Finite Group Databasebeta

← C4×#15689486 #26224347

Subgroups — C4×#15689486 #26224347

Order 12032.

970 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689486C211yesmaximal, characteristic
2C4×#13094020C211yesmaximal, characteristic
3C4×#13094015C211yesmaximal, characteristic, complemented
4#20244355C211yesmaximal, characteristic, complemented
5#20244210C211yesmaximal, characteristic
6#20244087C211yesmaximal, characteristic, complemented
7#20244086C211yesmaximal, characteristic, complemented
8#20244083C211yesmaximal, characteristic, complemented
9#20244082C211yesmaximal, characteristic, complemented
10#20243520C211yesmaximal, characteristic, complemented
11C4×#13093944C211yesmaximal, characteristic, complemented
12C4×#13093946C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14C4×#13093934C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C2×#13094020C2211yescharacteristic
17C2×#13094015C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4×C22⋊D47—21no—
20C2×C4×C22⋊D47—21no—
21#15689486C418yesdirect product factor
22C2×#13093946C2211yescharacteristic
23C2×#13093946C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093934C2211yescharacteristic
29C2×#13093934C2211yescharacteristic
30C2×#13093934C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15689026C2211yescharacteristic
34#15689024C2211yescharacteristic
35#15689023—21no—
36#15689023—21no—
37#15689022C2211yescharacteristic
38#15689019C2211yescharacteristic
39#15689010—21no—
40#15689006—21no—
41#15688992C2211yescharacteristic
42#15688988C2211yescharacteristic
43C4×Dic47⋊C4—21no—
44C4×C4⋊Dic47—21no—
45C4×C4⋊Dic47C2211yescharacteristic
46C42×Dic47C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C22⋊D47—21no—
62C22×C22⋊D47—21no—
63C22×C4×D47—21no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094020—22no—
67#13094020C2×C414yes—
68#13094015—22no—
69#13094015C2×C414yescomplemented
70C4×D188—22no—
71C4×D188—22no—
72C4×C22⋊D47—44no—
73C4×C22⋊D47—44no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×C22⋊Dic47—21no—
84C2×C22⋊Dic47—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47D411yescharacteristic
90C2×C4×Dic47D411yescharacteristic
91C2×C4×Dic47D411yescharacteristic
92C2×C4×Dic47D411yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94C2×C4×Dic47C2311yescharacteristic
95#13093946—22no—
96#13093946C2×C414yescomplemented
97#13093945—22no—
98#13093945C2×C414yescomplemented
99#13093944—22no—
100#13093944C2×C414yescomplemented
101#13093934—22no—
102#13093934—22no—
103#13093934—22no—
104#13093934C2×C414yescomplemented
105C4×C47⋊C8—22no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C22×D4×C47C2311yescharacteristic
112C23×C4×C47—21no—
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C4×D4×C47—22no—
116C4×D4×C47—22no—
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C22⋊C4×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123#102×C47—22no—
124#102×C47C2×C414yescomplemented
125C4×C8×C47—22no—
126#95×C47—21no—
127C24×C47—21no—
128C23×D47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47C22×C412yes—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2411yescharacteristic
144C2×C22⋊D47—24no—
145C2×C22⋊D47—24no—
146C2×C22⋊D47—42no—
147C2×C22⋊D47—42no—
148C2×C22⋊D47—42no—
149C2×C22⋊D47—42no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47C2×D411yescharacteristic
