Finite Group Databasebeta

← #20252934

Subgroups — #20252934

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×#13094044C211yesmaximal, characteristic
3#15689603C211yesmaximal, characteristic, complemented
4#15689342C212yesmaximal, complemented
5#15689335C212yesmaximal, complemented
6#15689330C212yesmaximal, complemented
7#15689325C212yesmaximal, complemented
8#15689150C211yesmaximal, characteristic, complemented
9#15689124C211yesmaximal, characteristic, complemented
10C2×#13093948C211yesmaximal, characteristic, complemented
11C47×#536C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13#13094055—24no—
14#13094044—24no—
15C2×#10625337C2211yescharacteristic
16C2×#10625337C2212yes—
17C2×#10625335C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625336C2212yes—
20C2×#10625334C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23C4×Dic94C2212yes—
24C4×D188C2212yes—
25(C22⋊D47)⋊C4—22no—
26#13093982—21no—
27C2×C4⋊Dic47C2211yescharacteristic
28C4⋊C4×D47—21no—
29C4⋊(C47⋊C8)C2212yes—
30C4⋊(C47⋊C8)C2212yes—
31#13093948C2212yes—
32#13093948C2212yes—
33#13093948C2212yes—
34#13093945C2212yes—
35C2×#41×C47C2211yescharacteristic
36C22×Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2212yes—
38#124×C47C2212yes—
39#123×C47—22no—
40C22⋊Q8×C47—21no—
41C22⋊Q8×C47—21no—
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×C47C2312yes—
49C2×Q8×C47C2311yescharacteristic
50C2×D4×C47—21no—
51C2×D4×C47C2311yescharacteristic
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47C2311yescharacteristic
55C2×C22⋊D47—21no—
56C22×Dic47—21no—
57#10625350—22no—
58#10625350D414yes—
59C2×D188C2311yescharacteristic
60C2×C4×D47—21no—
61C2×C4×D47—22no—
62C2×Dic94C2311yescharacteristic
63C4⋊C4×C47—22no—
64C4⋊C4×C47—22no—
65C4⋊C4×C47D411yescharacteristic
66C4⋊C4×C47D411yescharacteristic
67C22⋊C4×C47—22no—
68C22⋊C4×C47—22no—
69C22⋊C4×C47D412yes—
70C42×C47C2312yes—
71#10625337—22no—
72#10625337—24no—
73#10625336—22no—
74#10625336—24no—
75#10625335—22no—
76#10625334—22no—
77(C2×D47)⋊C4—22no—
78C4⋊Dic47—21no—
79C4⋊Dic47C2312yes—
80Dic47⋊C4—22no—
81C4×Dic47—22no—
82#10625329—22no—
83C2×C47⋊C8—22no—
84C2×C47⋊C8C2312yes—
85C2×C47⋊C8C2311yescharacteristic
86C2×C47⋊C8C2311yescharacteristic
87C23×C47—21no—
88C23×C47C2×D411yescharacteristic
89C22×D47—21no—
90Q8×C47—22no—
91Q8×C47—21no—
92Q8×C47—22no—
93Q8×C47—21no—
94Q8×C47—42no—
95D4×C47—21no—
96D4×C47—21no—
97D4×C47—42no—
98C2×C4×C47—22no—
99C2×C4×C47—21no—
100C2×C4×C47—42no—
101C2×C4×C47—42no—
102C2×C4×C47C2×D412yes—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47#4112yes—
107C2×C4×C47C2411yescharacteristic
108C22⋊D47—24no—
109C2×Dic47—21no—
110C2×Dic47—22no—
111C2×Dic47—81no—
112D188—21no—
113D188C2×D412yes—
114C4×D47—24no—
115C4×D47—82no—
116Dic94—21no—
117Dic94C2×D412yes—
118C47⋊C8—21no—
119C47⋊C8—21no—
120C47⋊C8—22no—
121C22×C47—21no—
122C22×C47—21no—
123C22×C47—41no—
124C22×C47—41no—
125C22×C47—41no—
126C22×C47#12112yes—
127C22×C47C22×D411yescharacteristic
128C2×D47—22no—
129C2×D47—41no—
130C2×D47—41no—
131C4×C47—22no—
132C4×C47—22no—
133C4×C47—41no—
134C4×C47—42no—
135C4×C47#12112yes—
136C4×C47C22×D411yescharacteristic
137C4×C47C2×#4111yescharacteristic
138Dic47—22no—
139Dic47—42no—
