Finite Group Databasebeta

← #20248343

Subgroups — #20248343

Order 6016.

724 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 151 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×#13093995C212yesmaximal, complemented
2C2×#13093995C211yesmaximal, characteristic, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4#15689055C211yesmaximal, characteristic, complemented
5#15689048C211yesmaximal, characteristic, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689016C212yesmaximal, complemented
8#15689003C212yesmaximal, complemented
9#15688999C212yesmaximal, complemented
10#95×D47C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2212yes—
13C22×C22⋊D47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C22×C4×D47C2212yes—
16C22×C4×D47C2211yescharacteristic
17#13093995—28no—
18#13093995—24no—
19(C22⋊D47)⋊C4—24no—
20C2×C4⋊Dic47C2212yes—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×C22⋊Dic47C2212yes—
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×C4×Dic47C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C47⋊#95C2212yes—
33C22×D4×C47C2212yes—
34C22×D4×C47C2211yescharacteristic
35C2×C22⋊C4×C47C2212yes—
36C2×C22⋊C4×C47C2211yescharacteristic
37#95×C47C2211yescharacteristic
38C24×C47C2312yes—
39C24×C47C2311yescharacteristic
40C23×D47C2311yescharacteristic
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C2×D4×C47—24no—
44C2×D4×C47—42no—
45C2×D4×C47—42no—
46C22×C4×C47C2311yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2312yes—
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C2×C22⋊D47—24no—
52C2×C22⋊D47—24no—
53C2×C22⋊D47—24no—
54C2×C22⋊D47D414yescomplemented
55C22×Dic47—22no—
56C22×Dic47—42no—
57C22×Dic47C2312yes—
58C22×Dic47C2311yescharacteristic
59C22×Dic47C2312yes—
60C22×Dic47C2311yescharacteristic
61C22×Dic47C2311yescharacteristic
62C2×C4×D47—24no—
63C2×C4×D47—24no—
64C2×C4×D47—42no—
65C2×C4×D47—42no—
66C2×C4×D47D414yescomplemented
67C22⋊C4×C47—22no—
68C22⋊C4×C47—24no—
69C22⋊Dic47—24no—
70C22⋊Dic47—24no—
71C22⋊Dic47—24no—
72C22⋊Dic47—42no—
73(C2×D47)⋊C4—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47—24no—
76Dic47⋊C4—22no—
77C4×Dic47—22no—
78C23×C47—21no—
79C23×C47—21no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—22no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—22no—
89C23×C47C2×D412yes—
90C23×C47C2411yescharacteristic
91C22×D47—22no—
92C22×D47—22no—
93C22×D47C2×D412yes—
94C22×D47C2×D412yes—
95C22×D47#4112yes—
96D4×C47—48no—
97D4×C47—44no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—22no—
103C2×C4×C47C2×D412yes—
104C2×C4×C47#4114yes—
105C22⋊D47—28no—
106C22⋊D47—48no—
107C2×Dic47—21no—
108C2×Dic47—21no—
109C2×Dic47—22no—
110C2×Dic47—21no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47—22no—
118C2×Dic47—44no—
119C2×Dic47C2×D412yes—
120C2×Dic47C2×D412yes—
121C4×D47—44no—
122C4×D47—48no—
123C22×C47—22no—
124C22×C47—24no—
125C22×C47—41no—
126C22×C47—41no—
127C22×C47—42no—
128C22×C47—42no—
129C22×C47—42no—
130C22×C47—42no—
131C22×C47—42no—
132C22×C47—42no—
133C22×C47—42no—
134C22×C47—42no—
135C22×C47C22×D411yescharacteristic
136C22×C47C22×D411yescharacteristic
137C22×C47C2×#4111yescharacteristic
138C22×C47C2×#4112yes—
139C22×C47H(5,𝔽2)12yes—
140C2×D47—22no—
141C2×D47—22no—
142C2×D47—24no—
143C2×D47—24no—
144C2×D47#12114yes—
145C4×C47—22no—
146C4×C47—24no—
147C4×C47—41no—
148Dic47—22no—
149Dic47—22no—
150Dic47—42no—
151Dic47—41no—
152Dic47—42no—