154C22×Dic47C2×D411yescharacteristic
155C22×Dic47C2×D411yescharacteristic
156C22×Dic47C2×D411yescharacteristic
157C2×D188—21no—
158C2×D188—21no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188C22×C412yes—
163C2×C4×D47—42no—
164C2×C4×D47—42no—
165C2×C4×D47—42no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47C22×C412yes—
171C2×C8×C47#4112yes—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47C22×C412yes—
178C22⋊C4×C47—42no—
179C42×C47—42no—
180C42×C47#4112yes—
181C42×C47#4112yes—
182C22⋊Dic47—42no—
183C22⋊Dic47—42no—
184(C2×D47)⋊C4—42no—
185(C2×D47)⋊C4—42no—
186(C2×D47)⋊C4—42no—
187C4⋊Dic47—21no—
188C4⋊Dic47—24no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—42no—
194C4⋊Dic47C22×C412yes—
195Dic47⋊C4—24no—
196Dic47⋊C4—42no—
197Dic47⋊C4—42no—
198Dic47⋊C4—42no—
199C4×Dic47—22no—
200C4×Dic47—22no—
201C4×Dic47—21no—
202C4×Dic47—21no—
203C4×Dic47—41no—
204C4×Dic47—41no—
205C4×Dic47—42no—
206C4×Dic47C22×C412yes—
207C4×Dic47#4112yes—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8C22×C412yes—
213C2×C47⋊C8#4112yes—
214C23×C47—22no—
215C23×C47—41no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—41no—
221C23×C47C22×D411yescharacteristic
222C22×D47—22no—
223C22×D47—41no—
224C22×D47—41no—
225C22×D47—41no—
226C22×D47—41no—
227C22×D47—41no—
228C22×D47—41no—
229D4×C47—22no—
230D4×C47—22no—
231D4×C47—41no—
232D4×C47—41no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—84no—
245C2×C4×C47#12412yes—
246C2×C4×C47#12412yes—
247C2×C4×C47AGL(1,ℤ/8)12yes—
248C2×C4×C47AGL(1,ℤ/8)12yes—
249C2×C4×C47C23×C411yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C22⋊D47—48no—
256C22⋊D47—48no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—22no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47C4×D412yes—
277C2×Dic47C4×D412yes—
278D188—22no—
279D188—22no—
280D188—41no—
281D188—41no—
282C4×D47—84no—
283C8×C47—22no—
284C8×C47—22no—
285C47⋊C8—22no—
286C47⋊C8—22no—
287C4×#490—471nomaximal, Sylow
288C22×C47—42no—
289C22×C47—42no—
290C22×C47—42no—
291C22×C47—81no—
292C22×C47—81no—
293C22×C47—81no—
294C22×C47—81no—
295C22×C47C2×C4×D411yescharacteristic
296C22×C47C2×#12411yescharacteristic
297C22×C47#53211yescharacteristic
298C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C47#57511yescharacteristic
301C22×C47#57511yescharacteristic
302C2×D47—42no—
303C2×D47—42no—
304C2×D47—42no—
305C2×D47—81no—
306C2×D47—81no—
307C2×D47—81no—
308C2×D47—81no—
309C4×C47—22no—
310C4×C47—42no—
311C4×C47—81no—
312C4×C47—81no—
313C4×C47#49014yescomplemented
314C4×C47C4×#4111yescharacteristic
315C4×C47C4×#4111yescharacteristic
316C4×C47#52911yescharacteristic
317C4×C47#52911yescharacteristic
318Dic47—22no—
319Dic47—22no—
320Dic47—41no—
321Dic47—41no—
322Dic47—42no—
323Dic47—81no—
324Dic47—81no—
325C2×#490—471no—
326C4×#127—471no—
327C4×#125—471no—
328#1992—471no—
329#1961—471no—
330#1936—471no—
331#1936—471no—
332#1936—471no—
333#1936—471no—
334#1836—471no—
335C4×#102—471no—
336C4×#102—471no—
337C4×#102—471no—
338C4×#102D4711yescharacteristic, complemented
339C4×#97—471no—
340C2×C47—82no—
341C2×C47C4×#12411yescharacteristic
342C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
343C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
344C2×C47C2×#49011yescharacteristic
345C2×C47#313511yescharacteristic
346C2×C47#317111yescharacteristic
347C2×C47#317111yescharacteristic
