Finite Group Databasebeta

← #25103496

Subgroups — #25103496

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583167C211yesmaximal, characteristic
2#19143408C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic, complemented
4C2×#14583008C211yesmaximal, characteristic, complemented
5#19143021C211yesmaximal, characteristic, complemented
6#19135502C211yesmaximal, characteristic, complemented
7#19135374C211yesmaximal, characteristic, complemented
8#19135258C211yesmaximal, characteristic, complemented
9#19135254C211yesmaximal, characteristic, complemented
10#19135103C211yesmaximal, characteristic, complemented
11#19134652C211yesmaximal, characteristic, complemented
12#19134500C211yesmaximal, characteristic, complemented
13#100×Dic43C211yesmaximal, characteristic, complemented
14#19134386C211yesmaximal, characteristic, complemented
15C43×#1907C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19#41×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22#14583167C418yescomplemented
23#14583011—21no—
24#14583008—21no—
25#14583008—21no—
26#14583008—21no—
27#14583008—21no—
28#14583008—21no—
29#14583002—21no—
30#14583000—21no—
31SD16×Dic43—21no—
32#14582984—21no—
33D8×Dic43—21no—
34#14582979—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39C2×#13063256C2211yescharacteristic
40#14582905C2211yescharacteristic
41#14582904C2211yescharacteristic
42#14582900C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45C2×#13063241C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47#14582857—21no—
48#14582857C2211yescharacteristic
49#14582854—21no—
50#14582854C2211yescharacteristic
51M16×Dic43—21no—
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55C2×#13063235—21no—
56C2×#13063235C2211yescharacteristic
57#14582668C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582664C2211yescharacteristic
61C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
62C2×#131×C43C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C2×#102×C43C2211yescharacteristic
65C2×#100×C43C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C22×D172C2311yescharacteristic
69C23×Dic43—21no—
70C22×C4×D43—21no—
71#13063350—22no—
72#13063350C2×C414yescomplemented
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882—22no—
78C2×#10621882C2×C414yescomplemented
79#13063332—22no—
80#13063332C2×C414yescomplemented
81C2×#10621877—21no—
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C22×C43⋊C8—21no—
86C22×C43⋊C8C2311yescharacteristic
87Q8×Dic43D411yescharacteristic
88Q8×Dic43D411yescharacteristic
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43—21no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95D4×Dic43D411yescharacteristic
96D4×Dic43D411yescharacteristic
97#13063287—21no—
98#13063287—21no—
99#13063287—21no—
100#13063287—21no—
101#13063284—21no—
102#13063284C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108#13063260—22no—
109#13063260C2×C414yescomplemented
110#13063259—21no—
111#13063258—21no—
112#13063257—21no—
113#13063256—21no—
114#13063256—21no—
115#13063256—21no—
116#13063249—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063242C2×C414yescomplemented
125#13063241—22no—
126#13063241C2×C414yescomplemented
127#13063235—21no—
128#13063235—21no—
129#13063235—21no—
130#13063235—21no—
131#13063235—21no—
132#13063235D411yescharacteristic
133#13063235D411yescharacteristic
134#13063235D411yescharacteristic
135#13063235D411yescharacteristic
136C8×Dic43—21no—
137C8×Dic43—21no—
138C8×Dic43—21no—
139C8×Dic43—21no—
140C8×Dic43—21no—
141C2×#41×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143AGL(1,ℤ/8)×C43—22no—
144AGL(1,ℤ/8)×C43C2×C414yescomplemented
145C2×SD16×C43—21no—
146C2×D8×C43—21no—
147#131×C43—22no—
148#131×C43—22no—
149C2×M16×C43—21no—
