Finite Group Databasebeta

← C47×#18032 #26057730

Subgroups — C47×#18032 #26057730

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3104C211yesmaximal, characteristic
2C47×#2986C211yesmaximal, characteristic
3C47×#2984C211yesmaximal, characteristic
4C47×#1593C211yesmaximal, characteristic, complemented
5C47×#1591C211yesmaximal, characteristic, complemented
6C47×#1587C211yesmaximal, characteristic, complemented
7C47×#1587C211yesmaximal, characteristic, complemented
8C47×#1584C211yesmaximal, characteristic, complemented
9C47×#1584C211yesmaximal, characteristic, complemented
10C47×#1579C211yesmaximal, characteristic, complemented
11C8×Q16×C47C211yesmaximal, characteristic, complemented
12C47×#1572C211yesmaximal, characteristic
13C47×#1497C211yesmaximal, characteristic
14C47×#1479C211yesmaximal, characteristic
15C47×#1454C211yesmaximal, characteristic
16C47×#533C2211yescharacteristic
17C2×C4×Q8×C47C2211yescharacteristic
18C47×#484C411yescharacteristic
19C47×#484C411yescharacteristic
20C47×#477C411yescharacteristic
21C47×#477C411yescharacteristic
22C47×#462C411yescharacteristic
23C47×#462C411yescharacteristic
24C47×#451C411yescharacteristic
25C47×#451C411yescharacteristic
26C47×#446—21no—
27C47×#446—21no—
28C47×#446—21no—
29C47×#446C2211yescharacteristic
30C47×#446C2211yescharacteristic
31C47×#446C2211yescharacteristic
32C47×#446C2211yescharacteristic
33C8×Q8×C47—21no—
34C8×Q8×C47C2211yescharacteristic
35C8×Q8×C47C2211yescharacteristic
36C8×Q8×C47C2211yescharacteristic
37C8×Q8×C47C2211yescharacteristic
38C4×Q16×C47C2211yescharacteristic
39C4×Q16×C47C2211yescharacteristic
40C4×Q16×C47C2211yescharacteristic
41C4×Q16×C47C2211yescharacteristic
42C47×#433—21no—
43C47×#433—21no—
44C47×#432—21no—
45C47×#432C2211yescharacteristic
46C47×#431—21no—
47C47×#431C2211yescharacteristic
48C47×#431C2211yescharacteristic
49C47×#431C2211yescharacteristic
50C47×#431C2211yescharacteristic
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×Q8⋊C8C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C22×Q8×C47C2×C411yescharacteristic
68C2×Q16×C47C2×C411yescharacteristic
69C2×Q16×C47C2×C411yescharacteristic
70C2×Q16×C47C2×C411yescharacteristic
71C2×Q16×C47C2×C411yescharacteristic
72C4⋊Q8×C47C2×C411yescharacteristic
73C4⋊Q8×C47C2×C411yescharacteristic
74#125×C47—21no—
75C22⋊Q8×C47—21no—
76C22⋊Q8×C47C2×C411yescharacteristic
77C22⋊Q8×C47C2×C411yescharacteristic
78C4×Q8×C47—21no—
79C4×Q8×C47—21no—
80C4×Q8×C47—21no—
81C4×Q8×C47C2×C411yescharacteristic
82C4×Q8×C47C2×C411yescharacteristic
83C4×Q8×C47C2311yescharacteristic
84C4×Q8×C47C2311yescharacteristic
85C4×Q8×C47C2311yescharacteristic
86C4×Q8×C47C2311yescharacteristic
87#117×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47C2×C411yescharacteristic
90C2×C42×C47—21no—
91C2×C42×C47C2311yescharacteristic
92#107×C47C2×C411yescharacteristic
93#107×C47C2×C411yescharacteristic
94#107×C47C2×C411yescharacteristic
95#107×C47C2×C411yescharacteristic
96C4⋊C8×C47—21no—
97C4⋊C8×C47—21no—
98C4⋊C8×C47—21no—
99C4⋊C8×C47—21no—
100C4⋊C8×C47—21no—
101C4⋊C8×C47—21no—
102C4⋊C8×C47—21no—
103C4⋊C8×C47—21no—
104C4⋊C8×C47—21no—
105C4⋊C8×C47C2×C411yescharacteristic
106C4⋊C8×C47C2×C411yescharacteristic
107C4⋊C8×C47D411yescharacteristic
108C4⋊C8×C47D411yescharacteristic
