Finite Group Databasebeta

← C47×#60312 #26100010

Subgroups — C47×#60312 #26100010

Order 12032.

1902 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3460C211yesmaximal, characteristic
2C47×#2994C214yesmaximal, complemented
3C47×#2988C212yesmaximal, complemented
4C47×#2979C214yesmaximal, complemented
5C47×#2976C214yesmaximal, complemented
6C47×#2975C211yesmaximal, characteristic, complemented
7C47×#2969C214yesmaximal, complemented
8C47×#2965C212yesmaximal, complemented
9C47×#2935C214yesmaximal, complemented
10C47×#2929C214yesmaximal, complemented
11C2×C8×D4×C47C211yesmaximal, characteristic, complemented
12C2×#131×C47C2214yescomplemented
13C23×C8×C47C2212yes—
14C47×#544C411yescharacteristic
15C47×#542C414yes—
16C47×#540C414yes—
17C47×#538C414yes—
18C47×#537C411yescharacteristic
19C47×#535C412yes—
20C47×#532C2214yes—
21C47×#529C2214yes—
22C47×#525C2214yes—
23C4×#41×C47C2212yes—
24C2×C4×D4×C47C2211yescharacteristic
25C47×#446C2212yescomplemented
26C47×#446C2212yescomplemented
27C8×Q8×C47C2214yescomplemented
28C47×#436C2214yes—
29C47×#436C2214yes—
30C47×#436C2212yescomplemented
31C47×#436C2212yescomplemented
32C47×#436C2218yescomplemented
33C47×#435C2214yes—
34C47×#435C2214yes—
35C47×#435C2218yescomplemented
36C47×#435C2218yescomplemented
37C8×D4×C47C2214yes—
38C8×D4×C47C2214yes—
39C8×D4×C47C2218yes—
40C8×D4×C47C2218yescomplemented
41C8×D4×C47C2214yescomplemented
42C47×#433C2218yescomplemented
43C47×#431C2212yes—
44C47×#431C2214yescomplemented
45C47×#431C2214yescomplemented
46C47×#424C2214yescomplemented
47C2×C4⋊C8×C47C2211yescharacteristic
48C2×C4⋊C8×C47C2214yescomplemented
49C47×#408C2214yescomplemented
50C47×#408C2218yescomplemented
51C47×#407C2214yes—
52C2×C22⋊C8×C47C2212yes—
53C47×#405C2214yescomplemented
54C4×M16×C47C2214yescomplemented
55C2×C4×C8×C47C2211yescharacteristic
56C2×#41×C47C2×C412yes—
57C2×#41×C47C2314yes—
58C22×D4×C47C2×C411yescharacteristic
59C23×C4×C47C2312yes—
60#131×C47—48no—
61C2×M16×C47C2314yes—
62C2×M16×C47C2314yes—
63C2×M16×C47C2314yes—
64C2×M16×C47C2314yes—
65C22×C8×C47—44no—
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2314yes—
68C22×C8×C47C2312yes—
69C22×C8×C47C2314yes—
70C22×C8×C47C2318yes—
71C22×C8×C47C2311yescharacteristic
72C4⋊Q8×C47C2×C414yes—
73#127×C47C2×C414yes—
74#126×C47C2×C418yes—
75#125×C47C2×C414yes—
76#124×C47C2×C414yes—
77#124×C47C2×C418yes—
78#123×C47C2×C418yes—
79#123×C47C2×C418yes—
80C22⋊Q8×C47C2×C414yes—
81C22⋊Q8×C47C2×C414yes—
82C22⋊Q8×C47C2×C414yes—
83#121×C47C2×C414yes—
84#121×C47C2×C414yes—
85#121×C47C2×C414yes—
86#121×C47C2×C414yes—
87#121×C47C2×C414yes—
88#121×C47C2×C418yes—
89#120×C47C2×C418yes—
90C4×Q8×C47C2×C412yes—
91C4×Q8×C47C2312yes—
92C4×D4×C47C2×C414yes—
93C4×D4×C47C2×C414yes—
94C4×D4×C47C2×C412yes—
95C4×D4×C47C2314yes—
96C4×D4×C47C2314yes—
97C4×D4×C47C2312yes—
98C4×D4×C47C2318yes—
99#117×C47C2×C412yes—
