Finite Group Databasebeta

← C4×#15689445 #26223427

Subgroups — C4×#15689445 #26223427

Order 12032.

972 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689445C211yesmaximal, characteristic
2C4×#13093995C211yesmaximal, characteristic
3C4×#13093982C211yesmaximal, characteristic, complemented
4#20244018C211yesmaximal, characteristic, complemented
5#20244010C211yesmaximal, characteristic, complemented
6#20243979C211yesmaximal, characteristic, complemented
7#20243971C211yesmaximal, characteristic, complemented
8#20243707C211yesmaximal, characteristic
9#20243590C211yesmaximal, characteristic, complemented
10#20243481C211yesmaximal, characteristic, complemented
11C4×#13093958C211yesmaximal, characteristic, complemented
12C4×#13093955C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C2×#13093995C2211yescharacteristic
17C2×C4×C22⋊D47—21no—
18C2×#13093982C2211yescharacteristic
19C2×#13093982C2211yescharacteristic
20C2×C42×D47C2211yescharacteristic
21#15689445C418yesdirect product factor
22C2×#13093958C2211yescharacteristic
23C2×#13093958C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×(C2×D47)⋊C8C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689026C2211yescharacteristic
32#15689019C2211yescharacteristic
33#15689011—21no—
34#15688999—21no—
35#15688980C2211yescharacteristic
36C4⋊C4×Dic47C2211yescharacteristic
37C4⋊C4×Dic47C2211yescharacteristic
38C4×C4⋊Dic47C2211yescharacteristic
39C4×C4⋊Dic47C2211yescharacteristic
40C4×(C2×D47)⋊C4—21no—
41C4×C22⋊Dic47—21no—
42#15688970—21no—
43#15688968—21no—
44C42×Dic47—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#102×C47C2211yescharacteristic
56C2×C4×C8×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×C22⋊D47—21no—
61C22×C4×D47D411yescharacteristic
62C22×C4×D47D411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093995—22no—
67#13093995C2×C414yes—
68C4×C22⋊D47—44no—
69#13093982—22no—
70#13093982—22no—
71#13093982—22no—
72#13093982C2×C414yescomplemented
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47D411yescharacteristic
91C2×C4×Dic47D411yescharacteristic
92C2×C4×Dic47C2311yescharacteristic
93C42×D47—22no—
94C42×D47—22no—
95#13093958—22no—
96#13093958C2×C414yescomplemented
97#13093955—22no—
98#13093955C2×C414yescomplemented
99#13093945—22no—
100#13093945C2×C414yescomplemented
101(C2×D47)⋊C8—22no—
102(C2×D47)⋊C8C2×C414yescomplemented
103C4×C47⋊C8—22no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C22×D4×C47C2311yescharacteristic
111C23×C4×C47—21no—
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C4×D4×C47—22no—
115C4×D4×C47—22no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122#102×C47—22no—
123#102×C47C2×C414yescomplemented
124C4×C8×C47—22no—
125#95×C47—21no—
126C24×C47—21no—
127C23×D47C2×D411yescharacteristic
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47C22×C412yes—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2411yescharacteristic
143C2×C22⋊D47—24no—
144C2×C22⋊D47—42no—
145C2×C22⋊D47—42no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47C2×D411yescharacteristic
151C22×Dic47C2×D411yescharacteristic
152C22×Dic47C2×D411yescharacteristic
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—41no—
163C2×C4×D47C22×C412yes—
