Finite Group Databasebeta

← #25166559

Subgroups — #25166559

Order 11008.

710 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#19144558C211yesmaximal, characteristic
2#19144431C211yesmaximal, characteristic, complemented
3#19143441C211yesmaximal, characteristic
4#19135962C211yesmaximal, characteristic, complemented
5#19135937C211yesmaximal, characteristic, complemented
6#19135892C211yesmaximal, characteristic
7#19135629C211yesmaximal, characteristic
8#19135395C211yesmaximal, characteristic, complemented
9#19135301C211yesmaximal, characteristic
10#19135250C211yesmaximal, characteristic, complemented
11#19135247C211yesmaximal, characteristic, complemented
12#19134985C211yesmaximal, characteristic, complemented
13#19134819C211yesmaximal, characteristic
14#19134475C211yesmaximal, characteristic, complemented
15C43×#3137C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583376C2211yescharacteristic
20#14583237—21no—
21#14583237—21no—
22#14583232—21no—
23#14583227—21no—
24#14583203—21no—
25#14583203—21no—
26#14583191—21no—
27#14583181—21no—
28#14583003—21no—
29#14582996—21no—
30#14582991—21no—
31#14582990—21no—
32C2×#13063260C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582939C2211yescharacteristic
36#14582935C2211yescharacteristic
37#14582926C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39#14582908C2211yescharacteristic
40#14582907C2211yescharacteristic
41C2×#13063250C2211yescharacteristic
42C2×#13063249C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063244C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46#14582866C2211yescharacteristic
47#14582854C2211yescharacteristic
48C2×C8×Dic43C2211yescharacteristic
49#14582768C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582660C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#536C2211yescharacteristic
58C43×#491—21no—
59C43×#489—21no—
60C43×#488—21no—
61C43×#487—21no—
62C43×#419C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621877C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063323—22no—
77#13063323—22no—
78Q8×Dic43—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063290—21no—
82#13063290—21no—
83D4×Dic43—21no—
84D4×Dic43—41no—
85#13063284—21no—
86#13063284C2311yescharacteristic
87#13063281—41no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—41no—
91C2×Dic43⋊C4—41no—
92C2×C4×Dic43C2311yescharacteristic
93#13063260—22no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258D411yescharacteristic
98#13063258D411yescharacteristic
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256D411yescharacteristic
103#13063256D411yescharacteristic
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)—21no—
106#13063252—22no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063249—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063244—22no—
118#13063243—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121#13063235—21no—
122C8×Dic43—21no—
123C8×Dic43—22no—
124C2×#41×C43C2311yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C2×M16×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4⋊Q8×C43—21no—
129C4⋊Q8×C43—21no—
130C4⋊Q8×C43—21no—
131#125×C43—21no—
132#125×C43—21no—
133#124×C43—21no—
134#123×C43—41no—
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C22⋊Q8×C43—41no—
138#117×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143#103×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#103×C43D411yescharacteristic
147#103×C43D411yescharacteristic
148#102×C43—21no—
149#102×C43D411yescharacteristic
150#102×C43D411yescharacteristic
151#97×C43—21no—
152C4×C8×C43—21no—
153#41×C43—21no—
154#41×C43—21no—
155#41×C43—21no—
156#41×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—41no—
164C2×Q8×C43C2×D411yescharacteristic
165C2×D4×C43—21no—
166C2×D4×C43C2×D411yescharacteristic
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—41no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86#4112yes—
181M16×C43—21no—