109C4⋊C8×C47C2311yescharacteristic
110C4⋊C8×C47C2311yescharacteristic
111C4⋊C8×C47C2311yescharacteristic
112C4⋊C8×C47C2311yescharacteristic
113#103×C47C2×C411yescharacteristic
114#103×C47C2×C411yescharacteristic
115#103×C47C2×C411yescharacteristic
116#103×C47C2×C411yescharacteristic
117#103×C47C2×C411yescharacteristic
118#103×C47C2×C411yescharacteristic
119#103×C47C2×C411yescharacteristic
120#103×C47C2×C411yescharacteristic
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123C22⋊C8×C47—21no—
124C22⋊C8×C47C2×C411yescharacteristic
125C22⋊C8×C47C2×C411yescharacteristic
126C22⋊C8×C47D411yescharacteristic
127C22⋊C8×C47D411yescharacteristic
128#97×C47—21no—
129#97×C47—21no—
130#97×C47—21no—
131#97×C47—21no—
132#97×C47—21no—
133C4×C8×C47—21no—
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×C47—21no—
146C2×Q8×C47—22no—
147C2×Q8×C47—41no—
148C2×Q8×C47C22×C411yescharacteristic
149C2×Q8×C47C22×C411yescharacteristic
150C2×Q8×C47C22×C411yescharacteristic
151C2×Q8×C47C22×C411yescharacteristic
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47#4111yescharacteristic
157Q16×C47—22no—
158Q16×C47—22no—
159Q16×C47—41no—
160Q16×C47—41no—
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×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
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×C47C22×C411yescharacteristic
188C4⋊C4×C47C22×C411yescharacteristic
189C4⋊C4×C47C22×C411yescharacteristic
190C4⋊C4×C47C22×C411yescharacteristic
191C22⋊C4×C47—21no—
192C22⋊C4×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47C22×C411yescharacteristic
200C42×C47C2×D411yescharacteristic
201C42×C47#4111yescharacteristic
202C42×C47C2411yescharacteristic
203C23×C47C4×D411yescharacteristic
204Q8×C47—21no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—42no—
212Q8×C47—42no—
213Q8×C47#13112yes—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
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—41no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C8×C47—21no—
236C8×C47—21no—
237C8×C47—21no—
238C8×C47—21no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C8×C47—41no—
246C8×C47—41no—
247C8×C47—41no—
248C8×C47—41no—
249#18032C4711yesmaximal, characteristic, direct product factor, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47C2×C4×D411yescharacteristic
254C4×C47—21no—
255C4×C47—22no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47—41no—
263C4×C47—41no—
264C4×C47—41no—
265C4×C47—41no—
266C4×C47C2×#13111yescharacteristic
267C4×C47#56811yescharacteristic
268C4×C47#57811yescharacteristic
269C4×C47#57811yescharacteristic
270#3104C2×C4711yescharacteristic
271#2986C2×C4711yescharacteristic
272#2984C2×C4711yescharacteristic
273#1593C2×C4711yescharacteristic, complemented
274#1591C2×C4711yescharacteristic, complemented
275#1587C2×C4711yescharacteristic, complemented
276#1587C2×C4711yescharacteristic, complemented
277#1584C2×C4711yescharacteristic, complemented
278#1584C2×C4711yescharacteristic, complemented
279#1579C2×C4711yescharacteristic, complemented
280C8×Q16C2×C4711yescharacteristic, complemented
281#1572C2×C4711yescharacteristic
282#1497C2×C4711yescharacteristic
283#1479C2×C4711yescharacteristic
284#1454C2×C4711yescharacteristic
