Finite Group Databasebeta

← #20253075

Subgroups — #20253075

Order 6016.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094031C211yesmaximal, characteristic, complemented
3#15689701C211yesmaximal, characteristic
4#15689379C212yesmaximal, complemented
5#15689371C212yesmaximal, complemented
6#15689362C212yesmaximal, complemented
7#15689354C212yesmaximal, complemented
8#15689166C211yesmaximal, characteristic, complemented
9#15689117C211yesmaximal, characteristic, complemented
10C2×#13093948C211yesmaximal, characteristic, complemented
11C47×#536C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13#13094055—24no—
14C2×#10625337C2212yes—
15C2×#10625336C2212yes—
16#13094031—24no—
17C2×#10625329C2212yes—
18C2×#10625329C2211yescharacteristic
19C22×C47⋊C8C2212yes—
20C22×C47⋊C8C2211yescharacteristic
21#13094003C2212yes—
22#13094000—21no—
23#13093998C2212yes—
24#13093996—22no—
25#13093995—21no—
26C2×C4⋊Dic47C2211yescharacteristic
27#13093957C2212yes—
28#13093955C2212yes—
29#13093948C2212yes—
30#13093948C2212yes—
31#13093947C2211yescharacteristic
32#13093947C2211yescharacteristic
33#13093944C2211yescharacteristic
34#13093944C2211yescharacteristic
35C2×#41×C47C2211yescharacteristic
36C22×Q8×C47C2211yescharacteristic
37C4⋊Q8×C47—21no—
38#124×C47—21no—
39#123×C47—22no—
40C22⋊Q8×C47C2212yes—
41C22⋊Q8×C47C2212yes—
42#117×C47C2211yescharacteristic
43#41×C47—22no—
44#41×C47—22no—
45C2×Q8×C47—21no—
46C2×Q8×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47D411yescharacteristic
49C2×Q8×C47C2312yes—
50C2×D4×C47D412yes—
51C2×D4×C47D411yescharacteristic
52C22×C4×C47—21no—
53C22×C4×C47C2312yes—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—21no—
56C2×C22⋊D47—22no—
57C22×Dic47—21no—
58#10625350—22no—
59#10625350—22no—
60C2×D188C2311yescharacteristic
61C2×C4×D47—21no—
62C2×Dic94C2311yescharacteristic
63C4⋊C4×C47—22no—
64C4⋊C4×C47—22no—
65C4⋊C4×C47C2311yescharacteristic
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68C22⋊C4×C47—22no—
69C22⋊C4×C47—22no—
70C42×C47—21no—
71C22⋊Dic47—22no—
72#10625337—24no—
73#10625336—24no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47—21no—
76C4⋊Dic47C2312yes—
77Dic47⋊C4—22no—
78#10625329—24no—
79#10625329D414yescomplemented
80C2×C47⋊C8—22no—
81C2×C47⋊C8—24no—
82C2×C47⋊C8C2311yescharacteristic
83C2×C47⋊C8C2311yescharacteristic
84C2×C47⋊C8C2312yes—
85C23×C47C2×D412yes—
86C23×C47C2×D411yescharacteristic
87C22×D47—21no—
88Q8×C47—22no—
89Q8×C47—22no—
90Q8×C47—22no—
91Q8×C47—42no—
92D4×C47—24no—
93D4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—22no—
99C2×C4×C47—42no—
100C2×C4×C47C2×D412yes—
101C2×C4×C47C2×D412yes—
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47#4112yes—
104C2×C4×C47C2411yescharacteristic
105C22⋊D47—42no—
106C22⋊D47—82no—
107C2×Dic47—21no—
108C2×Dic47—22no—
109C2×Dic47—81no—
110D188—21no—
111D188—21no—
112C4×D47—42no—
113Dic94—21no—
114Dic94—21no—
115C47⋊C8—21no—
116C47⋊C8—21no—
117C47⋊C8C2×D414yes—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—22no—
123C22×C47#12112yes—
124C22×C47C22×D411yescharacteristic
125C2×D47—41no—
126C2×D47—41no—
127C2×D47—41no—
128C4×C47—22no—
129C4×C47—42no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47#12112yes—
133C4×C47C22×D411yescharacteristic
