Finite Group Databasebeta

← #25126330

Subgroups — #25126330

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×#13063356C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19143244C211yesmaximal, characteristic, complemented
4#19136101C211yesmaximal, characteristic, complemented
5#19136036C211yesmaximal, characteristic, complemented
6#19135960C211yesmaximal, characteristic, complemented
7#19135953C211yesmaximal, characteristic, complemented
8#19135895C211yesmaximal, characteristic, complemented
9#19135888C211yesmaximal, characteristic
10#19135853C211yesmaximal, characteristic, complemented
11#19135707C211yesmaximal, characteristic
12#19134501C211yesmaximal, characteristic, complemented
13C4×#13063244C211yesmaximal, characteristic, complemented
14C4×#13063242C211yesmaximal, characteristic, complemented
15C2×C43×#440C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583009—21no—
20#14583004—21no—
21#14582999—21no—
22#14582997—21no—
23C4×#10621885—21no—
24C4×#10621884—21no—
25C4×#10621883—21no—
26C4×#10621882—21no—
27#14582961—22no—
28#14582954—22no—
29C2×#13063261C2211yescharacteristic
30C2×#13063261C2211yescharacteristic
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582925C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582908C2211yescharacteristic
36#14582904C2211yescharacteristic
37#14582898C2211yescharacteristic
38#14582898C2211yescharacteristic
39C2×#13063244C2211yescharacteristic
40C2×#13063244C2211yescharacteristic
41C2×#13063242C2211yescharacteristic
42C2×#13063242C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582865C2211yescharacteristic
45C4×#10621877C2211yescharacteristic
46C4×#10621877C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582664C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#440—22no—
58C43×#440—22no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C2×#10621898C2311yescharacteristic
64#13063356—22no—
65#13063356—22no—
66#13063351—22no—
67#13063351—22no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×Dic86D411yescharacteristic
80C4×D172D411yescharacteristic
81C4×D172D411yescharacteristic
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84#13063284C2311yescharacteristic
85#13063282—21no—
86C42×D43—21no—
87#13063261—22no—
88#13063261—22no—
89#13063258—21no—
90#13063258—21no—
91#13063256—21no—
92#13063256—21no—
93Dic43⋊C8—22no—
94Dic43⋊C8—22no—
95#13063249—21no—
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063245—21no—
102#13063245—21no—
103#13063244—22no—
104#13063244—22no—
105#13063242—22no—
106#13063242—22no—
107(C2×D43)⋊C8—22no—
108(C2×D43)⋊C8—22no—
109#13063236—21no—
110#13063236—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8—21no—
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C2×SD16×C43—22no—
119C2×SD16×C43—22no—
120C2×SD16×C43—22no—
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137#107×C43—22no—
138#103×C43—22no—
139#102×C43—22no—
140#97×C43D412yes—
141#97×C43D412yes—
142C24×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43#4112yes—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43#4112yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—82no—
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43#4111yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—21no—
165#10621898—21no—
166#10621898—21no—
167#10621898—21no—
168#10621898—21no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×Dic86C2×D411yescharacteristic
174SD16×C43—28no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C2×D412yes—
180C2×C8×C43C2×D412yes—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C42×C43—41no—
190C42×C43—41no—
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C22⋊Dic43—21no—
196#10621885—24no—
197#10621884—24no—
198#10621883—24no—
199#10621882—24no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—21no—
202C4⋊Dic43C2×D411yescharacteristic
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877#4112yes—
220#10621877#4112yes—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C23×C43—22no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—81no—
231C23×C43—81no—
232C23×C43C2×#4111yescharacteristic
233C22×D43—21no—
234Q8×C43—22no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—82no—
250C2×C4×C43—82no—
251C2×C4×C43—81no—
252C2×C4×C43—81no—
253C2×C4×C43#12111yescharacteristic
254C2×C4×C43#12111yescharacteristic
255C2×C4×C43#12111yescharacteristic
256C2×C4×C43#12111yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C22⋊D43—41no—
264C22⋊D43—41no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268D172—21no—
269D172—21no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—81no—
273C4×D43—81no—
274Dic86—21no—
275Dic86—21no—
276C8×C43—22no—
277C8×C43—22no—
278C43⋊C8—22no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#23721—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—42no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43C2×#12111yescharacteristic
293C22×C43#52911yescharacteristic
294C22×C43#52911yescharacteristic
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—42no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43#52511yescharacteristic
306C4×C43#52511yescharacteristic
307C4×C43#52511yescharacteristic
308C4×C43#53211yescharacteristic
309Dic43—41no—
310Dic43—41no—
311Dic43—41no—
312C4×#137—431no—
313C4×AGL(1,ℤ/8)—431no—
314C2×#440D4311yescharacteristic, complemented
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#1778—431no—
325C4×#101—431no—
