Finite Group Databasebeta

← #25103497

Subgroups — #25103497

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×#14583168C211yesmaximal, characteristic
2C4×#13063353C211yesmaximal, characteristic, complemented
3C4×#13063351C211yesmaximal, characteristic, complemented
4C2×#14583009C211yesmaximal, characteristic, complemented
5#19143024C211yesmaximal, characteristic, complemented
6#19135502C211yesmaximal, characteristic, complemented
7#19135374C211yesmaximal, characteristic, complemented
8#19135259C211yesmaximal, characteristic, complemented
9#19135255C211yesmaximal, characteristic, complemented
10#19135104C211yesmaximal, characteristic, complemented
11#19135100C211yesmaximal, characteristic, complemented
12#19134653C211yesmaximal, characteristic, complemented
13#19134502C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#100×C43C211yesmaximal, characteristic, complemented
16C2×#13063353C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C4×#10621898C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583168C418yescomplemented
24#14583012—21no—
25#14583009—21no—
26#14583009—21no—
27#14583009—21no—
28#14583009—21no—
29#14583009—21no—
30#14583001—21no—
31#14582999—21no—
32C4×#10621873—21no—
33C4×#10621883—21no—
34C4×D344—21no—
35C4×#10621882—21no—
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063256C2211yescharacteristic
41#14582905C2211yescharacteristic
42#14582904C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582898C2211yescharacteristic
45C2×#13063246C2211yescharacteristic
46C2×#13063245C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49#14582857C2211yescharacteristic
50#14582857C2211yescharacteristic
51#14582853—21no—
52#14582853—21no—
53C4×#10621877C2211yescharacteristic
54#14582851—21no—
55C2×#13063236C2211yescharacteristic
56#97×D43—21no—
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582663C2211yescharacteristic
61C2×C4×D4×C43C2211yescharacteristic
62C2×#100×C43C2211yescharacteristic
63C2×#100×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C4×M16×C43C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C4×D43—21no—
71#13063353—22no—
72#13063353C2×C414yescomplemented
73#13063351—22no—
74#13063351C2×C414yescomplemented
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×D344—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621882—22no—
82C2×#10621882C2×C414yescomplemented
83#13063333—22no—
84#13063333—22no—
85#13063333—22no—
86#13063333C2×C414yescomplemented
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94C2×C8×D43—21no—
95C4×Dic86D411yescharacteristic
96C4×Dic86D411yescharacteristic
97C4×D172—21no—
98C4×D172—21no—
99C4×D172—21no—
100C4×D172—21no—
101C4×D172D411yescharacteristic
102C4×D172D411yescharacteristic
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105#13063284C2311yescharacteristic
106#13063282—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C42×D43—21no—
110#13063260—22no—
111#13063260C2×C414yescomplemented
112#13063259—21no—
113#13063258—21no—
114#13063257—21no—
115#13063256—21no—
116#13063256—21no—
117#13063256—21no—
118#13063250—21no—
119#13063248—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063246—21no—
124#13063246—21no—
125#13063246—21no—
126#13063246—21no—
127#13063245—21no—
128#13063245—21no—
129#13063245—21no—
130#13063241—22no—
131#13063241C2×C414yescomplemented
132#13063236—21no—
133#13063236D411yescharacteristic
134#13063236D411yescharacteristic
135#13063236D411yescharacteristic
