Finite Group Databasebeta

← #20243328

Subgroups — #20243328

Order 6016.

612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13093948C212yesmaximal, complemented
2C2×#13093945C212yesmaximal, complemented
3C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
4#15688983C211yesmaximal, characteristic, complemented
5C22×#41×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2212yes—
7C2×C4⋊Dic47C2212yes—
8C2×C22⋊Dic47—21no—
9#13093948—24no—
10#13093945—24no—
11C22⋊(C47⋊C8)—22no—
12C47⋊#95—21no—
13C2×#41×C47—24no—
14C2×#41×C47—24no—
15C2×#41×C47—22no—
16C2×#41×C47C414yescomplemented
17C22×Q8×C47C2211yescharacteristic
18C22×D4×C47—21no—
19C22×D4×C47C2211yescharacteristic
20C23×C4×C47—21no—
21C23×C4×C47C2211yescharacteristic
22C24×C47—21no—
23C24×C47D411yescharacteristic
24#41×C47—216no—
25#41×C47—28no—
26#41×C47—28no—
27C2×Q8×C47—21no—
28C2×Q8×C47—22no—
29C2×Q8×C47C2×C412yes—
30C2×Q8×C47D414yes—
31C2×D4×C47—28no—
32C2×D4×C47—24no—
33C2×D4×C47—22no—
34C2×D4×C47—21no—
35C2×D4×C47C2×C412yes—
36C2×D4×C47D414yes—
37C22×C4×C47—28no—
38C22×C4×C47—21no—
39C22×C4×C47—24no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47C2×C412yes—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D412yes—
45C22×C4×C47C2311yescharacteristic
46C22×Dic47—22no—
47C22⋊Dic47—42no—
48C4⋊Dic47—22no—
49C4⋊Dic47—22no—
50C2×C47⋊C8—22no—
51C2×C47⋊C8—22no—
52C2×C47⋊C8—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—24no—
56C23×C47—22no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—42no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47C22⋊C412yes—
63C23×C47C2×D411yescharacteristic
64Q8×C47—22no—
65Q8×C47—24no—
66Q8×C47C22⋊C414yescomplemented
67D4×C47—216no—
68D4×C47—22no—
69D4×C47—24no—
70D4×C47C22⋊C414yescomplemented
71C2×C4×C47—216no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—24no—
78C2×C4×C47C22⋊C412yes—
79C2×C4×C47C22×C411yescharacteristic
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D411yescharacteristic
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C47⋊C8—42no—
87C22×C47—22no—
88C22×C47—24no—
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—44no—
95C22×C47—42no—
96C22×C47—44no—
97C22×C47C2×C22⋊C411yescharacteristic
98C22×C47#12012yes—
99C22×C47#13512yes—
100C22×C47AGL(1,ℤ/8)11yescharacteristic
101C22×C47#13711yescharacteristic
102C4×C47—22no—
103C4×C47—24no—
104C4×C47C2×C22⋊C411yescharacteristic
105C4×C47C2×C22⋊C411yescharacteristic
106C4×C47#12012yes—
107Dic47—82no—
108#1788—471nomaximal, Sylow
109C2×C47—42no—
110C2×C47—44no—
111C2×C47#37911yescharacteristic
112C2×C47#41611yescharacteristic
113C2×C47#41711yescharacteristic
114C2×C47#44912yes—
115C2×C47#45212yes—
116C22×#41D4711yescharacteristic
117C2×#103—472no—
118C2×#102—472no—
119C2×C22⋊C8—471no—
120#380—471no—
121C47#178811yescharacteristic, complemented, Sylow
122C2×#41—24no—
123C2×#41—24no—
124C2×#41—22no—
125C2×#41Dic4714yescomplemented
126C22×Q8C2×D4711yescharacteristic
127C22×D4—21no—
128C22×D4C2×D4711yescharacteristic
129C23×C4—21no—
130C23×C4C2×D4711yescharacteristic
131C22×C8—472no—
132C2×C4⋊C4—472no—
133C2×C22⋊C4—941no—
134#103—944no—
135#102—944no—
136C22⋊C8—942no—
137#95—941no—
138C24—21no—
139C24C22⋊D4711yescharacteristic
140#41—216no—
141#41—28no—
142#41—28no—
143C2×Q8—21no—
144C2×Q8—22no—
145C2×Q8C2×Dic4712yes—
146C2×Q8C22⋊D4714yes—
147C2×D4—28no—
148C2×D4—24no—
149C2×D4—22no—
150C2×D4—21no—
151C2×D4C2×Dic4712yes—
152C2×D4C22⋊D4714yes—
153C22×C4—28no—
154C22×C4—21no—
155C22×C4—24no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—942no—
159C22×C4C2×Dic4712yes—
160C22×C4C22⋊D4711yescharacteristic
161C22×C4C22⋊D4712yes—
162C22×C4C22×D4711yescharacteristic
163C2×C8—942no—
164C2×C8—942no—
165C2×C8—942no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C22⋊C4—1882no—
169C23—22no—
170C23—22no—
171C23—24no—
172C23—22no—
173C23—21no—
174C23—21no—
175C23—42no—
176C23—41no—
177C23—41no—
178C23C22⋊Dic4712yes—
179C23C2×C22⋊D4711yescharacteristic
180Q8—22no—
181Q8—24no—
182Q8C22⋊Dic4714yescomplemented
183D4—216no—
184D4—22no—
185D4—24no—
186D4C22⋊Dic4714yescomplemented
187C2×C4—216no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4C22⋊Dic4712yes—
198C2×C4C22×Dic4711yescharacteristic
199C2×C4C2×C22⋊D4712yes—
200C2×C4C2×C22⋊D4712yes—
201C2×C4C2×C22⋊D4711yescharacteristic
202C8—1882no—
203C22—22no—
204C22—24no—
205C22—22no—
206C22—22no—
207C22—42no—
208C22—44no—
209C22—42no—
210C22—44no—
211C22—42no—
212C22—42no—
213C22C2×C22⋊Dic4711yescharacteristic
214C22#1309399312yes—
215C22#1309404412yes—
216C22#1309404911yescharacteristic
217C22#1309405411yescharacteristic
218C4—22no—
219C4—24no—
220C4—3762no—
221C4C2×C22⋊Dic4711yescharacteristic
222C4C2×C22⋊Dic4711yescharacteristic
223C4#1309399312yes—
224C2—42no—
225C2—44no—
226C2#1568897911yescharacteristic
227C2#1568911911yescharacteristic
228C2#1568912411yescharacteristic
229C2#1568926812yes—
230C2#1568928512yes—
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×#41×C47C2
socleC23×C47C2×D4
hypercenterC22×#41D47
hypocenterC47#1788
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13093948C2semidirect
2. C2×#13093945C2semidirect
3. C2×C22⋊(C47⋊C8)C2semidirect
4. #15688983C2semidirect
16. C2×#41×C47C4semidirect
66. Q8×C47C22⋊C4semidirect
70. D4×C47C22⋊C4semidirect
121. C47#1788semidirect
125. C2×#41Dic47semidirect
182. Q8C22⋊Dic47semidirect
186. D4C22⋊Dic47semidirect