Finite Group Databasebeta

← C2×#19133596 #25068812

Subgroups — C2×#19133596 #25068812

Order 11008.

1308 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583476C211yesmaximal, characteristic
2C2×#14583212C211yesmaximal, characteristic, complemented
3C2×#14582830C211yesmaximal, characteristic, complemented
4#19133596C218yesmaximal, direct product factor
5C2×#14582634C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#480C211yesmaximal, 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⋊C4—21no—
21C22×Dic43⋊C4C2211yescharacteristic
22#14583212—22no—
23#14583212C2214yescomplemented
24C2×#13063258—21no—
25C2×#13063245—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582830—22no—
28#14582830C2214yescomplemented
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582634C2214yescomplemented
32#14582633C2214yescomplemented
33#14582624C2214yescomplemented
34C2×#121×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#480—22no—
37C43×#480C2214yescomplemented
38C2×#107×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⋊C4—24no—
77C2×Dic43⋊C4—44no—
78C2×Dic43⋊C4D412yes—
79C2×Dic43⋊C4C2312yes—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83#13063258—24no—
84#13063245—24no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)C2312yes—
87C43⋊#95—21no—
88C43⋊#95—24no—
89C43⋊#95C2312yes—
90C22×D4×C43—21no—
91C22×D4×C43D411yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94C22×C8×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43D412yes—
98#121×C43C2312yes—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43C2312yes—
106C2×C22⋊C4×C43—21no—
107#107×C43—24no—
108#102×C43—24no—
109C22⋊C8×C43—21no—
110C22⋊C8×C43C2312yes—
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—42no—
118C2×D4×C43—42no—
119C2×D4×C43—42no—
120C2×D4×C43C2×D412yes—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—42no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—24no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—44no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—82no—
142C22×Dic43—24no—
143C22×Dic43—24no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—44no—
154C22×Dic43—42no—
155C22×Dic43D814yes—
156C22×Dic43C2×D412yes—
157C22×Dic43C2×D412yes—
158#10621900—48no—
159#10621900—416no—
160#10621900—48no—
161C2×D172—21no—
162C2×D172—42no—
163C2×D172C2×D412yes—
164C2×C4×D43—24no—
165C2×C4×D43—44no—
166C2×Dic86—24no—
167C2×Dic86—44no—
168C2×C8×C43—22no—
169C2×C8×C43—42no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D412yes—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊Dic43—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—22no—
181(C2×D43)⋊C4—22no—
182C4⋊Dic43—21no—
183C4⋊Dic43C2×D412yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—48no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—42no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43#12011yescharacteristic
199C23×C43#12011yescharacteristic
200C23×C43C2×D812yes—
201C23×C43AGL(1,ℤ/8)12yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—44no—
211D4×C43—81no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—82no—
224C2×C4×C43—82no—
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C22⋊D43—48no—
230C22⋊D43—42no—
231C22⋊D43—42no—
232C22⋊D43—44no—
233C22⋊D43—84no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—48no—
242C2×Dic43—48no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—81no—
249C2×Dic43C2×D814yes—
250D172—42no—
251D172—81no—
252C4×D43—48no—
253Dic86—48no—
254C8×C43—42no—
255C43⋊C8—42no—
256C2×#1610—431nomaximal, Sylow
257C22×C43—24no—
258C22×C43—24no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—84no—
267C22×C43#44712yes—
268C22×C43#44712yes—
269C22×C43#45612yes—
270C22×C43#45812yes—
271C22×C43C2×#12011yescharacteristic
272C22×C43C22×D811yescharacteristic
273C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—84no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—42no—
283C4×C43—82no—
284Dic43—24no—
285Dic43—44no—
286Dic43—42no—
287Dic43—42no—
288C2×#537—431no—
289C2×#480—431no—
290C2×#480D4311yescharacteristic, complemented
291C2×#398—431no—
292#1610—438no—
293C2×#327—431no—
294C2×#327—431no—
295C2×#324—431no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—22no—
299C2×C43—82no—
300C2×C43#161014yescomplemented
301C2×C43C2×#44711yescharacteristic
302C2×C43C2×#45611yescharacteristic
303C2×C43C2×#45811yescharacteristic
304D43—82no—
305C22×#41—861no—
306#537—434no—
307#537—862no—
308#537—862no—
309#537—862no—
310C2×C22⋊Q8—861no—
311C2×C22⋊Q8—861no—
312C2×#121—431no—
313C2×#121—861no—
314C2×#121—861no—
315C2×#121—861no—
316C2×#121C2×D4311yescharacteristic
317C22×C4⋊C4—431no—
318C22×C4⋊C4—861no—
319C22×C4⋊C4C2×D4311yescharacteristic
320#480—22no—
321#480—434no—
322#480—862no—
323#480C2×D4314yescomplemented
324C2×#107—21no—
325C2×#107—861no—
326C2×#102—21no—
327C2×#102—861no—
328C2×C22⋊C8—431no—
