Finite Group Databasebeta

← C4×#14583159 #25103456

Subgroups — C4×#14583159 #25103456

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583159C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic, complemented
3C4×#13063351C211yesmaximal, characteristic
4C4×#13063331C211yesmaximal, characteristic, complemented
5#19135500C211yesmaximal, characteristic, complemented
6#19135373C211yesmaximal, characteristic, complemented
7#19135254C211yesmaximal, characteristic, complemented
8#19135247C211yesmaximal, characteristic, complemented
9#19135113C211yesmaximal, characteristic, complemented
10#19135106C211yesmaximal, characteristic
11#19134655C211yesmaximal, characteristic, complemented
12C4×#13063261C211yesmaximal, characteristic, complemented
13C4×#13063244C211yesmaximal, characteristic, complemented
14C4×#13063242C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C4×#10621898C2211yescharacteristic
21#14583159C418yesdirect product factor
22#14583009—21no—
23#14583004—21no—
24#14582999—21no—
25#14582997—21no—
26C4×#10621885—21no—
27C4×#10621884—21no—
28C4×#10621883—21no—
29C4×#10621882—21no—
30C2×#13063261C2211yescharacteristic
31C2×#13063261C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582939C2211yescharacteristic
34#14582908C2211yescharacteristic
35#14582904C2211yescharacteristic
36#14582898C2211yescharacteristic
37#14582898C2211yescharacteristic
38C2×#13063244C2211yescharacteristic
39C2×#13063244C2211yescharacteristic
40C2×#13063242C2211yescharacteristic
41C2×#13063242C2211yescharacteristic
42#14582854C2211yescharacteristic
43#14582854C2211yescharacteristic
44#14582853—21no—
45#14582853—21no—
46C4×#10621877C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49C4×#10621872—21no—
50C4×C8×D43—21no—
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582664C2211yescharacteristic
56#14582664C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C4×SD16×C43—21no—
61C4×SD16×C43—21no—
62C4×SD16×C43—21no—
63C4×SD16×C43—21no—
64C2×#106×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×C4×C8×C43C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063356—22no—
70#13063356C2×C414yescomplemented
71#13063351—22no—
72#13063351C2×C414yes—
73C2×#10621885—21no—
74C2×#10621883—21no—
75C2×#10621884—21no—
76C2×#10621882—21no—
77#13063331—22no—
78#13063331—22no—
79#13063331—22no—
80#13063331C2×C414yescomplemented
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C4×Dic86D411yescharacteristic
92C4×Dic86D411yescharacteristic
93C4×D172D411yescharacteristic
94C4×D172D411yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97#13063284C2311yescharacteristic
98#13063282—21no—
99C42×D43—21no—
100#13063261—22no—
101#13063261C2×C414yescomplemented
102#13063258—21no—
103#13063258—21no—
104#13063256—21no—
105#13063256—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063246—21no—
111#13063246—21no—
112#13063245—21no—
113#13063245—21no—
114#13063244—22no—
115#13063244C2×C414yescomplemented
116#13063242—22no—
117#13063242C2×C414yescomplemented
118#13063236—21no—
119#13063236—21no—
120#13063236—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C2×SD16×C43—22no—
134C2×SD16×C43C2×C414yescomplemented
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C4×Q8×C43—21no—
138C4×Q8×C43—21no—
139C4×Q8×C43—21no—
140C4×Q8×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43—21no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150C2×C42×C43C2311yescharacteristic
151#106×C43—21no—
152#106×C43—21no—
153#103×C43—21no—
154#103×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157C4×C8×C43D411yescharacteristic
158C4×C8×C43D411yescharacteristic
159C4×C8×C43D411yescharacteristic
160C4×C8×C43D411yescharacteristic
161C24×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C22×C412yes—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43C22×C412yes—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—82no—
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—21no—
184#10621898—21no—
185#10621898—21no—
186#10621898C22×C412yes—
187#10621898#4112yes—
188C2×D172C2×D411yescharacteristic
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×Dic86C2×D411yescharacteristic
193SD16×C43—24no—
194SD16×C43—24no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C22×C412yes—
198C2×C8×C43C2×D411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C2×C8×C43C2×D411yescharacteristic
201C2×C8×C43C2×D411yescharacteristic
202C2×C8×C43#4112yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43—41no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—41no—
212C42×C43—41no—
213C42×C43C2×D411yescharacteristic
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43C2×D411yescharacteristic
