Finite Group Databasebeta

← #20247857

Subgroups — #20247857

Order 6016.

708 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094008C211yesmaximal, characteristic, complemented
2C2×#13094007C211yesmaximal, characteristic, complemented
3C2×#13094005C211yesmaximal, characteristic, complemented
4C2×#13093996C211yesmaximal, characteristic
5C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
6#15689059C212yesmaximal, complemented
7#15689058C212yesmaximal, complemented
8#15689023C212yesmaximal, complemented
9#15688992C212yesmaximal, complemented
10C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C2×#123×C47C211yesmaximal, characteristic, complemented
12C22×C22⋊D47C2211yescharacteristic
13C22×C22⋊D47C2211yescharacteristic
14C23×Dic47C2211yescharacteristic
15C23×Dic47C2211yescharacteristic
16#13094008—24no—
17#13094007—24no—
18#13094005—24no—
19#13093996—24no—
20C2×C4⋊Dic47C2212yes—
21C2×Dic47⋊C4—24no—
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2212yes—
24C2×Dic47⋊C4C2212yes—
25C2×Dic47⋊C4C2212yes—
26C2×Dic47⋊C4C2212yes—
27C2×C22⋊Dic47C2212yes—
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×(C2×D47)⋊C4C2212yes—
31C2×(C2×D47)⋊C4C2212yes—
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×C4×Dic47C2212yes—
34C47⋊#95C2212yes—
35C22×D4×C47C2211yescharacteristic
36C23×C4×C47C2211yescharacteristic
37#123×C47—24no—
38C2×C4⋊C4×C47C2212yes—
39C2×C22⋊C4×C47C2212yes—
40C2×C22⋊C4×C47C2211yescharacteristic
41C24×C47C2311yescharacteristic
42C24×C47C2311yescharacteristic
43C23×D47C2311yescharacteristic
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2312yes—
53C2×C22⋊D47—22no—
54C2×C22⋊D47—22no—
55C2×C22⋊D47—22no—
56C2×C22⋊D47—22no—
57C2×C22⋊D47—24no—
58C22×Dic47—24no—
59C22×Dic47—22no—
60C22×Dic47—22no—
61C22×Dic47—22no—
62C22×Dic47D414yes—
63C22×Dic47C2312yes—
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2312yes—
67C22×Dic47C2311yescharacteristic
68C4⋊C4×C47—24no—
69C22⋊C4×C47—24no—
70C22⋊C4×C47D414yescomplemented
71C22⋊Dic47—22no—
72C22⋊Dic47—24no—
73C22⋊Dic47D414yescomplemented
74(C2×D47)⋊C4—24no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4—24no—
77C4⋊Dic47—24no—
78Dic47⋊C4—24no—
79Dic47⋊C4—24no—
80Dic47⋊C4—22no—
81Dic47⋊C4—24no—
82Dic47⋊C4—24no—
83C4×Dic47—24no—
84C23×C47—22no—
85C23×C47—22no—
86C23×C47—21no—
87C23×C47—21no—
88C23×C47—21no—
89C23×C47—22no—
90C23×C47—22no—
91C23×C47C2×D412yes—
92C23×C47C2×D412yes—
93C23×C47C2×D412yes—
94C23×C47C2411yescharacteristic
95C22×D47—21no—
96C22×D47—21no—
97C22×D47—21no—
98C22×D47—22no—
99C22×D47—22no—
100D4×C47—44no—
101C2×C4×C47—22no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47—21no—
105C2×C4×C47—22no—
106C2×C4×C47—21no—
107C2×C4×C47—22no—
108C2×C4×C47—21no—
109C2×C4×C47—44no—
110C2×C4×C47C2×D414yes—
111C22⋊D47—44no—
112C22⋊D47—44no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—28no—
117C2×Dic47—22no—
118C2×Dic47—21no—
119C2×Dic47—22no—
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—22no—
123C2×Dic47—44no—
124C2×Dic47C2×D414yes—
125C2×Dic47C2×D412yes—
126C2×Dic47C2×D412yes—
127C2×Dic47#4114yes—
128C22×C47—22no—
129C22×C47—22no—
130C22×C47—24no—
131C22×C47—24no—
132C22×C47—41no—
133C22×C47—41no—
134C22×C47—41no—
135C22×C47—42no—
136C22×C47—42no—
137C22×C47#12714yes—
138C22×C47C22×D411yescharacteristic
139C22×C47C22×D411yescharacteristic
140C22×C47C22×D411yescharacteristic
141C22×C47C2×#4112yes—
142C22×C472−1+412yes—
143C2×D47—41no—
144C2×D47—41no—
145C2×D47—41no—
146C2×D47—42no—
147C2×D47—42no—
148C4×C47—24no—
149C4×C47—42no—
150C4×C47—41no—
151Dic47—22no—
152Dic47—24no—
153Dic47—42no—
154Dic47—41no—
155Dic47#12314yescomplemented
