Finite Group Databasebeta

← C2×#19135827 #25124263

Subgroups — C2×#19135827 #25124263

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×#14582795C211yesmaximal, characteristic, complemented
6#19135827C218yesmaximal, 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⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4—21no—
19C22×C4×Dic43C2211yescharacteristic
20C2×#13063247—24no—
21C2×#13063247C2214yescomplemented
22C2×#13063246—24no—
23C2×#13063246C2214yescomplemented
24C2×#13063245—24no—
25C2×#13063245C2214yescomplemented
26#14582795—22no—
27#14582795C2214yescomplemented
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—21no—
41C22×D172—22no—
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—21no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43D414yescomplemented
65C2×C4⋊Dic43C2312yes—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—44no—
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—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—21no—
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—22no—
127C22×C4×C43—42no—
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—24no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
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—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—42no—
178C4⋊Dic43—24no—
179C4⋊Dic43—22no—
180C4⋊Dic43C2×D414yescomplemented
181Dic43⋊C4—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—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—84no—
234C2×C4×C43#12012yes—
235C2×C4×C43#12114yes—
236C2×C4×C43#12114yes—
237C2×C4×C43#12112yes—
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—24no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—48no—
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—82no—
300C4×C43#39414yes—
301C4×C43C2×#12111yescharacteristic
302C4×C43C2×#12111yescharacteristic
303C4×C43C2×#12311yescharacteristic
304C4×C43C2×#12311yescharacteristic
305Dic43—24no—
306Dic43—24no—
307Dic43—44no—
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—22no—
357C22×D4—22no—
358C22×D4—21no—
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—862no—
370C22×D4—861no—
371C22×D4—862no—
372C22×D4—862no—
373C22×D4—1724no—
374C22×D4—1724no—
375C22×D4—1724no—
376C22×D4—1724no—
377C22×D4C22⋊D4314yes—
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—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—434no—
399C2×C4⋊C4—432no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—864no—
403C2×C4⋊C4—1724no—
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—42no—
440C2×D4—44no—
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—1724no—
461C2×D4—1722no—
462C2×D4—1724no—
463C2×D4—1722no—
464C2×D4C2×C22⋊D4314yes—
465C22×C4—22no—
466C22×C4—42no—
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—864no—
478C22×C4—862no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4#1062189812yes—
482C22×C4#1062189812yes—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4312yes—
485C22×C4D4×D4312yes—
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—22no—
498C4⋊C4—22no—
499C4⋊C4—42no—
500C4⋊C4—434no—
501C4⋊C4—864no—
502C4⋊C4—862no—
503C4⋊C4—1728no—
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#1306329312yes—
536C23#1306329812yes—
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—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—84no—
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—864no—
568C2×C4—1728no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4#1306329312yes—
572C2×C4#1306329714yes—
573C2×C4#1306329812yes—
574C2×C4#1306329814yes—
575C2×C4#1306330714yes—
576C2×C4#1306330814yes—
577C2×C4#1306331112yes—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4C22×C22⋊D4311yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4C2×#1062189811yescharacteristic
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#1458281414yes—
603C22#1458303114yes—
604C22#1458304814yes—
605C22#1458309314yes—
606C22#1458309814yes—
607C22#1458324414yes—
608C22#1458326214yes—
609C22C2×#1306329311yescharacteristic
610C22C2×#1306329811yescharacteristic
611C22C2×#1306331111yescharacteristic
612C22C2×D8×D4311yescharacteristic
613C22C2×SD16×D4311yescharacteristic
614C22C2×#1306334911yescharacteristic
615C22C2×#1306335211yescharacteristic
616C4—82no—
617C4—864no—
618C4—864no—
619C4—1724no—
620C4#1458281414yes—
621C4C2×#1306329711yescharacteristic
622C4C2×#1306329811yescharacteristic
623C4C2×#1306330711yescharacteristic
624C4C2×#1306330811yescharacteristic
625C2—84no—
626C2—3444no—
627C2#1913582718yesdirect product factor
628C2C2×#1458281411yescharacteristic
629C2C2×#1458303111yescharacteristic
630C2C2×#1458304811yescharacteristic
631C2C2×#1458309311yescharacteristic
632C2C2×#1458309811yescharacteristic
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×#14582795C2semidirect
6. #19135827C2direct (N × H)
7. C2×#14582653C2semidirect
8. C22×#102×C43C2semidirect
21. C2×#13063247C22semidirect
23. C2×#13063246C22semidirect
25. C2×#13063245C22semidirect
27. #14582795C22semidirect
29. #14582653C22semidirect
34. C2×#102×C43C22semidirect
64. C2×C4⋊Dic43D4semidirect
180. C4⋊Dic43C2×D4semidirect
312. C22×#102D43semidirect
317. C2×C43#2041semidirect
347. C2×#102C2×D43semidirect
352. C43C2×#2041semidirect
627. C2#19135827direct (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×#145827952
#191358272
C2×#145826532
C22×#102×C432
C2×#204143