Finite Group Databasebeta

← C2×#19133630 #25068818

Subgroups — C2×#19133630 #25068818

Order 11008.

1264 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583476C211yesmaximal, characteristic
2C2×#14583217C211yesmaximal, characteristic, complemented
3C2×#14582837C211yesmaximal, characteristic, complemented
4#19133630C218yesmaximal, direct product factor
5C2×#14582634C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#481C211yesmaximal, characteristic, complemented
9C22×#10621900—21no—
10#14583476—22no—
11#14583476—22no—
12#14583476—22no—
13#14583476C2214yes—
14C2×#13063303—21no—
15C2×#13063302—21no—
16C2×#13063299C2211yescharacteristic
17C2×#13063298—21no—
18C2×#13063297—21no—
19C2×#13063297—21no—
20C22×Dic43⋊C4C2211yescharacteristic
21#14583217—22no—
22#14583217C2214yescomplemented
23C2×#13063256—21no—
24C2×#13063245—21no—
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26#14582837—22no—
27#14582837C2214yescomplemented
28C2×C43⋊#95—21no—
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582634C2214yescomplemented
32#14582633C2214yescomplemented
33#14582624C2214yescomplemented
34C2×#121×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#481—22no—
37C43×#481C2214yescomplemented
38C2×#106×C43—21no—
39C2×#102×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C2×#10621900—24no—
42C2×#10621900—24no—
43C2×#10621900—44no—
44C2×#10621900—44no—
45C22×Dic86—21no—
46C22×D172D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C22⋊D43—21no—
49C22×C22⋊D43—21no—
50C23×Dic43—21no—
51C23×Dic43—21no—
52C23×Dic43D411yescharacteristic
53C23×Dic43D411yescharacteristic
54C22×C4×D43—21no—
55C22×C43⋊C8—21no—
56#13063303—24no—
57#13063303—24no—
58#13063302—24no—
59#13063302—24no—
60#13063299—21no—
61#13063299—21no—
62#13063299D412yes—
63#13063299C2312yes—
64#13063298—24no—
65#13063298—24no—
66#13063297—24no—
67#13063297—24no—
68#13063297—24no—
69#13063297—24no—
70C2×C4⋊Dic43D411yescharacteristic
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×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81#13063256—24no—
82#13063245—24no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)C2312yes—
85C43⋊#95—21no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95C2312yes—
89C22×D4×C43—21no—
90C22×D4×C43D411yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C22×C8×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43D412yes—
97#121×C43C2312yes—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2312yes—
105C2×C22⋊C4×C43—21no—
106#106×C43—24no—
107#102×C43—24no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110C24×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—42no—
117C2×D4×C43—42no—
118C2×D4×C43—42no—
119C2×D4×C43C2×D412yes—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—44no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2411yescharacteristic
132C2×C22⋊D43—24no—
133C2×C22⋊D43—24no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—44no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—82no—
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—44no—
152C22×Dic43—42no—
153C22×Dic43SD1614yes—
154C22×Dic43C2×D412yes—
155C22×Dic43C2×D412yes—
156#10621900—48no—
157#10621900—416no—
158#10621900—48no—
159C2×D172—21no—
160C2×D172—42no—
161C2×D172C2×D412yes—
162C2×C4×D43—24no—
163C2×C4×D43—44no—
164C2×Dic86—24no—
165C2×Dic86—44no—
166C2×C8×C43—22no—
167C2×C8×C43—42no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D412yes—
174C22⋊C4×C43—22no—
175C22⋊C4×C43—22no—
176C22⋊Dic43—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43C2×D412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—42no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43#12011yescharacteristic
196C23×C43#12011yescharacteristic
197C23×C43C2×SD1612yes—
198C23×C43AGL(1,ℤ/8)12yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204D4×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—44no—
208D4×C43—81no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—44no—
218C2×C4×C43—42no—
219C2×C4×C43—82no—
220C2×C4×C43—82no—
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C22⋊D43—48no—
226C22⋊D43—42no—
227C22⋊D43—42no—
228C22⋊D43—44no—
229C22⋊D43—84no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—48no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—81no—
244C2×Dic43—84no—
245C2×Dic43C2×SD1614yes—
246D172—42no—
247D172—81no—
248C4×D43—48no—
249Dic86—48no—
250C8×C43—42no—
251C43⋊C8—42no—
252C2×#1616—431nomaximal, Sylow
253C22×C43—24no—
254C22×C43—24no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—84no—
263C22×C43#45012yes—
264C22×C43#45012yes—
265C22×C43#45412yes—
266C22×C43#45812yes—
267C22×C43C2×#12011yescharacteristic
268C22×C43C22×SD1611yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—84no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—42no—
279C4×C43—82no—
280Dic43—24no—
281Dic43—42no—
282Dic43—42no—
283Dic43—82no—
284C2×#537—431no—
285C2×#481—431no—
286C2×#481D4311yescharacteristic, complemented
287C2×#400—431no—
288#1616—438no—
289C2×#327—431no—
290C2×#327—431no—
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43—82no—
296C2×C43#161614yescomplemented
297C2×C43C2×#45011yescharacteristic
298C2×C43C2×#45411yescharacteristic
299C2×C43C2×#45811yescharacteristic
300D43—82no—
