Finite Group Databasebeta

← #20244589

Subgroups — #20244589

Order 6016.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094000C211yesmaximal, characteristic
2C2×#13093957C211yesmaximal, characteristic, complemented
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C8C211yesmaximal, characteristic
5#15688980C211yesmaximal, characteristic
6#15688886C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×C4×D47C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094000—22no—
11#13094000—22no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×(C2×D47)⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17#13093957—22no—
18#13093948—22no—
19(C2×D47)⋊C8—22no—
20C47⋊#95—21no—
21C22×Q8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—22no—
25C23×D47D411yescharacteristic
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47D412yes—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—21no—
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38C2×C4×D47—21no—
39C2×C4×D47—21no—
40C2×C4×D47—21no—
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×C4×D47—21no—
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49(C2×D47)⋊C4—24no—
50(C2×D47)⋊C4—42no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47D412yes—
55Dic47⋊C4—24no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8D412yes—
59C23×C47C2×D411yescharacteristic
60C22×D47—21no—
61C22×D47—21no—
62C22×D47—21no—
63C22×D47—21no—
64C22×D47—21no—
65C22×D47—21no—
66C22×D47Q1612yes—
67Q8×C47—22no—
68Q8×C47—22no—
69Q8×C47—41no—
70Q8×C47—41no—
71C2×C4×C47—22no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C4×D47—41no—
93C4×D47—41no—
94C4×D47—41no—
95C4×D47—41no—
96C8×C47—41no—
97C47⋊C8—22no—
98C22×C47#12011yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12311yescharacteristic
101C22×C47C2×Q1611yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47AGL(1,ℤ/8)11yescharacteristic
104C22×C47#13711yescharacteristic
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—41no—
112C4×C47—42no—
113C4×C47—81no—
114C4×C47#12111yescharacteristic
115C4×C47#12111yescharacteristic
116C4×C47#12311yescharacteristic
117C4×C47#12411yescharacteristic
118Dic47—41no—
119Dic47—42no—
120Dic47—81no—
121#2036—471nomaximal, Sylow
122C2×C47#39411yescharacteristic
123C2×C47#44911yescharacteristic
124C2×C47#45111yescharacteristic
125C2×C47#46711yescharacteristic
126C2×C47#46811yescharacteristic
127C2×C47#48411yescharacteristic
128C2×C47#48511yescharacteristic
129D47—42no—
130C2×C22⋊Q8—471no—
131C2×#107—471no—
132C2×#103—471no—
133C2×#103D4711yescharacteristic, complemented
134C2×C22⋊C8—471no—
135#380—471no—
136#340—471no—
137C47#203611yescharacteristic, complemented, Sylow
138C22×Q8C2×D4711yescharacteristic
139C23×C4—471no—
140C22×C8—471no—
141C22×C8C2×D4711yescharacteristic
142C22⋊Q8—942no—
143C22⋊Q8—942no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—941no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—941no—
149C2×C22⋊C4—941no—
150#107—942no—
151#103—22no—
152#103—942no—
153C22⋊C8—942no—
154#95—941no—
155C24—471no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D4712yes—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—471no—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4—941no—
168C22×C4—941no—
169C22×C4—941no—
170C22×C4—941no—
171C22×C4—941no—
172C22×C4—941no—
173C22×C4C22×D4711yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—472no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—472no—
183C4⋊C4—944no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C22⋊C4—944no—
188C22⋊C4—1882no—
189C23—472no—
190C23—941no—
191C23—941no—
192C23—941no—
193C23—941no—
194C23—941no—
195C23—941no—
196C23D4×D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—1881no—
212C2×C4—1881no—
213C2×C4—1881no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1881no—
220C2×C4#1062535011yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4#1062535211yescharacteristic
225C2×C4C2×C22⋊D4711yescharacteristic
226C8—41no—
227C8—942no—
228C22—942no—
229C22—942no—
230C22—942no—
231C22—1881no—
232C22—1881no—
233C22—1881no—
234C22—1881no—
235C22#1309399211yescharacteristic
236C22#1309399711yescharacteristic
237C22#1309400611yescharacteristic
238C22Q16×D4711yescharacteristic
239C22#1309404511yescharacteristic
240C22#1309405111yescharacteristic
241C22#1309405611yescharacteristic
242C4—42no—
243C4—81no—
244C4—3761no—
245C4—1882no—
246C4—1881no—
247C4#1309399611yescharacteristic
248C4#1309399711yescharacteristic
249C4#1309400711yescharacteristic
250C4#1309401011yescharacteristic
251C2—1882no—
252C2#1568903811yescharacteristic
253C2#1568926711yescharacteristic
254C2#1568927711yescharacteristic
255C2#1568936311yescharacteristic
256C2#1568937211yescharacteristic
257C2#1568945711yescharacteristic
258C2#1568946211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2036
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#13093957C2semidirect
3. C2×#13093948C2semidirect
6. #15688886C2semidirect
7. C2×#103×C47C2semidirect
133. C2×#103D47semidirect
137. C47#2036semidirect