Finite Group Databasebeta

← C47×#60625 #26100323

Subgroups — C47×#60625 #26100323

Order 12032.

2066 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3503C211yesmaximal, characteristic, complemented
2C47×#3500C211yesmaximal, characteristic
3C47×#3141C213yesmaximal, complemented
4C47×#3140C213yesmaximal, complemented
5C47×#3137C216yesmaximal, complemented
6C47×#3136C216yesmaximal, complemented
7C47×#3135C213yesmaximal, complemented
8C2×C47×#489C213yesmaximal, complemented
9C47×#2898C212yesmaximal, complemented
10C47×#2897C212yesmaximal, complemented
11C47×#2875C211yesmaximal, characteristic, complemented
12C2×2−1+4×C47C2211yescharacteristic
13C2×H(5,𝔽2)×C47C2211yescharacteristic
14C2×#131×C47C2212yes—
15Q82×C47—21no—
16C47×#557—21no—
17C47×#554—23no—
18D4×Q8×C47—23no—
19C47×#548—21no—
20C47×#548—21no—
21C47×#546—23no—
22C47×#546—23no—
23C47×#544C2216yescomplemented
24C47×#536C2213yes—
25C47×#535C2213yes—
26C47×#533C2213yescomplemented
27C47×#532C2213yes—
28C2×C4⋊Q8×C47C2213yescomplemented
29C2×#124×C47C2213yes—
30C47×#520C2212yes—
31C4×#41×C47C2211yescharacteristic
32C47×#491C2216yescomplemented
33C47×#490C2216yescomplemented
34C47×#489C2213yescomplemented
35C47×#489C22112yescomplemented
36C47×#489C2216yescomplemented
37C47×#489C2211yescharacteristic, complemented
38C47×#489C2213yescomplemented
39C47×#489C2213yescomplemented
40C47×#488C22112yescomplemented
41C47×#487C2216yescomplemented
42C47×#486C2216yescomplemented
43C47×#419C2216yescomplemented
44C47×#418C2216yes—
45C47×#417C2216yes—
46C47×#417C2216yescomplemented
47C47×#416C2216yes—
48C47×#416C2216yescomplemented
49C2×#103×C47C2216yescomplemented
50C2×#102×C47C2216yes—
51C47×#405C2216yescomplemented
52C4×M16×C47C2213yescomplemented
53C2×#97×C47C2213yescomplemented
542−1+4×C47—28no—
55H(5,𝔽2)×C47—28no—
56C2×#41×C47—21no—
57C2×#41×C47—23no—
58C2×#41×C47C2313yes—
59C2×#41×C47C2313yes—
60C2×#41×C47C2311yescharacteristic
61C22×Q8×C47—21no—
62C22×Q8×C47—23no—
63C22×Q8×C47C2313yes—
64C22×D4×C47—23no—
65C22×D4×C47C2313yes—
66#131×C47—28no—
67C2×M16×C47C2316yes—
68C22×C8×C47C2316yes—
69C4⋊Q8×C47—26no—
70C4⋊Q8×C47—23no—
71C4⋊Q8×C47—23no—
72C4⋊Q8×C47C2313yes—
73C4⋊Q8×C47C2316yes—
74C4⋊Q8×C47C2313yes—
75C4⋊Q8×C47C2311yescharacteristic
76#127×C47C2313yes—
77#125×C47—26no—
78#125×C47C2316yes—
79#124×C47—23no—
80#124×C47—23no—
81#124×C47C2316yes—
82#124×C47C2313yes—
83#124×C47C2311yescharacteristic
84#123×C47—26no—
85C22⋊Q8×C47—23no—
86C22⋊Q8×C47—23no—
87C22⋊Q8×C47—23no—
88C22⋊Q8×C47—23no—
89C22⋊Q8×C47—212no—
90#121×C47—23no—
91#121×C47—23no—
92#121×C47—23no—
93#121×C47—23no—
94#120×C47—26no—
95C4×Q8×C47—22no—
96C4×Q8×C47—23no—
97C4×Q8×C47—23no—
98C4×Q8×C47D411yescharacteristic
