Finite Group Databasebeta

← #20244804

Subgroups — #20244804

Order 6016.

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

normal subgroups only

This group has 258 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×#13093945C211yesmaximal, characteristic
2#15689026C211yesmaximal, characteristic
3#15688988C211yesmaximal, characteristic, complemented
4#15688886C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C22⋊Dic47—21no—
12C2×C22⋊Dic47—21no—
13C2×C4×Dic47C2211yescharacteristic
14#13093945—22no—
15C47⋊#95—21no—
16C47⋊#95—21no—
17C22×D4×C47C2211yescharacteristic
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20#102×C47—22no—
21C24×C47—21no—
22C2×D4×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47D412yes—
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C22×Dic47D411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C22⋊Dic47—42no—
40C22⋊Dic47—42no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4×Dic47—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—22no—
51C23×C47—41no—
52C23×C47—41no—
53C23×C47—41no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47C2×D411yescharacteristic
58D4×C47—22no—
59D4×C47—22no—
60D4×C47—41no—
61D4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C8×C47—41no—
84C47⋊C8—41no—
85C22×C47—42no—
86C22×C47—42no—
87C22×C47—42no—
88C22×C47—81no—
89C22×C47—81no—
90C22×C47—81no—
91C22×C47—81no—
92C22×C47#12111yescharacteristic
93C22×C47#12311yescharacteristic
94C22×C47#12411yescharacteristic
95C22×C47#13511yescharacteristic
96C22×C47#13511yescharacteristic
97C22×C47AGL(1,ℤ/8)11yescharacteristic
98C22×C47AGL(1,ℤ/8)11yescharacteristic
99C4×C47—81no—
100C4×C47#12311yescharacteristic
101C4×C47#12311yescharacteristic
102C4×C47#12611yescharacteristic
103C4×C47#12611yescharacteristic
104Dic47—41no—
105Dic47—41no—
106Dic47—81no—
107Dic47—81no—
108#2073—471nomaximal, Sylow
109C2×C47—82no—
110C2×C47#39711yescharacteristic
111C2×C47#46311yescharacteristic
112C2×C47#46311yescharacteristic
113C2×C47#48211yescharacteristic
114C2×C47#48211yescharacteristic
115C2×C47#48811yescharacteristic
116C2×C47#49011yescharacteristic
117C2×#102—471no—
118C2×#102D4711yescharacteristic
119#390—471no—
120#382—471no—
121#340—471no—
122#340—471no—
123#336—471no—
124C47#207311yescharacteristic, complemented, Sylow
125C22×D4C2×D4711yescharacteristic
126C22×C8—471no—
127C22×C8C2×D4711yescharacteristic
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C22⋊C4—941no—
132C2×C22⋊C4—941no—
133C2×C42—471no—
134#102—22no—
135#102—942no—
136#95—941no—
137#95—941no—
138C24—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C22⋊D4712yes—
145C22×C4—21no—
146C22×C4—471no—
147C22×C4—471no—
148C22×C4—941no—
149C22×C4—941no—
150C22×C4C22×D4711yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—941no—
155C2×C8—941no—
156C2×C8—941no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C22⋊C4—1882no—
164C22⋊C4—1882no—
165C42—941no—
166C42—941no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23—41no—
173C23—41no—
174C23D4×D4711yescharacteristic
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—941no—
185C2×C4—941no—
186C2×C4—941no—
187C2×C4—941no—
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#1062535211yescharacteristic
197C2×C4#1062535211yescharacteristic
198C2×C4#1062535211yescharacteristic
199C2×C4C2×C22⋊D4711yescharacteristic
200C8—41no—
201C8—1881no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—81no—
206C22—81no—
207C22—81no—
208C22—81no—
209C22#1309399611yescharacteristic
210C22#1309400611yescharacteristic
211C22#1309401011yescharacteristic
212C22#1309404311yescharacteristic
213C22#1309404511yescharacteristic
214C22#1309404811yescharacteristic
215C22#1309405111yescharacteristic
216C4—81no—
217C4—3761no—
218C4—3761no—
219C4—1881no—
220C4—1881no—
221C4#1309400511yescharacteristic
222C4#1309400711yescharacteristic
223C4#1309401711yescharacteristic
224C4#1309401711yescharacteristic
225C2—82no—
226C2#1568905111yescharacteristic
227C2#1568933611yescharacteristic
228C2#1568934011yescharacteristic
229C2#1568944511yescharacteristic
230C2#1568944611yescharacteristic
231C2#1568947611yescharacteristic
232C2#1568948611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2073
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
3. #15688988C2semidirect
4. #15688886C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
124. C47#2073semidirect