100#117×C47C2×C414yes—
101#117×C47C2314yes—
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47C2×C412yes—
104C2×C42×C47C2311yescharacteristic
105C2×C42×C47C2314yes—
106C4⋊C8×C47C2314yes—
107C4⋊C8×C47C2312yes—
108C4⋊C8×C47C2318yes—
109C4⋊C8×C47C2314yes—
110C4⋊C8×C47C2312yes—
111C4⋊C8×C47C2314yes—
112C22⋊C8×C47C2318yes—
113C22⋊C8×C47C2314yes—
114C22⋊C8×C47C2318yes—
115C22⋊C8×C47C2318yes—
116C22⋊C8×C47C2314yes—
117C22⋊C8×C47C2314yes—
118#97×C47C2314yes—
119#97×C47C2314yes—
120C4×C8×C47C2312yes—
121C4×C8×C47C2312yes—
122C4×C8×C47C2314yes—
123C4×C8×C47C2318yes—
124C24×C47C22×C412yes—
125#41×C47—28no—
126#41×C47—44no—
127#41×C47—44no—
128C2×Q8×C47C22×C412yes—
129C2×Q8×C47C22×C414yes—
130C2×D4×C47—24no—
131C2×D4×C47C22×C414yes—
132C2×D4×C47C22×C414yes—
133C2×D4×C47C22×C412yes—
134C2×D4×C47C22×C418yes—
135C2×D4×C47C22×C418yes—
136C2×D4×C47C22×C414yes—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47C22×C414yes—
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C414yes—
142C22×C4×C47C22×C412yes—
143C22×C4×C47C22×C414yes—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2411yescharacteristic
146C22×C4×C47C2414yes—
147C22×C4×C47C2414yes—
148M16×C47—28no—
149M16×C47—44no—
150M16×C47—44no—
151M16×C47—44no—
152C2×C8×C47—22no—
153C2×C8×C47—28no—
154C2×C8×C47—42no—
155C2×C8×C47—44no—
156C2×C8×C47—41no—
157C2×C8×C47—48no—
158C2×C8×C47C2414yes—
159C2×C8×C47C2411yescharacteristic
160C2×C8×C47C2414yes—
161C2×C8×C47C2412yes—
162C2×C8×C47C2414yes—
163C2×C8×C47C2411yescharacteristic
164C4⋊C4×C47C22×C414yes—
165C4⋊C4×C47C22×C412yes—
166C4⋊C4×C47C22×C414yes—
167C4⋊C4×C47C22×C412yes—
168C4⋊C4×C47C22×C414yes—
169C4⋊C4×C47C22×C414yes—
170C4⋊C4×C47C22×C414yes—
171C4⋊C4×C47C22×C418yes—
172C22⋊C4×C47C22×C418yes—
173C22⋊C4×C47C22×C414yes—
174C22⋊C4×C47C22×C414yes—
175C22⋊C4×C47C22×C414yes—
176C22⋊C4×C47C22×C418yes—
177C22⋊C4×C47C22×C418yes—
178C22⋊C4×C47C22×C418yes—
179C42×C47C22×C412yes—
180C42×C47C22×C414yes—
181C42×C47C22×C414yes—
182C42×C47C2412yes—
183C42×C47C2414yes—
184C23×C47—24no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47C23×C414yes—
188C23×C47C23×C414yes—
189C23×C47C23×C411yescharacteristic
190Q8×C47—24no—
191Q8×C47—44no—
192D4×C47—28no—
193D4×C47—28no—
194D4×C47—24no—
195D4×C47—48no—
196D4×C47—44no—
197D4×C47—48no—
198C2×C4×C47—28no—
199C2×C4×C47—21no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—21no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—44no—
206C2×C4×C47—42no—
207C2×C4×C47—41no—
208C2×C4×C47—44no—
209C2×C4×C47#13114yescomplemented
210C2×C4×C47C23×C412yes—
211C2×C4×C47C23×C411yescharacteristic
212C2×C4×C47C23×C414yes—
213C2×C4×C47C23×C414yes—
214C2×C4×C47C23×C414yes—
215C2×C4×C47C23×C414yes—
216C2×C4×C47C23×C412yes—
217C2×C4×C47C2511yescharacteristic
218C8×C47—21no—
219C8×C47—24no—
220C8×C47—24no—
221C8×C47—22no—
222C8×C47—24no—
