Finite Group Databasebeta

← #20243716

Subgroups — #20243716

Order 6016.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094046C211yesmaximal, characteristic
2C2×#13094032C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic, complemented
4C2×#13093950C211yesmaximal, characteristic, complemented
5#15689091C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#341C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625350C2211yescharacteristic
10#13094046—22no—
11#13094046—22no—
12C2×Dic188C411yescharacteristic, complemented
13C2×#10625325C411yescharacteristic, complemented
14C2×#10625325C411yescharacteristic, complemented
15C2×D376C411yescharacteristic, complemented
16#13094032—22no—
17#13094032—22no—
18C2×#10625324—21no—
19C22×C47⋊C8C2211yescharacteristic
20C2×C8×D47—21no—
21C2×C4×Dic47C2211yescharacteristic
22#13093950—22no—
23#13093950—22no—
24(C2×D47)⋊C8—21no—
25(C2×D47)⋊C8—21no—
26C2×M16×C47C2211yescharacteristic
27C2×M16×C47C2211yescharacteristic
28C22×C8×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#10625350D412yes—
40#10625350D412yes—
41C2×D188C2×C411yescharacteristic
42C2×D188C2×C411yescharacteristic
43C2×C4×D47—21no—
44C2×C4×D47—21no—
45C2×Dic94C2×C411yescharacteristic
46C2×Dic94C2×C411yescharacteristic
47M16×C47—21no—
48M16×C47—21no—
49M16×C47—21no—
50M16×C47D412yes—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47—21no—
54C2×C8×C47—21no—
55C2×C8×C47C2×C411yescharacteristic
56C2×C8×C47C2×C411yescharacteristic
57C4×Dic47—21no—
58C4×Dic47—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8D411yescharacteristic
62C2×C47⋊C8D411yescharacteristic
63Dic188—22no—
64D376—22no—
65#10625325—22no—
66#10625325—22no—
67#10625324—24no—
68C8×D47—24no—
69C23×C47#4111yescharacteristic
70C22×D47—21no—
71C22×D47—21no—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C22⋊D47—22no—
79C22⋊D47—22no—
80C22⋊D47—41no—
81C22⋊D47—41no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87D188—21no—
88D188—21no—
89D188—21no—
90D188C22⋊C412yes—
91C4×D47—22no—
92C4×D47—22no—
93C4×D47—41no—
94C4×D47—41no—
95Dic94—21no—
96Dic94—21no—
97Dic94—21no—
98Dic94C22⋊C412yes—
99C8×C47—21no—
100C8×C47—21no—
101C8×C47—22no—
102C8×C47—41no—
103C47⋊C8—21no—
104C47⋊C8—21no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47C4×D411yescharacteristic
108C22×C47#12111yescharacteristic
109C22×C47#12311yescharacteristic
110C2×D47—22no—
111C2×D47—41no—
112C2×D47—41no—
113C2×D47—41no—
114C2×D47—41no—
115C2×D47—41no—
116C4×C47C2×C22⋊C411yescharacteristic
117C4×C47C4×D411yescharacteristic
118C4×C47#12011yescharacteristic
119C4×C47#12111yescharacteristic
120Dic47—22no—
121Dic47—42no—
122Dic47—41no—
123#1876—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47#38611yescharacteristic
127C2×C47#44311yescharacteristic
128C2×C47#44411yescharacteristic
129D47—42no—
130D47—81no—
131C2×#135—471no—
132C2×#131—471no—
133C2×#104—471no—
134C2×#104—471no—
135#408—471no—
136#341D4711yescharacteristic, complemented
137#336—471no—
138C47#187611yescharacteristic, complemented, Sylow
139C2×#41—471no—
140C2×#41—471no—
141#135—942no—
142#135—942no—
143C2×Q16—471no—
144C2×SD16—471no—
145C2×SD16—471no—
146C2×D8—471no—
147#131—942no—
148#131—942no—
149C2×M16—941no—
150C2×M16C2×D4711yescharacteristic
151C2×M16C2×D4711yescharacteristic
152C22×C8—471no—
153C22×C8—941no—
154C22×C8C2×D4711yescharacteristic
155C2×C42—471no—
156#104—942no—
157#104—942no—
158C22⋊C8—941no—
159C22⋊C8—941no—
160#41—472no—
161#41—472no—
162#41—941no—
163#41—941no—
164#41—941no—
165#41—941no—
166#41—941no—
167#41—941no—
168C2×Q8—471no—
169C2×Q8—471no—
170C2×D4—471no—
171C2×D4—471no—
172C2×D4—941no—
173C2×D4—941no—
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—
185M16—944no—
186M16D18812yes—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—471no—
192C2×C8—471no—
193C2×C8—944no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8C4×D4711yescharacteristic
197C2×C8C4×D4711yescharacteristic
198C42—941no—
199C42—941no—
200C23—941no—
201C23—941no—
202C23#1062535411yescharacteristic
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—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—1881no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4C2×C4×D4711yescharacteristic
225C2×C4C2×D18811yescharacteristic
226C2×C4#1062535011yescharacteristic
227C2×C4D4×D4711yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C8—21no—
231C8—21no—
232C8—22no—
233C8—41no—
234C8—941no—
235C8—941no—
236C22—21no—
237C22—21no—
238C22—942no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22—1881no—
243C22—1881no—
244C22#1309398611yescharacteristic
245C22#1309399911yescharacteristic
246C22#1309400911yescharacteristic
247C4—942no—
248C4—1882no—
249C4—1881no—
250C4C22⋊C4×D4711yescharacteristic
251C4C4×D18811yescharacteristic
252C4#1309399411yescharacteristic
253C4#1309399711yescharacteristic
254C2—21no—
255C2—21no—
256C2—3761no—
257C2—1882no—
258C2#1568900111yescharacteristic
259C2#1568923911yescharacteristic
260C2#1568924411yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#341C2
socleC22×C47C4×D4
hypercenter#341D47
hypocenterC47#1876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
2. C2×#13094032C2semidirect
3. C2×#13093950C2semidirect
4. C2×#13093950C2semidirect
5. #15689091C2semidirect
6. #15688877C2semidirect
7. C47×#341C2semidirect
12. C2×Dic188C4semidirect
13. C2×#10625325C4semidirect
14. C2×#10625325C4semidirect
15. C2×D376C4semidirect
136. #341D47semidirect
138. C47#1876semidirect