Finite Group Databasebeta

← #20254608

Subgroups — #20254608

Order 6016.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689655C211yesmaximal, characteristic
3#15689530C212yesmaximal, complemented
4#15689481C212yesmaximal, complemented
5#15689455C212yesmaximal, complemented
6#15689435C212yesmaximal
7#15689419C211yesmaximal, characteristic, complemented
8#15689415C211yesmaximal, characteristic, complemented
9#15689413C211yesmaximal, characteristic, complemented
10#15689179C211yesmaximal, characteristic, complemented
11C47×#476C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094022—21no—
17#13094017—21no—
18#13094015C2211yescharacteristic
19#13094011C2211yescharacteristic
20#13094006—21no—
21#13094004C2211yescharacteristic
22#13093995C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24C4×C22⋊D47—21no—
25#13093983—21no—
26C4⋊C4×D47—21no—
27C4⋊C4×D47C2212yes—
28C42×D47C2211yescharacteristic
29#13093958C2212yes—
30#13093957C2212yes—
31#13093955C2212yes—
32C4⋊(C47⋊C8)C2211yescharacteristic
33#13093949C2212yes—
34#13093947C2212yes—
35#13093945C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093934C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×D4×C47C2211yescharacteristic
40#106×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#102×C47C2212yes—
43C2×Q8×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—21no—
47Q8×D47—44no—
48C2×C4×D47—22no—
49C2×C4×D47D411yescharacteristic
50C2×C4×D47D411yescharacteristic
51C2×C4×D47C2311yescharacteristic
52C2×Dic94—21no—
53C2×Dic94—22no—
54C2×Dic94C2311yescharacteristic
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2311yescharacteristic
58C4⋊C4×C47C2312yes—
59C22⋊C4×C47—21no—
60C42×C47C2311yescharacteristic
61C22⋊Dic47—21no—
62C22⋊Dic47—21no—
63C22⋊Dic47—21no—
64(C2×D47)⋊C4—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47C2312yes—
69C4⋊Dic47C2311yescharacteristic
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—42no—
82D4×C47—21no—
83D4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—42no—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C22⋊D47—42no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C4×D47—22no—
98C4×D47—22no—
99C4×D47—21no—
100C4×D47—21no—
101C4×D47—44no—
102Dic94—21no—
103Dic94—21no—
104Dic94—44no—
105Dic94—42no—
106C8×C47—22no—
107C47⋊C8—22no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47C22×D411yescharacteristic
112C2×D47—21no—
113C2×D47—21no—
114C2×D47AGL(1,ℤ/8)12yes—
115C4×C47—21no—
116C4×C47—42no—
117C4×C47—41no—
118C4×C47#13712yes—
119C4×C472−1+411yescharacteristic
120C4×C472−1+411yescharacteristic
121Dic47—21no—
122Dic47—21no—
123Dic47—21no—
124Dic47—41no—
125Dic47—42no—
126Dic47—41no—
127#3238—471nomaximal, Sylow
128C2×C47—81no—
129C2×C47#53611yescharacteristic
130C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
131C2×C47C2×#13711yescharacteristic
132D47—22no—
133C2×C4⋊Q8—471no—
134#529—471no—
135#501—472no—
136#489—472no—
137#483—472no—
138#480—472no—
139#477—471no—
140#477—471no—
141#476—471no—
142#476D4711yescharacteristic, complemented
143#432—471no—
144C47#323811yescharacteristic, complemented, Sylow
145C22×Q8—941no—
146C4⋊Q8—472no—
147C4⋊Q8—471no—
148C4⋊Q8—941no—
149C4⋊Q8—941no—
150C4⋊Q8C2×D4711yescharacteristic
151#126—941no—
152#125—471no—
153#124—471no—
154#123—941no—
155C22⋊Q8—471no—
156#121—471no—
157C4×Q8—471no—
158C4×D4—941no—
159C4×D4C2×D4711yescharacteristic
160#117—941no—
161C2×C4⋊C4—472no—
162C2×C4⋊C4—941no—
163C2×C42—471no—
164#107—472no—
165#107—472no—
166#106—472no—
167#106C2×D4712yes—
168C4⋊C8—471no—
169C4⋊C8C2×D4711yescharacteristic
170#103—472no—
171#103—472no—
172#102—472no—
173#102C2×D4712yes—
174C22⋊C8—472no—
175#97—472no—
176C2×Q8—21no—
177C2×Q8—471no—
178C2×Q8—942no—
179C2×Q8—941no—
180C2×Q8—1884no—
181C2×D4—941no—
182C2×D4C22×D4711yescharacteristic
183C22×C4—21no—
184C22×C4—471no—
185C22×C4—471no—
186C22×C4—471no—
187C22×C4—942no—
188C2×C8—472no—
189C2×C8C22×D4712yes—
190C4⋊C4—21no—
191C4⋊C4—472no—
192C4⋊C4—471no—
193C4⋊C4—942no—
194C4⋊C4—942no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4—941no—
200C4⋊C4C22×D4712yes—
201C4⋊C4C22×D4711yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—941no—
204C22⋊C4—941no—
205C22⋊C4—941no—
206C22⋊C4—941no—
207C42—471no—
208C42—471no—
209C42—471no—
210C42—941no—
211C42C22×D4711yescharacteristic
212C23—21no—
213C23—471no—
214Q8—42no—
215Q8—941no—
216Q8—941no—
217Q8—1882no—
218Q8—1884no—
219D4—21no—
220D4—21no—
221D4—1882no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—471no—
226C2×C4—471no—
227C2×C4—471no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—941no—
233C2×C4—941no—
234C2×C4—942no—
235C2×C4—1884no—
236C2×C4D4×D4711yescharacteristic
237C2×C4D4×D4711yescharacteristic
238C2×C4C23×D4711yescharacteristic
239C8—22no—
240C8—942no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—472no—
245C22—941no—
246C22—941no—
247C22C2×D4×D4711yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—941no—
252C4—941no—
253C4—941no—
254C4—1882no—
255C4—1881no—
256C4—1881no—
257C4#1309405312yes—
258C4#1309407111yescharacteristic
259C4#1309407211yescharacteristic
260C2—81no—
261C2—942no—
262C2#1568969611yescharacteristic
263C2AGL(1,ℤ/8)×D4711yescharacteristic
264C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3238
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D47C2semidirect
3. #15689530C2semidirect
4. #15689481C2semidirect
5. #15689455C2semidirect
7. #15689419C2semidirect
8. #15689415C2semidirect
9. #15689413C2semidirect
10. #15689179C2semidirect
11. C47×#476C2semidirect
142. #476D47semidirect
144. C47#3238semidirect