Finite Group Databasebeta

← #25126327

Subgroups — #25126327

Order 11008.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×Dic43C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic
3C2×#14583000C211yesmaximal, characteristic, complemented
4#19143242C211yesmaximal, characteristic, complemented
5#19136102C211yesmaximal, characteristic, complemented
6#19136035C211yesmaximal, characteristic, complemented
7#19135958C211yesmaximal, characteristic, complemented
8#19135951C211yesmaximal, characteristic, complemented
9#19135891C211yesmaximal, characteristic, complemented
10#19135884C211yesmaximal, characteristic
11#19135853C211yesmaximal, characteristic, complemented
12#19134500C211yesmaximal, characteristic, complemented
13#101×Dic43C211yesmaximal, characteristic, complemented
14#100×Dic43C211yesmaximal, characteristic, complemented
15C43×#2019C211yesmaximal, characteristic
16#41×Dic43C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583011—21no—
20#14583006—21no—
21#14583000—21no—
22#14583000—21no—
23#14583000—22no—
24#14583000—22no—
25Q16×Dic43—21no—
26SD16×Dic43—21no—
27SD16×Dic43—21no—
28D8×Dic43—21no—
29#14582957—22no—
30#14582953—22no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582941C2211yescharacteristic
34#14582941C2211yescharacteristic
35C2×#13063259C2211yescharacteristic
36#14582927C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582908C2211yescharacteristic
39#14582904C2211yescharacteristic
40#14582900C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063242C2211yescharacteristic
46#14582866C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49M16×Dic43C2211yescharacteristic
50C2×#13063235C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582664C2211yescharacteristic
56C2×#137×C43C2211yescharacteristic
57C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
58C22×SD16×C43C2211yescharacteristic
59C2×#101×C43C2211yescharacteristic
60C2×#100×C43C2211yescharacteristic
61C43×#408C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C23×Dic43—21no—
64C2×#10621877C2311yescharacteristic
65C2×#10621877C2311yescharacteristic
66C2×#10621877C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68Q8×Dic43—21no—
69Q8×Dic43—21no—
70Q8×Dic43—21no—
71Q8×Dic43—21no—
72Q8×Dic43D411yescharacteristic
73Q8×Dic43D411yescharacteristic
74D4×Dic43—21no—
75D4×Dic43—21no—
76D4×Dic43—21no—
77D4×Dic43—21no—
78D4×Dic43—21no—
79D4×Dic43—21no—
80D4×Dic43D411yescharacteristic
81D4×Dic43D411yescharacteristic
82#13063284—21no—
83#13063284C2311yescharacteristic
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91#13063260—22no—
92#13063260—22no—
93#13063259—22no—
94#13063259—21no—
95#13063259—21no—
96#13063257—21no—
97#13063257—21no—
98Dic43⋊C8—22no—
99Dic43⋊C8—22no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—22no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—22no—
110#13063244—22no—
111#13063242—22no—
112C22⋊(C43⋊C8)—22no—
113#13063235—21no—
114#13063235—21no—
115#13063235—21no—
116#13063235D412yes—
117#13063235D412yes—
118C8×Dic43—21no—
119C8×Dic43—21no—
120C8×Dic43—21no—
121C2×#41×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43C2311yescharacteristic
124#137×C43—22no—
125#137×C43—22no—
126AGL(1,ℤ/8)×C43—22no—
127AGL(1,ℤ/8)×C43—22no—
128C2×Q16×C43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—22no—
131C2×SD16×C43—21no—
132C2×SD16×C43—22no—
133C2×SD16×C43—22no—
134C2×D8×C43—21no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#101×C43—22no—
140#100×C43—22no—
141C22⋊C8×C43—22no—
142C24×C43—21no—
143#41×C43—21no—
144#41×C43—21no—
145#41×C43—21no—
146#41×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×Q8×C43#4112yes—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43#4112yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—41no—
170C22×Dic43—41no—