223C8×C47H(5,𝔽2)12yes—
224#60312C4711yesmaximal, characteristic, direct product factor, Sylow
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—24no—
228C22×C47—24no—
229C22×C47—24no—
230C22×C47—24no—
231C22×C47—24no—
232C22×C47—24no—
233C22×C47—48no—
234C22×C47C2×#13112yes—
235C22×C47C24×C411yescharacteristic
236C4×C47—21no—
237C4×C47—24no—
238C4×C47—24no—
239C4×C47—24no—
240C4×C47—22no—
241C4×C47—24no—
242C4×C47C2×#13114yes—
243C4×C47C2×H(5,𝔽2)11yescharacteristic
244C4×C47#58511yescharacteristic
245#3460C2×C4711yescharacteristic
246#2994C2×C4714yescomplemented
247#2988C2×C4712yescomplemented
248#2979C2×C4714yescomplemented
249#2976C2×C4714yescomplemented
250#2975C2×C4711yescharacteristic, complemented
251#2969C2×C4714yescomplemented
252#2965C2×C4712yescomplemented
253#2935C2×C4714yescomplemented
254#2929C2×C4714yescomplemented
255C2×C8×D4C2×C4711yescharacteristic, complemented
256C2×C47—22no—
257C2×C47—44no—
258C2×C47—44no—
259C2×C47C4×H(5,𝔽2)11yescharacteristic
260C2×C47C22×#13111yescharacteristic
261C2×C47#357311yescharacteristic
262C2×#131C22×C4714yescomplemented
263C23×C8C22×C4712yes—
264#544C4×C4711yescharacteristic
265#542C4×C4714yes—
266#540C4×C4714yes—
267#538C4×C4714yes—
268#537C4×C4711yescharacteristic
269#535C4×C4712yes—
270#532C22×C4714yes—
271#529C22×C4714yes—
272#525C22×C4714yes—
273C4×#41C22×C4712yes—
274C2×C4×D4C22×C4711yescharacteristic
275#446C22×C4712yescomplemented
276#446C22×C4712yescomplemented
277C8×Q8C22×C4714yescomplemented
278#436C22×C4714yes—
279#436C22×C4714yes—
280#436C22×C4712yescomplemented
281#436C22×C4712yescomplemented
282#436C22×C4718yescomplemented
283#435C22×C4714yes—
284#435C22×C4714yes—
285#435C22×C4718yescomplemented
286#435C22×C4718yescomplemented
287C8×D4C22×C4714yes—
288C8×D4C22×C4714yes—
289C8×D4C22×C4718yes—
290C8×D4C22×C4718yescomplemented
291C8×D4C22×C4714yescomplemented
292#433C22×C4718yescomplemented
293#431C22×C4712yes—
294#431C22×C4714yescomplemented
295#431C22×C4714yescomplemented
296#424C22×C4714yescomplemented
297C2×C4⋊C8C22×C4711yescharacteristic
298C2×C4⋊C8C22×C4714yescomplemented
299#408C22×C4714yescomplemented
300#408C22×C4718yescomplemented
301#407C22×C4714yes—
302C2×C22⋊C8C22×C4712yes—
303#405C22×C4714yescomplemented
304C4×M16C22×C4714yescomplemented
305C2×C4×C8C22×C4711yescharacteristic
306C47#6031211yescharacteristic, direct product factor, Sylow
307C2×#41C2×C4×C4712yes—
308C2×#41C23×C4714yes—
309C22×D4C2×C4×C4711yescharacteristic
310C23×C4C23×C4712yes—
311#131—48no—
312C2×M16C23×C4714yes—
313C2×M16C23×C4714yes—
314C2×M16C23×C4714yes—
315C2×M16C23×C4714yes—
316C22×C8—44no—
317C22×C8C23×C4711yescharacteristic
318C22×C8C23×C4714yes—
319C22×C8C23×C4712yes—
320C22×C8C23×C4714yes—
321C22×C8C23×C4718yes—
322C22×C8C23×C4711yescharacteristic
323C4⋊Q8C2×C4×C4714yes—
324#127C2×C4×C4714yes—
325#126C2×C4×C4718yes—
