Finite Group Databasebeta

← C47×#18949 #26058647

Subgroups — C47×#18949 #26058647

Order 12032.

846 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×#3550C211yesmaximal, characteristic
2C47×#3246C211yesmaximal, characteristic
3C47×#3237C211yesmaximal, characteristic, complemented
4C47×#3231C211yesmaximal, characteristic, complemented
5C47×#1651C212yesmaximal, complemented
6C47×#1650C212yesmaximal, complemented
7C47×#1638C212yesmaximal, complemented
8C47×#1637C212yesmaximal, complemented
9C47×#1552C211yesmaximal, characteristic, complemented
10C47×#1496C211yesmaximal, characteristic
11C47×#1481C211yesmaximal, characteristic, complemented
12C47×#563—22no—
13C47×#559—21no—
14Q82×C47—21no—
15C47×#556—21no—
16C47×#556C2212yes—
17D4×Q8×C47—21no—
18D4×Q8×C47C2212yes—
19C47×#542—22no—
20C47×#542—22no—
21C47×#536—22no—
22C47×#533C2211yescharacteristic
23C47×#533C2211yescharacteristic
24C47×#533C2211yescharacteristic
25C47×#532C2211yescharacteristic
26C47×#501—21no—
27C47×#500C2211yescharacteristic
28C47×#498C2211yescharacteristic
29C47×#491—21no—
30C47×#487C2211yescharacteristic
31C47×#487C2211yescharacteristic
32C47×#485—22no—
33C47×#485—22no—
34C47×#479—22no—
35C47×#477C2212yes—
36C47×#476C2212yes—
37C47×#475—21no—
38C47×#475C2212yes—
39C47×#465—22no—
40C47×#461C2212yes—
41C47×#460—21no—
42C47×#432C2211yescharacteristic
43C47×#431C2211yescharacteristic
44C2×C4⋊C8×C47C2211yescharacteristic
45C47×#332C2212yes—
46C47×#332C2212yes—
47C47×Q8⋊C8C2212yes—
48C47×Q8⋊C8C2212yes—
49C47×D4⋊C8C2212yes—
50C47×D4⋊C8C2212yes—
51C2×#41×C47—21no—
52C22×Q8×C47—22no—
53C2×SD16×C47—22no—
54C22×C8×C47—21no—
55C4⋊Q8×C47—24no—
56C4⋊Q8×C47—22no—
57C4⋊Q8×C47—22no—
58C4⋊Q8×C47D411yescharacteristic
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47C2311yescharacteristic
62C4⋊Q8×C47C2311yescharacteristic
63C4⋊Q8×C47C2311yescharacteristic
64C4⋊Q8×C47C2311yescharacteristic
65#127×C47D411yescharacteristic
66#126×C47—24no—
67#126×C47—24no—
68#125×C47—21no—
69#125×C47—21no—
70#125×C47D412yes—
71#124×C47—24no—
72#124×C47—22no—
73#124×C47—22no—
74#124×C47—21no—
75#123×C47—24no—
76#123×C47—24no—
77C22⋊Q8×C47—24no—
78C22⋊Q8×C47—22no—
79C22⋊Q8×C47—21no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—22no—
83C22⋊Q8×C47—24no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—21no—
86C22⋊Q8×C47D412yes—
87#121×C47—21no—
88#121×C47D412yes—
89C4×Q8×C47—22no—
90C4×Q8×C47—22no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47C2312yes—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99C4×D4×C47—21no—
100C4×D4×C47C2312yes—
101#117×C47—21no—
102#117×C47—22no—
103#117×C47—21no—
104#117×C47D412yes—
105C2×C42×C47C2311yescharacteristic
106#107×C47—22no—
107#107×C47—22no—
108#106×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2312yes—
114C4⋊C8×C47C2312yes—
115#103×C47—22no—
116#103×C47—22no—
117#103×C47—22no—
118#103×C47—22no—
119#103×C47—22no—
120#102×C47—22no—
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123#97×C47—21no—
124C4×C8×C47C2311yescharacteristic
125C4×C8×C47C2311yescharacteristic
126#41×C47—82no—
127C2×Q8×C47—24no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—84no—
135C2×Q8×C47C2×D412yes—
136C2×D4×C47—22no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47C2×D412yes—
140C22×C4×C47—24no—
141C22×C4×C47—22no—
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145SD16×C47—82no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—22no—
149C2×C8×C47—22no—
150C2×C8×C47—81no—
151C4⋊C4×C47—24no—
