Finite Group Databasebeta

← #20254579

Subgroups — #20254579

Order 6016.

368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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#15689674C211yesmaximal, characteristic
2#125×D47C211yesmaximal, characteristic, complemented
3#15689529C211yesmaximal, characteristic, complemented
4#15689489C211yesmaximal, characteristic, complemented
5#15689488C211yesmaximal, characteristic, complemented
6#15689443C212yesmaximal, complemented
7#15689438C212yesmaximal, complemented
8#15689426C212yesmaximal, complemented
9#15689422C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic, complemented
11C47×#501C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13#13094021C2211yescharacteristic
14#13094016C2211yescharacteristic
15#13094015C2211yescharacteristic
16#13094015C2211yescharacteristic
17#13094014—21no—
18#13094014—21no—
19#13094013—21no—
20#13093999—21no—
21#13093999C2212yes—
22#13093986—21no—
23#13093986C2212yes—
24C4⋊C4×D47—21no—
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2211yescharacteristic
27C4⋊C4×D47C2211yescharacteristic
28C42×D47C2211yescharacteristic
29#13093957C2212yes—
30#13093955C2212yes—
31Dic47⋊C8C2212yes—
32#13093946C2212yes—
33#13093946C2212yes—
34#13093944C2212yes—
35#13093944C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#107×C47C2212yes—
41#106×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44#10625354—44no—
45C2×D188—22no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188C2312yes—
49C2×C4×D47—21no—
50C2×C4×D47—21no—
51C2×C4×D47—22no—
52C2×C4×D47D411yescharacteristic
53C2×C4×D47D411yescharacteristic
54C2×C4×D47C2311yescharacteristic
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2311yescharacteristic
60C4⋊C4×C47C2312yes—
61C4⋊C4×C47C2311yescharacteristic
62C42×C47C2311yescharacteristic
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C2×C47⋊C8C2312yes—
79C22×D47—22no—
80C22×D47C2×D411yescharacteristic
81Q8×C47—42no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47C2×D411yescharacteristic
91C2×Dic47C2×D411yescharacteristic
92C2×Dic47C2×D411yescharacteristic
93D188—24no—
94D188—42no—
95D188—42no—
96D188—44no—
97C4×D47—22no—
98C4×D47—22no—
99C4×D47—41no—
100C4×D47—44no—
101C4×D47—42no—
102C4×D47—42no—
103C8×C47—22no—
104C47⋊C8—22no—
105C22×C47C22×D411yescharacteristic
106C2×D47—21no—
107C2×D47—21no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47AGL(1,ℤ/8)12yes—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47—41no—
116C4×C47—41no—
117C4×C472−1+412yes—
118Dic47—21no—
119Dic47—21no—
120Dic47—21no—
121Dic47—41no—
122Dic47—41no—
123#3234—471nomaximal, Sylow
124C2×C47#53611yescharacteristic
125C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C47#57511yescharacteristic
127D47—22no—
128D47—82no—
129#532—471no—
130C2×#125—471no—
131#501—471no—
132#501D4711yescharacteristic, complemented
133#490—471no—
134#490—471no—
135#481—472no—
136#480—472no—
137#478—472no—
138#478—472no—
139#432—471no—
140C47#323411yescharacteristic, complemented, Sylow
141C2×#41—941no—
142C4⋊Q8C2×D4711yescharacteristic
143#127—471no—
144#125—471no—
145#125—471no—
146#125—471no—
147#125—941no—
148#125—941no—
149#125C2×D4711yescharacteristic
150#124—941no—
151#121—472no—
152#121—941no—
153C4×D4—472no—
154C4×D4—941no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4—941no—
158C2×C4⋊C4—941no—
159C2×C42—471no—
160#107—472no—
161#107C2×D4712yes—
162#106—472no—
163#106C2×D4712yes—
164C4⋊C8—472no—
165#102—472no—
166#102—472no—
167#102—472no—
168#102—472no—
169C22⋊C8—472no—
170#97—471no—
171#97C2×D4711yescharacteristic
172#41—1884no—
173C2×Q8—21no—
174C2×D4—472no—
175C2×D4—942no—
176C2×D4—941no—
177C2×D4—941no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—942no—
182C22×C4—941no—
183C22×C4—941no—
184C2×C8—472no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—471no—
190C4⋊C4—471no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4C22×D4711yescharacteristic
200C4⋊C4C22×D4711yescharacteristic
201C4⋊C4C22×D4712yes—
202C22⋊C4—942no—
203C22⋊C4—942no—
204C42—471no—
205C42—471no—
206C42—471no—
207C42C22×D4711yescharacteristic
208C23—471no—
209C23—942no—
210Q8—42no—
211D4—944no—
212D4—1882no—
213D4—1882no—
214D4—1884no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—471no—
219C2×C4—471no—
220C2×C4—471no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—1881no—
226C2×C4—1884no—
227C2×C4—1882no—
228C2×C4—1882no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—22no—
233C8—942no—
234C22—472no—
235C22—941no—
236C22—941no—
237C22—1882no—
238C22—1882no—
239C22—1882no—
240C22C2×D4×D4711yescharacteristic
241C4—21no—
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—941no—
247C4—941no—
248C4—941no—
249C4—1881no—
250C4—1881no—
251C4#1309407212yes—
252C2—942no—
253C2—3762no—
254C2#1568969811yescharacteristic
255C2AGL(1,ℤ/8)×D4711yescharacteristic
256C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3234
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #125×D47C2semidirect
3. #15689529C2semidirect
4. #15689489C2semidirect
5. #15689488C2semidirect
6. #15689443C2semidirect
7. #15689438C2semidirect
8. #15689426C2semidirect
9. #15689422C2semidirect
10. #15689178C2semidirect
11. C47×#501C2semidirect
132. #501D47semidirect
140. C47#3234semidirect