×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C2×C22⋊D47—22no—
40C22×Dic47—22no—
41Q8×D47—44no—
42#10625352—28no—
43C2×C4×D47—22no—
44C2×C4×D47D411yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×C4×D47C2311yescharacteristic
47C2×Dic94—21no—
48C2×Dic94—22no—
49C2×Dic94C2312yes—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2312yes—
66#10625324—24no—
67C23×C47—22no—
68C22×D47C2×D411yescharacteristic
69Q8×C47—42no—
70D4×C47—24no—
71D4×C47—42no—
72D4×C47—42no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—44no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—44no—
81C2×Dic47C2×D411yescharacteristic
82C2×Dic47C2×D411yescharacteristic
83C2×Dic47C2×D411yescharacteristic
84C4×D47—22no—
85C4×D47—22no—
86C4×D47—44no—
87C4×D47#4114yes—
88Dic94—24no—
89Dic94—44no—
90Dic94—42no—
91C8×C47—22no—
92C47⋊C8—22no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47C22×D411yescharacteristic
97C2×D47—21no—
98C2×D47—21no—
99C2×D47#12412yes—
100C4×C47—42no—
101C4×C47AGL(1,ℤ/8)12yes—
102C4×C47#13712yes—
103C4×C47C2×#4112yes—
104Dic47—21no—
105Dic47—21no—
106Dic47—42no—
107Dic47—42no—
108Dic47#12412yes—
109#3141—471nomaximal, Sylow
110C2×C47—82no—
111C2×C47C2×#12411yescharacteristic
112C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
113C2×C47C2×#13711yescharacteristic
114D47—22no—
115#532—471no—
116C2×C4⋊Q8—471no—
117#489—474no—
118#487—471no—
119#487—471no—
120#486—471no—
121#486D4711yescharacteristic, complemented
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—471no—
131C4⋊Q8—941no—
132C4⋊Q8—941no—
133C4⋊Q8C2×D4711yescharacteristic
134#127C2×D4711yescharacteristic
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#103—474no—
145#102—474no—
146#102C2×D4714yes—
147#97—472no—
148C4×C8—471no—
149C4×C8C2×D4711yescharacteristic
150#41—948no—
151C2×Q8—21no—
152C2×Q8—472no—
153C2×Q8—942no—
154C2×Q8—941no—
155C2×Q8—1884no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—942no—
159C2×D4C22×D4712yes—
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—472no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C4⋊C4C22×D4712yes—
176C22⋊C4—942no—
177C22⋊C4—942no—
178C42—471no—
179C42—471no—
180C42—471no—
181C42C22×D4711yescharacteristic
182C23—22no—
183C23—471no—
184Q8—42no—
185Q8—944no—
186Q8—1884no—
187Q8—1882no—
188D4—24no—
189D4—42no—
190D4—42no—
191D4—1884no—
192C2×C4—22no—
193C2×C4—471no—
194C2×C4—474no—
195C2×C4—471no—
196C2×C4—471no—
197C2×C4—942no—
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—42no—
209C22—42no—
210C22—42no—
211C22—472no—
212C22—941no—
213C22—941no—
214C22C2×D4×D4711yescharacteristic
215C4—42no—
216C4—472no—
217C4—941no—
218C4—941no—
219C4—1882no—
220C4—1882no—
221C4#1309404812yes—
222C4#1309405312yes—
223C4#41×D4712yes—
224C2—82no—
225C2—942no—
226C2#124×D4711yescharacteristic
227C2C2×#1309404811yescharacteristic
228C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3141
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D47C2semidirect
3. #15689481C2semidirect
4. #15689475C2semidirect
5. #15689474C2semidirect
6. #15689469C2semidirect
7. #15689121C2semidirect
8. C4×#10625324C2semidirect
9. C47×#486C2semidirect
121. #486D47semidirect
124. C47#3141semidirect