Finite Group Databasebeta

← #20244317

Subgroups — #20244317

Order 6016.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13094013C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×#13093946C211yesmaximal, characteristic
5C2×#13093944C211yesmaximal, characteristic
6C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094013—22no—
11#13094013C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×(C2×D47)⋊C4—21no—
14C2×(C2×D47)⋊C4—21no—
15C2×C4×Dic47—21no—
16C2×C4×Dic47C2211yescharacteristic
17Dic47⋊C8—22no—
18#13093948—22no—
19#13093946—22no—
20#13093944—22no—
21C47⋊#95—21no—
22C22×Q8×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#103×C47—22no—
26C23×D47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47C2×C412yes—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38C22×Dic47D411yescharacteristic
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2×C412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47D412yes—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52C4⋊Dic47—21no—
53C4⋊Dic47D412yes—
54C4×Dic47—42no—
55C4×Dic47C2×C412yes—
56C4×Dic47D412yes—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C23×C47C2×D411yescharacteristic
61C22×D47—22no—
62C22×D47—41no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
67C22×D47—41no—
68Q8×C47—22no—
69Q8×C47—22no—
70Q8×C47—41no—
71Q8×C47—41no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47C22×C411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47C22⋊C412yes—
92C2×Dic47C22⋊C412yes—
93D188—22no—
94D188—22no—
95D188—41no—
96D188—41no—
97C8×C47—41no—
98C47⋊C8—41no—
99C22×C47C2×C22⋊C411yescharacteristic
100C22×C47#12111yescharacteristic
101C22×C47#12111yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47#13511yescharacteristic
104C22×C47AGL(1,ℤ/8)11yescharacteristic
105C22×C47#13711yescharacteristic
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—81no—
110C2×D47—81no—
111C2×D47—81no—
112C2×D47—81no—
113C4×C47—42no—
114C4×C47—42no—
115C4×C47C4×D411yescharacteristic
116C4×C47C4×D411yescharacteristic
117C4×C47#12411yescharacteristic
118C4×C47#12711yescharacteristic
119Dic47—22no—
120Dic47—22no—
121Dic47—42no—
122#1983—471nomaximal, Sylow
123C2×C47#39011yescharacteristic
124C2×C47#41611yescharacteristic
125C2×C47#41711yescharacteristic
126C2×C47#46311yescharacteristic
127C2×C47#46311yescharacteristic
128C2×C47#46411yescharacteristic
129C2×C47#46411yescharacteristic
130D47—82no—
131C2×#124—471no—
132C2×C4⋊C8—471no—
133C2×#103—471no—
134C2×#103D4711yescharacteristic, complemented
135C2×#102—471no—
136C2×#102—471no—
137C4×C4⋊C4—471no—
138C47#198311yescharacteristic, complemented, Sylow
139C22×Q8C2×D4711yescharacteristic
140C22×D4—471no—
141C22×C8—471no—
142C22×C8C2×D4711yescharacteristic
143#124—474no—
144#124—942no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—941no—
148C2×C22⋊C4—941no—
149C2×C42—471no—
150C2×C42—941no—
151C4⋊C8—942no—
152#103—22no—
153#103—942no—
154#102—942no—
155#102—942no—
156#95—941no—
157C24—941no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8C4×D4712yes—
164C2×D4—472no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4—941no—
168C2×D4—941no—
169C2×D4—941no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—471no—
173C22×C4—471no—
174C22×C4—941no—
175C22×C4C22×D4711yescharacteristic
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—941no—
180C2×C8—941no—
181C2×C8—941no—
182C4⋊C4—21no—
183C4⋊C4—472no—
184C4⋊C4—941no—
185C4⋊C4C22⋊D4712yes—
186C22⋊C4—944no—
187C22⋊C4—944no—
188C42—472no—
189C42—472no—
190C42—1882no—
191C23—942no—
192C23—1881no—
193C23—1881no—
194C23—1881no—
195C23—1881no—
196C23—1881no—
197C23—1881no—
198C23D4×D4711yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—41no—
202Q8—41no—
203D4—942no—
204D4—942no—
205D4—1881no—
206D4—1881no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—472no—
214C2×C4—472no—
215C2×C4—941no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—1881no—
221C2×C4—1881no—
222C2×C4C2×C4×D4711yescharacteristic
223C2×C4#1062535011yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4#1062535211yescharacteristic
227C2×C4C2×C22⋊D4711yescharacteristic
228C8—41no—
229C8—1881no—
230C22—3761no—
231C22—3761no—
232C22—3761no—
233C22—3761no—
234C22—1882no—
235C22—1882no—
236C22—1882no—
237C22C22⋊C4×D4711yescharacteristic
238C22#1309399611yescharacteristic
239C22#1309399711yescharacteristic
240C22#1309404511yescharacteristic
241C22#1309404711yescharacteristic
242C22#1309405111yescharacteristic
243C22#1309405611yescharacteristic
244C4—42no—
245C4—42no—
246C4—942no—
247C4—942no—
248C4—1882no—
249C4(C22⋊D47)⋊C411yescharacteristic
250C4C4×C22⋊D4711yescharacteristic
251C4#1309401011yescharacteristic
252C4#1309402011yescharacteristic
253C2—3762no—
254C2#1568902311yescharacteristic
255C2#1568911811yescharacteristic
256C2#1568912311yescharacteristic
257C2#1568934011yescharacteristic
258C2#1568934111yescharacteristic
259C2#1568934711yescharacteristic
260C2#1568934811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1983
LCSG ▷ C2×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×Dic47⋊C8C2semidirect
3. C2×#13093948C2semidirect
6. C4⋊C4×Dic47C2semidirect
7. C2×#103×C47C2semidirect
11. #13094013C4semidirect
134. C2×#103D47semidirect
138. C47#1983semidirect