182M16×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—41no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43C2×D411yescharacteristic
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C42×C43—21no—
204C42×C43—21no—
205C22⋊Dic43—21no—
206C22⋊Dic43—41no—
207#10621885—24no—
208#10621883—24no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—41no—
212C4⋊Dic43C2×D411yescharacteristic
213C4⋊Dic43C2×D411yescharacteristic
214Dic43⋊C4—44no—
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217Dic43⋊C4—82no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—41no—
221C4×Dic43—41no—
222C4×Dic43—41no—
223C4×Dic43#4112yes—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877#4112yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C2×D411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C23×C43—21no—
238C23×C43H(5,𝔽2)11yescharacteristic
239Q8×C43—21no—
240Q8×C43—21no—
241Q8×C43—41no—
242Q8×C43—41no—
243Q8×C43—41no—
244Q8×C43—41no—
245Q8×C43—161no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—41no—
249D4×C43—41no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—81no—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C432−1+411yescharacteristic
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—81no—
278C2×Dic43—161no—
279Dic86—22no—
280Dic86—22no—
281Dic86—41no—
282Dic86—41no—
283C8×C43—21no—
284C8×C43—21no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—21no—
288C43⋊C8—21no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#26849—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—41no—
297C22×C43#54211yescharacteristic
298C22×C43D4211yescharacteristic
299C22×C43#55111yescharacteristic
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#52511yescharacteristic
308C4×C43#53211yescharacteristic
309C4×C43#54711yescharacteristic
310C4×C43#54811yescharacteristic
311Dic43—24no—
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316#3137D4311yescharacteristic
317#3097—431no—
318#3082—431no—
319#2947—431no—
320#2064—431no—
321#2060—431no—
322#2052—431no—
323#2005—431no—
324#1956—431no—
325#1937—431no—
326#1930—431no—
327#1930—431no—
328#1886—431no—
329#1859—431no—
330#1772—431no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—81no—
334C2×C43#246111yescharacteristic
335C2×C43#329111yescharacteristic
336C2×C43#329311yescharacteristic
337C2×#137—431no—
338#544C2×D4311yescharacteristic
339#536C2×D4311yescharacteristic
340C2×C4⋊Q8—431no—
341#520—431no—
342#519—431no—
343#491—21no—
344#489—21no—
345#488—21no—
346#487—21no—
347#485—861no—
348#485—861no—
349#484—861no—
350#483—861no—
351#479—861no—
352#479—861no—
353#477—861no—
354#475—861no—
355#441—861no—
356#440—861no—
357C4×Q16—861no—
358C4×SD16—861no—
359C2×#108—431no—
360#428—431no—
361#428—431no—
362#428—431no—
363#427—431no—
364#424—431no—
365C2×#104—431no—
366#419—431no—
367#419—431no—
368#419C2×D4311yescharacteristic
369#417C2×D4311yescharacteristic
370#416C2×D4311yescharacteristic
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103C2×D4311yescharacteristic
375C2×#101—431no—
376C2×#101—431no—
377#408—431no—
378#405—431no—
379#405C2×D4311yescharacteristic
380C2×C4×C8—431no—
381#384—431no—
382#343—431no—
383#343—431no—
384#341—431no—
385#339—431no—
386#339—431no—
387#339—431no—
388C43#2684911yescharacteristic, complemented, Sylow
389C2×#41C22×D4311yescharacteristic
390C22×Q8—431no—
391C22×Q8C22×D4311yescharacteristic
392#137—862no—
393#137—862no—
394C2×Q16—861no—
395C2×SD16—861no—
396C2×M16—431no—
397C2×M16—431no—
398C2×M16—431no—
399C2×M16C22×D4311yescharacteristic
400C22×C8—431no—
401C22×C8C22×D4311yescharacteristic
402C4⋊Q8—21no—
403C4⋊Q8—21no—
404C4⋊Q8—21no—
405C4⋊Q8—862no—
406C4⋊Q8—862no—
407#125—21no—
408#125—21no—
409#124—21no—
410#123—41no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—41no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×D4—861no—
420C4×D4—1721no—
421#117—431no—
422#117—861no—
423#117—1721no—
424#117C22×D4311yescharacteristic
425#117C22×D4311yescharacteristic
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—1721no—