136#13063236D411yescharacteristic
137#13063235—21no—
138#13063235—21no—
139C4×C43⋊C8—21no—
140C8×Dic43—21no—
141C8×Dic43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C2×M16×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#100×C43—22no—
156#100×C43C2×C414yescomplemented
157#97×C43—21no—
158#97×C43—21no—
159C4×C8×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C23×D43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C22×C412yes—
169C22×C4×C43—21no—
170C22×C4×C43—41no—
171C22×C4×C43—41no—
172C22×C4×C43—82no—
173C22×C4×C43#4111yescharacteristic
174C22×C4×C43#4111yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—21no—
177C22×Dic43—21no—
178#10621898—21no—
179#10621898—21no—
180#10621898C22×C412yes—
181#10621898#4112yes—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172C22×C412yes—
188C2×D172C2×D411yescharacteristic
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—41no—
193C2×C4×D43—41no—
194C2×C4×D43—82no—
195C2×Dic86C2×D411yescharacteristic
196M16×C43—21no—
197M16×C43—21no—
198M16×C43—21no—
199M16×C43—21no—
200M16×C43—21no—
201M16×C43C22×C412yes—
202M16×C43C22×C412yes—
203M16×C43#4112yes—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—41no—
211C22⋊C4×C43—41no—
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C22⋊Dic43—21no—
217#10621883—24no—
218#10621882—24no—
219#10621882—24no—
220#10621882—24no—
221(C2×D43)⋊C4—21no—
222(C2×D43)⋊C4—21no—
223(C2×D43)⋊C4—41no—
224(C2×D43)⋊C4—41no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43C2×D411yescharacteristic
228C4⋊Dic43C2×D411yescharacteristic
229Dic43⋊C4—21no—
230Dic43⋊C4—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234#10621877—21no—
235#10621877—21no—
236#10621877—21no—
237#10621877C22×C412yes—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C22×C412yes—
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
246C2×C43⋊C8C2×D411yescharacteristic
247C2×C43⋊C8#4112yes—
248D344—24no—
249#10621873—24no—
250#10621872—24no—
251#10621872—24no—
252C8×D43—24no—
253C8×D43—24no—
254C23×C43—22no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—81no—
258C23×C43—81no—
259C23×C43C2×#4111yescharacteristic
260C22×D43—21no—
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—81no—
265C22×D43—81no—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—41no—
269D4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—82no—
274C2×C4×C43—82no—
275C2×C4×C43—81no—
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C22⋊D43—22no—
287C22⋊D43—22no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—41no—
292C2×Dic43—81no—
293D172—22no—
294D172—22no—
295D172—21no—
296D172—41no—
297D172—41no—
298D172C4×D412yes—
299C4×D43—22no—
300C4×D43—22no—
301C4×D43—81no—
302C4×D43—81no—
303C4×D43—82no—
304C4×D43—82no—
305Dic86—21no—
306Dic86C4×D412yes—
307C8×C43—22no—
308C8×C43—22no—
309C8×C43—22no—
310C8×C43—41no—
311C43⋊C8—22no—
312C43⋊C8—21no—
313C43⋊C8—21no—
314C43⋊C8—41no—
315C43⋊C8C4×D412yes—
316C43⋊C8C4×D412yes—
317#21555—431nomaximal, Sylow
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—42no—
321C22×C43—82no—
322C22×C43—82no—
323C22×C43—81no—
324C22×C43—81no—
325C22×C43C4×#4111yescharacteristic
326C22×C43C2×#12111yescharacteristic
327C22×C43#52911yescharacteristic
328C2×D43—22no—
329C2×D43—41no—
330C2×D43—41no—
331C2×D43—42no—
332C2×D43—82no—
333C2×D43—81no—
334C2×D43—81no—
335C2×D43—82no—
336C4×C43—21no—
337C4×C43—21no—
338C4×C43—21no—
339C4×C43—21no—
340C4×C43—81no—
