Finite Group Databasebeta

← C2×C47×#2036 #26063176

Subgroups — C2×C47×#2036 #26063176

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C47C211yesmaximal, characteristic
2C22×#107×C47C211yesmaximal, characteristic, complemented
3C22×#103×C47C211yesmaximal, characteristic, complemented
4C22×#103×C47C211yesmaximal, characteristic, complemented
5C22×C22⋊C8×C47C211yesmaximal, characteristic
6C2×C47×#380C211yesmaximal, characteristic
7C47×#2036C218yesmaximal, direct product factor
8C2×C47×#340C211yesmaximal, characteristic, complemented
9C23×Q8×C47C2211yescharacteristic
10C24×C4×C47C2211yescharacteristic
11C23×C8×C47C2211yescharacteristic
12C23×C8×C47C2211yescharacteristic
13C2×C22⋊Q8×C47—24no—
14C2×C22⋊Q8×C47—22no—
15C2×C22⋊Q8×C47—24no—
16C2×C22⋊Q8×C47C2214yes—
17C22×C4⋊C4×C47—21no—
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C22⋊C4×C47—21no—
22C22×C22⋊C4×C47—21no—
23C2×#107×C47—24no—
24C2×#107×C47C2214yescomplemented
25C2×#103×C47—24no—
26C2×#103×C47—24no—
27C2×#103×C47C2214yescomplemented
28C2×#103×C47C2214yescomplemented
29C2×C22⋊C8×C47—24no—
30C2×C22⋊C8×C47C2214yes—
31C47×#380—22no—
32C47×#380C2214yes—
33C2×#95×C47—21no—
34C47×#340C2214yescomplemented
35C25×C47D411yescharacteristic
36C22×Q8×C47—22no—
37C22×Q8×C47—21no—
38C22×Q8×C47—22no—
39C22×Q8×C47—22no—
40C22×Q8×C47—22no—
41C22×Q8×C47—22no—
42C22×Q8×C47D414yes—
43C22×Q8×C47C2312yes—
44C23×C4×C47—21no—
45C23×C4×C47—21no—
46C23×C4×C47—22no—
47C23×C4×C47—22no—
48C23×C4×C47—22no—
49C23×C4×C47—22no—
50C23×C4×C47—22no—
51C23×C4×C47—22no—
52C23×C4×C47—21no—
53C23×C4×C47—21no—
54C23×C4×C47D412yes—
55C23×C4×C47D411yescharacteristic
56C23×C4×C47C2312yes—
57C23×C4×C47C2311yescharacteristic
58C22×C8×C47—22no—
59C22×C8×C47—22no—
60C22×C8×C47—22no—
61C22×C8×C47—22no—
62C22×C8×C47—22no—
63C22×C8×C47D414yes—
64C22×C8×C47C2312yes—
65C22×C8×C47C2312yes—
66C22⋊Q8×C47—216no—
67C22⋊Q8×C47—28no—
68C22⋊Q8×C47—28no—
69C2×C4⋊C4×C47—28no—
70C2×C4⋊C4×C47—24no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—22no—
73C2×C4⋊C4×C47—22no—
74C2×C4⋊C4×C47—22no—
75C2×C4⋊C4×C47—22no—
76C2×C4⋊C4×C47—22no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47D414yes—
80C2×C4⋊C4×C47C2312yes—
81C2×C4⋊C4×C47C2312yes—
82C2×C4⋊C4×C47C2312yes—
83C2×C22⋊C4×C47—28no—
84C2×C22⋊C4×C47—24no—
85C2×C22⋊C4×C47—24no—
86C2×C22⋊C4×C47—44no—
87#107×C47—28no—
88#103×C47—28no—
89#103×C47—28no—
90C22⋊C8×C47—28no—
91#95×C47—24no—
92C24×C47—22no—
93C24×C47—22no—
94C24×C47—22no—
95C24×C47—22no—
96C24×C47—22no—
97C24×C47—22no—
98C24×C47Q1614yes—
99C24×C47C2×D412yes—
100C24×C47C2×D411yescharacteristic
101C2×Q8×C47—24no—
102C2×Q8×C47—22no—
103C2×Q8×C47—28no—
104C2×Q8×C47—28no—
105C2×Q8×C47—22no—
106C2×Q8×C47—22no—
107C2×Q8×C47—22no—
108C2×Q8×C47—22no—
109C2×Q8×C47—42no—
110C2×Q8×C47—44no—
111C2×Q8×C47—42no—
112C2×Q8×C47—44no—
113C2×Q8×C47C2×D414yes—
114C22×C4×C47—24no—
