Finite Group Databasebeta

← #20246623

Subgroups — #20246623

Order 6016.

696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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×D4×Dic47C212yesmaximal, complemented
2C2×D4×Dic47C211yesmaximal, characteristic, complemented
3C2×#13093980C211yesmaximal, characteristic, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689046C212yesmaximal, complemented
7#15689037C212yesmaximal, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15688974C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic47C212yesmaximal, complemented
11C47×#392C211yesmaximal, characteristic
12C23×Dic47C2212yes—
13C23×Dic47C2211yescharacteristic
14D4×Dic47—28no—
15D4×Dic47—24no—
16#13093980—24no—
17C2×C4⋊Dic47C2212yes—
18C2×C4⋊Dic47C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×C4×Dic47C2211yescharacteristic
28C2×C4×Dic47C2212yes—
29C2×C4×Dic47C2211yescharacteristic
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C47⋊#95C2211yescharacteristic
33C22×D4×C47C2211yescharacteristic
34C22×D4×C47C2212yes—
35C2×C22⋊C4×C47C2212yes—
36C2×C22⋊C4×C47C2211yescharacteristic
37#95×C47C2211yescharacteristic
38C24×C47C2311yescharacteristic
39C24×C47C2312yes—
40C2×D4×C47—24no—
41C2×D4×C47—24no—
42C2×D4×C47—24no—
43C2×D4×C47—22no—
44C2×D4×C47—24no—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2312yes—
48C22×Dic47—22no—
49C22×Dic47—22no—
50C22×Dic47—24no—
51C22×Dic47—24no—
52C22×Dic47—24no—
53C22×Dic47D414yescomplemented
54C22×Dic47C2311yescharacteristic
55C22×Dic47C2312yes—
56C22×Dic47C2312yes—
57C22×Dic47C2311yescharacteristic
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2311yescharacteristic
60C22⋊C4×C47—22no—
61C22⋊C4×C47—24no—
62C22⋊Dic47—24no—
63C22⋊Dic47—24no—
64C22⋊Dic47—22no—
65C22⋊Dic47—24no—
66C22⋊Dic47—24no—
67C4⋊Dic47—22no—
68C4⋊Dic47—24no—
69Dic47⋊C4—22no—
70Dic47⋊C4—24no—
71Dic47⋊C4—22no—
72C4×Dic47—22no—
73C4×Dic47—24no—
74C4×Dic47D414yescomplemented
75C23×C47—21no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47C2×D412yes—
86C23×C47#4114yes—
87C23×C47C2411yescharacteristic
88D4×C47—28no—
89D4×C47—216no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47C2×D412yes—
96C2×C4×C47#4114yes—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—28no—
101C2×Dic47—21no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47—48no—
110C2×Dic47C2×D412yes—
111C2×Dic47C2×D412yes—
112C2×Dic47C2×D412yes—
113C2×Dic47C2×D412yes—
114C2×Dic47#4112yes—
115C22×C47—22no—
116C22×C47—24no—
117C22×C47—24no—
118C22×C47—24no—
119C22×C47—24no—
120C22×C47—42no—
121C22×C47—41no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47—41no—
126C22×C47—42no—
127C22×C47C22×D411yescharacteristic
128C22×C47C22×D411yescharacteristic
129C22×C47C2×#4111yescharacteristic
130C22×C47C2×#4112yes—
131C22×C47C2×#4112yes—
132C4×C47—22no—
133C4×C47—24no—
134C4×C47—41no—
135Dic47—22no—
136Dic47—22no—
137Dic47—42no—
138Dic47—41no—
139Dic47—42no—
140Dic47#12114yes—
141#2392—471nomaximal, Sylow
142C2×C47—42no—
143C2×C47—44no—
144C2×C47C2×#12111yescharacteristic
145C2×C47#52511yescharacteristic
146C2×C47#52512yes—
147C2×C47#52912yes—
148C2×C47#53211yescharacteristic
149C2×C4×D4—471no—
150C2×C4×D4—472no—
151C2×#117—471no—
152#398—471no—
153#397—471no—
154#396—472no—
155#394—472no—
156#394—471no—
157#392D4711yescharacteristic
158C4×C4⋊C4—471no—
159C4×C22⋊C4—472no—
160C47#239211yescharacteristic, complemented, Sylow
161C22×D4C2×D4711yescharacteristic
162C22×D4C2×D4712yes—
163C23×C4—471no—
164C23×C4—472no—
165C4×D4—944no—
166C4×D4—948no—
167#117—944no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—471no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4—471no—
172C2×C4⋊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—471no—
181C2×C42—471no—
182C2×C42—472no—
183#95—472no—
184#95—472no—
185#95—471no—
186#95C2×D4711yescharacteristic
187C24C22×D4711yescharacteristic
188C24C22×D4712yes—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—22no—
193C2×D4—24no—
194C22×C4—471no—
195C22×C4—474no—
196C22×C4—471no—
197C22×C4—471no—
198C22×C4—472no—
199C22×C4—471no—
200C22×C4—472no—
201C22×C4—942no—
202C22×C4—942no—
203C22×C4—944no—
204C22×C4—944no—
205C22×C4—944no—
206C22×C4C22×D4711yescharacteristic
207C22×C4C22×D4711yescharacteristic
208C22×C4C22×D4712yes—
209C4⋊C4—942no—
210C4⋊C4—944no—
211C4⋊C4—942no—
212C4⋊C4—942no—
213C4⋊C4—944no—
214C22⋊C4—22no—
215C22⋊C4—24no—
216C22⋊C4—942no—
217C22⋊C4—944no—
218C22⋊C4—944no—
219C22⋊C4—944no—
220C22⋊C4—944no—
221C42—474no—
222C42—942no—
223C42—944no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23D4×D4712yes—
235C23#1062535214yes—
236C23C23×D4711yescharacteristic
237D4—28no—
238D4—216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—472no—
245C2×C4—472no—
246C2×C4—472no—
247C2×C4—472no—
248C2×C4—472no—
249C2×C4—948no—
250C2×C4—941no—
251C2×C4—941no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—941no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4—942no—
260C2×C4—942no—
261C2×C4—1888no—
262C2×C4D4×D4712yes—
263C2×C4#1062535214yes—
264C22—22no—
265C22—24no—
266C22—24no—
267C22—24no—
268C22—24no—
269C22—42no—
270C22—41no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—42no—
276C22C2×D4×D4711yescharacteristic
277C22C2×D4×D4711yescharacteristic
278C22#41×D4711yescharacteristic
279C22C2×#1062535212yes—
280C22C2×#1062535212yes—
281C4—22no—
282C4—24no—
283C4—41no—
284C4—474no—
285C4—942no—
286C4—942no—
287C4—1882no—
288C4—1882no—
289C4—1881no—
290C2—42no—
291C2—44no—
292C2#121×D4711yescharacteristic
293C2#1568962911yescharacteristic
294C2#1568962912yes—
295C2#1568965412yes—
296C2#1568967111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2392
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic47C2semidirect
2. C2×D4×Dic47C2semidirect
3. C2×#13093980C2semidirect
4. #15689055C2semidirect
5. #15689048C2semidirect
6. #15689046C2semidirect
7. #15689037C2semidirect
8. #15689037C2semidirect
9. #15688974C2semidirect
10. C22⋊C4×Dic47C2semidirect
53. C22×Dic47D4semidirect
74. C4×Dic47D4semidirect
160. C47#2392semidirect