Finite Group Databasebeta

← #20251444

Subgroups — #20251444

Order 6016.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13094015C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic
3#15689060C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic, complemented
5#15689049C211yesmaximal, characteristic, complemented
6#15689047C212yesmaximal, complemented
7#15689046C212yesmaximal, complemented
8#15689044C212yesmaximal, complemented
9#15689039C212yesmaximal
10#15688987C211yesmaximal, characteristic, complemented
11C47×#397C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14#13094015—24no—
15#13094010—24no—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—22no—
44C2×C22⋊D47—42no—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—42no—
52C4⋊C4×C47—22no—
53C22⋊C4×C47—22no—
54C22⋊C4×C47—42no—
55C22⋊Dic47—22no—
56C22⋊Dic47—42no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—42no—
60(C2×D47)⋊C4—42no—
61C4⋊Dic47—22no—
62C4⋊Dic47—24no—
63C4⋊Dic47—42no—
64Dic47⋊C4—24no—
65Dic47⋊C4—42no—
66Dic47⋊C4—42no—
67C4×Dic47D414yes—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—21no—
71C23×C47—22no—
72C23×C47—21no—
73C23×C47C2411yescharacteristic
74C22×D47—21no—
75C22×D47—21no—
76C22×D47—22no—
77C22×D47—22no—
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—21no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47C2×D412yes—
102C2×Dic47C2×D412yes—
103Dic94—44no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47—42no—
109C22×C47C22×D411yescharacteristic
110C22×C47H(5,𝔽2)11yescharacteristic
111C22×C47H(5,𝔽2)12yes—
112C22×C472−1+412yes—
113C22×C472−1+411yescharacteristic
114C2×D47—41no—
115C2×D47—41no—
116C2×D47—41no—
117C2×D47—42no—
118C2×D47—42no—
119C4×C47—22no—
120C4×C47—41no—
121C4×C47—42no—
122C4×C47—42no—
123Dic47—22no—
124Dic47—22no—
125Dic47—41no—
126Dic47—42no—
127Dic47—42no—
128#2820—471nomaximal, Sylow
129C2×C47—81no—
130C2×C47#53511yescharacteristic
131C2×C47#53611yescharacteristic
132C2×C47#53711yescharacteristic
133C2×C47#56212yes—
134C2×C47#56312yes—
135D47—81no—
136C2×#125—471no—
137C2×#124—471no—
138#399—471no—
139#399—471no—
140#397—471no—
141#397D4711yescharacteristic, complemented
142#396—472no—
143#396—472no—
144#395—472no—
145#394—472no—
146#382—471no—
147C47#282011yescharacteristic, complemented, Sylow
148C22×Q8—471no—
149C22×D4—471no—
150#125—944no—
151#124—944no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C22⋊C4—471no—
160C2×C22⋊C4—471no—
161C2×C22⋊C4—471no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4C2×D4712yes—
167C2×C42—471no—
168#95—472no—
169#95—471no—
170#95—472no—
171#95C2×D4711yescharacteristic
172#95C2×D4712yes—
173C24—471no—
174C24C22×D4711yescharacteristic
175C2×Q8—942no—
176C2×Q8—1882no—
177C2×D4—942no—
178C2×D4—1882no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—472no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4C22×D4712yes—
185C22×C4C22×D4712yes—
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4711yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—944no—
190C4⋊C4—944no—
191C4⋊C4—942no—
192C4⋊C4—1882no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C22⋊C4—1882no—
201C22⋊C4—1882no—
202C22⋊C4—1882no—
203C42—474no—
204C23—21no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—941no—
210C23—941no—
211C23—942no—
212C23—942no—
213C23—941no—
214C23C23×D4711yescharacteristic
215Q8—1884no—
216D4—1884no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—472no—
227C2×C4—472no—
228C2×C4—941no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4D4×D4712yes—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—1882no—
246C22—1882no—
247C22—1881no—
248C22—1881no—
249C22—1881no—
250C22C2×D4×D4711yescharacteristic
251C22#1309406911yescharacteristic
252C22#1309407012yes—
253C22#1309407112yes—
254C22#1309407111yescharacteristic
255C4—22no—
256C4—42no—
257C4—41no—
258C4—42no—
259C4—942no—
260C4—942no—
261C4—1882no—
262C4—1881no—
263C4—1882no—
264C2—81no—
265C2—3761no—
266C2#1568969111yescharacteristic
267C2#1568969511yescharacteristic
268C2#1568970211yescharacteristic
269C2#1568987012yes—
270C2#1568987512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2820
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
3. #15689060C2semidirect
4. #15689059C2semidirect
5. #15689049C2semidirect
6. #15689047C2semidirect
7. #15689046C2semidirect
8. #15689044C2semidirect
10. #15688987C2semidirect
11. C47×#397C2semidirect
141. #397D47semidirect
147. C47#2820semidirect