Finite Group Databasebeta

← #25138049

Subgroups — #25138049

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144406C211yesmaximal, characteristic, complemented
2C2×#14583178C211yesmaximal, characteristic, complemented
3#19143408C211yesmaximal, characteristic
4#19143257C211yesmaximal, characteristic, complemented
5#19136038C211yesmaximal, characteristic, complemented
6#19135886C211yesmaximal, characteristic
7#19135885C211yesmaximal, characteristic
8#19135582C211yesmaximal, characteristic, complemented
9#19135379C211yesmaximal, characteristic, complemented
10#19135378C211yesmaximal, characteristic, complemented
11#19135369C211yesmaximal, characteristic, complemented
12#19135258C211yesmaximal, characteristic, complemented
13#19135255C211yesmaximal, characteristic, complemented
14#19134586C211yesmaximal, characteristic, complemented
15C43×#2078C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20#14583192—21no—
21#14583187—21no—
22#14583182—21no—
23#14583178—21no—
24#14583178—21no—
25#14583178—21no—
26#14583178—21no—
27#14583177—21no—
28#14583008—21no—
29#14583002—21no—
30#14582984—21no—
31#14582979—21no—
32#14582957—21no—
33#14582957—21no—
34#14582953—21no—
35#14582949—21no—
36C2×#13063261C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582939C2211yescharacteristic
41C2×#13063258C2211yescharacteristic
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582905C2211yescharacteristic
46#14582900C2211yescharacteristic
47C2×#13063247C2211yescharacteristic
48C2×#13063245C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582866C2211yescharacteristic
52#14582857C2211yescharacteristic
53#14582854C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#107×C43C2211yescharacteristic
61C43×#417C2211yescharacteristic
62C43×#417C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×Dic86—21no—
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70#13063350—22no—
71#13063350—22no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82Q8×Dic43D411yescharacteristic
83Q8×Dic43D411yescharacteristic
84D4×Dic43—21no—
85D4×Dic43—21no—
86D4×Dic43D411yescharacteristic
87D4×Dic43D411yescharacteristic
88#13063287—21no—
89#13063287—21no—
90#13063287—21no—
91#13063287—21no—
92#13063284—21no—
93#13063284C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063261—22no—
100#13063260—22no—
101#13063259—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258—21no—
105#13063258—21no—
106#13063257—21no—
107#13063256—21no—
108#13063256—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116Dic43⋊C8D411yescharacteristic
117#13063249—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063246—21no—
123#13063245—21no—
124#13063245—21no—
125#13063241—22no—
126#13063241—22no—
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129#13063235—21no—
130#13063235—21no—
131#13063235—21no—
132C8×Dic43—21no—
133C8×Dic43—21no—
134C8×Dic43—21no—
135C2×#41×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142#107×C43—21no—
143#107×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#102×C43—21no—
147#102×C43—21no—
148C22⋊C8×C43—21no—
149C22⋊C8×C43—21no—
150C23×D43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155C2×Q8×C43C2×D411yescharacteristic
156C2×D4×C43—21no—
157C2×D4×C43C2×D411yescharacteristic
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43#4111yescharacteristic
166C22×Dic43#4111yescharacteristic
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172#4112yes—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×C4×D43—82no—
176C2×Dic86—41no—
177C2×Dic86—41no—
178C2×Dic86—82no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C2×D411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198C22⋊Dic43—21no—
199#10621884—24no—
200#10621882—24no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223#10621877#4112yes—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231C23×C43—21no—
232C23×C43C2×#4111yescharacteristic
233C22×D43—22no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—81no—
237C22×D43—81no—
238Q8×C43—21no—
239Q8×C43—21no—
240D4×C43—21no—
241D4×C43—21no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—81no—
250C2×C4×C43—81no—
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×C4×C432−1+411yescharacteristic
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—42no—
262C2×Dic43—41no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43#12111yescharacteristic
266C2×Dic43#12111yescharacteristic
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269D172—22no—
270D172—22no—
271D172—41no—
272D172—41no—
273C4×D43—82no—
274C4×D43—82no—
275Dic86—82no—
276Dic86—82no—
277C8×C43—21no—
278C8×C43—21no—
279C8×C43—41no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287#24720—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43C2×#12111yescharacteristic
294C22×C43#55211yescharacteristic
295C22×C43#55611yescharacteristic
296C2×D43—42no—
297C2×D43—82no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—82no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52511yescharacteristic
305C4×C43#53611yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#54811yescharacteristic
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—41no—
312Dic43—41no—
313Dic43—81no—
314Dic43#47212yes—
315#3079—431no—
316C2×#474—431no—
317C4×AGL(1,ℤ/8)—431no—
318#2925—431no—
319#2078—431no—
320#2078D4311yescharacteristic, complemented
321#2051—431no—
322#2051—431no—
323#1997—431no—
324#1952—431no—
325#1952—431no—
326#1950—431no—
327#1931—431no—
328#1931—431no—
