Finite Group Databasebeta

← #20254605

Subgroups — #20254605

Order 6016.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C4⋊Q8×D47C211yesmaximal, characteristic, complemented
2#15689652C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689529C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689452C212yesmaximal, complemented
7#15689435C212yesmaximal
8#15689416C212yesmaximal, complemented
9#15689411C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094022—21no—
17#13094017—21no—
18#13094016C2211yescharacteristic
19#13094006—21no—
20#13094000C2211yescharacteristic
21#13093995C2211yescharacteristic
22Q8×Dic47C2211yescharacteristic
23D4×Dic47C2211yescharacteristic
24(C22⋊D47)⋊C4—21no—
25#13093980—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47C2212yes—
28C42×D47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093956C2212yes—
32#13093955C2212yes—
33Dic47⋊C8C2212yes—
34#13093948C2212yes—
35#13093945C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#124×C47C2211yescharacteristic
40#103×C47C2212yes—
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48Q8×D47—44no—
49C2×C4×D47—22no—
50C2×C4×D47D411yescharacteristic
51C2×C4×D47D411yescharacteristic
52C2×C4×D47C2311yescharacteristic
53C2×Dic94—21no—
54C2×Dic94—22no—
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2312yes—
58C22⋊C4×C47—21no—
59C22⋊C4×C47—21no—
60C42×C47C2311yescharacteristic
61C22⋊Dic47—21no—
62C22⋊Dic47—21no—
63(C2×D47)⋊C4—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—21no—
74C4×Dic47—21no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79C23×C47—21no—
80C22×D47C2×D411yescharacteristic
81Q8×C47—22no—
82Q8×C47—42no—
83D4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C22⋊D47—42no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—42no—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C4×D47—22no—
98C4×D47—22no—
99C4×D47—22no—
100C4×D47—44no—
101Dic94—44no—
102Dic94—42no—
103C8×C47—22no—
104C47⋊C8—22no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47C22×D411yescharacteristic
109C2×D47—21no—
110C2×D47—21no—
111C2×D47AGL(1,ℤ/8)12yes—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—41no—
115C4×C47—42no—
116C4×C472−1+412yes—
117Dic47—21no—
118Dic47—21no—
119Dic47—42no—
120Dic47—41no—
121Dic47—41no—
122Dic47#13712yes—
123#3238—471nomaximal, Sylow
124C2×C47—81no—
125C2×C47#53611yescharacteristic
126C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C47C2×#13711yescharacteristic
128D47—22no—
129C2×C4⋊Q8—471no—
130#529—471no—
131#501—471no—
132#501—471no—
133#489—471no—
134#489D4711yescharacteristic, complemented
135#483—472no—
136#480—472no—
137#477—472no—
138#476—472no—
139#432—471no—
140C47#323811yescharacteristic, complemented, Sylow
141C22×Q8—941no—
142C4⋊Q8—472no—
143C4⋊Q8—471no—
144C4⋊Q8—941no—
145C4⋊Q8—941no—
146C4⋊Q8C2×D4711yescharacteristic
147#126—941no—
148#125—471no—
149#124C2×D4711yescharacteristic
150#123—941no—
151C22⋊Q8—471no—
152#121—471no—
153C4×Q8—471no—
154C4×D4—471no—
155C4×D4—941no—
156#117—941no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—941no—
159C2×C42—471no—
160#107—472no—
161#107—472no—
162#106—472no—
163#106—472no—
164C4⋊C8—472no—
165#103—472no—
166#103C2×D4712yes—
167#102—472no—
168#102C2×D4712yes—
169C22⋊C8—472no—
170#97—471no—
171#97C2×D4711yescharacteristic
172C2×Q8—21no—
173C2×Q8—942no—
174C2×Q8—941no—
175C2×Q8—1884no—
176C2×Q8C22×D4711yescharacteristic
177C2×D4—941no—
178C2×D4C22×D4711yescharacteristic
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—942no—
183C22×C4—941no—
184C2×C8—472no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—472no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4C22×D4712yes—
198C22⋊C4—21no—
199C22⋊C4—21no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C22⋊C4—941no—
203C42—471no—
204C42—471no—
205C42—471no—
206C42—941no—
207C42C22×D4711yescharacteristic
208C23—21no—
209C23—471no—
210Q8—22no—
211Q8—42no—
212Q8—1882no—
213Q8—1884no—
214D4—22no—
215D4—1882no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—471no—
219C2×C4—471no—
220C2×C4—471no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—1884no—
228C2×C4—1882no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—22no—
233C8—942no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—472no—
238C22—941no—
239C22—941no—
240C22C2×D4×D4711yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—472no—
246C4—941no—
247C4—941no—
248C4—1882no—
249C4—1881no—
250C4—1881no—
251C4#1309407112yes—
252C2—81no—
253C2—942no—
254C2#1568969311yescharacteristic
255C2AGL(1,ℤ/8)×D4711yescharacteristic
256C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3238
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D47C2semidirect
3. #15689532C2semidirect
4. #15689529C2semidirect
5. #15689482C2semidirect
6. #15689452C2semidirect
8. #15689416C2semidirect
9. #15689411C2semidirect
10. #15689178C2semidirect
11. C47×#489C2semidirect
134. #489D47semidirect
140. C47#3238semidirect