Finite Group Databasebeta

← C47×#13316 #26053014

Subgroups — C47×#13316 #26053014

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#509C211yesmaximal, characteristic, complemented
2C47×#3054C211yesmaximal, characteristic, complemented
3C2×C47×#469C211yesmaximal, characteristic, complemented
4C2×C47×#360C211yesmaximal, characteristic, complemented
5C47×#2140C211yesmaximal, characteristic, complemented
6C2×C47×#349C211yesmaximal, characteristic, complemented
7C47×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C22×D8×C47C2211yescharacteristic
10C22×M16×C47C2211yescharacteristic
11C47×#525—21no—
12C2×#121×C47—21no—
13C47×#509—22no—
14C47×#509—22no—
15C2×SD32×C47—21no—
16C2×D16×C47—21no—
17C2×M32×C47C2211yescharacteristic
18C2×M32×C47C2211yescharacteristic
19C47×#470—21no—
20C47×#469—22no—
21C47×#469—21no—
22C47×#469—22no—
23C47×#468—22no—
24C47×#427C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C47×#416—21no—
27C2×#102×C47—21no—
28C47×#360—22no—
29C47×#357—22no—
30C47×#349—22no—
31C2×#41×C47—21no—
32C22×D4×C47—21no—
33C22×D4×C47—41no—
34C23×C4×C47D411yescharacteristic
35#135×C47—21no—
36#135×C47—21no—
37#135×C47—21no—
38#135×C47—21no—
39C2×Q16×C47D411yescharacteristic, complemented
40C2×SD16×C47—21no—
41C2×D8×C47—21no—
42C2×D8×C47—21no—
43C2×D8×C47—21no—
44C2×D8×C47—21no—
45C2×D8×C47—21no—
46C2×D8×C47D411yescharacteristic, complemented
47C2×D8×C47D412yescomplemented
48C2×M16×C47—21no—
49C2×M16×C47—21no—
50C2×M16×C47—21no—
51C2×M16×C47—21no—
52C2×M16×C47—21no—
53C2×M16×C47—21no—
54C22×C8×C47D411yescharacteristic
55C22×C8×C47C2311yescharacteristic
56#123×C47—41no—
57C22⋊Q8×C47—22no—
58#121×C47—22no—
59#121×C47—24no—
60#121×C47—42no—
61#120×C47—41no—
62C4×D4×C47—42no—
63#117×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C22⋊C4×C47—41no—
66SD32×C47—24no—
67D16×C47—24no—
68M32×C47—21no—
69M32×C47—21no—
70M32×C47—21no—
71M32×C47D412yescomplemented
72C2×C16×C47—21no—
73C2×C16×C47—21no—
74#107×C47D412yescomplemented
75#106×C47—21no—
76#106×C47—21no—
77#106×C47D412yescomplemented
78#103×C47—22no—
79#102×C47—22no—
80#102×C47—24no—
81C24×C47—41no—
82C24×C47D811yescharacteristic
83#41×C47—41no—
84#41×C47—41no—
85#41×C47—41no—
86#41×C47—41no—
87C2×Q8×C47—21no—
88C2×D4×C47—22no—
89C2×D4×C47—21no—
90C2×D4×C47—42no—
91C2×D4×C47—44no—
92C2×D4×C47—41no—
93C2×D4×C47—41no—
94C2×D4×C47—41no—
95C2×D4×C47—41no—
96C2×D4×C47—41no—
97C2×D4×C47—41no—
98C2×D4×C47—84no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—41no—
106C22×C4×C47—41no—
107C22×C4×C47D811yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109Q16×C47—21no—
110Q16×C47—21no—
111SD16×C47—41no—
112SD16×C47—41no—
113D8×C47—21no—
114D8×C47—22no—
115D8×C47—22no—
116D8×C47—21no—
117D8×C47—41no—
118D8×C47—41no—
119M16×C47—41no—
120M16×C47—41no—
121M16×C47—41no—
122M16×C47—41no—
123C2×C8×C47—21no—
124C2×C8×C47—21no—
125C2×C8×C47—21no—
126C2×C8×C47C2×D411yescharacteristic
127C2×C8×C47C2×D411yescharacteristic
128C2×C8×C47C2×D411yescharacteristic
129C2×C8×C47C2×D411yescharacteristic
130C2×C8×C47C2×D411yescharacteristic
131C2×C8×C47#4111yescharacteristic
132C4⋊C4×C47—22no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—42no—
135C4⋊C4×C47—41no—
136C22⋊C4×C47—44no—
137C22⋊C4×C47—42no—
138C22⋊C4×C47—42no—
139C22⋊C4×C47—41no—
140C42×C47—41no—
141C16×C47—22no—
142C16×C47—41no—