99C4×Q8×C47D411yescharacteristic
100C4×D4×C47—26no—
101C4×D4×C47—23no—
102C4×D4×C47—23no—
103C4×D4×C47D413yes—
104C4×D4×C47D413yes—
105#117×C47C2316yes—
106#117×C47C2313yes—
107C2×C4⋊C4×C47—23no—
108C2×C4⋊C4×C47C2316yes—
109C2×C22⋊C4×C47—23no—
110C2×C22⋊C4×C47—23no—
111C2×C42×C47C2313yes—
112#103×C47C2316yes—
113#103×C47C23112yes—
114#103×C47C2316yes—
115#103×C47C2316yes—
116#103×C47C2312yes—
117#102×C47C2316yes—
118#102×C47C23112yes—
119#102×C47C2316yes—
120#102×C47C2316yes—
121#102×C47C2312yes—
122#97×C47C2311yescharacteristic
123#97×C47C2313yes—
124#97×C47C2316yes—
125C4×C8×C47C2316yes—
126C24×C47—23no—
127#41×C47—212no—
128#41×C47—212no—
129#41×C47—44no—
130#41×C47—412no—
131#41×C47#4118yes—
132C2×Q8×C47—21no—
133C2×Q8×C47—23no—
134C2×Q8×C47—23no—
135C2×Q8×C47—26no—
136C2×Q8×C47—212no—
137C2×Q8×C47—44no—
138C2×Q8×C47—86no—
139C2×Q8×C47C2×D411yescharacteristic
140C2×Q8×C47C2413yes—
141C2×Q8×C47C2411yescharacteristic
142C2×D4×C47—23no—
143C2×D4×C47—23no—
144C2×D4×C47—23no—
145C2×D4×C47—23no—
146C2×D4×C47—23no—
147C2×D4×C47—212no—
148C2×D4×C47—412no—
149C2×D4×C47C2×D413yes—
150C2×D4×C47C2413yes—
151C2×D4×C47C2411yescharacteristic
152C22×C4×C47—23no—
153C22×C4×C47—26no—
154C22×C4×C47—23no—
155C22×C4×C47—23no—
156C22×C4×C47C2×D413yes—
157C22×C4×C47C2×D413yes—
158C22×C4×C47C2413yes—
159M16×C47—212no—
160C2×C8×C47—212no—
161C2×C8×C47C2412yes—
162C2×C8×C47C2416yes—
163C4⋊C4×C47—23no—
164C4⋊C4×C47—26no—
165C4⋊C4×C47—26no—
166C4⋊C4×C47—23no—
167C4⋊C4×C47—23no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—26no—
170C4⋊C4×C47—26no—
171C4⋊C4×C47C2×D413yes—
172C4⋊C4×C47C2×D413yes—
173C4⋊C4×C47C2416yes—
174C4⋊C4×C47C2412yes—
175C22⋊C4×C47—26no—
176C22⋊C4×C47—23no—
177C22⋊C4×C47—23no—
178C22⋊C4×C47—26no—
179C22⋊C4×C47—26no—
180C22⋊C4×C47—21no—
181C22⋊C4×C47—21no—
182C22⋊C4×C47C2×D416yes—
183C42×C47—26no—
184C42×C47C2×D413yes—
185C42×C47C2×D413yes—
186C42×C47C2411yescharacteristic
187C42×C47C2413yes—
188C23×C47—23no—
189C23×C47—21no—
190C23×C47—46no—
191C23×C47—83no—
192C23×C47—83no—
193C23×C47C22×D413yes—
194Q8×C47—26no—
195Q8×C47—22no—
196Q8×C47—42no—
197Q8×C47—46no—
198Q8×C47—46no—
199Q8×C47—86no—
200Q8×C47#12414yes—
201D4×C47—26no—
202D4×C47—22no—
203D4×C47—46no—
204D4×C47—46no—
205D4×C47—46no—
206D4×C47—83no—
207D4×C47—83no—
208D4×C47#124112yes—
209C2×C4×C47—22no—
210C2×C4×C47—26no—
211C2×C4×C47—23no—
212C2×C4×C47—21no—
213C2×C4×C47—43no—
214C2×C4×C47—43no—
215C2×C4×C47—46no—
216C2×C4×C47—46no—
217C2×C4×C47—46no—
218C2×C4×C47—86no—
219C2×C4×C47C22×D411yescharacteristic
220C2×C4×C47C22×D411yescharacteristic
221C2×C4×C47C22×D413yes—
222C2×C4×C47C22×D413yes—
223C2×C4×C47C22×D413yes—
224C2×C4×C47C2×#41112yes—
