Finite Group Databasebeta

← C2×#20243738 #26217604

Subgroups — C2×#20243738 #26217604

Order 12032.

2470 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic47C211yesmaximal, characteristic, complemented
2C22×#13093945C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4C2×#15689026C211yesmaximal, characteristic, complemented
5#20243738C218yesmaximal, direct product factor
6C2×#15688886C211yesmaximal, characteristic, complemented
7C2×#15688877C211yesmaximal, characteristic, complemented
8C23×D8×C47C211yesmaximal, characteristic
9C24×Dic47—21no—
10C23×C47⋊C8C2211yescharacteristic
11C2×D4×Dic47—24no—
12C2×D4×Dic47—22no—
13C2×D4×Dic47—24no—
14C2×D4×Dic47C2214yescomplemented
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C22⋊Dic47—21no—
18C22×C22⋊Dic47—21no—
19C22×C22⋊Dic47—21no—
20C22×C4×Dic47C2211yescharacteristic
21C2×#13093945—24no—
22C2×#13093945—24no—
23C2×#13093945C2214yescomplemented
24C2×#13093945C2214yescomplemented
25#15689026—22no—
26#15689026C2214yescomplemented
27#15688886C2214yescomplemented
28#15688877C2214yescomplemented
29C23×D4×C47C2211yescharacteristic
30C23×D4×C47C2211yescharacteristic
31C22×D8×C47—24no—
32C22×D8×C47—24no—
33C22×D8×C47C418yescomplemented
34C22×D8×C47C2214yes—
35C23×C8×C47C2211yescharacteristic
36C23×Dic47—28no—
37C23×Dic47—21no—
38C23×Dic47—24no—
39C23×Dic47—21no—
40C23×Dic47—44no—
41C23×Dic47—44no—
42C23×Dic47D411yescharacteristic
43C23×Dic47D411yescharacteristic
44C22×C47⋊C8—22no—
45C22×C47⋊C8—22no—
46C22×C47⋊C8—22no—
47C22×C47⋊C8C2312yes—
48D4×Dic47—216no—
49D4×Dic47—28no—
50D4×Dic47—28no—
51C2×C4⋊Dic47—21no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47D414yes—
57C2×C4⋊Dic47C2312yes—
58C2×C4⋊Dic47C2312yes—
59C2×C22⋊Dic47—28no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47—44no—
64C2×C22⋊Dic47—44no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47D412yes—
68C2×C4×Dic47C2312yes—
69#13093945—28no—
70#13093945—28no—
71C25×C47—21no—
72C25×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47—21no—
79C22×D4×C47—22no—
80C22×D4×C47—22no—
81C22×D4×C47—22no—
82C22×D4×C47—22no—
83C22×D4×C47C2×C414yes—
84C22×D4×C47C2×C414yescomplemented
85C22×D4×C47D414yes—
86C22×D4×C47D414yes—
87C22×D4×C47C2312yes—
88C22×D4×C47C2312yes—
89C23×C4×C47C2311yescharacteristic
90C2×D8×C47—232no—
91C2×D8×C47—28no—
92C2×D8×C47—28no—
93C2×D8×C47C2×C4116yescomplemented
94C22×C8×C47—22no—
95C22×C8×C47—22no—
96C22×C8×C47C2×C414yescomplemented
97C22×C8×C47C2312yes—
98C24×C47—24no—
99C24×C47—24no—
100C24×C47—24no—
101C24×C47—22no—
102C24×C47—24no—
103C24×C47—22no—
104C24×C47—42no—
105C24×C47—42no—
106C24×C47—42no—
107C24×C47—42no—
108C24×C47—42no—
109C24×C47—42no—
110C24×C47—42no—
111C24×C47—42no—
112C24×C47—42no—
113C24×C47—42no—
114C24×C47C2×D411yescharacteristic
115C2×D4×C47—28no—
116C2×D4×C47—28no—
117C2×D4×C47—24no—
118C2×D4×C47—28no—
119C2×D4×C47—24no—
120C2×D4×C47—24no—
121C2×D4×C47—28no—
122C2×D4×C47—24no—
123C2×D4×C47—28no—
124C2×D4×C47—22no—
125C2×D4×C47—22no—
126C2×D4×C47—22no—
127C2×D4×C47—22no—
128C2×D4×C47—22no—
129C2×D4×C47—22no—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—42no—
133C2×D4×C47—44no—
134C2×D4×C47—42no—
135C2×D4×C47—44no—
136C2×D4×C47C22⋊C4116yescomplemented
137C2×D4×C47C22×C414yes—
138C2×D4×C47C22×C414yescomplemented
139C2×D4×C47C2×D414yes—
140C2×D4×C47C2×D414yes—
141C22×C4×C47C22×C412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D412yes—
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D412yes—
