Finite Group Databasebeta

← #20253996

Subgroups — #20253996

Order 6016.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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#15689678C211yesmaximal, characteristic, complemented
2#15689658C211yesmaximal, characteristic
3#15689517C211yesmaximal, characteristic, complemented
4#15689493C211yesmaximal, characteristic, complemented
5#15689485C211yesmaximal, characteristic, complemented
6#15689382C212yesmaximal, complemented
7#15689370C212yesmaximal
8#15689217C212yesmaximal, complemented
9#15689210C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#501C211yesmaximal, characteristic, complemented
12C2×Dic188C2212yes—
13C2×#10625325C2212yes—
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic
16#13094019—21no—
17#13094015—21no—
18#13094012C2211yescharacteristic
19#13094009—21no—
20#13094004C2212yes—
21#13094004C2211yescharacteristic
22#13094000—21no—
23#13093999C2211yescharacteristic
24Q8×Dic47—21no—
25#13093989C2211yescharacteristic
26#13093989C2212yes—
27#13093986—21no—
28#13093986C2211yescharacteristic
29#13093982—21no—
30#13093982—21no—
31C42×D47C2211yescharacteristic
32#13093947C2212yes—
33#13093947C2212yes—
34#13093947C2212yes—
35#13093944C2212yes—
36#13093935C2211yescharacteristic
37C8×Dic47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#107×C47C2212yes—
41#106×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×D188—21no—
45C2×D188C2311yescharacteristic
46C2×C4×D47—21no—
47C2×C4×D47D411yescharacteristic
48C2×C4×D47D411yescharacteristic
49C2×C4×D47C2311yescharacteristic
50C2×Dic94C2311yescharacteristic
51C2×Dic94C2312yes—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2311yescharacteristic
57C4⋊C4×C47C2312yes—
58C4⋊C4×C47C2311yescharacteristic
59C42×C47C2311yescharacteristic
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47—21no—
69C4⋊Dic47—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—21no—
72C4×Dic47—21no—
73C4×Dic47—22no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78Dic188—24no—
79#10625325—24no—
80#10625324—24no—
81C22×D47—21no—
82C22×D47C2×D411yescharacteristic
83Q8×C47—42no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47C2×D411yescharacteristic
93C2×Dic47C2×D411yescharacteristic
94C2×Dic47C2×D411yescharacteristic
95D188—22no—
96D188—42no—
97C4×D47—22no—
98C4×D47—22no—
99C4×D47—41no—
100C4×D47—42no—
101Dic94—22no—
102Dic94—22no—
103Dic94—22no—
104C8×C47#4114yes—
105C47⋊C8—22no—
106C22×C47C22×D411yescharacteristic
107C2×D47—21no—
108C2×D47—21no—
109C2×D47—21no—
110C2×D47—41no—
111C2×D47—41no—
112C2×D47—41no—
113C4×C47—21no—
114C4×C47—21no—
115C4×C47—41no—
116C4×C47—41no—
117C4×C47—42no—
118C4×C47C2×#4112yes—
119Dic47—21no—
120Dic47—21no—
121Dic47—42no—
122Dic47—41no—
123Dic47#13712yes—
124#3172—471nomaximal, Sylow
125C2×C47#53211yescharacteristic
126C2×C47C2×#13711yescharacteristic
127C2×C47#57511yescharacteristic
128D47—41no—
129D47—81no—
130#533—471no—
131#529—471no—
132#501D4711yescharacteristic, complemented
133#497—471no—
134#491—471no—
135#489—471no—
136#470—472no—
137#468—472no—
138C4×Q16—472no—
139C4×SD16—472no—
140C4×M16—471no—
141C47#317211yescharacteristic, complemented, Sylow
142C2×Q16—472no—
143C2×SD16—472no—
144C2×M16—472no—
145C4⋊Q8—471no—
146C4⋊Q8C2×D4711yescharacteristic
147#126—941no—
148#125—941no—
149#125C2×D4711yescharacteristic
150#124—471no—
151#123—941no—
152C22⋊Q8—471no—
153C22⋊Q8—472no—
154C22⋊Q8—941no—
155#121—471no—
156C4×Q8—471no—
157C4×Q8—472no—
158C4×Q8—941no—
159C4×D4—471no—
160C4×D4—941no—
161#117—941no—
162#117—941no—
163C2×C42—471no—
164#107C2×D4712yes—
165#106C2×D4712yes—
166#103—472no—
167#103—472no—
168#103—472no—
169#102—472no—
170#97—471no—
171#97C2×D4711yescharacteristic
172C4×C8—472no—
173C2×Q8—21no—
174C2×Q8—471no—
175C2×Q8—472no—
176C2×D4—471no—
177C2×D4—941no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—941no—
182Q16—944no—
183SD16—944no—
184M16—944no—
185C2×C8—472no—
186C2×C8C22×D4712yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—942no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—942no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C4⋊C4C22×D4712yes—
197C4⋊C4C22×D4711yescharacteristic
198C4⋊C4C22×D4711yescharacteristic
199C22⋊C4—941no—
200C22⋊C4—941no—
201C22⋊C4—942no—
202C22⋊C4—941no—
203C22⋊C4—941no—
204C22⋊C4—941no—
205C42—471no—
206C42—471no—
207C42—471no—
208C42—941no—
209C42—942no—
210C42C22×D4711yescharacteristic
211C23—471no—
212C23—941no—
213Q8—42no—
214Q8—942no—
215Q8—942no—
216Q8—942no—
217D4—942no—
218D4—1882no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—471no—
223C2×C4—471no—
224C2×C4—471no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—941no—
228C2×C4—942no—
229C2×C4—1881no—
230C2×C4—1882no—
231C2×C4D4×D4711yescharacteristic
232C2×C4D4×D4711yescharacteristic
233C2×C4C23×D4711yescharacteristic
234C8—942no—
235C8#1062535414yes—
236C22—941no—
237C22—941no—
238C22—941no—
239C22—1881no—
240C22—1881no—
241C22—1881no—
242C22C2×D4×D4711yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—472no—
249C4—941no—
250C4—941no—
251C4—1881no—
252C4—1882no—
253C4C2×#1062535412yes—
254C2—3761no—
255C2—1881no—
256C2#1568967411yescharacteristic
257C2#137×D4711yescharacteristic
258C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3172
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
1. #15689678C2semidirect
3. #15689517C2semidirect
4. #15689493C2semidirect
5. #15689485C2semidirect
6. #15689382C2semidirect
8. #15689217C2semidirect
9. #15689210C2semidirect
10. #15689075C2semidirect
11. C47×#501C2semidirect
132. #501D47semidirect
141. C47#3172semidirect