Finite Group Databasebeta

← #20253471

Subgroups — #20253471

Order 6016.

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

normal subgroups only

This group has 390 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#15689659C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3#15689436C211yesmaximal, characteristic
4#15689433C212yesmaximal, complemented
5#15689348C212yesmaximal, complemented
6#15689278C211yesmaximal, characteristic, complemented
7#15689264C211yesmaximal, characteristic
8#15689215C212yesmaximal, complemented
9#15689210C212yesmaximal, complemented
10#15689173C211yesmaximal, characteristic, complemented
11C47×#483C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C2×#10625337C2212yes—
14C2×#10625325C2212yes—
15#13094019—21no—
16#13094015C2211yescharacteristic
17#13094013C2211yescharacteristic
18#13094008—21no—
19#13093998C2211yescharacteristic
20Q8×Dic47C2211yescharacteristic
21#13093989—21no—
22#13093989—21no—
23#13093989C2212yes—
24#13093989C2212yes—
25#13093986C2211yescharacteristic
26(C22⋊D47)⋊C4—21no—
27#13093982—21no—
28C2×Dic47⋊C4—21no—
29C2×C4×Dic47—21no—
30C2×C4×Dic47C2211yescharacteristic
31#13093957C2212yes—
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093947C2212yes—
35#13093944C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37C8×Dic47C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×C47C2212yes—
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49C22×Dic47D411yescharacteristic
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×Dic94—21no—
53C2×Dic94—24no—
54C2×Dic94C2312yes—
55C2×C8×C47C2312yes—
56C4⋊C4×C47—21no—
57C4⋊C4×C47—21no—
58C4⋊C4×C47C2312yes—
59C4⋊C4×C47C2311yescharacteristic
60C22⋊C4×C47—21no—
61#10625337—24no—
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⋊Dic47C2311yescharacteristic
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—21no—
72C4×Dic47—22no—
73C4×Dic47—22no—
74C4×Dic47—21no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80#10625325—24no—
81C23×C47C2×D411yescharacteristic
82C22×D47—21no—
83Q8×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—42no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2411yescharacteristic
91C22⋊D47—42no—
92C2×Dic47—24no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101D188—22no—
102C4×D47—42no—
103Dic94—24no—
104Dic94—22no—
105Dic94#4114yes—
106C8×C47—22no—
107C47⋊C8—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47#13512yes—
111C22×C47C22×D411yescharacteristic
112C2×D47—41no—
113C2×D47—41no—
114C2×D47—41no—
115C4×C47—21no—
116C4×C47—41no—
117C4×C47—42no—
118C4×C47—41no—
119C4×C47C2×#4112yes—
120Dic47—24no—
121Dic47—21no—
122Dic47—21no—
123Dic47—21no—
124Dic47—41no—
125Dic47#13712yes—
126#3108—471nomaximal, Sylow
127C2×C47—22no—
128C2×C47#52511yescharacteristic
129C2×C47C2×#13511yescharacteristic
130C2×C47C2×#13711yescharacteristic
131D47—81no—
132#529—471no—
133C2×C4×Q8—471no—
134#483D4711yescharacteristic, complemented
135#480—471no—
136#479—472no—
137#464—472no—
138#451—471no—
139#448—471no—
140C4×Q16—472no—
141C4×SD16—472no—
142#431—471no—
143C47#310811yescharacteristic, complemented, Sylow
144C22×Q8—471no—
145C2×Q16—472no—
146C2×SD16—472no—
147#126—941no—
148#125—471no—
149#124—471no—
150#123—941no—
151C22⋊Q8C2×D4711yescharacteristic
152#121—471no—
153C4×Q8—471no—
154C4×Q8—472no—
155C4×Q8—472no—
156C4×Q8—941no—
157C4×Q8—941no—
158C4×D4—471no—
159C4×D4—941no—
160#117—941no—
161C2×C4⋊C4—941no—
162C2×C4⋊C4C2×D4711yescharacteristic
163C2×C42—471no—
164C2×C42—941no—
165#107—472no—
166#106C2×D4712yes—
167C4⋊C8—472no—
168#103—472no—
169#103—472no—
170#103C2×D4712yes—
171#102—472no—
172C22⋊C8—471no—
173C22⋊C8C2×D4711yescharacteristic
174C4×C8—472no—
175C2×Q8—472no—
176C2×Q8—944no—
177C2×Q8—941no—
178C2×Q8C22×D4711yescharacteristic
179C2×D4—471no—
180C2×D4—941no—
181C22×C4—21no—
182C22×C4—471no—
183C22×C4—471no—
184C22×C4—941no—
185C22×C4—941no—
186C22×C4C22×D4711yescharacteristic
187Q16—944no—
188SD16—944no—
189C2×C8—472no—
190C2×C8C22×D4712yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—471no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4C22×D4712yes—
200C4⋊C4C22×D4711yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—941no—
203C22⋊C4—941no—
204C22⋊C4—941no—
205C22⋊C4—941no—
206C42—471no—
207C42—471no—
208C42—471no—
209C42—471no—
210C42—942no—
211C42—942no—
212C42—941no—
213C23—941no—
214C23D4×D4711yescharacteristic
215Q8—22no—
216Q8—474no—
217Q8—944no—
218Q8—942no—
219D4—942no—
220D4—1882no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—471no—
227C2×C4—471no—
228C2×C4—471no—
229C2×C4—471no—
230C2×C4—942no—
231C2×C4—944no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—941no—
235C2×C4—1882no—
236C2×C4D4×D4711yescharacteristic
237C2×C4C23×D4711yescharacteristic
238C8—22no—
239C8—942no—
240C22—21no—
241C22—21no—
242C22—1881no—
243C22—1881no—
244C22—1881no—
245C22#1309404512yes—
246C22C2×D4×D4711yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—472no—
252C4—944no—
253C4—941no—
254C4—941no—
255C4—941no—
256C4—1881no—
257C4#41×D4712yes—
258C2—22no—
259C2—3761no—
260C2#1568963111yescharacteristic
261C2C2×#1309404511yescharacteristic
262C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
4. #15689433C2semidirect
5. #15689348C2semidirect
6. #15689278C2semidirect
8. #15689215C2semidirect
9. #15689210C2semidirect
10. #15689173C2semidirect
11. C47×#483C2semidirect
134. #483D47semidirect
143. C47#3108semidirect