150C2×M16×C43C2311yescharacteristic
151C2×M16×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C22×C8×C43—21no—
154C22×C8×C43C2311yescharacteristic
155C2×C4⋊C4×C43C2311yescharacteristic
156#103×C43—21no—
157#102×C43—21no—
158#102×C43—21no—
159#102×C43—21no—
160#100×C43—22no—
161C24×C43—21no—
162C23×D43—21no—
163#41×C43—21no—
164#41×C43—21no—
165#41×C43C22×C412yes—
166#41×C43#4112yes—
167C2×Q8×C43C2×D411yescharacteristic
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C2×D411yescharacteristic
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—41no—
183C22×Dic43—41no—
184C22×Dic43—82no—
185C22×Dic43#4111yescharacteristic
186C22×Dic43#4111yescharacteristic
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—41no—
194C2×C4×D43—41no—
195C2×C4×D43—82no—
196SD16×C43—24no—
197D8×C43—24no—
198M16×C43—24no—
199M16×C43—21no—
200M16×C43—21no—
201M16×C43—21no—
202M16×C43—21no—
203M16×C43C22×C412yes—
204M16×C43#4112yes—
205C2×C8×C43—24no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C2×D411yescharacteristic
212C2×C8×C43C2×D411yescharacteristic
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C22⋊Dic43—21no—
216C22⋊Dic43—21no—
217C22⋊Dic43—21no—
218C22⋊Dic43—41no—
219C22⋊Dic43—41no—
220#10621884—24no—
221#10621882—24no—
222#10621882—24no—
223#10621882—24no—
224(C2×D43)⋊C4—41no—
225(C2×D43)⋊C4—41no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C2×D411yescharacteristic
231C4⋊Dic43C2×D411yescharacteristic
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43C2×D411yescharacteristic
236C4×Dic43C2×D411yescharacteristic
237C4×Dic43C2×D411yescharacteristic
238C4×Dic43C2×D411yescharacteristic
239#10621877—21no—
240#10621877—21no—
241#10621877—24no—
242#10621877—21no—
243#10621877—21no—
244#10621877C22×C412yes—
245#10621877C22×C412yes—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—24no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8C22×C412yes—
251C2×C43⋊C8C2×D411yescharacteristic
252C2×C43⋊C8C2×D411yescharacteristic
253C2×C43⋊C8#4112yes—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—81no—
259C23×C43—81no—
260C23×C43C2×#4111yescharacteristic
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—81no—
265C22×D43—81no—
266Q8×C43—21no—
267Q8×C43C4×D412yes—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—21no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43C4×D412yes—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—41no—
280C2×C4×C43—81no—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—81no—
293C2×Dic43—81no—
294C2×Dic43—82no—
295C2×Dic43—82no—
296C2×Dic43—81no—
297C2×Dic43#12111yescharacteristic
298C2×Dic43#12111yescharacteristic
299C2×Dic43#12111yescharacteristic
300C2×Dic43#12111yescharacteristic
301D172—22no—
302D172—22no—
303D172—41no—
304D172—41no—
305C4×D43—82no—
306C4×D43—82no—
307C8×C43—22no—
308C8×C43—21no—
309C8×C43—22no—
310C8×C43—21no—
311C8×C43—41no—
312C43⋊C8—22no—
313C43⋊C8—22no—
314C43⋊C8—41no—
315C43⋊C8C4×D412yes—
316C43⋊C8C4×D412yes—
317#21555—431nomaximal, Sylow
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—42no—
324C22×C43—82no—
325C22×C43—82no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43C4×#4111yescharacteristic
329C22×C43C2×#12111yescharacteristic
330C22×C43#52911yescharacteristic
331C2×D43—42no—
332C2×D43—82no—
333C2×D43—81no—
334C2×D43—81no—
335C2×D43—82no—
336C4×C43—22no—
337C4×C43—81no—
338C4×C43C2×C4×D411yescharacteristic
339C4×C43C2×C4×D411yescharacteristic
340C4×C43#52511yescharacteristic
341C4×C43#53211yescharacteristic
342Dic43—21no—
343Dic43—21no—
344Dic43—21no—
345Dic43—21no—
346Dic43—41no—
347Dic43—41no—
348Dic43—81no—
349C2×#472—431no—
350C4×AGL(1,ℤ/8)—431no—
351C4×AGL(1,ℤ/8)—431no—
352C2×#442—431no—
353#2875—431no—
354#1978—431no—
355#1951—431no—
