Finite Group Databasebeta

← C47×#18077 #26057775

Subgroups — C47×#18077 #26057775

Order 12032.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3172C211yesmaximal, characteristic
2C47×#2969C211yesmaximal, characteristic
3C47×#2962C211yesmaximal, characteristic, complemented
4C47×#1592C211yesmaximal, characteristic, complemented
5C47×#1591C211yesmaximal, characteristic, complemented
6C47×#1588C211yesmaximal, characteristic, complemented
7C47×#1587C211yesmaximal, characteristic, complemented
8C47×#1584C211yesmaximal, characteristic, complemented
9C47×#1582C211yesmaximal, characteristic, complemented
10C47×#1579C211yesmaximal, characteristic, complemented
11C8×SD16×C47C211yesmaximal, characteristic, complemented
12C47×#1565C211yesmaximal, characteristic, complemented
13C47×#1485C211yesmaximal, characteristic, complemented
14C47×#1483C211yesmaximal, characteristic
15C47×#1455C211yesmaximal, 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×#446—21no—
28C47×#446C2211yescharacteristic
29C47×#446C2211yescharacteristic
30C47×#446C2211yescharacteristic
31C8×Q8×C47C2211yescharacteristic
32C8×Q8×C47C2211yescharacteristic
33C8×Q8×C47C2211yescharacteristic
34C4×Q16×C47C2211yescharacteristic
35C4×Q16×C47C2211yescharacteristic
36C4×SD16×C47C2211yescharacteristic
37C4×SD16×C47C2211yescharacteristic
38C47×#436—21no—
39C47×#436C2211yescharacteristic
40C47×#435—21no—
41C8×D4×C47C2211yescharacteristic
42C47×#433—21no—
43C47×#431C2211yescharacteristic
44C47×#424—21no—
45C2×C4⋊C8×C47C2211yescharacteristic
46C47×#405—21no—
47C47×#405—21no—
48C4×M16×C47C2211yescharacteristic
49C4×M16×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×C47—21no—
73C2×M16×C47C2×C411yescharacteristic
74C2×M16×C47C2×C411yescharacteristic
75C2×M16×C47D411yescharacteristic
76C2×M16×C47D411yescharacteristic
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C4⋊Q8×C47C2×C411yescharacteristic
80C4⋊Q8×C47C2×C411yescharacteristic
81#126×C47—21no—
82#125×C47—21no—
83#125×C47C2×C411yescharacteristic
84#124×C47C2×C411yescharacteristic
85#123×C47—21no—
86C22⋊Q8×C47—21no—
87C22⋊Q8×C47C2×C411yescharacteristic
88C22⋊Q8×C47C2×C411yescharacteristic
89C22⋊Q8×C47C2×C411yescharacteristic
90#121×C47C2×C411yescharacteristic
91C4×Q8×C47—21no—
92C4×Q8×C47C2311yescharacteristic
93C4×Q8×C47C2311yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47C2311yescharacteristic
97#117×C47—21no—
98#117×C47—21no—
99C2×C42×C47C2311yescharacteristic
100#107×C47C2×C411yescharacteristic
101#107×C47C2×C411yescharacteristic
102#106×C47C2×C411yescharacteristic
103#106×C47C2×C411yescharacteristic
104C4⋊C8×C47—21no—
105C4⋊C8×C47—21no—
106C4⋊C8×C47—21no—
107C4⋊C8×C47—21no—
108C4⋊C8×C47—21no—
109C4⋊C8×C47—21no—
110C4⋊C8×C47—21no—
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—
126#97×C47—21no—
127#97×C47—21no—
128#97×C47—21no—
129#97×C47—21no—
130#97×C47C2×C411yescharacteristic
131#97×C47C2×C411yescharacteristic
132#97×C47D411yescharacteristic
133#97×C47D411yescharacteristic
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—22no—
160M16×C47—41no—
161M16×C47—41no—
162M16×C47—42no—
163M16×C47—42no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—42no—
171C2×C8×C47—42no—
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C22×C411yescharacteristic
174C2×C8×C47C22×C411yescharacteristic
175C2×C8×C47C22×C411yescharacteristic
176C2×C8×C47C2×D411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
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×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22×C411yescharacteristic
192C4⋊C4×C47C22×C411yescharacteristic
193C4⋊C4×C47C22×C411yescharacteristic
194C4⋊C4×C47C22×C411yescharacteristic
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C22⋊C4×C47—21no—
198C22⋊C4×C47—21no—
199C22⋊C4×C47—21no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—21no—
205C42×C47C22×C411yescharacteristic
206C42×C47C2×D411yescharacteristic
207C42×C47#4111yescharacteristic
208C42×C47C2411yescharacteristic
209C23×C47—21no—
210C23×C47C4×D411yescharacteristic
211Q8×C47—21no—
212Q8×C47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47—81no—
