Finite Group Databasebeta

← C2×#19133590 #25068735

Subgroups — C2×#19133590 #25068735

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583496C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3C2×#14583212C211yesmaximal, characteristic
4#19133590C218yesmaximal, direct product factor
5C2×#14582635C211yesmaximal, characteristic, complemented
6C2×#14582632C211yesmaximal, characteristic
7C2×#14582625C211yesmaximal, characteristic, complemented
8C2×C43×#398C211yesmaximal, characteristic, complemented
9#14583496—22no—
10#14583496—22no—
11#14583496—22no—
12#14583496C2214yes—
13C2×#13063320—21no—
14C2×#13063315—21no—
15C2×#13063310—21no—
16C2×#13063308—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063303—21no—
19C2×#13063299C2211yescharacteristic
20C2×C4×C22⋊D43—21no—
21#14583229—22no—
22#14583229C2214yescomplemented
23#14583212—22no—
24#14583212C2214yes—
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#14582632C2214yes—
33#14582625C2214yescomplemented
34C22×C4⋊C4×C43—21no—
35C22×C4⋊C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43C2211yescharacteristic
37C43×#398—22no—
38C43×#398C2214yescomplemented
39C2×#95×C43—21no—
40C2×#95×C43C2211yescharacteristic
41C22×Dic86D411yescharacteristic
42C22×D172D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C4×D43—21no—
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47#13063320—24no—
48#13063320—24no—
49#13063315—24no—
50#13063315—24no—
51#13063310—24no—
52#13063310—24no—
53#13063308—24no—
54#13063308—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063303—24no—
60#13063303—24no—
61#13063299—21no—
62#13063299—21no—
63#13063299D412yes—
64#13063299C2312yes—
65C4×C22⋊D43—24no—
66C4×C22⋊D43—24no—
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43D411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×C22⋊Dic43—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—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—
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43D411yescharacteristic
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—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—24no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—44no—
103C2×C4⋊C4×C43D412yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2312yes—
106#95×C43—24no—
107#95×C43—21no—
108#95×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C23×D43—21no—
111C22×C4×C43—24no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—42no—
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×D412yes—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—42no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—42no—
145C2×D172C2×D412yes—
146C2×C4×D43—24no—
147C2×C4×D43—82no—
148C2×Dic86—21no—
149C2×Dic86—42no—
150C2×Dic86C2×D412yes—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—48no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—41no—
160C22⋊Dic43—22no—
161C22⋊Dic43—22no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—22no—
166(C2×D43)⋊C4—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43C2×D412yes—
170C4⋊Dic43C2×D412yes—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176C4×Dic43—24no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—42no—
180C2×C43⋊C8—42no—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43#12011yescharacteristic
184C23×C43#12011yescharacteristic
185C23×C43#13512yes—
186C23×C43AGL(1,ℤ/8)12yes—
187C23×C43C22×D411yescharacteristic
188C22×D43—22no—
189C22×D43—42no—
190C22×D43—42no—
191C22×D43—42no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—24no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—48no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—81no—
214C2×C4×C43—82no—
215C2×C4×C43—82no—
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C22⋊D43—42no—
221C22⋊D43—42no—
222C22⋊D43—44no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229D172—42no—
230D172—81no—
231C4×D43—84no—
232Dic86—42no—
233Dic86—81no—
234C43⋊C8—42no—
235C43⋊C8—42no—
236C2×#1609—431nomaximal, Sylow
237C22×C43—24no—
238C22×C43—24no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43#44912yes—
244C22×C43#44912yes—
245C22×C43#45612yes—
246C22×C43#45812yes—
247C22×C43C2×#12011yescharacteristic
248C22×C43C2×#13511yescharacteristic
249C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
250C2×D43—42no—
251C2×D43—42no—
252C2×D43—42no—
253C2×D43—84no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—44no—
259C4×C43—42no—
260C4×C43—42no—
261C4×C43—82no—
262Dic43—42no—
263Dic43—42no—
264Dic43—42no—
265C2×#539—431no—
266C2×#483—431no—
267C2×#480—431no—
268C2×#398D4311yescharacteristic, complemented
269#1609—438no—
270C2×#328—431no—
271C2×#327—431no—
272C2×#324—431no—
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—22no—
276C2×C43#160914yescomplemented
277C2×C43C2×#44911yescharacteristic
278C2×C43C2×#45611yescharacteristic
279C2×C43C2×#45811yescharacteristic
