Finite Group Databasebeta

← C47×#12795 #26052493

Subgroups — C47×#12795 #26052493

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2321C211yesmaximal, characteristic
2C2×C47×AΣL(1,𝔽16)C212yesmaximal
3C47×#1800C211yesmaximal, characteristic, complemented
4C47×#1799C211yesmaximal, characteristic, complemented
5C47×#1390C212yesmaximal, complemented
6C2×#120×C47C2211yescharacteristic
7C2×C4×D4×C47C2211yescharacteristic
8C22×C22⋊C4×C47C411yescharacteristic, complemented
9C47×#423—21no—
10C2×#100×C47C2212yes—
11C2×#99×C47C2212yes—
12C47×#390—21no—
13C47×#388—21no—
14C47×#388—21no—
15C47×#386—21no—
16C47×#386C2211yescharacteristic
17C47×#385C411yescharacteristic, complemented
18C47×#380—21no—
19C47×#379C411yescharacteristic, complemented
20C4×C22⋊C4×C47C411yescharacteristic, complemented
21C47×AΣL(1,𝔽16)—24no—
22C47×#343—21no—
23C47×#342—21no—
24C25×C47C2×C411yescharacteristic
25C22×D4×C47—21no—
26C22×D4×C47C2311yescharacteristic
27C23×C4×C47C2×C411yescharacteristic
28C23×C4×C47C2×C411yescharacteristic
29C23×C4×C47D411yescharacteristic
30C2×M16×C47—22no—
31#120×C47—21no—
32#120×C47—21no—
33#120×C47D412yes—
34#120×C47Q812yes—
35C4×D4×C47—41no—
36C4×D4×C47—41no—
37C2×C4⋊C4×C47—21no—
38C2×C4⋊C4×C47—41no—
39C2×C4⋊C4×C47D411yescharacteristic
40C2×C22⋊C4×C47—21no—
41C2×C22⋊C4×C47—21no—
42C2×C22⋊C4×C47—21no—
43C2×C22⋊C4×C47—22no—
44C2×C22⋊C4×C47—21no—
45C2×C22⋊C4×C47—21no—
46C2×C22⋊C4×C47—21no—
47C2×C22⋊C4×C47—41no—
48C2×C22⋊C4×C47—41no—
49C2×C22⋊C4×C47C2×C411yescharacteristic
50C2×C22⋊C4×C47C2×C411yescharacteristic
51C2×C22⋊C4×C47C2×C411yescharacteristic
52C2×C22⋊C4×C47D411yescharacteristic
53C2×C42×C47—21no—
54C2×C42×C47D411yescharacteristic
55C4⋊C8×C47—41no—
56C4⋊C8×C47—41no—
57#100×C47—22no—
58#100×C47—22no—
59#99×C47—22no—
60#99×C47—22no—
61#95×C47—21no—
62#95×C47—21no—
63#95×C47—21no—
64#95×C47—41no—
65C24×C47—21no—
66C24×C47—21no—
67C24×C47—41no—
68C24×C47—41no—
69C24×C47—81no—
70C24×C47—81no—
71C24×C47C4⋊C412yescomplemented
72C24×C47C22×C411yescharacteristic
73C24×C47C2×D411yescharacteristic
74C2×D4×C47—22no—
75C2×D4×C47—22no—
76C2×D4×C47—41no—
77C2×D4×C47—41no—
78C2×D4×C47—81no—
79C2×D4×C47—81no—
80C2×D4×C47C2×D411yescharacteristic
81C2×D4×C47C2×Q811yescharacteristic
82C2×D4×C47#4111yescharacteristic
83C2×D4×C47#4111yescharacteristic
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—41no—
92C22×C4×C47—42no—
93C22×C4×C47—81no—
94C22×C4×C47—81no—
95C22×C4×C47—81no—
96C22×C4×C47C22⋊C411yescharacteristic
97C22×C4×C47C22⋊C411yescharacteristic
98C22×C4×C47C22⋊C411yescharacteristic
99C22×C4×C47C22⋊C411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101M16×C47—42no—
102M16×C47—42no—
103C2×C8×C47—42no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—81no—
106C4⋊C4×C47—82no—
107C22⋊C4×C47—21no—
108C22⋊C4×C47—22no—
109C22⋊C4×C47—22no—
110C22⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—42no—
113C22⋊C4×C47—41no—
114C22⋊C4×C47—41no—
115C22⋊C4×C47—41no—
116C22⋊C4×C47—42no—
117C22⋊C4×C47—42no—
118C22⋊C4×C47—81no—
119C22⋊C4×C47—81no—
120C22⋊C4×C47—81no—
121C22⋊C4×C47C4⋊C412yescomplemented
122C42×C47—21no—
123C42×C47—21no—
124C42×C47—81no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—22no—
130C23×C47—41no—
131C23×C47—41no—
132C23×C47—41no—
