Finite Group Databasebeta

← #20252943

Subgroups — #20252943

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×#13094046C211yesmaximal, characteristic
3#15689697C211yesmaximal, characteristic, complemented
4#15689604C211yesmaximal, characteristic, complemented
5#15689348C212yesmaximal, complemented
6#15689341C212yesmaximal, complemented
7#15689332C212yesmaximal, complemented
8#15689327C212yesmaximal, complemented
9#15689149C211yesmaximal, characteristic, complemented
10#15689122C211yesmaximal, characteristic, complemented
11C2×#103×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C2×#10625350C2211yescharacteristic
14#13094055—24no—
15#13094046—24no—
16C2×Dic188C2211yescharacteristic
17C2×#10625337C2212yes—
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×#10625336C2212yes—
21C2×D376C2211yescharacteristic
22C2×#10625329C2211yescharacteristic
23#13094022C2212yes—
24#13094013C2212yes—
25#13094007—22no—
26#13094000—21no—
27#13094000—21no—
28#13093989C2212yes—
29#13093986C2212yes—
30C4×C22⋊D47—22no—
31#13093983C2211yescharacteristic
32#13093982—21no—
33C4⋊C4×D47—21no—
34Dic47⋊C8C2212yes—
35Dic47⋊C8C2212yes—
36#13093947C2212yes—
37#13093944C2212yes—
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⋊D47—21no—
52#10625350—22no—
53#10625350—22no—
54#10625350—22no—
55#10625350D414yes—
56C2×D188C2311yescharacteristic
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×C4×D47—21no—
60C2×C4×D47—22no—
61C2×Dic94C2311yescharacteristic
62C2×Dic94C2311yescharacteristic
63C2×C8×C47—22no—
64C2×C8×C47C2311yescharacteristic
65C2×C8×C47C2311yescharacteristic
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2312yes—
68C22⋊Dic47D412yes—
69#10625337—24no—
70#10625336—24no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—22no—
74C4⋊Dic47D411yescharacteristic
75C4⋊Dic47D411yescharacteristic
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—22no—
79C4×Dic47—22no—
80C4×Dic47C2312yes—
81#10625329—22no—
82C2×C47⋊C8C2312yes—
83Dic188—22no—
84D376—22no—
85#10625325—22no—
86#10625325—22no—
87C23×C47C2×D411yescharacteristic
88C22×D47—21no—
89C22×D47—21no—
90Q8×C47—22no—
91Q8×C47—22no—
92Q8×C47—42no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—42no—
96C2×C4×C47—81no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2×D412yes—
99C2×C4×C47#4112yes—
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—24no—
102C22⋊D47—42no—
103C2×Dic47—21no—
104C2×Dic47—21no—
105C2×Dic47C2×D412yes—
106C2×Dic47C2×D412yes—
107D188—21no—
108D188—21no—
109D188—21no—
110D188C2×D412yes—
111C4×D47—24no—
112C4×D47—42no—
113C4×D47—82no—
114Dic94—21no—
115Dic94—21no—
116Dic94—21no—
117Dic94C2×D412yes—
118C8×C47—21no—
119C8×C47—21no—
120C47⋊C8—22no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47#12112yes—
124C22×C47C22×D411yescharacteristic
125C2×D47—22no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—41no—
130C2×D47—41no—
131C4×C47—42no—
132C4×C47—42no—
133C4×C47#12112yes—
134C4×C47C22×D411yescharacteristic
135C4×C47C2×#4111yescharacteristic
136Dic47—22no—
137Dic47—22no—
138Dic47—22no—
139Dic47—41no—
140#3046—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47C2×#12111yescharacteristic
