Finite Group Databasebeta

← #20244795

Subgroups — #20244795

Order 6016.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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×#13093946C211yesmaximal, characteristic
2C2×#13093944C211yesmaximal, characteristic
3#15689024C211yesmaximal, characteristic
4#15688992C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14C2×(C2×D47)⋊C4—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093946—22no—
17#13093944—22no—
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C23×D47—21no—
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47D411yescharacteristic
27C22×Dic47D411yescharacteristic
28C2×D188—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—21no—
33C2×D188D412yes—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41(C2×D47)⋊C4—42no—
42(C2×D47)⋊C4—42no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45Dic47⋊C4—42no—
46Dic47⋊C4—42no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C23×C47C2×D411yescharacteristic
53C22×D47—22no—
54C22×D47—41no—
55C22×D47—41no—
56C22×D47—41no—
57C22×D47—41no—
58C22×D47—41no—
59C22×D47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47D812yes—
80C2×Dic47SD1612yes—
81D188—22no—
82D188—22no—
83D188—41no—
84D188—41no—
85C8×C47—41no—
86C47⋊C8—41no—
87C22×C47#12111yescharacteristic
88C22×C47#12311yescharacteristic
89C22×C47#12411yescharacteristic
90C22×C47C2×D811yescharacteristic
91C22×C47C2×SD1611yescharacteristic
92C22×C47AGL(1,ℤ/8)11yescharacteristic
93C22×C47#13711yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—81no—
98C2×D47—81no—
99C2×D47—81no—
100C2×D47—81no—
101C4×C47—81no—
102C4×C47—81no—
103C4×C47#12311yescharacteristic
104C4×C47#12311yescharacteristic
105C4×C47#12611yescharacteristic
106C4×C47#12611yescharacteristic
107Dic47—22no—
108Dic47—22no—
109Dic47—81no—
110#2071—471nomaximal, Sylow
111C2×C47#39711yescharacteristic
112C2×C47#45911yescharacteristic
113C2×C47#46111yescharacteristic
114C2×C47#48011yescharacteristic
115C2×C47#48111yescharacteristic
116C2×C47#48611yescharacteristic
117C2×C47#48911yescharacteristic
118D47—82no—
119C2×#102—471no—
120C2×#102—471no—
121#390—471no—
122#384—471no—
123#340—471no—
124#340D4711yescharacteristic, complemented
125#336—471no—
126C47#207111yescharacteristic, complemented, Sylow
127C22×D4—471no—
128C22×C8—471no—
129C22×C8C2×D4711yescharacteristic
130C2×C4⋊C4—471no—
131C2×C4⋊C4—941no—
132C2×C4⋊C4—941no—
133C2×C4⋊C4C2×D4711yescharacteristic
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C22⋊C4—941no—
136C2×C22⋊C4—941no—
137C2×C42—471no—
138#102—942no—
139#102—942no—
140C24—941no—
141C2×D4—472no—
142C2×D4—941no—
143C2×D4—941no—
144C2×D4—941no—
145C2×D4—941no—
146C2×D4—941no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—471no—
150C22×C4—471no—
151C22×C4—941no—
152C22×C4C22×D4711yescharacteristic
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—941no—
157C2×C8—941no—
158C2×C8—941no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—1882no—
166C4⋊C4—1882no—
167C22⋊C4—1882no—
168C22⋊C4—1882no—
169C42—941no—
170C42—941no—
171C23—942no—
172C23—1881no—
173C23—1881no—
174C23—1881no—
175C23—1881no—
176C23—1881no—
177C23—1881no—
178C23D4×D4711yescharacteristic
179D4—942no—
180D4—942no—
181D4—1881no—
182D4—1881no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—472no—
190C2×C4—472no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4#1062535011yescharacteristic
199C2×C4#1062535011yescharacteristic
200C2×C4#1062535011yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4#1062535211yescharacteristic
203C2×C4#1062535411yescharacteristic
204C8—41no—
205C8—1881no—
206C22—3761no—
207C22—3761no—
208C22—3761no—
209C22—3761no—
210C22—1882no—
211C22—1882no—
212C22—1882no—
213C22#1309399711yescharacteristic
214C22#1309400911yescharacteristic
215C22#1309401011yescharacteristic
216C22D8×D4711yescharacteristic
217C22SD16×D4711yescharacteristic
218C22#1309405111yescharacteristic
219C22#1309405611yescharacteristic
220C4—81no—
221C4—81no—
222C4—942no—
223C4—942no—
224C4—3761no—
225C4#1309400611yescharacteristic
226C4#1309400911yescharacteristic
227C4#1309401811yescharacteristic
228C4#1309401911yescharacteristic
229C2—3762no—
230C2#1568905211yescharacteristic
231C2#1568931711yescharacteristic
232C2#1568932711yescharacteristic
233C2#1568943811yescharacteristic
234C2#1568944311yescharacteristic
235C2#1568946811yescharacteristic
236C2#1568948411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2071
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
4. #15688992C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
7. C47×#340C2semidirect
124. #340D47semidirect
126. C47#2071semidirect