225C2×C4×C47C2511yescharacteristic
226C8×C47—22no—
227C8×C47—26no—
228#60625C4711yesmaximal, characteristic, direct product factor, Sylow
229C22×C47—23no—
230C22×C47—23no—
231C22×C47—41no—
232C22×C47—43no—
233C22×C47—41no—
234C22×C47—43no—
235C22×C47—41no—
236C22×C47—43no—
237C22×C47—166no—
238C22×C47C2×#12416yes—
239C22×C47C23×D411yescharacteristic
240C4×C47—21no—
241C4×C47—23no—
242C4×C47—21no—
243C4×C47—23no—
244C4×C47—46no—
245C4×C47—42no—
246C4×C47—41no—
247C4×C47—43no—
248C4×C47C2×#12416yes—
249C4×C47C22×#4112yes—
250#3503C2×C4711yescharacteristic, complemented
251#3500C2×C4711yescharacteristic
252#3141C2×C4713yescomplemented
253#3140C2×C4713yescomplemented
254#3137C2×C4716yescomplemented
255#3136C2×C4716yescomplemented
256#3135C2×C4713yescomplemented
257C2×#489C2×C4713yescomplemented
258#2898C2×C4712yescomplemented
259#2897C2×C4712yescomplemented
260#2875C2×C4711yescharacteristic, complemented
261C2×C47—26no—
262C2×C47—81no—
263C2×C47—83no—
264C2×C47C22×#12411yescharacteristic
265C2×C47#358511yescharacteristic
266C2×C47#358611yescharacteristic
267C2×2−1+4C22×C4711yescharacteristic
268C2×H(5,𝔽2)C22×C4711yescharacteristic
269C2×#131C22×C4712yes—
270Q82—21no—
271#557—21no—
272#554—23no—
273D4×Q8—23no—
274#548—21no—
275#548—21no—
276#546—23no—
277#546—23no—
278#544C22×C4716yescomplemented
279#536C22×C4713yes—
280#535C22×C4713yes—
281#533C22×C4713yescomplemented
282#532C22×C4713yes—
283C2×C4⋊Q8C22×C4713yescomplemented
284C2×#124C22×C4713yes—
285#520C22×C4712yes—
286C4×#41C22×C4711yescharacteristic
287#491C22×C4716yescomplemented
288#490C22×C4716yescomplemented
289#489C22×C4713yescomplemented
290#489C22×C47112yescomplemented
291#489C22×C4716yescomplemented
292#489C22×C4711yescharacteristic, complemented
293#489C22×C4713yescomplemented
294#489C22×C4713yescomplemented
295#488C22×C47112yescomplemented
296#487C22×C4716yescomplemented
297#486C22×C4716yescomplemented
298#419C22×C4716yescomplemented
299#418C22×C4716yes—
300#417C22×C4716yes—
301#417C22×C4716yescomplemented
302#416C22×C4716yes—
303#416C22×C4716yescomplemented
304C2×#103C22×C4716yescomplemented
305C2×#102C22×C4716yes—
306#405C22×C4716yescomplemented
307C4×M16C22×C4713yescomplemented
308C2×#97C22×C4713yescomplemented
309C47#6062511yescharacteristic, direct product factor, Sylow
3102−1+4—28no—
311H(5,𝔽2)—28no—
312C2×#41—21no—
313C2×#41—23no—
314C2×#41C23×C4713yes—
315C2×#41C23×C4713yes—
316C2×#41C23×C4711yescharacteristic
317C22×Q8—21no—
318C22×Q8—23no—
319C22×Q8C23×C4713yes—
320C22×D4—23no—
321C22×D4C23×C4713yes—
322#131—28no—
323C2×M16C23×C4716yes—
324C22×C8C23×C4716yes—
325C4⋊Q8—26no—
326C4⋊Q8—23no—
327C4⋊Q8—23no—
328C4⋊Q8C23×C4713yes—
329C4⋊Q8C23×C4713yes—
330C4⋊Q8C23×C4716yes—