156#2501—471nomaximal, Sylow
157C2×C47—24no—
158C2×C47—81no—
159C2×C47C2×#12311yescharacteristic
160C2×C47C2×#12711yescharacteristic
161C2×C47#53611yescharacteristic
162C2×C47#54712yes—
163C2×C47#54712yes—
164D47—81no—
165C2×#123—471no—
166C2×#123—471no—
167C2×#123—471no—
168C2×#123D4711yescharacteristic, complemented
169C2×#121—471no—
170C22×C4⋊C4—471no—
171#399—472no—
172#399—472no—
173#390—472no—
174#384—472no—
175C4×C22⋊C4—471no—
176C47#250111yescharacteristic, complemented, Sylow
177C22×D4—471no—
178C22×D4—471no—
179C22×D4C2×D4711yescharacteristic
180C23×C4—471no—
181C23×C4—471no—
182C23×C4C2×D4711yescharacteristic
183#123—24no—
184#123—944no—
185#123—944no—
186#123—944no—
187#121—944no—
188C2×C4⋊C4—472no—
189C2×C4⋊C4—472no—
190C2×C4⋊C4—471no—
191C2×C4⋊C4—472no—
192C2×C4⋊C4—472no—
193C2×C4⋊C4—472no—
194C2×C4⋊C4—944no—
195C2×C4⋊C4C2×D4712yes—
196C2×C22⋊C4—471no—
197C2×C22⋊C4—471no—
198C2×C22⋊C4—472no—
199C2×C22⋊C4—471no—
200C2×C22⋊C4—472no—
201C2×C22⋊C4—472no—
202C2×C22⋊C4C2×D4712yes—
203C2×C22⋊C4C2×D4711yescharacteristic
204C2×C42—472no—
205#95—472no—
206C24—471no—
207C24C22×D4711yescharacteristic
208C24C22×D4711yescharacteristic
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—942no—
213C2×D4—944no—
214C2×D4—942no—
215C2×D4—942no—
216C2×D4—942no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—471no—
221C22×C4—474no—
222C22×C4—471no—
223C22×C4—472no—
224C22×C4—472no—
225C22×C4—471no—
226C22×C4—944no—
227C22×C4—942no—
228C22×C4—942no—
229C22×C4—942no—
230C22×C4C22×D4712yes—
231C22×C4C22×D4711yescharacteristic
232C22×C4C22×D4712yes—
233C4⋊C4—24no—
234C4⋊C4—944no—
235C4⋊C4—944no—
236C4⋊C4—942no—
237C4⋊C4—944no—
238C4⋊C4—944no—
239C4⋊C4—944no—
240C22⋊C4—24no—
241C22⋊C4—474no—
242C22⋊C4—942no—
243C22⋊C4—944no—
244C22⋊C4—942no—
245C22⋊C4—944no—
246C22⋊C4—944no—
247C22⋊C4C22⋊D4714yescomplemented
248C42—944no—
249C23—22no—
250C23—22no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23—941no—
257C23—941no—
258C23—941no—
259C23—942no—
260C23—942no—
261C23D4×D4712yes—
262C23D4×D4712yes—
263C23C2×C22⋊D4712yes—
264C23C23×D4711yescharacteristic
265D4—44no—
266D4—1884no—
267D4—1884no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—44no—
277C2×C4—472no—
278C2×C4—474no—
279C2×C4—474no—
280C2×C4—472no—
281C2×C4—948no—
282C2×C4—942no—
283C2×C4—942no—
284C2×C4—942no—
285C2×C4—942no—
286C2×C4—941no—
287C2×C4—942no—
288C2×C4—941no—
289C2×C4—942no—
290C2×C4—941no—
291C2×C4—1884no—
292C2×C4C2×C22⋊D4714yes—
293C22—24no—
294C22—24no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—1882no—
303C22—1882no—
304C22—1881no—
305C22—1881no—
306C22—1881no—
307C22#1309402014yes—
308C22C2×D4×D4711yescharacteristic
309C22C2×D4×D4711yescharacteristic
310C22C22×C22⋊D4711yescharacteristic
311C22#41×D4712yes—
312C22#1309407112yes—
313C4—24no—
314C4—42no—
315C4—41no—
316C4—474no—
317C4—944no—
318C4—942no—
319C4—1882no—
320C4—1881no—
321C2—24no—
322C2—81no—
323C2—3761no—
324C2#123×D4711yescharacteristic
325C2C2×#1309402011yescharacteristic
326C2#1568969511yescharacteristic
327C2#1568977112yes—
328C2#1568977212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2501
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#13094008C2semidirect
2. C2×#13094007C2semidirect
3. C2×#13094005C2semidirect
5. C22×Dic47⋊C4C2semidirect
6. #15689059C2semidirect
7. #15689058C2semidirect
8. #15689023C2semidirect
9. #15688992C2semidirect
10. C22⋊C4×Dic47C2semidirect
11. C2×#123×C47C2semidirect
70. C22⋊C4×C47D4semidirect
73. C22⋊Dic47D4semidirect
155. Dic47#123semidirect
168. C2×#123D47semidirect
176. C47#2501semidirect
247. C22⋊C4C22⋊D47semidirect