115C22×C4×C47—24no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—24no—
122C22×C4×C47—24no—
123C22×C4×C47—24no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—42no—
133C22×C4×C47—42no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—44no—
137C22×C4×C47—44no—
138C22×C4×C47—44no—
139C22×C4×C47—44no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47C2×D412yes—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47#4112yes—
152C22×C4×C47#4112yes—
153C22×C4×C47#4112yes—
154C22×C4×C47C2411yescharacteristic
155C2×C8×C47—28no—
156C2×C8×C47—22no—
157C2×C8×C47—22no—
158C2×C8×C47—22no—
159C2×C8×C47—22no—
160C2×C8×C47—22no—
161C2×C8×C47—44no—
162C2×C8×C47C2×D414yes—
163C4⋊C4×C47—216no—
164C4⋊C4×C47—24no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—42no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47C2×D414yes—
173C22⋊C4×C47—216no—
174C22⋊C4×C47—48no—
175C23×C47—22no—
176C23×C47—22no—
177C23×C47—22no—
178C23×C47—22no—
179C23×C47—22no—
180C23×C47—22no—
181C23×C47—28no—
182C23×C47—28no—
183C23×C47—28no—
184C23×C47—44no—
185C23×C47—44no—
186C23×C47—44no—
187C23×C47—44no—
188C23×C47#12012yes—
189C23×C47#12112yes—
190C23×C47#12312yes—
191C23×C47C2×Q1614yes—
192C23×C47C2×Q1612yes—
193C23×C47#13512yes—
194C23×C47AGL(1,ℤ/8)12yes—
195C23×C47#13712yes—
196C23×C47C22×D411yescharacteristic
197Q8×C47—24no—
198Q8×C47—24no—
199Q8×C47—42no—
200Q8×C47—42no—
201Q8×C47—48no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—44no—
212C2×C4×C47—48no—
213C2×C4×C47—48no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—48no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—84no—
226C2×C4×C47—84no—
227C2×C4×C47#12012yes—
228C2×C4×C47#12114yes—
229C2×C4×C47#12114yes—
230C2×C4×C47#12112yes—
231C2×C4×C47#12314yes—
232C2×C4×C47#12312yes—
233C2×C4×C47#12414yes—
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C8×C47—24no—
241C8×C47—42no—
242C2×#2036C4711yesmaximal, characteristic, direct product factor, Sylow
243C22×C47—24no—
244C22×C47—24no—
245C22×C47—24no—
246C22×C47—42no—
247C22×C47—42no—
248C22×C47—42no—
249C22×C47—42no—
250C22×C47—416no—
251C22×C47#39414yes—
252C22×C47#44914yes—
253C22×C47#45114yes—
254C22×C47#46714yes—
255C22×C47#46814yes—
256C22×C47#48414yes—
257C22×C47#48514yes—
258C22×C47C2×#12011yescharacteristic
259C22×C47C2×#12111yescharacteristic
260C22×C47C2×#12311yescharacteristic
261C22×C47C22×Q1611yescharacteristic
262C22×C47C2×#13511yescharacteristic
263C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C47C2×#13711yescharacteristic
265C4×C47—42no—
266C4×C47—44no—
267C4×C47—44no—
268C4×C47—82no—
269C4×C47—82no—
270C4×C47#39414yes—
271C4×C47C2×#12111yescharacteristic
272C4×C47C2×#12111yescharacteristic
273C4×C47C2×#12311yescharacteristic
274C4×C47C2×#12411yescharacteristic
275C22×C22⋊Q8C2×C4711yescharacteristic
276C22×#107C2×C4711yescharacteristic, complemented
