Finite Group Databasebeta

← #20254311

Subgroups — #20254311

Order 6016.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×#13094022C211yesmaximal, characteristic, complemented
3#15689494C212yesmaximal, complemented
4#15689472C212yesmaximal, complemented
5#15689327C212yesmaximal, complemented
6#15689326C212yesmaximal, complemented
7#15689264C211yesmaximal, characteristic, complemented
8#15689262C211yesmaximal, characteristic, complemented
9#15689261C211yesmaximal, characteristic, complemented
10#15689173C211yesmaximal, characteristic, complemented
11C47×#448C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C22×Dic94C2211yescharacteristic
14C2×#10625325C2212yes—
15C2×#10625335C2212yes—
16C2×#10625336C2212yes—
17#13094023C2211yescharacteristic
18#13094022—21no—
19#13094022—21no—
20#13094022C2212yes—
21#13094022C2212yes—
22#13094020C2211yescharacteristic
23#13094010—21no—
24#13093998C2211yescharacteristic
25#13093996—21no—
26D4×Dic47C2211yescharacteristic
27#13093986C2211yescharacteristic
28(C22⋊D47)⋊C4—21no—
29C2×Dic47⋊C4—21no—
30C2×Dic47⋊C4—21no—
31C2×C4×Dic47C2211yescharacteristic
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093948C2212yes—
35#13093947C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37C8×Dic47C2212yes—
38C22×Q8×C47C2211yescharacteristic
39C2×SD16×C47C2212yes—
40#121×C47C2211yescharacteristic
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47—42no—
45C2×Q8×C47C2312yes—
46C2×D4×C47—21no—
47C2×D4×C47C2311yescharacteristic
48C22×C4×C47—21no—
49C22×C4×C47C2311yescharacteristic
50C2×C22⋊D47—21no—
51C2×C22⋊D47—21no—
52C2×C22⋊D47—21no—
53C22×Dic47—21no—
54C22×Dic47—21no—
55C22×Dic47D411yescharacteristic
56C22×Dic47D411yescharacteristic
57#10625352—44no—
58C2×D188C2311yescharacteristic
59C2×C4×D47—21no—
60C2×Dic94—21no—
61C2×Dic94—21no—
62C2×Dic94—42no—
63C2×Dic94C2312yes—
64SD16×C47—42no—
65C2×C8×C47C2312yes—
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68C22⋊Dic47—21no—
69#10625336—42no—
70#10625335—42no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73C4⋊Dic47C2311yescharacteristic
74Dic47⋊C4—22no—
75Dic47⋊C4—22no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—21no—
79C4×Dic47D411yescharacteristic
80C4×Dic47D411yescharacteristic
81C4×Dic47C2311yescharacteristic
82C4×Dic47C2311yescharacteristic
83C2×C47⋊C8C2312yes—
84#10625325—42no—
85C23×C47—21no—
86C23×C47C2×D411yescharacteristic
87C22×D47—21no—
88Q8×C47—22no—
89Q8×C47—22no—
90Q8×C47—42no—
91D4×C47—22no—
92D4×C47—42no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—42no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—42no—
100C22⋊D47—42no—
101C22⋊D47—42no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47SD1614yescomplemented
108C2×Dic47C2×D411yescharacteristic
109C2×Dic47C2×D411yescharacteristic
110C2×Dic47C2×D411yescharacteristic
111C2×Dic47C2×D411yescharacteristic
112D188—22no—
113C4×D47—42no—
114Dic94—22no—
115Dic94—22no—
116Dic94—42no—
117Dic94—42no—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—41no—
123C22×C47—41no—
124C22×C47—41no—
125C22×C47C2×SD1612yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—41no—
130C4×C47—21no—
131C4×C47—42no—
132C4×C47—41no—
133C4×C47H(5,𝔽2)12yes—
134Dic47—21no—
135Dic47—42no—
136Dic47—41no—
137Dic47C2×SD1612yes—
