Finite Group Databasebeta

← C2×#20243797 #26217892

Subgroups — C2×#20243797 #26217892

Order 12032.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689598C211yesmaximal, characteristic, complemented
2C22×#13093939C211yesmaximal, characteristic, complemented
3C2×#15688979C212yesmaximal, complemented
4#20243797C218yesmaximal, direct product factor
5C2×#15688889C212yesmaximal, complemented
6C22×#120×C47C211yesmaximal, characteristic
7#15689598—24no—
8#15689598—22no—
9#15689598C2214yescomplemented
10C2×D4×Dic47—24no—
11C2×#13093983—21no—
12C22×C22⋊Dic47—24no—
13C22×C22⋊Dic47—21no—
14C22×C22⋊Dic47C2212yes—
15C22×C22⋊Dic47C2212yes—
16C2×#13093939—24no—
17C2×#13093939C2214yescomplemented
18#15688979—24no—
19#15688979C2218yescomplemented
20#15688889C2218yescomplemented
21C26×C47C2211yescharacteristic
22C23×D4×C47—21no—
23C23×D4×C47C2211yescharacteristic
24C2×#120×C47—24no—
25C2×#120×C47—22no—
26C2×#120×C47C418yescomplemented
27C2×#120×C47C2214yes—
28C22×C22⋊C4×C47—21no—
29C22×C22⋊C4×C47C2211yescharacteristic
30C23×Dic47—22no—
31C23×Dic47—22no—
32C23×Dic47D414yescomplemented
33D4×Dic47—216no—
34D4×Dic47—216no—
35#13093983—24no—
36#13093983—24no—
37C2×C4⋊Dic47—22no—
38C2×C22⋊Dic47—22no—
39C2×C22⋊Dic47—24no—
40C2×C22⋊Dic47—22no—
41C2×C22⋊Dic47—24no—
42C2×C22⋊Dic47—22no—
43C2×C22⋊Dic47—22no—
44C2×C22⋊Dic47—22no—
45C2×C22⋊Dic47—24no—
46C2×C22⋊Dic47—24no—
47C2×C22⋊Dic47—22no—
48C2×C22⋊Dic47—216no—
49C2×C22⋊Dic47—416no—
50C2×C22⋊Dic47D414yescomplemented
51C2×C22⋊Dic47C2314yes—
52C2×C22⋊Dic47C2314yes—
53C2×C4×Dic47—22no—
54#13093939—28no—
55C25×C47—21no—
56C25×C47—22no—
57C25×C47—22no—
58C25×C47—22no—
59C25×C47—21no—
60C25×C47—24no—
61C25×C47—48no—
62C25×C47C2×C414yescomplemented
63C25×C47D411yescharacteristic
64C25×C47C2312yes—
65C25×C47C2311yescharacteristic
66C22×D4×C47—22no—
67C22×D4×C47—22no—
68C22×D4×C47—24no—
69C22×D4×C47—28no—
70C22×D4×C47—24no—
71C22×D4×C47—48no—
72C22×D4×C47C2×C414yes—
73C22×D4×C47D414yes—
74C22×D4×C47D412yes—
75C22×D4×C47C2312yes—
76C23×C4×C47—21no—
77C23×C4×C47D411yescharacteristic
78#120×C47—216no—
79#120×C47—28no—
80#120×C47C2×C4116yescomplemented
81C2×C22⋊C4×C47—21no—
82C2×C22⋊C4×C47—22no—
83C2×C22⋊C4×C47—28no—
84C2×C22⋊C4×C47—24no—
85C2×C22⋊C4×C47C2×C414yescomplemented
86C2×C22⋊C4×C47C2312yes—
87C24×C47—28no—
88C24×C47—216no—
89C24×C47—24no—
90C24×C47—28no—
91C24×C47—21no—
92C24×C47—22no—
93C24×C47—24no—
94C24×C47—21no—
95C24×C47—22no—
96C24×C47—24no—
97C24×C47—28no—
98C24×C47—22no—
99C24×C47—24no—
100C24×C47—416no—
101C24×C47—44no—
102C24×C47—48no—
103C24×C47—48no—
104C24×C47—44no—
105C24×C47—416no—
106C24×C47—416no—
107C24×C47—48no—
108C24×C47—432no—
109C24×C47—44no—
110C24×C47—41no—
111C24×C47—42no—
112C24×C47—41no—
113C24×C47—44no—