285C2×C47—41no—
286C2×C47#293311yescharacteristic
287C2×C47#295011yescharacteristic
288C2×C47#295511yescharacteristic
289#533C22×C4711yescharacteristic
290C2×C4×Q8C22×C4711yescharacteristic
291#484C4×C4711yescharacteristic
292#484C4×C4711yescharacteristic
293#477C4×C4711yescharacteristic
294#477C4×C4711yescharacteristic
295#462C4×C4711yescharacteristic
296#462C4×C4711yescharacteristic
297#451C4×C4711yescharacteristic
298#451C4×C4711yescharacteristic
299#446—21no—
300#446—21no—
301#446—21no—
302#446C22×C4711yescharacteristic
303#446C22×C4711yescharacteristic
304#446C22×C4711yescharacteristic
305#446C22×C4711yescharacteristic
306C8×Q8—21no—
307C8×Q8C22×C4711yescharacteristic
308C8×Q8C22×C4711yescharacteristic
309C8×Q8C22×C4711yescharacteristic
310C8×Q8C22×C4711yescharacteristic
311C4×Q16C22×C4711yescharacteristic
312C4×Q16C22×C4711yescharacteristic
313C4×Q16C22×C4711yescharacteristic
314C4×Q16C22×C4711yescharacteristic
315#433—21no—
316#433—21no—
317#432—21no—
318#432C22×C4711yescharacteristic
319#431—21no—
320#431C22×C4711yescharacteristic
321#431C22×C4711yescharacteristic
322#431C22×C4711yescharacteristic
323#431C22×C4711yescharacteristic
324#335C22×C4711yescharacteristic
325#335C22×C4711yescharacteristic
326#334C22×C4711yescharacteristic
327#334C22×C4711yescharacteristic
328Q8⋊C8C22×C4711yescharacteristic
329Q8⋊C8C22×C4711yescharacteristic
330Q8⋊C8C22×C4711yescharacteristic
331Q8⋊C8C22×C4711yescharacteristic
332Q8⋊C8C22×C4711yescharacteristic
333Q8⋊C8C22×C4711yescharacteristic
334Q8⋊C8C22×C4711yescharacteristic
335Q8⋊C8C22×C4711yescharacteristic
336#322C22×C4711yescharacteristic
337#322C22×C4711yescharacteristic
338#322C22×C4711yescharacteristic
339C82C22×C4711yescharacteristic
340C47#1803211yescharacteristic, direct product factor, Sylow
341C22×Q8C2×C4×C4711yescharacteristic
342C2×Q16C2×C4×C4711yescharacteristic
343C2×Q16C2×C4×C4711yescharacteristic
344C2×Q16C2×C4×C4711yescharacteristic
345C2×Q16C2×C4×C4711yescharacteristic
346C4⋊Q8C2×C4×C4711yescharacteristic
347C4⋊Q8C2×C4×C4711yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C2×C4×C4711yescharacteristic
351C22⋊Q8C2×C4×C4711yescharacteristic
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C2×C4×C4711yescharacteristic
356C4×Q8C2×C4×C4711yescharacteristic
357C4×Q8C23×C4711yescharacteristic
358C4×Q8C23×C4711yescharacteristic
359C4×Q8C23×C4711yescharacteristic
360C4×Q8C23×C4711yescharacteristic
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2×C4×C4711yescharacteristic
364C2×C42—21no—
365C2×C42C23×C4711yescharacteristic
366#107C2×C4×C4711yescharacteristic
367#107C2×C4×C4711yescharacteristic
368#107C2×C4×C4711yescharacteristic
369#107C2×C4×C4711yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8C2×C4×C4711yescharacteristic
380C4⋊C8C2×C4×C4711yescharacteristic
381C4⋊C8D4×C4711yescharacteristic
382C4⋊C8D4×C4711yescharacteristic
383C4⋊C8C23×C4711yescharacteristic
384C4⋊C8C23×C4711yescharacteristic
385C4⋊C8C23×C4711yescharacteristic
386C4⋊C8C23×C4711yescharacteristic
387#103C2×C4×C4711yescharacteristic
388#103C2×C4×C4711yescharacteristic
389#103C2×C4×C4711yescharacteristic
390#103C2×C4×C4711yescharacteristic
391#103C2×C4×C4711yescharacteristic
392#103C2×C4×C4711yescharacteristic
393#103C2×C4×C4711yescharacteristic
