Finite Group Databasebeta

← #20252602

Subgroups — #20252602

Order 6016.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D47C211yesmaximal, characteristic, complemented
2C2×#13094044C211yesmaximal, characteristic, complemented
3#15689630C211yesmaximal, characteristic, complemented
4#15689284C211yesmaximal, characteristic, complemented
5#15689282C211yesmaximal, characteristic, complemented
6#15689277C211yesmaximal, characteristic, complemented
7#15689272C211yesmaximal, characteristic, complemented
8#15689267C211yesmaximal, characteristic, complemented
9#15689265C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689255C211yesmaximal, characteristic, complemented
12#15689120C211yesmaximal, characteristic, complemented
13#15689119C211yesmaximal, characteristic, complemented
14C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
15C2×#135×C47C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350—21no—
18C2×#10625350C2211yescharacteristic
19C2×#10625352—21no—
20C2×#10625352C2211yescharacteristic
21#41×D47—24no—
22#41×D47—24no—
23C2×Q8×D47C2211yescharacteristic
24C2×D4×D47—21no—
25C2×D4×D47C2211yescharacteristic
26C22×C4×D47—21no—
27C22×C4×D47C2211yescharacteristic
28#13094044—24no—
29C2×#10625337C2211yescharacteristic, complemented
30C2×#10625335C2211yescharacteristic, complemented
31C2×#10625336C2211yescharacteristic, complemented
32C2×#10625334C2211yescharacteristic, complemented
33C22×C47⋊C8C2211yescharacteristic, complemented
34#13094005—21no—
35#13094000C2211yescharacteristic
36#13094000C2211yescharacteristic, complemented
37#13093995C2211yescharacteristic
38#13093995C2211yescharacteristic, complemented
39#13093992—21no—
40C4×C22⋊D47—21no—
41C4×C22⋊D47—21no—
42#13093983C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093946C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic, complemented
49#13093945C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic
52(C2×D47)⋊C8C2211yescharacteristic
53(C2×D47)⋊C8C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55C2×#41×C47C2211yescharacteristic
56C2×#41×C47C2211yescharacteristic, complemented
57#135×C47—24no—
58C2×Q16×C47C2211yescharacteristic, complemented
59C2×SD16×C47C2211yescharacteristic, complemented
60C2×SD16×C47C2211yescharacteristic, complemented
61C2×D8×C47C2211yescharacteristic, complemented
62C22×C8×C47C2211yescharacteristic, complemented
63C23×D47—21no—
64C23×D47D411yescharacteristic
65#41×C47—22no—
66#41×C47—22no—
67#41×C47—22no—
68#41×C47D414yescomplemented
69C2×Q8×C47C2311yescharacteristic
70C2×Q8×C47C2311yescharacteristic
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47C2311yescharacteristic
74C2×D4×C47C2311yescharacteristic
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47C2311yescharacteristic
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47—21no—
82C2×C22⋊D47—21no—
83C22×Dic47—21no—
84C22×Dic47D411yescharacteristic
