Finite Group Databasebeta

← #20246791

Subgroups — #20246791

Order 6016.

610 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13094005C211yesmaximal, characteristic
2C2×#13093980C211yesmaximal, characteristic, complemented
3C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
4#15689054C212yesmaximal, complemented
5#15689046C212yesmaximal, complemented
6#15689019C212yesmaximal, complemented
7#15689011C212yesmaximal, complemented
8#15689003C211yesmaximal, characteristic
9#15688998C211yesmaximal, characteristic, complemented
10#15688986C211yesmaximal, characteristic, complemented
11C2×#123×C47C211yesmaximal, characteristic
12C23×Dic47C2211yescharacteristic
13C23×Dic47C2211yescharacteristic
14#13094005—24no—
15#13093980—24no—
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4—24no—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C4×Dic47C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C22×D4×C47C2211yescharacteristic
34C23×C4×C47C2211yescharacteristic
35#123×C47—24no—
36C2×C4⋊C4×C47C2212yes—
37C2×C22⋊C4×C47C2212yes—
38C2×C22⋊C4×C47C2211yescharacteristic
39C24×C47C2311yescharacteristic
40C24×C47C2311yescharacteristic
41C2×D4×C47—22no—
42C2×D4×C47—22no—
43C2×D4×C47—22no—
44C22×C4×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2312yes—
50C22×Dic47—22no—
51C22×Dic47—22no—
52C22×Dic47—22no—
53C22×Dic47—24no—
54C22×Dic47D414yes—
55C22×Dic47C2311yescharacteristic
56C22×Dic47C2312yes—
57C22×Dic47C2311yescharacteristic
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2312yes—
61C4⋊C4×C47—24no—
62C22⋊C4×C47—24no—
63C22⋊C4×C47D414yes—
64C22⋊Dic47—22no—
65C22⋊Dic47—22no—
66C22⋊Dic47—22no—
67C22⋊Dic47—22no—
68C22⋊Dic47—24no—
69C4⋊Dic47—24no—
70Dic47⋊C4—24no—
71Dic47⋊C4—24no—
72Dic47⋊C4—24no—
73Dic47⋊C4—22no—
74Dic47⋊C4—22no—
75C4×Dic47—24no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47—21no—
82C23×C47—22no—
83C23×C47C2×D412yes—
84C23×C47C2×D412yes—
85C23×C47#4112yes—
86C23×C47C2411yescharacteristic
87D4×C47—44no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—21no—
96C2×C4×C47—44no—
97C2×C4×C47C2×D414yes—
98C2×Dic47—28no—
99C2×Dic47—28no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—22no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47—22no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47C2×D412yes—
114C2×Dic47C2×D412yes—
115C2×Dic47#4114yes—
116C22×C47—22no—
117C22×C47—22no—
118C22×C47—24no—
119C22×C47—24no—
120C22×C47—41no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47#12114yes—
126C22×C47C22×D411yescharacteristic
127C22×C47C22×D411yescharacteristic
128C22×C47C2×#4112yes—
129C22×C47C2×#4111yescharacteristic
130C22×C472−1+412yes—
131C4×C47—24no—
132C4×C47—42no—
133C4×C47—41no—
134Dic47—22no—
135Dic47—22no—
136Dic47—24no—
137Dic47—41no—
138Dic47—41no—
139Dic47—42no—
140#2413—471nomaximal, Sylow
141C2×C47—24no—
142C2×C47—81no—
143C2×C47C2×#12111yescharacteristic
144C2×C47#52511yescharacteristic
145C2×C47#53611yescharacteristic
146C2×C47#54712yes—
147C2×C47#55212yes—
148C2×#123—471no—
149C2×#123D4711yescharacteristic
150C2×#117—471no—
151C22×C4⋊C4—471no—
152#398—472no—
153#396—472no—
154#389—472no—
155#388—472no—
156#386—471no—
157#385—471no—
158#381—471no—
159C47#241311yescharacteristic, complemented, Sylow
160C22×D4C2×D4711yescharacteristic
161C23×C4—471no—
162C23×C4—471no—
163C23×C4C2×D4711yescharacteristic
164#123—24no—
165#123—944no—
166#117—944no—
167C2×C4⋊C4—472no—
168C2×C4⋊C4—472no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4—471no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4—472no—
173C2×C4⋊C4—944no—
174C2×C4⋊C4C2×D4712yes—
175C2×C22⋊C4—471no—
176C2×C22⋊C4—471no—
177C2×C22⋊C4—471no—
178C2×C22⋊C4—471no—
179C2×C22⋊C4—472no—
180C2×C22⋊C4C2×D4712yes—
181C2×C22⋊C4C2×D4711yescharacteristic
182C2×C42—472no—
183#95—472no—
184#95—472no—
185#95—472no—
186#95—472no—
187C24C22×D4711yescharacteristic
188C24C22×D4711yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—474no—
196C22×C4—472no—
197C22×C4—471no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—472no—
201C22×C4—471no—
202C22×C4—944no—
203C22×C4—942no—
204C22×C4—942no—
205C22×C4—942no—
206C22×C4C22×D4712yes—
207C22×C4C22×D4711yescharacteristic
208C22×C4C22×D4712yes—
209C4⋊C4—24no—
210C4⋊C4—944no—
211C4⋊C4—944no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—944no—
215C4⋊C4—944no—
216C22⋊C4—24no—
217C22⋊C4—944no—
218C22⋊C4—942no—
219C22⋊C4—942no—
220C22⋊C4—942no—
221C22⋊C4—942no—
222C22⋊C4C22⋊D4714yes—
223C42—944no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—22no—
231C23D4×D4712yes—
232C23#1062535212yes—
233C23C2×C22⋊D4712yes—
234C23C23×D4711yescharacteristic
235D4—44no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—44no—
245C2×C4—472no—
246C2×C4—472no—
247C2×C4—474no—
248C2×C4—948no—
249C2×C4—948no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—941no—
253C2×C4—942no—
254C2×C4—941no—
255C2×C4—941no—
256C2×C4—941no—
257C2×C4—941no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4C2×C22⋊D4714yes—
264C22—24no—
265C22—24no—
266C22—22no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22#1309399514yes—
274C22C2×D4×D4711yescharacteristic
275C22C22×C22⋊D4711yescharacteristic
276C22#41×D4712yes—
277C22C2×#1062535211yescharacteristic
278C22#1309407112yes—
279C4—24no—
280C4—42no—
281C4—41no—
282C4—942no—
283C4—942no—
284C4—944no—
285C4—1882no—
286C4—1881no—
287C4—1881no—
288C2—24no—
289C2—81no—
290C2C2×#1309399511yescharacteristic
291C2#1568963111yescharacteristic
292C2#1568969511yescharacteristic
293C2#1568977212yes—
294C2#1568981012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2413
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#13093980C2semidirect
3. C22×Dic47⋊C4C2semidirect
4. #15689054C2semidirect
5. #15689046C2semidirect
6. #15689019C2semidirect
7. #15689011C2semidirect
9. #15688998C2semidirect
10. #15688986C2semidirect
159. C47#2413semidirect