Finite Group Databasebeta

← C2×#19133533 #25068773

Subgroups — C2×#19133533 #25068773

Order 11008.

1372 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583528C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic
3C2×#14582813C211yesmaximal, characteristic
4#19133533C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582636C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#450C211yesmaximal, characteristic
9C22×#10621883—21no—
10#14583528—22no—
11#14583528—22no—
12#14583528—22no—
13#14583528C2214yescomplemented
14C2×#13063324—21no—
15C2×#13063323—21no—
16C2×#13063315—21no—
17C2×#13063315—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063302—21no—
20C2×#13063281—21no—
21C22×Dic43⋊C4C2211yescharacteristic
22C22×C22⋊Dic43—21no—
23C22×C22⋊Dic43—21no—
24#14583050—22no—
25#14583050C2214yes—
26C2×#13063246—21no—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28#14582813—22no—
29#14582813C2214yes—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yescomplemented
32#14582636C2214yescomplemented
33#14582624C2214yescomplemented
34C23×D4×C43C2211yescharacteristic
35C22×SD16×C43—21no—
36C2×C22⋊Q8×C43C2211yescharacteristic
37C43×#450—22no—
38C43×#450C2214yes—
39C2×#102×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C2×#10621883—24no—
47C2×#10621883—44no—
48C22×C43⋊C8—21no—
49#13063324—24no—
50#13063324—24no—
51#13063323—24no—
52#13063323—24no—
53#13063315—24no—
54#13063315—24no—
55#13063315—24no—
56#13063315—24no—
57#13063304—21no—
58#13063304—21no—
59#13063304D412yes—
60#13063304C2312yes—
61#13063302—24no—
62#13063302—24no—
63#13063281—24no—
64#13063281—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—21no—
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D412yes—
77C2×Dic43⋊C4C2312yes—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—24no—
80C2×C22⋊Dic43—24no—
81C2×C22⋊Dic43—44no—
82C2×C22⋊Dic43—44no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063246—24no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)C2312yes—
88C43⋊#95—21no—
89C43⋊#95C2312yes—
90C25×C43—21no—
91C22×Q8×C43D411yescharacteristic
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—44no—
98C22×D4×C43C2312yes—
99C23×C4×C43C2311yescharacteristic
100C2×SD16×C43—24no—
101C2×SD16×C43—44no—
102C22×C8×C43—21no—
103C22⋊Q8×C43—21no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43D412yes—
106C22⋊Q8×C43C2312yes—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C22⋊C4×C43—21no—
110#102×C43—24no—
111C22⋊C8×C43—21no—
112C22⋊C8×C43C2312yes—
113C24×C43—24no—
114C24×C43—22no—
115C24×C43—42no—
116C24×C43—42no—
117C24×C43—42no—
118C24×C43—41no—
119C24×C43—41no—
120C24×C43—42no—
121C24×C43—42no—
122C24×C43C2×D411yescharacteristic
123C2×Q8×C43—21no—
124C2×Q8×C43—42no—
125C2×Q8×C43C2×D412yes—
126C2×D4×C43—24no—
127C2×D4×C43—24no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—44no—
131C2×D4×C43—44no—
132C2×D4×C43—42no—
133C2×D4×C43—42no—
134C2×D4×C43—44no—
135C2×D4×C43—44no—
136C2×D4×C43—41no—
137C2×D4×C43—41no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—42no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43SD1614yescomplemented
160C22×Dic43C2×D412yes—
161C22×Dic43C2×D412yes—
162C2×Dic86—24no—
163C2×Dic86—21no—
164C2×Dic86—42no—
165C2×Dic86—82no—
166C2×Dic86C2×D412yes—
167SD16×C43—48no—
168C2×C8×C43—22no—
169C2×C8×C43—42no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43C2×D412yes—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—48no—
179C22⋊Dic43—48no—
180#10621883—48no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43C2×D412yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194C4×Dic43—24no—
