Finite Group Databasebeta

← #20249173

Subgroups — #20249173

Order 6016.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094006C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic, complemented
3#15689063C211yesmaximal, characteristic, complemented
4#15689061C211yesmaximal, characteristic, complemented
5#15689059C211yesmaximal, characteristic, complemented
6#15689056C212yesmaximal, complemented
7#15689051C212yesmaximal, complemented
8#15688999C212yesmaximal
9#15688994C212yesmaximal, complemented
10#15688985C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C22×C4×D47C2212yes—
15#13094006—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C4⋊C4×D47—24no—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
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×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—22no—
44C2×C22⋊D47—24no—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C2×C4×D47—24no—
51C2×C4×D47—24no—
52C2×C4×D47—42no—
53C2×C4×D47—42no—
54C2×C4×D47D414yes—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—42no—
57C22⋊C4×C47—22no—
58C22⋊C4×C47—42no—
59C22⋊Dic47—22no—
60C22⋊Dic47—42no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—24no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—24no—
67Dic47⋊C4—42no—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—21no—
73C23×C47C2411yescharacteristic
74C22×D47—22no—
75C22×D47—21no—
76C22×D47—21no—
77C22×D47C2×D412yes—
78C22×D47#4114yes—
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—21no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47C2×D412yes—
103C4×D47—28no—
104C4×D47—48no—
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—22no—
116C2×D47—22no—
117C2×D47—24no—
118C2×D47—24no—
119C2×D47#12314yes—
120C4×C47—22no—
121C4×C47—42no—
122C4×C47—41no—
123C4×C47—42no—
124Dic47—22no—
125Dic47—41no—
126Dic47—42no—
127Dic47—41no—
128Dic47—42no—
129#2623—471nomaximal, Sylow
130C2×C47—81no—
131C2×C47C2×#12311yescharacteristic
132C2×C47#53511yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#53912yes—
135C2×C47#53912yes—
136D47—24no—
137C2×#123—471no—
138C22×C4⋊C4—471no—
139#400—471no—
140#400—471no—
141#399—471no—
142#399D4711yescharacteristic, complemented
143#398—472no—
144#397—472no—
145#386—472no—
146#385—472no—
147#381—471no—
148C47#262311yescharacteristic, complemented, Sylow
149C22×D4—471no—
150C23×C4—471no—
151C23×C4—472no—
152#123—944no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—944no—
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C4⋊C4C2×D4712yes—
161C2×C22⋊C4—471no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4C2×D4711yescharacteristic
166C2×C22⋊C4C2×D4712yes—
167#95—472no—
168#95—471no—
169#95—472no—
170#95—472no—
171#95—472no—
172#95—472no—
173#95C2×D4711yescharacteristic
174C24—471no—
175C24C22×D4711yescharacteristic
176C2×D4—942no—
177C2×D4—944no—
178C22×C4—471no—
179C22×C4—474no—
180C22×C4—471no—
181C22×C4—472no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—944no—
185C22×C4—944no—
186C22×C4—1882no—
187C22×C4—1882no—
188C22×C4C22×D4712yes—
189C22×C4C22×D4712yes—
190C22×C4C22×D4711yescharacteristic
191C22×C4C22×D4711yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—944no—
195C4⋊C4—942no—
196C4⋊C4—942no—
197C4⋊C4—942no—
198C4⋊C4—1882no—
199C22⋊C4—22no—
200C22⋊C4—42no—
201C22⋊C4—944no—
202C22⋊C4—942no—
203C22⋊C4—942no—
204C22⋊C4—1882no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—472no—
211C23—474no—
212C23—942no—
213C23—941no—
214C23—941no—
215C23C23×D4711yescharacteristic
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—948no—
228C2×C4—942no—
229C2×C4—941no—
230C2×C4—942no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—941no—
238C2×C4—941no—
239C2×C4—942no—
240C2×C4—1888no—
241C2×C4D4×D4712yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—474no—
248C22—942no—
249C22—942no—
250C22—944no—
251C22—944no—
252C22C2×D4×D4711yescharacteristic
253C22#41×D4712yes—
254C22#1309406912yes—
255C22#1309407111yescharacteristic
256C22#1309407211yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—942no—
262C4—1881no—
263C4—1882no—
264C4—1881no—
265C4—1882no—
266C2—81no—
267C2—944no—
268C2#123×D4711yescharacteristic
269C2#1568968611yescharacteristic
270C2#1568969611yescharacteristic
271C2#1568971612yes—
272C2#1568971912yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2623
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D47C2semidirect
3. #15689063C2semidirect
4. #15689061C2semidirect
5. #15689059C2semidirect
6. #15689056C2semidirect
7. #15689051C2semidirect
9. #15688994C2semidirect
10. #15688985C2semidirect
11. C47×#399C2semidirect
142. #399D47semidirect
148. C47#2623semidirect