326#125C2×C4×C4714yes—
327#124C2×C4×C4714yes—
328#124C2×C4×C4718yes—
329#123C2×C4×C4718yes—
330#123C2×C4×C4718yes—
331C22⋊Q8C2×C4×C4714yes—
332C22⋊Q8C2×C4×C4714yes—
333C22⋊Q8C2×C4×C4714yes—
334#121C2×C4×C4714yes—
335#121C2×C4×C4714yes—
336#121C2×C4×C4714yes—
337#121C2×C4×C4714yes—
338#121C2×C4×C4714yes—
339#121C2×C4×C4718yes—
340#120C2×C4×C4718yes—
341C4×Q8C2×C4×C4712yes—
342C4×Q8C23×C4712yes—
343C4×D4C2×C4×C4714yes—
344C4×D4C2×C4×C4714yes—
345C4×D4C2×C4×C4712yes—
346C4×D4C23×C4714yes—
347C4×D4C23×C4714yes—
348C4×D4C23×C4712yes—
349C4×D4C23×C4718yes—
350#117C2×C4×C4712yes—
351#117C2×C4×C4714yes—
352#117C23×C4714yes—
353C2×C4⋊C4C2×C4×C4711yescharacteristic
354C2×C22⋊C4C2×C4×C4712yes—
355C2×C42C23×C4711yescharacteristic
356C2×C42C23×C4714yes—
357C4⋊C8C23×C4714yes—
358C4⋊C8C23×C4712yes—
359C4⋊C8C23×C4718yes—
360C4⋊C8C23×C4714yes—
361C4⋊C8C23×C4712yes—
362C4⋊C8C23×C4714yes—
363C22⋊C8C23×C4718yes—
364C22⋊C8C23×C4714yes—
365C22⋊C8C23×C4718yes—
366C22⋊C8C23×C4718yes—
367C22⋊C8C23×C4714yes—
368C22⋊C8C23×C4714yes—
369#97C23×C4714yes—
370#97C23×C4714yes—
371C4×C8C23×C4712yes—
372C4×C8C23×C4712yes—
373C4×C8C23×C4714yes—
374C4×C8C23×C4718yes—
375C24C22×C4×C4712yes—
376#41—28no—
377#41—44no—
378#41—44no—
379C2×Q8C22×C4×C4712yes—
380C2×Q8C22×C4×C4714yes—
381C2×D4—24no—
382C2×D4C22×C4×C4714yes—
383C2×D4C22×C4×C4714yes—
384C2×D4C22×C4×C4712yes—
385C2×D4C22×C4×C4718yes—
386C2×D4C22×C4×C4718yes—
387C2×D4C22×C4×C4714yes—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4C22×C4×C4714yes—
391C22×C4C22×C4×C4711yescharacteristic
392C22×C4C22×C4×C4714yes—
393C22×C4C22×C4×C4712yes—
394C22×C4C22×C4×C4714yes—
395C22×C4C22×C4×C4711yescharacteristic
396C22×C4C24×C4711yescharacteristic
397C22×C4C24×C4714yes—
398C22×C4C24×C4714yes—
399M16—28no—
400M16—44no—
401M16—44no—
402M16—44no—
403C2×C8—22no—
404C2×C8—28no—
405C2×C8—42no—
406C2×C8—44no—
407C2×C8—41no—
408C2×C8—48no—
409C2×C8C24×C4714yes—
410C2×C8C24×C4712yes—
411C2×C8C24×C4711yescharacteristic
412C2×C8C24×C4714yes—
413C2×C8C24×C4714yes—
414C2×C8C24×C4711yescharacteristic
415C4⋊C4C22×C4×C4714yes—
416C4⋊C4C22×C4×C4712yes—
417C4⋊C4C22×C4×C4714yes—
418C4⋊C4C22×C4×C4712yes—
419C4⋊C4C22×C4×C4714yes—
420C4⋊C4C22×C4×C4714yes—
421C4⋊C4C22×C4×C4714yes—
422C4⋊C4C22×C4×C4718yes—
423C22⋊C4C22×C4×C4718yes—
424C22⋊C4C22×C4×C4714yes—
425C22⋊C4C22×C4×C4714yes—
426C22⋊C4C22×C4×C4714yes—
427C22⋊C4C22×C4×C4718yes—
428C22⋊C4C22×C4×C4718yes—
429C22⋊C4C22×C4×C4718yes—
430C42C22×C4×C4712yes—
431C42C22×C4×C4714yes—
432C42C22×C4×C4714yes—
433C42C24×C4712yes—
434C42C24×C4714yes—
435C23—24no—
436C23—42no—
437C23—42no—
438C23C23×C4×C4714yes—
439C23C23×C4×C4714yes—
440C23C23×C4×C4711yescharacteristic
441Q8—24no—
442Q8—44no—
443D4—28no—
444D4—28no—
445D4—24no—
446D4—48no—
447D4—44no—
448D4—48no—
449C2×C4—28no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—44no—
460C2×C4#131×C4714yescomplemented