133C23×C47—41no—
134C23×C47—41no—
135C23×C47—41no—
136C23×C47—41no—
137C23×C47—41no—
138C23×C47—42no—
139C23×C47—42no—
140C23×C47—41no—
141C23×C47—41no—
142C23×C47—82no—
143C23×C47—82no—
144C23×C47—82no—
145C23×C47—82no—
146C23×C47—84no—
147C23×C47C2×C22⋊C411yescharacteristic
148C23×C47C2×C4⋊C411yescharacteristic
149C23×C47#11711yescharacteristic
150C23×C47#12111yescharacteristic
151C23×C47C22⋊Q811yescharacteristic
152D4×C47—41no—
153D4×C47—41no—
154D4×C47—41no—
155D4×C47—41no—
156D4×C47—82no—
157D4×C47—82no—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—22no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—41no—
165C2×C4×C47—42no—
166C2×C4×C47—41no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—41no—
174C2×C4×C47—41no—
175C2×C4×C47—41no—
176C2×C4×C47—41no—
177C2×C4×C47—81no—
178C2×C4×C47—81no—
179C2×C4×C47—81no—
180C2×C4×C47—82no—
181C2×C4×C47—82no—
182C2×C4×C47—82no—
183C2×C4×C47—82no—
184C2×C4×C47#9911yescharacteristic
185C2×C4×C47#9911yescharacteristic
186C2×C4×C47#12111yescharacteristic
187C2×C4×C47C22⋊Q811yescharacteristic
188C8×C47—82no—
189#12795C4711yesmaximal, characteristic, direct product factor, Sylow
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—21no—
193C22×C47—21no—
194C22×C47—21no—
195C22×C47—21no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—42no—
201C22×C47—42no—
202C22×C47—42no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—42no—
208C22×C47—81no—
209C22×C47—81no—
210C22×C47—81no—
211C22×C47—84no—
212C22×C47—84no—
213C22×C47—81no—
214C22×C47—81no—
215C22×C47#38011yescharacteristic
216C22×C47C2×#9911yescharacteristic
217C22×C47#41011yescharacteristic
218C4×C47—21no—
219C4×C47—21no—
220C4×C47—21no—
221C4×C47—21no—
222C4×C47—42no—
223C4×C47—41no—
224C4×C47—41no—
225C4×C47—41no—
226C4×C47—81no—
227C4×C47—81no—
228C4×C47—162no—
229#2321C2×C4711yescharacteristic
230C2×AΣL(1,𝔽16)C2×C4712yes—
231#1800C2×C4711yescharacteristic, complemented
232#1799C2×C4711yescharacteristic, complemented
233#1390C2×C4712yescomplemented
234C2×C47—21no—
235C2×C47—21no—
236C2×C47—41no—
237C2×C47—41no—
238C2×C47—41no—
239C2×C47—41no—
240C2×C47—82no—
241C2×C47#179911yescharacteristic
242C2×C47#212111yescharacteristic
243C2×C47#212211yescharacteristic
244C2×#120C22×C4711yescharacteristic
245C2×C4×D4C22×C4711yescharacteristic
246C22×C22⋊C4C4×C4711yescharacteristic, complemented
247#423—21no—
248C2×#100C22×C4712yes—
249C2×#99C22×C4712yes—
250#390—21no—
251#388—21no—
252#388—21no—
253#386—21no—
254#386C22×C4711yescharacteristic
255#385C4×C4711yescharacteristic, complemented
256#380—21no—
257#379C4×C4711yescharacteristic, complemented
258C4×C22⋊C4C4×C4711yescharacteristic, complemented
259AΣL(1,𝔽16)—24no—
260#343—21no—
261#342—21no—
262C47#1279511yescharacteristic, direct product factor, Sylow
263C25C2×C4×C4711yescharacteristic
264C22×D4—21no—
265C22×D4C23×C4711yescharacteristic
266C23×C4C2×C4×C4711yescharacteristic
267C23×C4C2×C4×C4711yescharacteristic
268C23×C4D4×C4711yescharacteristic
269C2×M16—22no—
270#120—21no—
271#120—21no—
272#120D4×C4712yes—
273#120Q8×C4712yes—
274C4×D4—41no—
275C4×D4—41no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4D4×C4711yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4C2×C4×C4711yescharacteristic
