Finite Group Databasebeta

← #25103528

Subgroups — #25103528

Order 11008.

906 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×#14583161C211yesmaximal, characteristic
2#19143413C211yesmaximal, characteristic, complemented
3#19143399C211yesmaximal, characteristic
4C2×#14582996C211yesmaximal, characteristic, complemented
5#19143022C211yesmaximal, characteristic, complemented
6#19135501C211yesmaximal, characteristic, complemented
7#19135377C211yesmaximal, characteristic, complemented
8#19135250C211yesmaximal, characteristic, complemented
9#19135109C211yesmaximal, characteristic, complemented
10#19135106C211yesmaximal, characteristic
11#19134658C211yesmaximal, characteristic, complemented
12#19134500C211yesmaximal, characteristic, complemented
13#19134390C211yesmaximal, characteristic, complemented
14#100×Dic43C211yesmaximal, characteristic, complemented
15C43×#1931C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21#14583367C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24#14583161C418yescomplemented
25#14583008—21no—
26#14583005—21no—
27#14582998—21no—
28#14582996—21no—
29#14582996—21no—
30#14582996—21no—
31#14582996—21no—
32#14582996—21no—
33#14582993—21no—
34#14582990—21no—
35#14582986—21no—
36#14582979—21no—
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582942C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41#14582907C2211yescharacteristic
42#14582901C2211yescharacteristic
43#14582898C2211yescharacteristic
44C2×#13063250C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48#14582856—21no—
49#14582855C2211yescharacteristic
50#14582853—21no—
51M16×Dic43C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54C4×#10621872—21no—
55C2×#13063235C2211yescharacteristic
56#97×D43—21no—
57#14582668C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582664C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#418C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#100×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71#13063358—22no—
72#13063358C2×C414yescomplemented
73#13063351—22no—
74#13063351C2×C414yes—
75C2×Dic172—21no—
76C2×#10621873—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621883—21no—
80C2×#10621883—22no—
81C2×#10621883C2×C414yescomplemented
82C2×#10621882—21no—
83#13063333—22no—
84#13063333C2×C414yescomplemented
85#13063331—22no—
86#13063331—22no—
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621877C2311yescharacteristic
90C2×#10621872—21no—
91C2×#10621872—21no—
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94C2×C8×D43—21no—
95#13063290—21no—
96#13063290—21no—
97#13063290—21no—
98#13063290—21no—
99#13063290D411yescharacteristic
100#13063290D411yescharacteristic
101D4×Dic43—21no—
102D4×Dic43—21no—
103D4×Dic43—21no—
104D4×Dic43—21no—
105#13063287D411yescharacteristic
106#13063287D411yescharacteristic
107(C22⋊D43)⋊C4—21no—
108(C22⋊D43)⋊C4—21no—
109#13063282—21no—
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4—21no—
112C2×C22⋊Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43C2311yescharacteristic
115C42×D43—21no—
116#13063260—22no—
117#13063260C2×C414yescomplemented
118#13063258—21no—
119#13063258—21no—
120#13063258—21no—
121#13063256—21no—
122#13063250—21no—
123#13063250—21no—
124#13063250—21no—
125#13063248—21no—
126#13063248—21no—
127#13063248—21no—
128#13063247—21no—
129#13063245—21no—
130#13063243—22no—
131#13063243C2×C414yescomplemented
132#13063242—22no—
133#13063236—21no—
134#13063235—21no—
135#13063235—21no—
136#13063235—21no—
137#13063235D411yescharacteristic
138#13063235D411yescharacteristic
139#13063235D411yescharacteristic
140#13063235D411yescharacteristic
141C4×C43⋊C8—21no—
142C8×Dic43—21no—
143C8×Dic43—21no—
144C8×Dic43—21no—
145C22×D4×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152#107×C43—21no—
153#106×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156#102×C43—21no—
157#102×C43—21no—
158#100×C43C2×C414yescomplemented
159#97×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43C2411yescharacteristic
170C2×C22⋊D43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—41no—
174C22×Dic43—41no—
175C22×Dic43—82no—
176C22×Dic43#4111yescharacteristic
177C22×Dic43#4111yescharacteristic
178#10621898—21no—
179#10621898—21no—
180#10621898C22×C412yes—
181#10621898#4112yes—
182C2×D172C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C22×C412yes—
192C2×Dic86C2×D411yescharacteristic
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43C22×C412yes—