356#1931—431no—
357#1931—431no—
358#1907—431no—
359#1907D4311yescharacteristic, complemented
360#1815—431no—
361#1778—431no—
362C4×#100—431no—
363C4×#100—431no—
364C2×C43—21no—
365C2×C43—21no—
366C2×C43—42no—
367C2×C43—82no—
368C2×C43C4×#12111yescharacteristic
369C2×C43#306811yescharacteristic
370C2×C43#306811yescharacteristic
371D43—82no—
372C2×AGL(1,ℤ/8)—431no—
373C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
374C22×D8—431no—
375C2×#131—431no—
376C2×#131C2×D4311yescharacteristic
377C4×#41—431no—
378C2×C4×D4—431no—
379C2×C4×D4—431no—
380#472—438no—
381#442—861no—
382#442—861no—
383#442—861no—
384#442—861no—
385#442—861no—
386#442—861no—
387#440—861no—
388#440—861no—
389C4×SD16—861no—
390C4×SD16—861no—
391C4×D8—861no—
392C4×D8—861no—
393C2×#108—431no—
394C2×#108—431no—
395#428—431no—
396#428—431no—
397C2×#106—431no—
398#418—431no—
399#418—431no—
400#417—431no—
401#417C2×D4311yescharacteristic
402C2×#102—431no—
403C2×#102C2×D4311yescharacteristic
404C2×#100—431no—
405C2×#100—431no—
406C2×#100—431no—
407C2×#100C2×D4311yescharacteristic
408#405—431no—
409#405—431no—
410#405—861no—
411#405—861no—
412C4×M16—431no—
413C4×M16—431no—
414C4×M16—431no—
415C4×M16—861no—
416C2×#97—431no—
417C2×#97—861no—
418#343—431no—
419#343—431no—
420#343—431no—
421#343C2×D4311yescharacteristic
422#341—431no—
423#341C2×D4311yescharacteristic
424C43#2155511yescharacteristic, complemented, Sylow
425C2×#41C22×D4311yescharacteristic
426C22×D4—431no—
427C22×D4C22×D4311yescharacteristic
428C23×C4—861no—
429C23×C4—861no—
430AGL(1,ℤ/8)—22no—
431AGL(1,ℤ/8)—434no—
432AGL(1,ℤ/8)—862no—
433AGL(1,ℤ/8)C4×D4314yescomplemented
434C2×SD16—21no—
435C2×SD16—861no—
436C2×D8—21no—
437C2×D8—434no—
438C2×D8—862no—
439C2×D8—861no—
440C2×D8—861no—
441C2×D8—861no—
442#131—22no—
443#131—22no—
444#131—434no—
445#131—862no—
446C2×M16—21no—
447C2×M16—431no—
448C2×M16—431no—
449C2×M16—431no—
450C2×M16—861no—
451C2×M16C22×D4311yescharacteristic
452C2×M16C22×D4311yescharacteristic
453C2×M16C22×D4311yescharacteristic
454C22×C8—21no—
455C22×C8—431no—
456C22×C8—861no—
457C22×C8C22×D4311yescharacteristic
458C4×Q8—431no—
459C4×Q8—431no—
460C4×D4—431no—
461C4×D4—431no—
462C4×D4—861no—
463C4×D4—861no—
464C4×D4—861no—
465C4×D4—861no—
466C4×D4—861no—
467C4×D4—861no—
468C4×D4—861no—
469C4×D4—861no—
470C4×D4—861no—
471C4×D4—861no—
472#117—431no—
473#117—861no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C42—431no—
479C2×C42—861no—
480#108—434no—
481#108—862no—
482#107—861no—
483#107—861no—
484#106—861no—
485#106—861no—
486#106—861no—
487#106—861no—
488#103—21no—
489#103—861no—
490#102—21no—
491#102—21no—
492#102—21no—
493#102—861no—
494#102—861no—
495#102—861no—
496#102—861no—
497#102—861no—
498#102—861no—
499#102—861no—
500#100—22no—
501#100—434no—
502#100—434no—
503#100—862no—
504#97—431no—
505#97—431no—
506#97—431no—
507#97—431no—
508#97—861no—
509#97—861no—
510#97—861no—
511#97—861no—
512#97—861no—
513C4×C8—861no—
514C4×C8—861no—
515C4×C8—861no—
516C4×C8—861no—
517C4×C8—861no—
518C24—21no—
519C24—861no—
520#41—21no—
521#41—21no—
522#41C2×C4×D4312yes—
523#41#1062190012yes—
524C2×Q8D4×D4311yescharacteristic
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—432no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4C2×C4×D4312yes—
538C2×D4D4×D4311yescharacteristic
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—431no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—3442no—
547C22×C4—3442no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4—1721no—
551C22×C4—1721no—
552C22×C4C23×D4311yescharacteristic
553SD16—24no—
554SD16—864no—
555D8—24no—
556D8—864no—
557D8—864no—
558D8—864no—
559M16—24no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—432no—
565M16—432no—
566M16—864no—
