Finite Group Databasebeta

← #20244615

Subgroups — #20244615

Order 6016.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689701C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic, complemented
4#15689122C211yesmaximal, characteristic, complemented
5#15688988C211yesmaximal, characteristic, complemented
6#15688891C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094003—21no—
11#13094000—21no—
12#13093998—21no—
13#13093996—22no—
14#13093995—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4×Dic47C2211yescharacteristic
17#13093951—22no—
18#13093950—22no—
19#13093947—21no—
20#13093944—21no—
21C47⋊#95—22no—
22C2×#41×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#103×C47—21no—
26#102×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31C2×Q8×C47D411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47D411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—21no—
38C2×C22⋊D47—22no—
39C22×Dic47—21no—
40C22×Dic47D412yes—
41#10625350—21no—
42#10625350—21no—
43#10625350—21no—
44#10625350—21no—
45C2×D188D411yescharacteristic
46C2×C4×D47—21no—
47C2×Dic94D411yescharacteristic
48M16×C47—21no—
49M16×C47—21no—
50C2×C8×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C22⋊Dic47—22no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57Dic47⋊C4—22no—
58C4×Dic47—21no—
59C4×Dic47D412yescomplemented
60#10625329—21no—
61#10625329—21no—
62C2×C47⋊C8—21no—
63C23×C47—21no—
64C23×C47C2×D411yescharacteristic
65C22×D47—21no—
66Q8×C47—21no—
67Q8×C47—21no—
68D4×C47—21no—
69D4×C47—21no—
70D4×C47—41no—
71D4×C47—41no—
72C2×C4×C47—21no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—42no—
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
83C22⋊D47—41no—
84C22⋊D47—41no—
85C22⋊D47—82no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47—42no—
92D188—21no—
93D188—21no—
94C4×D47—41no—
95C4×D47—41no—
96Dic94—21no—
97Dic94—21no—
98C8×C47—41no—
99C47⋊C8—41no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47#12011yescharacteristic
106C22×C47#12111yescharacteristic
107C22×C47#12411yescharacteristic
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—41no—
111C4×C47—41no—
112C4×C47—81no—
113C4×C47#12111yescharacteristic
114C4×C47#12111yescharacteristic
115C4×C47#12311yescharacteristic
116C4×C47#12311yescharacteristic
117Dic47—42no—
118Dic47—41no—
119Dic47—42no—
120#2040—471nomaximal, Sylow
121C2×C47—21no—
122C2×C47—21no—
123C2×C47—81no—
124C2×C47#39411yescharacteristic
125C2×C47#45411yescharacteristic
126C2×C47#45511yescharacteristic
127D47—81no—
128#537—471no—
129C2×#104—471no—
130C2×#104—471no—
131#417—471no—
132#417D4711yescharacteristic, complemented
133#382—471no—
134#343—471no—
135C47#204011yescharacteristic, complemented, Sylow
136C2×#41—471no—
137C2×#41C2×D4711yescharacteristic
138C2×M16—471no—
139C2×M16C2×D4711yescharacteristic
140C22⋊Q8—941no—
141C22⋊Q8—941no—
142#121—941no—
143#121—942no—
144#121—941no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C42—471no—
148#104—942no—
149#104—942no—
150#103—21no—
151#103—941no—
152#102—21no—
153#102—941no—
154#95—942no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—941no—
160#41—941no—
161#41—941no—
162#41—941no—
163C2×Q8—471no—
164C2×Q8C22⋊D4711yescharacteristic
165C2×D4—21no—
166C2×D4—471no—
167C2×D4—942no—
168C2×D4—941no—
169C2×D4C22⋊D4711yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—472no—
173C22×C4—941no—
174C22×C4—941no—
175C22×C4C22×D4711yescharacteristic
176M16—21no—
177M16—21no—
178M16—941no—
179M16—941no—
180C2×C8—21no—
181C2×C8—941no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C42—472no—
190C42—941no—
191C23—21no—
192C23—941no—
193C23D4×D4711yescharacteristic
194Q8—21no—
195Q8—21no—
196Q8—941no—
197Q8—941no—
198D4—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—941no—
203D4—941no—
204D4—3762no—
205D4—1881no—
206D4—1881no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1882no—
220C2×C4#1062535011yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4#1062535211yescharacteristic
225C2×C4C2×C22⋊D4711yescharacteristic
226C8—41no—
227C8—1881no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—1881no—
234C22—1881no—
235C22—1881no—
236C22#1309399211yescharacteristic
237C22#1309399711yescharacteristic
238C22#1309401011yescharacteristic
239C4—41no—
240C4—81no—
241C4—1882no—
242C4—1881no—
243C4—1882no—
244C4#1309399611yescharacteristic
245C4#1309399711yescharacteristic
246C4#1309400611yescharacteristic
247C4#1309400711yescharacteristic
248C2—21no—
249C2—21no—
250C2—81no—
251C2—3761no—
252C2#1568903811yescharacteristic
253C2#1568929411yescharacteristic
254C2#1568929911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#120
hypercenter#417D47
hypocenterC47#2040
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#13093951C2semidirect
3. C2×#13093950C2semidirect
4. #15689122C2semidirect
5. #15688988C2semidirect
6. #15688891C2semidirect
7. C47×#417C2semidirect
59. C4×Dic47D4semidirect
132. #417D47semidirect
135. C47#2040semidirect