329#1800—431no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—81no—
333C2×C43#241511yescharacteristic
334C2×C43C2×#47211yescharacteristic
335C2×C43#306911yescharacteristic
336D43—82no—
337C2×AGL(1,ℤ/8)—431no—
338C2×C4⋊Q8—431no—
339C4×#41—431no—
340C2×C4×D4—431no—
341#477—861no—
342#476—861no—
343#475—861no—
344#474—861no—
345#474—861no—
346#474—861no—
347#474—861no—
348#474—861no—
349#442—861no—
350#440—861no—
351C4×SD16—861no—
352C4×D8—861no—
353#433—861no—
354#433—861no—
355#432—861no—
356#431—861no—
357C2×#108—431no—
358C2×#108—431no—
359#428—431no—
360#428—431no—
361#428—431no—
362C2×#107—431no—
363C2×#107C2×D4311yescharacteristic
364#423—431no—
365#423—431no—
366C2×C4⋊C8—431no—
367#418—431no—
368#417—431no—
369#417C2×D4311yescharacteristic
370#417C2×D4311yescharacteristic
371C2×#102—431no—
372C2×#102—431no—
373C2×#100—431no—
374C2×#100—431no—
375#408—431no—
376#408C2×D4311yescharacteristic
377#405—431no—
378#405—431no—
379C4×M16—431no—
380#343—431no—
381#343—431no—
382#343—431no—
383#343—431no—
384#343C2×D4311yescharacteristic
385#343C2×D4311yescharacteristic
386#341—431no—
387#341C2×D4311yescharacteristic
388C43#2472011yescharacteristic, complemented, Sylow
389C2×#41C22×D4311yescharacteristic
390C22×Q8—861no—
391C22×D4—431no—
392C23×C4—861no—
393AGL(1,ℤ/8)—862no—
394AGL(1,ℤ/8)—862no—
395C2×SD16—861no—
396C2×D8—861no—
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—861no—
406C4⋊Q8—861no—
407C4⋊Q8—861no—
408C4⋊Q8—861no—
409C4×Q8—431no—
410C4×Q8—431no—
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—861no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—861no—
428#108—862no—
429#108—862no—
430#107—21no—
431#107—21no—
432#107—861no—
433#107—861no—
434#107—861no—
435#107—861no—
436#107—861no—
437#106—861no—
438#106—861no—
439#106—861no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448#103—21no—
449#103—21no—
450#103—861no—
451#102—21no—
452#102—21no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#100—862no—
461#100—862no—
462C22⋊C8—21no—
463C22⋊C8—21no—
464C22⋊C8—861no—
465C22⋊C8—861no—
466#97—861no—
467#97—861no—
468#97—861no—
469C4×C8—861no—
470C4×C8—861no—
471C4×C8—861no—
472C24—861no—
473#41—21no—
474#41—21no—
475#41—21no—
476#41—21no—
477C2×Q8—3442no—
478C2×Q8—1721no—
479C2×Q8—1721no—
480C2×Q8D4×D4311yescharacteristic
481C2×D4—21no—
482C2×D4—432no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4D4×D4311yescharacteristic
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—3442no—
498C22×C4—1721no—
499C22×C4—1721no—
500C22×C4C23×D4311yescharacteristic
501SD16—864no—
502D8—864no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16—21no—
509M16—432no—
510M16—861no—
511M16—861no—
512M16—861no—
513M16—861no—
514M16—861no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—431no—
521C2×C8—431no—
522C2×C8—861no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8D4×D4311yescharacteristic
528C2×C8D4×D4311yescharacteristic
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—431no—
534C4⋊C4—431no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—1721no—
540C4⋊C4—1721no—
541C22⋊C4—861no—
542C22⋊C4—861no—
543C22⋊C4—861no—
544C22⋊C4—1721no—
545C22⋊C4—1721no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—861no—
551C42—861no—
552C42—861no—
553C23—21no—
554C23—862no—
555C23—3441no—
556C23—3441no—
557C23—1721no—
558C23—1721no—
559C23#41×D4311yescharacteristic
560Q8—21no—
561Q8—21no—
562Q8—3442no—
563Q8—3442no—
564D4—21no—
565D4—21no—
566D4—41no—
567D4—41no—
568D4—862no—
569D4—862no—
570D4—1721no—
571D4—1721no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3442no—
587C2×C4—3442no—
588C2×C4—3441no—
589C2×C4—3441no—
590C2×C4—1722no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4C2×D4×D4311yescharacteristic
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#1306337211yescharacteristic
598C2×C4#1306337211yescharacteristic
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—862no—
605C8—861no—
606C8—861no—
607C8—1721no—
608C8—1721no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—3442no—
615C22—3442no—
616C22—3441no—
617C22—3441no—
618C22—1722no—
619C22#121×D4311yescharacteristic
620C22#1458358511yescharacteristic
621C22#1458361611yescharacteristic
622C4—41no—
623C4—81no—
624C4—81no—
625C4—432no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—3441no—
630C4—1721no—
631C4—1721no—
632C4#1458340711yescharacteristic
633C4#1458347111yescharacteristic
634C4#1458354711yescharacteristic
635C4#1458355711yescharacteristic
636C2—21no—
637C2—21no—
638C2—81no—
639C2—3442no—
640C2#1913801911yescharacteristic
641C2#472×D4311yescharacteristic
642C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2078C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
hypercenter#2078D43
hypocenterC43#24720
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2078

Complements

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

NH ≅ G/Ntype
1. #19144406C2semidirect
2. C2×#14583178C2semidirect
4. #19143257C2semidirect
5. #19136038C2semidirect
8. #19135582C2semidirect
9. #19135379C2semidirect
10. #19135378C2semidirect
11. #19135369C2semidirect
12. #19135258C2semidirect
13. #19135255C2semidirect
14. #19134586C2semidirect
15. C43×#2078C2semidirect
320. #2078D43semidirect
388. C43#24720semidirect

Maximal subgroups

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

subgroupindex
#191444062
C2×#145831782
#191434082
#191432572
#191360382
#191358862
#191358852
#191355822
#191353792
#191353782
#191353692
#191352582
#191352552
#191345862
C43×#20782
#2472043