277C22×#103C2×C4711yescharacteristic, complemented
278C22×#103C2×C4711yescharacteristic, complemented
279C22×C22⋊C8C2×C4711yescharacteristic
280C2×#380C2×C4711yescharacteristic
281#2036C2×C4718yesdirect product factor
282C2×#340C2×C4711yescharacteristic, complemented
283C2×C47—44no—
284C2×C47#203618yesdirect product factor
285C2×C47C2×#39411yescharacteristic
286C2×C47C2×#45111yescharacteristic
287C2×C47C2×#44911yescharacteristic
288C2×C47C2×#46711yescharacteristic
289C2×C47C2×#46811yescharacteristic
290C2×C47C2×#48511yescharacteristic
291C2×C47C2×#48411yescharacteristic
292C23×Q8C22×C4711yescharacteristic
293C24×C4C22×C4711yescharacteristic
294C23×C8C22×C4711yescharacteristic
295C23×C8C22×C4711yescharacteristic
296C2×C22⋊Q8—24no—
297C2×C22⋊Q8—22no—
298C2×C22⋊Q8—24no—
299C2×C22⋊Q8C22×C4714yes—
300C22×C4⋊C4—21no—
301C22×C4⋊C4C22×C4711yescharacteristic
302C22×C4⋊C4C22×C4711yescharacteristic
303C22×C4⋊C4C22×C4711yescharacteristic
304C22×C22⋊C4—21no—
305C22×C22⋊C4—21no—
306C2×#107—24no—
307C2×#107C22×C4714yescomplemented
308C2×#103—24no—
309C2×#103—24no—
310C2×#103C22×C4714yescomplemented
311C2×#103C22×C4714yescomplemented
312C2×C22⋊C8—24no—
313C2×C22⋊C8C22×C4714yes—
314#380—22no—
315#380C22×C4714yes—
316C2×#95—21no—
317#340C22×C4714yescomplemented
318C47C2×#203611yescharacteristic, direct product factor, Sylow
319C25D4×C4711yescharacteristic
320C22×Q8—22no—
321C22×Q8—21no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8D4×C4714yes—
327C22×Q8C23×C4712yes—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—21no—
337C23×C4—21no—
338C23×C4D4×C4711yescharacteristic
339C23×C4D4×C4712yes—
340C23×C4C23×C4712yes—
341C23×C4C23×C4711yescharacteristic
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8D4×C4714yes—
348C22×C8C23×C4712yes—
349C22×C8C23×C4712yes—
350C22⋊Q8—216no—
351C22⋊Q8—28no—
352C22⋊Q8—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C4714yes—
364C2×C4⋊C4C23×C4712yes—
365C2×C4⋊C4C23×C4712yes—
366C2×C4⋊C4C23×C4712yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—44no—
371#107—28no—
372#103—28no—
373#103—28no—
374C22⋊C8—28no—
375#95—24no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24Q16×C4714yes—
383C24C2×D4×C4712yes—
384C24C2×D4×C4711yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—28no—
388C2×Q8—28no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—42no—
394C2×Q8—44no—
395C2×Q8—42no—
396C2×Q8—44no—
397C2×Q8C2×D4×C4714yes—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C4712yes—
431C22×C4C2×D4×C4711yescharacteristic
432C22×C4C2×D4×C4712yes—
433C22×C4C2×D4×C4712yes—
434C22×C4C2×D4×C4712yes—
435C22×C4#41×C4712yes—
436C22×C4#41×C4712yes—
437C22×C4#41×C4712yes—
438C22×C4C24×C4711yescharacteristic
439C2×C8—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—44no—
446C2×C8C2×D4×C4714yes—
447C4⋊C4—216no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4C2×D4×C4714yes—
