Finite Group Databasebeta

← #20244591

Subgroups — #20244591

Order 6016.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13094003C211yesmaximal, characteristic
2C2×#13093957C211yesmaximal, characteristic, complemented
3C2×#13093947C211yesmaximal, characteristic, complemented
4C2×#13093947C211yesmaximal, characteristic, complemented
5C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C47×#380C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13094003—22no—
12#13094003—22no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C22⋊Dic47—21no—
16#13093957—22no—
17#13093947—22no—
18#13093947—22no—
19C22⋊(C47⋊C8)—22no—
20C23×C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C22⋊C4×C47—21no—
24#95×C47—21no—
25C24×C47D411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94D412yes—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—21no—
48C22⋊C4×C47—42no—
49C22⋊Dic47—24no—
50C4⋊Dic47—21no—
51C4⋊Dic47D412yes—
52Dic47⋊C4—24no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8D412yes—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—21no—
65C23×C47Q1612yes—
66C23×C47C2×D411yescharacteristic
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C2×C4×C47#4111yescharacteristic
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92Dic94—22no—
93Dic94—22no—
94Dic94—41no—
95Dic94—41no—
96C47⋊C8—22no—
97C47⋊C8—41no—
98C22×C47—22no—
99C22×C47—22no—
100C22×C47—22no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47#12011yescharacteristic
106C22×C47#12111yescharacteristic
107C22×C47#12311yescharacteristic
108C22×C47C2×Q1611yescharacteristic
109C22×C47#13511yescharacteristic
110C22×C47AGL(1,ℤ/8)11yescharacteristic
111C22×C47#13711yescharacteristic
112C4×C47—41no—
113C4×C47—81no—
114C4×C47—81no—
115C4×C47#12111yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12311yescharacteristic
118C4×C47#12411yescharacteristic
119Dic47—42no—
120Dic47—42no—
121#2036—471nomaximal, Sylow
122C2×C47—42no—
123C2×C47#39411yescharacteristic
124C2×C47#44911yescharacteristic
125C2×C47#45111yescharacteristic
126C2×C47#46711yescharacteristic
127C2×C47#46811yescharacteristic
128C2×C47#48411yescharacteristic
129C2×C47#48511yescharacteristic
130C2×C22⋊Q8—471no—
131C2×#107—471no—
132C2×#103—471no—
133C2×#103—471no—
134C2×C22⋊C8—471no—
135#380D4711yescharacteristic
136#340—471no—
137C47#203611yescharacteristic, complemented, Sylow
138C22×Q8—471no—
139C23×C4C2×D4711yescharacteristic
140C22×C8—471no—
141C22×C8—471no—
142C22⋊Q8—942no—
143C22⋊Q8—942no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—941no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—21no—
149C2×C22⋊C4—941no—
150#107—942no—
151#103—942no—
152#103—942no—
153C22⋊C8—942no—
154#95—21no—
155C24C22⋊D4711yescharacteristic
156C2×Q8—472no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—941no—
171C22×C4—941no—
172C22×C4C22⋊D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174C2×C8—472no—
175C2×C8—941no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—472no—
185C4⋊C4—944no—
186C4⋊C4—941no—
187C22⋊C4—42no—
188C22⋊C4—944no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23#1062533712yes—
196C23C2×C22⋊D4711yescharacteristic
197Q8—942no—
198Q8—942no—
199Q8—1881no—
200Q8—1881no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4—1881no—
220C2×C4#1062535011yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4#1062535211yescharacteristic
226C8—942no—
227C8—1881no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1309399211yescharacteristic
236C22#1309399611yescharacteristic
237C22#1309400711yescharacteristic
238C22C2×#1062533711yescharacteristic
239C22#1309404411yescharacteristic
240C22#1309405011yescharacteristic
241C22#1309405411yescharacteristic
242C4—41no—
243C4—81no—
244C4—81no—
245C4—1882no—
246C4—1882no—
247C4#1309399711yescharacteristic
248C4#1309399711yescharacteristic
249C4#1309400611yescharacteristic
250C4#1309401011yescharacteristic
251C2—42no—
252C2#1568903811yescharacteristic
253C2#1568926611yescharacteristic
254C2#1568927811yescharacteristic
255C2#1568936211yescharacteristic
256C2#1568936711yescharacteristic
257C2#1568945811yescharacteristic
258C2#1568946411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#380C2
socleC23×C47C2×D4
hypercenter#380D47
hypocenterC47#2036
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#13093957C2semidirect
3. C2×#13093947C2semidirect
4. C2×#13093947C2semidirect
6. #15688885C2semidirect
137. C47#2036semidirect