Finite Group Databasebeta

← #20253991

Subgroups — #20253991

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#15689652C211yesmaximal, characteristic
3#15689532C211yesmaximal, characteristic, complemented
4#15689491C211yesmaximal, characteristic, complemented
5#15689482C211yesmaximal, characteristic, complemented
6#15689378C212yesmaximal, complemented
7#15689366C212yesmaximal
8Q16×Dic47C212yesmaximal, complemented
9SD16×Dic47C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#497C211yesmaximal, characteristic, complemented
12C2×#10625324C2212yes—
13#13094024C2211yescharacteristic
14#13094017—21no—
15#13094016C2211yescharacteristic
16#13094015—21no—
17#13094006—21no—
18#13094004—21no—
19#13094000C2212yes—
20#13094000C2211yescharacteristic
21#13093995C2211yescharacteristic
22Q8×Dic47C2211yescharacteristic
23Q8×Dic47C2212yes—
24#13093989—21no—
25D4×Dic47C2211yescharacteristic
26(C22⋊D47)⋊C4—21no—
27#13093982—21no—
28#13093980—21no—
29C42×D47C2211yescharacteristic
30#13093958C2212yes—
31#13093956C2212yes—
32#13093948C2212yes—
33#13093948C2212yes—
34#13093948C2212yes—
35#13093945C2212yes—
36#13093935C2211yescharacteristic
37C8×Dic47C2212yes—
38C2×Q16×C47C2212yes—
39C2×SD16×C47C2212yes—
40C4⋊Q8×C47C2211yescharacteristic
41#124×C47C2211yescharacteristic
42#97×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C2×Q8×C47C2312yes—
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C2×C4×D47D411yescharacteristic
49C2×C4×D47D411yescharacteristic
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—21no—
52Q16×C47—24no—
53SD16×C47—24no—
54C2×C8×C47C2312yes—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C22⋊C4×C47—21no—
58C22⋊C4×C47—21no—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—21no—
61C22⋊Dic47—21no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—22no—
66C4⋊Dic47—21no—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—22no—
74C4×Dic47—21no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80#10625324—24no—
81C23×C47—21no—
82C22×D47C2×D411yescharacteristic
83Q8×C47—22no—
84Q8×C47—22no—
85Q8×C47—22no—
86D4×C47—22no—
87C2×C4×C47—21no—
88C2×C4×C47—22no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—42no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—42no—
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C4×D47—22no—
101C4×D47—22no—
102C4×D47—41no—
103Dic94—42no—
104C8×C47#4114yes—
105C47⋊C8—22no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47—41no—
109C22×C47C22×D411yescharacteristic
110C2×D47—21no—
111C2×D47—21no—
112C2×D47—21no—
113C4×C47—21no—
114C4×C47—21no—
115C4×C47—41no—
116C4×C47—42no—
117C4×C47C2×#4112yes—
118Dic47—21no—
119Dic47—21no—
120Dic47—41no—
121Dic47—42no—
122Dic47—41no—
123Dic47#13712yes—
124#3172—471nomaximal, Sylow
125C2×C47—81no—
126C2×C47#53211yescharacteristic
127C2×C47C2×#13711yescharacteristic
128C2×C47#57511yescharacteristic
129D47—41no—
130#533—471no—
131#529—471no—
132#501—471no—
133#497D4711yescharacteristic, complemented
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×Q16C2×D4712yes—
143C2×SD16C2×D4712yes—
144C2×M16—472no—
145C4⋊Q8—471no—
146C4⋊Q8C2×D4711yescharacteristic
147#126—941no—
148#125—471no—
149#125—941no—
150#124C2×D4711yescharacteristic
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#107—472no—
165#106—472no—
166#103—472no—
167#103—472no—
168#103—472no—
169#102—472no—
170#97—471no—
171#97C2×D4711yescharacteristic
172C4×C8—472no—
173C2×Q8—941no—
174C2×Q8C22×D4711yescharacteristic
175C2×Q8C22×D4712yes—
176C2×D4—941no—
177C2×D4C22×D4711yescharacteristic
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—941no—
182Q16—24no—
183SD16—24no—
184M16—944no—
185C2×C8—472no—
186C2×C8C22×D4712yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—472no—
190C4⋊C4—471no—
191C4⋊C4—471no—
192C4⋊C4—941no—
193C4⋊C4—942no—
194C4⋊C4—942no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C22⋊C4—21no—
200C22⋊C4—21no—
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—21no—
212C23—471no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—1882no—
217D4—22no—
218D4—1882no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—471no—
222C2×C4—471no—
223C2×C4—471no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—941no—
227C2×C4—942no—
228C2×C4—941no—
229C2×C4—1881no—
230C2×C4—1882no—
231C2×C4D4×D4711yescharacteristic
232C2×C4D4×D4711yescharacteristic
233C2×C4C23×D4711yescharacteristic
234C8—942no—
235C8#1062535214yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—941no—
240C22—941no—
241C22—941no—
242C22C2×D4×D4711yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—472no—
248C4—941no—
249C4—941no—
250C4—1881no—
251C4—1881no—
252C4—1882no—
253C4C2×#1062535212yes—
254C2—81no—
255C2—1881no—
256C2#1568967111yescharacteristic
257C2#137×D4711yescharacteristic
258C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3172
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689532C2semidirect
4. #15689491C2semidirect
5. #15689482C2semidirect
6. #15689378C2semidirect
8. Q16×Dic47C2semidirect
9. SD16×Dic47C2semidirect
10. #15689075C2semidirect
11. C47×#497C2semidirect
133. #497D47semidirect
141. C47#3172semidirect