146C22×C4×C47#4112yes—
147C22×C4×C47#4112yes—
148C22×C4×C47C2411yescharacteristic
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—216no—
152C22×Dic47—22no—
153C22×Dic47—24no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—48no—
159C22×Dic47—432no—
160C22×Dic47—42no—
161C22×Dic47—42no—
162C22×Dic47—48no—
163C22×Dic47—42no—
164C22×Dic47—42no—
165C22×Dic47—42no—
166C22×Dic47D814yescomplemented
167C22×Dic47C2×D412yes—
168C22×Dic47C2×D412yes—
169D8×C47—232no—
170C2×C8×C47—28no—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47C22×C414yescomplemented
174C22⋊Dic47—216no—
175C22⋊Dic47—48no—
176C22⋊Dic47—48no—
177C4⋊Dic47—24no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—42no—
182C4⋊Dic47C2×D414yes—
183C4×Dic47—24no—
184C4×Dic47—22no—
185C4×Dic47—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—44no—
190C23×C47—24no—
191C23×C47—24no—
192C23×C47—24no—
193C23×C47—216no—
194C23×C47—24no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47—48no—
200C23×C47—48no—
201C23×C47—48no—
202C23×C47—48no—
203C23×C47—48no—
204C23×C47—48no—
205C23×C47—42no—
206C23×C47—42no—
207C23×C47—42no—
208C23×C47—42no—
209C23×C47—42no—
210C23×C47—42no—
211C23×C47—48no—
212C23×C47—48no—
213C23×C47—48no—
214C23×C47—84no—
215C23×C47—84no—
216C23×C47—84no—
217C23×C47—84no—
218C23×C47C4×D412yes—
219C23×C47#12012yes—
220C23×C47#12112yes—
221C23×C47C2×D812yes—
222C23×C47#13512yes—
223C23×C47AGL(1,ℤ/8)12yes—
224C23×C47AGL(1,ℤ/8)12yes—
225C23×C47C22×D411yescharacteristic
226D4×C47—24no—
227D4×C47—24no—
228D4×C47—24no—
229D4×C47—24no—
230D4×C47—24no—
231D4×C47—216no—
232D4×C47—42no—
233D4×C47—42no—
234D4×C47—48no—
235D4×C47C2×C22⋊C418yescomplemented
236C2×C4×C47C2×C22⋊C414yes—
237C2×C4×C47C4×D414yes—
238C2×C4×C47C4×D412yes—
239C2×C4×C47#12012yes—
240C2×C4×C47#12114yes—
241C2×C4×C47#12112yes—
242C2×C4×C47#12314yes—
243C2×C4×C47C23×C411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—28no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—432no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—48no—
260C2×Dic47—44no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—84no—
265C2×Dic47C2×D814yescomplemented
266C8×C47—24no—
267C47⋊C8—42no—
268C2×#1879—471nomaximal, Sylow
269C22×C47—28no—
270C22×C47—432no—
271C22×C47—44no—
272C22×C47—44no—
273C22×C47—44no—
274C22×C47—44no—
275C22×C47—44no—
276C22×C47—44no—
277C22×C47—44no—
278C22×C47—44no—
279C22×C47—44no—
280C22×C47—816no—
281C22×C47—82no—
282C22×C47—82no—
283C22×C47—82no—
284C22×C47—82no—
285C22×C47#38614yes—
286C22×C47C4×D814yes—
287C22×C47#44214yes—
288C22×C47#44714yes—
289C22×C47#44914yes—
290C22×C47#45914yes—
291C22×C47#46314yes—
292C22×C47C2×C4×D411yescharacteristic
293C22×C47C2×#12011yescharacteristic
294C22×C47C2×#12111yescharacteristic
295C22×C47C22×D811yescharacteristic
296C22×C47C2×#13511yescharacteristic
297C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C47#38614yes—
300C4×C47C22×C22⋊C411yescharacteristic
301C4×C47C2×C4×D411yescharacteristic
302C4×C47C2×#12111yescharacteristic
303C4×C47C2×#12311yescharacteristic
304Dic47—24no—
305Dic47—44no—
306Dic47—42no—
307Dic47—82no—
308C23×D8D4711yescharacteristic
309C22×C4×D4—471no—
310C22×#102—471no—
311C22×#102—471no—
312C2×#390—471no—
313#1879—478no—
314C2×#340—471no—
315C2×#336—471no—
316C2×C47—48no—
317C2×C47—84no—
318C2×C47#187918yescomplemented
319C2×C47C2×#38611yescharacteristic
320C2×C47C2×C4×D811yescharacteristic
321C2×C47C2×#44211yescharacteristic
