Finite Group Databasebeta

← C47×#18083 #26057781

Subgroups — C47×#18083 #26057781

Order 12032.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3172C211yesmaximal, characteristic
2C47×#2994C211yesmaximal, characteristic
3C47×#2986C211yesmaximal, characteristic, complemented
4C47×#1593C211yesmaximal, characteristic, complemented
5C47×#1590C211yesmaximal, characteristic, complemented
6C47×#1588C211yesmaximal, characteristic, complemented
7C47×#1587C211yesmaximal, characteristic, complemented
8C47×#1584C211yesmaximal, characteristic, complemented
9C47×#1582C211yesmaximal, characteristic, complemented
10C47×SD16⋊C8C211yesmaximal, characteristic, complemented
11C8×Q16×C47C211yesmaximal, characteristic, complemented
12C47×#1565C211yesmaximal, characteristic, complemented
13C47×#1482C211yesmaximal, characteristic
14C47×#1481C211yesmaximal, characteristic, complemented
15C47×#1453C211yesmaximal, characteristic, complemented
16C47×#533C2211yescharacteristic
17C47×#529C2211yescharacteristic
18C47×#501C411yescharacteristic
19C47×#497C411yescharacteristic
20C47×#491C411yescharacteristic
21C47×#489C411yescharacteristic
22C47×#470C411yescharacteristic
23C47×#470C411yescharacteristic
24C47×#468C411yescharacteristic
25C47×#468C411yescharacteristic
26C47×#446—21no—
27C47×#446C2211yescharacteristic
28C47×#446C2211yescharacteristic
29C47×#446C2211yescharacteristic
30C8×Q8×C47—21no—
31C8×Q8×C47C2211yescharacteristic
32C8×Q8×C47C2211yescharacteristic
33C8×Q8×C47C2211yescharacteristic
34C4×Q16×C47C2211yescharacteristic
35C4×Q16×C47C2211yescharacteristic
36C4×SD16×C47C2211yescharacteristic
37C4×SD16×C47C2211yescharacteristic
38C47×#436C2211yescharacteristic
39C47×#435—21no—
40C8×D4×C47—21no—
41C8×D4×C47C2211yescharacteristic
42C47×#433—21no—
43C47×#433—21no—
44C47×#433—21no—
45C47×#431C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#431C2211yescharacteristic
48C47×#424—21no—
49C2×C4⋊C8×C47C2211yescharacteristic
50C4×M16×C47C2211yescharacteristic
51C47×#335C2211yescharacteristic
52C47×#335C2211yescharacteristic
53C47×#334C2211yescharacteristic
54C47×#334C2211yescharacteristic
55C47×Q8⋊C8C2211yescharacteristic
56C47×Q8⋊C8C2211yescharacteristic
57C47×Q8⋊C8C2211yescharacteristic
58C47×Q8⋊C8C2211yescharacteristic
59C47×Q8⋊C8C2211yescharacteristic
60C47×Q8⋊C8C2211yescharacteristic
61C47×D4⋊C8C2211yescharacteristic
62C47×D4⋊C8C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×Q16×C47C2×C411yescharacteristic
68C2×Q16×C47C2×C411yescharacteristic
69C2×SD16×C47C2×C411yescharacteristic
70C2×SD16×C47C2×C411yescharacteristic
71C2×M16×C47—21no—
72C2×M16×C47C2×C411yescharacteristic
73C2×M16×C47C2×C411yescharacteristic
74C22×C8×C47—21no—
75C22×C8×C47—21no—
76C4⋊Q8×C47C2×C411yescharacteristic
77C4⋊Q8×C47C2×C411yescharacteristic
78#126×C47—21no—
79#125×C47—21no—
80#125×C47C2×C411yescharacteristic
81#124×C47C2×C411yescharacteristic
82#123×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47C2×C411yescharacteristic
85C22⋊Q8×C47C2×C411yescharacteristic
86C22⋊Q8×C47C2×C411yescharacteristic
87#121×C47C2×C411yescharacteristic
88C4×Q8×C47—21no—
89C4×Q8×C47C2311yescharacteristic
90C4×Q8×C47C2311yescharacteristic
91C4×Q8×C47C2311yescharacteristic
92C4×D4×C47—21no—
93C4×D4×C47C2311yescharacteristic
94#117×C47—21no—
95#117×C47—21no—
96C2×C42×C47C2311yescharacteristic
97#107×C47C2×C411yescharacteristic
