Finite Group Databasebeta

← #20251400

Subgroups — #20251400

Order 6016.

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

normal subgroups only

This group has 478 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×#13094009C211yesmaximal, characteristic
2C2×#13094000C211yesmaximal, characteristic, complemented
3#15689054C212yesmaximal, complemented
4#15689053C211yesmaximal, characteristic, complemented
5#15689052C212yesmaximal, complemented
6#15689050C211yesmaximal, characteristic, complemented
7#15689047C212yesmaximal, complemented
8#15689040C212yesmaximal
9#15689034C211yesmaximal, characteristic, complemented
10#15688982C211yesmaximal, characteristic, complemented
11C47×#395C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14#13094009—24no—
15#13094000—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2211yescharacteristic
25C2×(C2×D47)⋊C4C2212yes—
26C2×(C2×D47)⋊C4C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C23×D47C2311yescharacteristic
39C2×Q8×C47—22no—
40C2×Q8×C47—42no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2312yes—
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C2×D188—22no—
51C2×D188—42no—
52C2×C4×D47—42no—
53C2×C4×D47D414yes—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—42no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—42no—
61(C2×D47)⋊C4—42no—
62(C2×D47)⋊C4—42no—
63C4⋊Dic47—22no—
64Dic47⋊C4—24no—
65Dic47⋊C4—22no—
66Dic47⋊C4—42no—
67Dic47⋊C4—42no—
68C23×C47C2411yescharacteristic
69C22×D47—21no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—21no—
78C22×D47C2×D412yes—
79Q8×C47—44no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47C2×D412yes—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—21no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47C2×D412yes—
103D188—44no—
104C4×D47—44no—
105C22×C47C22×D411yescharacteristic
106C22×C47H(5,𝔽2)12yes—
107C22×C47H(5,𝔽2)11yescharacteristic
108C22×C472−1+412yes—
109C22×C472−1+411yescharacteristic
110C2×D47—22no—
111C2×D47—22no—
112C2×D47—22no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—41no—
116C2×D47—41no—
117C2×D47—41no—
118C2×D47—42no—
119C2×D47—42no—
120C4×C47—22no—
121C4×C47—41no—
122C4×C47—42no—
123C4×C47—41no—
124C4×C47—42no—
125Dic47—22no—
126Dic47—41no—
127Dic47—42no—
128Dic47—42no—
129#2814—471nomaximal, Sylow
130C2×C47#53411yescharacteristic
131C2×C47#53611yescharacteristic
132C2×C47#53711yescharacteristic
133C2×C47#56212yes—
134C2×C47#56312yes—
135D47—42no—
136D47—81no—
137C2×#123—471no—
138C2×C22⋊Q8—471no—
139#398—471no—
140#398—472no—
141#397—471no—
142#397—472no—
143#396—472no—
144#395D4711yescharacteristic, complemented
145#394—472no—
146#393—471no—
147#380—471no—
148C47#281411yescharacteristic, complemented, Sylow
149C22×Q8C2×D4711yescharacteristic
150C22×D4—471no—
151C23×C4—471no—
152#123—944no—
153C22⋊Q8—944no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—471no—
156C2×C4⋊C4—471no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4C2×D4711yescharacteristic
160C2×C4⋊C4C2×D4712yes—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—471no—
163C2×C22⋊C4—471no—
164C2×C22⋊C4—471no—
165C2×C22⋊C4—472no—
166C2×C22⋊C4—472no—
167C2×C22⋊C4—472no—
168#95—471no—
169#95—472no—
170#95—472no—
171#95—472no—
172#95C2×D4711yescharacteristic
173#95C2×D4712yes—
174C24—471no—
175C24—471no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—942no—
179C2×D4—1882no—
180C22×C4—471no—
181C22×C4—474no—
182C22×C4—471no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—1882no—
186C22×C4C22×D4711yescharacteristic
187C22×C4C22×D4712yes—
188C22×C4C22×D4712yes—
189C22×C4C22×D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—1882no—
197C4⋊C4—1882no—
198C22⋊C4—942no—
199C22⋊C4—944no—
200C22⋊C4—942no—
201C22⋊C4—942no—
202C22⋊C4—1882no—
203C22⋊C4—1882no—
204C22⋊C4—1882no—
205C23—472no—
206C23—942no—
207C23—941no—
208C23—942no—
209C23—941no—
210C23—941no—
211C23—942no—
212C23—941no—
213C23—942no—
214C23—941no—
215C23C23×D4711yescharacteristic
216Q8—44no—
217D4—1884no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—472no—
231C2×C4—942no—
232C2×C4—941no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—1884no—
241C2×C4D4×D4712yes—
242C22—942no—
243C22—942no—
244C22—942no—
245C22—1882no—
246C22—1882no—
247C22—1881no—
248C22—1881no—
249C22—1881no—
250C22—1882no—
251C22—1882no—
252C22C2×D4×D4711yescharacteristic
253C22#1309406912yes—
254C22#1309407011yescharacteristic
255C22#1309407212yes—
256C22#1309407211yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—41no—
262C4—942no—
263C4—1882no—
264C4—1881no—
265C4—1882no—
266C2—3761no—
267C2—1882no—
268C2#1568968311yescharacteristic
269C2#1568969811yescharacteristic
270C2#1568970311yescharacteristic
271C2#1568986912yes—
272C2#1568987212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2814
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#13094000C2semidirect
3. #15689054C2semidirect
4. #15689053C2semidirect
5. #15689052C2semidirect
6. #15689050C2semidirect
7. #15689047C2semidirect
9. #15689034C2semidirect
10. #15688982C2semidirect
11. C47×#395C2semidirect
144. #395D47semidirect
148. C47#2814semidirect