Finite Group Databasebeta

← #20253507

Subgroups — #20253507

Order 6016.

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

normal subgroups only

This group has 424 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#15689668C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3#15689436C211yesmaximal, characteristic, complemented
4#15689417C212yesmaximal, complemented
5#15689322C212yesmaximal, complemented
6#15689264C211yesmaximal, characteristic, complemented
7#15689261C211yesmaximal, characteristic, complemented
8#15689222C212yesmaximal, complemented
9#15689220C212yesmaximal, complemented
10#15689177C211yesmaximal, characteristic, complemented
11C47×#480C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C22×Dic94C2211yescharacteristic
14C2×#10625325C2212yes—
15C2×#10625335C2212yes—
16#13094023C2211yescharacteristic
17#13094020C2211yescharacteristic
18#13094010—21no—
19#13093998C2211yescharacteristic
20#13093996—21no—
21#13093989—21no—
22#13093989—21no—
23#13093989C2212yes—
24#13093989C2212yes—
25D4×Dic47C2211yescharacteristic
26#13093986C2211yescharacteristic
27(C22⋊D47)⋊C4—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
37#13093934C2212yes—
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yes—
41#102×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—21no—
48C2×C22⋊D47—21no—
49C2×C22⋊D47—21no—
50C22×Dic47—21no—
51C22×Dic47—21no—
52C22×Dic47D411yescharacteristic
53C22×Dic47D411yescharacteristic
54#10625352—44no—
55C2×D188C2311yescharacteristic
56C2×C4×D47—21no—
57C2×Dic94—21no—
58C2×Dic94—24no—
59C2×Dic94—21no—
60C2×Dic94C2312yes—
61C2×C8×C47C2312yes—
62C4⋊C4×C47—21no—
63C4⋊C4×C47C2311yescharacteristic
64C4⋊C4×C47C2312yes—
65C22⋊C4×C47—21no—
66C22⋊Dic47—21no—
67#10625335—24no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—21no—
70C4⋊Dic47C2311yescharacteristic
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—21no—
74C4×Dic47—22no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81#10625325—24no—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—21no—
85D4×C47—22no—
86D4×C47—42no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—42no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—42no—
94C22⋊D47—42no—
95C22⋊D47—42no—
96C2×Dic47—24no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—42no—
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C2×Dic47C2×D411yescharacteristic
106D188—22no—
107C4×D47—42no—
108Dic94—24no—
109Dic94—22no—
110Dic94—42no—
111Dic94#4114yescomplemented
112C8×C47—22no—
113C47⋊C8—22no—
114C22×C47—21no—
115C22×C47—21no—
116C22×C47—41no—
117C22×C47—41no—
118C22×C47—41no—
119C22×C47AGL(1,ℤ/8)12yes—
120C22×C47C22×D411yescharacteristic
121C2×D47—41no—
122C2×D47—41no—
123C2×D47—41no—
124C4×C47—21no—
125C4×C47—41no—
126C4×C47—42no—
127C4×C47C2×#4112yes—
128Dic47—24no—
129Dic47—21no—
130Dic47—21no—
131Dic47—21no—
132Dic47—41no—
133Dic47#13712yes—
134#3112—471nomaximal, Sylow
135C2×C47—22no—
136C2×C47—81no—
137C2×C47#52511yescharacteristic
138C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C47C2×#13711yescharacteristic
140D47—81no—
141#532—471no—
142C2×C4×Q8—471no—
143#480—471no—
144#480D4711yescharacteristic, complemented
145#477—472no—
146#460—472no—
147#448—471no—
148#448—471no—
149#440—472no—
150#440—472no—
151#432—471no—
152C47#311211yescharacteristic, complemented, Sylow
153C2×#41—941no—
154C22×Q8—471no—
155C2×SD16—472no—
156C2×SD16—472no—
157C4⋊Q8—471no—
158#127—471no—
159#124—941no—
160#121—471no—
161#121—941no—
162#121C2×D4711yescharacteristic
163C4×Q8—472no—
164C4×Q8—472no—
165C4×Q8—941no—
166C4×Q8—941no—
167C4×D4—471no—
168C4×D4—471no—
169C4×D4—941no—
170C2×C4⋊C4—941no—
171C2×C4⋊C4C2×D4711yescharacteristic
172C2×C42—471no—
173C2×C42—941no—
174#107—472no—
175#107C2×D4712yes—
176C4⋊C8—472no—
177#103—472no—
178#103—472no—
179#102—472no—
180#102C2×D4712yes—
181C22⋊C8—471no—
182C22⋊C8C2×D4711yescharacteristic
183#97—472no—
184#41—1884no—
185C2×Q8—472no—
186C2×Q8—941no—
187C2×Q8—944no—
188C2×Q8—941no—
189C2×D4—21no—
190C2×D4—471no—
191C2×D4—941no—
192C2×D4—941no—
193C2×D4—941no—
194C2×D4C22×D4711yescharacteristic
195C22×C4—21no—
196C22×C4—471no—
197C22×C4—471no—
198C22×C4—941no—
199C22×C4—941no—
200C22×C4—941no—
201C22×C4C22×D4711yescharacteristic
202SD16—944no—
203SD16—944no—
204C2×C8—472no—
205C2×C8C22×D4712yes—
206C4⋊C4—21no—
207C4⋊C4—471no—
208C4⋊C4—942no—
209C4⋊C4—942no—
210C4⋊C4—941no—
211C4⋊C4C22×D4712yes—
212C4⋊C4C22×D4711yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—941no—
215C22⋊C4—941no—
216C22⋊C4—941no—
217C42—471no—
218C42—471no—
219C42—471no—
220C42—471no—
221C42—942no—
222C42—942no—
223C23—21no—
224C23—941no—
225C23D4×D4711yescharacteristic
226Q8—474no—
227Q8—944no—
228Q8—942no—
229Q8—1882no—
230D4—22no—
231D4—42no—
232D4—942no—
233D4—1882no—
234D4—1882no—
235D4—1882no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—471no—
241C2×C4—471no—
242C2×C4—471no—
243C2×C4—471no—
244C2×C4—942no—
245C2×C4—944no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—941no—
249C2×C4—1882no—
250C2×C4—1882no—
251C2×C4D4×D4711yescharacteristic
252C2×C4C23×D4711yescharacteristic
253C8—22no—
254C8—942no—
255C22—21no—
256C22—21no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—1881no—
261C22—1881no—
262C22—1881no—
263C22#1309404812yes—
264C22C2×D4×D4711yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—472no—
269C4—944no—
270C4—941no—
271C4—941no—
272C4—941no—
273C4—1881no—
274C4#41×D4712yes—
275C2—22no—
276C2—81no—
277C2—3761no—
278C2#1568963111yescharacteristic
279C2C2×#1309404811yescharacteristic
280C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3112
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
3. #15689436C2semidirect
4. #15689417C2semidirect
5. #15689322C2semidirect
6. #15689264C2semidirect
7. #15689261C2semidirect
8. #15689222C2semidirect
9. #15689220C2semidirect
10. #15689177C2semidirect
11. C47×#480C2semidirect
111. Dic94#41semidirect
144. #480D47semidirect
152. C47#3112semidirect