394#103C2×C4×C4711yescharacteristic
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8C2×C4×C4711yescharacteristic
399C22⋊C8C2×C4×C4711yescharacteristic
400C22⋊C8D4×C4711yescharacteristic
401C22⋊C8D4×C4711yescharacteristic
402#97—21no—
403#97—21no—
404#97—21no—
405#97—21no—
406#97—21no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8C23×C4711yescharacteristic
413C4×C8C23×C4711yescharacteristic
414C4×C8C23×C4711yescharacteristic
415C4×C8C23×C4711yescharacteristic
416C4×C8C23×C4711yescharacteristic
417C4×C8C23×C4711yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—41no—
422C2×Q8C22×C4×C4711yescharacteristic
423C2×Q8C22×C4×C4711yescharacteristic
424C2×Q8C22×C4×C4711yescharacteristic
425C2×Q8C22×C4×C4711yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4C22×C4×C4711yescharacteristic
429C22×C4C2×D4×C4711yescharacteristic
430C22×C4#41×C4711yescharacteristic
431Q16—22no—
432Q16—22no—
433Q16—41no—
434Q16—41no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8C22×C4×C4711yescharacteristic
442C2×C8C22×C4×C4711yescharacteristic
443C2×C8C22×C4×C4711yescharacteristic
444C2×C8C22×C4×C4711yescharacteristic
445C2×C8C2×D4×C4711yescharacteristic
446C2×C8C2×D4×C4711yescharacteristic
447C2×C8C2×D4×C4711yescharacteristic
448C2×C8C2×D4×C4711yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4C22×C4×C4711yescharacteristic
462C4⋊C4C22×C4×C4711yescharacteristic
463C4⋊C4C22×C4×C4711yescharacteristic
464C4⋊C4C22×C4×C4711yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42C22×C4×C4711yescharacteristic
474C42C2×D4×C4711yescharacteristic
475C42#41×C4711yescharacteristic
476C42C24×C4711yescharacteristic
477C23C4×D4×C4711yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—42no—
486Q8—42no—
487Q8#131×C4712yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4C4×D4×C4711yescharacteristic
504C2×C4C4×D4×C4711yescharacteristic
505C2×C4C4×D4×C4711yescharacteristic
506C2×C4C23×C4×C4711yescharacteristic
507C2×C4C22×D4×C4711yescharacteristic
508C2×C4C2×#41×C4711yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×D4×C4711yescharacteristic
527C4—21no—
528C4—22no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4C2×#131×C4711yescharacteristic
540C4C47×#56811yescharacteristic
541C4C47×#57811yescharacteristic
542C4C47×#57811yescharacteristic
543C2—41no—
544C2C47×#293311yescharacteristic
545C2C47×#295011yescharacteristic
546C2C47×#295511yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC42C24×C47
socleC22×C47C2×C4×D4
prime radicalC23×C47C4×D4
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
4. C47×#1593C2semidirect
5. C47×#1591C2semidirect
6. C47×#1587C2semidirect
7. C47×#1587C2semidirect
8. C47×#1584C2semidirect
9. C47×#1584C2semidirect
10. C47×#1579C2semidirect
11. C8×Q16×C47C2semidirect
249. #18032C47direct (N × H)
273. #1593C2×C47semidirect
274. #1591C2×C47semidirect
275. #1587C2×C47semidirect
276. #1587C2×C47semidirect
277. #1584C2×C47semidirect
278. #1584C2×C47semidirect
279. #1579C2×C47semidirect
280. C8×Q16C2×C47semidirect
340. C47#18032direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31042
C47×#29862
C47×#29842
C47×#15932
C47×#15912
C47×#15872
C47×#15842
C47×#15792
C8×Q16×C472
C47×#15722
C47×#14972
C47×#14792
C47×#14542
#1803247