Finite Group Databasebeta

← #20243890

Subgroups — #20243890

Order 6016.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#15689923C211yesmaximal, characteristic
2#15689591C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic, complemented
4C2×#13093950C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15688884C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625350C2211yescharacteristic
10#13094057—21no—
11#13094057C412yescomplemented
12#13094052—21no—
13#13094052C412yescomplemented
14#13094046—22no—
15#13093989—21no—
16#13093986—21no—
17(C22⋊D47)⋊C4—22no—
18#13093983C2211yescharacteristic
19#13093981—21no—
20C2×C4×Dic47C2211yescharacteristic
21C42×D47—21no—
22#13093950—22no—
23#13093950—21no—
24#13093950—21no—
25#13093938—22no—
26C2×M16×C47C2211yescharacteristic
27C2×M16×C47C2211yescharacteristic
28#117×C47C2211yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C2×C22⋊D47—21no—
32C22×Dic47—21no—
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39#10625350C2×C412yes—
40#10625350D412yes—
41C2×D188C2×C411yescharacteristic, complemented
42C2×D188D411yescharacteristic
43C2×C4×D47—21no—
44C2×C4×D47—22no—
45C2×C4×D47—21no—
46C2×Dic94C2×C411yescharacteristic, complemented
47C2×Dic94D411yescharacteristic
48M16×C47—21no—
49M16×C47—21no—
50M16×C47—21no—
51M16×C47C2×C412yescomplemented
52C2×C8×C47—21no—
53C2×C8×C47—21no—
54C4⋊C4×C47—21no—
55C22⋊C4×C47D412yes—
56C42×C47—21no—
57C22⋊Dic47—21no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47—21no—
63C4×Dic47—21no—
64C4×Dic47D411yescharacteristic
65C4×Dic47D411yescharacteristic
66Dic188—22no—
67D376—22no—
68#10625325—22no—
69#10625325—22no—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72C22×D47—21no—
73C2×C4×C47—22no—
74C2×C4×C47C22×C411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C22⋊D47—22no—
81C22⋊D47—22no—
82C22⋊D47—41no—
83C22⋊D47—41no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—42no—
89C2×Dic47—41no—
90D188—21no—
91D188—21no—
92D188—21no—
93D188C22⋊C412yes—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—44no—
97C4×D47—41no—
98C4×D47—41no—
99Dic94—21no—
100Dic94—21no—
101Dic94—21no—
102Dic94C22⋊C412yes—
103C8×C47—22no—
104C8×C47—41no—
105C22×C47—41no—
106C22×C47C4×D411yescharacteristic
107C22×C47#12011yescharacteristic
108C22×C47#12111yescharacteristic
109C2×D47—22no—
110C2×D47—42no—
111C2×D47—41no—
112C2×D47—81no—
113C4×C47—42no—
114C4×C47C2×C22⋊C411yescharacteristic
115C4×C47C4×D411yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12311yescharacteristic
118Dic47—22no—
119Dic47—22no—
120Dic47—41no—
121Dic47—41no—
122Dic47—81no—
123#1906—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—21no—
127C2×C47#38611yescharacteristic
128D47—42no—
129D47—81no—
130#575—471no—
131C4×#41—471no—
132#421—471no—
133C2×#104—471no—
134#410—471no—
135#344D4711yescharacteristic, complemented
136#339—471no—
137C47#190611yescharacteristic, complemented, Sylow
138C2×#41—471no—
139C2×#41—471no—
140#137—472no—
141#137—941no—
142AGL(1,ℤ/8)—472no—
143AGL(1,ℤ/8)—941no—
144#135—942no—
145C2×M16C2×D4711yescharacteristic
146C2×M16C2×D4711yescharacteristic
147C4×Q8—941no—
148C4×D4—941no—
149C4×D4—942no—
150#117—471no—
151#117—941no—
152#117C2×D4711yescharacteristic
153C2×C42—471no—
154C2×C42—941no—
155#104—941no—
156#104—941no—
157#104—942no—
158#99—942no—
159#41—472no—
160#41—472no—
161#41—941no—
162#41—941no—
163#41—941no—
164#41—941no—
165#41—941no—
166#41—941no—
167C2×Q8—471no—
168C2×Q8—471no—
169C2×D4—471no—
170C2×D4—471no—
171C2×D4—941no—
172C2×D4—941no—
173C22×C4—942no—
174C22×C4—941no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—21no—
183M16—21no—
184M16—21no—
185M16C4×D4712yescomplemented
186C2×C8—21no—
187C2×C8—21no—
188C4⋊C4—21no—
189C4⋊C4—942no—
190C4⋊C4—941no—
191C22⋊C4—942no—
192C22⋊C4—941no—
193C22⋊C4D18812yes—
194C42—21no—
195C42—471no—
196C42—471no—
197C42—942no—
198C42—941no—
199C42—941no—
200C23—941no—
201C23—941no—
202C23C2×D18811yescharacteristic
203Q8—472no—
204Q8—941no—
205Q8—941no—
206Q8—941no—
207D4—472no—
208D4—942no—
209D4—942no—
210D4—941no—
211D4—941no—
212D4—941no—
213D4—1881no—
214D4—1881no—
215C2×C4—22no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—1884no—
223C2×C4—1882no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4C2×C4×D4711yescharacteristic
228C2×C4#1062535011yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4#1062535411yescharacteristic
233C8—22no—
234C8—41no—
235C22—41no—
236C22—942no—
237C22—3761no—
238C22—1882no—
239C22—1881no—
240C22C4×D18811yescharacteristic
241C22#1309399411yescharacteristic
242C22#1309399911yescharacteristic
243C4—42no—
244C4—942no—
245C4—942no—
246C4—3761no—
247C4—1881no—
248C4—1881no—
249C4C22⋊C4×D4711yescharacteristic
250C4#1309398611yescharacteristic
251C4#1309399711yescharacteristic
252C4#1309400911yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—3761no—
257C2—1882no—
258C2#1568900111yescharacteristic
subgroupG/H
centerC4#13093997
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1906
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #15689591C2semidirect
3. #15689139C2semidirect
4. C2×#13093950C2semidirect
5. #15689096C2semidirect
6. #15688884C2semidirect
7. C47×#344C2semidirect
11. #13094057C4semidirect
13. #13094052C4semidirect
41. C2×D188C2×C4semidirect
46. C2×Dic94C2×C4semidirect
51. M16×C47C2×C4semidirect
135. #344D47semidirect
137. C47#1906semidirect
185. M16C4×D47semidirect