Finite Group Databasebeta

← C47×#33875 #26073573

Subgroups — C47×#33875 #26073573

Order 12032.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3334C211yesmaximal, characteristic, complemented
2C47×#3285C211yesmaximal, characteristic, complemented
3C47×#2243C211yesmaximal, characteristic, complemented
4C47×#2236C211yesmaximal, characteristic, complemented
5C47×#2232C211yesmaximal, characteristic, complemented
6C47×#2227C211yesmaximal, characteristic, complemented
7C47×#2220C211yesmaximal, characteristic, complemented
8C47×#2215C211yesmaximal, characteristic, complemented
9C47×#2210C211yesmaximal, characteristic, complemented
10C47×#2186C211yesmaximal, characteristic, complemented
11C47×#2185C211yesmaximal, characteristic, complemented
12C47×#2175C211yesmaximal, characteristic, complemented
13C47×#2168C211yesmaximal, characteristic, complemented
14C47×#2139C211yesmaximal, characteristic, complemented
15C2×C47×#358C211yesmaximal, characteristic, complemented
16C2×#135×C47C2211yescharacteristic
17C22×Q16×C47C2211yescharacteristic
18C47×#548—21no—
19C47×#547—21no—
20C2×SD32×C47C2211yescharacteristic
21C2×SD32×C47C2211yescharacteristic
22C2×D16×C47C2211yescharacteristic
23C2×M32×C47C2211yescharacteristic
24C22×C16×C47C2211yescharacteristic
25C47×#500C2211yescharacteristic
26C47×#495C2211yescharacteristic
27C47×#480—21no—
28C47×#480—21no—
29C47×#474—21no—
30C47×#467C2211yescharacteristic
31C47×#466C2211yescharacteristic
32C47×#466C2211yescharacteristic
33C47×#466C2211yescharacteristic
34C47×#464—21no—
35C47×#452—21no—
36C47×#448—21no—
37C4×Q16×C47C2211yescharacteristic
38C4×D8×C47C2211yescharacteristic
39C8×D4×C47C2211yescharacteristic
40C2×#107×C47C2211yescharacteristic
41C2×#107×C47C2211yescharacteristic
42C47×#366C2211yescharacteristic
43C47×#366C2211yescharacteristic
44C47×#366C2211yescharacteristic
45C47×C4⋊C16C2211yescharacteristic
46C47×#358C2211yescharacteristic
47C47×#358C2211yescharacteristic
48C47×#358C2211yescharacteristic
49C47×#358C2211yescharacteristic
50C47×#358C2211yescharacteristic
51C47×#358C2211yescharacteristic
52C47×#357C2211yescharacteristic
53C47×#357C2211yescharacteristic
54C47×#357C2211yescharacteristic
55C47×#357C2211yescharacteristic
56C47×C22⋊C16C2211yescharacteristic
57C47×C22⋊C16C2211yescharacteristic
58C47×#346C2211yescharacteristic
59C2×#41×C47—21no—
60C2×#41×C47—41no—
61C22×Q8×C47—21no—
62#135×C47—22no—
63#135×C47—41no—
64C2×Q16×C47—22no—
65C2×Q16×C47—21no—
66C2×Q16×C47—41no—
67C2×Q16×C47C2311yescharacteristic
68C2×Q16×C47C2311yescharacteristic
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×D8×C47C2311yescharacteristic
72C2×D8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C22×C8×C47C2311yescharacteristic
75C4⋊Q8×C47—21no—
76#124×C47—21no—
77#124×C47—41no—
78#123×C47—41no—
79#123×C47—41no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—41no—
82C22⋊Q8×C47—41no—
83#121×C47—21no—
84#121×C47—21no—
85#121×C47—21no—
86#121×C47—41no—
87C4×Q8×C47—21no—
88C4×D4×C47—21no—
89C4×D4×C47—41no—
90C4×D4×C47D411yescharacteristic
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93SD32×C47—22no—
94SD32×C47—41no—
95D16×C47—41no—
96M32×C47—41no—
97C2×C16×C47—41no—
98C2×C16×C47C2311yescharacteristic
99C2×C16×C47C2311yescharacteristic
100C2×C16×C47C2311yescharacteristic
101C2×C16×C47C2311yescharacteristic
102#107×C47—21no—
103#107×C47—21no—
104#107×C47—21no—
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#107×C47C2311yescharacteristic
108#107×C47C2311yescharacteristic
109C4⋊C8×C47D411yescharacteristic
110#103×C47—21no—
111#103×C47—21no—
112#102×C47—21no—
113#102×C47—21no—
114#102×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119#41×C47—42no—
120#41×C47—81no—
121#41×C47—84no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—42no—
125C2×Q8×C47—41no—
126C2×Q8×C47—41no—
127C2×Q8×C47—81no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47—41no—
134C2×D4×C47D811yescharacteristic
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47—41no—
138C22×C4×C47—41no—
139C22×C4×C47—41no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142Q16×C47—21no—
143Q16×C47—21no—
144Q16×C47—21no—
145Q16×C47—42no—
146Q16×C47#4112yescomplemented
147SD16×C47—42no—
148SD16×C47—81no—