289C2×C22⋊C4C2×C4×C4711yescharacteristic
290C2×C22⋊C4C2×C4×C4711yescharacteristic
291C2×C22⋊C4D4×C4711yescharacteristic
292C2×C42—21no—
293C2×C42D4×C4711yescharacteristic
294C4⋊C8—41no—
295C4⋊C8—41no—
296#100—22no—
297#100—22no—
298#99—22no—
299#99—22no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—41no—
304C24—21no—
305C24—21no—
306C24—41no—
307C24—41no—
308C24—81no—
309C24—81no—
310C24C4⋊C4×C4712yescomplemented
311C24C22×C4×C4711yescharacteristic
312C24C2×D4×C4711yescharacteristic
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—81no—
318C2×D4—81no—
319C2×D4C2×D4×C4711yescharacteristic
320C2×D4C2×Q8×C4711yescharacteristic
321C2×D4#41×C4711yescharacteristic
322C2×D4#41×C4711yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—81no—
333C22×C4—81no—
334C22×C4—81no—
335C22×C4C22⋊C4×C4711yescharacteristic
336C22×C4C22⋊C4×C4711yescharacteristic
337C22×C4C22⋊C4×C4711yescharacteristic
338C22×C4C22⋊C4×C4711yescharacteristic
339C22×C4C2×D4×C4711yescharacteristic
340M16—42no—
341M16—42no—
342C2×C8—42no—
343C4⋊C4—41no—
344C4⋊C4—81no—
345C4⋊C4—82no—
346C22⋊C4—21no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—81no—
358C22⋊C4—81no—
359C22⋊C4—81no—
360C22⋊C4C4⋊C4×C4712yescomplemented
361C42—21no—
362C42—21no—
363C42—81no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—42no—
379C23—41no—
380C23—41no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23—82no—
385C23—84no—
386C23C2×C22⋊C4×C4711yescharacteristic
387C23C2×C4⋊C4×C4711yescharacteristic
388C23#117×C4711yescharacteristic
389C23#121×C4711yescharacteristic
390C23C22⋊Q8×C4711yescharacteristic
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—82no—
396D4—82no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4#99×C4711yescharacteristic
424C2×C4#99×C4711yescharacteristic
425C2×C4#121×C4711yescharacteristic
426C2×C4C22⋊Q8×C4711yescharacteristic
427C8—82no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—42no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—84no—
450C22—84no—
451C22—81no—
452C22—81no—
453C22C47×#38011yescharacteristic
454C22C2×#99×C4711yescharacteristic
455C22C47×#41011yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—81no—
466C4—162no—
467C2—21no—
468C2—21no—
469C2—41no—
470C2—41no—
471C2—41no—
472C2—41no—
473C2—82no—
474C2C47×#179911yescharacteristic
475C2C47×#212111yescharacteristic
476C2C47×#212211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#99
commutatorC24C22×C4×C47
Frattini, cosocleC22×D4C23×C47
prime radicalC2×#120×C47C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1800C2semidirect
4. C47×#1799C2semidirect
5. C47×#1390C2semidirect
8. C22×C22⋊C4×C47C4semidirect
17. C47×#385C4semidirect
19. C47×#379C4semidirect
20. C4×C22⋊C4×C47C4semidirect
71. C24×C47C4⋊C4semidirect
121. C22⋊C4×C47C4⋊C4semidirect
189. #12795C47direct (N × H)
231. #1800C2×C47semidirect
232. #1799C2×C47semidirect
233. #1390C2×C47semidirect
246. C22×C22⋊C4C4×C47semidirect
255. #385C4×C47semidirect
257. #379C4×C47semidirect
258. C4×C22⋊C4C4×C47semidirect
262. C47#12795direct (N × H)
310. C24C4⋊C4×C47semidirect
360. C22⋊C4C4⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#23212
C2×C47×AΣL(1,𝔽16)2
C47×#18002
C47×#17992
C47×#13902
#1279547