Finite Group Databasebeta

← #25169793

Subgroups — #25169793

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139179C211yesmaximal, characteristic
2#19137653C211yesmaximal, characteristic, complemented
3#19136135C211yesmaximal, characteristic, complemented
4#19135911C211yesmaximal, characteristic
5#19135842C211yesmaximal, characteristic, complemented
6#19135677C211yesmaximal, characteristic
7#19135450C211yesmaximal, characteristic
8#19135228C211yesmaximal, characteristic, complemented
9#19135173C211yesmaximal, characteristic, complemented
10#19135153C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic
12#19134947C211yesmaximal, characteristic
13#19134599C211yesmaximal, characteristic, complemented
14#19134414C211yesmaximal, characteristic, complemented
15C43×#1926C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×#13063318—21no—
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582827—21no—
32#14582822—21no—
33#14582804C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582797—21no—
38#14582797C2211yescharacteristic
39#14582793—21no—
40#14582784—21no—
41#14582784—21no—
42#14582768C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×#10621883—22no—
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883—41no—
65C2×#10621883—41no—
66C2×#10621883—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063325—22no—
70#13063325—22no—
71#13063318—44no—
72#13063290—22no—
73#13063290—22no—
74#13063290—41no—
75#13063290—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063256—22no—
97Dic43⋊C8—41no—
98#13063250—22no—
99#13063250—22no—
100#13063250—41no—
101#13063250—41no—
102#13063248—22no—
103#13063248—41no—
104C8×Dic43—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43—41no—
124#102×C43—22no—
125#102×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
159C2×Dic86#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43#4112yes—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C22⋊Dic43—42no—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180C22⋊Dic43—81no—
181#10621883—44no—
182#10621883—44no—
183C4⋊Dic43—24no—
184C4⋊Dic43—24no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43SD1614yescomplemented
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8#4112yes—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C2×SD1612yes—
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43C2×SD1612yes—
265C2×Dic43C2×SD1612yes—
266Dic86—22no—
267Dic86—22no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278#27066—431nomaximal, Sylow
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43#52511yescharacteristic
287C22×C43#54611yescharacteristic
288C22×C43#55011yescharacteristic
289C22×C43C22×SD1611yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57811yescharacteristic
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—42no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#52911yescharacteristic
299C4×C43#53811yescharacteristic
300C4×C43#55111yescharacteristic
301C4×C43#55311yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—42no—
305Dic43—42no—
306Dic43—41no—
307Dic43—41no—
308Dic43—81no—
309Dic43—81no—
310#2512—431no—
311#2365—431no—
312#2096—431no—
313#2055—431no—
314#2043—431no—
315#2013—431no—
316#1968—431no—
317#1927—431no—
318#1926D4311yescharacteristic
319#1919—431no—
320#1916—431no—
321#1880—431no—
322#1880—431no—
323#1803—431no—
324C4×#103—431no—
325C2×C43—161no—
326C2×C43#246711yescharacteristic
327C2×C43#310311yescharacteristic
328C2×C43#312111yescharacteristic
329C2×C43#329811yescharacteristic
330C2×C43#330711yescharacteristic
331C2×C43#339211yescharacteristic
332C2×C43#340211yescharacteristic
333C22×SD16—431no—
334C22×SD16—431no—
335C2×C4⋊Q8—431no—
336C2×#126—861no—
337C2×C4×Q8—431no—
338C2×C4×Q8—431no—
339C2×#106—431no—
340C2×#106C2×D4311yescharacteristic
341C2×C4⋊C8—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#102C2×D4311yescharacteristic
349C2×#102C2×D4311yescharacteristic
350C2×C4×C8—431no—
351#397—861no—
352#396—861no—
353#391—431no—
354#391—431no—
355#390—431no—
356#390—431no—
357#390C2×D4311yescharacteristic
358#389—431no—
359#389—861no—
360#388—861no—
361#387—861no—
362#387—861no—
363#384—431no—
364C4×C4⋊C4—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—861no—
367C4×C4⋊C4C2×D4311yescharacteristic
368#340—431no—
369#340—431no—
370#340—431no—
371#340C2×D4311yescharacteristic
372#336—431no—
373#336—431no—
374#336—431no—
375#336C2×D4311yescharacteristic
376C43#2706611yescharacteristic, complemented, Sylow
377C22×Q8—431no—
378C22×Q8—431no—
379C22×D4C22×D4311yescharacteristic
380C2×SD16—862no—
381C2×SD16—862no—
382C2×SD16—862no—
383C2×SD16—1721no—
384C2×SD16—1721no—
385C2×SD16—1721no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—862no—
391C4⋊Q8—862no—
392#126—1724no—
393C4×Q8—862no—
394C4×Q8—862no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#106—41no—
425#106—862no—
426C4⋊C8—1721no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—1721no—
431#103—1721no—
432#103—1721no—
433#102—22no—
434#102—41no—
435C4×C8—1721no—
436#95—21no—
437#95—431no—
438#95—431no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—21no—
446C2×Q8—432no—
447C2×Q8—432no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—1724no—
479SD16—1724no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—434no—
498C4⋊C4—864no—
499C4⋊C4—864no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3441no—
505C4⋊C4—1721no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4#1062189812yes—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—3441no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—1722no—
525C42—1722no—
526C42—1722no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×D4×D4311yescharacteristic
535Q8—862no—
536Q8—862no—
537Q8—862no—
538Q8—862no—
539Q8—1721no—
540Q8—1721no—
541Q8—1721no—
542Q8—1721no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4SD16×D4312yes—
586C2×C4#41×D4311yescharacteristic
587C2×C4#41×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337111yescharacteristic
592C8—41no—
593C8—41no—
594C8—862no—
595C8—1721no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1458340711yescharacteristic
604C22#1458354511yescharacteristic
605C22#1458356711yescharacteristic
606C22C2×SD16×D4311yescharacteristic
607C22#1458369511yescharacteristic
608C22#1458370911yescharacteristic
609C22#1458371311yescharacteristic
610C4—22no—
611C4—42no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—862no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—1721no—
620C4—1721no—
621C4—1722no—
622C4—1722no—
623C4#1458342711yescharacteristic
624C4#1458348311yescharacteristic
625C4#1458357411yescharacteristic
626C4#1458359911yescharacteristic
627C2—161no—
628C2#1913864511yescharacteristic
629C2#1914462311yescharacteristic
630C2#1914481911yescharacteristic
631C2#1914646211yescharacteristic
632C2#1914657611yescharacteristic
633C2#1914757511yescharacteristic
634C2#1914767311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1926D43
hypocenterC43#27066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. #19137653C2semidirect
3. #19136135C2semidirect
5. #19135842C2semidirect
8. #19135228C2semidirect
9. #19135173C2semidirect
10. #19135153C2semidirect
13. #19134599C2semidirect
14. #19134414C2semidirect
190. C4⋊Dic43SD16semidirect
376. C43#27066semidirect

Maximal subgroups

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

subgroupindex
#191391792
#191376532
#191361352
#191359112
#191358422
#191356772
#191354502
#191352282
#191351732
#191351532
#191349472
#191345992
#191344142
C43×#19262
#2706643