Finite Group Databasebeta

← #20244532

Subgroups — #20244532

Order 6016.

294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13093945C211yesmaximal, characteristic
3#15689026C211yesmaximal, characteristic
4#15688886C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9#13094015—22no—
10#13094015—22no—
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C22⋊Dic47—21no—
16C2×C22⋊Dic47—21no—
17C2×C4×Dic47C2211yescharacteristic
18#13093945—22no—
19C22×D4×C47C2211yescharacteristic
20C22×C8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22#102×C47—22no—
23C24×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47Q812yes—
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33C22×Dic47—21no—
34C22×Dic47D411yescharacteristic
35C22×Dic47D411yescharacteristic
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47D412yes—
41C22⋊Dic47—42no—
42C22⋊Dic47—42no—
43C4⋊Dic47—24no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47D412yes—
48Dic47⋊C4—24no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—22no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47—41no—
59C23×C47—41no—
60C23×C47—41no—
61C23×C47C2×D411yescharacteristic
62D4×C47—22no—
63D4×C47—22no—
64D4×C47—41no—
65D4×C47—41no—
66C2×C4×C47—22no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×Q811yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—22no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C8×C47—41no—
88C47⋊C8—41no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—81no—
93C22×C47—81no—
94C22×C47—81no—
95C22×C47—81no—
96C22×C47#12011yescharacteristic
97C22×C47C22⋊Q811yescharacteristic
98C22×C47#12411yescharacteristic
99C22×C47#13511yescharacteristic
100C22×C47#13511yescharacteristic
101C22×C47AGL(1,ℤ/8)11yescharacteristic
102C22×C47AGL(1,ℤ/8)11yescharacteristic
103C4×C47—42no—
104C4×C47C22⋊Q811yescharacteristic
105C4×C47C22⋊Q811yescharacteristic
106C4×C47#12411yescharacteristic
107C4×C47#12411yescharacteristic
108Dic47—41no—
109Dic47—41no—
110Dic47—42no—
111Dic47—81no—
112#2025—471nomaximal, Sylow
113C2×C47—82no—
114C2×C47#39311yescharacteristic
115C2×C47#44911yescharacteristic
116C2×C47#44911yescharacteristic
117C2×C47#47811yescharacteristic
118C2×C47#47811yescharacteristic
119C2×C47#48811yescharacteristic
120C2×C47#49011yescharacteristic
121C2×#125—471no—
122C2×#102—471no—
123C2×#102D4711yescharacteristic
124#390—471no—
125#340—471no—
126#340—471no—
127#336—471no—
128C47#202511yescharacteristic, complemented, Sylow
129C22×D4C2×D4711yescharacteristic
130C22×C8—471no—
131C22×C8C2×D4711yescharacteristic
132#125—942no—
133#125—942no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—941no—
137C2×C4⋊C4—941no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—941no—
140C2×C22⋊C4—941no—
141C2×C42—471no—
142#102—22no—
143#102—942no—
144C24—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4Dic9412yes—
151C22×C4—21no—
152C22×C4—471no—
153C22×C4—471no—
154C22×C4—941no—
155C22×C4—941no—
156C22×C4C22×D4711yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—941no—
161C2×C8—941no—
162C2×C8—941no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—944no—
166C4⋊C4—944no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C4⋊C4—941no—
170C4⋊C4C22⋊D4712yes—
171C22⋊C4—1882no—
172C22⋊C4—1882no—
173C42—941no—
174C42—941no—
175C23—22no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23D4×D4711yescharacteristic
183D4—22no—
184D4—22no—
185D4—41no—
186D4—41no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4—1881no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4C2×Dic9411yescharacteristic
203C2×C4#1062535011yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4#1062535211yescharacteristic
206C2×C4#1062535211yescharacteristic
207C2×C4C2×C22⋊D4711yescharacteristic
208C8—41no—
209C8—1881no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#1309399211yescharacteristic
218C22#1309400111yescharacteristic
219C22#1309401011yescharacteristic
220C22#1309404311yescharacteristic
221C22#1309404511yescharacteristic
222C22#1309404811yescharacteristic
223C22#1309405111yescharacteristic
224C4—42no—
225C4—3761no—
226C4—1881no—
227C4—1881no—
228C4—1882no—
229C4#1309400111yescharacteristic
230C4#1309400311yescharacteristic
231C4#1309401011yescharacteristic
232C4#1309401111yescharacteristic
233C2—82no—
234C2#1568903511yescharacteristic
235C2#1568926511yescharacteristic
236C2#1568926711yescharacteristic
237C2#1568942111yescharacteristic
238C2#1568942511yescharacteristic
239C2#1568947611yescharacteristic
240C2#1568948611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2025
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
1. C2×#13094015C2semidirect
4. #15688886C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
128. C47#2025semidirect