Finite Group Databasebeta

← C47×#25361 #26065059

Subgroups — C47×#25361 #26065059

Order 12032.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3141C211yesmaximal, characteristic
2C2×C47×#475C211yesmaximal, characteristic, complemented
3C47×#3037C211yesmaximal, characteristic
4C47×#2935C211yesmaximal, characteristic
5C47×#2079C212yesmaximal, complemented
6C47×#2052C212yesmaximal, complemented
7C47×#1997C211yesmaximal, characteristic, complemented
8C47×#1950C211yesmaximal, characteristic, complemented
9C47×#1908C212yesmaximal, complemented
10C47×#1815C212yesmaximal, complemented
11C4×#101×C47C211yesmaximal, characteristic, complemented
12C2×#137×C47C2212yes—
13C2×#131×C47C2212yes—
14C47×#532C2211yescharacteristic
15C2×C4⋊Q8×C47C2211yescharacteristic
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#489—22no—
18C47×#487—21no—
19C47×#486—21no—
20C47×#475—21no—
21C47×#475—22no—
22C47×#475—21no—
23C47×#464—22no—
24C47×#462—21no—
25C47×#460—21no—
26C47×#436—21no—
27C47×#435—22no—
28C8×D4×C47—21no—
29C2×#108×C47C2212yes—
30C2×#106×C47C2212yes—
31C47×#423C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C47×#417C2212yes—
34C47×#417C2212yes—
35C47×#417C2212yes—
36C2×#103×C47C2212yes—
37C2×#101×C47C2211yescharacteristic
38C2×#101×C47C2211yescharacteristic
39C47×#408C2212yes—
40C4×M16×C47C2211yescharacteristic
41C4×M16×C47C2211yescharacteristic
42C47×#343C2211yescharacteristic
43C47×#343C2211yescharacteristic
44C47×#343C2212yes—
45C47×#343C2212yes—
46C47×#341C2212yes—
47C2×#41×C47C2312yes—
48C22×Q8×C47—21no—
49C22×Q8×C47C2311yescharacteristic
50#137×C47—24no—
51#137×C47—42no—
52C2×Q16×C47—22no—
53C2×SD16×C47—22no—
54#131×C47—24no—
55#131×C47—42no—
56C2×M16×C47—22no—
57C2×M16×C47C2312yes—
58C2×M16×C47C2311yescharacteristic
59C2×M16×C47C2311yescharacteristic
60C2×M16×C47C2311yescharacteristic
61C2×M16×C47C2311yescharacteristic
62C22×C8×C47—22no—
63C22×C8×C47C2312yes—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47D411yescharacteristic
69#127×C47D411yescharacteristic
70#124×C47D412yes—
71#121×C47—21no—
72#121×C47—21no—
73C4×Q8×C47—21no—
74C4×Q8×C47—21no—
75C4×Q8×C47—21no—
76C4×Q8×C47—21no—
77C4×D4×C47—21no—
78C4×D4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2312yes—
83C2×C42×C47—21no—
84C2×C42×C47C2311yescharacteristic
85#108×C47—42no—
86#106×C47—22no—
87#106×C47—22no—
88C4⋊C8×C47—21no—
89C4⋊C8×C47—21no—
90C4⋊C8×C47D411yescharacteristic
91C4⋊C8×C47D412yes—
92C4⋊C8×C47D411yescharacteristic
93#103×C47—22no—
94#103×C47—22no—
95#103×C47—22no—
96#103×C47—22no—
97#103×C47—22no—
98#102×C47—22no—
99#102×C47—22no—
100#102×C47—22no—
101#101×C47—22no—
102#101×C47—22no—
103C22⋊C8×C47—22no—
104C22⋊C8×C47—22no—
105#97×C47—21no—
106#97×C47—21no—
107C4×C8×C47—21no—
108C4×C8×C47—21no—
109#41×C47—22no—
110#41×C47—22no—
111#41×C47—22no—
112#41×C47—22no—
113C2×Q8×C47—21no—
114C2×Q8×C47—21no—
115C2×Q8×C47—21no—
116C2×Q8×C47—21no—
117C2×Q8×C47—21no—
118C2×Q8×C47—41no—
119C2×Q8×C47—41no—
120C2×Q8×C47—82no—
121C2×Q8×C47C2×D412yes—
122C2×Q8×C47#4112yes—
123C2×D4×C47—22no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47C2×D412yes—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—21no—
130C22×C4×C47—22no—
131C22×C4×C47#4111yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47C2411yescharacteristic
134Q16×C47—44no—
135SD16×C47—44no—
136M16×C47—21no—
137M16×C47—22no—
138M16×C47—21no—
139M16×C47—21no—
140M16×C47—21no—
141M16×C47—21no—
142M16×C47—22no—
143M16×C47—21no—
144M16×C47—21no—
145M16×C47—44no—
146M16×C47#4112yes—
147C2×C8×C47—21no—
148C2×C8×C47—22no—
149C2×C8×C47—22no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—22no—
153C2×C8×C47—21no—
154C2×C8×C47—44no—