98#107×C47C2×C411yescharacteristic
99#106×C47C2×C411yescharacteristic
100#106×C47C2×C411yescharacteristic
101C4⋊C8×C47—21no—
102C4⋊C8×C47—21no—
103C4⋊C8×C47—21no—
104C4⋊C8×C47—21no—
105C4⋊C8×C47—21no—
106C4⋊C8×C47—21no—
107C4⋊C8×C47—21no—
108C4⋊C8×C47—21no—
109C4⋊C8×C47D411yescharacteristic
110C4⋊C8×C47D411yescharacteristic
111C4⋊C8×C47C2311yescharacteristic
112C4⋊C8×C47C2311yescharacteristic
113C4⋊C8×C47C2311yescharacteristic
114C4⋊C8×C47C2311yescharacteristic
115#103×C47C2×C411yescharacteristic
116#103×C47C2×C411yescharacteristic
117#103×C47C2×C411yescharacteristic
118#103×C47C2×C411yescharacteristic
119#103×C47C2×C411yescharacteristic
120#103×C47C2×C411yescharacteristic
121#102×C47C2×C411yescharacteristic
122#102×C47C2×C411yescharacteristic
123C22⋊C8×C47—21no—
124C22⋊C8×C47—21no—
125C22⋊C8×C47—21no—
126C22⋊C8×C47—21no—
127C22⋊C8×C47D411yescharacteristic
128C22⋊C8×C47D411yescharacteristic
129#97×C47—21no—
130#97×C47—21no—
131#97×C47—21no—
132#97×C47C2×C411yescharacteristic
133#97×C47C2×C411yescharacteristic
134C4×C8×C47—21no—
135C4×C8×C47—21no—
136C4×C8×C47—21no—
137C4×C8×C47—21no—
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47—21no—
149C2×D4×C47C22×C411yescharacteristic
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4111yescharacteristic
154Q16×C47—22no—
155Q16×C47—41no—
156SD16×C47—22no—
157SD16×C47—41no—
158M16×C47—22no—
159M16×C47—41no—
160M16×C47—81no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—81no—
168C2×C8×C47—81no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C2×C8×C47C2×D411yescharacteristic
176C2×C8×C47C2×D411yescharacteristic
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47C22×C411yescharacteristic
189C4⋊C4×C47C22×C411yescharacteristic
190C4⋊C4×C47C22×C411yescharacteristic
191C4⋊C4×C47C22×C411yescharacteristic
192C22⋊C4×C47—21no—
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47C22×C411yescharacteristic
203C42×C47C2×D411yescharacteristic
204C42×C47#4111yescharacteristic
205C42×C47C2411yescharacteristic
206C23×C47—21no—
207C23×C47C4×D411yescharacteristic
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—42no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—42no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C8×C47—21no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47#13112yes—
252#18083C4711yesmaximal, characteristic, direct product factor, Sylow
253C22×C47—21no—
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47C2×C4×D411yescharacteristic
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47C2×#13111yescharacteristic
272C4×C47#56811yescharacteristic
273C4×C47#57711yescharacteristic
274C4×C47#57811yescharacteristic
275#3172C2×C4711yescharacteristic
276#2994C2×C4711yescharacteristic
277#2986C2×C4711yescharacteristic, complemented
278#1593C2×C4711yescharacteristic, complemented
279#1590C2×C4711yescharacteristic, complemented
280#1588C2×C4711yescharacteristic, complemented
281#1587C2×C4711yescharacteristic, complemented
282#1584C2×C4711yescharacteristic, complemented
283#1582C2×C4711yescharacteristic, complemented
284SD16⋊C8C2×C4711yescharacteristic, complemented
285C8×Q16C2×C4711yescharacteristic, complemented
286#1565C2×C4711yescharacteristic, complemented
287#1482C2×C4711yescharacteristic
288#1481C2×C4711yescharacteristic, complemented
289#1453C2×C4711yescharacteristic, complemented