171C22×Dic43—82no—
172C22×Dic43#4111yescharacteristic
173C22×Dic43#4111yescharacteristic
174Q16×C43—24no—
175SD16×C43—28no—
176SD16×C43—24no—
177SD16×C43—24no—
178D8×C43—24no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182M16×C43—21no—
183M16×C43#4112yes—
184M16×C43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C2×D412yes—
191C22⋊Dic43—21no—
192C22⋊Dic43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—41no—
195C22⋊Dic43—41no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—41no—
210C4×Dic43—41no—
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8C2×D412yes—
227C23×C43—21no—
228C23×C43—22no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—81no—
232C23×C43—81no—
233C23×C43C2×#4111yescharacteristic
234Q8×C43—22no—
235Q8×C43—21no—
236Q8×C43—22no—
237Q8×C43—21no—
238Q8×C43—41no—
239Q8×C43—41no—
240D4×C43—21no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—21no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—81no—
267C2×Dic43—81no—
268C2×Dic43—82no—
269C2×Dic43—82no—
270C2×Dic43—81no—
271C2×Dic43—81no—
272C2×Dic43#12111yescharacteristic
273C2×Dic43#12111yescharacteristic
274C2×Dic43#12111yescharacteristic
275C2×Dic43#12111yescharacteristic
276C8×C43—22no—
277C8×C43—22no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—22no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#23721—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—42no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43C2×#12111yescharacteristic
296C22×C43#52911yescharacteristic
297C22×C43#52911yescharacteristic
298C4×C43—41no—
299C4×C43—42no—
300C4×C43#52511yescharacteristic
301C4×C43#52511yescharacteristic
302C4×C43#52511yescharacteristic
303C4×C43#53211yescharacteristic
304Dic43—21no—
305Dic43—21no—
306Dic43—21no—
307Dic43—21no—
308Dic43—41no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312C4×#137—431no—
313C4×AGL(1,ℤ/8)—431no—
314C2×#440—431no—
315#2923—431no—
316#2089—431no—
317#2078—431no—
318#2064—431no—
319#2063—431no—
320#2052—431no—
321#2051—431no—
322#2046—431no—
323#2019D4311yescharacteristic
324#1778—431no—
325C4×#101—431no—
326C4×#100—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—81no—
330C2×C43—82no—
331C2×C43#239211yescharacteristic
332C2×C43#306811yescharacteristic
333C2×C43#306911yescharacteristic
334C2×#137C2×D4311yescharacteristic
335C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
336C22×SD16C2×D4311yescharacteristic
337C4×#41—431no—
338C2×C4×Q8—431no—
339C2×C4×D4—431no—
340#442—861no—
341#441—861no—
342#440—862no—
343#440—862no—
344#440—861no—
345#440—861no—
346C4×Q16—861no—
347C4×SD16—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—862no—
351#432—862no—
352C2×#108—431no—
353C2×#108—431no—
354#428—431no—
355#428—431no—
356C2×#107—431no—
357#424—431no—
358#424—431no—
359#419—431no—
360#418—431no—
361#417—431no—
362#417—431no—
363C2×#103—431no—
364C2×#102—431no—
365C2×#101—431no—
366C2×#101C2×D4311yescharacteristic
367C2×#100—431no—
368C2×#100C2×D4311yescharacteristic
369#408—431no—
370#408C2×D4311yescharacteristic
371C4×M16—431no—
372C4×M16—431no—
373C4×M16—431no—
374C2×#97—431no—
375#343—431no—
376#343—431no—
377#343—431no—
378#343—431no—
379#341—431no—
380#341C2×D4311yescharacteristic
381C43#2372111yescharacteristic, complemented, Sylow
382C2×#41C22×D4311yescharacteristic
383C22×Q8C22×D4311yescharacteristic
384C22×D4C22×D4311yescharacteristic
385C23×C4—861no—
386#137—22no—
387#137—22no—
388AGL(1,ℤ/8)—22no—
389AGL(1,ℤ/8)—22no—
390C2×Q16—21no—
391C2×SD16—21no—
392C2×SD16—22no—
393C2×SD16—21no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×D8—21no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16C22×D4311yescharacteristic
401C2×M16C22×D4311yescharacteristic
402C2×M16C22×D4311yescharacteristic
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C4×Q8—431no—
