Finite Group Databasebeta

← #20255337

Subgroups — #20255337

Order 6016.

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

normal subgroups only

This group has 408 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#15689839C211yesmaximal, characteristic, complemented
2#15689793C211yesmaximal, characteristic, complemented
3#15689446C212yesmaximal, complemented
4#15689415C211yesmaximal, characteristic, complemented
5#15689358C212yesmaximal, complemented
6#15689315C211yesmaximal, characteristic, complemented
7#15689269C212yesmaximal, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9C8×D188C211yesmaximal, characteristic, complemented
10#15689116C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×#10625352C2212yes—
13C2×#10625325C2211yescharacteristic
14C2×#10625334C2212yes—
15C2×C8×D47C2212yes—
16#13094020—21no—
17#13094013—22no—
18#13093999—21no—
19#13093999C2212yes—
20#13093996—22no—
21#13093995C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24C4×D188C2211yescharacteristic
25D4×Dic47—21no—
26#13093982—21no—
27#13093982C2212yes—
28#13093957C2212yes—
29#13093956C2211yescharacteristic
30C4⋊(C47⋊C8)C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093945C2212yes—
35(C2×D47)⋊C8C2212yes—
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—24no—
49#10625352—42no—
50C2×D188—22no—
51C2×D188D411yescharacteristic
52C2×D188C2311yescharacteristic
53C2×C4×D47—21no—
54C2×C4×D47C2312yes—
55C2×Dic94C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C2×C8×C47C2311yescharacteristic
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2312yes—
60C42×C47C2311yescharacteristic
61C22⋊Dic47—22no—
62#10625334—42no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71C4×Dic47—21no—
72C4×Dic47—22no—
73C2×C47⋊C8C2312yes—
74#10625325—22no—
75C8×D47—42no—
76C23×C47—22no—
77C22×D47—21no—
78C22×D47C2×D412yes—
79Q8×C47—81no—
80D4×C47—22no—
81D4×C47—22no—
82D4×C47—42no—
83D4×C47—81no—
84C2×C4×C47—22no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—44no—
89C22⋊D47—82no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—44no—
94C2×Dic47C2×D412yes—
95D188—22no—
96D188—21no—
97D188—21no—
98D188—82no—
99C4×D47—22no—
100C4×D47—22no—
101C4×D47—42no—
102Dic94—21no—
103Dic94#4112yes—
104C8×C47—21no—
105C8×C47—21no—
106C47⋊C8—22no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47C22×D411yescharacteristic
111C2×D47—22no—
112C2×D47—22no—
113C2×D47—22no—
114C2×D47—41no—
115C2×D47—41no—
116C2×D47—41no—
117C4×C47—21no—
118C4×C47—42no—
119C4×C47#13512yes—
120C4×C47C2×#4111yescharacteristic
121C4×C47H(5,𝔽2)11yescharacteristic
122Dic47—22no—
123Dic47—22no—
124Dic47—41no—
125Dic47—41no—
126#3305—471nomaximal, Sylow
127C2×C47—82no—
128C2×C47#54611yescharacteristic
129C2×C47C2×#13511yescharacteristic
130C2×C47#57611yescharacteristic
131D47—42no—
132D47—81no—
133#555—471no—
134#550—471no—
135#486D4711yescharacteristic, complemented
136#482—472no—
137#477—471no—
138#466—472no—
139#459—471no—
140#449—472no—
141C4×SD16—471no—
142C8×D4—471no—
143#416—472no—
144C47#330511yescharacteristic, complemented, Sylow
145C2×#41—472no—
146C2×SD16—471no—
147C2×D8—472no—
148C22×C8—472no—
149C4⋊Q8C2×D4711yescharacteristic
150#127—941no—
151#127C2×D4711yescharacteristic
152#124—942no—
153#121—472no—
154#121—472no—
155#121—942no—
156#121—941no—
157C4×Q8—471no—
158C4×D4—471no—
159C4×D4—471no—
160C4×D4—941no—
161#117—472no—
162#117—941no—
163#107—472no—
164#106—471no—
165C4⋊C8—471no—
166#103—471no—
167#103—472no—
168#102—472no—
169#102—471no—
170#102C2×D4712yes—
171#102C2×D4712yes—
172C22⋊C8—472no—
173C4×C8C2×D4711yescharacteristic
174#41—944no—
175#41—1882no—
176C2×Q8—21no—
177C2×Q8—471no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—471no—
181C2×D4—471no—
182C2×D4—942no—
183C2×D4—942no—
184C2×D4—942no—
185C2×D4C22×D4712yes—
186C22×C4—472no—
187C22×C4—942no—
188C22×C4—941no—
189SD16—942no—
190D8—1882no—
191C2×C8—472no—
192C2×C8—1882no—
193C2×C8C22×D4711yescharacteristic
194C2×C8C22×D4711yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—471no—
197C4⋊C4—471no—
198C4⋊C4—471no—
199C4⋊C4—941no—
200C4⋊C4C22×D4712yes—
201C22⋊C4—472no—
202C22⋊C4—942no—
203C22⋊C4—942no—
204C22⋊C4—942no—
205C22⋊C4—941no—
206C42—942no—
207C42—941no—
208C42C22×D4711yescharacteristic
209C23—22no—
210C23—472no—
211C23—941no—
212Q8—81no—
213Q8—472no—
214Q8—941no—
215D4—22no—
216D4—22no—
217D4—42no—
218D4—81no—
219D4—942no—
220D4—941no—
221D4—941no—
222D4—3762no—
223D4—3762no—
224D4—1884no—
225C2×C4—22no—
226C2×C4—472no—
227C2×C4—941no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—1884no—
233C2×C4—1882no—
234C2×C4D4×D4711yescharacteristic
235C2×C4D4×D4711yescharacteristic
236C2×C4C23×D4711yescharacteristic
237C8—21no—
238C8—21no—
239C8—942no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—942no—
244C22—942no—
245C22—942no—
246C22—1881no—
247C22—1881no—
248C22—1881no—
249C22C2×D4×D4711yescharacteristic
250C4—21no—
251C4—42no—
252C4—942no—
253C4—942no—
254C4—1881no—
255C4—1881no—
256C4#1309404512yes—
257C4#41×D4711yescharacteristic
258C4#1309407011yescharacteristic
259C2—82no—
260C2—3761no—
261C2—1882no—
262C2#1568976611yescharacteristic
263C2C2×#1309404511yescharacteristic
264C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3305
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. #15689839C2semidirect
2. #15689793C2semidirect
3. #15689446C2semidirect
4. #15689415C2semidirect
5. #15689358C2semidirect
6. #15689315C2semidirect
7. #15689269C2semidirect
8. C4×#10625325C2semidirect
9. C8×D188C2semidirect
10. #15689116C2semidirect
11. C47×#486C2semidirect
135. #486D47semidirect
144. C47#3305semidirect