290C2×C47—41no—
291C2×C47—81no—
292C2×C47#293511yescharacteristic
293C2×C47#294711yescharacteristic
294C2×C47#295511yescharacteristic
295#533C22×C4711yescharacteristic
296#529C22×C4711yescharacteristic
297#501C4×C4711yescharacteristic
298#497C4×C4711yescharacteristic
299#491C4×C4711yescharacteristic
300#489C4×C4711yescharacteristic
301#470C4×C4711yescharacteristic
302#470C4×C4711yescharacteristic
303#468C4×C4711yescharacteristic
304#468C4×C4711yescharacteristic
305#446—21no—
306#446C22×C4711yescharacteristic
307#446C22×C4711yescharacteristic
308#446C22×C4711yescharacteristic
309C8×Q8—21no—
310C8×Q8C22×C4711yescharacteristic
311C8×Q8C22×C4711yescharacteristic
312C8×Q8C22×C4711yescharacteristic
313C4×Q16C22×C4711yescharacteristic
314C4×Q16C22×C4711yescharacteristic
315C4×SD16C22×C4711yescharacteristic
316C4×SD16C22×C4711yescharacteristic
317#436C22×C4711yescharacteristic
318#435—21no—
319C8×D4—21no—
320C8×D4C22×C4711yescharacteristic
321#433—21no—
322#433—21no—
323#433—21no—
324#431C22×C4711yescharacteristic
325#431C22×C4711yescharacteristic
326#431C22×C4711yescharacteristic
327#424—21no—
328C2×C4⋊C8C22×C4711yescharacteristic
329C4×M16C22×C4711yescharacteristic
330#335C22×C4711yescharacteristic
331#335C22×C4711yescharacteristic
332#334C22×C4711yescharacteristic
333#334C22×C4711yescharacteristic
334Q8⋊C8C22×C4711yescharacteristic
335Q8⋊C8C22×C4711yescharacteristic
336Q8⋊C8C22×C4711yescharacteristic
337Q8⋊C8C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339Q8⋊C8C22×C4711yescharacteristic
340D4⋊C8C22×C4711yescharacteristic
341D4⋊C8C22×C4711yescharacteristic
342#322C22×C4711yescharacteristic
343#322C22×C4711yescharacteristic
344#322C22×C4711yescharacteristic
345C82C22×C4711yescharacteristic
346C47#1808311yescharacteristic, direct product factor, Sylow
347C2×Q16C2×C4×C4711yescharacteristic
348C2×Q16C2×C4×C4711yescharacteristic
349C2×SD16C2×C4×C4711yescharacteristic
350C2×SD16C2×C4×C4711yescharacteristic
351C2×M16—21no—
352C2×M16C2×C4×C4711yescharacteristic
353C2×M16C2×C4×C4711yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C4⋊Q8C2×C4×C4711yescharacteristic
357C4⋊Q8C2×C4×C4711yescharacteristic
358#126—21no—
359#125—21no—
360#125C2×C4×C4711yescharacteristic
361#124C2×C4×C4711yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8C2×C4×C4711yescharacteristic
365C22⋊Q8C2×C4×C4711yescharacteristic
366C22⋊Q8C2×C4×C4711yescharacteristic
367#121C2×C4×C4711yescharacteristic
368C4×Q8—21no—
369C4×Q8C23×C4711yescharacteristic
370C4×Q8C23×C4711yescharacteristic
371C4×Q8C23×C4711yescharacteristic
372C4×D4—21no—
373C4×D4C23×C4711yescharacteristic
374#117—21no—
375#117—21no—
376C2×C42C23×C4711yescharacteristic
377#107C2×C4×C4711yescharacteristic
378#107C2×C4×C4711yescharacteristic
379#106C2×C4×C4711yescharacteristic
380#106C2×C4×C4711yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8D4×C4711yescharacteristic
390C4⋊C8D4×C4711yescharacteristic
391C4⋊C8C23×C4711yescharacteristic
392C4⋊C8C23×C4711yescharacteristic
393C4⋊C8C23×C4711yescharacteristic
394C4⋊C8C23×C4711yescharacteristic
395#103C2×C4×C4711yescharacteristic
396#103C2×C4×C4711yescharacteristic
397#103C2×C4×C4711yescharacteristic
398#103C2×C4×C4711yescharacteristic
399#103C2×C4×C4711yescharacteristic
400#103C2×C4×C4711yescharacteristic
401#102C2×C4×C4711yescharacteristic
402#102C2×C4×C4711yescharacteristic