138Dic47C2×SD1612yes—
139Dic47#13712yes—
140#3206—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47—81no—
143C2×C47#53511yescharacteristic
144C2×C47C22×SD1611yescharacteristic
145C2×C47C2×#13711yescharacteristic
146D47—81no—
147#532—471no—
148C2×C4⋊Q8—471no—
149#492—472no—
150#487—472no—
151#461—472no—
152#461—472no—
153#448—471no—
154#448—471no—
155#448—471no—
156#448D4711yescharacteristic, complemented
157#431—471no—
158C47#320611yescharacteristic, complemented, Sylow
159C2×#41—941no—
160C22×Q8—471no—
161C22×Q8C2×D4711yescharacteristic
162C2×SD16—472no—
163C2×SD16—472no—
164C2×SD16—472no—
165C2×SD16C2×D4712yes—
166C4⋊Q8—471no—
167C4⋊Q8—472no—
168C4⋊Q8—472no—
169C4⋊Q8—941no—
170C4⋊Q8—941no—
171#127—471no—
172#124—941no—
173#121—471no—
174#121—941no—
175#121C2×D4711yescharacteristic
176C4×D4—471no—
177C4×D4—471no—
178C4×D4—941no—
179C2×C4⋊C4—941no—
180C2×C4⋊C4—941no—
181C2×C42—471no—
182C4⋊C8—472no—
183#103—472no—
184#103—472no—
185#103—472no—
186#103C2×D4712yes—
187C22⋊C8—471no—
188C22⋊C8C2×D4711yescharacteristic
189C4×C8—472no—
190#41—1884no—
191C2×Q8—21no—
192C2×Q8—42no—
193C2×Q8—472no—
194C2×Q8—941no—
195C2×Q8—941no—
196C2×Q8—1882no—
197C2×Q8C22×D4712yes—
198C2×D4—21no—
199C2×D4—471no—
200C2×D4—941no—
201C2×D4—941no—
202C2×D4—941no—
203C2×D4C22×D4711yescharacteristic
204C22×C4—21no—
205C22×C4—471no—
206C22×C4—471no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4C22×D4711yescharacteristic
211SD16—42no—
212SD16—1882no—
213SD16—1882no—
214SD16—1882no—
215C2×C8—472no—
216C2×C8C22×D4712yes—
217C4⋊C4—471no—
218C4⋊C4—942no—
219C4⋊C4—942no—
220C4⋊C4—942no—
221C4⋊C4—942no—
222C4⋊C4—941no—
223C4⋊C4C22×D4711yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—941no—
226C22⋊C4—941no—
227C22⋊C4—941no—
228C42—471no—
229C42—471no—
230C42—471no—
231C42—471no—
232C23—21no—
233C23—941no—
234C23D4×D4711yescharacteristic
235Q8—22no—
236Q8—22no—
237Q8—42no—
238Q8—942no—
239Q8—942no—
240Q8—1882no—
241Q8—1882no—
242D4—22no—
243D4—42no—
244D4—942no—
245D4—1882no—
246D4—1882no—
247D4—1882no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—474no—
253C2×C4—471no—
254C2×C4—471no—
255C2×C4—471no—
256C2×C4—471no—
257C2×C4—942no—
258C2×C4—941no—
259C2×C4—942no—
260C2×C4—1882no—
261C2×C4—1882no—
262C2×C4—1882no—
263C2×C4D4×D4711yescharacteristic
264C2×C4C23×D4711yescharacteristic
265C8—22no—
266C8—942no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—1881no—
273C22—1881no—
274C22—1881no—
275C22SD16×D4712yes—
276C22C2×D4×D4711yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—472no—
281C4—472no—
282C4—472no—
283C4—941no—
284C4—1881no—
285C4—1882no—
286C4#1309406912yes—
287C2—22no—
288C2—81no—
289C2—3761no—
290C2#1568968811yescharacteristic
291C2C2×SD16×D4711yescharacteristic
292C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#448C2
socleC22×C47C22×D4
hypercenter#448D47
hypocenterC47#3206
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. C2×#13094022C2semidirect
3. #15689494C2semidirect
4. #15689472C2semidirect
5. #15689327C2semidirect
6. #15689326C2semidirect
7. #15689264C2semidirect
8. #15689262C2semidirect
9. #15689261C2semidirect
10. #15689173C2semidirect
11. C47×#448C2semidirect
107. C2×Dic47SD16semidirect
156. #448D47semidirect
158. C47#3206semidirect