218D4×C47—21no—
219D4×C47—21no—
220D4×C47—81no—
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—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47C23×C411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C8×C47—22no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47#13112yes—
254C8×C47#13712yes—
255#18077C4711yesmaximal, characteristic, direct product factor, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47C2×C4×D411yescharacteristic
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47C2×#13111yescharacteristic
275C4×C47#56811yescharacteristic
276C4×C47C2×#13711yescharacteristic
277C4×C47#57511yescharacteristic
278#3172C2×C4711yescharacteristic
279#2969C2×C4711yescharacteristic
280#2962C2×C4711yescharacteristic, complemented
281#1592C2×C4711yescharacteristic, complemented
282#1591C2×C4711yescharacteristic, complemented
283#1588C2×C4711yescharacteristic, complemented
284#1587C2×C4711yescharacteristic, complemented
285#1584C2×C4711yescharacteristic, complemented
286#1582C2×C4711yescharacteristic, complemented
287#1579C2×C4711yescharacteristic, complemented
288C8×SD16C2×C4711yescharacteristic, complemented
289#1565C2×C4711yescharacteristic, complemented
290#1485C2×C4711yescharacteristic, complemented
291#1483C2×C4711yescharacteristic
292#1455C2×C4711yescharacteristic, complemented
293C2×C47—41no—
294C2×C47—81no—
295C2×C47#293511yescharacteristic
296C2×C47C4×#13711yescharacteristic
297C2×C47#295611yescharacteristic
298#533C22×C4711yescharacteristic
299#529C22×C4711yescharacteristic
300#501C4×C4711yescharacteristic
301#497C4×C4711yescharacteristic
302#491C4×C4711yescharacteristic
303#489C4×C4711yescharacteristic
304#470C4×C4711yescharacteristic
305#470C4×C4711yescharacteristic
306#468C4×C4711yescharacteristic
307#468C4×C4711yescharacteristic
308#446—21no—
309#446—21no—
310#446C22×C4711yescharacteristic
311#446C22×C4711yescharacteristic
312#446C22×C4711yescharacteristic
313C8×Q8C22×C4711yescharacteristic
314C8×Q8C22×C4711yescharacteristic
315C8×Q8C22×C4711yescharacteristic
316C4×Q16C22×C4711yescharacteristic
317C4×Q16C22×C4711yescharacteristic
318C4×SD16C22×C4711yescharacteristic
319C4×SD16C22×C4711yescharacteristic
320#436—21no—
321#436C22×C4711yescharacteristic
322#435—21no—
323C8×D4C22×C4711yescharacteristic
324#433—21no—
325#431C22×C4711yescharacteristic
326#424—21no—
327C2×C4⋊C8C22×C4711yescharacteristic
328#405—21no—
329#405—21no—
330C4×M16C22×C4711yescharacteristic
331C4×M16C22×C4711yescharacteristic
332C4×M16C22×C4711yescharacteristic
333#335C22×C4711yescharacteristic
334#335C22×C4711yescharacteristic
335#334C22×C4711yescharacteristic
336#334C22×C4711yescharacteristic
337Q8⋊C8C22×C4711yescharacteristic
338Q8⋊C8C22×C4711yescharacteristic
339Q8⋊C8C22×C4711yescharacteristic
340Q8⋊C8C22×C4711yescharacteristic
341Q8⋊C8C22×C4711yescharacteristic
342Q8⋊C8C22×C4711yescharacteristic
343D4⋊C8C22×C4711yescharacteristic
344D4⋊C8C22×C4711yescharacteristic
345#322C22×C4711yescharacteristic
346#322C22×C4711yescharacteristic
347#322C22×C4711yescharacteristic
348C82C22×C4711yescharacteristic
349C47#1807711yescharacteristic, direct product factor, Sylow
350C2×Q16C2×C4×C4711yescharacteristic
351C2×Q16C2×C4×C4711yescharacteristic
352C2×SD16C2×C4×C4711yescharacteristic
353C2×SD16C2×C4×C4711yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16C2×C4×C4711yescharacteristic
357C2×M16C2×C4×C4711yescharacteristic
358C2×M16D4×C4711yescharacteristic
359C2×M16D4×C4711yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C4⋊Q8C2×C4×C4711yescharacteristic
363C4⋊Q8C2×C4×C4711yescharacteristic
364#126—21no—
365#125—21no—
366#125C2×C4×C4711yescharacteristic
367#124C2×C4×C4711yescharacteristic
368#123—21no—
369C22⋊Q8—21no—
370C22⋊Q8C2×C4×C4711yescharacteristic
371C22⋊Q8C2×C4×C4711yescharacteristic
372C22⋊Q8C2×C4×C4711yescharacteristic
373#121C2×C4×C4711yescharacteristic
374C4×Q8—21no—
375C4×Q8C23×C4711yescharacteristic
376C4×Q8C23×C4711yescharacteristic
377C4×Q8C23×C4711yescharacteristic
378C4×D4—21no—
379C4×D4C23×C4711yescharacteristic
380#117—21no—
381#117—21no—