348D47—82no—
349C2×#127—471no—
350C2×#125—471no—
351C2×C4×D4—471no—
352C2×C4×D4—941no—
353C2×C4×D4—941no—
354C2×C4×D4C2×D4711yescharacteristic
355#490—478no—
356C2×#102—471no—
357C2×#102—471no—
358C2×#102—471no—
359C2×#102—471no—
360C2×#102—471no—
361C2×#102—471no—
362C2×#102C2×D4711yescharacteristic
363C2×#102C2×D4711yescharacteristic
364C2×#97—471no—
365C2×#97—471no—
366C2×#97—471no—
367C2×#97—471no—
368C2×C4×C8—471no—
369C2×C4×C8C2×D4711yescharacteristic
370#390—471no—
371#390—471no—
372#390—941no—
373#390—941no—
374#389—471no—
375#389—471no—
376#387—941no—
377#387—941no—
378#384—471no—
379#382—471no—
380C4×C4⋊C4—471no—
381C4×C4⋊C4—941no—
382C4×C4⋊C4—941no—
383C4×C4⋊C4C2×D4711yescharacteristic
384C43—471no—
385#340—471no—
386#340—471no—
387#340—471no—
388#340—471no—
389#340—471no—
390#340—471no—
391#340C2×D4711yescharacteristic
392#340C2×D4711yescharacteristic
393C47C4×#49011yescharacteristic, complemented, Sylow
394C22×D4—471no—
395C22×D4—941no—
396C22×D4—941no—
397C22×D4C22×D4711yescharacteristic
398C23×C4—21no—
399C23×C4—941no—
400C22×C8—471no—
401C22×C8—471no—
402C22×C8C22×D4711yescharacteristic
403C22×C8C22×D4711yescharacteristic
404#127—474no—
405#127—942no—
406#125—474no—
407#125—942no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—942no—
411C4×D4—942no—
412C4×D4—1884no—
413C4×D4—1884no—
414C2×C4⋊C4—471no—
415C2×C4⋊C4—471no—
416C2×C4⋊C4—471no—
417C2×C4⋊C4—941no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—941no—
423C2×C4⋊C4C22×D4711yescharacteristic
424C2×C4⋊C4C22×D4711yescharacteristic
425C2×C4⋊C4C22×D4711yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—941no—
428C2×C22⋊C4—941no—
429C2×C22⋊C4—941no—
430C2×C22⋊C4—941no—
431C2×C22⋊C4—941no—
432C2×C42—21no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—471no—
438C2×C42—471no—
439C2×C42—941no—
440C2×C42C22×D4711yescharacteristic
441#102—22no—
442#102—474no—
443#102—474no—
444#102—474no—
445#102—942no—
446#102—942no—
447#102—942no—
448#102C4×D4714yescomplemented
449#97—474no—
450#97—942no—
451#97—942no—
452#97—942no—
453C4×C8—22no—
454C4×C8—942no—
455#95—21no—
456#95—941no—
457#95—941no—
458#95—941no—
459#95—941no—
460#95—941no—
461C24—21no—
462C24—941no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—472no—
469C2×D4—944no—
470C2×D4—944no—
471C2×D4—941no—
472C2×D4—941no—
473C2×D4—941no—
474C2×D4—941no—
475C2×D4—941no—
476C2×D4—1882no—
477C2×D4—1882no—
478C2×D4—1882no—
479C2×D4—1882no—
480C2×D4C2×C4×D4712yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—471no—
488C22×C4—471no—
489C22×C4—471no—
490C22×C4—471no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—1882no—
495C22×C4—1882no—
496C22×C4—1882no—
497C22×C4D4×D4711yescharacteristic
498C22×C4D4×D4711yescharacteristic
499C22×C4C23×D4711yescharacteristic
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—472no—
505C2×C8—472no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8C2×C4×D4712yes—
511C2×C8#1062535012yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—472no—
518C4⋊C4—944no—
519C4⋊C4—944no—
520C4⋊C4—941no—
521C4⋊C4—941no—
522C4⋊C4—941no—
523C4⋊C4—941no—
524C4⋊C4—941no—
525C4⋊C4—1882no—
526C4⋊C4—1882no—
527C4⋊C4—1882no—
528C4⋊C4—1882no—
529C4⋊C4C2×C4×D4712yes—
530C22⋊C4—42no—
531C22⋊C4—1882no—
532C22⋊C4—1882no—
533C22⋊C4—1882no—
534C22⋊C4—1882no—
535C22⋊C4—1882no—
536C42—42no—
537C42—472no—