143C23×C47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—42no—
147C23×C47—42no—
148C23×C47—41no—
149C23×C47—82no—
150C23×C47—82no—
151C23×C47—81no—
152C23×C47—81no—
153C23×C47C2×D811yescharacteristic
154Q8×C47—41no—
155Q8×C47—41no—
156D4×C47—42no—
157D4×C47—41no—
158D4×C47—42no—
159D4×C47—41no—
160D4×C47—84no—
161D4×C47—88no—
162D4×C47—81no—
163D4×C47—81no—
164D4×C47—81no—
165D4×C47—81no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—41no—
170C2×C4×C47—41no—
171C2×C4×C47—41no—
172C2×C4×C47—41no—
173C2×C4×C47—42no—
174C2×C4×C47—42no—
175C2×C4×C47—41no—
176C2×C4×C47—82no—
177C2×C4×C47—81no—
178C2×C4×C47—81no—
179C2×C4×C47#12011yescharacteristic
180C2×C4×C47#12011yescharacteristic
181C2×C4×C47#12111yescharacteristic
182C2×C4×C47#13511yescharacteristic
183C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
185C8×C47—41no—
186C8×C47#12011yescharacteristic
187C8×C47#12111yescharacteristic
188C8×C47#12111yescharacteristic
189C8×C47#12711yescharacteristic
190#13316C4711yesmaximal, characteristic, direct product factor, Sylow
191C22×C47—22no—
192C22×C47—42no—
193C22×C47—42no—
194C22×C47—41no—
195C22×C47—81no—
196C22×C47—82no—
197C22×C47—82no—
198C22×C47—82no—
199C22×C47—81no—
200C22×C47—82no—
201C22×C47—162no—
202C22×C47—162no—
203C22×C47#44711yescharacteristic
204C22×C47#44711yescharacteristic
205C22×C47#46611yescharacteristic
206C4×C47—41no—
207C4×C47—82no—
208C4×C47—82no—
209C4×C47—81no—
210C4×C47#39211yescharacteristic
211C4×C47#44911yescharacteristic
212C4×C47#44911yescharacteristic
213C4×C47#46911yescharacteristic
214C2×#509C2×C4711yescharacteristic, complemented
215#3054C2×C4711yescharacteristic, complemented
216C2×#469C2×C4711yescharacteristic, complemented
217C2×#360C2×C4711yescharacteristic, complemented
218#2140C2×C4711yescharacteristic, complemented
219C2×#349C2×C4711yescharacteristic, complemented
220#1386C2×C4711yescharacteristic, complemented
221C2×C47—21no—
222C2×C47—21no—
223C2×C47—81no—
224C2×C47—161no—
225C2×C47—162no—
226C2×C47#199911yescharacteristic
227C2×C47#219012yes—
228C2×#135C22×C4711yescharacteristic
229C22×D8C22×C4711yescharacteristic
230C22×M16C22×C4711yescharacteristic
231#525—21no—
232C2×#121—21no—
233#509—22no—
234#509—22no—
235C2×SD32—21no—
236C2×D16—21no—
237C2×M32C22×C4711yescharacteristic
238C2×M32C22×C4711yescharacteristic
239#470—21no—
240#469—22no—
241#469—21no—
242#469—22no—
243#468—22no—
244#427C22×C4711yescharacteristic
245C2×#106C22×C4711yescharacteristic
246#416—21no—
247C2×#102—21no—
248#360—22no—
249#357—22no—
250#349—22no—
251C47#1331611yescharacteristic, direct product factor, Sylow
252C2×#41—21no—
253C22×D4—21no—
254C22×D4—41no—
255C23×C4D4×C4711yescharacteristic
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260C2×Q16D4×C4711yescharacteristic, complemented
261C2×SD16—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8D4×C4712yescomplemented
268C2×D8D4×C4711yescharacteristic, complemented
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C22×C8D4×C4711yescharacteristic
276C22×C8C23×C4711yescharacteristic
277#123—41no—
278C22⋊Q8—22no—
279#121—24no—
280#121—22no—
281#121—42no—
282#120—41no—
283C4×D4—42no—
284#117—21no—
285C2×C4⋊C4—21no—
286C2×C22⋊C4—41no—
287SD32—24no—
288D16—24no—
289M32—21no—
290M32—21no—
291M32—21no—
292M32D4×C4712yescomplemented
293C2×C16—21no—
294C2×C16—21no—