140#3046—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47—81no—
143C2×C47C2×#12111yescharacteristic
144C2×C47#57711yescharacteristic
145C2×C47#57811yescharacteristic
146D47—42no—
147C2×#137—471no—
148C2×#135—471no—
149#536D4711yescharacteristic, complemented
150#520—471no—
151#464—472no—
152#463—472no—
153#462—472no—
154#461—472no—
155#424—471no—
156#417—471no—
157C2×#103—471no—
158C47#304611yescharacteristic, complemented, Sylow
159C2×#41—471no—
160C2×#41C2×D4711yescharacteristic
161C22×Q8C2×D4711yescharacteristic
162#137—944no—
163#135—944no—
164C2×Q16—471no—
165C2×Q16—472no—
166C2×SD16—471no—
167C2×SD16—472no—
168C2×SD16—471no—
169C2×D8—471no—
170C2×M16—471no—
171C22×C8—471no—
172C4⋊Q8C2×D4712yes—
173#124C2×D4712yes—
174#123—22no—
175C22⋊Q8—21no—
176C22⋊Q8—21no—
177C4×Q8—472no—
178C4×D4—472no—
179C4×D4—942no—
180#117—941no—
181#117C2×D4711yescharacteristic
182C2×C4⋊C4—471no—
183C2×C4⋊C4—941no—
184C4⋊C8—472no—
185C4⋊C8—472no—
186#103—472no—
187#103—472no—
188#103—472no—
189#102—472no—
190#41—22no—
191#41—22no—
192#41—474no—
193#41—942no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—471no—
198C2×Q8C22×D4712yes—
199C2×Q8C22×D4711yescharacteristic
200C2×D4—21no—
201C2×D4—471no—
202C2×D4—941no—
203C2×D4C22×D4711yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—941no—
207C22×C4—941no—
208C22×C4—942no—
209C22×C4C22×D4711yescharacteristic
210Q16—942no—
211Q16—944no—
212SD16—942no—
213SD16—942no—
214SD16—944no—
215D8—942no—
216M16—942no—
217C2×C8—472no—
218C2×C8—471no—
219C2×C8—471no—
220C2×C8—942no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—472no—
224C4⋊C4—942no—
225C4⋊C4—941no—
226C4⋊C4C22⋊D4711yescharacteristic
227C4⋊C4C22⋊D4711yescharacteristic
228C22⋊C4—22no—
229C22⋊C4—22no—
230C22⋊C4—942no—
231C22⋊C4C22⋊D4712yes—
232C42—942no—
233C42C22×D4712yes—
234C23—21no—
235C23—941no—
236C23C2×C22⋊D4711yescharacteristic
237Q8—22no—
238Q8—21no—
239Q8—22no—
240Q8—21no—
241Q8—42no—
242Q8—472no—
243Q8—941no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—472no—
248D4—944no—
249D4—941no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—941no—
255C2×C4—944no—
256C2×C4—942no—
257C2×C4—3762no—
258C2×C4—3761no—
259C2×C4D4×D4712yes—
260C2×C4#1062535212yes—
261C2×C4C2×C22⋊D4712yes—
262C2×C4C2×C22⋊D4712yes—
263C2×C4C2×C22⋊D4711yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—941no—
266C8—941no—
267C8—942no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—942no—
274C22—1881no—
275C22—1881no—
276C22#1309399512yes—
277C22C22×C22⋊D4711yescharacteristic
278C4—22no—
279C4—22no—
280C4—41no—
281C4—42no—
282C4—942no—
283C4—1882no—
284C4#1309399512yes—
285C4C2×D4×D4711yescharacteristic
286C4C2×#1062535211yescharacteristic
287C2—22no—
288C2—81no—
289C2—1882no—
290C2C2×#1309399511yescharacteristic
291C2#1568993111yescharacteristic
292C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#536C2
socleC22×C47C22×D4
hypercenter#536D47
hypocenterC47#3046
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
3. #15689603C2semidirect
4. #15689342C2semidirect
5. #15689335C2semidirect
6. #15689330C2semidirect
7. #15689325C2semidirect
8. #15689150C2semidirect
9. #15689124C2semidirect
10. C2×#13093948C2semidirect
11. C47×#536C2semidirect
149. #536D47semidirect
158. C47#3046semidirect