Finite Group Databasebeta

← C2×#19133606 #25068836

Subgroups — C2×#19133606 #25068836

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583486C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3C2×#14582825C211yesmaximal, characteristic, complemented
4#19133606C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic, complemented
7C2×#14582622C211yesmaximal, characteristic, complemented
8C2×C43×#480C211yesmaximal, characteristic, complemented
9#14583486—22no—
10#14583486—22no—
11#14583486—22no—
12#14583486C2214yes—
13C2×#13063320—21no—
14C2×#13063311—21no—
15C2×#13063309—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063297—21no—
18C2×#13063293—21no—
19C2×D4×Dic43—21no—
20C22×(C2×D43)⋊C4—21no—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22#14583229—22no—
23#14583229C2214yescomplemented
24C2×#13063256—21no—
25C2×#13063248—21no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582825—22no—
28#14582825C2214yescomplemented
29C2×C43⋊#95—21no—
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yescomplemented
32#14582633C2214yescomplemented
33#14582622C2214yescomplemented
34C2×#121×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#480—22no—
37C43×#480C2214yescomplemented
38C2×#107×C43—21no—
39C2×#102×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C24×D43D411yescharacteristic
42C22×Dic86D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C22×C43⋊C8—21no—
49#13063320—24no—
50#13063320—24no—
51#13063311—24no—
52#13063311—24no—
53#13063309—24no—
54#13063309—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063297—24no—
60#13063297—24no—
61#13063293—24no—
62#13063293—24no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—44no—
78C2×(C2×D43)⋊C4D412yes—
79C2×(C2×D43)⋊C4C2312yes—
80C2×C4×Dic43—21no—
81#13063256—24no—
82#13063248—24no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)C2312yes—
85C43⋊#95—21no—
86C43⋊#95—24no—
87C43⋊#95C2312yes—
88C22×D4×C43—21no—
89C22×D4×C43D411yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43—21no—
93#121×C43—21no—
94#121×C43—21no—
95#121×C43D412yes—
96#121×C43C2312yes—
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#107×C43—24no—
106#102×C43—24no—
107C22⋊C8×C43—21no—
108C22⋊C8×C43C2312yes—
109C24×C43—21no—
110C24×C43C2×D411yescharacteristic
111C23×D43—21no—
112C23×D43—22no—
113C23×D43—21no—
114C23×D43—22no—
115C23×D43—42no—
116C23×D43—42no—
117C23×D43C2×D412yes—
118C2×D4×C43—21no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43C2×D412yes—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43—42no—
128C22×C4×C43—41no—
129C22×C4×C43—41no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C2×C22⋊D43—24no—
139C2×C22⋊D43—24no—
140C2×C22⋊D43—82no—
141C2×C22⋊D43—82no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—82no—
153C22×Dic43C2×D412yes—
154C2×Dic86—21no—
155C2×Dic86—42no—
156C2×Dic86C2×D412yes—
157C2×C8×C43—22no—
158C2×C8×C43—42no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43C2×D412yes—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊Dic43—24no—
168C22⋊Dic43—22no—
169C22⋊Dic43—22no—
170(C2×D43)⋊C4—24no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4—48no—
177C4⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43C2×D412yes—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182C4×Dic43—24no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—42no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43#12011yescharacteristic
192C23×C43#12011yescharacteristic
193C23×C43#13512yes—
194C23×C43AGL(1,ℤ/8)12yes—
195C23×C43C22×D411yescharacteristic
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—48no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—81no—
207C22×D43—81no—
208C22×D43—84no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—44no—
213D4×C43—81no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—82no—
226C2×C4×C43—82no—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C22⋊D43—84no—
232C22⋊D43—84no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—81no—
244C2×Dic43—84no—
245C2×Dic43—84no—
246Dic86—42no—
247Dic86—81no—
248C8×C43—42no—
249C43⋊C8—42no—
250C2×#1612—431nomaximal, Sylow
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—84no—
261C22×C43#44912yes—
262C22×C43#44912yes—
263C22×C43#45512yes—
264C22×C43#45812yes—
265C22×C43C2×#12011yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
268C2×D43—44no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—84no—
273C2×D43—84no—
274C2×D43—82no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—42no—
280C4×C43—82no—
281Dic43—42no—
282Dic43—42no—
283Dic43—42no—
284Dic43—82no—
285C2×#538—431no—
286C2×#483—431no—
287C2×#480D4311yescharacteristic, complemented
288C2×#397—431no—
289#1612—438no—
290C2×#328—431no—
291C2×#327—431no—
292C2×#323—431no—
293C2×C43—21no—
294C2×C43—21no—
295C2×C43—22no—
296C2×C43—82no—
297C2×C43#161214yescomplemented
298C2×C43C2×#44911yescharacteristic
299C2×C43C2×#45511yescharacteristic
300C2×C43C2×#45811yescharacteristic
301D43—82no—
302#538—434no—
303#538—862no—
304#538—862no—
305#538—862no—
306C2×#126—861no—