155C2×C8×C47C2×D412yes—
156C2×C8×C47C2×D412yes—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C22⋊C4×C47—22no—
168C22⋊C4×C47—22no—
169C42×C47—41no—
170C42×C47—41no—
171C42×C47C2×D411yescharacteristic
172C42×C47C2×D411yescharacteristic
173C42×C47C2×D411yescharacteristic
174C42×C47C2×D411yescharacteristic
175C23×C47—22no—
176C23×C47C2×#4111yescharacteristic
177Q8×C47—22no—
178Q8×C47—22no—
179Q8×C47—22no—
180Q8×C47—22no—
181Q8×C47—41no—
182Q8×C47—41no—
183Q8×C47—82no—
184Q8×C47—82no—
185D4×C47—22no—
186D4×C47—22no—
187D4×C47—42no—
188D4×C47—42no—
189D4×C47—42no—
190D4×C47—81no—
191C2×C4×C47—22no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—41no—
195C2×C4×C47—41no—
196C2×C4×C47—41no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—81no—
202C2×C4×C47—82no—
203C2×C4×C47#12111yescharacteristic
204C2×C4×C47#12111yescharacteristic
205C2×C4×C47#12111yescharacteristic
206C2×C4×C47#12111yescharacteristic
207C2×C4×C47C22×D411yescharacteristic
208C2×C4×C47C22×D411yescharacteristic
209C2×C4×C47C2×#4111yescharacteristic
210C2×C4×C47C2×#4111yescharacteristic
211C2×C4×C47H(5,𝔽2)11yescharacteristic
212C2×C4×C472−1+411yescharacteristic
213C8×C47—22no—
214C8×C47—22no—
215C8×C47—22no—
216C8×C47—41no—
217C8×C47—42no—
218C8×C47—41no—
219C8×C47—41no—
220#25361C4711yesmaximal, characteristic, direct product factor, Sylow
221C22×C47—21no—
222C22×C47—21no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—42no—
226C22×C47C2×#12111yescharacteristic
227C22×C47#52911yescharacteristic
228C22×C47#54211yescharacteristic
229C4×C47—21no—
230C4×C47—21no—
231C4×C47—21no—
232C4×C47—42no—
233C4×C47—42no—
234C4×C47—82no—
235C4×C47—81no—
236C4×C47#47112yes—
237C4×C47#54611yescharacteristic
238C4×C47#54611yescharacteristic
239C4×C47#54711yescharacteristic
240C4×C47#54811yescharacteristic
241#3141C2×C4711yescharacteristic
242C2×#475C2×C4711yescharacteristic, complemented
243#3037C2×C4711yescharacteristic
244#2935C2×C4711yescharacteristic
245#2079C2×C4712yescomplemented
246#2052C2×C4712yescomplemented
247#1997C2×C4711yescharacteristic, complemented
248#1950C2×C4711yescharacteristic, complemented
249#1908C2×C4712yescomplemented
250#1815C2×C4712yescomplemented
251C4×#101C2×C4711yescharacteristic, complemented
252C2×C47—21no—
253C2×C47—21no—
254C2×C47—82no—
255C2×C47#242711yescharacteristic
256C2×C47C2×#47111yescharacteristic
257C2×C47#306911yescharacteristic
258C2×#137C22×C4712yes—
259C2×#131C22×C4712yes—
260#532C22×C4711yescharacteristic
261C2×C4⋊Q8C22×C4711yescharacteristic
262C2×C4×Q8C22×C4711yescharacteristic
263#489—22no—
264#487—21no—
265#486—21no—
266#475—21no—
267#475—22no—
268#475—21no—
269#464—22no—
270#462—21no—
271#460—21no—
272#436—21no—
273#435—22no—
274C8×D4—21no—
275C2×#108C22×C4712yes—
276C2×#106C22×C4712yes—
277#423C22×C4711yescharacteristic
278C2×C4⋊C8C22×C4711yescharacteristic
279#417C22×C4712yes—
280#417C22×C4712yes—
281#417C22×C4712yes—
282C2×#103C22×C4712yes—
283C2×#101C22×C4711yescharacteristic
284C2×#101C22×C4711yescharacteristic
285#408C22×C4712yes—
286C4×M16C22×C4711yescharacteristic
287C4×M16C22×C4711yescharacteristic
288#343C22×C4712yes—
289#343C22×C4711yescharacteristic
290#343C22×C4712yes—
291#343C22×C4711yescharacteristic
292#341C22×C4712yes—
293C47#2536111yescharacteristic, direct product factor, Sylow
294C2×#41C23×C4712yes—
295C22×Q8—21no—
296C22×Q8C23×C4711yescharacteristic
297#137—24no—
298#137—42no—
299C2×Q16—22no—
300C2×SD16—22no—
301#131—24no—
302#131—42no—
303C2×M16—22no—
304C2×M16C23×C4712yes—
305C2×M16C23×C4711yescharacteristic
306C2×M16C23×C4711yescharacteristic
307C2×M16C23×C4711yescharacteristic
308C2×M16C23×C4711yescharacteristic
309C22×C8—22no—
