Finite Group Databasebeta

← #20254505

Subgroups — #20254505

Order 6016.

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

normal subgroups only

This group has 404 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#15689528C211yesmaximal, characteristic, complemented
4#15689526C211yesmaximal, characteristic, complemented
5#15689469C211yesmaximal, characteristic, complemented
6#15689435C214yesmaximal, complemented
7#15689401C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#486C211yesmaximal, characteristic, complemented
10C2×#10625352—21no—
11C2×Q8×D47—21no—
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094022—21no—
17#13094011—21no—
18#13093995—21no—
19#13093995C2212yes—
20D4×Dic47—21no—
21D4×Dic47C2212yes—
22C4⋊C4×D47—21no—
23C4⋊C4×D47C2212yes—
24C42×D47C2211yescharacteristic
25#13093958C2214yes—
26#13093957C2214yes—
27Dic47⋊C8C2212yes—
28#13093945C2214yes—
29(C2×D47)⋊C8C2212yes—
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—44no—
43C2×C4×D47—22no—
44C2×C4×D47D411yescharacteristic
45C2×C4×D47D411yescharacteristic
46C2×C4×D47C2311yescharacteristic
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—22no—
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⋊Dic47C2312yes—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2312yes—
66C23×C47—22no—
67C22×D47C2×D411yescharacteristic
68Q8×C47—42no—
69D4×C47—24no—
70D4×C47—42no—
71D4×C47—42no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2411yescharacteristic
76C22⋊D47—44no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—44no—
80C2×Dic47C2×D411yescharacteristic
81C2×Dic47C2×D411yescharacteristic
82C2×Dic47C2×D411yescharacteristic
83C4×D47—22no—
84C4×D47—22no—
85C4×D47—44no—
86C4×D47D814yes—
87Dic94—42no—
88Dic94—42no—
89Dic94—44no—
90C8×C47—22no—
91C47⋊C8—22no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47C22×D411yescharacteristic
96C2×D47—21no—
97C2×D47—21no—
98C2×D47C2×D812yes—
99C4×C47—42no—
100C4×C47C2×D812yes—
101C4×C47#13712yes—
102C4×C472−1+412yes—
103Dic47—21no—
104Dic47—21no—
105Dic47—42no—
106Dic47—42no—
107Dic47C2×D812yes—
108#3226—471nomaximal, Sylow
109C2×C47—82no—
110C2×C47#53611yescharacteristic
111C2×C47C22×D811yescharacteristic
112C2×C47C2×#13711yescharacteristic
113D47—22no—
114#532—471no—
115C2×C4⋊Q8—471no—
116#500—471no—
117#500—471no—
118#486—471no—
119#486D4711yescharacteristic, complemented
120#480—474no—
121#474—474no—
122#431—471no—
123C47#322611yescharacteristic, complemented, Sylow
124C2×#41—941no—
125C22×Q8—941no—
126C4⋊Q8—472no—
127C4⋊Q8—471no—
128C4⋊Q8—471no—
129C4⋊Q8—941no—
130C4⋊Q8—941no—
131C4⋊Q8C2×D4711yescharacteristic
132#127C2×D4711yescharacteristic
133#124—941no—
134#121—472no—
135#121—941no—
136C4×D4—472no—
137C4×D4—941no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—941no—
140C2×C42—471no—
141#107—474no—
142#107—474no—
143C4⋊C8—472no—
144#102—474no—
145#102C2×D4714yes—
146C22⋊C8—472no—
147C4×C8—471no—
148C4×C8C2×D4711yescharacteristic
149#41—1884no—
150C2×Q8—21no—
151C2×Q8—942no—
152C2×Q8—941no—
153C2×Q8—941no—
154C2×Q8—1884no—
155C2×D4—21no—
156C2×D4—21no—
157C2×D4—942no—
158C2×D4C22×D4712yes—
159C22×C4—471no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—942no—
163C22×C4—942no—
164C2×C8—472no—
165C2×C8C22×D4712yes—
166C4⋊C4—21no—
167C4⋊C4—472no—
168C4⋊C4—472no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—941no—
172C4⋊C4—941no—
173C4⋊C4C22×D4712yes—
174C22⋊C4—942no—
175C22⋊C4—942no—
176C42—471no—
177C42—471no—
178C42—471no—
179C42C22×D4711yescharacteristic
180C23—22no—
181C23—471no—
182Q8—42no—
183Q8—1884no—
184Q8—1882no—
185Q8—1882no—
186D4—24no—
187D4—42no—
188D4—42no—
189D4—1884no—
190C2×C4—22no—
191C2×C4—471no—
192C2×C4—474no—
193C2×C4—471no—
194C2×C4—471no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—1884no—
200C2×C4—1884no—
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4C23×D4711yescharacteristic
204C8—22no—
205C8—942no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—472no—
210C22—941no—
211C22—941no—
212C22C2×D4×D4711yescharacteristic
213C4—42no—
214C4—472no—
215C4—941no—
216C4—941no—
217C4—1882no—
218C4—1882no—
219C4D8×D4712yes—
220C4#1309405312yes—
221C4#1309407112yes—
222C2—82no—
223C2—942no—
224C2#1568969311yescharacteristic
225C2C2×D8×D4711yescharacteristic
226C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3226
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. #15689528C2semidirect
4. #15689526C2semidirect
5. #15689469C2semidirect
6. #15689435C2semidirect
7. #15689401C2semidirect
8. #15689174C2semidirect
9. C47×#486C2semidirect
119. #486D47semidirect
123. C47#3226semidirect