Finite Group Databasebeta

← C2×#20244621 #26243945

Subgroups — C2×#20244621 #26243945

Order 12032.

2230 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×#13094020C211yesmaximal, characteristic
2C22×#13093946C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4C22×#13093944C211yesmaximal, characteristic, complemented
5C2×#15689022C211yesmaximal, characteristic, complemented
6#20244621C218yesmaximal, direct product factor
7C2×#15688877C211yesmaximal, characteristic, complemented
8C22×#102×C47C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C23×C22⋊D47—21no—
11C23×C22⋊D47—21no—
12C23×C47⋊C8C2211yescharacteristic
13C2×#13094020—24no—
14C2×#13094020—22no—
15C2×#13094020—24no—
16C2×#13094020C2214yes—
17C22×C4⋊Dic47—21no—
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C2×#13093946—24no—
21C2×#13093946C2214yescomplemented
22C2×#13093945—24no—
23C2×#13093945C2214yescomplemented
24C2×#13093944—24no—
25C2×#13093944C2214yescomplemented
26#15689022—22no—
27#15689022C2214yescomplemented
28C2×C47⋊#95—21no—
29#15688877C2214yescomplemented
30C23×D4×C47C2211yescharacteristic
31C23×C8×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C2×#102×C47—24no—
34C2×#102×C47C2214yescomplemented
35C24×D47—21no—
36C22×D188—22no—
37C22×D188—22no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188—21no—
41C22×D188—22no—
42C22×D188D414yes—
43C22×D188C2312yes—
44C22×C22⋊D47—28no—
45C22×C22⋊D47—28no—
46C22×C22⋊D47—24no—
47C22×C22⋊D47—24no—
48C22×C22⋊D47—44no—
49C22×C22⋊D47—44no—
50C22×C22⋊D47—44no—
51C22×C22⋊D47—44no—
52C23×Dic47—21no—
53C23×Dic47D411yescharacteristic
54C23×Dic47D411yescharacteristic
55C22×C47⋊C8—22no—
56C22×C47⋊C8—22no—
57C22×C47⋊C8—22no—
58C22×C47⋊C8C2312yes—
59#13094020—216no—
60#13094020—28no—
61#13094020—28no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—24no—
66C2×C4⋊Dic47—44no—
67C2×C4⋊Dic47C2312yes—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47D412yes—
71C2×C4×Dic47C2312yes—
72#13093946—28no—
73#13093945—28no—
74#13093944—28no—
75C47⋊#95—24no—
76C25×C47—21no—
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×C47D414yes—
84C22×D4×C47C2312yes—
85C23×C4×C47—21no—
86C23×C4×C47C2311yescharacteristic
87C22×C8×C47—22no—
88C22×C8×C47—22no—
89C22×C8×C47—22no—
90C22×C8×C47C2312yes—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47D414yescomplemented
94C2×C4⋊C4×C47C2312yes—
95#102×C47—28no—
96C24×C47—24no—
97C24×C47—22no—
98C24×C47—42no—
99C24×C47—42no—
100C24×C47—42no—
101C24×C47—42no—
102C24×C47—42no—
103C24×C47—42no—
104C24×C47C2×D411yescharacteristic
105C23×D47—24no—
106C23×D47—22no—
107C23×D47—42no—
108C23×D47—42no—
109C23×D47—42no—
110C23×D47—42no—
111C23×D47—42no—
112C23×D47—42no—
113C2×D4×C47—24no—
114C2×D4×C47—28no—
115C2×D4×C47—28no—
116C2×D4×C47—22no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—44no—
122C2×D4×C47—42no—
123C2×D4×C47—44no—
124C2×D4×C47—42no—
125C2×D4×C47C2×D414yes—
126C22×C4×C47—24no—
127C22×C4×C47—22no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D412yes—
132C22×C4×C47C2×D412yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47#4112yes—
135C22×C4×C47#4112yes—
136C22×C4×C47#4112yes—
137C22×C4×C47C2411yescharacteristic
138C2×C22⋊D47—216no—
139C2×C22⋊D47—216no—
140C2×C22⋊D47—48no—
141C2×C22⋊D47—48no—
142C2×C22⋊D47—432no—
143C2×C22⋊D47—432no—
144C2×C22⋊D47—48no—