322C2×C47C2×#44711yescharacteristic
323C2×C47C2×#44911yescharacteristic
324C2×C47C2×#45911yescharacteristic
325C2×C47C2×#46311yescharacteristic
326C23×D4C2×D4711yescharacteristic
327C23×D4C2×D4711yescharacteristic
328C24×C4—941no—
329C22×D8—24no—
330C22×D8—24no—
331C22×D8Dic4718yescomplemented
332C22×D8C2×D4714yes—
333C23×C8—471no—
334C23×C8C2×D4711yescharacteristic
335C2×C4×D4—474no—
336C2×C4×D4—942no—
337C2×C4×D4—944no—
338C2×C4×D4—944no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C22⋊C4—941no—
342C22×C22⋊C4—941no—
343C22×C22⋊C4—941no—
344C22×C42—471no—
345C2×#102—474no—
346C2×#102—474no—
347C2×#102—944no—
348C2×#102—944no—
349#390—474no—
350#390—942no—
351#340—474no—
352#336—474no—
353C47C2×#187911yescharacteristic, complemented, Sylow
354C25—21no—
355C25—21no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—21no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4C2×Dic4714yes—
367C22×D4C2×Dic4714yescomplemented
368C22×D4C22⋊D4714yes—
369C22×D4C22⋊D4714yes—
370C22×D4C22×D4712yes—
371C22×D4C22×D4712yes—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—944no—
375C23×C4—948no—
376C23×C4—941no—
377C23×C4—941no—
378C23×C4—1884no—
379C23×C4—1884no—
380C23×C4C22×D4711yescharacteristic
381C2×D8—232no—
382C2×D8—28no—
383C2×D8—28no—
384C2×D8C2×Dic47116yescomplemented
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—472no—
388C22×C8—942no—
389C22×C8—942no—
390C22×C8—942no—
391C22×C8C2×Dic4714yescomplemented
392C22×C8C22×D4712yes—
393C4×D4—948no—
394C4×D4—9416no—
395C4×D4—948no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—472no—
398C2×C4⋊C4—472no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—941no—
404C2×C22⋊C4—944no—
405C2×C22⋊C4—948no—
406C2×C22⋊C4—944no—
407C2×C22⋊C4—944no—
408C2×C22⋊C4—1884no—
409C2×C22⋊C4—1884no—
410C2×C42—472no—
411C2×C42—472no—
412C2×C42—942no—
413C2×C42—942no—
414#102—948no—
415#102—948no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24D4×D4711yescharacteristic
433C2×D4—28no—
434C2×D4—24no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4C22⋊Dic47116yescomplemented
455C2×D4C22×Dic4714yes—
456C2×D4C22×Dic4714yescomplemented
457C2×D4C2×C22⋊D4714yes—
458C2×D4C2×C22⋊D4714yes—
459C22×C4—474no—
460C22×C4—472no—
461C22×C4—472no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—9416no—
465C22×C4—942no—
466C22×C4—944no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—1888no—
472C22×C4—18832no—
473C22×C4—1888no—
474C22×C4—1882no—
475C22×C4—1882no—
476C22×C4—1882no—
477C22×C4—1882no—
478C22×C4—1882no—
479C22×C4D4×D4711yescharacteristic
480C22×C4D4×D4712yes—
481C22×C4#1062535212yes—
482C22×C4#1062535212yes—
483C22×C4C22×Dic4712yes—
484C22×C4C2×C22⋊D4712yes—
485C22×C4C2×C22⋊D4712yes—
486C22×C4C23×D4711yescharacteristic
487D8—232no—
488C2×C8—28no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—942no—
492C2×C8—942no—
493C2×C8—942no—
494C2×C8—1884no—
495C2×C8C22×Dic4714yescomplemented
496C4⋊C4—474no—
497C4⋊C4—944no—
498C4⋊C4—942no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—1882no—
502C22⋊C4—9416no—
503C22⋊C4—1888no—
504C22⋊C4—1888no—
505C42—944no—
506C42—942no—
507C42—942no—
508C23—216no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—48no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23—48no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—48no—
523C23—48no—
524C23—48no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—48no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—84no—
