Finite Group Databasebeta

← C2×#19133641 #25068845

Subgroups — C2×#19133641 #25068845

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583487C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3C2×#14583217C211yesmaximal, characteristic, complemented
4#19133641C218yesmaximal, direct product factor
5C2×#14582635C211yesmaximal, characteristic, complemented
6C2×#14582632C211yesmaximal, characteristic, complemented
7C2×#14582623C211yesmaximal, characteristic, complemented
8C2×C43×#399C211yesmaximal, characteristic, complemented
9#14583487—22no—
10#14583487—22no—
11#14583487—22no—
12#14583487C2214yes—
13C2×#13063318—21no—
14C2×#13063311—21no—
15C2×#13063307—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063298—21no—
19C2×#13063294—21no—
20C2×C4×C22⋊D43—21no—
21#14583234—22no—
22#14583234C2214yescomplemented
23#14583217—22no—
24#14583217C2214yescomplemented
25C2×#13063258—21no—
26C2×#13063256—21no—
27C2×#13063248—21no—
28C2×#13063245—21no—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582635C2214yescomplemented
32#14582632C2214yescomplemented
33#14582623C2214yescomplemented
34C22×C4⋊C4×C43—21no—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43—21no—
37C22×C22⋊C4×C43C2211yescharacteristic
38C43×#399—22no—
39C43×#399C2214yescomplemented
40C2×#95×C43C2211yescharacteristic
41C22×Dic86D411yescharacteristic
42C22×D172D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C22×C22⋊D43—21no—
46C22×C4×D43—21no—
47C22×C43⋊C8—21no—
48C22×C43⋊C8—21no—
49#13063318—24no—
50#13063318—24no—
51#13063311—24no—
52#13063311—24no—
53#13063307—24no—
54#13063307—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063299—21no—
60#13063299—21no—
61#13063299D412yes—
62#13063299C2312yes—
63#13063298—24no—
64#13063298—24no—
65#13063294—24no—
66#13063294—24no—
67C4×C22⋊D43—24no—
68C4×C22⋊D43—24no—
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43D411yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×C4×Dic43—21no—
79#13063258—24no—
80#13063256—24no—
81#13063248—24no—
82#13063245—24no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85C22⋊(C43⋊C8)C2312yes—
86C22⋊(C43⋊C8)C2312yes—
87C25×C43D411yescharacteristic
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C23×C4×C43D411yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—24no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—44no—
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—24no—
105C2×C22⋊C4×C43—44no—
106C2×C22⋊C4×C43D412yes—
107C2×C22⋊C4×C43C2312yes—
108#95×C43—21no—
109#95×C43C2312yes—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—21no—
113C24×C43—22no—
114C24×C43—42no—
115C24×C43—42no—
116C24×C43C2×D411yescharacteristic
117C24×C43C2×D412yes—
118C23×D43—21no—
119C22×C4×C43—24no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×C4×C43—42no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43—22no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—42no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—82no—
146C2×C22⋊D43—82no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—42no—
152C2×D172C2×D412yes—
153C2×C4×D43—24no—
154C2×C4×D43—82no—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86C2×D412yes—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—48no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43—41no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—48no—
168C22⋊Dic43—24no—
169C22⋊Dic43—24no—
170C22⋊Dic43—22no—
171C22⋊Dic43—22no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43C2×D412yes—
178C4⋊Dic43C2×D412yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182C4×Dic43—24no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—42no—
186C2×C43⋊C8—42no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—48no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—81no—
200C23×C43—81no—
201C23×C43—84no—
202C23×C43#12011yescharacteristic
203C23×C43#12011yescharacteristic
204C23×C43#13512yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—48no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—81no—
228C2×C4×C43—82no—
229C2×C4×C43—82no—
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—44no—
237C22⋊D43—84no—
238C22⋊D43—84no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245D172—42no—
246D172—81no—
247C4×D43—84no—
248Dic86—42no—
249Dic86—81no—
250C43⋊C8—42no—
251C43⋊C8—42no—
252C2×#1618—431nomaximal, Sylow
253C22×C43—24no—
254C22×C43—24no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—44no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—82no—
264C22×C43—84no—
265C22×C43—84no—
266C22×C43#45212yes—
267C22×C43#45212yes—
268C22×C43#45312yes—
269C22×C43#45812yes—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—84no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—44no—
282C4×C43—42no—
283C4×C43—82no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287C2×#538—431no—
288C2×#484—431no—
289C2×#481—431no—
290C2×#399D4311yescharacteristic, complemented
291#1618—438no—
292C2×#328—431no—
293C2×#327—431no—
294C2×#323—431no—
295C2×C43—21no—
296C2×C43—21no—
297C2×C43—22no—