301C22×#41—861no—
302#537—434no—
303#537—862no—
304#537—862no—
305#537—862no—
306C2×C22⋊Q8—861no—
307C2×C22⋊Q8—861no—
308C2×#121—431no—
309C2×#121—861no—
310C2×#121—861no—
311C2×#121—861no—
312C2×#121C2×D4311yescharacteristic
313C22×C4⋊C4—431no—
314C22×C4⋊C4C2×D4311yescharacteristic
315#481—22no—
316#481—434no—
317#481—862no—
318#481C2×D4314yescomplemented
319C2×#106—21no—
320C2×#106—861no—
321C2×#102—21no—
322C2×#102—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8C2×D4311yescharacteristic
325#400—434no—
326#400—862no—
327C2×#95—431no—
328C2×#95—861no—
329C2×#95—861no—
330#327—434no—
331#327—434no—
332#324—434no—
333C43C2×#161611yescharacteristic, complemented, Sylow
334C2×#41—864no—
335C2×#41—864no—
336C2×#41—1724no—
337C2×#41—1724no—
338C22×Q8—861no—
339C22×D4—21no—
340C22×D4—431no—
341C22×D4—861no—
342C22×D4—861no—
343C22×D4—861no—
344C22×D4C22⋊D4311yescharacteristic
345C23×C4—21no—
346C23×C4—431no—
347C23×C4—431no—
348C23×C4—861no—
349C23×C4—861no—
350C23×C4—861no—
351C23×C4C22×D4311yescharacteristic
352C22×C8—21no—
353C22×C8—861no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356C22⋊Q8—864no—
357C22⋊Q8—864no—
358#121—21no—
359#121—21no—
360#121—432no—
361#121—432no—
362#121—864no—
363#121—864no—
364#121—864no—
365#121—864no—
366#121—864no—
367#121—864no—
368#121—861no—
369#121—861no—
370#121C22⋊D4312yes—
371#121C22×D4312yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—432no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4C22⋊D4311yescharacteristic
386C2×C4⋊C4C22×D4312yes—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391#106—24no—
392#106—864no—
393#102—24no—
394#102—864no—
395C22⋊C8—21no—
396C22⋊C8—432no—
397C22⋊C8—861no—
398C22⋊C8C22×D4312yes—
399#95—432no—
400#95—864no—
401#95—864no—
402#95—861no—
403C24—21no—
404C24—861no—
405C24D4×D4311yescharacteristic
406#41—1728no—
407#41—17216no—
408#41—1728no—
409C2×Q8—864no—
410C2×Q8—1724no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—432no—
418C2×D4—864no—
419C2×D4—864no—
420C2×D4—862no—
421C2×D4—862no—
422C2×D4—861no—
423C2×D4—3442no—
424C2×D4—1722no—
425C2×D4—1724no—
426C2×D4—1722no—
427C2×D4—1722no—
428C2×D4C2×C22⋊D4312yes—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—434no—
436C22×C4—432no—
437C22×C4—432no—
438C22×C4—864no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—862no—
442C22×C4—861no—
443C22×C4—864no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—862no—
447C22×C4—1724no—
448C22×C4—1724no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459C2×C8—22no—
460C2×C8—42no—
461C2×C8—862no—
462C2×C8—1722no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—432no—
469C4⋊C4—864no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—861no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4C2×C22⋊D4312yes—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—862no—
481C22⋊C4—862no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—862no—
489C23—1722no—
490C23—1722no—
491C23—1722no—
492C23#1306329311yescharacteristic
493C23#1306329311yescharacteristic
494C23SD16×D4312yes—
495C23#1306335212yes—
496C23C2×D4×D4311yescharacteristic
497Q8—1728no—
498D4—42no—
499D4—44no—
500D4—42no—
501D4—42no—
502D4—81no—
503D4—3441no—
504D4—3444no—
505D4—1722no—
506D4—1728no—
507D4—1724no—
508D4—1722no—
509D4—1722no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—434no—
523C2×C4—864no—
524C2×C4—864no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—3444no—
530C2×C4—3441no—
531C2×C4—1728no—
532C2×C4—1728no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4#1306329311yescharacteristic
540C2×C4#1306329311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C22×C22⋊D4311yescharacteristic
543C8—42no—
544C8—1722no—
545C22—21no—
546C22—21no—
547C22—24no—
548C22—24no—
549C22—21no—
550C22—21no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—84no—
555C22—3444no—
556C22—1722no—
557C22—1722no—
558C22—1722no—
559C22#1458304812yes—
560C22#1458304812yes—
561C22#1458307012yes—
562C22#1458308812yes—
563C22C2×#1306329311yescharacteristic
564C22C2×SD16×D4311yescharacteristic
565C22C2×#1306335211yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—42no—
571C4—82no—
572C4—864no—
573C4—3442no—
574C4—1722no—
575C4—1722no—
576C2—21no—
577C2—22no—
578C2—21no—
579C2—82no—
580C2—3442no—
581C2#1913363014yesdirect product factor
582C2C2×#1458304811yescharacteristic
583C2C2×#1458307011yescharacteristic
584C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#481C2
socleC23×C43#120
prime radicalC2×#14583476C2
hypercenterC2×#481D43
hypocenterC43C2×#1616
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#14583217C2semidirect
3. C2×#14582837C2semidirect
4. #19133630C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×#14582633C2semidirect
7. C2×#14582624C2semidirect
8. C2×C43×#481C2semidirect
22. #14583217C22semidirect
27. #14582837C22semidirect
31. #14582634C22semidirect
32. #14582633C22semidirect
33. #14582624C22semidirect
37. C43×#481C22semidirect
286. C2×#481D43semidirect
296. C2×C43#1616semidirect
318. #481C2×D43semidirect
333. C43C2×#1616semidirect
581. C2#19133630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834762
C2×#145832172
C2×#145828372
#191336302
C2×#145826342
C2×#145826332
C2×#145826242
C2×C43×#4812
C2×#161643