Finite Group Databasebeta

← #25126332

Subgroups — #25126332

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
1C4×#13063358C211yesmaximal, characteristic, complemented
2C4×#13063353C211yesmaximal, characteristic
3C2×#14583001C211yesmaximal, characteristic, complemented
4#19143244C211yesmaximal, characteristic, complemented
5#19136102C211yesmaximal, characteristic, complemented
6#19136037C211yesmaximal, characteristic, complemented
7#19135957C211yesmaximal, characteristic, complemented
8#19135950C211yesmaximal, characteristic, complemented
9#19135896C211yesmaximal, characteristic, complemented
10#19135889C211yesmaximal, characteristic
11#19135859C211yesmaximal, characteristic, complemented
12#19135712C211yesmaximal, characteristic
13C4×#13063243C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C43×#1778C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063353C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22#14583012—21no—
23#14583007—21no—
24#14583001—21no—
25#14583001—21no—
26#14583001—22no—
27#14583001—22no—
28C4×Dic172—21no—
29C4×#10621873—21no—
30C4×#10621873—21no—
31C4×D344—21no—
32#14582961—22no—
33#14582954—22no—
34#14582941C2211yescharacteristic
35#14582941C2211yescharacteristic
36C2×#13063259C2211yescharacteristic
37#14582925C2211yescharacteristic
38#14582925C2211yescharacteristic
39#14582909C2211yescharacteristic
40#14582905C2211yescharacteristic
41#14582901C2211yescharacteristic
42#14582901C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49#14582865C2211yescharacteristic
50#14582865C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56C2×#108×C43C2211yescharacteristic
57C2×#108×C43C2211yescharacteristic
58C4×M16×C43C2211yescharacteristic
59C4×M16×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C43×#341C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C2×#10621898C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×D172C2311yescharacteristic
66C22×C4×D43—21no—
67#13063358—22no—
68#13063358—22no—
69#13063353—22no—
70#13063353—22no—
71C2×Dic172—21no—
72C2×#10621873—21no—
73C2×#10621873—22no—
74C2×#10621873—21no—
75C2×#10621873—22no—
76C2×#10621873—22no—
77C2×D344—21no—
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86D411yescharacteristic
85C4×Dic86D411yescharacteristic
86C4×D172—21no—
87C4×D172—21no—
88C4×D172—21no—
89C4×D172—21no—
90C4×D172D411yescharacteristic
91C4×D172D411yescharacteristic
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94#13063284C2311yescharacteristic
95#13063282—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C42×D43—21no—
102#13063259—22no—
103#13063259—21no—
104#13063259—21no—
105#13063257—21no—
106#13063257—21no—
107Dic43⋊C8—22no—
108Dic43⋊C8—22no—
109#13063250—21no—
110#13063250—21no—
111#13063250—22no—
112#13063250—21no—
113#13063250—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—22no—
117#13063247—21no—
118#13063247—21no—
119#13063243—22no—
120#13063243—22no—
121#13063241—22no—
122#13063241—22no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125#13063236—21no—
126C4×C43⋊C8—21no—
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C2×M16×C43C2311yescharacteristic
130C2×M16×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#108×C43—22no—
135#108×C43—22no—
136#97×C43—21no—
137#97×C43—21no—
138#97×C43D412yes—
139#97×C43D412yes—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C23×D43—21no—
143C22×C4×C43#4111yescharacteristic
144C22×C4×C43#4111yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150#10621898—21no—
151#10621898—21no—
152#10621898—21no—
153#10621898—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×D411yescharacteristic
160C2×D172#4112yes—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×C4×D43—82no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C2×D411yescharacteristic
173C2×Dic86#4112yes—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43#4112yes—
181M16×C43#4112yes—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×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×D412yes—
191C2×C8×C43C2×D412yes—
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206C4⋊Dic43C2×D411yescharacteristic
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—41no—
210Dic43⋊C4—41no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—41no—
215C4×Dic43—41no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222Dic172—24no—
223D344—24no—
224#10621873—28no—
225#10621873—24no—
226#10621873—24no—
227C23×C43C2×#4111yescharacteristic
228C22×D43—21no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—81no—
233C22×D43—81no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C22⋊D43—41no—
247C22⋊D43—41no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258D172—22no—
259D172—21no—
260D172—22no—
261D172—21no—
262D172—41no—
263D172—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—81no—
267C4×D43—81no—
268C4×D43—82no—
269C4×D43—82no—
270Dic86—22no—
271Dic86—21no—
272Dic86—22no—
273Dic86—21no—
274Dic86—41no—
275Dic86—41no—
276C8×C43—22no—
277C8×C43—22no—
278C8×C43—22no—
279C8×C43—22no—
280C8×C43—41no—
281C8×C43—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#23721—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43C2×#12111yescharacteristic
288C22×C43#52911yescharacteristic
289C22×C43#52911yescharacteristic
290C2×D43—42no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—82no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—82no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43#52511yescharacteristic
303C4×C43#52511yescharacteristic