429C2×C4⋊C4—1721no—
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C42—431no—
432#108—862no—
433#107—431no—
434#107—431no—
435#107—861no—
436#107—861no—
437#107—861no—
438#106—431no—
439#106—431no—
440#106—861no—
441#106—861no—
442#106—861no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#104—862no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—861no—
452#103—861no—
453#103—861no—
454#103—861no—
455#103—861no—
456#103—861no—
457#103—861no—
458#103—861no—
459#103—861no—
460#103—861no—
461#103C22⋊D4311yescharacteristic
462#103C22⋊D4311yescharacteristic
463#102—21no—
464#102C22⋊D4311yescharacteristic
465#102C22⋊D4311yescharacteristic
466#101—862no—
467#101—862no—
468C22⋊C8—861no—
469C22⋊C8—861no—
470#97—21no—
471#97—861no—
472C4×C8—21no—
473C4×C8—862no—
474C4×C8—861no—
475#41—21no—
476#41—21no—
477#41—21no—
478#41—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—41no—
486C2×Q8—432no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8C2×C22⋊D4311yescharacteristic
493C2×D4—21no—
494C2×D4C2×C22⋊D4311yescharacteristic
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—1721no—
502C22×C4C23×D4311yescharacteristic
503Q16—864no—
504SD16—864no—
505M16—21no—
506M16—21no—
507M16—432no—
508M16—861no—
509M16—861no—
510M16—861no—
511M16—861no—
512M16—861no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—431no—
517C2×C8—431no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C2×C8C2×C22⋊D4311yescharacteristic
524C2×C8C2×C22⋊D4311yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—431no—
533C4⋊C4—431no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—3442no—
537C4⋊C4—1721no—
538C4⋊C4—1721no—
539C4⋊C4—1721no—
540C4⋊C4—1724no—
541C4⋊C4D4×D4311yescharacteristic
542C4⋊C4D4×D4311yescharacteristic
543C4⋊C4C2×C22⋊D4311yescharacteristic
544C4⋊C4C2×C22⋊D4311yescharacteristic
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—861no—
550C22⋊C4—1721no—
551C42—21no—
552C42—21no—
553C42—432no—
554C42—861no—
555C42—861no—
556C42—1721no—
557C42—1721no—
558C42—1721no—
559C23—21no—
560C23#1306337011yescharacteristic
561Q8—21no—
562Q8—21no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—161no—
568Q8—862no—
569Q8—862no—
570Q8—1721no—
571Q8—1721no—
572D4—21no—
573D4—21no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—81no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—3441no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—6881no—
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4C22×C22⋊D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#1306337211yescharacteristic
605C8—21no—
606C8—21no—
607C8—41no—
608C8—862no—
609C8—861no—
610C8—861no—
611C8—1721no—
612C8—1721no—
613C22—21no—
614C22—21no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22#1458351311yescharacteristic
619C22D4×C22⋊D4311yescharacteristic
620C22#1458357911yescharacteristic
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—81no—
628C4—864no—
629C4—3441no—
630C4—1721no—
631C4—1721no—
632C4—1722no—
633C4#1458340611yescharacteristic
634C4#1458344811yescharacteristic
635C4#1458354811yescharacteristic
636C4#1458355711yescharacteristic
637C2—21no—
638C2—21no—
639C2—81no—
640C2#1913855811yescharacteristic
641C2#1914638611yescharacteristic
642C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3137C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#3137D43
hypocenterC43#26849
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3137

Complements

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

NH ≅ G/Ntype
2. #19144431C2semidirect
4. #19135962C2semidirect
5. #19135937C2semidirect
8. #19135395C2semidirect
10. #19135250C2semidirect
11. #19135247C2semidirect
12. #19134985C2semidirect
14. #19134475C2semidirect
388. C43#26849semidirect

Maximal subgroups

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

subgroupindex
#191445582
#191444312
#191434412
#191359622
#191359372
#191358922
#191356292
#191353952
#191353012
#191352502
#191352472
#191349852
#191348192
#191344752
C43×#31372
#2684943