538C42—472no—
539C42—942no—
540C42—942no—
541C42—941no—
542C42—941no—
543C42—1881no—
544C42—1881no—
545C42—1882no—
546C42#1062535012yes—
547C42#1062535212yes—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—942no—
556C23—1881no—
557C23—1881no—
558C23—1881no—
559C23—1881no—
560C23—1881no—
561C23—1881no—
562C23C2×D4×D4711yescharacteristic
563D4—22no—
564D4—22no—
565D4—41no—
566D4—41no—
567D4—942no—
568D4—942no—
569D4—1888no—
570D4—1888no—
571D4—1881no—
572D4—1881no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—84no—
585C2×C4—472no—
586C2×C4—472no—
587C2×C4—941no—
588C2×C4—941no—
589C2×C4—941no—
590C2×C4—941no—
591C2×C4—942no—
592C2×C4—941no—
593C2×C4—941no—
594C2×C4—941no—
595C2×C4—941no—
596C2×C4—941no—
597C2×C4—941no—
598C2×C4—3764no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4—1881no—
607C2×C4#1309401012yes—
608C2×C4#1309401012yes—
609C2×C4#1309404812yes—
610C2×C4#1309405112yes—
611C2×C4C22×C4×D4711yescharacteristic
612C2×C4#41×D4711yescharacteristic
613C2×C4#41×D4711yescharacteristic
614C2×C4C2×#1062535211yescharacteristic
615C2×C4C2×#1062535011yescharacteristic
616C2×C4C2×#1062535011yescharacteristic
617C8—22no—
618C8—22no—
619C8—942no—
620C8—942no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—3761no—
629C22—3761no—
630C22—3761no—
631C22—3761no—
632C22—1882no—
633C22—1882no—
634C22—1882no—
635C22C4×D4×D4711yescharacteristic
636C22C2×#1309401011yescharacteristic
637C22#1568967011yescharacteristic
638C22C2×#1309404811yescharacteristic
639C22C2×#1309405111yescharacteristic
640C22#1568992011yescharacteristic
641C22#1568992011yescharacteristic
642C4—22no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—942no—
647C4—942no—
648C4—3761no—
649C4—3761no—
650C4—1881no—
651C4—1881no—
652C4—1882no—
653C4#1568948614yesdirect product factor
654C4C4×#1062535211yescharacteristic
655C4C4×#1062535011yescharacteristic
656C4#1568965111yescharacteristic
657C4#1568965311yescharacteristic
658C2—82no—
659C2—3762no—
660C2C4×#1309401011yescharacteristic
661C2C4×#1309404811yescharacteristic
662C2C4×#1309405111yescharacteristic
663C2C2×#1568948611yescharacteristic
664C2#2025373111yescharacteristic
665C2#2025397911yescharacteristic
666C2#2025398111yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#102×C47C2
socleC23×C47C22×D4
prime radicalC2×#13094020C22
cosocleC22×C4×C47C24
hypercenterC4×#102D47
hypocenterC47C4×#490
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C4×#13094015C2semidirect
4. #20244355C2semidirect
6. #20244087C2semidirect
7. #20244086C2semidirect
8. #20244083C2semidirect
9. #20244082C2semidirect
10. #20243520C2semidirect
11. C4×#13093944C2semidirect
12. C4×#13093946C2semidirect
13. C4×#13093945C2semidirect
14. C4×#13093934C2semidirect
15. C4×#102×C47C2semidirect
21. #15689486C4direct (N × H)
69. #13094015C2×C4semidirect
96. #13093946C2×C4semidirect
98. #13093945C2×C4semidirect
100. #13093944C2×C4semidirect
104. #13093934C2×C4semidirect
124. #102×C47C2×C4semidirect
313. C4×C47#490semidirect
338. C4×#102D47semidirect
393. C47C4×#490semidirect
448. #102C4×D47semidirect
653. C4#15689486direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156894862
C4×#130940202
C4×#130940152
#202443552
#202442102
#202440872
#202440862
#202440832
#202440822
#202435202
C4×#130939442
C4×#130939462
C4×#130939452
C4×#130939342
C4×#102×C472
C4×#49047