Finite Group Databasebeta

← #20249181

Subgroups — #20249181

Order 6016.

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

normal subgroups only

This group has 548 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×#13093997C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic, complemented
3#15689058C211yesmaximal, characteristic, complemented
4#15689050C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689040C212yesmaximal, complemented
7#15689038C212yesmaximal, complemented
8#15689023C212yesmaximal, complemented
9#15689018C212yesmaximal, complemented
10#15688982C211yesmaximal, characteristic, complemented
11C47×#399C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C22×C22⋊D47C2211yescharacteristic
15C22×C4×D47C2211yescharacteristic
16#13093997—24no—
17#13093982—24no—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×C4×Dic47C2212yes—
29C47⋊#95C2211yescharacteristic
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
39C23×D47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—22no—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—42no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2311yescharacteristic
52C2×D188—22no—
53C2×D188—42no—
54C2×C4×D47—24no—
55C2×C4×D47D414yes—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—42no—
58C22⋊C4×C47—22no—
59C22⋊C4×C47—42no—
60C22⋊Dic47—42no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—42no—
64(C2×D47)⋊C4—42no—
65(C2×D47)⋊C4—42no—
66C4⋊Dic47—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4—24no—
69Dic47⋊C4—42no—
70C4×Dic47—24no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47—21no—
76C23×C47C2411yescharacteristic
77C22×D47—22no—
78C22×D47—21no—
79C22×D47—22no—
80C22×D47—21no—
81C22×D47—21no—
82C22×D47—22no—
83C22×D47—21no—
84C22×D47—22no—
85C22×D47—21no—
86C22×D47C2×D412yes—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—21no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47C2×D412yes—
97C22⋊D47—44no—
98C22⋊D47—44no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47C2×D412yes—
108C2×Dic47#4114yes—
109D188—44no—
110C4×D47—28no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47C22×D411yescharacteristic
117C22×C47C2×#4112yes—
118C22×C47H(5,𝔽2)12yes—
119C22×C47H(5,𝔽2)11yescharacteristic
120C22×C472−1+411yescharacteristic
121C2×D47—22no—
122C2×D47—22no—
123C2×D47—22no—
124C2×D47—42no—
125C2×D47—42no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47—41no—
129C2×D47—42no—
130C2×D47—42no—
131C4×C47—22no—
132C4×C47—41no—
133C4×C47—42no—
134C4×C47—42no—
135Dic47—41no—
136Dic47—42no—
137Dic47—42no—
138Dic47#12314yes—
139#2624—471nomaximal, Sylow
140C2×C47—81no—
141C2×C47C2×#12311yescharacteristic
142C2×C47#53511yescharacteristic
143C2×C47#53711yescharacteristic
144C2×C47#54012yes—
145C2×C47#54212yes—
146D47—42no—
147D47—81no—
148C2×#121—471no—
149C2×#117—471no—
150#399—471no—
151#399D4711yescharacteristic, complemented
152#397—471no—
153#397—471no—
154#394—472no—
155#394—472no—
156#390—472no—
157#389—472no—
158#380—471no—
159C47#262411yescharacteristic, complemented, Sylow
160C22×D4—471no—
161C22×D4—471no—
162C22×D4—471no—
163C23×C4—471no—
164#121—944no—
165#117—944no—
166C2×C4⋊C4—471no—
167C2×C4⋊C4—471no—
168C2×C4⋊C4—472no—
169C2×C4⋊C4—472no—
170C2×C4⋊C4C2×D4711yescharacteristic
171C2×C4⋊C4C2×D4712yes—
172C2×C22⋊C4—472no—
173C2×C22⋊C4—471no—
174C2×C22⋊C4—472no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—472no—
177C2×C22⋊C4—472no—
178C2×C22⋊C4C2×D4711yescharacteristic
179C2×C22⋊C4C2×D4712yes—
180C2×C42—472no—
181#95—471no—
182#95—472no—
183#95—472no—
184#95C2×D4711yescharacteristic
185C24—471no—
186C24—471no—
187C24C22×D4711yescharacteristic
188C2×D4—942no—
189C2×D4—942no—
190C2×D4—944no—
191C2×D4—942no—
192C2×D4—1882no—
193C2×D4—1882no—
194C22×C4—471no—
195C22×C4—474no—
196C22×C4—472no—
197C22×C4—472no—
198C22×C4—471no—
199C22×C4—944no—
200C22×C4C22×D4711yescharacteristic
201C22×C4C22×D4712yes—
202C22×C4C22×D4712yes—
203C22×C4C22×D4711yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—944no—
207C4⋊C4—942no—
208C4⋊C4—942no—
209C4⋊C4—1882no—
210C22⋊C4—22no—
211C22⋊C4—42no—
212C22⋊C4—944no—
213C22⋊C4—942no—
214C22⋊C4—1882no—
215C22⋊C4—1882no—
216C22⋊C4—1882no—
217C22⋊C4—1882no—
218C42—944no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23—21no—
223C23—21no—
224C23—472no—
225C23—942no—
226C23—942no—
227C23—941no—
228C23—941no—
229C23—941no—
230C23—942no—
231C23—942no—
232C23—941no—
233C23—941no—
234C23C23×D4711yescharacteristic
235D4—1884no—
236D4—1884no—
237D4—1884no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—472no—
248C2×C4—474no—
249C2×C4—948no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4D4×D4712yes—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—42no—
264C22—942no—
265C22—942no—
266C22—942no—
267C22—1882no—
268C22—1881no—
269C22—1881no—
270C22—1881no—
271C22—1882no—
272C22—1882no—
273C22—1882no—
274C22C2×D4×D4711yescharacteristic
275C22#41×D4712yes—
276C22#1309406912yes—
277C22#1309407011yescharacteristic
278C22#1309407211yescharacteristic
279C4—22no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—474no—
284C4—1881no—
285C4—1882no—
286C4—1882no—
287C2—81no—
288C2—3761no—
289C2—1882no—
290C2#123×D4711yescharacteristic
291C2#1568968611yescharacteristic
292C2#1568970311yescharacteristic
293C2#1568972512yes—
294C2#1568974312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2624
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#13093982C2semidirect
3. #15689058C2semidirect
4. #15689050C2semidirect
5. #15689048C2semidirect
6. #15689040C2semidirect
7. #15689038C2semidirect
8. #15689023C2semidirect
9. #15689018C2semidirect
10. #15688982C2semidirect
11. C47×#399C2semidirect
151. #399D47semidirect
159. C47#2624semidirect