567M16—861no—
568M16—861no—
569M16—861no—
570M16—861no—
571M16C2×C4×D4312yes—
572M16#1062190012yes—
573C2×C8—24no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—432no—
580C2×C8—431no—
581C2×C8—431no—
582C2×C8—432no—
583C2×C8—864no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8D4×D4311yescharacteristic
588C2×C8D4×D4311yescharacteristic
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—431no—
592C4⋊C4—431no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C22⋊C4—861no—
598C22⋊C4—861no—
599C22⋊C4—861no—
600C22⋊C4—1721no—
601C22⋊C4—1721no—
602C22⋊C4—1721no—
603C22⋊C4—1721no—
604C42—431no—
605C42—431no—
606C42—431no—
607C42—431no—
608C42—861no—
609C42—861no—
610C42—861no—
611C23—21no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—81no—
616C23—81no—
617C23—862no—
618C23—3441no—
619C23—3441no—
620C23—1721no—
621C23—1721no—
622C23#41×D4311yescharacteristic
623Q8—21no—
624Q8(C22⋊D43)⋊C412yes—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—22no—
629D4—21no—
630D4—41no—
631D4—41no—
632D4—862no—
633D4—862no—
634D4—1721no—
635D4—1721no—
636D4(C22⋊D43)⋊C412yes—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—81no—
642C2×C4—431no—
643C2×C4—431no—
644C2×C4—431no—
645C2×C4—431no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—3442no—
649C2×C4—3442no—
650C2×C4—3442no—
651C2×C4—3442no—
652C2×C4—3441no—
653C2×C4—3441no—
654C2×C4—3441no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4C22×C4×D4311yescharacteristic
659C2×C4C2×D4×D4311yescharacteristic
660C2×C4C2×D4×D4311yescharacteristic
661C2×C4#41×D4311yescharacteristic
662C2×C4C2×#1062190011yescharacteristic
663C2×C4C2×#1062190011yescharacteristic
664C8—22no—
665C8—21no—
666C8—22no—
667C8—21no—
668C8—41no—
669C8—432no—
670C8—432no—
671C8—862no—
672C8—862no—
673C8—1721no—
674C22—21no—
675C22—21no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—42no—
680C22—82no—
681C22—82no—
682C22—81no—
683C22—81no—
684C22—3442no—
685C22—3442no—
686C22—3441no—
687C22—3441no—
688C22—1722no—
689C22C4×#1062190011yescharacteristic
690C22#121×D4311yescharacteristic
691C22#1458342611yescharacteristic
692C4—22no—
693C4—81no—
694C4—861no—
695C4—861no—
696C4—861no—
697C4—861no—
698C4—3441no—
699C4—1721no—
700C4—1721no—
701C4C4×D4×D4311yescharacteristic
702C4C2×(C22⋊D43)⋊C411yescharacteristic
703C4#1458340511yescharacteristic
704C4#1458344411yescharacteristic
705C2—21no—
706C2—21no—
707C2—42no—
708C2—82no—
709C2—3442no—
710C2#1913710511yescharacteristic
711C2#1914431811yescharacteristic
712C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1907C2
socleC22×C43C2×#121
prime radicalC2×#14583167C2
cosocleC22×C4×C43C24
hypercenter#1907D43
hypocenterC43#21555
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1907

Complements

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

NH ≅ G/Ntype
2. #19143408C2semidirect
3. AGL(1,ℤ/8)×Dic43C2semidirect
4. C2×#14583008C2semidirect
5. #19143021C2semidirect
6. #19135502C2semidirect
7. #19135374C2semidirect
8. #19135258C2semidirect
9. #19135254C2semidirect
10. #19135103C2semidirect
11. #19134652C2semidirect
12. #19134500C2semidirect
13. #100×Dic43C2semidirect
14. #19134386C2semidirect
15. C43×#1907C2semidirect
22. #14583167C4semidirect
72. #13063350C2×C4semidirect
78. C2×#10621882C2×C4semidirect
80. #13063332C2×C4semidirect
109. #13063260C2×C4semidirect
124. #13063242C2×C4semidirect
126. #13063241C2×C4semidirect
144. AGL(1,ℤ/8)×C43C2×C4semidirect
359. #1907D43semidirect
424. C43#21555semidirect
433. AGL(1,ℤ/8)C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831672
#191434082
AGL(1,ℤ/8)×Dic432
C2×#145830082
#191430212
#191355022
#191353742
#191352582
#191352542
#191351032
#191346522
#191345002
#100×Dic432
#191343862
C43×#19072
#2155543