195C4×Dic43—24no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—42no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—24no—
201C23×C43—42no—
202C23×C43—44no—
203C23×C43—48no—
204C23×C43—48no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—44no—
211C23×C43—84no—
212C23×C43—84no—
213C23×C43—82no—
214C23×C43—82no—
215C23×C43—82no—
216C23×C43—82no—
217C23×C43#12011yescharacteristic
218C23×C43#12011yescharacteristic
219C23×C43C2×SD1612yes—
220C23×C43#13712yes—
221C23×C43C22×D411yescharacteristic
222Q8×C43—42no—
223Q8×C43—81no—
224D4×C43—24no—
225D4×C43—24no—
226D4×C43—42no—
227D4×C43—42no—
228D4×C43—44no—
229D4×C43—44no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—81no—
259C2×Dic43—84no—
260C2×Dic43C2×SD1614yescomplemented
261Dic86—42no—
262Dic86—81no—
263Dic86—84no—
264C8×C43—42no—
265C43⋊C8—42no—
266C2×#1599—431nomaximal, Sylow
267C22×C43—24no—
268C22×C43—24no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—44no—
274C22×C43—44no—
275C22×C43—44no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—88no—
279C22×C43—88no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43#44812yes—
283C22×C43#44812yes—
284C22×C43#45412yes—
285C22×C43B(4,𝔽2)12yes—
286C22×C43C2×#12011yescharacteristic
287C22×C43C22×SD1611yescharacteristic
288C22×C43C2×#13711yescharacteristic
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—42no—
294C4×C43—42no—
295Dic43—24no—
296Dic43—42no—
297Dic43—42no—
298Dic43—42no—
299Dic43—82no—
300C2×#544—431no—
301C2×#450—431no—
302C2×#450D4311yescharacteristic
303C2×#394—431no—
304#1599—438no—
305C2×#328—431no—
306C2×#328—431no—
307C2×#324—431no—
308C2×C43—21no—
309C2×C43—21no—
310C2×C43—22no—
311C2×C43—84no—
312C2×C43#159914yescomplemented
313C2×C43C2×#44811yescharacteristic
314C2×C43C2×#45411yescharacteristic
315C2×C43C2×B(4,𝔽2)11yescharacteristic
316C23×D4C2×D4311yescharacteristic
317C22×SD16—21no—
318C22×SD16—861no—
319#544—434no—
320#544—862no—
321#544—862no—
322#544—862no—
323C2×C4⋊Q8—861no—
324C2×C4⋊Q8—861no—
325C2×#125—861no—
326C2×#125—861no—
327C2×C22⋊Q8—431no—
328C2×C22⋊Q8—861no—
329C2×C22⋊Q8C2×D4311yescharacteristic
330C2×#117—861no—
331C22×C4⋊C4—431no—
332C22×C22⋊C4—861no—
333C22×C22⋊C4—861no—
334#450—22no—
335#450—434no—
336#450—862no—
337#450C2×D4314yes—
338C2×#102—21no—
339C2×#102—861no—
340C2×C22⋊C8—431no—
341C2×C22⋊C8C2×D4311yescharacteristic
342#394—434no—
343#394—862no—
344C2×#95—431no—
345#328—434no—
346#328—434no—
347#324—434no—
348C43C2×#159911yescharacteristic, complemented, Sylow
349C25—21no—
350C22×Q8—431no—
351C22×Q8—861no—
352C22×Q8C22⋊D4311yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—44no—
359C22×D4C22×D4312yes—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—861no—
363C23×C4C22×D4311yescharacteristic
364C2×SD16—24no—
365C2×SD16—44no—
366C2×SD16—864no—
367C2×SD16—1724no—
368C22×C8—21no—
369C22×C8—861no—
370C4⋊Q8—864no—
371C4⋊Q8—864no—
372C4⋊Q8—864no—
373C4⋊Q8—864no—
374#125—864no—
375#125—864no—
376#125—864no—
377#125—864no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—432no—
381C22⋊Q8—432no—
382C22⋊Q8—864no—
383C22⋊Q8—864no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8C22⋊D4312yes—
387C22⋊Q8C22×D4312yes—
388#117—864no—
389#117—864no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—432no—
393C2×C4⋊C4—432no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22⋊D4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—864no—
408C2×C22⋊C4—864no—
409C2×C22⋊C4—1724no—
410C2×C22⋊C4—1724no—
411C2×C42—861no—
