Finite Group Databasebeta

← #20248339

Subgroups — #20248339

Order 6016.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13094023C211yesmaximal, characteristic, complemented
2C2×#13094001C214yesmaximal, complemented
3C2×D4×Dic47C211yesmaximal, characteristic
4#15689059C214yesmaximal, complemented
5#15689026C211yesmaximal, characteristic
6#15688993C211yesmaximal, characteristic, complemented
7#15688992C211yesmaximal, characteristic, complemented
8C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
9C47×#390C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11C23×Dic47C2212yes—
12#13094023—24no—
13#13094001—216no—
14D4×Dic47—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2214yes—
18C2×Dic47⋊C4C2214yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×C22⋊Dic47C2214yes—
22C2×C22⋊Dic47C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C22×D4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2214yes—
29C2×C42×C47C2211yescharacteristic
30C24×C47C2312yes—
31C2×D4×C47—22no—
32C2×D4×C47—22no—
33C2×D4×C47Q814yescomplemented
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—24no—
38C22×Dic47—28no—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C2×Dic94—28no—
45C2×Dic94—24no—
46C4⋊C4×C47—22no—
47C22⋊C4×C47—28no—
48C42×C47—22no—
49C22⋊Dic47—24no—
50C22⋊Dic47—28no—
51C4⋊Dic47—22no—
52C4⋊Dic47—28no—
53C4⋊Dic47—22no—
54Dic47⋊C4—28no—
55Dic47⋊C4—24no—
56Dic47⋊C4D418yescomplemented
57C4×Dic47—22no—
58C4×Dic47D414yes—
59C23×C47—24no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—24no—
63C23×C47C2×Q814yes—
64C23×C47C2411yescharacteristic
65D4×C47—28no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—24no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D414yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×Q812yes—
73C2×C4×C47#4112yes—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—22no—
81C2×Dic47—48no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D414yes—
84C2×Dic47C2×D412yes—
85C2×Dic47C2×D414yes—
86Dic94—48no—
87C22×C47—24no—
88C22×C47—28no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—44no—
92C22×C47C22×D411yescharacteristic
93C22×C47C22×D412yes—
94C22×C47C22×Q811yescharacteristic
95C22×C47C2×#4111yescharacteristic
96C22×C472−1+412yes—
97C4×C47—24no—
98C4×C47—42no—
99C4×C47C22⋊Q814yescomplemented
100Dic47—22no—
101Dic47—24no—
102Dic47—42no—
103Dic47—42no—
104Dic47#12714yes—
105#2542—471nomaximal, Sylow
106C2×C47—44no—
107C2×C47C2×C22⋊Q811yescharacteristic
108C2×C47C2×#12711yescharacteristic
109C2×C47#53611yescharacteristic
110C2×C47#54712yes—
111C2×C47D4×Q812yes—
112C2×C4⋊Q8—471no—
113C2×C22⋊Q8—474no—
114C2×C4×D4—471no—
115#399—474no—
116#390—471no—
117#390D4711yescharacteristic
118#384—471no—
119#384—471no—
120C4×C4⋊C4—471no—
121C47#254211yescharacteristic, complemented, Sylow
122C22×Q8—472no—
123C22×D4C2×D4711yescharacteristic
124C23×C4—472no—
125C4⋊Q8—944no—
126C22⋊Q8—9416no—
127C4×D4—944no—
128C2×C4⋊C4—472no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—474no—
131C2×C4⋊C4—474no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C22⋊C4—472no—
136C2×C22⋊C4—474no—
137C2×C22⋊C4C2×D4714yes—
138C2×C42—471no—
139C2×C42—471no—
140C2×C42C2×D4711yescharacteristic
141#95—472no—
142C24C22×D4712yes—
143C2×Q8—948no—
144C2×Q8—944no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4Dic9414yescomplemented
148C22×C4—471no—
149C22×C4—471no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4—472no—
153C22×C4—944no—
154C22×C4—948no—
155C22×C4C22×D4712yes—
156C22×C4C22×D4712yes—
157C22×C4C22×D4711yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—478no—
160C4⋊C4—948no—
161C4⋊C4—944no—
162C4⋊C4—942no—
163C4⋊C4—948no—
164C4⋊C4—942no—
165C22⋊C4—28no—
166C22⋊C4—944no—
167C22⋊C4—948no—
168C42—22no—
169C42—474no—
170C42—942no—
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic9414yes—
176C23C23×D4711yescharacteristic
177Q8—1888no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—472no—
184C2×C4—474no—
185C2×C4—472no—
186C2×C4—474no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—944no—
192C2×C4—944no—
193C2×C4—942no—
194C2×C4—1888no—
195C2×C4C2×Dic9412yes—
196C2×C4D4×D4714yes—
197C2×C4D4×D4712yes—
198C2×C4#1062535212yes—
199C22—28no—
200C22—24no—
201C22—44no—
202C22—42no—
203C22—42no—
204C22C2×D4×D4712yes—
205C22C2×D4×D4711yescharacteristic
206C22C22×Dic9411yescharacteristic
207C22C2×#1062535211yescharacteristic
208C22#1309407112yes—
209C4—24no—
210C4—42no—
211C4—474no—
212C4—944no—
213C4—942no—
214C4—1882no—
215C4—1882no—
216C4#1309400114yescomplemented
217C2—44no—
218C2C2×#1309400111yescharacteristic
219C2#127×D4711yescharacteristic
220C2#1568969311yescharacteristic
221C2#1568977312yes—
222C2D4×Dic9412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2542
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
2. C2×#13094001C2semidirect
4. #15689059C2semidirect
6. #15688993C2semidirect
7. #15688992C2semidirect
8. C4×Dic47⋊C4C2semidirect
33. C2×D4×C47Q8semidirect
56. Dic47⋊C4D4semidirect
99. C4×C47C22⋊Q8semidirect
121. C47#2542semidirect
147. C2×D4Dic94semidirect
216. C4#13094001semidirect