382C2×C42C23×C4711yescharacteristic
383#107C2×C4×C4711yescharacteristic
384#107C2×C4×C4711yescharacteristic
385#106C2×C4×C4711yescharacteristic
386#106C2×C4×C4711yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C4711yescharacteristic
395C4⋊C8C23×C4711yescharacteristic
396C4⋊C8C23×C4711yescharacteristic
397C4⋊C8C23×C4711yescharacteristic
398#103C2×C4×C4711yescharacteristic
399#103C2×C4×C4711yescharacteristic
400#103C2×C4×C4711yescharacteristic
401#103C2×C4×C4711yescharacteristic
402#103C2×C4×C4711yescharacteristic
403#103C2×C4×C4711yescharacteristic
404#102C2×C4×C4711yescharacteristic
405#102C2×C4×C4711yescharacteristic
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409#97—21no—
410#97—21no—
411#97—21no—
412#97—21no—
413#97C2×C4×C4711yescharacteristic
414#97C2×C4×C4711yescharacteristic
415#97D4×C4711yescharacteristic
416#97D4×C4711yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—21no—
421C4×C8C23×C4711yescharacteristic
422C4×C8C23×C4711yescharacteristic
423C4×C8C23×C4711yescharacteristic
424C4×C8C23×C4711yescharacteristic
425C4×C8C23×C4711yescharacteristic
426C4×C8C23×C4711yescharacteristic
427C2×Q8—21no—
428C2×Q8C22×C4×C4711yescharacteristic
429C2×Q8C22×C4×C4711yescharacteristic
430C2×Q8C22×C4×C4711yescharacteristic
431C2×D4—21no—
432C2×D4C22×C4×C4711yescharacteristic
433C22×C4—21no—
434C22×C4C22×C4×C4711yescharacteristic
435C22×C4C2×D4×C4711yescharacteristic
436C22×C4#41×C4711yescharacteristic
437Q16—22no—
438Q16—41no—
439SD16—22no—
440SD16—41no—
441M16—22no—
442M16—22no—
443M16—41no—
444M16—41no—
445M16—42no—
446M16—42no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8C22×C4×C4711yescharacteristic
456C2×C8C22×C4×C4711yescharacteristic
457C2×C8C22×C4×C4711yescharacteristic
458C2×C8C22×C4×C4711yescharacteristic
459C2×C8C2×D4×C4711yescharacteristic
460C2×C8C2×D4×C4711yescharacteristic
461C2×C8C2×D4×C4711yescharacteristic
462C2×C8C2×D4×C4711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4C22×C4×C4711yescharacteristic
475C4⋊C4C22×C4×C4711yescharacteristic
476C4⋊C4C22×C4×C4711yescharacteristic
477C4⋊C4C22×C4×C4711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42C22×C4×C4711yescharacteristic
489C42C2×D4×C4711yescharacteristic
490C42#41×C4711yescharacteristic
491C42C24×C4711yescharacteristic
492C23—21no—
493C23C4×D4×C4711yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—81no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4C4×D4×C4711yescharacteristic
519C2×C4C4×D4×C4711yescharacteristic
520C2×C4C4×D4×C4711yescharacteristic
521C2×C4C23×C4×C4711yescharacteristic
522C2×C4C22×D4×C4711yescharacteristic
523C2×C4C2×#41×C4711yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8#131×C4712yes—
537C8#137×C4712yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×D4×C4711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4C2×#131×C4711yescharacteristic
557C4C47×#56811yescharacteristic
558C4C2×#137×C4711yescharacteristic
559C4C47×#57511yescharacteristic
560C2—41no—
561C2—81no—
562C2C47×#293511yescharacteristic
563C2C4×#137×C4711yescharacteristic
564C2C47×#295611yescharacteristic
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 ◁ C4×M16×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2962C2semidirect
4. C47×#1592C2semidirect
5. C47×#1591C2semidirect
6. C47×#1588C2semidirect
7. C47×#1587C2semidirect
8. C47×#1584C2semidirect
9. C47×#1582C2semidirect
10. C47×#1579C2semidirect
11. C8×SD16×C47C2semidirect
12. C47×#1565C2semidirect
13. C47×#1485C2semidirect
15. C47×#1455C2semidirect
255. #18077C47direct (N × H)
280. #2962C2×C47semidirect
281. #1592C2×C47semidirect
282. #1591C2×C47semidirect
283. #1588C2×C47semidirect
284. #1587C2×C47semidirect
285. #1584C2×C47semidirect
286. #1582C2×C47semidirect
287. #1579C2×C47semidirect
288. C8×SD16C2×C47semidirect
289. #1565C2×C47semidirect
290. #1485C2×C47semidirect
292. #1455C2×C47semidirect
349. C47#18077direct (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×#29692
C47×#29622
C47×#15922
C47×#15912
C47×#15882
C47×#15872
C47×#15842
C47×#15822
C47×#15792
C8×SD16×C472
C47×#15652
C47×#14852
C47×#14832
C47×#14552
#1807747