Finite Group Databasebeta

← #20253077

Subgroups — #20253077

Order 6016.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094030C211yesmaximal, characteristic, complemented
3#15689704C211yesmaximal, characteristic
4#15689697C211yesmaximal, characteristic, complemented
5#15689380C212yesmaximal, complemented
6#15689372C212yesmaximal, complemented
7#15689363C212yesmaximal, complemented
8#15689355C212yesmaximal, complemented
9#15689163C211yesmaximal, characteristic, complemented
10#15689120C211yesmaximal, characteristic, complemented
11C2×#103×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14#13094055—24no—
15C2×#10625337C2212yes—
16C2×#10625336C2212yes—
17#13094030—24no—
18C2×#10625329C2211yescharacteristic
19C2×#10625324C2212yes—
20C2×C8×D47C2212yes—
21#13094022—21no—
22#13094013—21no—
23#13094007—22no—
24#13094004—21no—
25#13094004C2212yes—
26#13094000C2212yes—
27#13094000C2212yes—
28#13093999—21no—
29#13093999C2212yes—
30#13093998—22no—
31#13093983C2211yescharacteristic
32#13093957C2212yes—
33#13093955C2212yes—
34#13093949C2211yescharacteristic
35#13093949C2211yescharacteristic
36#13093946C2211yescharacteristic
37#13093946C2211yescharacteristic
38C22×Q8×C47C2211yescharacteristic
39C22×C8×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41#103×C47C2212yes—
42#103×C47C2212yes—
43C2×Q8×C47—21no—
44C2×Q8×C47—22no—
45C2×Q8×C47—22no—
46C2×Q8×C47C2312yes—
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47D412yes—
52#10625350—22no—
53#10625350—22no—
54#10625350—22no—
55#10625350—22no—
56C2×D188—22no—
57C2×D188D411yescharacteristic
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×C4×D47C2312yes—
61C2×Dic94D411yescharacteristic
62C2×Dic94C2311yescharacteristic
63C2×C8×C47—22no—
64C2×C8×C47C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2312yes—
68C22⋊Dic47—21no—
69#10625337—24no—
70#10625336—24no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47—22no—
76C4⋊Dic47C2311yescharacteristic
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—22no—
79Dic47⋊C4—22no—
80C4×Dic47—21no—
81#10625329D414yescomplemented
82C2×C47⋊C8C2312yes—
83#10625324—24no—
84C8×D47—24no—
85C23×C47C2×D411yescharacteristic
86C22×D47—21no—
87C22×D47C2×D412yes—
88Q8×C47—22no—
89Q8×C47—22no—
90Q8×C47—42no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—42no—
94C2×C4×C47—81no—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47#4112yes—
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—24no—
100C22⋊D47—42no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47C2×D412yes—
105D188—22no—
106D188—21no—
107D188—21no—
108D188—82no—
109C4×D47—22no—
110C4×D47—22no—
111C4×D47—42no—
112Dic94—22no—
113Dic94—21no—
114Dic94—21no—
115C8×C47—21no—
116C8×C47—21no—
117C47⋊C8C2×D414yes—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47#12112yes—
121C22×C47C22×D411yescharacteristic
122C2×D47—22no—
123C2×D47—22no—
124C2×D47—22no—
125C2×D47—41no—
126C2×D47—41no—
127C2×D47—41no—
128C4×C47—42no—
129C4×C47—42no—
130C4×C47#12112yes—
131C4×C47C22×D411yescharacteristic
132C4×C47C2×#4111yescharacteristic
133Dic47—22no—
134Dic47—41no—
135Dic47—41no—
136Dic47—41no—
137#3063—471nomaximal, Sylow
138C2×C47—22no—