307C2×#124—861no—
308C2×#123—861no—
309C2×C22⋊Q8—431no—
310C2×#121—861no—
311C2×#121C2×D4311yescharacteristic
312C2×#120—861no—
313C2×C4×D4—861no—
314C22×C4⋊C4C2×D4311yescharacteristic
315C22×C22⋊C4—431no—
316C22×C22⋊C4—861no—
317#483—434no—
318#483—862no—
319#480—22no—
320#480C2×D4314yescomplemented
321C2×#107—21no—
322C2×#106—861no—
323C2×#103—861no—
324C2×#102—21no—
325C2×C22⋊C8—431no—
326C2×C22⋊C8C2×D4311yescharacteristic
327#397—434no—
328#397—862no—
329C2×#95—431no—
330C2×#95—861no—
331#328—434no—
332#327—434no—
333#323—434no—
334C43C2×#161211yescharacteristic, complemented, Sylow
335C25—431no—
336C22×Q8—431no—
337C22×D4—21no—
338C22×D4—861no—
339C22×D4—861no—
340C22×D4C22⋊D4311yescharacteristic
341C23×C4—21no—
342C23×C4—431no—
343C23×C4—861no—
344C23×C4—861no—
345C23×C4C22×D4311yescharacteristic
346C22×C8—21no—
347C22×C8—861no—
348#126—864no—
349#126—864no—
350#124—864no—
351#124—864no—
352#123—864no—
353#123—864no—
354C22⋊Q8—432no—
355C22⋊Q8—432no—
356C22⋊Q8—861no—
357C22⋊Q8—861no—
358#121—21no—
359#121—21no—
360#121—864no—
361#121—864no—
362#121C22⋊D4312yes—
363#121C22×D4312yes—
364#120—864no—
365#120—864no—
366C4×D4—864no—
367C4×D4—864no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4C22⋊D4311yescharacteristic
377C2×C4⋊C4C22×D4312yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—432no—
380C2×C22⋊C4—432no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—864no—
390C2×C22⋊C4—1724no—
391C2×C42—861no—
392#107—24no—
393#106—864no—
394#103—864no—
395#102—24no—
396C22⋊C8—21no—
397C22⋊C8—432no—
398C22⋊C8—861no—
399C22⋊C8C22×D4312yes—
400#95—432no—
401#95—864no—
402#95—861no—
403C24—21no—
404C24—432no—
405C24—861no—
406C24—862no—
407C24—861no—
408C24—862no—
409C24—1722no—
410C24—1722no—
411C24D4×D4311yescharacteristic
412C2×Q8—432no—
413C2×Q8—861no—
414C2×Q8—1722no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—864no—
422C2×D4—864no—
423C2×D4—3442no—
424C2×D4—3442no—
425C2×D4C2×C22⋊D4312yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—432no—
434C22×C4—864no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—862no—
440C22×C4—3442no—
441C22×C4—1722no—
442C22×C4—1722no—
443C22×C4—1722no—
444C22×C4—1722no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449C22×C4C2×C22⋊D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—22no—
452C2×C8—42no—
453C2×C8—862no—
454C2×C8—1722no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—432no—
461C4⋊C4—864no—
462C4⋊C4—861no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4C2×C22⋊D4312yes—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—862no—
472C22⋊C4—862no—
473C22⋊C4—862no—
474C22⋊C4—862no—
475C22⋊C4—862no—
476C22⋊C4—862no—
477C22⋊C4—1728no—
478C42—864no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—862no—
486C23—862no—
487C23—862no—
488C23—3444no—
489C23—3441no—
490C23—3441no—
491C23—1728no—
492C23—1722no—
493C23—1722no—
494C23—1722no—
495C23—1722no—
496C23—1722no—
497C23—1722no—
498C23#1306329311yescharacteristic
499C23#1306329311yescharacteristic
500C23#1306334412yes—
501C23#1306334912yes—
502C23C2×D4×D4311yescharacteristic
503Q8—3441no—
504Q8—1722no—
505D4—42no—
506D4—44no—
507D4—42no—
508D4—42no—
509D4—81no—
510D4—3444no—
511D4—3444no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—3444no—
529C2×C4—3441no—
530C2×C4—3444no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4#1306329311yescharacteristic
539C2×C4#1306329311yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C8—42no—
543C8—1722no—
544C22—21no—
545C22—21no—
546C22—24no—
547C22—24no—
548C22—21no—
549C22—21no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—84no—
554C22—3442no—
555C22—3444no—
556C22—3444no—
557C22—1724no—
558C22—1722no—
559C22—1722no—
560C22—1722no—
561C22#1458304112yes—
562C22#1458304112yes—
563C22#1458307512yes—
564C22#1458308812yes—
565C22C2×#1306329311yescharacteristic
566C22C2×#1306334411yescharacteristic
567C22C2×#1306334911yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—82no—
574C4—3442no—
575C4—1722no—
576C4—1722no—
577C4—1722no—
578C2—21no—
579C2—22no—
580C2—21no—
581C2—82no—
582C2—3442no—
583C2#1913360614yesdirect product factor
584C2C2×#1458304111yescharacteristic
585C2C2×#1458307511yescharacteristic
586C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#480C2
socleC23×C43#120
prime radicalC2×#14583486C2
hypercenterC2×#480D43
hypocenterC43C2×#1612
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×#14583229C2semidirect
3. C2×#14582825C2semidirect
4. #19133606C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×#14582633C2semidirect
7. C2×#14582622C2semidirect
8. C2×C43×#480C2semidirect
23. #14583229C22semidirect
28. #14582825C22semidirect
31. #14582637C22semidirect
32. #14582633C22semidirect
33. #14582622C22semidirect
37. C43×#480C22semidirect
287. C2×#480D43semidirect
297. C2×C43#1612semidirect
320. #480C2×D43semidirect
334. C43C2×#1612semidirect
583. C2#19133606direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834862
C2×#145832292
C2×#145828252
#191336062
C2×#145826372
C2×#145826332
C2×#145826222
C2×C43×#4802
C2×#161243