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8D4×C4711yescharacteristic
408C22⋊C8D4×C4711yescharacteristic
409#97—21no—
410#97—21no—
411#97—21no—
412#97C2×C4×C4711yescharacteristic
413#97C2×C4×C4711yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C4711yescharacteristic
419C4×C8C23×C4711yescharacteristic
420C4×C8C23×C4711yescharacteristic
421C4×C8C23×C4711yescharacteristic
422C4×C8C23×C4711yescharacteristic
423C4×C8C23×C4711yescharacteristic
424C2×Q8—21no—
425C2×Q8C22×C4×C4711yescharacteristic
426C2×Q8C22×C4×C4711yescharacteristic
427C2×Q8C22×C4×C4711yescharacteristic
428C2×D4—21no—
429C2×D4C22×C4×C4711yescharacteristic
430C22×C4—21no—
431C22×C4C22×C4×C4711yescharacteristic
432C22×C4C2×D4×C4711yescharacteristic
433C22×C4#41×C4711yescharacteristic
434Q16—22no—
435Q16—41no—
436SD16—22no—
437SD16—41no—
438M16—22no—
439M16—41no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8C22×C4×C4711yescharacteristic
450C2×C8C22×C4×C4711yescharacteristic
451C2×C8C22×C4×C4711yescharacteristic
452C2×C8C22×C4×C4711yescharacteristic
453C2×C8C2×D4×C4711yescharacteristic
454C2×C8C2×D4×C4711yescharacteristic
455C2×C8C2×D4×C4711yescharacteristic
456C2×C8C2×D4×C4711yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4C22×C4×C4711yescharacteristic
469C4⋊C4C22×C4×C4711yescharacteristic
470C4⋊C4C22×C4×C4711yescharacteristic
471C4⋊C4C22×C4×C4711yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42C22×C4×C4711yescharacteristic
483C42C2×D4×C4711yescharacteristic
484C42#41×C4711yescharacteristic
485C42C24×C4711yescharacteristic
486C23—21no—
487C23C4×D4×C4711yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4C4×D4×C4711yescharacteristic
513C2×C4C4×D4×C4711yescharacteristic
514C2×C4C4×D4×C4711yescharacteristic
515C2×C4C23×C4×C4711yescharacteristic
516C2×C4C22×D4×C4711yescharacteristic
517C2×C4C2×#41×C4711yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8#131×C4712yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×C4×D4×C4711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4C2×#131×C4711yescharacteristic
551C4C47×#56811yescharacteristic
552C4C47×#57711yescharacteristic
553C4C47×#57811yescharacteristic
554C2—41no—
555C2—81no—
556C2C47×#293511yescharacteristic
557C2C47×#294711yescharacteristic
558C2C47×#295511yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC42C24×C47
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C47×#431 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2986C2semidirect
4. C47×#1593C2semidirect
5. C47×#1590C2semidirect
6. C47×#1588C2semidirect
7. C47×#1587C2semidirect
8. C47×#1584C2semidirect
9. C47×#1582C2semidirect
10. C47×SD16⋊C8C2semidirect
11. C8×Q16×C47C2semidirect
12. C47×#1565C2semidirect
14. C47×#1481C2semidirect
15. C47×#1453C2semidirect
252. #18083C47direct (N × H)
277. #2986C2×C47semidirect
278. #1593C2×C47semidirect
279. #1590C2×C47semidirect
280. #1588C2×C47semidirect
281. #1587C2×C47semidirect
282. #1584C2×C47semidirect
283. #1582C2×C47semidirect
284. SD16⋊C8C2×C47semidirect
285. C8×Q16C2×C47semidirect
286. #1565C2×C47semidirect
288. #1481C2×C47semidirect
289. #1453C2×C47semidirect
346. C47#18083direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31722
C47×#29942
C47×#29862
C47×#15932
C47×#15902
C47×#15882
C47×#15872
C47×#15842
C47×#15822
C47×SD16⋊C82
C8×Q16×C472
C47×#15652
C47×#14822
C47×#14812
C47×#14532
#1808347