139C2×C47C2×#12111yescharacteristic
140C2×C47#57711yescharacteristic
141C2×C47#57811yescharacteristic
142D47—42no—
143D47—81no—
144C2×#137—471no—
145C2×#131—471no—
146#537—471no—
147#536—471no—
148#470—472no—
149#468—472no—
150#467—472no—
151#465—472no—
152#428—471no—
153#416—471no—
154C2×#103D4711yescharacteristic, complemented
155C47#306311yescharacteristic, complemented, Sylow
156C2×#41—471no—
157C2×#41—471no—
158C22×Q8C2×D4711yescharacteristic
159#137—944no—
160C2×Q16—472no—
161C2×SD16—472no—
162#131—944no—
163C2×M16—471no—
164C2×M16—472no—
165C22×C8—472no—
166C22×C8C2×D4711yescharacteristic
167C4⋊Q8—941no—
168#124—941no—
169#123—942no—
170C22⋊Q8—472no—
171C22⋊Q8—472no—
172C22⋊Q8—472no—
173C22⋊Q8—941no—
174#121—472no—
175#121—941no—
176#121—942no—
177#117—471no—
178C2×C4⋊C4C2×D4711yescharacteristic
179#107—472no—
180#106—472no—
181#103—471no—
182#103—471no—
183#103C2×D4712yes—
184#103C2×D4712yes—
185#102—471no—
186#102—471no—
187#41—942no—
188#41—942no—
189#41—942no—
190#41—942no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—471no—
195C2×Q8—471no—
196C2×Q8C22×D4712yes—
197C2×D4—472no—
198C2×D4—471no—
199C2×D4—471no—
200C2×D4—942no—
201C2×D4—941no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—472no—
205C22×C4—941no—
206C22×C4C22×D4711yescharacteristic
207Q16—944no—
208SD16—944no—
209M16—474no—
210M16—944no—
211C2×C8—22no—
212C2×C8—472no—
213C2×C8—944no—
214C2×C8C22×D4711yescharacteristic
215C2×C8C22×D4711yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—471no—
218C4⋊C4—471no—
219C4⋊C4—942no—
220C4⋊C4—942no—
221C4⋊C4—942no—
222C4⋊C4C22×D4712yes—
223C22⋊C4—942no—
224C22⋊C4—942no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C22⋊C4—941no—
228C42—941no—
229C23—472no—
230C23—941no—
231C23D4×D4711yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—42no—
235Q8—942no—
236Q8—941no—
237Q8—941no—
238D4—944no—
239D4—942no—
240D4—941no—
241D4—941no—
242D4—3762no—
243D4—1882no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—472no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—941no—
253C2×C4—941no—
254C2×C4—1882no—
255C2×C4#1062535012yes—
256C2×C4D4×D4711yescharacteristic
257C2×C4D4×D4712yes—
258C2×C4C23×D4711yescharacteristic
259C8—21no—
260C8—21no—
261C8—474no—
262C22—21no—
263C22—21no—
264C22—942no—
265C22—942no—
266C22—942no—
267C22—1881no—
268C22—1881no—
269C22—1881no—
270C22#1309399712yes—
271C22C2×D4×D4711yescharacteristic
272C4—42no—
273C4—42no—
274C4—942no—
275C4—1881no—
276C4—1881no—
277C4—1881no—
278C4#1309399712yes—
279C4C2×D4×D4711yescharacteristic
280C4C2×#1062535011yescharacteristic
281C2—22no—
282C2—3761no—
283C2—1882no—
284C2C2×#1309399711yescharacteristic
285C2#1568992911yescharacteristic
286C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC22×C47C22×D4
hypercenterC2×#103D47
hypocenterC47#3063
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094030C2semidirect
4. #15689697C2semidirect
5. #15689380C2semidirect
6. #15689372C2semidirect
7. #15689363C2semidirect
8. #15689355C2semidirect
9. #15689163C2semidirect
10. #15689120C2semidirect
11. C2×#103×C47C2semidirect
81. #10625329D4semidirect
154. C2×#103D47semidirect
155. C47#3063semidirect