198M16×C43C22×C412yes—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43C2×D411yescharacteristic
205C2×C8×C43C2×D411yescharacteristic
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—21no—
211C42×C43—21no—
212C22⋊Dic43—41no—
213C22⋊Dic43—41no—
214#10621883—24no—
215#10621883—24no—
216#10621883—24no—
217#10621882—24no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222Dic43⋊C4—21no—
223Dic43⋊C4—21no—
224Dic43⋊C4—41no—
225Dic43⋊C4—41no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—41no—
229C4×Dic43—41no—
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232C4×Dic43C2×D411yescharacteristic
233C4×Dic43C2×D411yescharacteristic
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877—21no—
238#10621877C22×C412yes—
239#10621877#4112yes—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
246C2×C43⋊C8#4112yes—
247Dic172—24no—
248#10621873—24no—
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—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—41no—
267C2×C4×C43—81no—
268C2×C4×C43C23×C411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C22⋊D43—22no—
275C22⋊D43—22no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—82no—
284C2×Dic43—82no—
285C2×Dic43—81no—
286C2×Dic43#12111yescharacteristic
287C2×Dic43#12111yescharacteristic
288C2×Dic43#12111yescharacteristic
289C2×Dic43#12111yescharacteristic
290D172—21no—
291D172C4×D412yes—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—81no—
295C4×D43—81no—
296Dic86—21no—
297Dic86—22no—
298Dic86—22no—
299Dic86—41no—
300Dic86—41no—
301Dic86C4×D412yes—
302C8×C43—22no—
303C8×C43—22no—
304C8×C43—21no—
305C8×C43—21no—
306C8×C43—41no—
307C43⋊C8—22no—
308C43⋊C8—22no—
309C43⋊C8—41no—
310C43⋊C8C4×D412yes—
311C43⋊C8C4×D412yes—
312#21557—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—41no—
327C4×C43—41no—
328C4×C43—81no—
329C4×C43C2×C4×D411yescharacteristic
330C4×C43C2×C4×D411yescharacteristic
331C4×C43#52511yescharacteristic
332C4×C43#53211yescharacteristic
333Dic43—22no—
334Dic43—21no—
335Dic43—21no—
336Dic43—21no—
337Dic43—21no—
338Dic43—42no—
339Dic43—81no—
340C2×#471—431no—
341C4×#137—431no—
342C4×AGL(1,ℤ/8)—431no—
343C2×#440—431no—
344#2875—431no—
345#1977—431no—
346#1952—431no—
347#1931D4311yescharacteristic, complemented
348#1930—431no—
349#1908—431no—
350#1907—431no—
351#1816—431no—
352#1778—431no—
353C4×#101—431no—
354C4×#100—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—82no—
358C2×C43C4×#12111yescharacteristic
359C2×C43#306811yescharacteristic
360C2×C43#306911yescharacteristic
361D43—42no—
362C2×#137—431no—
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16—431no—
365C2×#131—431no—
366C2×#131—431no—
367C4×#41—431no—
368C2×C4×Q8—431no—
369C2×C4×D4—431no—
370#471—438no—
371#442—861no—
372#441—861no—
373#440—861no—
374#440—861no—
375#440—861no—
376#440—861no—
377#440—861no—
378#440—861no—
379C4×Q16—861no—
380C4×SD16—861no—
381C4×SD16—861no—
382C4×D8—861no—
383C2×#108—431no—
384C2×#108—431no—
385#428—431no—
386#428C2×D4311yescharacteristic
387C2×#107—431no—
388#419—431no—
389#418C2×D4311yescharacteristic
390#417—431no—
391#417—431no—
392C2×#103—431no—
393C2×#102C2×D4311yescharacteristic
394C2×#101—431no—
395C2×#101—431no—
396C2×#100—431no—
397C2×#100C2×D4311yescharacteristic
398#405—431no—
399#405—861no—
400#405—861no—
401#405C2×D4311yescharacteristic
402C4×M16—431no—
403C4×M16—431no—
404C4×M16—431no—
405C4×M16—861no—
406C2×#97—431no—
407C2×#97—861no—
408#343—431no—
409#343—431no—
410#343—431no—
411#343C2×D4311yescharacteristic
412#341—431no—
413#341C2×D4311yescharacteristic
414C43#2155711yescharacteristic, complemented, Sylow
415C2×#41—431no—
416C22×Q8—431no—
417C22×D4C22×D4311yescharacteristic
418C23×C4—861no—
419#137—434no—
420#137—862no—
421AGL(1,ℤ/8)—434no—
422AGL(1,ℤ/8)—862no—
423C2×Q16—861no—
424C2×SD16—434no—
425C2×SD16—861no—
426C2×SD16—862no—
427C2×SD16—861no—
428C2×SD16—861no—
429C2×SD16—861no—
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—861no—
439C2×M16—861no—
440C2×M16C22×D4311yescharacteristic
441C2×M16C22×D4311yescharacteristic
442C2×M16C22×D4311yescharacteristic
443C22×C8—431no—
444C22×C8—861no—
445C22×C8—861no—
446C22×C8C22×D4311yescharacteristic
447C4×Q8—431no—
448C4×Q8—431no—
449C4×Q8—861no—
450C4×Q8—861no—
451C4×Q8—861no—
452C4×Q8—861no—
453C4×D4—431no—
454C4×D4—431no—
455C4×D4—861no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4—861no—
459C4×D4—861no—
460C4×D4—861no—
461#117—861no—
462#117C22×D4311yescharacteristic
463C2×C4⋊C4—431no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—861no—
467C2×C42—431no—
