Finite Group Databasebeta

← #20252839

Subgroups — #20252839

Order 6016.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094044C211yesmaximal, characteristic, complemented
2#15689669C211yesmaximal, characteristic, complemented
3#41×Dic47C211yesmaximal, characteristic, complemented
4#15689347C211yesmaximal, characteristic, complemented
5#15689343C211yesmaximal, characteristic, complemented
6#15689340C211yesmaximal, characteristic, complemented
7#15689336C211yesmaximal, characteristic, complemented
8#15689331C211yesmaximal, characteristic, complemented
9#15689326C211yesmaximal, characteristic, complemented
10#15689321C211yesmaximal, characteristic, complemented
11#15689316C211yesmaximal, characteristic, complemented
12C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
13#15689120C211yesmaximal, characteristic, complemented
14#15689119C211yesmaximal, characteristic, complemented
15C2×#135×C47C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17#13094044—24no—
18C2×#10625337C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094022C2211yescharacteristic
24#13094020C2211yescharacteristic
25#13094013C2211yescharacteristic
26#13094011C2211yescharacteristic
27#13093996—21no—
28#13093996—21no—
29Q8×Dic47C2211yescharacteristic
30Q8×Dic47C2211yescharacteristic
31D4×Dic47—21no—
32D4×Dic47—21no—
33D4×Dic47C2211yescharacteristic
34D4×Dic47C2211yescharacteristic
35C4×C22⋊D47—21no—
36C4×C22⋊D47—21no—
37#13093983—21no—
38#13093983C2211yescharacteristic
39C2×C4×Dic47—21no—
40C2×C4×Dic47C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43Dic47⋊C8C2211yescharacteristic
44Dic47⋊C8C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093945C2211yescharacteristic
52#13093945C2211yescharacteristic
53C2×#41×C47C2211yescharacteristic
54C2×#41×C47C2211yescharacteristic
55#135×C47—24no—
56C2×Q16×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic
58C2×SD16×C47C2211yescharacteristic
59C2×D8×C47C2211yescharacteristic
60C22×C8×C47C2211yescharacteristic
61#41×C47—22no—
62#41×C47—22no—
63#41×C47—22no—
64#41×C47D414yescomplemented
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—21no—
68C2×D4×C47—21no—
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C2×C22⋊D47—21no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79C22×Dic47D411yescharacteristic
80C22×Dic47D411yescharacteristic
81#10625350—22no—
82#10625350—22no—
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×Dic94C2311yescharacteristic
86Q16×C47—22no—
87SD16×C47—22no—
88SD16×C47—22no—
89D8×C47—22no—
90C2×C8×C47—22no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98#10625337—22no—
99#10625336—22no—
100#10625335—22no—
101#10625334—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104C4⋊Dic47—21no—
105C4⋊Dic47—21no—
106C4⋊Dic47C2311yescharacteristic
107C4⋊Dic47C2311yescharacteristic
108Dic47⋊C4—21no—
109Dic47⋊C4—21no—
110C4×Dic47—21no—
111C4×Dic47—21no—
112C4×Dic47—21no—
113C4×Dic47D411yescharacteristic
114C4×Dic47D411yescharacteristic
115C4×Dic47C2311yescharacteristic
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C23×C47—21no—
121C23×C47—21no—
122C23×C47C2×D411yescharacteristic
123C22×D47—21no—
124Q8×C47—21no—
125Q8×C47—21no—
126Q8×C47—21no—
127Q8×C47C2×D412yes—
128D4×C47—24no—
129D4×C47—21no—
130D4×C47—21no—
131D4×C47—21no—
132D4×C47—42no—
133D4×C47C2×D412yes—
134C2×C4×C47—21no—
135C2×C4×C47—24no—
136C2×C4×C47—21no—
137C2×C4×C47—42no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D412yes—
140C2×C4×C47#4112yes—
141C2×C4×C47C2411yescharacteristic
142C22⋊D47—42no—
143C22⋊D47—42no—
144C22⋊D47—42no—
145C2×Dic47—22no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—41no—
150C2×Dic47—42no—
151C2×Dic47—42no—
152C2×Dic47C2×D411yescharacteristic
153C2×Dic47C2×D411yescharacteristic
154C2×Dic47C2×D411yescharacteristic
155C2×Dic47C2×D411yescharacteristic
156D188—21no—
157D188—21no—
158C4×D47—42no—
159Dic94—21no—
160Dic94—21no—
161C8×C47—21no—
162C8×C47—21no—
163C47⋊C8—21no—
164C47⋊C8—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47#12112yes—
174C22×C47C22×D411yescharacteristic
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—22no—
179C4×C47—41no—
180C4×C47#12112yes—
181C4×C47C22×D411yescharacteristic