329C2×C22⋊C8C2×D4311yescharacteristic
330#398—434no—
331#398—862no—
332C2×#95—431no—
333C2×#95—861no—
334#327—434no—
335#327—434no—
336#324—434no—
337C43C2×#161011yescharacteristic, complemented, Sylow
338C2×#41—864no—
339C2×#41—864no—
340C2×#41—1724no—
341C2×#41—1724no—
342C22×Q8—861no—
343C22×D4—21no—
344C22×D4—431no—
345C22×D4—861no—
346C22×D4—861no—
347C22×D4—861no—
348C22×D4C22⋊D4311yescharacteristic
349C23×C4—21no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4—861no—
355C23×C4C22×D4311yescharacteristic
356C22×C8—21no—
357C22×C8—861no—
358C22⋊Q8—864no—
359C22⋊Q8—864no—
360C22⋊Q8—864no—
361C22⋊Q8—864no—
362#121—21no—
363#121—21no—
364#121—432no—
365#121—432no—
366#121—864no—
367#121—864no—
368#121—864no—
369#121—864no—
370#121—864no—
371#121—864no—
372#121—861no—
373#121—861no—
374#121C22⋊D4312yes—
375#121C22×D4312yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—432no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—1724no—
391C2×C4⋊C4C22⋊D4311yescharacteristic
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397#107—24no—
398#107—864no—
399#102—24no—
400#102—864no—
401C22⋊C8—21no—
402C22⋊C8—432no—
403C22⋊C8—861no—
404C22⋊C8C22×D4312yes—
405#95—432no—
406#95—864no—
407#95—861no—
408C24—21no—
409C24—861no—
410C24D4×D4311yescharacteristic
411#41—1728no—
412#41—1728no—
413#41—17216no—
414C2×Q8—864no—
415C2×Q8—1724no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—432no—
423C2×D4—864no—
424C2×D4—864no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—861no—
428C2×D4—3442no—
429C2×D4—1722no—
430C2×D4—1724no—
431C2×D4—1722no—
432C2×D4—1722no—
433C2×D4C2×C22⋊D4312yes—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—434no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—864no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—862no—
448C22×C4—861no—
449C22×C4—864no—
450C22×C4—864no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4—1722no—
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C23×D4311yescharacteristic
465C2×C8—22no—
466C2×C8—42no—
467C2×C8—862no—
468C2×C8—1722no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—432no—
475C4⋊C4—864no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—861no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—1728no—
482C4⋊C4C2×C22⋊D4312yes—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—864no—
486C22⋊C4—864no—
487C22⋊C4—862no—
488C22⋊C4—862no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—862no—
496C23—1722no—
497C23—1722no—
498C23—1722no—
499C23#1306329311yescharacteristic
500C23#1306329311yescharacteristic
501C23D8×D4312yes—
502C23#1306334912yes—
503C23C2×D4×D4311yescharacteristic
504Q8—1728no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510D4—3441no—
511D4—3444no—
512D4—1722no—
513D4—1728no—
514D4—1722no—
515D4—1722no—
516D4—1724no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—434no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—864no—
534C2×C4—864no—
535C2×C4—864no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—3441no—
539C2×C4—1728no—
540C2×C4—1728no—
541C2×C4—1722no—
542C2×C4—1728no—
543C2×C4—1722no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4#1306329311yescharacteristic
548C2×C4#1306329311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4C22×C22⋊D4311yescharacteristic
551C8—42no—
552C8—1722no—
553C22—21no—
554C22—21no—
555C22—24no—
556C22—24no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—84no—
563C22—3444no—
564C22—1722no—
565C22—1722no—
566C22—1722no—
567C22#1458303112yes—
568C22#1458303112yes—
569C22#1458308012yes—
570C22#1458308812yes—
571C22C2×#1306329311yescharacteristic
572C22C2×D8×D4311yescharacteristic
573C22C2×#1306334911yescharacteristic
574C4—21no—
575C4—21no—
576C4—21no—
577C4—21no—
578C4—42no—
579C4—82no—
580C4—864no—
581C4—1724no—
582C4—1722no—
583C4—1722no—
584C2—21no—
585C2—21no—
586C2—22no—
587C2—82no—
588C2—3442no—
589C2#1913359614yesdirect product factor
590C2C2×#1458303111yescharacteristic
591C2C2×#1458308011yescharacteristic
592C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#480C2
socleC23×C43#120
prime radicalC2×#14583476C2
hypercenterC2×#480D43
hypocenterC43C2×#1610
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#14583212C2semidirect
3. C2×#14582830C2semidirect
4. #19133596C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×#14582633C2semidirect
7. C2×#14582624C2semidirect
8. C2×C43×#480C2semidirect
23. #14583212C22semidirect
28. #14582830C22semidirect
31. #14582634C22semidirect
32. #14582633C22semidirect
33. #14582624C22semidirect
37. C43×#480C22semidirect
290. C2×#480D43semidirect
300. C2×C43#1610semidirect
323. #480C2×D43semidirect
337. C43C2×#1610semidirect
589. C2#19133596direct (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×#145832122
C2×#145828302
#191335962
C2×#145826342
C2×#145826332
C2×#145826242
C2×C43×#4802
C2×#161043