Finite Group Databasebeta

← C2×#19135828 #25124264

Subgroups — C2×#19135828 #25124264

Order 11008.

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×#13063321C211yesmaximal, characteristic
2C22×#13063247C211yesmaximal, characteristic, complemented
3C22×#13063246C211yesmaximal, characteristic, complemented
4C22×#13063245C211yesmaximal, characteristic, complemented
5C2×#14582798C211yesmaximal, characteristic, complemented
6#19135828C218yesmaximal, direct product factor
7C2×#14582653C211yesmaximal, characteristic, complemented
8C22×#102×C43C211yesmaximal, characteristic, complemented
9C23×D172C2211yescharacteristic
10C23×C22⋊D43—21no—
11C23×C22⋊D43—21no—
12C23×C43⋊C8C2211yescharacteristic
13C2×#13063321—24no—
14C2×#13063321—22no—
15C2×#13063321—24no—
16C2×#13063321C2214yes—
17C22×C4⋊Dic43—21no—
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063247—24no—
21C2×#13063247C2214yescomplemented
22C2×#13063246—24no—
23C2×#13063246C2214yescomplemented
24C2×#13063245—24no—
25C2×#13063245C2214yescomplemented
26#14582798—22no—
27#14582798C2214yescomplemented
28C2×C43⋊#95—21no—
29#14582653C2214yescomplemented
30C23×D4×C43C2211yescharacteristic
31C23×C8×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C2×#102×C43—24no—
34C2×#102×C43C2214yescomplemented
35C24×D43—21no—
36C22×D172—22no—
37C22×D172—22no—
38C22×D172—22no—
39C22×D172—22no—
40C22×D172—22no—
41C22×D172—21no—
42C22×D172D414yes—
43C22×D172C2312yes—
44C22×C22⋊D43—28no—
45C22×C22⋊D43—28no—
46C22×C22⋊D43—24no—
47C22×C22⋊D43—24no—
48C22×C22⋊D43—44no—
49C22×C22⋊D43—44no—
50C22×C22⋊D43—44no—
51C22×C22⋊D43—44no—
52C23×Dic43—21no—
53C23×Dic43D411yescharacteristic
54C23×Dic43D411yescharacteristic
55C22×C43⋊C8—22no—
56C22×C43⋊C8—22no—
57C22×C43⋊C8—22no—
58C22×C43⋊C8C2312yes—
59#13063321—216no—
60#13063321—28no—
61#13063321—28no—
62C2×C4⋊Dic43—22no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—24no—
66C2×C4⋊Dic43—44no—
67C2×C4⋊Dic43C2312yes—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43D412yes—
71C2×C4×Dic43C2312yes—
72#13063247—28no—
73#13063246—28no—
74#13063245—28no—
75C43⋊#95—24no—
76C25×C43—21no—
77C22×D4×C43—22no—
78C22×D4×C43—22no—
79C22×D4×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—22no—
82C22×D4×C43—22no—
83C22×D4×C43D414yes—
84C22×D4×C43C2312yes—
85C23×C4×C43—21no—
86C23×C4×C43C2311yescharacteristic
87C22×C8×C43—22no—
88C22×C8×C43—22no—
89C22×C8×C43—22no—
90C22×C8×C43C2312yes—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43D414yescomplemented
94C2×C4⋊C4×C43C2312yes—
95#102×C43—28no—
96C24×C43—24no—
97C24×C43—22no—
98C24×C43—42no—
99C24×C43—42no—
100C24×C43—42no—
101C24×C43—42no—
102C24×C43—42no—
103C24×C43—42no—
104C24×C43C2×D411yescharacteristic
105C23×D43—24no—
106C23×D43—22no—
107C23×D43—42no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43—42no—
111C23×D43—42no—
112C23×D43—42no—
113C2×D4×C43—24no—
114C2×D4×C43—22no—
115C2×D4×C43—28no—
116C2×D4×C43—28no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—42no—
122C2×D4×C43—44no—
123C2×D4×C43—44no—
124C2×D4×C43—42no—
125C2×D4×C43C2×D414yes—
126C22×C4×C43—24no—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4112yes—
135C22×C4×C43#4112yes—
136C22×C4×C43#4112yes—
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—216no—
139C2×C22⋊D43—216no—
140C2×C22⋊D43—48no—