182C4×C47C2×#4111yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—21no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189Dic47#13512yescomplemented
190#3035—471nomaximal, Sylow
191C2×C47—22no—
192C2×C47—42no—
193C2×C47—81no—
194C2×C47C2×#12111yescharacteristic
195C2×C47C2×#13511yescharacteristic
196C2×C47#57511yescharacteristic
197D47—81no—
198C2×#135—471no—
199C2×#135D4711yescharacteristic, complemented
200#532—471no—
201C4×#41—471no—
202#464—471no—
203#464—471no—
204#463—471no—
205#463—471no—
206#462—471no—
207#461—471no—
208#460—471no—
209#459—471no—
210C2×C4⋊C8—471no—
211#416—471no—
212#416—471no—
213C47#303511yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C2×#41C2×D4711yescharacteristic
216C2×#41C2×D4711yescharacteristic
217#135—24no—
218#135—944no—
219C2×Q16—471no—
220C2×Q16C2×D4711yescharacteristic
221C2×SD16—471no—
222C2×SD16—471no—
223C2×SD16C2×D4711yescharacteristic
224C2×SD16C2×D4711yescharacteristic
225C2×D8—471no—
226C2×D8C2×D4711yescharacteristic
227C22×C8—471no—
228C22×C8C2×D4711yescharacteristic
229C4⋊Q8—471no—
230#127—471no—
231#124—471no—
232#124—471no—
233#121—941no—
234#121—941no—
235C4×Q8—471no—
236C4×Q8—471no—
237C4×D4—471no—
238C4×D4—471no—
239C4×D4—941no—
240C4×D4—941no—
241C4×D4—941no—
242C4×D4—941no—
243#117—471no—
244#117—941no—
245C2×C42—471no—
246C2×C42—941no—
247C4⋊C8—471no—
248C4⋊C8—471no—
249C4⋊C8—471no—
250C4⋊C8—471no—
251#103—471no—
252#103—471no—
253#103—471no—
254#103—471no—
255#102—471no—
256#102—471no—
257#102—471no—
258#102—471no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—942no—
263#41—942no—
264#41C22⋊D4714yescomplemented
265C2×Q8—471no—
266C2×Q8C22×D4711yescharacteristic
267C2×Q8C22×D4711yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—471no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—941no—
274C2×D4C22×D4711yescharacteristic
275C2×D4C22×D4711yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4C22×D4711yescharacteristic
284Q16—22no—
285Q16—942no—
286SD16—22no—
287SD16—22no—
288SD16—942no—
289SD16—942no—
290D8—22no—
291D8—942no—
292C2×C8—22no—
293C2×C8—471no—
294C2×C8—471no—
295C2×C8—942no—
296C2×C8C22×D4711yescharacteristic
297C2×C8C22×D4711yescharacteristic
298C4⋊C4—471no—
299C4⋊C4—471no—
300C4⋊C4—941no—
301C4⋊C4—941no—
302C4⋊C4—941no—
303C4⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C42—471no—
312C42—471no—
313C42—471no—
314C42—471no—
315C42—941no—
316C42—941no—
317C42—941no—
318C23—21no—
319C23—21no—
320C23—941no—
321C23D4×D4711yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—941no—
326Q8—941no—
327Q8C2×C22⋊D4712yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—941no—
334D4—941no—
335D4—1882no—
336D4—1882no—
337D4—1882no—
338D4C2×C22⋊D4712yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—471no—
344C2×C4—471no—
345C2×C4—471no—
346C2×C4—471no—
347C2×C4—942no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—1882no—
352C2×C4—1881no—
353C2×C4—1882no—
354C2×C4—1882no—
355C2×C4D4×D4711yescharacteristic
356C2×C4#1062535212yes—
357C2×C4C2×C22⋊D4712yes—
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—941no—
362C8—941no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22#1309399612yes—
375C22C2×D4×D4711yescharacteristic
376C4—22no—
377C4—41no—
378C4—472no—
379C4—941no—
380C4—941no—
381C4—941no—
382C4—1881no—
383C4—1881no—
384C4—1881no—
385C4#1309399612yes—
386C4C22×C22⋊D4711yescharacteristic
387C4C2×#1062535211yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—3761no—
392C2C2×#1309399611yescharacteristic
393C2#135×D4711yescharacteristic
394C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3035
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094044C2semidirect
2. #15689669C2semidirect
3. #41×Dic47C2semidirect
4. #15689347C2semidirect
5. #15689343C2semidirect
6. #15689340C2semidirect
7. #15689336C2semidirect
8. #15689331C2semidirect
9. #15689326C2semidirect
10. #15689321C2semidirect
11. #15689316C2semidirect
12. C2×Dic47⋊C8C2semidirect
13. #15689120C2semidirect
14. #15689119C2semidirect
15. C2×#135×C47C2semidirect
64. #41×C47D4semidirect
189. Dic47#135semidirect
199. C2×#135D47semidirect
213. C47#3035semidirect
264. #41C22⋊D47semidirect