Finite Group Databasebeta

← #20249539

Subgroups — #20249539

Order 6016.

498 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13094007C211yesmaximal, characteristic
2#15689061C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689051C212yesmaximal, complemented
5#15689042C211yesmaximal, characteristic, complemented
6#15689038C212yesmaximal
7#15689034C211yesmaximal, characteristic, complemented
8#15689018C212yesmaximal, complemented
9#15689013C212yesmaximal, complemented
10C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13#13094007—24no—
14C2×Dic47⋊C4C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×(C2×D47)⋊C4C2211yescharacteristic
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2211yescharacteristic
23C2×(C2×D47)⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C22×Q8×C47C2211yescharacteristic
32C23×C4×C47C2211yescharacteristic
33C22⋊Q8×C47—24no—
34C2×C4⋊C4×C47C2212yes—
35C2×C4⋊C4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47—42no—
42C22×C4×C47D414yes—
43C22×C4×C47C2312yes—
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—22no—
48C2×C22⋊D47—42no—
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C22×Dic47C2311yescharacteristic
53C22×Dic47C2312yes—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—24no—
56C22⋊C4×C47—24no—
57C22⋊Dic47—22no—
58C22⋊Dic47—24no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—42no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—24no—
66Dic47⋊C4—42no—
67C4×Dic47—42no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47C2×D412yes—
73C23×C47C2411yescharacteristic
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—21no—
78C22×D47—21no—
79Q8×C47—44no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—44no—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2×D412yes—
91C22⋊D47—44no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47#4114yes—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—42no—
109C22×C47—42no—
110C22×C47C22×D411yescharacteristic
111C22×C47C2×#4112yes—
112C22×C47H(5,𝔽2)12yes—
113C22×C472−1+411yescharacteristic
114C22×C472−1+411yescharacteristic
115C2×D47—41no—
116C2×D47—41no—
117C2×D47—41no—
118C2×D47—42no—
119C2×D47—42no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—42no—
123C4×C47—42no—
124Dic47—24no—
125Dic47—41no—
126Dic47—41no—
127Dic47—41no—
128Dic47—42no—
129#2663—471nomaximal, Sylow
130C2×C47—42no—
131C2×C47#53211yescharacteristic
132C2×C47#53411yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#53912yes—
135C2×C47#54212yes—
136D47—81no—
137C2×#123—471no—
138C2×C22⋊Q8D4711yescharacteristic, complemented
139#400—471no—
140#399—471no—
141#397—472no—
142#395—471no—
143#394—472no—
144#393—471no—
145#389—472no—
146#388—472no—
147C4×C22⋊C4—471no—
148C47#266311yescharacteristic, complemented, Sylow
149C22×Q8C2×D4711yescharacteristic
150C22×D4—471no—
151C23×C4C2×D4711yescharacteristic
152#123—944no—
153C22⋊Q8—24no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4C2×D4712yes—
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C22⋊C4—471no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—471no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4—472no—
166C2×C22⋊C4C2×D4712yes—
167C2×C42—472no—
168#95—471no—
169#95—471no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95—472no—
174C24—471no—
175C24C22×D4711yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—942no—
179C2×D4—1882no—
180C22×C4—42no—
181C22×C4—472no—
182C22×C4—472no—
183C22×C4—471no—
184C22×C4—471no—
185C22×C4—471no—
186C22×C4C22⋊D4714yes—
187C22×C4C22×D4712yes—
188C22×C4C22×D4712yes—
189C22×C4C22×D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—1882no—
197C22⋊C4—24no—
198C22⋊C4—944no—
199C22⋊C4—944no—
200C22⋊C4—942no—
201C22⋊C4—942no—
202C22⋊C4—942no—
203C22⋊C4—1882no—
204C42—1882no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—941no—
210C23—942no—
211C23—942no—
212C23—941no—
213C23—941no—
214C23C2×C22⋊D4712yes—
215C23C23×D4711yescharacteristic
216Q8—44no—
217D4—1884no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—474no—
228C2×C4—942no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—941no—
239C2×C4—941no—
240C2×C4C2×C22⋊D4712yes—
241C2×C4C2×C22⋊D4712yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—1882no—
248C22—1881no—
249C22—1881no—
250C22—1881no—
251C22—1882no—
252C22C22×C22⋊D4711yescharacteristic
253C22#41×D4712yes—
254C22#1309406912yes—
255C22#1309407211yescharacteristic
256C22#1309407211yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—944no—
262C4—1882no—
263C4—1881no—
264C4—1881no—
265C4—1881no—
266C2—42no—
267C2—3761no—
268C2#1568966911yescharacteristic
269C2#1568968211yescharacteristic
270C2#1568969711yescharacteristic
271C2#1568971912yes—
272C2#1568974312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2663
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689051C2semidirect
5. #15689042C2semidirect
7. #15689034C2semidirect
8. #15689018C2semidirect
9. #15689013C2semidirect
10. C4×C22⋊Dic47C2semidirect
11. C2×C22⋊Q8×C47C2semidirect
138. C2×C22⋊Q8D47semidirect
148. C47#2663semidirect