85#10625354—22no—
86#10625354—22no—
87Q8×D47—22no—
88Q8×D47—22no—
89#10625352—28no—
90#10625352—22no—
91#10625352—22no—
92D4×D47—28no—
93D4×D47—22no—
94D4×D47—22no—
95#10625350—28no—
96#10625350—22no—
97#10625350D414yescomplemented
98C2×D188—21no—
99C2×D188C2311yescharacteristic
100C2×C4×D47—28no—
101C2×C4×D47—21no—
102C2×C4×D47—21no—
103C2×C4×D47—22no—
104C2×C4×D47—22no—
105C2×C4×D47—21no—
106C2×C4×D47D411yescharacteristic
107C2×C4×D47D411yescharacteristic
108C2×C4×D47C2311yescharacteristic
109C2×C4×D47C2311yescharacteristic
110C2×Dic94—21no—
111C2×Dic94C2311yescharacteristic
112Q16×C47—22no—
113SD16×C47—22no—
114SD16×C47—22no—
115D8×C47—22no—
116C2×C8×C47—22no—
117C2×C8×C47C2311yescharacteristic
118C2×C8×C47C2311yescharacteristic
119C22⋊Dic47—21no—
120C22⋊Dic47—21no—
121C22⋊Dic47—21no—
122#10625337—22no—
123#10625336—22no—
124#10625335—22no—
125#10625334—22no—
126(C2×D47)⋊C4—21no—
127(C2×D47)⋊C4—21no—
128C4⋊Dic47C2311yescharacteristic
129C4⋊Dic47C2311yescharacteristic
130Dic47⋊C4—21no—
131Dic47⋊C4—21no—
132C4×Dic47—21no—
133C2×C47⋊C8—22no—
134C2×C47⋊C8C2311yescharacteristic
135C2×C47⋊C8C2311yescharacteristic
136C23×C47—21no—
137C23×C47—21no—
138C23×C47C2×D411yescharacteristic
139C22×D47—24no—
140C22×D47—22no—
141C22×D47—21no—
142C22×D47—22no—
143C22×D47—41no—
144C22×D47—42no—
145C22×D47—42no—
146C22×D47C2×D411yescharacteristic
147C22×D47C2×D411yescharacteristic
148Q8×C47—21no—
149Q8×C47—21no—
150Q8×C47—21no—
151Q8×C47C2×D412yes—
152D4×C47—24no—
153D4×C47—21no—
154D4×C47—21no—
155D4×C47—21no—
156D4×C47—42no—
157D4×C47C2×D412yes—
158C2×C4×C47—21no—
159C2×C4×C47—24no—
160C2×C4×C47—21no—
161C2×C4×C47—42no—
162C2×C4×C47C2×D412yes—
163C2×C4×C47C2×D411yescharacteristic
164C2×C4×C47C2×D412yes—
165C2×C4×C47C2411yescharacteristic
166C22⋊D47—24no—
167C22⋊D47—24no—
168C22⋊D47—24no—
169C22⋊D47—42no—
170C22⋊D47—42no—
171C2×Dic47—24no—
172C2×Dic47—22no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47C2×D411yescharacteristic
177C2×Dic47C2×D411yescharacteristic
178D188—24no—
179D188—21no—
180D188C2×D412yes—
181C4×D47—24no—
182C4×D47—24no—
183C4×D47—22no—
184C4×D47—24no—
185C4×D47—22no—
186C4×D47—21no—
187C4×D47—21no—
188C4×D47—21no—
189C4×D47—21no—
190Dic94—24no—
191Dic94—21no—
192Dic94C2×D412yes—
193C8×C47—21no—
194C8×C47—21no—
195C47⋊C8—21no—
196C47⋊C8—21no—
197C22×C47—21no—
198C22×C47—21no—
199C22×C47—22no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47#12012yes—
206C22×C47C22×D411yescharacteristic
207C2×D47—21no—
208C2×D47—21no—
209C2×D47—21no—
210C2×D47—22no—
211C2×D47—21no—
212C2×D47—21no—
213C2×D47—44no—
214C2×D47—48no—
215C2×D47—41no—
216C2×D47—41no—
217C2×D47#13512yescomplemented
218C4×C47—22no—
219C4×C47—41no—
220C4×C47#12012yes—
221C4×C47C22×D411yescharacteristic
222C4×C47C22×D411yescharacteristic
223Dic47—21no—
224Dic47—22no—
225Dic47—21no—
226Dic47—41no—
227Dic47—41no—
228#3002—471nomaximal, Sylow