134C4×C47C2×#4111yescharacteristic
135Dic47—41no—
136Dic47—42no—
137#3063—471nomaximal, Sylow
138C2×C47—22no—
139C2×C47—42no—
140C2×C47C2×#12111yescharacteristic
141C2×C47#57711yescharacteristic
142C2×C47#57811yescharacteristic
143D47—81no—
144C2×#137—471no—
145C2×#131—471no—
146#537—471no—
147#536D4711yescharacteristic, complemented
148#470—472no—
149#468—472no—
150#467—472no—
151#465—472no—
152#428—471no—
153#416—471no—
154C2×#103—471no—
155C47#306311yescharacteristic, complemented, Sylow
156C2×#41—471no—
157C2×#41C2×D4711yescharacteristic
158C22×Q8C2×D4711yescharacteristic
159#137—944no—
160C2×Q16—472no—
161C2×SD16—472no—
162#131—944no—
163C2×M16—471no—
164C2×M16—472no—
165C22×C8—471no—
166C22×C8—472no—
167C4⋊Q8—21no—
168#124—21no—
169#123—22no—
170C22⋊Q8—472no—
171C22⋊Q8—941no—
172C22⋊Q8C2×D4712yes—
173C22⋊Q8C2×D4712yes—
174#121—472no—
175#121—941no—
176#121—942no—
177#117C2×D4711yescharacteristic
178C2×C4⋊C4—471no—
179#107—472no—
180#106—472no—
181#103—472no—
182#103—472no—
183#103—471no—
184#103—471no—
185#102—471no—
186#102—471no—
187#41—22no—
188#41—22no—
189#41—942no—
190#41—942no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—471no—
195C2×Q8C22⋊D4711yescharacteristic
196C2×Q8C22×D4712yes—
197C2×D4—471no—
198C2×D4—942no—
199C2×D4—941no—
200C2×D4C22⋊D4712yes—
201C2×D4C22⋊D4711yescharacteristic
202C22×C4—21no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4C22×D4712yes—
206C22×C4C22×D4711yescharacteristic
207Q16—944no—
208SD16—944no—
209M16—474no—
210M16—944no—
211C2×C8—472no—
212C2×C8—471no—
213C2×C8—471no—
214C2×C8—944no—
215C2×C8—942no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—472no—
219C4⋊C4—942no—
220C4⋊C4—941no—
221C4⋊C4C22×D4711yescharacteristic
222C4⋊C4C22×D4711yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C22⋊C4—942no—
227C22⋊C4—942no—
228C42—21no—
229C23—941no—
230C23C2×C22⋊D4712yes—
231C23C2×C22⋊D4711yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—22no—
235Q8—42no—
236Q8—941no—
237Q8—941no—
238D4—24no—
239D4—22no—
240D4—941no—
241D4—941no—
242D4—3762no—
243D4—1882no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—42no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—3761no—
253C2×C4—1882no—
254C2×C4D4×D4712yes—
255C2×C4#1062535212yes—
256C2×C4C2×C22⋊D4712yes—
257C2×C4C2×C22⋊D4711yescharacteristic
258C2×C4C23×D4711yescharacteristic
259C8—474no—
260C8—941no—
261C8—941no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—1881no—
268C22—1881no—
269C22—1881no—
270C22#1309399612yes—
271C22C22×C22⋊D4711yescharacteristic
272C4—22no—
273C4—42no—
274C4—41no—
275C4—41no—
276C4—1881no—
277C4—1882no—
278C4#1309399612yes—
279C4C2×D4×D4711yescharacteristic
280C4C2×#1062535211yescharacteristic
281C2—22no—
282C2—42no—
283C2—3761no—
284C2C2×#1309399611yescharacteristic
285C2#1568993111yescharacteristic
286C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3063
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094031C2semidirect
4. #15689379C2semidirect
5. #15689371C2semidirect
6. #15689362C2semidirect
7. #15689354C2semidirect
8. #15689166C2semidirect
9. #15689117C2semidirect
10. C2×#13093948C2semidirect
11. C47×#536C2semidirect
79. #10625329D4semidirect
147. #536D47semidirect
155. C47#3063semidirect