143C2×C47#57711yescharacteristic
144C2×C47#57811yescharacteristic
145D47—42no—
146D47—81no—
147C2×#137—471no—
148C2×#135—471no—
149#536—471no—
150#520—471no—
151#464—472no—
152#463—472no—
153#462—472no—
154#461—472no—
155#424—471no—
156#417—471no—
157C2×#103D4711yescharacteristic, complemented
158C47#304611yescharacteristic, complemented, Sylow
159C2×#41—471no—
160C2×#41—471no—
161C22×Q8C2×D4711yescharacteristic
162#137—944no—
163#135—944no—
164C2×Q16—472no—
165C2×Q16—471no—
166C2×SD16—472no—
167C2×SD16—471no—
168C2×SD16—471no—
169C2×D8—471no—
170C2×M16—471no—
171C22×C8C2×D4711yescharacteristic
172C4⋊Q8—472no—
173#124—472no—
174#123—942no—
175C22⋊Q8—941no—
176C22⋊Q8—941no—
177C4×Q8—472no—
178C4×D4—472no—
179C4×D4—942no—
180#117—471no—
181#117—941no—
182C2×C4⋊C4—941no—
183C2×C4⋊C4C2×D4711yescharacteristic
184C4⋊C8—472no—
185C4⋊C8—472no—
186#103—472no—
187#103C2×D4712yes—
188#103C2×D4712yes—
189#102—472no—
190#41—474no—
191#41—942no—
192#41—942no—
193#41—942no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—471no—
198C2×Q8—471no—
199C2×Q8C22×D4712yes—
200C2×D4—471no—
201C2×D4—471no—
202C2×D4—941no—
203C2×D4—941no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—942no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4C22×D4711yescharacteristic
210Q16—942no—
211Q16—944no—
212SD16—942no—
213SD16—942no—
214SD16—944no—
215D8—942no—
216M16—942no—
217C2×C8—22no—
218C2×C8—472no—
219C2×C8C22×D4711yescharacteristic
220C2×C8C22×D4711yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—471no—
223C4⋊C4—471no—
224C4⋊C4—942no—
225C4⋊C4—942no—
226C4⋊C4—942no—
227C4⋊C4C22×D4712yes—
228C22⋊C4—472no—
229C22⋊C4—942no—
230C22⋊C4—942no—
231C22⋊C4—942no—
232C42—472no—
233C42—942no—
234C23—941no—
235C23—941no—
236C23D4×D4711yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—472no—
241Q8—941no—
242Q8—941no—
243Q8—941no—
244D4—472no—
245D4—944no—
246D4—941no—
247D4—941no—
248D4—941no—
249D4—1882no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—472no—
255C2×C4—472no—
256C2×C4—941no—
257C2×C4—944no—
258C2×C4—941no—
259C2×C4—3762no—
260C2×C4—1882no—
261C2×C4#1062535012yes—
262C2×C4D4×D4711yescharacteristic
263C2×C4D4×D4712yes—
264C2×C4C23×D4711yescharacteristic
265C8—21no—
266C8—21no—
267C8—942no—
268C22—21no—
269C22—21no—
270C22—942no—
271C22—1881no—
272C22—1881no—
273C22—1881no—
274C22—1881no—
275C22—1881no—
276C22#1309399712yes—
277C22C2×D4×D4711yescharacteristic
278C4—42no—
279C4—42no—
280C4—942no—
281C4—942no—
282C4—942no—
283C4—1881no—
284C4#1309399712yes—
285C4C2×D4×D4711yescharacteristic
286C4C2×#1062535011yescharacteristic
287C2—22no—
288C2—3761no—
289C2—1882no—
290C2C2×#1309399711yescharacteristic
291C2#1568992911yescharacteristic
292C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC22×C47C22×D4
hypercenterC2×#103D47
hypocenterC47#3046
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
3. #15689697C2semidirect
4. #15689604C2semidirect
5. #15689348C2semidirect
6. #15689341C2semidirect
7. #15689332C2semidirect
8. #15689327C2semidirect
9. #15689149C2semidirect
10. #15689122C2semidirect
11. C2×#103×C47C2semidirect
157. C2×#103D47semidirect
158. C47#3046semidirect