Finite Group Databasebeta

← #20246600

Subgroups — #20246600

Order 6016.

944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C22×#10625352C211yesmaximal, characteristic, complemented
2C2×D4×Dic47C212yesmaximal, complemented
3C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
4#15689044C211yesmaximal, characteristic, complemented
5#15689039C212yesmaximal, complemented
6#15689037C211yesmaximal, characteristic, complemented
7#15689035C211yesmaximal, characteristic, complemented
8#15689031C212yesmaximal, complemented
9C22⋊C4×Dic47C212yesmaximal, complemented
10#15688970C211yesmaximal, characteristic, complemented
11C47×#392C211yesmaximal, characteristic, complemented
12C2×#10625352—28no—
13C2×#10625352—24no—
14C22×Dic94C2211yescharacteristic
15C22×C22⋊D47C2211yescharacteristic
16C22×C22⋊D47C2212yes—
17C23×Dic47C2211yescharacteristic
18C23×Dic47C2212yes—
19C22×C4×D47C2211yescharacteristic
20D4×Dic47—28no—
21(C22⋊D47)⋊C4—24no—
22C2×C4⋊Dic47C2212yes—
23C2×Dic47⋊C4C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C22⋊Dic47C2212yes—
26C2×C22⋊Dic47C2212yes—
27C2×(C2×D47)⋊C4C2212yes—
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×C4×Dic47C2212yes—
30C2×C4×Dic47C2211yescharacteristic
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2212yes—
33C47⋊#95C2212yes—
34C22×D4×C47C2212yes—
35C22×D4×C47C2211yescharacteristic
36C2×C22⋊C4×C47C2212yes—
37C2×C22⋊C4×C47C2211yescharacteristic
38#95×C47C2211yescharacteristic
39C24×C47C2312yes—
40C24×C47C2311yescharacteristic
41C23×D47C2311yescharacteristic
42C2×D4×C47—24no—
43C2×D4×C47—24no—
44C2×D4×C47—24no—
45C2×D4×C47—22no—
46C2×D4×C47—24no—
47C22×C4×C47C2311yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2312yes—
50C2×C22⋊D47—24no—
51C2×C22⋊D47—22no—
52C2×C22⋊D47—22no—
53C2×C22⋊D47—24no—
54C2×C22⋊D47—24no—
55C2×C22⋊D47—22no—
56C22×Dic47—24no—
57C22×Dic47—24no—
58C22×Dic47—22no—
59C22×Dic47—24no—
60C22×Dic47D418yescomplemented
61C22×Dic47C2312yes—
62C22×Dic47C2311yescharacteristic
63C22×Dic47C2312yes—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66#10625352—232no—
67C2×C4×D47—24no—
68C2×C4×D47D414yescomplemented
69C2×Dic94—22no—
70C2×Dic94—24no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47—24no—
73C22⋊Dic47—24no—
74C22⋊Dic47—24no—
75C22⋊Dic47—24no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—24no—
78C4⋊Dic47—24no—
79Dic47⋊C4—22no—
80C4×Dic47—22no—
81C4×Dic47—24no—
82C23×C47—22no—
83C23×C47—21no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—22no—
87C23×C47—22no—
88C23×C47—21no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47—22no—
92C23×C47C2×D414yes—
93C23×C47#4112yescomplemented
94C23×C47C2411yescharacteristic
95C22×D47—22no—
96C22×D47—22no—
97C22×D47—21no—
98C22×D47—21no—
99C22×D47C2×D412yes—
100D4×C47—28no—
101D4×C47—216no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—22no—
105C2×C4×C47—21no—
106C2×C4×C47—22no—
107C2×C4×C47C2×D412yes—
108C2×C4×C47#4114yescomplemented
109C22⋊D47—216no—
110C22⋊D47—28no—
111C2×Dic47—21no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—21no—
115C2×Dic47—216no—
116C2×Dic47—22no—
117C2×Dic47—21no—
118C2×Dic47—22no—
119C2×Dic47—22no—
120C2×Dic47—22no—
121C2×Dic47—44no—
122C2×Dic47C2×D414yes—
123C2×Dic47C2×D414yes—
124C2×Dic47C2×D412yes—
125C2×Dic47#4112yescomplemented
126C4×D47—28no—
127Dic94—28no—
128C22×C47—24no—
129C22×C47—22no—
130C22×C47—24no—
131C22×C47—24no—
132C22×C47—24no—
133C22×C47—41no—
134C22×C47—42no—
135C22×C47—42no—
136C22×C47—42no—
137C22×C47—42no—
138C22×C47—41no—
139C22×C47—42no—
140C22×C47C22×D411yescharacteristic
141C22×C47C22×D412yes—
142C22×C47C2×#4111yescharacteristic
143C22×C47C2×#4111yescharacteristic
144C22×C47C2×#4112yes—
145C2×D47—22no—
146C2×D47—22no—
147C2×D47—22no—
148C2×D47—42no—
149C2×D47—42no—
150C4×C47—22no—
151C4×C47—24no—
152C4×C47—41no—