468C2×C42—861no—
469C2×C42—861no—
470#108—434no—
471#108—862no—
472#107—21no—
473#107—861no—
474#107—861no—
475#107—861no—
476#106—21no—
477#106—861no—
478#103—861no—
479#103—861no—
480#103—861no—
481#103—861no—
482#103—861no—
483#103—861no—
484#102—21no—
485#102—21no—
486#102—21no—
487#102—21no—
488#102—861no—
489#102—861no—
490#101—434no—
491#101—862no—
492#100—862no—
493#100C4×D4314yescomplemented
494#97—21no—
495#97—431no—
496#97—431no—
497#97—431no—
498#97—431no—
499#97—861no—
500#97—861no—
501#97—861no—
502#97—861no—
503C4×C8—21no—
504C4×C8—861no—
505C4×C8—861no—
506C4×C8—861no—
507C4×C8—861no—
508C24—21no—
509#41—432no—
510#41—432no—
511#41—861no—
512#41—861no—
513C2×Q8—432no—
514C2×Q8—431no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8—861no—
518C2×Q8—861no—
519C2×Q8—861no—
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—431no—
530C22×C4—431no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—3442no—
537C22×C4—1721no—
538C22×C4—1721no—
539C22×C4C23×D4311yescharacteristic
540Q16—864no—
541SD16—864no—
542SD16—864no—
543SD16—864no—
544SD16—864no—
545D8—864no—
546M16—21no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—432no—
551M16—432no—
552M16—864no—
553M16—864no—
554M16—861no—
555M16—861no—
556M16—861no—
557M16—861no—
558M16C2×C4×D4312yes—
559M16C2×C4×D4312yes—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—432no—
566C2×C8—431no—
567C2×C8—431no—
568C2×C8—432no—
569C2×C8—864no—
570C2×C8—864no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8D4×D4311yescharacteristic
575C2×C8D4×D4311yescharacteristic
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—1721no—
583C4⋊C4—1721no—
584C4⋊C4D4×D4311yescharacteristic
585C4⋊C4D4×D4311yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—861no—
588C22⋊C4—861no—
589C22⋊C4—1721no—
590C22⋊C4—1721no—
591C42—21no—
592C42—431no—
593C42—431no—
594C42—431no—
595C42—431no—
596C42—861no—
597C42—861no—
598C42—1721no—
599C42—1721no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—81no—
604C23—81no—
605C23—861no—
606C23#41×D4311yescharacteristic
607Q8—432no—
608Q8—861no—
609Q8—862no—
610Q8—862no—
611Q8—1721no—
612Q8—1721no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—432no—
618D4—862no—
619D4—862no—
620D4—861no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—81no—
625C2×C4—431no—
626C2×C4—431no—
627C2×C4—431no—
628C2×C4—431no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—3441no—
634C2×C4—3441no—
635C2×C4—3442no—
636C2×C4—3442no—
637C2×C4—3441no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4C22×C4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#41×D4311yescharacteristic
649C8—22no—
650C8—22no—
651C8—21no—
652C8—21no—
653C8—41no—
654C8—432no—
655C8—432no—
656C8—862no—
657C8—862no—
658C8—1721no—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—82no—
663C22—82no—
664C22—81no—
665C22—81no—
666C22—862no—
667C22—1721no—
668C22—1721no—
669C22#1458336711yescharacteristic
670C22#121×D4311yescharacteristic
671C22#1458343211yescharacteristic
672C4—41no—
673C4—41no—
674C4—81no—
675C4—862no—
676C4—861no—
677C4—861no—
678C4—861no—
679C4—861no—
680C4—3441no—
681C4—1722no—
682C4C4×D4×D4311yescharacteristic
683C4C4×D4×D4311yescharacteristic
684C4#1458340711yescharacteristic
685C4#1458344811yescharacteristic
686C2—21no—
687C2—21no—
688C2—82no—
689C2—1722no—
690C2#1913710711yescharacteristic
691C2#1914432111yescharacteristic
692C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1931C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
cosocleC22×C4×C43C24
hypercenter#1931D43
hypocenterC43#21557
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1931

Complements

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

NH ≅ G/Ntype
2. #19143413C2semidirect
4. C2×#14582996C2semidirect
5. #19143022C2semidirect
6. #19135501C2semidirect
7. #19135377C2semidirect
8. #19135250C2semidirect
9. #19135109C2semidirect
11. #19134658C2semidirect
12. #19134500C2semidirect
13. #19134390C2semidirect
14. #100×Dic43C2semidirect
15. C43×#1931C2semidirect
24. #14583161C4semidirect
72. #13063358C2×C4semidirect
81. C2×#10621883C2×C4semidirect
84. #13063333C2×C4semidirect
117. #13063260C2×C4semidirect
131. #13063243C2×C4semidirect
158. #100×C43C2×C4semidirect
347. #1931D43semidirect
414. C43#21557semidirect
493. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831612
#191434132
#191433992
C2×#145829962
#191430222
#191355012
#191353772
#191352502
#191351092
#191351062
#191346582
#191345002
#191343902
#100×Dic432
C43×#19312
#2155743