341C4×C43C2×C4×D411yescharacteristic
342C4×C43C2×C4×D411yescharacteristic
343C4×C43#52511yescharacteristic
344C4×C43#53211yescharacteristic
345Dic43—22no—
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#1907—431no—
360#1815—431no—
361#1778—431no—
362C4×#100—431no—
363C4×#100D4311yescharacteristic, complemented
364C2×C43—21no—
365C2×C43—21no—
366C2×C43—82no—
367C2×C43C4×#12111yescharacteristic
368C2×C43#306811yescharacteristic
369C2×C43#306811yescharacteristic
370D43—42no—
371D43—82no—
372C2×AGL(1,ℤ/8)—431no—
373C2×AGL(1,ℤ/8)—431no—
374C22×D8—431no—
375C2×#131—431no—
376C2×#131—431no—
377C4×#41—431no—
378C2×C4×D4—431no—
379C2×C4×D4C2×D4311yescharacteristic
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#417—431no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#100—431no—
405C2×#100—431no—
406C2×#100C2×D4311yescharacteristic
407C2×#100C2×D4311yescharacteristic
408#405—431no—
409#405—431no—
410#405—861no—
411#405—861no—
412C4×M16—431no—
413C4×M16—861no—
414C4×M16C2×D4311yescharacteristic
415C4×M16C2×D4311yescharacteristic
416C2×#97—431no—
417C2×#97—861no—
418#343—431no—
419#343—431no—
420#343C2×D4311yescharacteristic
421#343C2×D4311yescharacteristic
422#341—431no—
423#341—431no—
424C43#2155511yescharacteristic, complemented, Sylow
425C2×#41—431no—
426C22×D4—431no—
427C22×D4C22×D4311yescharacteristic
428C23×C4—21no—
429C23×C4—861no—
430AGL(1,ℤ/8)—434no—
431AGL(1,ℤ/8)—434no—
432AGL(1,ℤ/8)—862no—
433AGL(1,ℤ/8)—862no—
434C2×SD16—861no—
435C2×SD16—861no—
436C2×D8—434no—
437C2×D8—861no—
438C2×D8—862no—
439C2×D8—861no—
440C2×D8—861no—
441C2×D8—861no—
442#131—434no—
443#131—862no—
444#131—862no—
445#131—862no—
446C2×M16—431no—
447C2×M16—431no—
448C2×M16—861no—
449C2×M16—861no—
450C2×M16C22×D4311yescharacteristic
451C2×M16C22×D4311yescharacteristic
452C2×M16C22×D4311yescharacteristic
453C2×M16C22×D4311yescharacteristic
454C22×C8—431no—
455C22×C8—431no—
456C22×C8—861no—
457C22×C8—861no—
458C4×Q8—431no—
459C4×Q8—431no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—431no—
465C4×D4—431no—
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—21no—
477C2×C22⋊C4—861no—
478C2×C42—861no—
479C2×C42C22×D4311yescharacteristic
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—861no—
489#103—861no—
490#102—861no—
491#102—861no—
492#102—861no—
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—862no—
503#100C4×D4314yescomplemented
504#97—21no—
505#97—21no—
506#97—431no—
507#97—431no—
508#97—431no—
509#97—431no—
510#97—861no—
511#97—861no—
512#97—861no—
513C4×C8—21no—
514C4×C8—21no—
515C4×C8—861no—
516C4×C8—861no—
517C4×C8—861no—
518C24—21no—
519C24—861no—
520#41—432no—
521#41—432no—
522#41—861no—
523#41—861no—
524C2×Q8—431no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—432no—
531C2×D4—431no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4C2×C4×D4312yes—
539C22×C4—21no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—82no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—3442no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4#1062189811yescharacteristic
551C22×C4#1062189811yescharacteristic
552C22×C4C23×D4311yescharacteristic
553SD16—864no—
554SD16—864no—
555D8—864no—
556D8—864no—
557D8—864no—
558D8—864no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—432no—
565M16—864no—
566M16—864no—
567M16—861no—
568M16—861no—
569M16—861no—
570M16C2×C4×D4312yes—
571M16C2×C4×D4312yes—
572M16#1062189812yes—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—432no—