149D8×C47—21no—
150D8×C47—21no—
151D8×C47—21no—
152D8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47C2×D411yescharacteristic
158C2×C8×C47C2×D411yescharacteristic
159C2×C8×C47C2×D411yescharacteristic
160C2×C8×C47C2411yescharacteristic
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47—41no—
169C4⋊C4×C47—41no—
170C4⋊C4×C47D811yescharacteristic
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C22⋊C4×C47—41no—
174C22⋊C4×C47—41no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47—41no—
177C22⋊C4×C47—41no—
178C22⋊C4×C47D811yescharacteristic
179C22⋊C4×C47D811yescharacteristic
180C42×C47—41no—
181C42×C47C2×D411yescharacteristic
182C16×C47—21no—
183C16×C47—21no—
184C16×C47—21no—
185C16×C47—21no—
186C23×C47—41no—
187C23×C47—41no—
188C23×C47C2×D811yescharacteristic
189C23×C47C2×D811yescharacteristic
190Q8×C47—22no—
191Q8×C47—41no—
192Q8×C47—41no—
193Q8×C47—41no—
194Q8×C47—82no—
195Q8×C47—82no—
196D4×C47—22no—
197D4×C47—41no—
198D4×C47—41no—
199D4×C47—41no—
200D4×C47—41no—
201D4×C47—82no—
202D4×C47—82no—
203D4×C47—82no—
204D4×C47—82no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—82no—
216C2×C4×C47—82no—
217C2×C4×C47—82no—
218C2×C4×C47—82no—
219C2×C4×C47—82no—
220C2×C4×C47C2×D811yescharacteristic
221C2×C4×C47C2×D811yescharacteristic
222C2×C4×C47C2×D811yescharacteristic
223C2×C4×C47C2×D811yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C8×C47—21no—
226C8×C47—21no—
227C8×C47—21no—
228C8×C47C2×#4111yescharacteristic
229C8×C47H(5,𝔽2)11yescharacteristic
230#33875C4711yesmaximal, characteristic, direct product factor, Sylow
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—81no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47#50912yes—
243C22×C47C22×D811yescharacteristic
244C4×C47—21no—
245C4×C47—21no—
246C4×C47—21no—
247C4×C47—21no—
248C4×C47—42no—
249C4×C47—81no—
250C4×C47—81no—
251C4×C47—81no—
252C4×C47—81no—
253C4×C47—81no—
254C4×C47#54611yescharacteristic
255C4×C47#57711yescharacteristic
256#3334C2×C4711yescharacteristic, complemented
257#3285C2×C4711yescharacteristic, complemented
258#2243C2×C4711yescharacteristic, complemented
259#2236C2×C4711yescharacteristic, complemented
260#2232C2×C4711yescharacteristic, complemented
261#2227C2×C4711yescharacteristic, complemented
262#2220C2×C4711yescharacteristic, complemented
263#2215C2×C4711yescharacteristic, complemented
264#2210C2×C4711yescharacteristic, complemented
265#2186C2×C4711yescharacteristic, complemented
266#2185C2×C4711yescharacteristic, complemented
267#2175C2×C4711yescharacteristic, complemented
268#2168C2×C4711yescharacteristic, complemented
269#2139C2×C4711yescharacteristic, complemented
270C2×#358C2×C4711yescharacteristic, complemented
271C2×C47—22no—
272C2×C47—41no—
273C2×C47—161no—
274C2×C47—161no—
275C2×C47#329411yescharacteristic
276C2×C47C2×#50911yescharacteristic
277C2×C47#341711yescharacteristic
278C2×#135C22×C4711yescharacteristic
279C22×Q16C22×C4711yescharacteristic
280#548—21no—
281#547—21no—
282C2×SD32C22×C4711yescharacteristic
283C2×SD32C22×C4711yescharacteristic
284C2×D16C22×C4711yescharacteristic
285C2×M32C22×C4711yescharacteristic
286C22×C16C22×C4711yescharacteristic
287#500C22×C4711yescharacteristic
288#495C22×C4711yescharacteristic
289#480—21no—
290#480—21no—
291#474—21no—
292#467C22×C4711yescharacteristic
293#466C22×C4711yescharacteristic
294#466C22×C4711yescharacteristic
295#466C22×C4711yescharacteristic
296#464—21no—
297#452—21no—
298#448—21no—
299C4×Q16C22×C4711yescharacteristic
300C4×D8C22×C4711yescharacteristic
301C8×D4C22×C4711yescharacteristic
302C2×#107C22×C4711yescharacteristic
303C2×#107C22×C4711yescharacteristic
304#366C22×C4711yescharacteristic
305#366C22×C4711yescharacteristic
306#366C22×C4711yescharacteristic
307C4⋊C16C22×C4711yescharacteristic
308#358C22×C4711yescharacteristic
309#358C22×C4711yescharacteristic
310#358C22×C4711yescharacteristic
311#358C22×C4711yescharacteristic
312#358C22×C4711yescharacteristic
313#358C22×C4711yescharacteristic
314#357C22×C4711yescharacteristic
315#357C22×C4711yescharacteristic
316#357C22×C4711yescharacteristic
317#357C22×C4711yescharacteristic
318C22⋊C16C22×C4711yescharacteristic
319C22⋊C16C22×C4711yescharacteristic
320#346C22×C4711yescharacteristic