141C2×C22⋊D43—48no—
142C2×C22⋊D43—432no—
143C2×C22⋊D43—432no—
144C2×C22⋊D43—48no—
145C2×C22⋊D43—48no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—42no—
154C22×Dic43D814yes—
155C22×Dic43SD1614yes—
156C22×Dic43C2×D412yes—
157C22×Dic43C2×D412yes—
158C2×D172—24no—
159C2×D172—22no—
160C2×D172—28no—
161C2×D172—28no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172—42no—
167C2×D172—44no—
168C2×D172—44no—
169C2×D172—42no—
170C2×D172C2×D414yes—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—44no—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43C2×D414yescomplemented
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—42no—
181C4⋊Dic43—48no—
182C4×Dic43—24no—
183C4×Dic43—22no—
184C4×Dic43—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—44no—
189C23×C43—24no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—48no—
197C23×C43—48no—
198C23×C43—48no—
199C23×C43—84no—
200C23×C43—84no—
201C23×C43—84no—
202C23×C43—84no—
203C23×C43#12012yes—
204C23×C43#12112yes—
205C23×C43#12412yes—
206C23×C43C2×D812yes—
207C23×C43C2×SD1612yes—
208C23×C43AGL(1,ℤ/8)12yes—
209C23×C43AGL(1,ℤ/8)12yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—24no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—42no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—48no—
219C22×D43—48no—
220C22×D43—48no—
221C22×D43—84no—
222C22×D43—84no—
223C22×D43—84no—
224C22×D43—84no—
225D4×C43—24no—
226D4×C43—24no—
227D4×C43—42no—
228D4×C43—42no—
229D4×C43—48no—
230C2×C4×C43—24no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—48no—
234C2×C4×C43#12012yes—
235C2×C4×C43#12114yes—
236C2×C4×C43#12112yes—
237C2×C4×C43#12114yes—
238C2×C4×C43#12314yes—
239C2×C4×C43#12314yes—
240C2×C4×C43#12412yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—432no—
248C22⋊D43—432no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—28no—
254C2×Dic43—28no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—84no—
259C2×Dic43C2×D814yes—
260C2×Dic43C2×SD1614yes—
261D172—24no—
262D172—24no—
263D172—42no—
264D172—42no—
265D172—48no—
266C8×C43—42no—
267C43⋊C8—42no—
268C2×#2041—431nomaximal, Sylow
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—82no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43—82no—
276C22×C43—816no—
277C22×C43#39414yes—
278C22×C43#44714yes—
279C22×C43#45014yes—
280C22×C43#45914yes—
281C22×C43#46014yes—
282C22×C43#48614yes—
283C22×C43#49014yes—
284C22×C43C2×#12011yescharacteristic
285C22×C43C2×#12111yescharacteristic
286C22×C43C2×#12411yescharacteristic
287C22×C43C22×D811yescharacteristic
288C22×C43C22×SD1611yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C2×D43—44no—
292C2×D43—44no—
293C2×D43—44no—
294C2×D43—82no—
295C2×D43—82no—
296C2×D43—82no—
297C2×D43—82no—
298C2×D43—816no—
299C4×C43—44no—
300C4×C43#39414yes—
301C4×C43C2×#12111yescharacteristic
302C4×C43C2×#12111yescharacteristic
303C4×C43C2×#12311yescharacteristic
304C4×C43C2×#12311yescharacteristic
305Dic43—24no—
306Dic43—24no—
307Dic43—82no—
308C22×#127—431no—
309C22×#102—431no—
310C22×#102—431no—
311C22×#102—431no—
312C22×#102D4311yescharacteristic, complemented
313C2×#389—431no—
314#2041—438no—
315C2×#336—431no—
316C2×C43—84no—
317C2×C43#204118yescomplemented
318C2×C43C2×#39411yescharacteristic
319C2×C43C2×#44711yescharacteristic