310C22×C8C23×C4712yes—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8D4×C4711yescharacteristic
316#127D4×C4711yescharacteristic
317#124D4×C4712yes—
318#121—21no—
319#121—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—21no—
325C4×D4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C23×C4711yescharacteristic
329C2×C4⋊C4C23×C4712yes—
330C2×C42—21no—
331C2×C42C23×C4711yescharacteristic
332#108—42no—
333#106—22no—
334#106—22no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8D4×C4711yescharacteristic
338C4⋊C8D4×C4712yes—
339C4⋊C8D4×C4711yescharacteristic
340#103—22no—
341#103—22no—
342#103—22no—
343#103—22no—
344#103—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#101—22no—
349#101—22no—
350C22⋊C8—22no—
351C22⋊C8—22no—
352#97—21no—
353#97—21no—
354C4×C8—21no—
355C4×C8—21no—
356#41—22no—
357#41—22no—
358#41—22no—
359#41—22no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—82no—
368C2×Q8C2×D4×C4712yes—
369C2×Q8#41×C4712yes—
370C2×D4—22no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4C2×D4×C4712yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4#41×C4711yescharacteristic
379C22×C4#41×C4711yescharacteristic
380C22×C4C24×C4711yescharacteristic
381Q16—44no—
382SD16—44no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—22no—
388M16—21no—
389M16—22no—
390M16—21no—
391M16—21no—
392M16—44no—
393M16#41×C4712yes—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8—44no—
402C2×C8C2×D4×C4712yes—
403C2×C8C2×D4×C4712yes—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C42—41no—
417C42—41no—
418C42C2×D4×C4711yescharacteristic
419C42C2×D4×C4711yescharacteristic
420C42C2×D4×C4711yescharacteristic
421C42C2×D4×C4711yescharacteristic
422C23—22no—
423C23C2×#41×C4711yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—22no—
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—82no—
431Q8—82no—
432D4—22no—
433D4—22no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—81no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—81no—
449C2×C4—82no—
450C2×C4#121×C4711yescharacteristic
451C2×C4#121×C4711yescharacteristic
452C2×C4#121×C4711yescharacteristic
453C2×C4#121×C4711yescharacteristic
454C2×C4C22×D4×C4711yescharacteristic
455C2×C4C22×D4×C4711yescharacteristic
456C2×C4C2×#41×C4711yescharacteristic
457C2×C4C2×#41×C4711yescharacteristic
458C2×C4H(5,𝔽2)×C4711yescharacteristic
459C2×C42−1+4×C4711yescharacteristic
460C8—22no—
461C8—22no—
462C8—22no—
463C8—41no—
464C8—42no—
465C8—41no—
466C8—41no—
467C22—21no—
468C22—21no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22C2×#121×C4711yescharacteristic
473C22C47×#52911yescharacteristic
474C22C47×#54211yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—42no—
480C4—82no—
481C4—81no—
482C4C47×#47112yes—
483C4C47×#54611yescharacteristic
484C4C47×#54611yescharacteristic
485C4C47×#54711yescharacteristic
486C4C47×#54811yescharacteristic
487C2—21no—
488C2—21no—
489C2—82no—
490C2C47×#242711yescharacteristic
491C2C2×C47×#47111yescharacteristic
492C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#475C2semidirect
5. C47×#2079C2semidirect
6. C47×#2052C2semidirect
7. C47×#1997C2semidirect
8. C47×#1950C2semidirect
9. C47×#1908C2semidirect
10. C47×#1815C2semidirect
11. C4×#101×C47C2semidirect
220. #25361C47direct (N × H)
242. C2×#475C2×C47semidirect
245. #2079C2×C47semidirect
246. #2052C2×C47semidirect
247. #1997C2×C47semidirect
248. #1950C2×C47semidirect
249. #1908C2×C47semidirect
250. #1815C2×C47semidirect
251. C4×#101C2×C47semidirect
293. C47#25361direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31412
C2×C47×#4752
C47×#30372
C47×#29352
C47×#20792
C47×#20522
C47×#19972
C47×#19502
C47×#19082
C47×#18152
C4×#101×C472
#2536147