Finite Group Databasebeta

← #20246013

Subgroups — #20246013

Order 6016.

600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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×#13093982C211yesmaximal, characteristic
2C2×#13093981C211yesmaximal, characteristic
3C2×C4⋊C4×D47C211yesmaximal, characteristic
4#15689020C214yesmaximal, complemented
5#15688997C214yesmaximal
6#15688993C211yesmaximal, characteristic, complemented
7#15688992C211yesmaximal, characteristic, complemented
8#15688988C211yesmaximal, characteristic, complemented
9C47×#382C211yesmaximal, characteristic, complemented
10C22×C4×D47C2212yes—
11C22×C4×D47C2211yescharacteristic
12#13093982—24no—
13#13093981C418yescomplemented
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2214yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2214yes—
19C2×Dic47⋊C4C2212yes—
20C4⋊C4×D47—24no—
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×C4×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2214yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29#95×C47C2214yes—
30C23×D47C2311yescharacteristic
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47C2312yes—
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2311yescharacteristic
39C2×C4×D47—24no—
40C2×C4×D47—44no—
41C2×C4×D47C2×C414yes—
42C2×C4×D47D414yes—
43C2×C4×D47Q814yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—22no—
46C42×C47C2×C414yescomplemented
47(C2×D47)⋊C4—24no—
48(C2×D47)⋊C4C2×C418yes—
49C4⋊Dic47—22no—
50C4⋊Dic47—22no—
51C4⋊Dic47—44no—
52Dic47⋊C4—24no—
53Dic47⋊C4—44no—
54Dic47⋊C4C2×C418yescomplemented
55C4×Dic47—24no—
56C4×Dic47C2×C414yescomplemented
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—22no—
60C22×D47C22×C412yes—
61C22×D47C2×D412yes—
62C22×D47C2×Q812yes—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—24no—
69C2×C4×C47C22×C414yes—
70C2×C4×C47C22×C412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×Q812yes—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47C22×C414yes—
80C2×Dic47C22×C412yes—
81C2×Dic47C2×D412yes—
82C2×Dic47C2×Q812yes—
83C4×D47—48no—
84C4×D47C4⋊C4116yescomplemented
85C22×C47C23×C411yescharacteristic
86C22×C47C22×D411yescharacteristic
87C22×C47C22×Q811yescharacteristic
88C22×C47H(5,𝔽2)12yes—
89C22×C472−1+412yes—
90C2×D47—24no—
91C2×D47—22no—
92C2×D47—22no—
93C2×D47—24no—
94C2×D47C2×C4⋊C414yes—
95C4×C47—24no—
96C4×C47—42no—
97C4×C47—42no—
98C4×C47C2×C4⋊C414yes—
99Dic47—24no—
100Dic47—42no—
101Dic47—42no—
102Dic47C2×C4⋊C414yes—
103#2317—471nomaximal, Sylow
104C2×C47C22×C4⋊C411yescharacteristic
105C2×C47#52012yes—
106C2×C47#53511yescharacteristic
107C2×C47#53611yescharacteristic
108C2×C47#54412yes—
109D47—24no—
110C2×#117—471no—
111C2×#117—471no—
112C22×C4⋊C4—471no—
113#389—474no—
114#385—474no—
115#384—471no—
116#384—471no—
117#382—471no—
118#382D4711yescharacteristic, complemented
119C47#231711yescharacteristic, complemented, Sylow
120C23×C4—471no—
121C23×C4—472no—
122#117—478no—
123#117—944no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—471no—
128C2×C4⋊C4—474no—
129C2×C4⋊C4—474no—
130C2×C4⋊C4—944no—
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C42—471no—
136C2×C42—472no—
137C2×C42C2×D4711yescharacteristic
138#95—474no—
139#95C2×D4714yes—
140C24—471no—
141C22×C4—471no—
142C22×C4—474no—
143C22×C4—474no—
144C22×C4—474no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4—944no—
149C22×C4—1884no—
150C22×C4C22×D4712yes—
151C22×C4C22×D4712yes—
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—478no—
157C4⋊C4—944no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—1884no—
161C4⋊C4—1884no—
162C22⋊C4—478no—
163C22⋊C4—944no—
164C42—474no—
165C42—944no—
166C42C4×D4714yescomplemented
167C23—472no—
168C23—472no—
169C23—472no—
170C23—942no—
171C23—942no—
172C23C23×D4711yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—472no—
180C2×C4—472no—
181C2×C4—472no—
182C2×C4—4716no—
183C2×C4—474no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—944no—
189C2×C4—944no—
190C2×C4—1888no—
191C2×C4C2×C4×D4714yes—
192C2×C4C2×C4×D4712yes—
193C2×C4D4×D4712yes—
194C2×C4Q8×D4712yes—
195C22—474no—
196C22—944no—
197C22—944no—
198C22—942no—
199C22—942no—
200C22C22×C4×D4711yescharacteristic
201C22C2×D4×D4711yescharacteristic
202C22C2×Q8×D4711yescharacteristic
203C22#1309407012yes—
204C22#1309407112yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—474no—
209C4—944no—
210C4—1882no—
211C4—1882no—
212C4C4⋊C4×D4714yes—
213C2—944no—
214C2C2×C4⋊C4×D4711yescharacteristic
215C2#1568960312yes—
216C2#1568969111yescharacteristic
217C2#1568969311yescharacteristic
218C2#1568975312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#382C2
socleC23×C47C24
hypercenter#382D47
hypocenterC47#2317
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
4. #15689020C2semidirect
6. #15688993C2semidirect
7. #15688992C2semidirect
8. #15688988C2semidirect
9. C47×#382C2semidirect
13. #13093981C4semidirect
46. C42×C47C2×C4semidirect
54. Dic47⋊C4C2×C4semidirect
56. C4×Dic47C2×C4semidirect
84. C4×D47C4⋊C4semidirect
118. #382D47semidirect
119. C47#2317semidirect
166. C42C4×D47semidirect