114C24×C47—44no—
115C24×C47—42no—
116C24×C47—42no—
117C24×C47C22⋊C414yescomplemented
118C24×C47C22×C412yes—
119C24×C47C22×C414yescomplemented
120C24×C47C2×D411yescharacteristic
121C24×C47C2×D412yes—
122C24×C47C2×D412yes—
123C24×C47C2×D411yescharacteristic
124C24×C47C2×D412yes—
125C24×C47C2×D412yes—
126C24×C47#4114yes—
127C24×C47C2411yescharacteristic
128C2×D4×C47—28no—
129C2×D4×C47—28no—
130C2×D4×C47—24no—
131C2×D4×C47—28no—
132C2×D4×C47—28no—
133C2×D4×C47—24no—
134C2×D4×C47—24no—
135C2×D4×C47—24no—
136C2×D4×C47—216no—
137C2×D4×C47—432no—
138C2×D4×C47—416no—
139C2×D4×C47C22⋊C418yescomplemented
140C2×D4×C47C22×C414yes—
141C2×D4×C47C2×D414yes—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—22no—
145C22×C4×C47—24no—
146C22×C4×C47—22no—
147C22×C4×C47—44no—
148C22×C4×C47C22⋊C414yescomplemented
149C22×C4×C47C2×D412yes—
150C22×Dic47—24no—
151C22×Dic47—28no—
152C22×Dic47—24no—
153C22×Dic47—24no—
154C22×Dic47—48no—
155C22×Dic47—48no—
156C22×Dic47—44no—
157C22×Dic47—84no—
158C22×Dic47C2×D418yescomplemented
159C22⋊C4×C47—24no—
160C22⋊C4×C47—22no—
161C22⋊C4×C47—216no—
162C22⋊C4×C47C22×C414yescomplemented
163C22⋊Dic47—28no—
164C22⋊Dic47—24no—
165C22⋊Dic47—24no—
166C22⋊Dic47—24no—
167C22⋊Dic47—24no—
168C22⋊Dic47—24no—
169C22⋊Dic47—24no—
170C22⋊Dic47—432no—
171C22⋊Dic47—44no—
172C4⋊Dic47—28no—
173C4×Dic47—28no—
174C23×C47—28no—
175C23×C47—24no—
176C23×C47—216no—
177C23×C47—216no—
178C23×C47—28no—
179C23×C47—232no—
180C23×C47—24no—
181C23×C47—28no—
182C23×C47—22no—
183C23×C47—24no—
184C23×C47—22no—
185C23×C47—24no—
186C23×C47—44no—
187C23×C47—48no—
188C23×C47—44no—
189C23×C47—44no—
190C23×C47—42no—
191C23×C47—48no—
192C23×C47—42no—
193C23×C47—432no—
194C23×C47—48no—
195C23×C47—416no—
196C23×C47—416no—
197C23×C47—48no—
198C23×C47—416no—
199C23×C47—44no—
200C23×C47—48no—
201C23×C47—416no—
202C23×C47—48no—
203C23×C47—432no—
204C23×C47—416no—
205C23×C47—48no—
206C23×C47—44no—
207C23×C47—432no—
208C23×C47—416no—
209C23×C47—42no—
210C23×C47—44no—
211C23×C47—42no—
212C23×C47—44no—
213C23×C47—48no—
214C23×C47—44no—
215C23×C47—44no—
216C23×C47—48no—
217C23×C47—84no—
218C23×C47—82no—
219C23×C47C2×C22⋊C412yes—
220C23×C47C2×C22⋊C412yes—
221C23×C47C2×C22⋊C414yescomplemented
222C23×C47C4×D414yes—
223C23×C47C4×D414yes—
224C23×C47#12011yescharacteristic
225C23×C47#12012yes—
226C23×C47#12011yescharacteristic
227C23×C47#12114yes—
228C23×C47#12114yes—
229C23×C47#12312yes—
230C23×C47#12312yes—
231C23×C47C23×C411yescharacteristic
232C23×C47C22×D412yes—
233C23×C47C22×D411yescharacteristic
234C23×C47C22×D411yescharacteristic
235C23×C47C2×#4112yes—
236D4×C47—28no—
237D4×C47—28no—
238D4×C47—216no—
239D4×C47—432no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—48no—
