Finite Group Databasebeta

← #20246795

Subgroups — #20246795

Order 6016.

610 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C2×#13094007C211yesmaximal, characteristic
3C2×#13093983C211yesmaximal, characteristic, complemented
4#15689056C212yesmaximal, complemented
5#15689045C212yesmaximal, complemented
6#15689018C212yesmaximal, complemented
7#15689013C212yesmaximal, complemented
8#15689002C211yesmaximal, characteristic
9#15688996C211yesmaximal, characteristic, complemented
10#15688986C211yesmaximal, characteristic, complemented
11C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13#13094007—24no—
14#13094007—24no—
15#13093983—24no—
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C22⋊Dic47C2211yescharacteristic
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×C4×Dic47C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C23×C4×C47C2211yescharacteristic
34C23×C4×C47C2211yescharacteristic
35C23×C4×C47C2211yescharacteristic
36C2×C4⋊C4×C47—24no—
37C2×C4⋊C4×C47C2212yes—
38C2×C4⋊C4×C47C2212yes—
39C24×C47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47—24no—
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47D414yes—
49C22×C4×C47C2312yes—
50C22×C4×C47C2311yescharacteristic
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2312yes—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—22no—
56C22×Dic47C2311yescharacteristic
57C22×Dic47C2312yes—
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22×Dic47C2312yes—
61C4⋊C4×C47—24no—
62C4⋊C4×C47—24no—
63C22⋊Dic47—22no—
64C22⋊Dic47—22no—
65C22⋊Dic47D414yes—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—24no—
69(C2×D47)⋊C4—24no—
70C4⋊Dic47—24no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73Dic47⋊C4—24no—
74Dic47⋊C4—24no—
75C4×Dic47—24no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47C2×D412yes—
79C23×C47C2×D412yes—
80C23×C47#4112yes—
81C23×C47C2411yescharacteristic
82C22×D47—21no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47—21no—
86C22×D47—22no—
87C2×C4×C47—28no—
88C2×C4×C47—28no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—44no—
99C2×C4×C47C2×D412yes—
100C2×C4×C47C2×D412yes—
101C2×C4×C47#4114yes—
102C22⋊D47—44no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—21no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—21no—
110C2×Dic47—22no—
111C2×Dic47—22no—
112C2×Dic47—21no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47C2×D414yes—
116C22×C47—22no—
117C22×C47—22no—
118C22×C47—24no—
119C22×C47—24no—
120C22×C47#12114yes—
121C22×C47C22×D411yescharacteristic
122C22×C47C22×D411yescharacteristic
123C22×C47C2×#4111yescharacteristic
124C22×C47C2×#4112yes—
125C22×C472−1+412yes—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—42no—
131C4×C47—22no—
132C4×C47—22no—
133C4×C47—24no—
134C4×C47—42no—
135Dic47—24no—
136Dic47—41no—
137Dic47—41no—
138Dic47—41no—
139Dic47—42no—
140#2413—471nomaximal, Sylow
141C2×C47—24no—
142C2×C47C2×#12111yescharacteristic
143C2×C47#52511yescharacteristic
144C2×C47#53611yescharacteristic
145C2×C47#54712yes—
146C2×C47#55212yes—
147D47—81no—
148C2×#123—471no—
149C2×#123—471no—
150C2×#117—471no—
151C22×C4⋊C4D4711yescharacteristic, complemented
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×D4—471no—
161C23×C4C2×D4711yescharacteristic
162C23×C4C2×D4711yescharacteristic
163C23×C4C2×D4711yescharacteristic
164#123—944no—
165#123—944no—
166#117—944no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—472no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4—471no—
172C2×C4⋊C4—472no—
173C2×C4⋊C4C2×D4712yes—
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⋊C4—471no—
181C2×C22⋊C4—472no—
182C2×C42—472no—
183#95—472no—
184#95—472no—
185#95—472no—
186#95—472no—
187C24—471no—
188C24C22×D4711yescharacteristic
189C2×D4—942no—
190C2×D4—942no—
191C2×D4—942no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—472no—
200C22×C4—471no—
201C22×C4—472no—
202C22×C4—471no—
203C22×C4—471no—
204C22×C4C22⋊D4714yes—
205C22×C4C22×D4712yes—
206C22×C4C22×D4712yes—
207C22×C4C22×D4711yescharacteristic
208C22×C4C22×D4711yescharacteristic
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—944no—
212C4⋊C4—944no—
213C4⋊C4—944no—
214C4⋊C4—942no—
215C4⋊C4—942no—
216C22⋊C4—474no—
217C22⋊C4—944no—
218C22⋊C4—942no—
219C22⋊C4—942no—
220C22⋊C4—944no—
221C22⋊C4—942no—
222C22⋊C4—942no—
223C42—944no—
224C23—22no—
225C23—22no—
226C23—941no—
227C23—941no—
228C23—941no—
229C23—942no—
230C23—942no—
231C23D4×D4712yes—
232C23#1062535212yes—
233C23C2×C22⋊D4712yes—
234C23C23×D4711yescharacteristic
235D4—1884no—
236C2×C4—28no—
237C2×C4—28no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—474no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—941no—
253C2×C4—941no—
254C2×C4—941no—
255C2×C4—941no—
256C2×C4—941no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4#1062535014yes—
262C2×C4C2×C22⋊D4712yes—
263C2×C4C2×C22⋊D4712yes—
264C22—24no—
265C22—24no—
266C22—22no—
267C22—22no—
268C22—1882no—
269C22—1882no—
270C22—1881no—
271C22—1881no—
272C22—1881no—
273C22#1309399614yes—
274C22C2×D4×D4711yescharacteristic
275C22C22×C22⋊D4711yescharacteristic
276C22C2×#1062535211yescharacteristic
277C22C2×#1062535012yes—
278C22#1309407212yes—
279C4—22no—
280C4—22no—
281C4—24no—
282C4—42no—
283C4—944no—
284C4—1882no—
285C4—1881no—
286C4—1881no—
287C4—1881no—
288C2—24no—
289C2—3761no—
290C2C2×#1309399611yescharacteristic
291C2#1568963411yescharacteristic
292C2#1568969711yescharacteristic
293C2#1568977412yes—
294C2#1568980812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C4⋊C4×C47C2
hypercenterC22×C4⋊C4D47
hypocenterC47#2413
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#13093983C2semidirect
4. #15689056C2semidirect
5. #15689045C2semidirect
6. #15689018C2semidirect
7. #15689013C2semidirect
9. #15688996C2semidirect
10. #15688986C2semidirect
11. C22×C4⋊C4×C47C2semidirect
151. C22×C4⋊C4D47semidirect
159. C47#2413semidirect