320C2×C43C2×#45011yescharacteristic
321C2×C43C2×#45911yescharacteristic
322C2×C43C2×#46011yescharacteristic
323C2×C43C2×#48611yescharacteristic
324C2×C43C2×#49011yescharacteristic
325D43—84no—
326C23×D4—431no—
327C23×D4—861no—
328C23×D4—861no—
329C23×D4C2×D4311yescharacteristic
330C23×C8—431no—
331C23×C8C2×D4311yescharacteristic
332C2×#127—434no—
333C2×#127—862no—
334C2×#127—864no—
335C2×#127—864no—
336C22×C4⋊C4—431no—
337C22×C4⋊C4—861no—
338C22×C4⋊C4C2×D4311yescharacteristic
339C22×C42—431no—
340C2×#102—24no—
341C2×#102—434no—
342C2×#102—434no—
343C2×#102—434no—
344C2×#102—864no—
345C2×#102—864no—
346C2×#102—864no—
347C2×#102C2×D4314yescomplemented
348#389—434no—
349#389—862no—
350C2×#95—861no—
351#336—434no—
352C43C2×#204111yescharacteristic, complemented, Sylow
353C25—21no—
354C25—861no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—434no—
362C22×D4—432no—
363C22×D4—864no—
364C22×D4—864no—
365C22×D4—868no—
366C22×D4—868no—
367C22×D4—862no—
368C22×D4—862no—
369C22×D4—861no—
370C22×D4—862no—
371C22×D4—862no—
372C22×D4—862no—
373C22×D4—1724no—
374C22×D4—1724no—
375C22×D4—1724no—
376C22×D4—1724no—
377C22×D4D17214yes—
378C22×D4C22×D4312yes—
379C23×C4—21no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—861no—
383C23×C4C22×D4311yescharacteristic
384C22×C8—22no—
385C22×C8—22no—
386C22×C8—22no—
387C22×C8—432no—
388C22×C8—862no—
389C22×C8—862no—
390C22×C8—862no—
391C22×C8C22×D4312yes—
392#127—868no—
393#127—8616no—
394#127—868no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—432no—
398C2×C4⋊C4—862no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—864no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—1724no—
403C2×C4⋊C4C22⋊D4314yescomplemented
404C2×C4⋊C4C22×D4312yes—
405C2×C42—432no—
406C2×C42—432no—
407C2×C42—862no—
408C2×C42—862no—
409#102—28no—
410#102—868no—
411#102—868no—
412#102—868no—
413#95—864no—
414C24—24no—
415C24—22no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—864no—
423C24—862no—
424C24—1722no—
425C24—1722no—
426C24—1722no—
427C24—1722no—
428C24—1722no—
429C24—1722no—
430C24D4×D4311yescharacteristic
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—434no—
444C2×D4—8616no—
445C2×D4—8616no—
446C2×D4—864no—
447C2×D4—868no—
448C2×D4—868no—
449C2×D4—862no—
450C2×D4—862no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4—1728no—
455C2×D4—1728no—
456C2×D4—17232no—
457C2×D4—1728no—
458C2×D4—1728no—
459C2×D4—17232no—
460C2×D4—1722no—
461C2×D4—1724no—
462C2×D4—1724no—
463C2×D4—1722no—
464C2×D4C2×D17214yes—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—434no—
470C22×C4—434no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4C2×D17212yes—
482C22×C4#1062189812yes—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4312yes—
485C22×C4#1062190012yes—
486C22×C4#1062190012yes—
487C22×C4C2×C22⋊D4312yes—
488C22×C4C23×D4311yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—44no—
493C2×C8—862no—
494C2×C8—862no—
495C2×C8—862no—
496C2×C8—1724no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—1728no—
502C4⋊C4—1722no—
503C4⋊C4C2×C22⋊D4314yescomplemented
504C42—864no—
505C42—862no—
506C42—862no—
507C23—24no—
508C23—48no—
509C23—48no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—48no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—864no—
522C23—3444no—
523C23—3444no—