246C2×C4×C47—44no—
247C2×C4×C47C2×C22⋊C414yescomplemented
248C2×Dic47—28no—
249C2×Dic47—48no—
250C2×Dic47—48no—
251C2×Dic47—48no—
252C2×Dic47—44no—
253C2×Dic47—84no—
254C2×Dic47—88no—
255C2×Dic47—88no—
256C2×#1889—471nomaximal, Sylow
257C22×C47—28no—
258C22×C47—24no—
259C22×C47—28no—
260C22×C47—24no—
261C22×C47—24no—
262C22×C47—24no—
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—28no—
266C22×C47—216no—
267C22×C47—24no—
268C22×C47—42no—
269C22×C47—44no—
270C22×C47—44no—
271C22×C47—42no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—42no—
275C22×C47—44no—
276C22×C47—416no—
277C22×C47—44no—
278C22×C47—48no—
279C22×C47—48no—
280C22×C47—416no—
281C22×C47—432no—
282C22×C47—416no—
283C22×C47—48no—
284C22×C47—44no—
285C22×C47—48no—
286C22×C47—44no—
287C22×C47—82no—
288C22×C47—84no—
289C22×C47#38612yes—
290C22×C47#38614yes—
291C22×C47#38612yes—
292C22×C47B(4,𝔽2)14yes—
293C22×C47C22×C22⋊C411yescharacteristic
294C22×C47C2×C4×D412yes—
295C22×C47C2×#12011yescharacteristic
296C22×C47C2×#12112yes—
297C22×C47C2×#12311yescharacteristic
298C4×C47—24no—
299C4×C47—44no—
300Dic47—48no—
301Dic47—84no—
302C22×#120D4711yescharacteristic
303C2×#518—471no—
304C22×#99—471no—
305C2×#379—472no—
306#1889—478no—
307C2×#342—472no—
308C2×C47—22no—
309C2×C47—21no—
310C2×C47—22no—
311C2×C47—21no—
312C2×C47—22no—
313C2×C47—24no—
314C2×C47—48no—
315C2×C47—44no—
316C2×C47#188914yescomplemented
317C2×C47C2×#38611yescharacteristic
318C2×C47C2×B(4,𝔽2)12yes—
319C26C2×D4711yescharacteristic
320C23×D4—21no—
321C23×D4C2×D4711yescharacteristic
322C2×#120—24no—
323C2×#120—22no—
324C2×#120Dic4718yescomplemented
325C2×#120C2×D4714yes—
326#518—474no—
327#518—944no—
328#518—942no—
329C2×C4×D4—944no—
330C2×#117—941no—
331C22×C22⋊C4—21no—
332C22×C22⋊C4—472no—
333C22×C22⋊C4—472no—
334C22×C22⋊C4—941no—
335C22×C22⋊C4—944no—
336C22×C22⋊C4C2×D4711yescharacteristic
337C2×#99—474no—
338C2×#99—944no—
339#379—478no—
340#379—944no—
341#342—478no—
342C47C2×#188911yescharacteristic, complemented, Sylow
343C25—22no—
344C25—21no—
345C25—22no—
346C25—24no—
347C25—22no—
348C25—21no—
349C25—48no—
350C25C2×Dic4714yescomplemented
351C25C22⋊D4711yescharacteristic
352C25C22×D4712yes—
353C25C22×D4711yescharacteristic
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—28no—
358C22×D4—24no—
359C22×D4—48no—
360C22×D4C2×Dic4714yes—
361C22×D4C22⋊D4714yes—
362C22×D4C22⋊D4712yes—
363C22×D4C22×D4712yes—
364C23×C4—21no—
365C23×C4—474no—
366C23×C4—942no—
367C23×C4—942no—
368C23×C4C22⋊D4711yescharacteristic
369#120—216no—
370#120—28no—
371#120C2×Dic47116yescomplemented
372C4×D4—9416no—
373C4×D4—9416no—
374#117—944no—
375#117—944no—
376C2×C4⋊C4—942no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—474no—
382C2×C22⋊C4—474no—