217C22⋊Dic43—21no—
218#10621885—24no—
219#10621884—24no—
220#10621883—24no—
221#10621882—24no—
222(C2×D43)⋊C4—21no—
223(C2×D43)⋊C4—21no—
224C4⋊Dic43C2×D411yescharacteristic
225C4⋊Dic43C2×D411yescharacteristic
226Dic43⋊C4—21no—
227Dic43⋊C4—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877—21no—
238#10621877—21no—
239#10621877C22×C412yes—
240#10621877C22×C412yes—
241#10621877C22×C412yes—
242#10621877#4112yes—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249#10621872—24no—
250#10621872—24no—
251C8×D43—24no—
252C8×D43—24no—
253C23×C43—22no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—81no—
257C23×C43—81no—
258C23×C43C2×#4111yescharacteristic
259C22×D43—21no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—82no—
276C2×C4×C43—82no—
277C2×C4×C43—81no—
278C2×C4×C43—81no—
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43#12111yescharacteristic
283C2×C4×C43C23×C411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C22⋊D43—22no—
290C22⋊D43—22no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294D172—21no—
295D172C4×D412yes—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—42no—
299C4×D43—42no—
300Dic86—21no—
301Dic86C4×D412yes—
302C8×C43—21no—
303C8×C43—21no—
304C8×C43C4×D412yes—
305C8×C43C4×D412yes—
306C43⋊C8—22no—
307C43⋊C8—22no—
308C43⋊C8—22no—
309C43⋊C8—22no—
310C43⋊C8—41no—
311C43⋊C8—41no—
312C4×#471—431nomaximal, Sylow
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—42no—
316C22×C43—82no—
317C22×C43—82no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C4×#4111yescharacteristic
321C22×C43C2×#12111yescharacteristic
322C22×C43#52911yescharacteristic
323C2×D43—22no—
324C2×D43—41no—
325C2×D43—41no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—42no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43#47112yescomplemented
333C4×C43C2×C4×D411yescharacteristic
334C4×C43C2×C4×D411yescharacteristic
335C4×C43#52511yescharacteristic
336C4×C43#53211yescharacteristic
337Dic43—22no—
338Dic43—41no—
339Dic43—41no—
340C2×#471—431no—
341C4×#137—431no—
342C4×AGL(1,ℤ/8)—431no—
343C2×C4×SD16D4311yescharacteristic, complemented
344C4×#131—431no—
345#1977—431no—
346#1951—431no—
347#1931—431no—
348#1930—431no—
349#1908—431no—
350#1907—431no—
351#1815—431no—
352C4×#108—431no—
353C4×#101—431no—
354C4×#100—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—82no—
358C2×C43C4×#12111yescharacteristic
359C2×C43C2×#47111yescharacteristic
360C2×C43#306711yescharacteristic
361D43—42no—
362C2×#137—431no—
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16C2×D4311yescharacteristic
365C2×#131—431no—
366C2×#131—431no—
367C4×#41—431no—
368C2×C4×Q8C2×D4311yescharacteristic
369C2×C4×D4C2×D4311yescharacteristic
370#471—438no—
371#442—861no—
372#441—861no—
373#440—861no—
374#440—861no—
375C4×Q16—861no—
376C4×SD16—21no—
377C4×SD16—21no—
378C4×SD16—21no—
379C4×SD16—21no—
380C4×SD16—861no—
381C4×SD16—861no—
382C4×D8—861no—
383C2×#108—431no—
384C2×#108—431no—
385#428—431no—
386#428—431no—
387C2×#106C2×D4311yescharacteristic
388#419—431no—
389#418—431no—
390#417—431no—
391#417—431no—
392C2×#103C2×D4311yescharacteristic
393C2×#102C2×D4311yescharacteristic
394C2×#101—431no—
395C2×#101—431no—
396C2×#100—431no—
397C2×#100—431no—
398#405—431no—
399#405—431no—
400#405—861no—
401#405—861no—
402C4×M16—431no—
403C4×M16—431no—
404C4×M16—431no—
405C4×M16—861no—
406C2×C4×C8—861no—
407C2×C4×C8C2×D4311yescharacteristic
408#343—431no—
409#343—431no—
410#343—431no—
411#343—431no—
412#341—431no—
413#341—431no—
414C43C4×#47111yescharacteristic, complemented, Sylow
415C2×#41—431no—
416C22×Q8C22×D4311yescharacteristic
417C22×D4C22×D4311yescharacteristic
418C23×C4—21no—
419#137—434no—
420#137—862no—
421AGL(1,ℤ/8)—434no—
422AGL(1,ℤ/8)—862no—
423C2×Q16—861no—
424C2×SD16—22no—
425C2×SD16—21no—
426C2×SD16—21no—
427C2×SD16—861no—
428C2×SD16—861no—
429C2×SD16C4×D4314yescomplemented
430C2×D8—861no—
431#131—434no—
432#131—862no—
433#131—862no—
434#131—862no—
435C2×M16—431no—
436C2×M16—431no—
437C2×M16—431no—
438C2×M16—431no—
439C2×M16—431no—
440C2×M16—431no—
441C2×M16—861no—
442C2×M16—861no—
443C22×C8—861no—
444C22×C8—861no—
445C22×C8C22×D4311yescharacteristic
446C22×C8C22×D4311yescharacteristic
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8—431no—
452C4×Q8—431no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—431no—
458C4×D4—431no—
459C4×D4—861no—
460C4×D4—861no—
461#117—431no—
462#117—861no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4C22×D4311yescharacteristic
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470#108—434no—
471#108—862no—
472#107—861no—
473#107—861no—
474#106—21no—
475#106—21no—
476#106—861no—
477#106—861no—
