Finite Group Databasebeta

← #20249250

Subgroups — #20249250

Order 6016.

500 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13094010C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689043C212yesmaximal, complemented
5#15689038C212yesmaximal
6#15689036C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15689017C212yesmaximal, complemented
9#15689013C212yesmaximal, complemented
10#15688990C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15#13094010—24no—
16#13093989—24no—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—22no—
44C2×C22⋊D47—42no—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2312yes—
50C2×Dic94—22no—
51C2×Dic94—24no—
52C2×Dic94—22no—
53C2×Dic94—42no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—42no—
56C22⋊C4×C47—22no—
57C22⋊C4×C47—42no—
58C22⋊Dic47—22no—
59C22⋊Dic47—24no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—24no—
63(C2×D47)⋊C4—42no—
64Dic47⋊C4—24no—
65Dic47⋊C4—42no—
66C4×Dic47—24no—
67C4×Dic47D414yes—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47C2411yescharacteristic
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—21no—
78C22×D47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
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×C47C2×D412yes—
89C22⋊D47—44no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47C2×D412yes—
101C2×Dic47C2×D412yes—
102C2×Dic47#4114yes—
103Dic94—28no—
104Dic94—44no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47—41no—
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—41no—
122C4×C47—42no—
123C4×C47—42no—
124Dic47—24no—
125Dic47—22no—
126Dic47—22no—
127Dic47—41no—
128Dic47—42no—
129#2632—471nomaximal, Sylow
130C2×C47—81no—
131C2×C47#52511yescharacteristic
132C2×C47#53511yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#54212yes—
135C2×C47#54212yes—
136D47—81no—
137C2×#124—471no—
138C2×C4×Q8—471no—
139#399—471no—
140#399D4711yescharacteristic, complemented
141#395—472no—
142#394—472no—
143#393—471no—
144#393—471no—
145#388—472no—
146#388—472no—
147#383—471no—
148C47#263211yescharacteristic, complemented, Sylow
149C22×Q8—471no—
150C22×Q8—471no—
151C22×D4—471no—
152#124—944no—
153C4×Q8—944no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4C2×D4711yescharacteristic
157C2×C4⋊C4C2×D4712yes—
158C2×C22⋊C4—471no—
159C2×C22⋊C4—472no—
160C2×C22⋊C4—471no—
161C2×C22⋊C4—471no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4C2×D4711yescharacteristic
165C2×C22⋊C4C2×D4712yes—
166C2×C42—471no—
167C2×C42—472no—
168#95—472no—
169#95—471no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95C2×D4711yescharacteristic
174C24—471no—
175C24C22×D4711yescharacteristic
176C2×Q8—944no—
177C2×Q8—942no—
178C2×Q8—942no—
179C2×Q8—1882no—
180C2×D4—942no—
181C2×D4—1882no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—471no—
185C22×C4—472no—
186C22×C4—471no—
187C22×C4C22×D4712yes—
188C22×C4C22×D4711yescharacteristic
189C22×C4C22×D4712yes—
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—944no—
194C4⋊C4—1882no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—944no—
198C22⋊C4—942no—
199C22⋊C4—944no—
200C22⋊C4—942no—
201C22⋊C4—942no—
202C22⋊C4—1882no—
203C42—474no—
204C42—944no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—941no—
211C23—942no—
212C23—942no—
213C23—941no—
214C23—941no—
215C23C23×D4711yescharacteristic
216Q8—948no—
217Q8—1884no—
218D4—1884no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—472no—
229C2×C4—472no—
230C2×C4—474no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—941no—
235C2×C4—941no—
236C2×C4—941no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4D4×D4712yes—
242C22—42no—
243C22—42no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—1882no—
248C22—1882no—
249C22—1881no—
250C22—1881no—
251C22—1881no—
252C22C2×D4×D4711yescharacteristic
253C22#41×D4712yes—
254C22#1309406912yes—
255C22#1309407111yescharacteristic
256C22#1309407211yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—944no—
262C4—942no—
263C4—942no—
264C4—1882no—
265C4—1881no—
266C2—81no—
267C2—3761no—
268C2#1568963111yescharacteristic
269C2#1568968611yescharacteristic
270C2#1568969611yescharacteristic
271C2#1568974112yes—
272C2#1568974312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2632
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
3. #15689058C2semidirect
4. #15689043C2semidirect
6. #15689036C2semidirect
7. #15689035C2semidirect
8. #15689017C2semidirect
9. #15689013C2semidirect
10. #15688990C2semidirect
11. C47×#399C2semidirect
140. #399D47semidirect
148. C47#2632semidirect