Finite Group Databasebeta

← #20244587

Subgroups — #20244587

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×#13094004C211yesmaximal, characteristic
2C2×#13093955C211yesmaximal, characteristic, complemented
3C2×#13093949C211yesmaximal, characteristic, complemented
4C2×#13093947C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic
6#15688980C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×C4×D47C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13094004—22no—
12#13094004—22no—
13C2×C4⋊Dic47—21no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×(C2×D47)⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17#13093955—22no—
18#13093949—22no—
19#13093947—22no—
20(C2×D47)⋊C8—22no—
21C47⋊#95—21no—
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C23×D47D411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C22×Dic47—21no—
30C22×Dic47—21no—
31C22×Dic47D411yescharacteristic
32C2×C4×D47—21no—
33C2×C4×D47—21no—
34C2×C4×D47—21no—
35C2×C4×D47—21no—
36C2×C4×D47—21no—
37C2×C4×D47—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94D412yes—
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47D412yes—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—42no—
53C4⋊Dic47—24no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
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×D47SD1612yes—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C2×Dic47—41no—
88C4×D47—41no—
89C4×D47—41no—
90C4×D47—41no—
91C4×D47—41no—
92Dic94—22no—
93Dic94—22no—
94Dic94—41no—
95Dic94—41no—
96C8×C47—41no—
97C47⋊C8—22no—
98C22×C47#12011yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12311yescharacteristic
101C22×C47C2×SD1611yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47#13711yescharacteristic
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—42no—
119Dic47—41no—
120Dic47—81no—
121#2035—471nomaximal, Sylow
122C2×C47#39411yescharacteristic
123C2×C47#44811yescharacteristic
124C2×C47#45211yescharacteristic
125C2×C47#46511yescharacteristic
126C2×C47#47011yescharacteristic
127C2×C47#48311yescharacteristic
128C2×C47#48511yescharacteristic
129D47—42no—
130C2×C22⋊Q8—471no—
131C2×#106—471no—
132C2×#103—471no—
133C2×#103—471no—
134C2×C22⋊C8—471no—
135#380—471no—
136#340D4711yescharacteristic, complemented
137C47#203511yescharacteristic, complemented, Sylow
138C22×Q8—471no—
139C23×C4—471no—
140C22×C8—471no—
141C22×C8C2×D4711yescharacteristic
142C22⋊Q8—942no—
143C22⋊Q8—942no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—941no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—941no—
149C2×C22⋊C4—941no—
150#106—942no—
151#103—942no—
152#103—942no—
153C22⋊C8—942no—
154#95—941no—
155C24—471no—
156C2×Q8—472no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
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—21no—
183C4⋊C4—944no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4D18812yes—
187C22⋊C4—944no—
188C22⋊C4—1882no—
189C23—472no—
190C23—941no—
191C23—941no—
192C23—941no—
193C23—941no—
194C23—941no—
195C23—941no—
196C23D4×D4711yescharacteristic
197Q8—942no—
198Q8—942no—
199Q8—1881no—
200Q8—1881no—
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×C4C2×D18811yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4#1062535011yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4#1062535411yescharacteristic
226C8—41no—
227C8—942no—
228C22—942no—
229C22—942no—
230C22—942no—
231C22—1881no—
232C22—1881no—
233C22—1881no—
234C22—1881no—
235C22#1309399411yescharacteristic
236C22#1309399711yescharacteristic
237C22#1309400911yescharacteristic
238C22SD16×D4711yescharacteristic
239C22#1309404311yescharacteristic
240C22#1309405311yescharacteristic
241C22#1309405611yescharacteristic
242C4—42no—
243C4—81no—
244C4—3761no—
245C4—1881no—
246C4—1882no—
247C4#1309399711yescharacteristic
248C4#1309399911yescharacteristic
249C4#1309400911yescharacteristic
250C4#1309401211yescharacteristic
251C2—1882no—
252C2#1568904111yescharacteristic
253C2#1568926311yescharacteristic
254C2#1568928611yescharacteristic
255C2#1568935111yescharacteristic
256C2#1568938011yescharacteristic
257C2#1568945511yescharacteristic
258C2#1568946611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2035
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#13093955C2semidirect
3. C2×#13093949C2semidirect
4. C2×#13093947C2semidirect
7. C47×#340C2semidirect
136. #340D47semidirect
137. C47#2035semidirect