383C2×C22⋊C4—474no—
384C2×C22⋊C4—942no—
385C2×C22⋊C4—944no—
386C2×C22⋊C4—942no—
387C2×C22⋊C4—942no—
388C2×C22⋊C4—942no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—944no—
391C2×C22⋊C4—944no—
392C2×C22⋊C4—944no—
393C2×C22⋊C4—9416no—
394C2×C22⋊C4—942no—
395C2×C22⋊C4—18816no—
396C2×C22⋊C4C2×Dic4714yescomplemented
397C2×C22⋊C4C22×D4712yes—
398C2×C42—942no—
399#99—948no—
400C24—216no—
401C24—28no—
402C24—24no—
403C24—28no—
404C24—21no—
405C24—24no—
406C24—22no—
407C24—21no—
408C24—22no—
409C24—24no—
410C24—28no—
411C24—22no—
412C24—24no—
413C24—416no—
414C24—48no—
415C24—44no—
416C24—44no—
417C24—48no—
418C24—416no—
419C24—416no—
420C24—48no—
421C24—432no—
422C24—44no—
423C24—41no—
424C24—42no—
425C24—41no—
426C24—44no—
427C24—44no—
428C24—42no—
429C24—42no—
430C24C22⋊Dic4714yescomplemented
431C24D4×D4712yes—
432C24D4×D4712yes—
433C24#1062535214yes—
434C24C22×Dic4712yes—
435C24C22×Dic4714yescomplemented
436C24C2×C22⋊D4711yescharacteristic
437C24C2×C22⋊D4712yes—
438C24C2×C22⋊D4711yescharacteristic
439C24C2×C22⋊D4712yes—
440C24C23×D4711yescharacteristic
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—216no—
450C2×D4—432no—
451C2×D4—416no—
452C2×D4C22⋊Dic4718yescomplemented
453C2×D4C22×Dic4714yes—
454C2×D4C2×C22⋊D4714yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—478no—
462C22×C4—948no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—944no—
466C22×C4—3764no—
467C22×C4—1888no—
468C22×C4—1884no—
469C22×C4—1888no—
470C22×C4C22⋊Dic4714yescomplemented
471C22×C4C2×C22⋊D4712yes—
472C4⋊C4—948no—
473C22⋊C4—24no—
474C22⋊C4—22no—
475C22⋊C4—216no—
476C22⋊C4—948no—
477C22⋊C4—944no—
478C22⋊C4—944no—
479C22⋊C4—944no—
480C22⋊C4—944no—
481C22⋊C4—944no—
482C22⋊C4—944no—
483C22⋊C4—18832no—
484C22⋊C4—1884no—
485C22⋊C4C22×Dic4714yescomplemented
486C42—948no—
487C23—24no—
488C23—28no—
489C23—216no—
490C23—216no—
491C23—28no—
492C23—232no—
493C23—24no—
494C23—24no—
495C23—28no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—48no—
503C23—44no—
504C23—42no—
505C23—42no—
506C23—48no—
507C23—432no—
508C23—416no—
509C23—416no—
510C23—44no—
511C23—416no—
512C23—48no—
513C23—48no—
514C23—416no—
515C23—48no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—44no—
520C23—432no—
521C23—416no—
522C23—44no—
523C23—48no—
524C23—44no—
525C23—44no—
526C23—48no—
527C23—42no—
528C23—44no—
529C23—42no—
530C23—84no—
531C23—82no—
532C23C2×C22⋊Dic4712yes—
533C23C2×C22⋊Dic4712yes—
534C23C2×C22⋊Dic4714yescomplemented
535C23D4×Dic4714yes—
536C23D4×Dic4714yes—
537C23#1309399211yescharacteristic
538C23#1309399212yes—
539C23#1309399211yescharacteristic
540C23#1309399614yes—
541C23#1309399614yes—
542C23#1309400512yes—
543C23#1309400512yes—
544C23C23×Dic4711yescharacteristic