295#107D4×C4712yescomplemented
296#106—21no—
297#106—21no—
298#106D4×C4712yescomplemented
299#103—22no—
300#102—24no—
301#102—22no—
302C24—41no—
303C24D8×C4711yescharacteristic
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—44no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—84no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4D8×C4711yescharacteristic
329C22×C4C2×D4×C4711yescharacteristic
330Q16—21no—
331Q16—21no—
332SD16—41no—
333SD16—41no—
334D8—21no—
335D8—22no—
336D8—22no—
337D8—21no—
338D8—41no—
339D8—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8C2×D4×C4711yescharacteristic
348C2×C8C2×D4×C4711yescharacteristic
349C2×C8C2×D4×C4711yescharacteristic
350C2×C8C2×D4×C4711yescharacteristic
351C2×C8C2×D4×C4711yescharacteristic
352C2×C8#41×C4711yescharacteristic
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—42no—
356C4⋊C4—41no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—41no—
361C42—41no—
362C16—22no—
363C16—41no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—42no—
368C23—41no—
369C23—42no—
370C23—82no—
371C23—82no—
372C23—81no—
373C23—81no—
374C23C2×D8×C4711yescharacteristic
375Q8—41no—
376Q8—41no—
377D4—42no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—84no—
382D4—88no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4#120×C4711yescharacteristic
401C2×C4#120×C4711yescharacteristic
402C2×C4#121×C4711yescharacteristic
403C2×C4#135×C4711yescharacteristic
404C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
405C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
406C8—41no—
407C8#120×C4711yescharacteristic
408C8#121×C4711yescharacteristic
409C8#121×C4711yescharacteristic
410C8#127×C4711yescharacteristic
411C22—22no—
412C22—42no—
413C22—42no—
414C22—41no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—81no—
420C22—82no—
421C22—162no—
422C22—162no—
423C22C47×#44711yescharacteristic
424C22C47×#44711yescharacteristic
425C22C47×#46611yescharacteristic
426C4—41no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4C47×#39211yescharacteristic
431C4C47×#44911yescharacteristic
432C4C47×#44911yescharacteristic
433C4C47×#46911yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2—161no—
439C2C47×#199911yescharacteristic
440C2C47×#219012yes—
subgroupG/H
center, socleC22×C47#447
commutator, Frattini, cosocleC22×C8C23×C47
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C22×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#509C2semidirect
2. C47×#3054C2semidirect
3. C2×C47×#469C2semidirect
4. C2×C47×#360C2semidirect
5. C47×#2140C2semidirect
6. C2×C47×#349C2semidirect
7. C47×#1386C2semidirect
39. C2×Q16×C47D4semidirect
46. C2×D8×C47D4semidirect
47. C2×D8×C47D4semidirect
71. M32×C47D4semidirect
74. #107×C47D4semidirect
77. #106×C47D4semidirect
190. #13316C47direct (N × H)
214. C2×#509C2×C47semidirect
215. #3054C2×C47semidirect
216. C2×#469C2×C47semidirect
217. C2×#360C2×C47semidirect
218. #2140C2×C47semidirect
219. C2×#349C2×C47semidirect
220. #1386C2×C47semidirect
251. C47#13316direct (N × H)
260. C2×Q16D4×C47semidirect
267. C2×D8D4×C47semidirect
268. C2×D8D4×C47semidirect
292. M32D4×C47semidirect
295. #107D4×C47semidirect
298. #106D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5092
C47×#30542
C2×C47×#4692
C2×C47×#3602
C47×#21402
C2×C47×#3492
C47×#13862
#1331647