164C2×C4×D47#4112yes—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47C22×C412yes—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47C22×C412yes—
176C4⋊C4×C47#4112yes—
177C22⋊C4×C47—42no—
178C42×C47—42no—
179C42×C47#4112yes—
180C42×C47#4112yes—
181C22⋊Dic47—24no—
182C22⋊Dic47—42no—
183C22⋊Dic47—42no—
184(C2×D47)⋊C4—24no—
185(C2×D47)⋊C4—24no—
186(C2×D47)⋊C4—42no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47C22×C412yes—
193C4⋊Dic47C22×C412yes—
194C4⋊Dic47#4112yes—
195Dic47⋊C4—42no—
196C4×Dic47—24no—
197C4×Dic47—22no—
198C4×Dic47—22no—
199C4×Dic47—21no—
200C4×Dic47—21no—
201C4×Dic47—24no—
202C4×Dic47—42no—
203C4×Dic47—42no—
204C4×Dic47—42no—
205C4×Dic47—42no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8C22×C412yes—
212C23×C47—22no—
213C23×C47—41no—
214C23×C47—41no—
215C23×C47—41no—
216C23×C47—41no—
217C23×C47—41no—
218C23×C47—41no—
219C23×C47C22×D411yescharacteristic
220C22×D47—21no—
221C22×D47—21no—
222C22×D47—21no—
223C22×D47—21no—
224C22×D47—21no—
225C22×D47—21no—
226C22×D47C4×D412yes—
227D4×C47—22no—
228D4×C47—22no—
229D4×C47—41no—
230D4×C47—41no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—41no—
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—84no—
243C2×C4×C47#12312yes—
244C2×C4×C47#12312yes—
245C2×C4×C47#13512yes—
246C2×C4×C47AGL(1,ℤ/8)12yes—
247C2×C4×C47C23×C411yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C22⋊D47—48no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—21no—
261C2×Dic47—22no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47C4×D412yes—
274C2×Dic47#13512yes—
275C4×D47—22no—
276C4×D47—22no—
277C4×D47—22no—
278C4×D47—22no—
279C4×D47—44no—
280C4×D47—44no—
281C8×C47—22no—
282C8×C47—41no—
283C47⋊C8—22no—
284C47⋊C8—41no—
285C4×#482—471nomaximal, Sylow
286C22×C47—42no—
287C22×C47—42no—
288C22×C47—42no—
289C22×C47—81no—
290C22×C47—81no—
291C22×C47—81no—
292C22×C47—81no—
293C22×C47C2×C4×D411yescharacteristic
294C22×C47C2×#12311yescharacteristic
295C22×C47#52511yescharacteristic
296C22×C47C2×#13511yescharacteristic
297C22×C47C2×#13511yescharacteristic
298C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C47#57511yescharacteristic
300C2×D47—22no—
301C2×D47—22no—
302C2×D47—22no—
303C2×D47—41no—
304C2×D47—41no—
305C2×D47—41no—
306C2×D47—41no—
307C4×C47—22no—
308C4×C47—42no—
309C4×C47—42no—
310C4×C47—81no—
311C4×C47#48214yescomplemented
312C4×C47C4×#4111yescharacteristic
313C4×C47C4×#4111yescharacteristic
314C4×C47#52911yescharacteristic
315C4×C47#52911yescharacteristic
316Dic47—22no—
317Dic47—22no—
318Dic47—41no—
319Dic47—42no—
320Dic47—42no—
321Dic47—42no—
322Dic47—81no—
323C2×#482—471no—
324C4×#121—471no—
325C4×#117—471no—
326#1926—471no—
327#1925—471no—
328#1921—471no—
329#1920—471no—
330#1875—471no—
331#1854—471no—
332#1825—471no—
333C4×#107—471no—
334C4×#106—471no—
335C4×#102—471no—
336C4×#102D4711yescharacteristic, complemented
337C4×C22⋊C8—471no—
338C2×C47—82no—
339C2×C47C4×#12311yescharacteristic
340C2×C47C4×#13511yescharacteristic
341C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
342C2×C47C2×#48211yescharacteristic
343C2×C47#309111yescharacteristic
344C2×C47#310211yescharacteristic
345C2×C47#310611yescharacteristic
346D47—42no—
347C2×#121—471no—
348C2×C4×D4—941no—
349C2×C4×D4C2×D4711yescharacteristic