280D43—82no—
281#539—434no—
282#539—862no—
283#539—862no—
284#539—862no—
285C2×#126—861no—
286C2×#125—861no—
287C2×#123—861no—
288C2×#123—861no—
289C2×C22⋊Q8—431no—
290C2×C22⋊Q8—861no—
291C2×#121—431no—
292C2×C4×D4—861no—
293C22×C4⋊C4—21no—
294C22×C4⋊C4C2×D4311yescharacteristic
295C22×C4⋊C4C2×D4311yescharacteristic
296#483—434no—
297#483—862no—
298#480—434no—
299#480—862no—
300C2×#107—861no—
301C2×#106—861no—
302C2×#103—861no—
303C2×#102—861no—
304C2×C22⋊C8—431no—
305C2×C22⋊C8—431no—
306#398—22no—
307#398C2×D4314yescomplemented
308C2×#95—21no—
309C2×#95C2×D4311yescharacteristic
310#328—434no—
311#327—434no—
312#324—434no—
313C43C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8—431no—
315C22×D4—431no—
316C22×D4—861no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—861no—
320C23×C4C22⋊D4311yescharacteristic
321C23×C4C22⋊D4311yescharacteristic
322C23×C4C22×D4311yescharacteristic
323C22×C8—861no—
324C22×C8—861no—
325#126—864no—
326#126—864no—
327#125—864no—
328#125—864no—
329#123—864no—
330#123—864no—
331#123—864no—
332#123—864no—
333C22⋊Q8—432no—
334C22⋊Q8—432no—
335C22⋊Q8—864no—
336C22⋊Q8—864no—
337C22⋊Q8—861no—
338C22⋊Q8—861no—
339#121—432no—
340#121—432no—
341#121—861no—
342#121—861no—
343C4×D4—864no—
344C4×D4—864no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—431no—
357C2×C4⋊C4—431no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4C22⋊D4312yes—
363C2×C4⋊C4C22×D4312yes—
364C2×C4⋊C4C22×D4312yes—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C42—861no—
371#107—864no—
372#106—864no—
373#103—864no—
374#102—864no—
375C22⋊C8—432no—
376C22⋊C8—432no—
377C22⋊C8—861no—
378C22⋊C8—861no—
379#95—24no—
380#95—21no—
381#95C22×D4312yes—
382C24—861no—
383C24C2×C22⋊D4311yescharacteristic
384C2×Q8—432no—
385C2×Q8—861no—
386C2×Q8—1722no—
387C2×D4—432no—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—861no—
391C2×D4—1722no—
392C2×D4—1722no—
393C2×D4—1722no—
394C22×C4—24no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—864no—
412C22×C4—861no—
413C22×C4—861no—
414C22×C4—861no—
415C22×C4—3442no—
416C22×C4D4×D4311yescharacteristic
417C22×C4D4×D4311yescharacteristic
418C22×C4D4×D4311yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4C2×C22⋊D4312yes—
421C22×C4C2×C22⋊D4312yes—
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C23×D4311yescharacteristic
424C2×C8—862no—
425C2×C8—862no—
426C2×C8—1722no—
427C2×C8—1722no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—48no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—432no—
438C4⋊C4—432no—
439C4⋊C4—864no—
440C4⋊C4—864no—
441C4⋊C4—864no—
442C4⋊C4—861no—
443C4⋊C4—861no—
444C4⋊C4—862no—
445C4⋊C4—862no—
446C22⋊C4—864no—
447C22⋊C4—864no—
448C22⋊C4—864no—
449C22⋊C4—862no—
450C22⋊C4—862no—
451C22⋊C4—862no—
452C22⋊C4—862no—
453C42—864no—
454C23—22no—
455C23—22no—
456C23—862no—
457C23—1722no—
458C23—1722no—
459C23—1722no—
460C23#1306329311yescharacteristic
461C23#1306329311yescharacteristic
462C23#1306334512yes—
463C23#1306335112yes—
464C23C22×C22⋊D4311yescharacteristic
465Q8—3441no—
466Q8—1722no—
467D4—3441no—
468D4—1722no—
469D4—1724no—
470D4—1722no—
471D4—1722no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—48no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—81no—
494C2×C4—82no—
495C2×C4—82no—
496C2×C4—862no—
497C2×C4—862no—
498C2×C4—862no—
499C2×C4—3444no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4#1306329311yescharacteristic
504C2×C4#1306329311yescharacteristic
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4C2×D4×D4311yescharacteristic
507C8—1722no—
508C8—1722no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—3444no—
516C22—1722no—
517C22—1722no—
518C22—1722no—
519C22#1458304212yes—
520C22#1458304212yes—
521C22#1458308112yes—
522C22#1458308812yes—
523C22C2×#1306329311yescharacteristic
524C22C2×#1306334511yescharacteristic
525C22C2×#1306335111yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—44no—
531C4—42no—
532C4—42no—
533C4—82no—
534C4—1722no—
535C4—1722no—
536C4—1722no—
537C2—21no—
538C2—22no—
539C2—21no—
540C2—3442no—
541C2#1913359014yesdirect product factor
542C2C2×#1458304211yescharacteristic
543C2C2×#1458308111yescharacteristic
544C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#398C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#398D43
hypocenterC43C2×#1609
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C2×#14583229C2semidirect
4. #19133590C2direct (N × H)
5. C2×#14582635C2semidirect
7. C2×#14582625C2semidirect
8. C2×C43×#398C2semidirect
22. #14583229C22semidirect
31. #14582635C22semidirect
33. #14582625C22semidirect
38. C43×#398C22semidirect
268. C2×#398D43semidirect
276. C2×C43#1609semidirect
307. #398C2×D43semidirect
313. C43C2×#1609semidirect
541. C2#19133590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834962
C2×#145832292
C2×#145832122
#191335902
C2×#145826352
C2×#145826322
C2×#145826252
C2×C43×#3982
C2×#160943