406C4×Q8—431no—
407C4×Q8—861no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×Q8—861no—
411C4×D4—431no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4—861no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419#117—431no—
420#117—861no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42—861no—
428#108—862no—
429#108—862no—
430#107—861no—
431#107—861no—
432#107—862no—
433#106—861no—
434#106—861no—
435C4⋊C8—862no—
436C4⋊C8—862no—
437#103—861no—
438#103—861no—
439#103—862no—
440#103—861no—
441#103—861no—
442#102—861no—
443#102—861no—
444#102—862no—
445#102—861no—
446#102—861no—
447#101—22no—
448#101—862no—
449#100—22no—
450#100—862no—
451C22⋊C8—22no—
452C22⋊C8—862no—
453#97—432no—
454#97—432no—
455#97—861no—
456#97—861no—
457#97—861no—
458C4×C8—861no—
459C4×C8—861no—
460C4×C8—861no—
461C24—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8D4×D4311yescharacteristic
472C2×Q8#1062190012yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4D4×D4311yescharacteristic
480C2×D4#1062190012yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—3442no—
490C22×C4—1721no—
491C22×C4—1721no—
492C22×C4C23×D4311yescharacteristic
493Q16—24no—
494SD16—28no—
495SD16—24no—
496SD16—24no—
497D8—24no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16#1062190012yes—
509M16#1062190012yes—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—432no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8D4×D4312yes—
522C4⋊C4—431no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—1721no—
531C4⋊C4—1721no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—1721no—
536C22⋊C4—1721no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42—1721no—
545C42—1721no—
546C23—21no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—81no—
551C23—81no—
552C23#41×D4311yescharacteristic
553Q8—22no—
554Q8—21no—
555Q8—22no—
556Q8—21no—
557Q8—41no—
558Q8—41no—
559D4—21no—
560D4—22no—
561D4—22no—
562D4—21no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—3442no—
580C2×C4—3442no—
581C2×C4—3441no—
582C2×C4—3441no—
583C2×C4—3441no—
584C2×C4—3441no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×#1062190011yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4C2×#1062190011yescharacteristic
594C2×C4C2×#1062190011yescharacteristic
595C8—22no—
596C8—22no—
597C8—22no—
598C8—41no—
599C8—862no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22#121×D4311yescharacteristic
614C22#1458343011yescharacteristic
615C22#1458343011yescharacteristic
616C4—41no—
617C4—42no—
618C4—861no—
619C4—861no—
620C4—861no—
621C4—861no—
622C4—3441no—
623C4—3441no—
624C4—1721no—
625C4—1721no—
626C4#1458340511yescharacteristic
627C4#1458340511yescharacteristic
628C4#1458340511yescharacteristic
629C4#1458344711yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—82no—
634C2#1913783011yescharacteristic
635C2#1914431811yescharacteristic
636C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2019C2
socleC22×C43C2×#121
prime radicalC2×AGL(1,ℤ/8)×C43C22
hypercenter#2019D43
hypocenterC43#23721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2019

Complements

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

NH ≅ G/Ntype
1. #137×Dic43C2semidirect
3. C2×#14583000C2semidirect
4. #19143242C2semidirect
5. #19136102C2semidirect
6. #19136035C2semidirect
7. #19135958C2semidirect
8. #19135951C2semidirect
9. #19135891C2semidirect
11. #19135853C2semidirect
12. #19134500C2semidirect
13. #101×Dic43C2semidirect
14. #100×Dic43C2semidirect
381. C43#23721semidirect

Maximal subgroups

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

subgroupindex
#137×Dic432
AGL(1,ℤ/8)×Dic432
C2×#145830002
#191432422
#191361022
#191360352
#191359582
#191359512
#191358912
#191358842
#191358532
#191345002
#101×Dic432
#100×Dic432
C43×#20192
#2372143