145C2×C22⋊D47—48no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—42no—
152C22×Dic47—42no—
153C22×Dic47—42no—
154C22×Dic47D814yes—
155C22×Dic47SD1614yes—
156C22×Dic47C2×D412yes—
157C22×Dic47C2×D412yes—
158C2×D188—28no—
159C2×D188—28no—
160C2×D188—22no—
161C2×D188—22no—
162C2×D188—22no—
163C2×D188—22no—
164C2×D188—24no—
165C2×D188—22no—
166C2×D188—44no—
167C2×D188—42no—
168C2×D188—44no—
169C2×D188—42no—
170C2×D188C2×D414yes—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C2×C8×C47—44no—
175C4⋊C4×C47—24no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47C2×D414yescomplemented
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47—42no—
181C4⋊Dic47—48no—
182C4×Dic47—24no—
183C4×Dic47—22no—
184C4×Dic47—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—44no—
189C23×C47—24no—
190C23×C47—42no—
191C23×C47—42no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47—48no—
197C23×C47—48no—
198C23×C47—48no—
199C23×C47—84no—
200C23×C47—84no—
201C23×C47—84no—
202C23×C47—84no—
203C23×C47#12012yes—
204C23×C47#12112yes—
205C23×C47#12412yes—
206C23×C47C2×D812yes—
207C23×C47C2×SD1612yes—
208C23×C47AGL(1,ℤ/8)12yes—
209C23×C47AGL(1,ℤ/8)12yes—
210C23×C47C22×D411yescharacteristic
211C22×D47—24no—
212C22×D47—42no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47—48no—
219C22×D47—48no—
220C22×D47—48no—
221C22×D47—84no—
222C22×D47—84no—
223C22×D47—84no—
224C22×D47—84no—
225D4×C47—24no—
226D4×C47—24no—
227D4×C47—42no—
228D4×C47—42no—
229D4×C47—48no—
230C2×C4×C47—24no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—48no—
234C2×C4×C47#12012yes—
235C2×C4×C47#12114yes—
236C2×C4×C47#12112yes—
237C2×C4×C47#12114yes—
238C2×C4×C47#12314yes—
239C2×C4×C47#12314yes—
240C2×C4×C47#12412yes—
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C22⋊D47—432no—
248C22⋊D47—432no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—28no—
254C2×Dic47—28no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—84no—
259C2×Dic47C2×D814yes—
260C2×Dic47C2×SD1614yes—
261D188—24no—
262D188—24no—
263D188—42no—
264D188—42no—
265D188—48no—
266C8×C47—42no—
267C47⋊C8—42no—
268C2×#2041—471nomaximal, Sylow
269C22×C47—44no—
270C22×C47—44no—
271C22×C47—44no—
272C22×C47—82no—
273C22×C47—82no—
274C22×C47—82no—
275C22×C47—82no—
276C22×C47—816no—
277C22×C47#39414yes—
278C22×C47#44714yes—
279C22×C47#45014yes—
280C22×C47#45914yes—
281C22×C47#46014yes—
282C22×C47#48614yes—
283C22×C47#49014yes—
284C22×C47C2×#12011yescharacteristic
285C22×C47C2×#12111yescharacteristic
286C22×C47C2×#12411yescharacteristic
287C22×C47C22×D811yescharacteristic
288C22×C47C22×SD1611yescharacteristic
289C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
291C2×D47—44no—
292C2×D47—44no—
293C2×D47—44no—
294C2×D47—82no—
295C2×D47—82no—
296C2×D47—82no—
297C2×D47—82no—
298C2×D47—816no—
299C4×C47—44no—
300C4×C47#39414yes—
301C4×C47C2×#12111yescharacteristic
302C4×C47C2×#12111yescharacteristic
303C4×C47C2×#12311yescharacteristic
304C4×C47C2×#12311yescharacteristic
305Dic47—24no—
306Dic47—24no—
307Dic47—82no—
308C22×#127—471no—
309C22×#102—471no—
310C22×#102—471no—
311C22×#102—471no—
312C22×#102D4711yescharacteristic, complemented
313C2×#389—471no—
314#2041—478no—
315C2×#336—471no—
316C2×C47—84no—
317C2×C47#204118yescomplemented
318C2×C47C2×#39411yescharacteristic
319C2×C47C2×#44711yescharacteristic
320C2×C47C2×#45011yescharacteristic
321C2×C47C2×#45911yescharacteristic