350C2×#117—471no—
351C2×#117—471no—
352C22×C42—471no—
353#482—478no—
354C2×#107—471no—
355C2×#107—471no—
356C2×#106—471no—
357C2×#106—471no—
358C2×#102—471no—
359C2×#102—471no—
360C2×#102C2×D4711yescharacteristic
361C2×#102C2×D4711yescharacteristic
362C2×C22⋊C8—471no—
363C2×C22⋊C8—471no—
364C2×C4×C8—471no—
365C2×C4×C8C2×D4711yescharacteristic
366#390—471no—
367#389—471no—
368#388—941no—
369#386—941no—
370#380—471no—
371C4×C4⋊C4—471no—
372C4×C4⋊C4—471no—
373C4×C4⋊C4—471no—
374C4×C4⋊C4—471no—
375C4×C4⋊C4C2×D4711yescharacteristic
376C4×C22⋊C4—941no—
377C4×C22⋊C4—941no—
378C4×C22⋊C4—941no—
379#376—941no—
380C43—941no—
381#340—471no—
382#340—471no—
383#340—471no—
384#340—471no—
385#340—471no—
386#340—471no—
387#340C2×D4711yescharacteristic
388#340C2×D4711yescharacteristic
389#336—471no—
390#336—471no—
391C47C4×#48211yescharacteristic, complemented, Sylow
392C22×D4—941no—
393C22×D4C22×D4711yescharacteristic
394C23×C4—21no—
395C23×C4—471no—
396C23×C4—471no—
397C23×C4—471no—
398C22×C8—471no—
399C22×C8—471no—
400C22×C8C22×D4711yescharacteristic
401C22×C8C22×D4711yescharacteristic
402#121—474no—
403#121—942no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—1884no—
407#117—474no—
408#117—942no—
409#117—942no—
410#117—942no—
411C2×C4⋊C4—471no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C4⋊C4—471no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4C22×D4711yescharacteristic
417C2×C4⋊C4C22×D4711yescharacteristic
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—941no—
421C2×C22⋊C4—941no—
422C2×C22⋊C4—941no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C22⋊C4—941no—
426C2×C42—21no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—471no—
430C2×C42—941no—
431C2×C42—941no—
432C2×C42—942no—
433C2×C42—942no—
434C2×C42—941no—
435C2×C42—941no—
436C2×C42—941no—
437C2×C42—941no—
438C2×C42C22×D4711yescharacteristic
439#107—474no—
440#107—942no—
441#106—474no—
442#106—942no—
443#102—22no—
444#102—474no—
445#102—942no—
446#102C4×D4714yescomplemented
447C22⋊C8—474no—
448C22⋊C8—942no—
449C4×C8—22no—
450C4×C8—942no—
451#95—21no—
452#95—941no—
453#95—941no—
454#95—941no—
455#95—941no—
456#95—941no—
457#95—941no—
458C24—21no—
459C24—471no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—944no—
466C2×D4—1882no—
467C2×D4—1882no—
468C2×D4C2×C4×D4712yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—472no—
478C22×C4—472no—
479C22×C4—471no—
480C22×C4—942no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—941no—
493C22×C4—1881no—
494C22×C4D4×D4711yescharacteristic
495C22×C4D4×D4711yescharacteristic
496C22×C4C23×D4711yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—472no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8C2×C4×D4712yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—472no—
514C4⋊C4—472no—
515C4⋊C4—472no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4—941no—
519C4⋊C4—941no—
520C4⋊C4—941no—
521C4⋊C4—1882no—
522C4⋊C4C2×C4×D4712yes—
523C4⋊C4#1062535012yes—
524C22⋊C4—42no—
525C22⋊C4—944no—
526C22⋊C4—944no—
527C22⋊C4—944no—
528C22⋊C4—1882no—
529C22⋊C4—1882no—
530C22⋊C4—1882no—
531C42—42no—
532C42—944no—
533C42—944no—
534C42—942no—
535C42—942no—
536C42—941no—
537C42—941no—
538C42—1882no—
539C42—1882no—
540C42—1882no—
541C42—1882no—