578C2×C8—431no—
579C2×C8—431no—
580C2×C8—432no—
581C2×C8—431no—
582C2×C8—431no—
583C2×C8—864no—
584C2×C8—864no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—861no—
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—41no—
598C22⋊C4—41no—
599C22⋊C4—861no—
600C22⋊C4—861no—
601C22⋊C4—861no—
602C22⋊C4—1721no—
603C22⋊C4—1721no—
604C42—861no—
605C42—861no—
606C42—861no—
607C42D4×D4311yescharacteristic
608C42D4×D4311yescharacteristic
609C42D4×D4311yescharacteristic
610C42D4×D4311yescharacteristic
611C23—22no—
612C23—41no—
613C23—41no—
614C23—81no—
615C23—81no—
616C23—861no—
617C23—862no—
618C23—3441no—
619C23—3441no—
620C23—1721no—
621C23—1721no—
622C23C2×#1062189811yescharacteristic
623Q8—432no—
624Q8—861no—
625D4—22no—
626D4—22no—
627D4—41no—
628D4—41no—
629D4—432no—
630D4—862no—
631D4—862no—
632D4—862no—
633D4—862no—
634D4—861no—
635D4—1721no—
636D4—1721no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—81no—
643C2×C4—861no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—3442no—
649C2×C4—3442no—
650C2×C4—3441no—
651C2×C4—3441no—
652C2×C4—3441no—
653C2×C4—1721no—
654C2×C4#1306329811yescharacteristic
655C2×C4#1306329811yescharacteristic
656C2×C4#1306329811yescharacteristic
657C2×C4#1306329811yescharacteristic
658C2×C4C22×C4×D4311yescharacteristic
659C2×C4C2×D4×D4311yescharacteristic
660C2×C4C2×D4×D4311yescharacteristic
661C2×C4#41×D4311yescharacteristic
662C2×C4#41×D4311yescharacteristic
663C2×C4C2×#1062189811yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—41no—
668C8—432no—
669C8—432no—
670C8—862no—
671C8—861no—
672C8—861no—
673C8—1721no—
674C22—21no—
675C22—21no—
676C22—42no—
677C22—82no—
678C22—82no—
679C22—81no—
680C22—81no—
681C22—862no—
682C22—3442no—
683C22—3442no—
684C22—3441no—
685C22—3441no—
686C22—1722no—
687C22—1721no—
688C22—1721no—
689C22C4×#1062189811yescharacteristic
690C22C2×#1306329811yescharacteristic
691C22#1458342711yescharacteristic
692C4—21no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—81no—
697C4—862no—
698C4—3441no—
699C4—1721no—
700C4—1721no—
701C4C4×D4×D4311yescharacteristic
702C4C4×D4×D4311yescharacteristic
703C4#1458340811yescharacteristic
704C4#1458344611yescharacteristic
705C2—21no—
706C2—21no—
707C2—82no—
708C2—3442no—
709C2—1722no—
710C2C4×#1306329811yescharacteristic
711C2#1914432211yescharacteristic
712C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C2×#121
prime radicalC2×#14583168C2
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43#21555
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. C4×#13063353C2semidirect
3. C4×#13063351C2semidirect
4. C2×#14583009C2semidirect
5. #19143024C2semidirect
6. #19135502C2semidirect
7. #19135374C2semidirect
8. #19135259C2semidirect
9. #19135255C2semidirect
10. #19135104C2semidirect
11. #19135100C2semidirect
12. #19134653C2semidirect
13. #19134502C2semidirect
14. C4×#13063241C2semidirect
15. C4×#100×C43C2semidirect
23. #14583168C4semidirect
72. #13063353C2×C4semidirect
74. #13063351C2×C4semidirect
82. C2×#10621882C2×C4semidirect
86. #13063333C2×C4semidirect
111. #13063260C2×C4semidirect
131. #13063241C2×C4semidirect
156. #100×C43C2×C4semidirect
363. C4×#100D43semidirect
424. C43#21555semidirect
503. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831682
C4×#130633532
C4×#130633512
C2×#145830092
#191430242
#191355022
#191353742
#191352592
#191352552
#191351042
#191351002
#191346532
#191345022
C4×#130632412
C4×#100×C432
#2155543