229C2×C47—22no—
230C2×C47—42no—
231C2×C47—81no—
232C2×C47C2×#12011yescharacteristic
233C2×C47C2×#13511yescharacteristic
234C2×C47#57511yescharacteristic
235D47—22no—
236D47—41no—
237D47—42no—
238C22×#41—471no—
239C2×#135—471no—
240C2×#135D4711yescharacteristic, complemented
241#525—471no—
242#452—471no—
243#452—471no—
244#451—471no—
245#450—471no—
246#449—471no—
247#449—471no—
248#448—471no—
249#447—471no—
250#416—471no—
251#416—471no—
252C2×C22⋊C8—471no—
253C47#300211yescharacteristic, complemented, Sylow
254C2×#41—471no—
255C2×#41—471no—
256C2×#41—471no—
257C2×#41—941no—
258C2×#41—941no—
259C2×#41—944no—
260C2×#41—944no—
261C2×#41C2×D4711yescharacteristic
262C2×#41C2×D4711yescharacteristic, complemented
263C22×Q8—471no—
264C22×D4—471no—
265C22×D4—941no—
266C23×C4—471no—
267C23×C4—941no—
268#135—24no—
269#135—944no—
270C2×Q16—471no—
271C2×Q16C2×D4711yescharacteristic, complemented
272C2×SD16—471no—
273C2×SD16—471no—
274C2×SD16C2×D4711yescharacteristic, complemented
275C2×SD16C2×D4711yescharacteristic, complemented
276C2×D8—471no—
277C2×D8C2×D4711yescharacteristic, complemented
278C22×C8—471no—
279C22×C8C2×D4711yescharacteristic, complemented
280#123—941no—
281C22⋊Q8—471no—
282C22⋊Q8—471no—
283#121—471no—
284#121—471no—
285#120—941no—
286C4×D4—941no—
287C4×D4—941no—
288#117—471no—
289#103—471no—
290#103—471no—
291#103—471no—
292#103—471no—
293#102—471no—
294#102—471no—
295#102—471no—
296#102—471no—
297C22⋊C8—471no—
298C22⋊C8—471no—
299C22⋊C8—471no—
300C22⋊C8—471no—
301C24—471no—
302C24—941no—
303#41—22no—
304#41—22no—
305#41—22no—
306#41—474no—
307#41—948no—
308#41—942no—
309#41—948no—
310#41—942no—
311#41—942no—
312#41—942no—
313#41—942no—
314#41C22⋊D4714yescomplemented
315C2×Q8—471no—
316C2×Q8—941no—
317C2×Q8—942no—
318C2×Q8—942no—
319C2×Q8C22×D4711yescharacteristic
320C2×Q8C22×D4711yescharacteristic
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—471no—
324C2×D4—941no—
325C2×D4—941no—
326C2×D4—942no—
327C2×D4—948no—
328C2×D4—941no—
329C2×D4—941no—
330C2×D4—942no—
331C2×D4—941no—
332C2×D4—941no—
333C2×D4C22×D4711yescharacteristic
334C2×D4C22×D4711yescharacteristic
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—471no—
340C22×C4—471no—
341C22×C4—471no—
342C22×C4—941no—
343C22×C4—941no—
344C22×C4—948no—
345C22×C4—941no—
346C22×C4—942no—
347C22×C4—941no—
348C22×C4—942no—
349C22×C4C22×D4711yescharacteristic
350Q16—22no—
351Q16—942no—
352SD16—22no—
353SD16—22no—
354SD16—942no—
355SD16—942no—
356D8—22no—
357D8—942no—
358C2×C8—22no—
359C2×C8—471no—
360C2×C8—471no—
361C2×C8—942no—
362C2×C8C22×D4711yescharacteristic
363C2×C8C22×D4711yescharacteristic
364C4⋊C4—471no—
365C4⋊C4—471no—
366C4⋊C4—941no—
367C4⋊C4—941no—
368C22⋊C4—941no—
369C22⋊C4—941no—
370C22⋊C4—941no—
371C22⋊C4—941no—
372C22⋊C4—941no—
373C42—941no—
374C23—21no—
375C23—21no—
376C23—471no—
377C23—471no—
378C23—942no—
379C23—944no—
380C23—942no—
381C23—941no—