153Dic47—24no—
154Dic47—22no—
155Dic47—41no—
156Dic47—42no—
157Dic47#12014yes—
158#2388—471nomaximal, Sylow
159C2×C47—44no—
160C2×C47—42no—
161C2×C47C2×#12011yescharacteristic
162C2×C47#52512yes—
163C2×C47#52511yescharacteristic
164C2×C47#53212yes—
165C2×C47#53211yescharacteristic
166D47—42no—
167C22×#41—471no—
168C2×C4×D4—472no—
169C2×C4×D4—471no—
170#395—471no—
171#394—471no—
172#394—472no—
173#393—471no—
174#392—472no—
175#392D4711yescharacteristic, complemented
176C4×C22⋊C4—472no—
177C4×C22⋊C4—471no—
178C47#238811yescharacteristic, complemented, Sylow
179C2×#41—948no—
180C2×#41—944no—
181C22×Q8—471no—
182C22×D4—471no—
183C22×D4—472no—
184C22×D4C2×D4712yes—
185C22×D4C2×D4711yescharacteristic
186C23×C4—472no—
187C23×C4—471no—
188C23×C4—471no—
189C4×D4—944no—
190C4×D4—948no—
191C2×C4⋊C4—471no—
192C2×C4⋊C4—472no—
193C2×C22⋊C4—472no—
194C2×C22⋊C4—472no—
195C2×C22⋊C4—472no—
196C2×C22⋊C4—471no—
197C2×C22⋊C4—472no—
198C2×C22⋊C4C2×D4711yescharacteristic
199C2×C22⋊C4C2×D4712yes—
200C2×C42—471no—
201C2×C42—472no—
202#95—472no—
203#95—472no—
204#95—471no—
205#95C2×D4711yescharacteristic
206C24—471no—
207C24C22×D4712yes—
208C24C22×D4711yescharacteristic
209#41—9432no—
210C2×Q8—944no—
211C2×Q8—942no—
212C2×D4—24no—
213C2×D4—24no—
214C2×D4—24no—
215C2×D4—22no—
216C2×D4—24no—
217C2×D4—942no—
218C2×D4—944no—
219C2×D4—942no—
220C2×D4—944no—
221C2×D4—944no—
222C2×D4—942no—
223C22×C4—471no—
224C22×C4—478no—
225C22×C4—471no—
226C22×C4—472no—
227C22×C4—474no—
228C22×C4—472no—
229C22×C4—471no—
230C22×C4—944no—
231C22×C4—944no—
232C22×C4—944no—
233C22×C4—942no—
234C22×C4—944no—
235C22×C4C22×D4711yescharacteristic
236C22×C4C22×D4711yescharacteristic
237C22×C4C22×D4712yes—
238C4⋊C4—944no—
239C4⋊C4—942no—
240C22⋊C4—22no—
241C22⋊C4—24no—
242C22⋊C4—942no—
243C22⋊C4—944no—
244C22⋊C4—944no—
245C22⋊C4—944no—
246C22⋊C4—944no—
247C42—944no—
248C42—942no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—472no—
260C23—942no—
261C23—941no—
262C23—942no—
263C23—941no—
264C23D4×D4714yes—
265C23#1062535212yescomplemented
266C23C23×D4711yescharacteristic
267Q8—948no—
268D4—216no—
269D4—28no—
270D4—948no—
271D4—9416no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—474no—
278C2×C4—472no—
279C2×C4—474no—
280C2×C4—472no—
281C2×C4—948no—
282C2×C4—9416no—
283C2×C4—941no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—941no—
287C2×C4—942no—
288C2×C4—942no—
289C2×C4—941no—
290C2×C4—942no—
291C2×C4—942no—
292C2×C4—1884no—
293C2×C4D4×D4712yes—
294C2×C4#1062535214yescomplemented
295C22—24no—
296C22—24no—
297C22—24no—
298C22—22no—
299C22—24no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—42no—
307C22—942no—
308C22—942no—
309C22—942no—
310C22—1882no—
311C22—1882no—
312C22C2×D4×D4712yes—
313C22C2×D4×D4711yescharacteristic
314C22#41×D4711yescharacteristic
315C22C2×#1062535211yescharacteristic
316C22C2×#1062535212yes—
317C4—22no—
318C4—24no—
319C4—41no—
320C4—474no—
321C4—944no—
322C4—942no—
323C4—1881no—
324C4—1882no—
325C2—44no—
326C2—42no—
327C2—1882no—
328C2#120×D4711yescharacteristic
329C2#1568962912yes—
330C2#1568963311yescharacteristic
331C2#1568966812yes—
332C2#1568967111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#392C2
hypercenter#392D47
hypocenterC47#2388
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#10625352C2semidirect
2. C2×D4×Dic47C2semidirect
3. C2×(C22⋊D47)⋊C4C2semidirect
4. #15689044C2semidirect
5. #15689039C2semidirect
6. #15689037C2semidirect
7. #15689035C2semidirect
8. #15689031C2semidirect
9. C22⋊C4×Dic47C2semidirect
10. #15688970C2semidirect
11. C47×#392C2semidirect
60. C22×Dic47D4semidirect
68. C2×C4×D47D4semidirect
93. C23×C47#41semidirect
108. C2×C4×C47#41semidirect
125. C2×Dic47#41semidirect
175. #392D47semidirect
178. C47#2388semidirect
265. C23#10625352semidirect
294. C2×C4#10625352semidirect