322C2×C47C2×#46011yescharacteristic
323C2×C47C2×#48611yescharacteristic
324C2×C47C2×#49011yescharacteristic
325D47—84no—
326C23×D4—471no—
327C23×D4—941no—
328C23×D4—941no—
329C23×D4C2×D4711yescharacteristic
330C23×C8—471no—
331C23×C8C2×D4711yescharacteristic
332C2×#127—474no—
333C2×#127—942no—
334C2×#127—944no—
335C2×#127—944no—
336C22×C4⋊C4—471no—
337C22×C4⋊C4—941no—
338C22×C4⋊C4C2×D4711yescharacteristic
339C22×C42—471no—
340C2×#102—24no—
341C2×#102—474no—
342C2×#102—474no—
343C2×#102—474no—
344C2×#102—944no—
345C2×#102—944no—
346C2×#102—944no—
347C2×#102C2×D4714yescomplemented
348#389—474no—
349#389—942no—
350C2×#95—941no—
351#336—474no—
352C47C2×#204111yescharacteristic, complemented, Sylow
353C25—21no—
354C25—941no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—474no—
362C22×D4—472no—
363C22×D4—944no—
364C22×D4—944no—
365C22×D4—948no—
366C22×D4—948no—
367C22×D4—942no—
368C22×D4—942no—
369C22×D4—941no—
370C22×D4—942no—
371C22×D4—942no—
372C22×D4—942no—
373C22×D4—1884no—
374C22×D4—1884no—
375C22×D4—1884no—
376C22×D4—1884no—
377C22×D4D18814yes—
378C22×D4C22×D4712yes—
379C23×C4—21no—
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—941no—
383C23×C4C22×D4711yescharacteristic
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—472no—
388C22×C8—942no—
389C22×C8—942no—
390C22×C8—942no—
391C22×C8C22×D4712yes—
392#127—948no—
393#127—9416no—
394#127—948no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—472no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—942no—
400C2×C4⋊C4—944no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—1884no—
403C2×C4⋊C4C22⋊D4714yescomplemented
404C2×C4⋊C4C22×D4712yes—
405C2×C42—472no—
406C2×C42—472no—
407C2×C42—942no—
408C2×C42—942no—
409#102—28no—
410#102—948no—
411#102—948no—
412#102—948no—
413#95—944no—
414C24—24no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—944no—
423C24—942no—
424C24—1882no—
425C24—1882no—
426C24—1882no—
427C24—1882no—
428C24—1882no—
429C24—1882no—
430C24D4×D4711yescharacteristic
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—44no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—474no—
444C2×D4—9416no—
445C2×D4—9416no—
446C2×D4—944no—
447C2×D4—948no—
448C2×D4—948no—
449C2×D4—942no—
450C2×D4—942no—
451C2×D4—942no—
452C2×D4—942no—
453C2×D4—942no—
454C2×D4—1888no—
455C2×D4—1888no—
456C2×D4—18832no—
457C2×D4—18832no—
458C2×D4—1888no—
459C2×D4—1888no—
460C2×D4—1882no—
461C2×D4—1884no—
462C2×D4—1884no—
463C2×D4—1882no—
464C2×D4C2×D18814yes—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—474no—
470C22×C4—474no—
471C22×C4—472no—
472C22×C4—472no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—942no—
478C22×C4—1882no—
479C22×C4—1882no—
480C22×C4—1882no—
481C22×C4C2×D18812yes—
482C22×C4#1062535012yes—
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4712yes—
485C22×C4#1062535212yes—
486C22×C4#1062535212yes—
487C22×C4C2×C22⋊D4712yes—
488C22×C4C23×D4711yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—44no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—942no—
496C2×C8—1884no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—1888no—
502C4⋊C4—1882no—
503C4⋊C4C2×C22⋊D4714yescomplemented
504C42—944no—
505C42—942no—
506C42—942no—
507C23—24no—
508C23—48no—
509C23—48no—
510C23—48no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—944no—
522C23—3764no—
