Finite Group Databasebeta

← #20256100

Subgroups — #20256100

Order 6016.

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

normal subgroups only

This group has 396 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
1#15689834C211yesmaximal, characteristic, complemented
2#15689793C211yesmaximal, characteristic, complemented
3#15689486C212yesmaximal, complemented
4#15689421C212yesmaximal, complemented
5#15689410C211yesmaximal, characteristic, complemented
6#15689317C212yesmaximal, complemented
7#15689315C211yesmaximal, characteristic, complemented
8#15689253C211yesmaximal, characteristic, complemented
9#15689232C212yesmaximal, complemented
10C4×D376C211yesmaximal, characteristic, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C2×D376C2211yescharacteristic
14C2×#10625334C2212yes—
15#13094020C2212yes—
16#13094015C2212yes—
17#13094004—21no—
18#13094000—22no—
19#13093996—22no—
20#13093995—21no—
21C4×Dic94C2211yescharacteristic
22C4×D188C2211yescharacteristic
23C4×D188C2211yescharacteristic
24D4×Dic47C2212yes—
25#13093986C2212yes—
26C4⋊C4×D47—21no—
27#13093958C2211yescharacteristic
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093946C2211yescharacteristic
32#13093946C2211yescharacteristic
33#13093945C2212yes—
34#13093944C2212yes—
35#13093934C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic
38#102×C47C2212yes—
39#102×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C22×Dic47—22no—
48#10625352—44no—
49C2×D188C2311yescharacteristic
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C4×D47—21no—
53C2×C4×D47—22no—
54C2×Dic94D411yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C4⋊C4×C47—21no—
58C4⋊C4×C47C2312yes—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61#10625334—24no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4—22no—
65C4⋊Dic47—22no—
66C4⋊Dic47D411yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—22no—
70Dic47⋊C4D412yes—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73D376—22no—
74C23×C47—22no—
75C22×D47—21no—
76C22×D47—21no—
77Q8×C47—81no—
78D4×C47—22no—
79D4×C47—22no—
80D4×C47—42no—
81D4×C47—81no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C22⋊D47—44no—
87C22⋊D47—82no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—44no—
91C2×Dic47C2×D412yes—
92C2×Dic47C2×D412yes—
93D188—21no—
94D188—21no—
95D188—21no—
96D188#4112yescomplemented
97C4×D47—42no—
98C4×D47—42no—
99C4×D47—82no—
100Dic94—22no—
101C8×C47—21no—
102C8×C47—21no—
103C47⋊C8—22no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47C22×D411yescharacteristic
108C2×D47—22no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—41no—
112C2×D47—41no—
113C2×D47—41no—
114C4×C47—21no—
115C4×C47—42no—
116C4×C47AGL(1,ℤ/8)12yes—
117C4×C47C2×#4111yescharacteristic
118C4×C472−1+411yescharacteristic
119Dic47—22no—
120Dic47—22no—
121Dic47—41no—
122Dic47—41no—
123#3366—471nomaximal, Sylow
124C2×C47—82no—
125C2×C47#54811yescharacteristic
126C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C47#57611yescharacteristic
128D47—42no—
129D47—81no—
130#554—471no—
131#550—471no—
132#490—472no—
133#486D4711yescharacteristic, complemented
134#478—472no—
135#476—471no—
136#459—471no—
137#459—472no—
138#446—471no—
139#442—472no—
140C4×D8—471no—
141C47#336611yescharacteristic, complemented, Sylow
142C2×#41—941no—
143C2×D8—472no—
144C2×D8—471no—
145C4⋊Q8C2×D4711yescharacteristic
146#127—472no—
147#127C2×D4711yescharacteristic
148#125—472no—
149C22⋊Q8—941no—
150C22⋊Q8—942no—
151#121—941no—
152#121—942no—
153C4×Q8—471no—
154C4×D4—472no—
155C4×D4—472no—
156C4×D4—471no—
157C4×D4—471no—
158C2×C4⋊C4—941no—
159#107—471no—
160#106—472no—
161C4⋊C8—472no—
162C4⋊C8—471no—
163#102—472no—
164#102—471no—
165#102—471no—
166#102—472no—
167#102C2×D4712yes—
168#102C2×D4712yes—
169#97—472no—
170C4×C8C2×D4711yescharacteristic
171#41—1884no—
172C2×Q8—21no—
173C2×Q8—471no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—471no—
177C2×D4—471no—
178C2×D4—942no—
179C2×D4—942no—
180C2×D4C22×D4712yes—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—941no—
184C22×C4—941no—
185D8—942no—
186D8—944no—
187C2×C8—472no—
188C2×C8C22×D4711yescharacteristic
189C2×C8C22×D4711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—472no—
192C4⋊C4—471no—
193C4⋊C4—471no—
194C4⋊C4—471no—
195C4⋊C4—942no—
196C4⋊C4—942no—
197C4⋊C4C22×D4712yes—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C42—472no—
203C42C22×D4711yescharacteristic
204C23—22no—
205C23—941no—
206C23—941no—
207Q8—81no—
208Q8—942no—
209D4—22no—
210D4—22no—
211D4—42no—
212D4—81no—
213D4—472no—
214D4—941no—
215D4—941no—
216D4—941no—
217D4—3762no—
218D4—1884no—
219C2×C4—22no—
220C2×C4—472no—
221C2×C4—472no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—3762no—
225C2×C4—1884no—
226C2×C4—1882no—
227C2×C4—1882no—
228C2×C4D4×D4711yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4C23×D4711yescharacteristic
231C8—21no—
232C8—21no—
233C8—942no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—942no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22—1881no—
243C22C2×D4×D4711yescharacteristic
244C4—21no—
245C4—42no—
246C4—942no—
247C4—942no—
248C4—1881no—
249C4—1881no—
250C4#1309405112yes—
251C4#41×D4711yescharacteristic
252C4#1309407111yescharacteristic
253C2—82no—
254C2—3761no—
255C2—1882no—
256C2#1568978111yescharacteristic
257C2C2×#1309405111yescharacteristic
258C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3366
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
2. #15689793C2semidirect
3. #15689486C2semidirect
4. #15689421C2semidirect
5. #15689410C2semidirect
6. #15689317C2semidirect
7. #15689315C2semidirect
8. #15689253C2semidirect
9. #15689232C2semidirect
10. C4×D376C2semidirect
11. C47×#486C2semidirect
96. D188#41semidirect
133. #486D47semidirect
141. C47#3366semidirect