457C22⋊C4—216no—
458C22⋊C4—48no—
459C23—28no—
460C23—28no—
461C23—28no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#120×C4712yes—
473C23#121×C4712yes—
474C23#123×C4712yes—
475C23C2×Q16×C4714yes—
476C23C2×Q16×C4712yes—
477C23#135×C4712yes—
478C23AGL(1,ℤ/8)×C4712yes—
479C23#137×C4712yes—
480C23C22×D4×C4711yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—48no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4#120×C4712yes—
512C2×C4#121×C4714yes—
513C2×C4#121×C4714yes—
514C2×C4#121×C4712yes—
515C2×C4#123×C4714yes—
516C2×C4#123×C4712yes—
517C2×C4#124×C4714yes—
518C2×C4C22×D4×C4711yescharacteristic
519C2×C4C22×D4×C4711yescharacteristic
520C2×C4C22×D4×C4711yescharacteristic
521C2×C4C2×#41×C4711yescharacteristic
522C2×C4C2×#41×C4711yescharacteristic
523C2×C4C2×#41×C4711yescharacteristic
524C8—24no—
525C8—42no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—416no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22C47×#39414yes—
535C22C47×#44914yes—
536C22C47×#45114yes—
537C22C47×#46714yes—
538C22C47×#46814yes—
539C22C47×#48414yes—
540C22C47×#48514yes—
541C22C2×#120×C4711yescharacteristic
542C22C2×#121×C4711yescharacteristic
543C22C2×#123×C4711yescharacteristic
544C22C22×Q16×C4711yescharacteristic
545C22C2×#135×C4711yescharacteristic
546C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
547C22C2×#137×C4711yescharacteristic
548C4—42no—
549C4—44no—
550C4—44no—
551C4—82no—
552C4—82no—
553C4C47×#39414yes—
554C4C2×#121×C4711yescharacteristic
555C4C2×#121×C4711yescharacteristic
556C4C2×#123×C4711yescharacteristic
557C4C2×#124×C4711yescharacteristic
558C2—44no—
559C2C47×#203618yesdirect product factor
560C2C2×C47×#39411yescharacteristic
561C2C2×C47×#45111yescharacteristic
562C2C2×C47×#44911yescharacteristic
563C2C2×C47×#46711yescharacteristic
564C2C2×C47×#46811yescharacteristic
565C2C2×C47×#48511yescharacteristic
566C2C2×C47×#48411yescharacteristic
subgroupG/H
center, socleC24×C47C2×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC25×C47D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#107×C47C2semidirect
3. C22×#103×C47C2semidirect
4. C22×#103×C47C2semidirect
7. C47×#2036C2direct (N × H)
8. C2×C47×#340C2semidirect
24. C2×#107×C47C22semidirect
27. C2×#103×C47C22semidirect
28. C2×#103×C47C22semidirect
34. C47×#340C22semidirect
242. C2×#2036C47direct (N × H)
276. C22×#107C2×C47semidirect
277. C22×#103C2×C47semidirect
278. C22×#103C2×C47semidirect
281. #2036C2×C47direct (N × H)
282. C2×#340C2×C47semidirect
284. C2×C47#2036direct (N × H)
307. C2×#107C22×C47semidirect
310. C2×#103C22×C47semidirect
311. C2×#103C22×C47semidirect
317. #340C22×C47semidirect
318. C47C2×#2036direct (N × H)
559. C2C47×#2036direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C472
C22×#107×C472
C22×#103×C472
C22×C22⋊C8×C472
C2×C47×#3802
C47×#20362
C2×C47×#3402
C2×#203647