326C4×#100—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43—82no—
330C2×C43#239211yescharacteristic
331C2×C43#306811yescharacteristic
332C2×C43#306911yescharacteristic
333D43—81no—
334C2×#137—431no—
335C2×AGL(1,ℤ/8)—431no—
336C22×SD16C2×D4311yescharacteristic
337C4×#41—431no—
338C2×C4×Q8C2×D4311yescharacteristic
339C2×C4×D4C2×D4311yescharacteristic
340#442—861no—
341#441—861no—
342#440—22no—
343#440—22no—
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×#107C2×D4311yescharacteristic
357#424—431no—
358#424—431no—
359#419—431no—
360#418—431no—
361#417—431no—
362#417—431no—
363C2×#103C2×D4311yescharacteristic
364C2×#102C2×D4311yescharacteristic
365C2×#101—431no—
366C2×#101—431no—
367C2×#100—431no—
368C2×#100—431no—
369#408—431no—
370#408—431no—
371C4×M16—431no—
372C4×M16—431no—
373C4×M16—431no—
374C2×#97C2×D4311yescharacteristic
375#343—431no—
376#343—431no—
377#343—431no—
378#343—431no—
379#341—431no—
380#341—431no—
381C43#2372111yescharacteristic, complemented, Sylow
382C2×#41—431no—
383C22×Q8C22×D4311yescharacteristic
384C22×D4C22×D4311yescharacteristic
385C23×C4—21no—
386#137—862no—
387#137—862no—
388AGL(1,ℤ/8)—862no—
389AGL(1,ℤ/8)—862no—
390C2×Q16—861no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×D8—861no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16—431no—
401C2×M16—431no—
402C2×M16—431no—
403C22×C8C22×D4311yescharacteristic
404C22×C8C22×D4311yescharacteristic
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—431no—
410C4×Q8—431no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—431no—
416C4×D4—431no—
417C4×D4—861no—
418C4×D4—861no—
419#117—431no—
420#117—861no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C42—21no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#108—862no—
429#108—862no—
430#107—22no—
431#107—861no—
432#107—861no—
433#106—861no—
434#106—861no—
435C4⋊C8—862no—
436C4⋊C8—862no—
437#103—22no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#102—22no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#101—862no—
448#101—862no—
449#100—862no—
450#100—862no—
451C22⋊C8—862no—
452C22⋊C8—862no—
453#97—861no—
454#97—861no—
455#97—861no—
456#97C22⋊D4312yes—
457#97C22⋊D4312yes—
458C4×C8—861no—
459C4×C8—861no—
460C4×C8—861no—
461C24—21no—
462#41—861no—
463#41—861no—
464#41—861no—
465#41—861no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—431no—
472C2×Q8#1062189812yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—431no—
479C2×D4—861no—
480C2×D4#1062189812yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—82no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4#1062190011yescharacteristic
491C22×C4#1062190011yescharacteristic
492C22×C4C23×D4311yescharacteristic
493Q16—864no—
494SD16—28no—
495SD16—864no—
496SD16—864no—
497D8—864no—
498M16—432no—
499M16—432no—
500M16—861no—
501M16—861no—
502M16—861no—
503M16—861no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16—861no—
509M16—861no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8C2×C22⋊D4312yes—
521C2×C8C2×C22⋊D4312yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—431no—
529C4⋊C4—431no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C42—41no—
538C42—41no—
539C42—861no—
540C42—861no—
541C42—861no—
542C42D4×D4311yescharacteristic
543C42D4×D4311yescharacteristic
544C42C2×C22⋊D4311yescharacteristic
545C42C2×C22⋊D4311yescharacteristic
546C23—22no—
547C23—41no—
548C23—41no—
549C23—81no—
550C23—81no—
551C23—861no—
552C23C2×#1062190011yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—861no—
558Q8—861no—
559D4—22no—
560D4—22no—
561D4—41no—
562D4—41no—
563D4—861no—
564D4—861no—
565D4—1721no—
566D4—1721no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—3441no—
582C2×C4—3441no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#1306329611yescharacteristic
586C2×C4#1306329611yescharacteristic
587C2×C4#1306329611yescharacteristic
588C2×C4#1306329611yescharacteristic
589C2×C4C2×D4×D4311yescharacteristic
590C2×C4C22×C22⋊D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C8—22no—
596C8—22no—
597C8—862no—
598C8—862no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—81no—
609C22—81no—
610C22—1721no—
611C22—1721no—
612C22—1721no—
613C22C2×#1306329611yescharacteristic
614C22#1458342911yescharacteristic
615C22#1458342911yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4#1458340811yescharacteristic
627C4#1458340811yescharacteristic
628C4#1458341011yescharacteristic
629C4#1458344511yescharacteristic
630C2—21no—
631C2—21no—
632C2—82no—
633C2—3441no—
634C2#1913783311yescharacteristic
635C2#1914431911yescharacteristic
636C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#440C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
hypercenterC2×#440D43
hypocenterC43#23721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C4×#13063356C2semidirect
3. #19143244C2semidirect
4. #19136101C2semidirect
5. #19136036C2semidirect
6. #19135960C2semidirect
7. #19135953C2semidirect
8. #19135895C2semidirect
10. #19135853C2semidirect
12. #19134501C2semidirect
13. C4×#13063244C2semidirect
14. C4×#13063242C2semidirect
15. C2×C43×#440C2semidirect
314. C2×#440D43semidirect
381. C43#23721semidirect

Maximal subgroups

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

subgroupindex
C4×#130633562
C4×#130633512
#191432442
#191361012
#191360362
#191359602
#191359532
#191358952
#191358882
#191358532
#191357072
#191345012
C4×#130632442
C4×#130632422
C2×C43×#4402
#2372143