545C23C2×D4×D4712yes—
546C23C22×C22⋊D4711yescharacteristic
547C23C22×C22⋊D4711yescharacteristic
548C23C2×#1062535212yes—
549D4—216no—
550D4—28no—
551D4—28no—
552D4—432no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—48no—
559C2×C4—44no—
560C2×C4—948no—
561C2×C4—3768no—
562C2×C4—3764no—
563C2×C4—3768no—
564C2×C4—1888no—
565C2×C4—1884no—
566C2×C4—1888no—
567C2×C4—1888no—
568C2×C4C2×C22⋊Dic4714yescomplemented
569C22—24no—
570C22—28no—
571C22—28no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—22no—
577C22—28no—
578C22—216no—
579C22—24no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—416no—
590C22—48no—
591C22—416no—
592C22—48no—
593C22—432no—
594C22—44no—
595C22—416no—
596C22—48no—
597C22—44no—
598C22—48no—
599C22—84no—
600C22—82no—
601C22#1568900312yes—
602C22#1568900314yes—
603C22#1568900312yes—
604C22#1568930914yes—
605C22C22×C22⋊Dic4711yescharacteristic
606C22C2×D4×Dic4712yes—
607C22C2×#1309399211yescharacteristic
608C22C2×#1309399612yes—
609C22C2×#1309400511yescharacteristic
610C4—24no—
611C4—44no—
612C4—3764no—
613C4—1888no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—24no—
620C2—48no—
621C2—44no—
622C2#2024379714yesdirect product factor
623C2C2×#1568900311yescharacteristic
624C2C2×#1568930912yes—
subgroupG/H
centerC23#13093992
commutatorC23×C47C23×C4
FrattiniC24C23×D47
Fitting, prime radicalC22×#120×C47C2
socleC23×C47#120
cosocleC24×C47C24
hypercenterC22×#120D47
hypocenterC47C2×#1889
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C2×#15689598C2semidirect
2. C22×#13093939C2semidirect
3. C2×#15688979C2semidirect
4. #20243797C2direct (N × H)
5. C2×#15688889C2semidirect
9. #15689598C22semidirect
17. C2×#13093939C22semidirect
19. #15688979C22semidirect
20. #15688889C22semidirect
26. C2×#120×C47C4semidirect
32. C23×Dic47D4semidirect
50. C2×C22⋊Dic47D4semidirect
62. C25×C47C2×C4semidirect
80. #120×C47C2×C4semidirect
85. C2×C22⋊C4×C47C2×C4semidirect
117. C24×C47C22⋊C4semidirect
119. C24×C47C22×C4semidirect
139. C2×D4×C47C22⋊C4semidirect
148. C22×C4×C47C22⋊C4semidirect
158. C22×Dic47C2×D4semidirect
162. C22⋊C4×C47C22×C4semidirect
221. C23×C47C2×C22⋊C4semidirect
247. C2×C4×C47C2×C22⋊C4semidirect
316. C2×C47#1889semidirect
324. C2×#120Dic47semidirect
342. C47C2×#1889semidirect
350. C25C2×Dic47semidirect
371. #120C2×Dic47semidirect
396. C2×C22⋊C4C2×Dic47semidirect
430. C24C22⋊Dic47semidirect
435. C24C22×Dic47semidirect
452. C2×D4C22⋊Dic47semidirect
470. C22×C4C22⋊Dic47semidirect
485. C22⋊C4C22×Dic47semidirect
534. C23C2×C22⋊Dic47semidirect
568. C2×C4C2×C22⋊Dic47semidirect
622. C2#20243797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895982
C22×#130939392
C2×#156889792
#202437972
C2×#156888892
C22×#120×C472
C2×#188947