298C2×C43—82no—
299C2×C43#161814yescomplemented
300C2×C43C2×#45211yescharacteristic
301C2×C43C2×#45311yescharacteristic
302C2×C43C2×#45811yescharacteristic
303D43—82no—
304#538—434no—
305#538—862no—
306#538—862no—
307#538—862no—
308C2×#126—861no—
309C2×#124—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×#121—431no—
313C2×#121—861no—
314C2×#120—861no—
315C2×C4×D4—861no—
316C22×C4⋊C4—21no—
317C22×C4⋊C4C2×D4311yescharacteristic
318C22×C22⋊C4—21no—
319C22×C22⋊C4C2×D4311yescharacteristic
320#484—434no—
321#484—862no—
322#481—434no—
323#481—862no—
324C2×#107—861no—
325C2×#106—861no—
326C2×#103—861no—
327C2×#102—861no—
328C2×C22⋊C8—431no—
329C2×C22⋊C8—431no—
330#399—22no—
331#399C2×D4314yescomplemented
332C2×#95C2×D4311yescharacteristic
333#328—434no—
334#327—434no—
335#323—434no—
336C43C2×#161811yescharacteristic, complemented, Sylow
337C25C22⋊D4311yescharacteristic
338C22×Q8—431no—
339C22×D4—431no—
340C22×D4—861no—
341C22×D4—861no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—861no—
346C23×C4C22⋊D4311yescharacteristic
347C23×C4C22×D4311yescharacteristic
348C22×C8—861no—
349C22×C8—861no—
350#126—864no—
351#126—864no—
352#124—864no—
353#124—864no—
354#123—864no—
355#123—864no—
356C22⋊Q8—432no—
357C22⋊Q8—432no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360#121—432no—
361#121—432no—
362#121—864no—
363#121—864no—
364#121—861no—
365#121—861no—
366#120—864no—
367#120—864no—
368C4×D4—864no—
369C4×D4—864no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4C22⋊D4312yes—
394C2×C22⋊C4C22×D4312yes—
395C2×C42—861no—
396#107—864no—
397#106—864no—
398#103—864no—
399#102—864no—
400C22⋊C8—432no—
401C22⋊C8—432no—
402C22⋊C8—861no—
403C22⋊C8—861no—
404#95—21no—
405#95C22×D4312yes—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24—42no—
411C24—42no—
412C24—861no—
413C24C2×C22⋊D4311yescharacteristic
414C24C2×C22⋊D4312yes—
415C2×Q8—432no—
416C2×Q8—861no—
417C2×Q8—1722no—
418C2×D4—432no—
419C2×D4—864no—
420C2×D4—864no—
421C2×D4—862no—
422C2×D4—862no—
423C2×D4—861no—
424C2×D4—3442no—
425C2×D4—3442no—
426C2×D4—1722no—
427C2×D4—1722no—
428C2×D4—1722no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—864no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—3442no—
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4C2×C22⋊D4312yes—
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—862no—
455C2×C8—862no—
456C2×C8—1722no—
457C2×C8—1722no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—48no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—432no—
464C4⋊C4—432no—
465C4⋊C4—864no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—48no—
475C22⋊C4—864no—
476C22⋊C4—864no—
477C22⋊C4—864no—
478C22⋊C4—862no—
479C22⋊C4—862no—
480C22⋊C4—862no—
481C22⋊C4—862no—
482C42—864no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—48no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23—862no—
499C23—1722no—
500C23—1722no—
501C23—1722no—
502C23#1306329311yescharacteristic
503C23#1306329311yescharacteristic
504C23#1306334512yes—
505C23#1306335612yes—
506C23C22×C22⋊D4311yescharacteristic
507Q8—3441no—
508Q8—1722no—
509D4—3441no—
510D4—3444no—
511D4—3444no—
512D4—1722no—
513D4—1724no—
514D4—1722no—
515D4—1722no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—862no—
538C2×C4—3444no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4#1306329311yescharacteristic
543C2×C4#1306329311yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C2×D4×D4311yescharacteristic
546C8—1722no—
547C8—1722no—
548C22—21no—
549C22—21no—
550C22—24no—
551C22—24no—
552C22—21no—
553C22—21no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—82no—
559C22—84no—
560C22—84no—
561C22—3444no—
562C22—1722no—
563C22—1722no—
564C22—1722no—
565C22#1458305912yes—
566C22#1458305912yes—
567C22#1458306612yes—
568C22#1458308812yes—
569C22C2×#1306329311yescharacteristic
570C22C2×#1306334511yescharacteristic
571C22C2×#1306335611yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—44no—
577C4—42no—
578C4—82no—
579C4—1722no—
580C4—1722no—
581C4—1722no—
582C2—21no—
583C2—21no—
584C2—22no—
585C2—82no—
586C2—3442no—
587C2#1913364114yesdirect product factor
588C2C2×#1458305911yescharacteristic
589C2C2×#1458306611yescharacteristic
590C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#399C2
socleC23×C43#120
prime radicalC2×#14583487C2
hypercenterC2×#399D43
hypocenterC43C2×#1618
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
3. C2×#14583217C2semidirect
4. #19133641C2direct (N × H)
5. C2×#14582635C2semidirect
6. C2×#14582632C2semidirect
7. C2×#14582623C2semidirect
8. C2×C43×#399C2semidirect
22. #14583234C22semidirect
24. #14583217C22semidirect
31. #14582635C22semidirect
32. #14582632C22semidirect
33. #14582623C22semidirect
39. C43×#399C22semidirect
290. C2×#399D43semidirect
299. C2×C43#1618semidirect
331. #399C2×D43semidirect
336. C43C2×#1618semidirect
587. C2#19133641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834872
C2×#145832342
C2×#145832172
#191336412
C2×#145826352
C2×#145826322
C2×#145826232
C2×C43×#3992
C2×#161843