152C4⋊C4×C47—24no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—22no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47—41no—
169C4⋊C4×C47C2×D412yes—
170C4⋊C4×C47C2×D412yes—
171C4⋊C4×C47C2×D412yes—
172C4⋊C4×C47C2×D412yes—
173C22⋊C4×C47—24no—
174C22⋊C4×C47—24no—
175C22⋊C4×C47—24no—
176C22⋊C4×C47—22no—
177C22⋊C4×C47—22no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—41no—
181C42×C47—24no—
182C42×C47—22no—
183C42×C47—22no—
184C42×C47—41no—
185C42×C47C2×D411yescharacteristic
186C42×C47C2×D411yescharacteristic
187C42×C47C2×D411yescharacteristic
188C42×C47C2411yescharacteristic
189C23×C47—22no—
190C23×C47#12011yescharacteristic
191Q8×C47—24no—
192Q8×C47—42no—
193Q8×C47—42no—
194Q8×C47—41no—
195Q8×C47—42no—
196Q8×C47—41no—
197Q8×C47—41no—
198Q8×C47—41no—
199Q8×C47—81no—
200Q8×C47—84no—
201D4×C47—22no—
202D4×C47—22no—
203D4×C47—42no—
204D4×C47—81no—
205D4×C47—82no—
206C2×C4×C47—21no—
207C2×C4×C47—22no—
208C2×C4×C47—21no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—41no—
215C2×C4×C47—44no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—84no—
219C2×C4×C47#12011yescharacteristic
220C2×C4×C47#12011yescharacteristic
221C2×C4×C47#12011yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C22×D411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C8×C47—41no—
226C8×C47—41no—
227C8×C47—42no—
228C8×C47—42no—
229#18949C4711yesmaximal, characteristic, direct product factor, Sylow
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—42no—
234C22×C47—42no—
235C22×C47—42no—
236C22×C47C2×#12011yescharacteristic
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—21no—
241C4×C47—42no—
242C4×C47—42no—
243C4×C47—42no—
244C4×C47—42no—
245C4×C47—42no—
246C4×C47—81no—
247C4×C47—81no—
248C4×C47#57712yes—
249C4×C47#57711yescharacteristic
250C4×C47#57811yescharacteristic
251#3550C2×C4711yescharacteristic
252#3246C2×C4711yescharacteristic
253#3237C2×C4711yescharacteristic, complemented
254#3231C2×C4711yescharacteristic, complemented
255#1651C2×C4712yescomplemented
256#1650C2×C4712yescomplemented
257#1638C2×C4712yescomplemented
258#1637C2×C4712yescomplemented
259#1552C2×C4711yescharacteristic, complemented
260#1496C2×C4711yescharacteristic
261#1481C2×C4711yescharacteristic, complemented
262C2×C47—41no—
263C2×C47—82no—
264C2×C47#300911yescharacteristic
265C2×C47#301311yescharacteristic
266C2×C47#302011yescharacteristic
267#563—22no—
268#559—21no—
269Q82—21no—
270#556—21no—
271#556C22×C4712yes—
272D4×Q8—21no—
273D4×Q8C22×C4712yes—
274#542—22no—
275#542—22no—
276#536—22no—
277#533C22×C4711yescharacteristic
278#533C22×C4711yescharacteristic
279#533C22×C4711yescharacteristic
280#532C22×C4711yescharacteristic
281#501—21no—
282#500C22×C4711yescharacteristic
283#498C22×C4711yescharacteristic
284#491—21no—
285#487C22×C4711yescharacteristic
286#487C22×C4711yescharacteristic
287#485—22no—
288#485—22no—
289#479—22no—
290#477C22×C4712yes—
291#476C22×C4712yes—
292#475—21no—
293#475C22×C4712yes—
294#465—22no—
295#461C22×C4712yes—
296#460—21no—
297#432C22×C4711yescharacteristic
298#431C22×C4711yescharacteristic
299C2×C4⋊C8C22×C4711yescharacteristic
300#332C22×C4712yes—
301#332C22×C4712yes—
302Q8⋊C8C22×C4712yes—
303Q8⋊C8C22×C4712yes—
304D4⋊C8C22×C4712yes—
305D4⋊C8C22×C4712yes—
306C47#1894911yescharacteristic, direct product factor, Sylow
307C2×#41—21no—
308C22×Q8—22no—
309C2×SD16—22no—
310C22×C8—21no—
311C4⋊Q8—24no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8D4×C4711yescharacteristic
315C4⋊Q8D4×C4711yescharacteristic
316C4⋊Q8D4×C4711yescharacteristic
