Finite Group Databasebeta

← C2×#19133591 #25068736

Subgroups — C2×#19133591 #25068736

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×#14583498C211yesmaximal, characteristic
2C2×#14583212C211yesmaximal, characteristic
3C2×#14582830C211yesmaximal, characteristic, complemented
4#19133591C218yesmaximal, direct product factor
5C2×#14582636C211yesmaximal, characteristic, complemented
6C2×#14582634C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#483C211yesmaximal, characteristic, complemented
9#14583498—22no—
10#14583498—22no—
11#14583498—22no—
12#14583498C2214yes—
13C2×#13063320—21no—
14C2×#13063316—21no—
15C2×#13063310—21no—
16C2×#13063309—21no—
17C2×#13063301—21no—
18C2×#13063299C2211yescharacteristic
19C2×(C22⋊D43)⋊C4—21no—
20C22×Dic43⋊C4—21no—
21C22×Dic43⋊C4C2211yescharacteristic
22#14583212—22no—
23#14583212C2214yes—
24C2×#13063258—21no—
25C2×#13063245—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582830—22no—
28#14582830C2214yescomplemented
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582636C2214yescomplemented
32#14582634C2214yes—
33#14582624C2214yescomplemented
34C2×C22⋊Q8×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#483—22no—
37C43×#483C2214yescomplemented
38C2×#106×C43—21no—
39C2×#103×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C22×D172D411yescharacteristic
42C22×C22⋊D43—21no—
43C23×Dic43—21no—
44C23×Dic43D411yescharacteristic
45C23×Dic43D411yescharacteristic
46C22×C4×D43—21no—
47C22×C43⋊C8—21no—
48#13063320—24no—
49#13063320—24no—
50#13063316—24no—
51#13063316—24no—
52#13063310—24no—
53#13063310—24no—
54#13063309—24no—
55#13063309—24no—
56#13063301—24no—
57#13063301—24no—
58#13063299—21no—
59#13063299—21no—
60#13063299D412yes—
61#13063299C2312yes—
62(C22⋊D43)⋊C4—24no—
63(C22⋊D43)⋊C4—24no—
64C2×C4⋊Dic43—21no—
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—24no—
73C2×Dic43⋊C4—44no—
74C2×Dic43⋊C4D412yes—
75C2×Dic43⋊C4C2312yes—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43—21no—
81#13063258—24no—
82#13063245—24no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)C2312yes—
85C43⋊#95—21no—
86C43⋊#95—24no—
87C43⋊#95C2312yes—
88C22×Q8×C43D411yescharacteristic
89C23×C4×C43—21no—
90C23×C4×C43C2311yescharacteristic
91C22×C8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43D412yes—
95C22⋊Q8×C43C2312yes—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105#106×C43—24no—
106#103×C43—24no—
107C22⋊C8×C43—21no—
108C22⋊C8×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C23×D43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—42no—
113C2×Q8×C43C2×D412yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—42no—
118C22×C4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—22no—
129C2×C22⋊D43—22no—
130C2×C22⋊D43—42no—
131C2×C22⋊D43—42no—
132C22×Dic43—24no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43C2×D412yes—
145C22×Dic43C2×D412yes—
146C2×D172—21no—
147C2×D172—42no—
148C2×D172C2×D412yes—
149C2×C4×D43—24no—
150C2×C4×D43—82no—
151C2×C8×C43—22no—
152C2×C8×C43—42no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43—41no—
160C4⋊C4×C43C2×D412yes—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—22no—
168C4⋊Dic43—24no—
169C4⋊Dic43—24no—
170C4⋊Dic43—21no—
171C4⋊Dic43C2×D412yes—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—48no—
178C4×Dic43—24no—
179C2×C43⋊C8—22no—
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—
192Q8×C43—42no—
193Q8×C43—81no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—82no—
208C2×C4×C43—82no—
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C22⋊D43—42no—
214C22⋊D43—42no—
215C22⋊D43—44no—
216C2×Dic43—24no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—48no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—42no—
230C2×Dic43—81no—
231D172—42no—
232D172—81no—
233C4×D43—84no—
234C8×C43—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—42no—
259C4×C43—42no—
260C4×C43—82no—
261Dic43—44no—
262Dic43—42no—
263Dic43—42no—
264Dic43—42no—
265C2×#539—431no—
266C2×#483D4311yescharacteristic, complemented
267C2×#480—431no—
268C2×#398—431no—
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—861no—
290C2×C22⋊Q8C2×D4311yescharacteristic
291C2×#121—431no—
292C2×C4×D4—861no—
293C22×C4⋊C4—431no—
294C22×C4⋊C4—861no—
295C22×C4⋊C4C2×D4311yescharacteristic
296#483—22no—
297#483C2×D4314yescomplemented
298#480—434no—
299#480—862no—
300C2×#107—861no—