478#103—21no—
479#103—21no—
480#103—861no—
481#103—861no—
482#103—861no—
483#103—861no—
484#102—21no—
485#102—21no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#101—434no—
491#101—862no—
492#100—434no—
493#100—862no—
494#97—861no—
495#97—861no—
496#97—861no—
497#97—861no—
498#97—861no—
499C4×C8—861no—
500C4×C8—861no—
501C4×C8—861no—
502C4×C8—861no—
503C4×C8—861no—
504C4×C8C22⋊D4311yescharacteristic
505C4×C8C22⋊D4311yescharacteristic
506C4×C8C22⋊D4311yescharacteristic
507C4×C8C22⋊D4311yescharacteristic
508C24—21no—
509#41—432no—
510#41—432no—
511#41—861no—
512#41—861no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—431no—
519C2×Q8C2×C4×D4312yes—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—431no—
526C2×D4—861no—
527C2×D4C2×C4×D4312yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—82no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4#1062190011yescharacteristic
538C22×C4#1062190011yescharacteristic
539C22×C4C23×D4311yescharacteristic
540Q16—864no—
541SD16—24no—
542SD16—24no—
543SD16—864no—
544SD16—864no—
545D8—864no—
546M16—432no—
547M16—432no—
548M16—432no—
549M16—432no—
550M16—864no—
551M16—861no—
552M16—861no—
553M16—861no—
554M16—861no—
555M16—864no—
556M16—861no—
557M16—861no—
558M16—861no—
559M16—861no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—864no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—864no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8C2×C4×D4312yes—
571C2×C8#1062189812yes—
572C2×C8C2×C22⋊D4311yescharacteristic
573C2×C8C2×C22⋊D4311yescharacteristic
574C2×C8C2×C22⋊D4311yescharacteristic
575C2×C8C2×C22⋊D4311yescharacteristic
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—431no—
583C4⋊C4—431no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—861no—
589C22⋊C4—861no—
590C22⋊C4—861no—
591C42—41no—
592C42—41no—
593C42—861no—
594C42—861no—
595C42—861no—
596C42D4×D4311yescharacteristic
597C42D4×D4311yescharacteristic
598C42C2×C22⋊D4311yescharacteristic
599C42C2×C22⋊D4311yescharacteristic
600C23—22no—
601C23—41no—
602C23—41no—
603C23—81no—
604C23—81no—
605C23—861no—
606C23C2×#1062190011yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—432no—
612Q8—861no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—432no—
618D4—862no—
619D4—862no—
620D4—861no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—82no—
629C2×C4—82no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—861no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4#1306329611yescharacteristic
640C2×C4#1306329611yescharacteristic
641C2×C4#1306329611yescharacteristic
642C2×C4#1306329611yescharacteristic
643C2×C4C22×C4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C22×C22⋊D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4C2×#1062189811yescharacteristic
649C8—21no—
650C8—21no—
651C8—862no—
652C8—862no—
653C8—862no—
654C8—862no—
655C8—1721no—
656C8—1721no—
657C8C4×C22⋊D4312yes—
658C8C4×C22⋊D4312yes—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—82no—
663C22—82no—
664C22—81no—
665C22—81no—
666C22—862no—
667C22—1721no—
668C22—1721no—
669C22C4×#1062190011yescharacteristic
670C22C2×#1306329611yescharacteristic
671C22#1458343111yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—862no—
679C4—1721no—
680C4—1721no—
681C4#1458315912yesdirect product factor
682C4C4×D4×D4311yescharacteristic
683C4C2×C4×C22⋊D4311yescharacteristic
684C4#1458340611yescharacteristic
685C4#1458344611yescharacteristic
686C2—21no—
687C2—21no—
688C2—82no—
689C2—1722no—
690C2C4×#1306329611yescharacteristic
691C2C2×#1458315911yescharacteristic
692C2#1914431111yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
cosocleC22×C4×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43C4×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#13063356C2semidirect
4. C4×#13063331C2semidirect
5. #19135500C2semidirect
6. #19135373C2semidirect
7. #19135254C2semidirect
8. #19135247C2semidirect
9. #19135113C2semidirect
11. #19134655C2semidirect
12. C4×#13063261C2semidirect
13. C4×#13063244C2semidirect
14. C4×#13063242C2semidirect
15. C2×C4×SD16×C43C2semidirect
21. #14583159C4direct (N × H)
70. #13063356C2×C4semidirect
80. #13063331C2×C4semidirect
101. #13063261C2×C4semidirect
115. #13063244C2×C4semidirect
117. #13063242C2×C4semidirect
134. C2×SD16×C43C2×C4semidirect
332. C4×C43#471semidirect
343. C2×C4×SD16D43semidirect
414. C43C4×#471semidirect
429. C2×SD16C4×D43semidirect
681. C4#14583159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831592
C4×#130633562
C4×#130633512
C4×#130633312
#191355002
#191353732
#191352542
#191352472
#191351132
#191351062
#191346552
C4×#130632612
C4×#130632442
C4×#130632422
C2×C4×SD16×C432
C4×#47143