331C4⋊Q8C23×C4711yescharacteristic
332#127C23×C4713yes—
333#125—26no—
334#125C23×C4716yes—
335#124—23no—
336#124—23no—
337#124C23×C4713yes—
338#124C23×C4716yes—
339#124C23×C4711yescharacteristic
340#123—26no—
341C22⋊Q8—23no—
342C22⋊Q8—23no—
343C22⋊Q8—23no—
344C22⋊Q8—23no—
345C22⋊Q8—212no—
346#121—23no—
347#121—23no—
348#121—23no—
349#121—23no—
350#120—26no—
351C4×Q8—22no—
352C4×Q8—23no—
353C4×Q8—23no—
354C4×Q8D4×C4711yescharacteristic
355C4×Q8D4×C4711yescharacteristic
356C4×D4—26no—
357C4×D4—23no—
358C4×D4—23no—
359C4×D4D4×C4713yes—
360C4×D4D4×C4713yes—
361#117C23×C4716yes—
362#117C23×C4713yes—
363C2×C4⋊C4—23no—
364C2×C4⋊C4C23×C4716yes—
365C2×C22⋊C4—23no—
366C2×C22⋊C4—23no—
367C2×C42C23×C4713yes—
368#103C23×C4716yes—
369#103C23×C47112yes—
370#103C23×C4712yes—
371#103C23×C4716yes—
372#103C23×C4716yes—
373#102C23×C4716yes—
374#102C23×C47112yes—
375#102C23×C4716yes—
376#102C23×C4712yes—
377#102C23×C4716yes—
378#97C23×C4711yescharacteristic
379#97C23×C4713yes—
380#97C23×C4716yes—
381C4×C8C23×C4716yes—
382C24—23no—
383#41—212no—
384#41—212no—
385#41—44no—
386#41—412no—
387#41#41×C4718yes—
388C2×Q8—21no—
389C2×Q8—23no—
390C2×Q8—23no—
391C2×Q8—26no—
392C2×Q8—212no—
393C2×Q8—44no—
394C2×Q8—86no—
395C2×Q8C2×D4×C4711yescharacteristic
396C2×Q8C24×C4713yes—
397C2×Q8C24×C4711yescharacteristic
398C2×D4—23no—
399C2×D4—23no—
400C2×D4—23no—
401C2×D4—23no—
402C2×D4—23no—
403C2×D4—212no—
404C2×D4—412no—
405C2×D4C2×D4×C4713yes—
406C2×D4C24×C4713yes—
407C2×D4C24×C4711yescharacteristic
408C22×C4—23no—
409C22×C4—26no—
410C22×C4—23no—
411C22×C4—23no—
412C22×C4C2×D4×C4713yes—
413C22×C4C2×D4×C4713yes—
414C22×C4C24×C4713yes—
415M16—212no—
416C2×C8—212no—
417C2×C8C24×C4716yes—
418C2×C8C24×C4712yes—
419C4⋊C4—23no—
420C4⋊C4—26no—
421C4⋊C4—26no—
422C4⋊C4—23no—
423C4⋊C4—23no—
424C4⋊C4—21no—
425C4⋊C4—26no—
426C4⋊C4—26no—
427C4⋊C4C2×D4×C4713yes—
428C4⋊C4C2×D4×C4713yes—
429C4⋊C4C24×C4716yes—
430C4⋊C4C24×C4712yes—
431C22⋊C4—26no—
432C22⋊C4—23no—
433C22⋊C4—23no—
434C22⋊C4—26no—
435C22⋊C4—26no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4C2×D4×C4716yes—
439C42—26no—
440C42C2×D4×C4713yes—
441C42C2×D4×C4713yes—
442C42C24×C4713yes—
443C42C24×C4711yescharacteristic
444C23—23no—
445C23—21no—
446C23—46no—
447C23—83no—
448C23—83no—
449C23C22×D4×C4713yes—
450Q8—26no—
451Q8—22no—
452Q8—42no—
453Q8—46no—
454Q8—46no—
455Q8—86no—
456Q8#124×C4714yes—
457D4—26no—
458D4—22no—
459D4—46no—
460D4—46no—
461D4—46no—
462D4—83no—
463D4—83no—
464D4#124×C47112yes—
465C2×C4—22no—
466C2×C4—26no—
467C2×C4—23no—
468C2×C4—21no—
469C2×C4—43no—
470C2×C4—43no—
471C2×C4—46no—
472C2×C4—46no—
473C2×C4—46no—
474C2×C4—86no—
475C2×C4C22×D4×C4711yescharacteristic
476C2×C4C22×D4×C4711yescharacteristic
