Finite Group Databasebeta

← #20251736

Subgroups — #20251736

Order 6016.

644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094003C211yesmaximal, characteristic
3C22×C4×Dic47C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15689018C214yesmaximal, complemented
7#15688992C211yesmaximal, characteristic, complemented
8#15688981C214yesmaximal
9C2×C22⋊Q8×C47C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2212yes—
12#13094022—24no—
13#13094003—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2214yes—
16C2×Dic47⋊C4C2214yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C4×Dic47—24no—
20C2×C4×Dic47C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2214yes—
24C47⋊#95C2214yes—
25C22×Q8×C47C2211yescharacteristic
26C23×C4×C47C2211yescharacteristic
27C22⋊Q8×C47—24no—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2212yes—
31C24×C47C2311yescharacteristic
32C2×Q8×C47—22no—
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47—22no—
37C22×C4×C47D414yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—24no—
43C22×Dic47—24no—
44C22×Dic47Q818yescomplemented
45C22×Dic47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C2×Dic94—22no—
50C2×Dic94—22no—
51C2×Dic94—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—24no—
54C22⋊C4×C47—24no—
55C22⋊Dic47—24no—
56C4⋊Dic47—22no—
57Dic47⋊C4—24no—
58Dic47⋊C4—28no—
59Dic47⋊C4—28no—
60C4×Dic47—22no—
61C4×Dic47—24no—
62C4×Dic47D414yes—
63C23×C47—21no—
64C23×C47—22no—
65C23×C47—21no—
66C23×C47C2×D412yes—
67C23×C47C2×Q814yes—
68C23×C47C2411yescharacteristic
69Q8×C47—44no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—28no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—24no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D412yes—
81C2×C4×C47#4112yes—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—216no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—24no—
89C2×Dic47—22no—
90C2×Dic47C2×D414yes—
91C2×Dic47C2×Q814yes—
92C2×Dic47C2×Q814yes—
93C2×Dic47#4114yes—
94Dic94—44no—
95C22×C47—22no—
96C22×C47—24no—
97C22×C47—22no—
98C22×C47—24no—
99C22×C47C4⋊Q814yescomplemented
100C22×C47C22×D411yescharacteristic
101C22×C47C22×D411yescharacteristic
102C22×C47C22×Q812yes—
103C22×C47C2×#4112yes—
104C22×C47C2×#4111yescharacteristic
105C4×C47—22no—
106C4×C47—42no—
107C4×C47—42no—
108C4×C47#12114yes—
109Dic47—24no—
110Dic47—42no—
111Dic47—42no—
112Dic47C22⋊Q818yescomplemented
113#2857—471nomaximal, Sylow
114C2×C47—24no—
115C2×C47C2×#12111yescharacteristic
116C2×C47C2×C22⋊Q812yes—
117C2×C47C2×C4⋊Q811yescharacteristic
118C2×C47#53211yescharacteristic
119C2×C47#53312yes—
120C2×C4⋊Q8—471no—
121C2×C22⋊Q8—471no—
122C2×C22⋊Q8D4711yescharacteristic
123C22×C42—471no—
124#391—471no—
125#391—471no—
126#389—474no—
127#384—471no—
128#380—474no—
129C47#285711yescharacteristic, complemented, Sylow
130C22×Q8—471no—
131C22×Q8C2×D4711yescharacteristic
132C23×C4—472no—
133C23×C4C2×D4711yescharacteristic
134C4⋊Q8—944no—
135C22⋊Q8—24no—
136C22⋊Q8—944no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—474no—
140C2×C4⋊C4—474no—
141C2×C4⋊C4C2×D4711yescharacteristic
142C2×C4⋊C4C2×D4712yes—
143C2×C22⋊C4—472no—
144C2×C22⋊C4C2×D4712yes—
145C2×C42—471no—
146C2×C42—472no—
147C2×C42—471no—
148C2×C42—944no—
149#95—474no—
150#95—474no—
151C24C22×D4711yescharacteristic
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—942no—
156C2×Q8—942no—
157C2×Q8—942no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—472no—
161C22×C4—478no—
162C22×C4—472no—
163C22×C4—472no—
164C22×C4—472no—
165C22×C4—944no—
166C22×C4—944no—
167C22×C4C22⋊D4714yes—
168C22×C4C22×D4712yes—
169C22×C4C22×D4712yes—
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4711yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—24no—
174C4⋊C4—948no—
175C4⋊C4—948no—
176C4⋊C4—944no—
177C4⋊C4—942no—
178C22⋊C4—24no—
179C22⋊C4—944no—
180C42—474no—
181C42—944no—
182C42—942no—
183C23—21no—
184C23—22no—
185C23—21no—
186C23Q8×D4714yes—
187C23C2×C22⋊D4712yes—
188C23C23×D4711yescharacteristic
189Q8—44no—
190Q8—1884no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—28no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—474no—
200C2×C4—474no—
201C2×C4—474no—
202C2×C4—474no—
203C2×C4—9416no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—944no—
210C2×C4—942no—
211C2×C4D4×D4712yes—
212C2×C4#1062535212yes—
213C2×C4C2×C22⋊D4712yes—
214C2×C4C2×C22⋊D4712yes—
215C22—22no—
216C22—24no—
217C22—22no—
218C22—24no—
219C22#1309402214yescomplemented
220C22C2×D4×D4711yescharacteristic
221C22C22×C22⋊D4711yescharacteristic
222C22C2×Q8×D4712yes—
223C22#41×D4712yes—
224C22C2×#1062535211yescharacteristic
225C4—22no—
226C4—42no—
227C4—42no—
228C4—478no—
229C4—944no—
230C4—1882no—
231C4—1882no—
232C4#1309399614yes—
233C2—24no—
234C2C2×#1309399611yescharacteristic
235C2C22⋊Q8×D4712yes—
236C2C2×#1309402211yescharacteristic
237C2#1568966911yescharacteristic
238C2#1568967512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2857
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
4. #15689030C2semidirect
5. #15689028C2semidirect
6. #15689018C2semidirect
7. #15688992C2semidirect
44. C22×Dic47Q8semidirect
99. C22×C47C4⋊Q8semidirect
112. Dic47C22⋊Q8semidirect
129. C47#2857semidirect
219. C22#13094022semidirect