153#2543—471nomaximal, Sylow
154C2×C47—42no—
155C2×C47—82no—
156C2×C47C2×#12111yescharacteristic
157C2×C47#53211yescharacteristic
158C2×C47#53411yescharacteristic
159C2×C47#54612yes—
160C2×C47#55312yes—
161D47—24no—
162C2×#121—471no—
163C2×#121—472no—
164C2×C4×D4—471no—
165#398—471no—
166#397—471no—
167#394—471no—
168#392D4711yescharacteristic, complemented
169#388—472no—
170#386—472no—
171#386—472no—
172C2×#95—471no—
173C47#254311yescharacteristic, complemented, Sylow
174C22×D4—471no—
175C22×D4—472no—
176C22×D4C2×D4712yes—
177C22×D4C2×D4711yescharacteristic
178C23×C4—471no—
179C23×C4—471no—
180C23×C4—472no—
181#121—944no—
182#121—948no—
183C4×D4—944no—
184C2×C4⋊C4—471no—
185C2×C4⋊C4—472no—
186C2×C4⋊C4—471no—
187C2×C22⋊C4—472no—
188C2×C22⋊C4—472no—
189C2×C22⋊C4—472no—
190C2×C22⋊C4—471no—
191C2×C22⋊C4—472no—
192C2×C22⋊C4C2×D4711yescharacteristic
193C2×C22⋊C4C2×D4712yes—
194C2×C42—471no—
195#95—472no—
196#95—471no—
197#95—472no—
198#95—472no—
199#95C2×D4711yescharacteristic
200C24—471no—
201C24C22×D4712yes—
202C24C22×D4711yescharacteristic
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—24no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—474no—
209C2×D4—942no—
210C2×D4—942no—
211C2×D4—944no—
212C2×D4—944no—
213C2×D4—944no—
214C22×C4—471no—
215C22×C4—471no—
216C22×C4—474no—
217C22×C4—472no—
218C22×C4—471no—
219C22×C4—472no—
220C22×C4—944no—
221C22×C4—942no—
222C22×C4—944no—
223C22×C4—1882no—
224C22×C4—1882no—
225C22×C4—1882no—
226C22×C4C22×D4711yescharacteristic
227C22×C4C22×D4711yescharacteristic
228C22×C4C22×D4712yes—
229C4⋊C4—944no—
230C4⋊C4—942no—
231C4⋊C4—942no—
232C22⋊C4—22no—
233C22⋊C4—24no—
234C22⋊C4—942no—
235C22⋊C4—944no—
236C22⋊C4—944no—
237C22⋊C4—944no—
238C22⋊C4—1882no—
239C42—942no—
240C23—21no—
241C23—21no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—472no—
252C23—472no—
253C23—472no—
254C23—942no—
255C23—942no—
256C23D4×D4712yes—
257C23C23×D4711yescharacteristic
258D4—48no—
259D4—44no—
260D4—948no—
261D4—1888no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—472no—
268C2×C4—472no—
269C2×C4—941no—
270C2×C4—941no—
271C2×C4—942no—
272C2×C4—942no—
273C2×C4—941no—
274C2×C4—942no—
275C2×C4—942no—
276C2×C4—942no—
277C2×C4—942no—
278C2×C4—942no—
279C2×C4—942no—
280C2×C4—1884no—
281C2×C4—1888no—
282C2×C4—1884no—
283C2×C4D4×D4712yes—
284C2×C4#1062535214yes—
285C22—24no—
286C22—22no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—474no—
298C22—944no—
299C22—944no—
300C22—942no—
301C22—942no—
302C22C2×D4×D4711yescharacteristic
303C22C2×D4×D4711yescharacteristic
304C22#41×D4711yescharacteristic
305C22C2×#1062535212yes—
306C22#1309406912yes—
307C4—24no—
308C4—22no—
309C4—41no—
310C4—942no—
311C4—942no—
312C4—1882no—
313C4—1882no—
314C4—1881no—
315C2—42no—
316C2—82no—
317C2—944no—
318C2#121×D4711yescharacteristic
319C2#1568967111yescharacteristic
320C2#1568968311yescharacteristic
321C2#1568976012yes—
322C2#1568982012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2543
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13093995C2semidirect
2. C2×#13093995C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. #15689055C2semidirect
5. #15689048C2semidirect
6. #15689037C2semidirect
7. #15689016C2semidirect
8. #15689003C2semidirect
9. #15688999C2semidirect
10. #95×D47C2semidirect
11. C47×#392C2semidirect
54. C2×C22⋊D47D4semidirect
66. C2×C4×D47D4semidirect
168. #392D47semidirect
173. C47#2543semidirect