321C47#3387511yescharacteristic, direct product factor, Sylow
322C2×#41—21no—
323C2×#41—41no—
324C22×Q8—21no—
325#135—22no—
326#135—41no—
327C2×Q16—22no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16C23×C4711yescharacteristic
331C2×Q16C23×C4711yescharacteristic
332C2×SD16—21no—
333C2×SD16—21no—
334C2×D8C23×C4711yescharacteristic
335C2×D8C23×C4711yescharacteristic
336C22×C8C23×C4711yescharacteristic
337C22×C8C23×C4711yescharacteristic
338C4⋊Q8—21no—
339#124—21no—
340#124—41no—
341#123—41no—
342#123—41no—
343C22⋊Q8—21no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—41no—
350C4×Q8—21no—
351C4×D4—21no—
352C4×D4—41no—
353C4×D4D4×C4711yescharacteristic
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356SD32—22no—
357SD32—41no—
358D16—41no—
359M32—41no—
360C2×C16—41no—
361C2×C16C23×C4711yescharacteristic
362C2×C16C23×C4711yescharacteristic
363C2×C16C23×C4711yescharacteristic
364C2×C16C23×C4711yescharacteristic
365#107—21no—
366#107—21no—
367#107—21no—
368#107C23×C4711yescharacteristic
369#107C23×C4711yescharacteristic
370#107C23×C4711yescharacteristic
371#107C23×C4711yescharacteristic
372C4⋊C8D4×C4711yescharacteristic
373#103—21no—
374#103—21no—
375#102—21no—
376#102—21no—
377#102—21no—
378#102—21no—
379C22⋊C8D4×C4711yescharacteristic
380C22⋊C8D4×C4711yescharacteristic
381C4×C8C23×C4711yescharacteristic
382#41—42no—
383#41—81no—
384#41—84no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—81no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4D8×C4711yescharacteristic
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4C2×D4×C4711yescharacteristic
404C22×C4C2×D4×C4711yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—21no—
408Q16—42no—
409Q16#41×C4712yescomplemented
410SD16—42no—
411SD16—81no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×D4×C4711yescharacteristic
421C2×C8C2×D4×C4711yescharacteristic
422C2×C8C2×D4×C4711yescharacteristic
423C2×C8C24×C4711yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4D8×C4711yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4D8×C4711yescharacteristic
442C22⋊C4D8×C4711yescharacteristic
443C42—41no—
444C42C2×D4×C4711yescharacteristic
445C16—21no—
446C16—21no—
447C16—21no—
448C16—21no—
449C23—41no—
450C23—41no—
451C23C2×D8×C4711yescharacteristic
452C23C2×D8×C4711yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—82no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4C2×D8×C4711yescharacteristic
484C2×C4C2×D8×C4711yescharacteristic
485C2×C4C2×D8×C4711yescharacteristic
486C2×C4C2×D8×C4711yescharacteristic
487C2×C4C22×D4×C4711yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#41×C4711yescharacteristic
492C8H(5,𝔽2)×C4711yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22C47×#50912yes—
505C22C22×D8×C4711yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4C47×#54611yescharacteristic
517C4C47×#57711yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C47×#329411yescharacteristic
523C2C2×C47×#50911yescharacteristic
524C2C47×#341711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ C8×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3334C2semidirect
2. C47×#3285C2semidirect
3. C47×#2243C2semidirect
4. C47×#2236C2semidirect
5. C47×#2232C2semidirect
6. C47×#2227C2semidirect
7. C47×#2220C2semidirect
8. C47×#2215C2semidirect
9. C47×#2210C2semidirect
10. C47×#2186C2semidirect
11. C47×#2185C2semidirect
12. C47×#2175C2semidirect
13. C47×#2168C2semidirect
14. C47×#2139C2semidirect
15. C2×C47×#358C2semidirect
146. Q16×C47#41semidirect
230. #33875C47direct (N × H)
256. #3334C2×C47semidirect
257. #3285C2×C47semidirect
258. #2243C2×C47semidirect
259. #2236C2×C47semidirect
260. #2232C2×C47semidirect
261. #2227C2×C47semidirect
262. #2220C2×C47semidirect
263. #2215C2×C47semidirect
264. #2210C2×C47semidirect
265. #2186C2×C47semidirect
266. #2185C2×C47semidirect
267. #2175C2×C47semidirect
268. #2168C2×C47semidirect
269. #2139C2×C47semidirect
270. C2×#358C2×C47semidirect
321. C47#33875direct (N × H)
409. Q16#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33342
C47×#32852
C47×#22432
C47×#22362
C47×#22322
C47×#22272
C47×#22202
C47×#22152
C47×#22102
C47×#21862
C47×#21852
C47×#21752
C47×#21682
C47×#21392
C2×C47×#3582
#3387547