317C4⋊Q8C23×C4711yescharacteristic
318C4⋊Q8C23×C4711yescharacteristic
319C4⋊Q8C23×C4711yescharacteristic
320C4⋊Q8C23×C4711yescharacteristic
321#127D4×C4711yescharacteristic
322#126—24no—
323#126—24no—
324#125—21no—
325#125—21no—
326#125D4×C4712yes—
327#124—24no—
328#124—22no—
329#124—22no—
330#124—21no—
331#123—24no—
332#123—24no—
333C22⋊Q8—24no—
334C22⋊Q8—22no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—22no—
339C22⋊Q8—24no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8D4×C4712yes—
343#121—21no—
344#121D4×C4712yes—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8C23×C4712yes—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4C23×C4712yes—
357#117—21no—
358#117—22no—
359#117—21no—
360#117D4×C4712yes—
361C2×C42C23×C4711yescharacteristic
362#107—22no—
363#107—22no—
364#106—22no—
365#106—22no—
366#106—22no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C4712yes—
370C4⋊C8C23×C4712yes—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#102—22no—
377C22⋊C8—21no—
378C22⋊C8—21no—
379#97—21no—
380C4×C8C23×C4711yescharacteristic
381C4×C8C23×C4711yescharacteristic
382#41—82no—
383C2×Q8—24no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—84no—
391C2×Q8C2×D4×C4712yes—
392C2×D4—22no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4C2×D4×C4712yes—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4C2×D4×C4711yescharacteristic
399C22×C4C2×D4×C4711yescharacteristic
400C22×C4C2×D4×C4711yescharacteristic
401SD16—82no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—81no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4C2×D4×C4712yes—
426C4⋊C4C2×D4×C4712yes—
427C4⋊C4C2×D4×C4712yes—
428C4⋊C4C2×D4×C4712yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—41no—
437C42—24no—
438C42—22no—
439C42—22no—
440C42—41no—
441C42C2×D4×C4711yescharacteristic
442C42C2×D4×C4711yescharacteristic
443C42C2×D4×C4711yescharacteristic
444C42C24×C4711yescharacteristic
445C23—22no—
446C23#120×C4711yescharacteristic
447Q8—24no—
448Q8—42no—
449Q8—42no—
450Q8—41no—
451Q8—42no—
452Q8—41no—
453Q8—41no—
454Q8—41no—
455Q8—81no—
456Q8—84no—
457D4—22no—
458D4—22no—
459D4—42no—
460D4—81no—
461D4—82no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—84no—
475C2×C4#120×C4711yescharacteristic
476C2×C4#120×C4711yescharacteristic
477C2×C4#120×C4711yescharacteristic
478C2×C4C22×D4×C4711yescharacteristic
479C2×C4C22×D4×C4711yescharacteristic
480C2×C4C22×D4×C4711yescharacteristic
481C8—41no—
482C8—41no—
483C8—42no—
484C8—42no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22C2×#120×C4711yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4—81no—
502C4—81no—
503C4C47×#57712yes—
504C4C47×#57711yescharacteristic
505C4C47×#57811yescharacteristic
506C2—41no—
507C2—82no—
508C2C47×#300911yescharacteristic
509C2C47×#301311yescharacteristic
510C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#3237C2semidirect
4. C47×#3231C2semidirect
5. C47×#1651C2semidirect
6. C47×#1650C2semidirect
7. C47×#1638C2semidirect
8. C47×#1637C2semidirect
9. C47×#1552C2semidirect
11. C47×#1481C2semidirect
229. #18949C47direct (N × H)
253. #3237C2×C47semidirect
254. #3231C2×C47semidirect
255. #1651C2×C47semidirect
256. #1650C2×C47semidirect
257. #1638C2×C47semidirect
258. #1637C2×C47semidirect
259. #1552C2×C47semidirect
261. #1481C2×C47semidirect
306. C47#18949direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35502
C47×#32462
C47×#32372
C47×#32312
C47×#16512
C47×#16502
C47×#16382
C47×#16372
C47×#15522
C47×#14962
C47×#14812
#1894947