Finite Group Databasebeta

← #20256027

Subgroups — #20256027

Order 6016.

370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#15689848C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic
3#15689472C212yesmaximal, complemented
4#15689406C212yesmaximal, complemented
5#15689405C211yesmaximal, characteristic, complemented
6#15689327C212yesmaximal
7#15689325C211yesmaximal, characteristic
8C8×Dic94C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic
10#15689208C212yesmaximal
11C47×#487C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13C2×#10625325C2211yescharacteristic
14C2×#10625336C2212yes—
15#13094023C2212yes—
16#13094022C2212yes—
17#13094015—21no—
18#13094014—22no—
19#13094002—22no—
20#13094000—21no—
21Q8×Dic47C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24#13093989—21no—
25C4×D188C2211yescharacteristic
26#13093986C2212yes—
27#13093956C2211yescharacteristic
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093948C2212yes—
33#13093947C2212yes—
34#13093946C2211yescharacteristic
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#103×C47C2212yes—
39#103×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47C2312yes—
43Q8×D47—44no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×C4×D47—22no—
47C2×Dic94—22no—
48C2×Dic94D411yescharacteristic
49C2×Dic94C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C42×C47C2311yescharacteristic
57#10625336—24no—
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47D411yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64Dic47⋊C4—21no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—21no—
70C4×Dic47—22no—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73#10625325—22no—
74C22×D47—21no—
75Q8×C47—22no—
76Q8×C47—22no—
77Q8×C47—42no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88D188—21no—
89D188#4112yes—
90C4×D47—42no—
91C4×D47—44no—
92Dic94—21no—
93Dic94—21no—
94Dic94—44no—
95Dic94SD1614yescomplemented
96C8×C47—21no—
97C8×C47—21no—
98C47⋊C8—22no—
99C22×C47C22×D411yescharacteristic
100C2×D47—22no—
101C2×D47—41no—
102C2×D47—41no—
103C4×C47—21no—
104C4×C47—42no—
105C4×C47—42no—
106C4×C47C2×SD1612yes—
107C4×C47C2×#4111yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—41no—
111Dic47—41no—
112Dic47—41no—
113Dic47C2×SD1614yes—
114#3359—471nomaximal, Sylow
115C2×C47#54811yescharacteristic
116C2×C47C22×SD1611yescharacteristic
117C2×C47#57811yescharacteristic
118D47—42no—
119#557—471no—
120D4×Q8—471no—
121#487—472no—
122#487D4711yescharacteristic, complemented
123#475—471no—
124#475—472no—
125#461—471no—
126#461—472no—
127C8×Q8—471no—
128C4×SD16—472no—
129C4×SD16—471no—
130C47#335911yescharacteristic, complemented, Sylow
131C22×Q8—941no—
132C2×SD16—472no—
133C2×SD16—471no—
134C4⋊Q8—472no—
135C4⋊Q8—472no—
136C4⋊Q8C2×D4711yescharacteristic
137C4⋊Q8C2×D4711yescharacteristic
138#125—942no—
139#125—941no—
140C22⋊Q8—942no—
141C22⋊Q8—941no—
142C4×Q8—471no—
143C4×Q8—472no—
144C4×Q8—471no—
145C4×Q8—941no—
146C4×D4—472no—
147C4×D4—471no—
148#106—471no—
149#106—472no—
150C4⋊C8—472no—
151C4⋊C8—471no—
152#103—472no—
153#103—471no—
154#103—472no—
155#103C2×D4712yes—
156#103C2×D4712yes—
157#102—471no—
158C4×C8—472no—
159C4×C8C2×D4711yescharacteristic
160C2×Q8—21no—
161C2×Q8—471no—
162C2×Q8—471no—
163C2×Q8—942no—
164C2×Q8—1884no—
165C2×Q8C22×D4712yes—
166C2×D4—471no—
167C22×C4—942no—
168C22×C4—941no—
169SD16—942no—
170SD16—944no—
171C2×C8—472no—
172C2×C8C22×D4711yescharacteristic
173C2×C8C22×D4711yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—472no—
178C4⋊C4—471no—
179C4⋊C4—471no—
180C4⋊C4—471no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4C22×D4712yes—
187C22⋊C4—942no—
188C22⋊C4—941no—
189C42—472no—
190C42—942no—
191C42—941no—
192C42C22×D4711yescharacteristic
193C23—941no—
194Q8—22no—
195Q8—22no—
196Q8—42no—
197Q8—474no—
198Q8—941no—
199Q8—941no—
200Q8—1884no—
201D4—472no—
202D4—941no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—472no—
206C2×C4—472no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—1884no—
211C2×C4—1882no—
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—21no—
216C8—21no—
217C8—942no—
218C22—942no—
219C22—1881no—
220C22—1881no—
221C22C2×D4×D4711yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—474no—
226C4—942no—
227C4—1881no—
228C4—1881no—
229C4—1881no—
230C4SD16×D4712yes—
231C4#41×D4711yescharacteristic
232C4#1309407111yescharacteristic
233C2—1882no—
234C2#1568978111yescharacteristic
235C2C2×SD16×D4711yescharacteristic
236C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3359
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
3. #15689472C2semidirect
4. #15689406C2semidirect
5. #15689405C2semidirect
8. C8×Dic94C2semidirect
11. C47×#487C2semidirect
95. Dic94SD16semidirect
122. #487D47semidirect
130. C47#3359semidirect