304C4×C43#52511yescharacteristic
305C4×C43#53211yescharacteristic
306Dic43—42no—
307Dic43—41no—
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#2019—431no—
324#1778D4311yescharacteristic, complemented
325C4×#101—431no—
326C4×#100—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#239211yescharacteristic
330C2×C43#306811yescharacteristic
331C2×C43#306911yescharacteristic
332D43—81no—
333D43—82no—
334C2×#137—431no—
335C2×AGL(1,ℤ/8)—431no—
336C22×SD16—431no—
337C4×#41—431no—
338C2×C4×Q8—431no—
339C2×C4×D4—431no—
340#442—861no—
341#441—861no—
342#440—861no—
343#440—861no—
344#440—862no—
345#440—862no—
346C4×Q16—861no—
347C4×SD16—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—862no—
351#432—862no—
352C2×#108C2×D4311yescharacteristic
353C2×#108C2×D4311yescharacteristic
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×#101—431no—
367C2×#100—431no—
368C2×#100—431no—
369#408—431no—
370#408—431no—
371C4×M16—431no—
372C4×M16C2×D4311yescharacteristic
373C4×M16C2×D4311yescharacteristic
374C2×#97C2×D4311yescharacteristic
375#343—431no—
376#343—431no—
377#343—431no—
378#343—431no—
379#341C2×D4311yescharacteristic
380#341C2×D4311yescharacteristic
381C43#2372111yescharacteristic, complemented, Sylow
382C2×#41—431no—
383C22×Q8—431no—
384C22×D4—431no—
385C23×C4—861no—
386#137—862no—
387#137—862no—
388AGL(1,ℤ/8)—862no—
389AGL(1,ℤ/8)—862no—
390C2×Q16—861no—
391C2×SD16—862no—
392C2×SD16—861no—
393C2×SD16—862no—
394C2×SD16—861no—
395C2×SD16—862no—
396C2×D8—861no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16C22×D4311yescharacteristic
400C2×M16C22×D4311yescharacteristic
401C2×M16C22×D4311yescharacteristic
402C2×M16C22×D4311yescharacteristic
403C22×C8C22×D4311yescharacteristic
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—861no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#108—22no—
429#108—22no—
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—861no—
440#103—861no—
441#103—862no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—862no—
447#101—862no—
448#101—862no—
449#100—862no—
450#100—862no—
451C22⋊C8—862no—
452C22⋊C8—862no—
453#97—21no—
454#97—21no—
455#97—861no—
456#97D17212yes—
457#97D17212yes—
458C4×C8—21no—
459C4×C8—21no—
460C4×C8—861no—
461C24—861no—
462#41—861no—
463#41—861no—
464#41—861no—
465#41—861no—
466C2×Q8—431no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×D4—431no—
474C2×D4—432no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—3442no—
488C22×C4—1721no—
489C22×C4—1721no—
490C22×C4#1062190211yescharacteristic
491C22×C4#1062190211yescharacteristic
492C22×C4C23×D4311yescharacteristic
493Q16—864no—
494SD16—868no—
495SD16—864no—
496SD16—864no—
497D8—864no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16#1062189812yes—
509M16#1062189812yes—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8C2×D17212yes—
521C2×C8C2×D17212yes—
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—861no—
538C42—861no—
539C42—861no—
540C42—1721no—
541C42—1721no—
542C42C2×D17211yescharacteristic
543C42C2×D17211yescharacteristic
544C42D4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C23—862no—
547C23—861no—
548C23—3441no—
549C23—3441no—
550C23—1721no—
551C23—1721no—
552C23C2×#1062190211yescharacteristic
553Q8—861no—
554Q8—862no—
555Q8—861no—
556Q8—862no—
557Q8—1721no—
558Q8—1721no—
559D4—861no—
560D4—862no—
561D4—861no—
562D4—862no—
563D4—1721no—
564D4—1721no—
565D4—1721no—
566D4—1721no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—3442no—
574C2×C4—3442no—
575C2×C4—3441no—
576C2×C4—3441no—
577C2×C4—3441no—
578C2×C4—3441no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#1306330011yescharacteristic
586C2×C4#1306330011yescharacteristic
587C2×C4#1306330011yescharacteristic
588C2×C4#1306330011yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C22×D17211yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C8—22no—
596C8—22no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—41no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—3442no—
606C22—3442no—
607C22—3441no—
608C22—3441no—
609C22—1721no—
610C22—1722no—
611C22—1721no—
612C22—1721no—
613C22C2×#1306330011yescharacteristic
614C22#1458343611yescharacteristic
615C22#1458343611yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—3441no—
621C4—3441no—
622C4—1721no—
623C4—1722no—
624C4—1721no—
625C4—1721no—
626C4#1458340811yescharacteristic
627C4#1458340811yescharacteristic
628C4#1458341111yescharacteristic
629C4#1458344911yescharacteristic
630C2—21no—
631C2—21no—
632C2—3442no—
633C2—3441no—
634C2#1913783511yescharacteristic
635C2#1914432411yescharacteristic
636C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1778C2
socleC22×C43C2×#121
prime radicalC2×#13063353C22
hypercenter#1778D43
hypocenterC43#23721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1778

Complements

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

NH ≅ G/Ntype
1. C4×#13063358C2semidirect
3. C2×#14583001C2semidirect
4. #19143244C2semidirect
5. #19136102C2semidirect
6. #19136037C2semidirect
7. #19135957C2semidirect
8. #19135950C2semidirect
9. #19135896C2semidirect
11. #19135859C2semidirect
13. C4×#13063243C2semidirect
14. C4×#13063241C2semidirect
15. C43×#1778C2semidirect
324. #1778D43semidirect
381. C43#23721semidirect

Maximal subgroups

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

subgroupindex
C4×#130633582
C4×#130633532
C2×#145830012
#191432442
#191361022
#191360372
#191359572
#191359502
#191358962
#191358892
#191358592
#191357122
C4×#130632432
C4×#130632412
C43×#17782
#2372143