Finite Group Databasebeta

← C2×#19133595 #25068740

Subgroups — C2×#19133595 #25068740

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×#14583227C211yesmaximal, characteristic, complemented
3C2×#14583213C211yesmaximal, characteristic
4C2×#14582831C211yesmaximal, characteristic, complemented
5#19133595C218yesmaximal, direct product factor
6C2×#14582632C211yesmaximal, characteristic
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#328C211yesmaximal, 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×C4⋊Dic43—21no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23#14583227—22no—
24#14583227C2214yescomplemented
25#14583213—22no—
26#14583213C2214yes—
27C2×#13063259—21no—
28C2×#13063256—21no—
29C2×#13063249—21no—
30C2×#13063247—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582831—22no—
33#14582831C2214yescomplemented
34C2×C43⋊#95—21no—
35#14582632C2214yes—
36#14582624C2214yescomplemented
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#328C2214yescomplemented
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⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43—44no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D412yes—
81C2×Dic43⋊C4C2312yes—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063259—24no—
88#13063256—24no—
89#13063249—24no—
90#13063247—24no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)C2312yes—
93C43⋊#95—24no—
94C22×Q8×C43D411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C22×C8×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43D412yes—
101C22⋊Q8×C43C2312yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43—21no—
105C22⋊C8×C43—21no—
106C22⋊C8×C43C2312yes—
107#95×C43—21no—
108#95×C43C2312yes—
109C24×C43C2×D411yescharacteristic
110C23×D43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—42no—
113C2×Q8×C43C2×D412yes—
114C22×C4×C43—24no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—22no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—42no—
140C22×Dic43—41no—
141C22×Dic43—41no—
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×C43C2×D412yes—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—22no—
163(C2×D43)⋊C4—22no—
164C4⋊Dic43—24no—
165C4⋊Dic43—24no—
166C4⋊Dic43—21no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—48no—
170C4⋊Dic43—41no—
171C4⋊Dic43—41no—
172C4⋊Dic43C2×D412yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
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—24no—
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#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C22⋊D43—42no—
213C22⋊D43—42no—
214C22⋊D43—44no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—22no—
218C2×Dic43—22no—
219C2×Dic43—22no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—42no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—81no—
229C2×Dic43—82no—
230C2×Dic43—82no—
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—44no—
259C4×C43—42no—
260C4×C43—42no—
261Dic43—42no—
262Dic43—42no—
263Dic43—42no—
264Dic43—82no—
265C2×#539—431no—
266C2×#483—431no—
267C2×#480—431no—
268C2×#398—431no—
269#1609—438no—
270C2×#328D4311yescharacteristic, complemented
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—431no—
295C22×C4⋊C4—861no—
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⋊C8C2×D4311yescharacteristic
306#398—434no—
307#398—862no—
308C2×#95—861no—
309C2×#95C2×D4311yescharacteristic
310#328C2×D4314yescomplemented
311#327—434no—
312#324—434no—
313C43C2×#160911yescharacteristic, complemented, Sylow
314C22×Q8D17211yescharacteristic
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⋊Q8D17212yes—
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—431no—
347C2×C4⋊C4—432no—
348C2×C4⋊C4—432no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
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—861no—
363C2×C4⋊C4—1724no—
364C2×C4⋊C4D17211yescharacteristic
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—864no—
373#103—864no—
374#102—864no—
375C22⋊C8—21no—
376C22⋊C8—432no—
377C22⋊C8—861no—
378C22⋊C8C22×D4312yes—
379#95—21no—
380#95—864no—
381#95C22×D4312yes—
382C24—861no—
383C24D4×D4311yescharacteristic
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8C2×D17212yes—
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—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—432no—
402C22×C4—432no—
403C22×C4—864no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—862no—
410C22×C4—862no—
411C22×C4—862no—
412C22×C4—3442no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4C2×D17211yescharacteristic
419C22×C4C2×D17211yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4D4×D4311yescharacteristic
422C22×C4D4×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—432no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—864no—
435C4⋊C4—862no—
436C4⋊C4—862no—
437C4⋊C4—861no—
438C4⋊C4—862no—
439C4⋊C4—862no—
440C4⋊C4—862no—
441C4⋊C4—862no—
442C4⋊C4—1728no—
443C4⋊C4—1721no—
444C4⋊C4—1721no—
445C4⋊C4C2×D17212yes—
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#1306329511yescharacteristic
461C23#1306329511yescharacteristic
462C23#1306334812yes—
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—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—48no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—862no—
487C2×C4—862no—
488C2×C4—862no—
489C2×C4—862no—
490C2×C4—862no—
491C2×C4—3444no—
492C2×C4—3442no—
493C2×C4—3442no—
494C2×C4—3441no—
495C2×C4—1722no—
496C2×C4—1722no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4#1306329511yescharacteristic
504C2×C4#1306329511yescharacteristic
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4C22×D17211yescharacteristic
507C8—42no—
508C8—1722no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—24no—
514C22—24no—
515C22—3444no—
516C22—1722no—
517C22—1722no—
518C22—1722no—
519C22#1458304712yes—
520C22#1458304712yes—
521C22#1458308312yes—
522C22#1458309012yes—
523C22C2×#1306329511yescharacteristic
524C22C2×#1306334811yescharacteristic
525C22C2×#1306335211yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—44no—
531C4—42no—
532C4—42no—
533C4—3442no—
534C4—1722no—
535C4—1722no—
536C4—1722no—
537C2—21no—
538C2—22no—
539C2—21no—
540C2—3442no—
541C2#1913359514yesdirect product factor
542C2C2×#1458304711yescharacteristic
543C2C2×#1458308311yescharacteristic
544C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#328C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#328D43
hypocenterC43C2×#1609
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#14583227C2semidirect
4. C2×#14582831C2semidirect
5. #19133595C2direct (N × H)
7. C2×#14582624C2semidirect
8. C2×C43×#328C2semidirect
24. #14583227C22semidirect
33. #14582831C22semidirect
36. #14582624C22semidirect
40. C43×#328C22semidirect
270. C2×#328D43semidirect
276. C2×C43#1609semidirect
310. #328C2×D43semidirect
313. C43C2×#1609semidirect
541. C2#19133595direct (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×#145832272
C2×#145832132
C2×#145828312
#191335952
C2×#145826322
C2×#145826242
C2×C43×#3282
C2×#160943