524C23—3444no—
525C23—3444no—
526C23—1728no—
527C23—1728no—
528C23—1722no—
529C23—1722no—
530C23—1722no—
531C23—1722no—
532C23—1722no—
533C23—1722no—
534C23—1728no—
535C23#1306329512yes—
536C23#1306329712yes—
537C23#1306331112yes—
538C23D8×D4312yes—
539C23SD16×D4312yes—
540C23#1306334912yes—
541C23#1306335212yes—
542C23C2×D4×D4311yescharacteristic
543D4—24no—
544D4—24no—
545D4—48no—
546D4—42no—
547D4—42no—
548D4—864no—
549D4—864no—
550D4—17232no—
551D4—17232no—
552D4—1728no—
553D4—1722no—
554D4—1722no—
555C2×C4—24no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—434no—
560C2×C4—434no—
561C2×C4—868no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—868no—
567C2×C4—3444no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4#1306329512yes—
572C2×C4#1306329614yes—
573C2×C4#1306329712yes—
574C2×C4#1306329914yes—
575C2×C4#1306330714yes—
576C2×C4#1306330914yes—
577C2×C4#1306331112yes—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C22×C22⋊D4311yescharacteristic
580C2×C4C22×D17211yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4C2×#1062189811yescharacteristic
584C8—42no—
585C8—1722no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—816no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—3442no—
595C22—34416no—
596C22—3442no—
597C22—3442no—
598C22—3442no—
599C22—1724no—
600C22—1724no—
601C22—1724no—
602C22#1458281514yes—
603C22#1458303414yes—
604C22#1458305114yes—
605C22#1458309214yes—
606C22#1458309714yes—
607C22#1458324414yes—
608C22#1458326214yes—
609C22C2×#1306329511yescharacteristic
610C22C2×#1306329711yescharacteristic
611C22C2×#1306331111yescharacteristic
612C22C2×D8×D4311yescharacteristic
613C22C2×SD16×D4311yescharacteristic
614C22C2×#1306334911yescharacteristic
615C22C2×#1306335211yescharacteristic
616C4—44no—
617C4—864no—
618C4—864no—
619C4—3442no—
620C4#1458281514yes—
621C4C2×#1306329611yescharacteristic
622C4C2×#1306329911yescharacteristic
623C4C2×#1306330711yescharacteristic
624C4C2×#1306330911yescharacteristic
625C2—84no—
626C2—3444no—
627C2#1913582818yesdirect product factor
628C2C2×#1458281511yescharacteristic
629C2C2×#1458303411yescharacteristic
630C2C2×#1458305111yescharacteristic
631C2C2×#1458309211yescharacteristic
632C2C2×#1458309711yescharacteristic
633C2C2×#1458324411yescharacteristic
634C2C2×#1458326211yescharacteristic
subgroupG/H
centerC24D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063321C2
hypercenterC22×#102D43
hypocenterC43C2×#2041
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#13063247C2semidirect
3. C22×#13063246C2semidirect
4. C22×#13063245C2semidirect
5. C2×#14582798C2semidirect
6. #19135828C2direct (N × H)
7. C2×#14582653C2semidirect
8. C22×#102×C43C2semidirect
21. C2×#13063247C22semidirect
23. C2×#13063246C22semidirect
25. C2×#13063245C22semidirect
27. #14582798C22semidirect
29. #14582653C22semidirect
34. C2×#102×C43C22semidirect
93. C2×C4⋊C4×C43D4semidirect
177. C4⋊C4×C43C2×D4semidirect
312. C22×#102D43semidirect
317. C2×C43#2041semidirect
347. C2×#102C2×D43semidirect
352. C43C2×#2041semidirect
403. C2×C4⋊C4C22⋊D43semidirect
503. C4⋊C4C2×C22⋊D43semidirect
627. C2#19135828direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633212
C22×#130632472
C22×#130632462
C22×#130632452
C2×#145827982
#191358282
C2×#145826532
C22×#102×C432
C2×#204143