536C23D4×Dic4712yes—
537C23#1309399212yes—
538C23#1309399612yes—
539C23D8×D4712yes—
540C23#1309404312yes—
541C23#1309404812yes—
542C23#1309404812yes—
543C23C2×D4×D4711yescharacteristic
544D4—216no—
545D4—24no—
546D4—24no—
547D4—24no—
548D4—24no—
549D4—24no—
550D4—48no—
551D4—42no—
552D4—42no—
553D4C2×C22⋊Dic4718yescomplemented
554C2×C4—474no—
555C2×C4—948no—
556C2×C4—942no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—944no—
560C2×C4—942no—
561C2×C4—942no—
562C2×C4—3764no—
563C2×C4—18832no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4—1888no—
568C2×C4—1884no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4C2×C22⋊Dic4714yes—
572C2×C4D4×Dic4712yes—
573C2×C4D4×Dic4714yes—
574C2×C4#1309399212yes—
575C2×C4#1309399612yes—
576C2×C4#1309399614yes—
577C2×C4#1309400514yes—
578C2×C4C23×Dic4711yescharacteristic
579C2×C4C2×D4×D4711yescharacteristic
580C2×C4C22×C22⋊D4711yescharacteristic
581C2×C4C22×C22⋊D4711yescharacteristic
582C2×C4C2×#1062535211yescharacteristic
583C2×C4C2×#1062535211yescharacteristic
584C8—24no—
585C8—1882no—
586C22—28no—
587C22—44no—
588C22—432no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22#1568900314yes—
603C22D8×Dic4714yes—
604C22#1568923514yes—
605C22#1568925514yes—
606C22#1568926514yes—
607C22#1568931614yes—
608C22#1568933614yes—
609C22C2×D4×Dic4711yescharacteristic
610C22C2×#1309399211yescharacteristic
611C22C2×#1309399611yescharacteristic
612C22C2×D8×D4711yescharacteristic
613C22C2×#1309404311yescharacteristic
614C22C2×#1309404811yescharacteristic
615C22C2×#1309404811yescharacteristic
616C4—944no—
617C4—3762no—
618C4—1884no—
619C4—1882no—
620C4#1568900314yes—
621C4C22×C22⋊Dic4711yescharacteristic
622C4C2×D4×Dic4711yescharacteristic
623C4C2×#1309399611yescharacteristic
624C4C2×#1309400511yescharacteristic
625C2—48no—
626C2—84no—
627C2#2024373818yesdirect product factor
628C2C2×#1568900311yescharacteristic
629C2C2×D8×Dic4711yescharacteristic
630C2C2×#1568923511yescharacteristic
631C2C2×#1568925511yescharacteristic
632C2C2×#1568926511yescharacteristic
633C2C2×#1568931611yescharacteristic
634C2C2×#1568933611yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC23×D8×C47C2
socleC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC23×D8D47
hypocenterC47C2×#1879
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic47C2semidirect
2. C22×#13093945C2semidirect
3. C22×#13093945C2semidirect
4. C2×#15689026C2semidirect
5. #20243738C2direct (N × H)
6. C2×#15688886C2semidirect
7. C2×#15688877C2semidirect
14. C2×D4×Dic47C22semidirect
23. C2×#13093945C22semidirect
24. C2×#13093945C22semidirect
26. #15689026C22semidirect
27. #15688886C22semidirect
28. #15688877C22semidirect
33. C22×D8×C47C4semidirect
84. C22×D4×C47C2×C4semidirect
93. C2×D8×C47C2×C4semidirect
96. C22×C8×C47C2×C4semidirect
136. C2×D4×C47C22⋊C4semidirect
138. C2×D4×C47C22×C4semidirect
166. C22×Dic47D8semidirect
173. C2×C8×C47C22×C4semidirect
235. D4×C47C2×C22⋊C4semidirect
265. C2×Dic47C2×D8semidirect
318. C2×C47#1879semidirect
331. C22×D8Dic47semidirect
353. C47C2×#1879semidirect
367. C22×D4C2×Dic47semidirect
384. C2×D8C2×Dic47semidirect
391. C22×C8C2×Dic47semidirect
454. C2×D4C22⋊Dic47semidirect
456. C2×D4C22×Dic47semidirect
495. C2×C8C22×Dic47semidirect
553. D4C2×C22⋊Dic47semidirect
627. C2#20243738direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C22×#130939452
C2×#156890262
#202437382
C2×#156888862
C2×#156888772
C23×D8×C472
C2×#187947