412C2×C42—861no—
413#102—24no—
414#102—864no—
415C22⋊C8—21no—
416C22⋊C8—432no—
417C22⋊C8—861no—
418C22⋊C8C22×D4312yes—
419#95—432no—
420#95—861no—
421C24—24no—
422C24—22no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—41no—
427C24—41no—
428C24—42no—
429C24—42no—
430C24D4×D4311yescharacteristic
431C2×Q8—21no—
432C2×Q8—42no—
433C2×Q8—432no—
434C2×Q8—864no—
435C2×Q8—861no—
436C2×Q8—3442no—
437C2×Q8—1722no—
438C2×Q8C2×C22⋊D4312yes—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—41no—
450C2×D4—41no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—434no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—862no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4D4×D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C23×D4311yescharacteristic
475SD16—48no—
476SD16—1728no—
477C2×C8—22no—
478C2×C8—42no—
479C2×C8—862no—
480C2×C8—1722no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—432no—
485C4⋊C4—864no—
486C4⋊C4—864no—
487C4⋊C4—864no—
488C4⋊C4—864no—
489C4⋊C4—864no—
490C4⋊C4—862no—
491C4⋊C4—862no—
492C4⋊C4—861no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4C2×C22⋊D4312yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—862no—
501C22⋊C4—862no—
502C22⋊C4—1728no—
503C22⋊C4—1728no—
504C42—864no—
505C42—864no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—44no—
510C23—42no—
511C23—48no—
512C23—48no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—84no—
520C23—84no—
521C23—82no—
522C23—82no—
523C23—82no—
524C23—82no—
525C23#1306329311yescharacteristic
526C23#1306329311yescharacteristic
527C23SD16×D4312yes—
528C23#1306335412yes—
529C23C2×D4×D4311yescharacteristic
530Q8—42no—
531Q8—81no—
532Q8—3441no—
533Q8—3444no—
534Q8—1722no—
535D4—24no—
536D4—24no—
537D4—42no—
538D4—42no—
539D4—44no—
540D4—44no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—434no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—3444no—
560C2×C4—3441no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4#1306329311yescharacteristic
569C2×C4#1306329311yescharacteristic
570C2×C4C2×D4×D4311yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C8—42no—
573C8—1722no—
574C22—21no—
575C22—21no—
576C22—24no—
577C22—24no—
578C22—21no—
579C22—21no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—82no—
584C22—82no—
585C22—88no—
586C22—88no—
587C22—82no—
588C22—82no—
589C22#1458303612yes—
590C22#1458303612yes—
591C22#1458307012yes—
592C22#1458308512yes—
593C22C2×#1306329311yescharacteristic
594C22C2×SD16×D4311yescharacteristic
595C22C2×#1306335411yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—42no—
602C4—864no—
603C4—3442no—
604C4—1722no—
605C4—1722no—
606C4—1722no—
607C2—21no—
608C2—21no—
609C2—22no—
610C2—84no—
611C2#1913353314yesdirect product factor
612C2C2×#1458303611yescharacteristic
613C2C2×#1458307011yescharacteristic
614C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#450C2
socleC23×C43#120
prime radicalC23×D4×C43C22
hypercenterC2×#450D43
hypocenterC43C2×#1599
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#14583528C2semidirect
4. #19133533C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×#14582636C2semidirect
7. C2×#14582624C2semidirect
13. #14583528C22semidirect
31. #14582637C22semidirect
32. #14582636C22semidirect
33. #14582624C22semidirect
159. C22×Dic43SD16semidirect
260. C2×Dic43C2×SD16semidirect
312. C2×C43#1599semidirect
348. C43C2×#1599semidirect
611. C2#19133533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835282
C2×#145830502
C2×#145828132
#191335332
C2×#145826372
C2×#145826362
C2×#145826242
C2×C43×#4502
C2×#159943