Finite Group Databasebeta

← #20244702

Subgroups — #20244702

Order 6016.

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

normal subgroups only

This group has 324 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
1C22×#10625336C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic, complemented
5#15689024C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625336—22no—
10C2×#10625336—22no—
11C2×#10625336—22no—
12C22×C47⋊C8C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×(C2×D47)⋊C4—21no—
15C2×(C2×D47)⋊C4—21no—
16C2×C4×Dic47C2211yescharacteristic
17Dic47⋊C8—22no—
18#13093946—22no—
19C47⋊#95—21no—
20C47⋊#95—21no—
21C22×Q8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—22no—
25C23×D47—21no—
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×Dic47D411yescharacteristic
37C22×Dic47D411yescharacteristic
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188D412yes—
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49#10625336—28no—
50(C2×D47)⋊C4—42no—
51(C2×D47)⋊C4—42no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4×Dic47—21no—
55C4×Dic47—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8D412yes—
59C23×C47C2×D411yescharacteristic
60C22×D47—22no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
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—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47SD1612yescomplemented
92D188—22no—
93D188—22no—
94D188—41no—
95D188—41no—
96C8×C47—41no—
97C47⋊C8—22no—
98C22×C47#12111yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12111yescharacteristic
101C22×C47C2×SD1611yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47AGL(1,ℤ/8)11yescharacteristic
104C22×C47#13711yescharacteristic
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—81no—
109C2×D47—81no—
110C2×D47—81no—
111C2×D47—81no—
112C4×C47—42no—
113C4×C47—81no—
114C4×C47#12011yescharacteristic
115C4×C47#12311yescharacteristic
116C4×C47#12311yescharacteristic
117C4×C47#12411yescharacteristic
118Dic47—22no—
119Dic47—41no—
120Dic47—81no—
121#2055—471nomaximal, Sylow
122C2×C47#39411yescharacteristic
123C2×C47#46011yescharacteristic
124C2×C47#46111yescharacteristic
125C2×C47#46311yescharacteristic
126C2×C47#46411yescharacteristic
127C2×C47#46511yescharacteristic
128C2×C47#46811yescharacteristic
129D47—82no—
130C22×SD16—471no—
131C2×C4⋊C8—471no—
132C2×#103D4711yescharacteristic, complemented
133C2×#102—471no—
134#391—471no—
135#390—471no—
136#340—471no—
137C47#205511yescharacteristic, complemented, Sylow
138C22×Q8C2×D4711yescharacteristic
139C22×D4—471no—
140C2×SD16—942no—
141C2×SD16—942no—
142C2×SD16—942no—
143C22×C8—471no—
144C22×C8C2×D4711yescharacteristic
145C2×C4⋊C4—471no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—941no—
148C2×C22⋊C4—941no—
149C2×C42—471no—
150C4⋊C8—942no—
151#103—22no—
152#102—942no—
153#95—941no—
154#95—941no—
155C24—941no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D4712yes—
162C2×D4—472no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4—941no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—471no—
171C22×C4—471no—
172C22×C4—941no—
173C22×C4C22×D4711yescharacteristic
174SD16—948no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—472no—
179C2×C8—941no—
180C2×C8—941no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C22⋊C4—1882no—
186C22⋊C4—1882no—
187C42—941no—
188C42—941no—
189C23—942no—
190C23—1881no—
191C23—1881no—
192C23—1881no—
193C23—1881no—
194C23—1881no—
195C23—1881no—
196C23D4×D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—942no—
202D4—942no—
203D4—1881no—
204D4—1881no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—472no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—941no—
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—3761no—
229C22—3761no—
230C22—3761no—
231C22—3761no—
232C22—1882no—
233C22—1882no—
234C22—1882no—
235C22#1309399611yescharacteristic
236C22#1309399711yescharacteristic
237C22#1309399711yescharacteristic
238C22SD16×D4711yescharacteristic
239C22#1309404711yescharacteristic
240C22#1309405111yescharacteristic
241C22#1309405611yescharacteristic
242C4—42no—
243C4—81no—
244C4—942no—
245C4—3761no—
246C4—1881no—
247C4#1309399211yescharacteristic
248C4#1309400611yescharacteristic
249C4#1309400711yescharacteristic
250C4#1309401011yescharacteristic
251C2—3762no—
252C2#1568903811yescharacteristic
253C2#1568932111yescharacteristic
254C2#1568932711yescharacteristic
255C2#1568934111yescharacteristic
256C2#1568934711yescharacteristic
257C2#1568935511yescharacteristic
258C2#1568937211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2055
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×Dic47⋊C8C2semidirect
4. #15689030C2semidirect
6. #15688885C2semidirect
7. C2×#103×C47C2semidirect
91. C2×Dic47SD16semidirect
132. C2×#103D47semidirect
137. C47#2055semidirect