477C2×C4C22×D4×C4713yes—
478C2×C4C22×D4×C4713yes—
479C2×C4C22×D4×C4713yes—
480C2×C4C2×#41×C47112yes—
481C2×C4C25×C4711yescharacteristic
482C8—22no—
483C8—26no—
484C22—23no—
485C22—23no—
486C22—41no—
487C22—43no—
488C22—41no—
489C22—43no—
490C22—41no—
491C22—43no—
492C22—166no—
493C22C2×#124×C4716yes—
494C22C23×D4×C4711yescharacteristic
495C4—21no—
496C4—23no—
497C4—21no—
498C4—23no—
499C4—46no—
500C4—42no—
501C4—41no—
502C4—43no—
503C4C2×#124×C4716yes—
504C4C22×#41×C4712yes—
505C2—26no—
506C2—83no—
507C2—81no—
508C2C22×#124×C4711yescharacteristic
509C2C47×#358511yescharacteristic
510C2C47×#358611yescharacteristic
subgroupG/H
center, socleC22×C47C23×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC47×#3500C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3503C2semidirect
3. C47×#3141C2semidirect
4. C47×#3140C2semidirect
5. C47×#3137C2semidirect
6. C47×#3136C2semidirect
7. C47×#3135C2semidirect
8. C2×C47×#489C2semidirect
9. C47×#2898C2semidirect
10. C47×#2897C2semidirect
11. C47×#2875C2semidirect
23. C47×#544C22semidirect
26. C47×#533C22semidirect
28. C2×C4⋊Q8×C47C22semidirect
32. C47×#491C22semidirect
33. C47×#490C22semidirect
34. C47×#489C22semidirect
35. C47×#489C22semidirect
36. C47×#489C22semidirect
37. C47×#489C22semidirect
38. C47×#489C22semidirect
39. C47×#489C22semidirect
40. C47×#488C22semidirect
41. C47×#487C22semidirect
42. C47×#486C22semidirect
43. C47×#419C22semidirect
46. C47×#417C22semidirect
48. C47×#416C22semidirect
49. C2×#103×C47C22semidirect
51. C47×#405C22semidirect
52. C4×M16×C47C22semidirect
53. C2×#97×C47C22semidirect
228. #60625C47direct (N × H)
250. #3503C2×C47semidirect
252. #3141C2×C47semidirect
253. #3140C2×C47semidirect
254. #3137C2×C47semidirect
255. #3136C2×C47semidirect
256. #3135C2×C47semidirect
257. C2×#489C2×C47semidirect
258. #2898C2×C47semidirect
259. #2897C2×C47semidirect
260. #2875C2×C47semidirect
278. #544C22×C47semidirect
281. #533C22×C47semidirect
283. C2×C4⋊Q8C22×C47semidirect
287. #491C22×C47semidirect
288. #490C22×C47semidirect
289. #489C22×C47semidirect
290. #489C22×C47semidirect
291. #489C22×C47semidirect
292. #489C22×C47semidirect
293. #489C22×C47semidirect
294. #489C22×C47semidirect
295. #488C22×C47semidirect
296. #487C22×C47semidirect
297. #486C22×C47semidirect
298. #419C22×C47semidirect
301. #417C22×C47semidirect
303. #416C22×C47semidirect
304. C2×#103C22×C47semidirect
306. #405C22×C47semidirect
307. C4×M16C22×C47semidirect
308. C2×#97C22×C47semidirect
309. C47#60625direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35032
C47×#35002
C47×#31412
C47×#31402
C47×#31372
C47×#31362
C47×#31352
C2×C47×#4892
C47×#28982
C47×#28972
C47×#28752
#6062547