301C2×#106—21no—
302C2×#103—21no—
303C2×#102—861no—
304C2×C22⋊C8—431no—
305C2×C22⋊C8C2×D4311yescharacteristic
306#398—434no—
307#398—862no—
308C2×#95—431no—
309C2×#95—861no—
310#328—434no—
311#327—434no—
312#324—434no—
313C43C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8C22⋊D4311yescharacteristic
315C22×D4—431no—
316C22×D4—861no—
317C23×C4—21no—
318C23×C4—431no—
319C23×C4—431no—
320C23×C4—861no—
321C23×C4—861no—
322C23×C4C22×D4311yescharacteristic
323C22×C8—21no—
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—21no—
334C22⋊Q8—21no—
335C22⋊Q8—864no—
336C22⋊Q8—864no—
337C22⋊Q8C22⋊D4312yes—
338C22⋊Q8C22×D4312yes—
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—431no—
352C2×C4⋊C4—432no—
353C2×C4⋊C4—432no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—861no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—864no—
362C2×C4⋊C4—1724no—
363C2×C4⋊C4C22⋊D4311yescharacteristic
364C2×C4⋊C4C22×D4312yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C42—861no—
371#107—864no—
372#106—24no—
373#103—24no—
374#102—864no—
375C22⋊C8—21no—
376C22⋊C8—432no—
377C22⋊C8—861no—
378C22⋊C8C22×D4312yes—
379#95—432no—
380#95—864no—
381#95—861no—
382C24—861no—
383C24D4×D4311yescharacteristic
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8C2×C22⋊D4312yes—
387C2×D4—432no—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—861no—
391C2×D4—1722no—
392C2×D4—1722no—
393C2×D4—1722no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—432no—
403C22×C4—432no—
404C22×C4—864no—
405C22×C4—861no—
406C22×C4—864no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—861no—
410C22×C4—861no—
411C22×C4—862no—
412C22×C4—862no—
413C22×C4—862no—
414C22×C4—3442no—
415C22×C4—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4D4×D4311yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4C2×C22⋊D4311yescharacteristic
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C23×D4311yescharacteristic
424C2×C8—22no—
425C2×C8—42no—
426C2×C8—862no—
427C2×C8—1722no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—432no—
436C4⋊C4—864no—
437C4⋊C4—864no—
438C4⋊C4—864no—
439C4⋊C4—862no—
440C4⋊C4—862no—
441C4⋊C4—861no—
442C4⋊C4—862no—
443C4⋊C4—862no—
444C4⋊C4—1728no—
445C4⋊C4C2×C22⋊D4312yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—864no—
449C22⋊C4—864no—
450C22⋊C4—864no—
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#1306334612yes—
463C23#1306335212yes—
464C23C2×D4×D4311yescharacteristic
465Q8—42no—
466Q8—81no—
467D4—3441no—
468D4—1722no—
469D4—1724no—
470D4—1722no—
471D4—1722no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—82no—
486C2×C4—82no—
487C2×C4—864no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—862no—
491C2×C4—862no—
492C2×C4—862no—
493C2×C4—3444no—
494C2×C4—3441no—
495C2×C4—1722no—
496C2×C4—1728no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4#1306329311yescharacteristic
504C2×C4#1306329311yescharacteristic
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4C22×C22⋊D4311yescharacteristic
507C8—42no—
508C8—1722no—
509C22—21no—
510C22—21no—
511C22—24no—
512C22—24no—
513C22—21no—
514C22—21no—
515C22—3444no—
516C22—1722no—
517C22—1722no—
518C22—1722no—
519C22#1458304312yes—
520C22#1458304312yes—
521C22#1458308012yes—
522C22#1458308812yes—
523C22C2×#1306329311yescharacteristic
524C22C2×#1306334611yescharacteristic
525C22C2×#1306335211yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—42no—
532C4—82no—
533C4—1724no—
534C4—1722no—
535C4—1722no—
536C4—1722no—
537C2—21no—
538C2—22no—
539C2—21no—
540C2—3442no—
541C2#1913359114yesdirect product factor
542C2C2×#1458304311yescharacteristic
543C2C2×#1458308011yescharacteristic
544C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#483C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#483D43
hypocenterC43C2×#1609
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. C2×#14582830C2semidirect
4. #19133591C2direct (N × H)
5. C2×#14582636C2semidirect
7. C2×#14582624C2semidirect
8. C2×C43×#483C2semidirect
28. #14582830C22semidirect
31. #14582636C22semidirect
33. #14582624C22semidirect
37. C43×#483C22semidirect
266. C2×#483D43semidirect
276. C2×C43#1609semidirect
297. #483C2×D43semidirect
313. C43C2×#1609semidirect
541. C2#19133591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834982
C2×#145832122
C2×#145828302
#191335912
C2×#145826362
C2×#145826342
C2×#145826242
C2×C43×#4832
C2×#160943