382C23—1881no—
383C23—1882no—
384C23—1882no—
385C23D4×D4711yescharacteristic
386Q8—21no—
387Q8—21no—
388Q8—21no—
389Q8—472no—
390Q8—944no—
391Q8—941no—
392Q8C2×C22⋊D4712yes—
393D4—24no—
394D4—21no—
395D4—21no—
396D4—21no—
397D4—42no—
398D4—472no—
399D4—944no—
400D4—944no—
401D4—944no—
402D4—944no—
403D4—941no—
404D4—1882no—
405D4—1882no—
406D4C2×C22⋊D4712yes—
407C2×C4—21no—
408C2×C4—24no—
409C2×C4—21no—
410C2×C4—42no—
411C2×C4—471no—
412C2×C4—471no—
413C2×C4—944no—
414C2×C4—944no—
415C2×C4—944no—
416C2×C4—942no—
417C2×C4—941no—
418C2×C4—942no—
419C2×C4—942no—
420C2×C4—944no—
421C2×C4—941no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4D4×D4712yes—
428C2×C4D4×D4711yescharacteristic
429C2×C4C2×C22⋊D4712yes—
430C2×C4C23×D4711yescharacteristic
431C8—21no—
432C8—21no—
433C8—941no—
434C8—941no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—472no—
444C22—941no—
445C22—941no—
446C22—942no—
447C22—941no—
448C22—941no—
449C22—941no—
450C22—1884no—
451C22—1888no—
452C22—1881no—
453C22—1881no—
454C22#1309399212yes—
455C22C2×D4×D4711yescharacteristic
456C4—22no—
457C4—41no—
458C4—941no—
459C4—941no—
460C4—942no—
461C4—1881no—
462C4—1881no—
463C4#1309399212yes—
464C4C2×D4×D4711yescharacteristic
465C4C22×C22⋊D4711yescharacteristic
466C2—22no—
467C2—42no—
468C2—81no—
469C2—942no—
470C2—1881no—
471C2—1882no—
472C2C2×#1309399211yescharacteristic
473C2#135×D4711yescharacteristic
474C2#1568992011yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3002
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×#41×D47C2semidirect
2. C2×#13094044C2semidirect
3. #15689630C2semidirect
4. #15689284C2semidirect
5. #15689282C2semidirect
6. #15689277C2semidirect
7. #15689272C2semidirect
8. #15689267C2semidirect
9. #15689265C2semidirect
10. #15689260C2semidirect
11. #15689255C2semidirect
12. #15689120C2semidirect
13. #15689119C2semidirect
14. C2×(C2×D47)⋊C8C2semidirect
15. C2×#135×C47C2semidirect
29. C2×#10625337C22semidirect
30. C2×#10625335C22semidirect
31. C2×#10625336C22semidirect
32. C2×#10625334C22semidirect
33. C22×C47⋊C8C22semidirect
36. #13094000C22semidirect
38. #13093995C22semidirect
42. #13093983C22semidirect
43. #13093949C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
47. #13093946C22semidirect
48. #13093946C22semidirect
49. #13093945C22semidirect
50. #13093945C22semidirect
53. (C2×D47)⋊C8C22semidirect
54. (C2×D47)⋊C8C22semidirect
56. C2×#41×C47C22semidirect
58. C2×Q16×C47C22semidirect
59. C2×SD16×C47C22semidirect
60. C2×SD16×C47C22semidirect
61. C2×D8×C47C22semidirect
62. C22×C8×C47C22semidirect
68. #41×C47D4semidirect
97. #10625350D4semidirect
217. C2×D47#135semidirect
240. C2×#135D47semidirect
253. C47#3002semidirect
262. C2×#41C2×D47semidirect
271. C2×Q16C2×D47semidirect
274. C2×SD16C2×D47semidirect
275. C2×SD16C2×D47semidirect
277. C2×D8C2×D47semidirect
279. C22×C8C2×D47semidirect
314. #41C22⋊D47semidirect