461C2×C4C23×C4×C4712yes—
462C2×C4C23×C4×C4711yescharacteristic
463C2×C4C23×C4×C4714yes—
464C2×C4C23×C4×C4714yes—
465C2×C4C23×C4×C4714yes—
466C2×C4C23×C4×C4714yes—
467C2×C4C23×C4×C4712yes—
468C2×C4C25×C4711yescharacteristic
469C8—21no—
470C8—24no—
471C8—24no—
472C8—22no—
473C8—24no—
474C8H(5,𝔽2)×C4712yes—
475C22—21no—
476C22—21no—
477C22—24no—
478C22—24no—
479C22—24no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—48no—
484C22C2×#131×C4712yes—
485C22C24×C4×C4711yescharacteristic
486C4—24no—
487C4—22no—
488C4—24no—
489C4—21no—
490C4—24no—
491C4—24no—
492C4C2×#131×C4714yes—
493C4C2×H(5,𝔽2)×C4711yescharacteristic
494C4C47×#58511yescharacteristic
495C2—22no—
496C2—44no—
497C2—44no—
498C2C4×H(5,𝔽2)×C4711yescharacteristic
499C2C22×#131×C4711yescharacteristic
500C2C47×#357311yescharacteristic
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC47×#3460C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2994C2semidirect
3. C47×#2988C2semidirect
4. C47×#2979C2semidirect
5. C47×#2976C2semidirect
6. C47×#2975C2semidirect
7. C47×#2969C2semidirect
8. C47×#2965C2semidirect
9. C47×#2935C2semidirect
10. C47×#2929C2semidirect
11. C2×C8×D4×C47C2semidirect
12. C2×#131×C47C22semidirect
25. C47×#446C22semidirect
26. C47×#446C22semidirect
27. C8×Q8×C47C22semidirect
30. C47×#436C22semidirect
31. C47×#436C22semidirect
32. C47×#436C22semidirect
35. C47×#435C22semidirect
36. C47×#435C22semidirect
40. C8×D4×C47C22semidirect
41. C8×D4×C47C22semidirect
42. C47×#433C22semidirect
44. C47×#431C22semidirect
45. C47×#431C22semidirect
46. C47×#424C22semidirect
48. C2×C4⋊C8×C47C22semidirect
49. C47×#408C22semidirect
50. C47×#408C22semidirect
53. C47×#405C22semidirect
54. C4×M16×C47C22semidirect
209. C2×C4×C47#131semidirect
224. #60312C47direct (N × H)
246. #2994C2×C47semidirect
247. #2988C2×C47semidirect
248. #2979C2×C47semidirect
249. #2976C2×C47semidirect
250. #2975C2×C47semidirect
251. #2969C2×C47semidirect
252. #2965C2×C47semidirect
253. #2935C2×C47semidirect
254. #2929C2×C47semidirect
255. C2×C8×D4C2×C47semidirect
262. C2×#131C22×C47semidirect
275. #446C22×C47semidirect
276. #446C22×C47semidirect
277. C8×Q8C22×C47semidirect
280. #436C22×C47semidirect
281. #436C22×C47semidirect
282. #436C22×C47semidirect
285. #435C22×C47semidirect
286. #435C22×C47semidirect
290. C8×D4C22×C47semidirect
291. C8×D4C22×C47semidirect
292. #433C22×C47semidirect
294. #431C22×C47semidirect
295. #431C22×C47semidirect
296. #424C22×C47semidirect
298. C2×C4⋊C8C22×C47semidirect
299. #408C22×C47semidirect
300. #408C22×C47semidirect
303. #405C22×C47semidirect
304. C4×M16C22×C47semidirect
306. C47#60312direct (N × H)
460. C2×C4#131×C47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#34602
C47×#29942
C47×#29882
C47×#29792
C47×#29762
C47×#29752
C47×#29692
C47×#29652
C47×#29352
C47×#29292
C2×C8×D4×C472
#6031247