Finite Group Databasebeta

← #20244826

Subgroups — #20244826

Order 6016.

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

normal subgroups only

This group has 256 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
1C2×#13093955C211yesmaximal, characteristic, complemented
2C2×(C2×D47)⋊C8C211yesmaximal, characteristic
3#15688980C211yesmaximal, characteristic
4#15688980C211yesmaximal, characteristic
5#15688886C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×C4×D47C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×(C2×D47)⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14#13093955—22no—
15(C2×D47)⋊C8—22no—
16C47⋊#95—21no—
17C47⋊#95—21no—
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C23×D47D411yescharacteristic
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47D411yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47—21no—
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47—21no—
33C2×C4×D47—21no—
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—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8D412yes—
50C23×C47C2×D411yescharacteristic
51C22×D47—21no—
52C22×D47—21no—
53C22×D47—21no—
54C22×D47—21no—
55C22×D47—21no—
56C22×D47—21no—
57C22×D47SD1612yes—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C4×D47—41no—
80C4×D47—41no—
81C4×D47—41no—
82C4×D47—41no—
83C8×C47—41no—
84C47⋊C8—22no—
85C22×C47#12111yescharacteristic
86C22×C47#12311yescharacteristic
87C22×C47#12311yescharacteristic
88C22×C47C2×SD1611yescharacteristic
89C22×C47#13511yescharacteristic
90C22×C47AGL(1,ℤ/8)11yescharacteristic
91C22×C47#13711yescharacteristic
92C2×D47—22no—
93C2×D47—22no—
94C2×D47—22no—
95C2×D47—41no—
96C2×D47—41no—
97C2×D47—41no—
98C2×D47—41no—
99C4×C47—81no—
100C4×C47—81no—
101C4×C47#12311yescharacteristic
102C4×C47#12411yescharacteristic
103C4×C47#12611yescharacteristic
104C4×C47#12611yescharacteristic
105Dic47—41no—
106Dic47—81no—
107Dic47—81no—
108#2077—471nomaximal, Sylow
109C2×C47#39711yescharacteristic
110C2×C47#46511yescharacteristic
111C2×C47#46811yescharacteristic
112C2×C47#48111yescharacteristic
113C2×C47#48211yescharacteristic
114C2×C47#48311yescharacteristic
115C2×C47#48511yescharacteristic
116D47—42no—
117C2×#106—471no—
118C2×C22⋊C8—471no—
119#380—471no—
120#380—471no—
121#340—471no—
122#340—471no—
123#340D4711yescharacteristic, complemented
124C47#207711yescharacteristic, complemented, Sylow
125C23×C4—471no—
126C22×C8—471no—
127C22×C8C2×D4711yescharacteristic
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C22⋊C4—941no—
133C2×C22⋊C4—941no—
134#106—942no—
135C22⋊C8—942no—
136#95—941no—
137#95—941no—
138C24—471no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—471no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4—941no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4—941no—
150C22×C4C22×D4711yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—472no—
155C2×C8—941no—
156C2×C8—941no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C22⋊C4—1882no—
166C22⋊C4—1882no—
167C23—472no—
168C23—941no—
169C23—941no—
170C23—941no—
171C23—941no—
172C23—941no—
173C23—941no—
174C23D4×D4711yescharacteristic
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4—1881no—
192C2×C4—1881no—
193C2×C4—1881no—
194C2×C4#1062535011yescharacteristic
195C2×C4#1062535011yescharacteristic
196C2×C4#1062535011yescharacteristic
197C2×C4D4×D4711yescharacteristic
198C2×C4#1062535211yescharacteristic
199C2×C4#1062535411yescharacteristic
200C8—41no—
201C8—942no—
202C22—942no—
203C22—942no—
204C22—942no—
205C22—1881no—
206C22—1881no—
207C22—1881no—
208C22—1881no—
209C22#1309399711yescharacteristic
210C22#1309400611yescharacteristic
211C22#1309400911yescharacteristic
212C22SD16×D4711yescharacteristic
213C22#1309404311yescharacteristic
214C22#1309405111yescharacteristic
215C22#1309405611yescharacteristic
216C4—81no—
217C4—81no—
218C4—3761no—
219C4—3761no—
220C4—1881no—
221C4#1309400911yescharacteristic
222C4#1309401011yescharacteristic
223C4#1309401811yescharacteristic
224C4#1309401911yescharacteristic
225C2—1882no—
226C2#1568905211yescharacteristic
227C2#1568935111yescharacteristic
228C2#1568937211yescharacteristic
229C2#1568944311yescharacteristic
230C2#1568944511yescharacteristic
231C2#1568945211yescharacteristic
232C2#1568946611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2077
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
1. C2×#13093955C2semidirect
5. #15688886C2semidirect
6. #15688885C2semidirect
7. C47×#340C2semidirect
123. #340D47semidirect
124. C47#2077semidirect