523C23—3764no—
524C23—3764no—
525C23—3764no—
526C23—1888no—
527C23—1888no—
528C23—1888no—
529C23—1882no—
530C23—1882no—
531C23—1882no—
532C23—1882no—
533C23—1882no—
534C23—1882no—
535C23#1309399412yes—
536C23#1309399612yes—
537C23#1309401012yes—
538C23D8×D4712yes—
539C23SD16×D4712yes—
540C23#1309404812yes—
541C23#1309405112yes—
542C23C2×D4×D4711yescharacteristic
543D4—24no—
544D4—24no—
545D4—48no—
546D4—42no—
547D4—42no—
548D4—944no—
549D4—944no—
550D4—18832no—
551D4—18832no—
552D4—1888no—
553D4—1882no—
554D4—1882no—
555C2×C4—24no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—474no—
560C2×C4—474no—
561C2×C4—948no—
562C2×C4—948no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—3764no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4#1309399412yes—
572C2×C4#1309399514yes—
573C2×C4#1309399612yes—
574C2×C4#1309399814yes—
575C2×C4#1309400614yes—
576C2×C4#1309400814yes—
577C2×C4#1309401012yes—
578C2×C4C2×D4×D4711yescharacteristic
579C2×C4C22×C22⋊D4711yescharacteristic
580C2×C4C22×D18811yescharacteristic
581C2×C4C2×#1062535211yescharacteristic
582C2×C4C2×#1062535211yescharacteristic
583C2×C4C2×#1062535011yescharacteristic
584C8—42no—
585C8—1882no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—82no—
591C22—816no—
592C22—82no—
593C22—82no—
594C22—3762no—
595C22—3762no—
596C22—37616no—
597C22—3762no—
598C22—3762no—
599C22—1884no—
600C22—1884no—
601C22—1884no—
602C22#1568903914yes—
603C22#1568925814yes—
604C22#1568927514yes—
605C22#1568931614yes—
606C22#1568932114yes—
607C22#1568946814yes—
608C22#1568948614yes—
609C22C2×#1309399411yescharacteristic
610C22C2×#1309399611yescharacteristic
611C22C2×#1309401011yescharacteristic
612C22C2×D8×D4711yescharacteristic
613C22C2×SD16×D4711yescharacteristic
614C22C2×#1309404811yescharacteristic
615C22C2×#1309405111yescharacteristic
616C4—44no—
617C4—944no—
618C4—944no—
619C4—3762no—
620C4#1568903914yes—
621C4C2×#1309399511yescharacteristic
622C4C2×#1309399811yescharacteristic
623C4C2×#1309400611yescharacteristic
624C4C2×#1309400811yescharacteristic
625C2—84no—
626C2—3764no—
627C2#2024462118yesdirect product factor
628C2C2×#1568903911yescharacteristic
629C2C2×#1568925811yescharacteristic
630C2C2×#1568927511yescharacteristic
631C2C2×#1568931611yescharacteristic
632C2C2×#1568932111yescharacteristic
633C2C2×#1568946811yescharacteristic
634C2C2×#1568948611yescharacteristic
subgroupG/H
centerC24D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC22×#13094020C2
hypercenterC22×#102D47
hypocenterC47C2×#2041
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#13093946C2semidirect
3. C22×#13093945C2semidirect
4. C22×#13093944C2semidirect
5. C2×#15689022C2semidirect
6. #20244621C2direct (N × H)
7. C2×#15688877C2semidirect
8. C22×#102×C47C2semidirect
21. C2×#13093946C22semidirect
23. C2×#13093945C22semidirect
25. C2×#13093944C22semidirect
27. #15689022C22semidirect
29. #15688877C22semidirect
34. C2×#102×C47C22semidirect
93. C2×C4⋊C4×C47D4semidirect
177. C4⋊C4×C47C2×D4semidirect
312. C22×#102D47semidirect
317. C2×C47#2041semidirect
347. C2×#102C2×D47semidirect
352. C47C2×#2041semidirect
403. C2×C4⋊C4C22⋊D47semidirect
503. C4⋊C4C2×C22⋊D47semidirect
627. C2#20244621direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940202
C22×#130939462
C22×#130939452
C22×#130939442
C2×#156890222
#202446212
C2×#156888772
C22×#102×C472
C2×#204147