542C42#1062535012yes—
543C42#1062535212yes—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—472no—
552C23—941no—
553C23—941no—
554C23—941no—
555C23—941no—
556C23—941no—
557C23—941no—
558C23C2×D4×D4711yescharacteristic
559D4—22no—
560D4—22no—
561D4—41no—
562D4—41no—
563D4—1888no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—472no—
577C2×C4—472no—
578C2×C4—941no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—942no—
583C2×C4—942no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—942no—
587C2×C4—942no—
588C2×C4—941no—
589C2×C4—942no—
590C2×C4—941no—
591C2×C4—941no—
592C2×C4—1884no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4—1881no—
598C2×C4—1881no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1884no—
603C2×C4#1309400612yes—
604C2×C4#1309400612yes—
605C2×C4#1309404312yes—
606C2×C4#1309405112yes—
607C2×C4C22×C4×D4711yescharacteristic
608C2×C4#41×D4711yescharacteristic
609C2×C4#41×D4711yescharacteristic
610C2×C4C2×#1062535211yescharacteristic
611C2×C4C2×#1062535011yescharacteristic
612C2×C4C2×#1062535011yescharacteristic
613C8—22no—
614C8—41no—
615C8—942no—
616C8—1881no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—942no—
625C22—942no—
626C22—942no—
627C22—1881no—
628C22—1881no—
629C22—1881no—
630C22—1881no—
631C22C4×D4×D4711yescharacteristic
632C22C2×#1309400611yescharacteristic
633C22#1568963211yescharacteristic
634C22#135×D4711yescharacteristic
635C22C2×#1309404311yescharacteristic
636C22C2×#1309405111yescharacteristic
637C22#1568992011yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—942no—
643C4—942no—
644C4—3761no—
645C4—1882no—
646C4—1882no—
647C4—1882no—
648C4—1881no—
649C4#1568944514yesdirect product factor
650C4C4×#1062535211yescharacteristic
651C4C4×#1062535011yescharacteristic
652C4#1568965111yescharacteristic
653C4#1568965511yescharacteristic
654C2—82no—
655C2—1882no—
656C2C4×#1309400611yescharacteristic
657C2C4×#1309404311yescharacteristic
658C2C4×#1309405111yescharacteristic
659C2C2×#1568944511yescharacteristic
660C2#2025329911yescharacteristic
661C2#2025340211yescharacteristic
662C2#2025344611yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#102×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093995C22
cosocleC22×C4×C47C24
hypercenterC4×#102D47
hypocenterC47C4×#482
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×#13093982C2semidirect
4. #20244018C2semidirect
5. #20244010C2semidirect
6. #20243979C2semidirect
7. #20243971C2semidirect
9. #20243590C2semidirect
10. #20243481C2semidirect
11. C4×#13093958C2semidirect
12. C4×#13093955C2semidirect
13. C4×#13093945C2semidirect
14. C4×(C2×D47)⋊C8C2semidirect
15. C4×#102×C47C2semidirect
21. #15689445C4direct (N × H)
72. #13093982C2×C4semidirect
96. #13093958C2×C4semidirect
98. #13093955C2×C4semidirect
100. #13093945C2×C4semidirect
102. (C2×D47)⋊C8C2×C4semidirect
123. #102×C47C2×C4semidirect
311. C4×C47#482semidirect
336. C4×#102D47semidirect
391. C47C4×#482semidirect
446. #102C4×D47semidirect
649. C4#15689445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156894452
C4×#130939952
C4×#130939822
#202440182
#202440102
#202439792
#202439712
#202437072
#202435902
#202434812
C4×#130939582
C4×#130939552
C4×#130939452
C4×(C2×D47)⋊C82
C4×#102×C472
C4×#48247