Finite Group Databasebeta

← #25200668

Subgroups — #25200668

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142959C211yesmaximal, characteristic
2#19137164C211yesmaximal, characteristic, complemented
3#19136069C211yesmaximal, characteristic, complemented
4#19136001C211yesmaximal, characteristic
5#19135840C211yesmaximal, characteristic, complemented
6#19135676C211yesmaximal, characteristic
7#19135475C211yesmaximal, characteristic
8#19135288C211yesmaximal, characteristic, complemented
9#19135285C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic
11#19134947C211yesmaximal, characteristic
12#19134847C211yesmaximal, characteristic, complemented
13#19134846C211yesmaximal, characteristic, complemented
14#19134343C211yesmaximal, characteristic, complemented
15C43×#1973C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×#13063318—21no—
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29#14582805C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582796—21no—
35#14582796—21no—
36#14582795C2211yescharacteristic
37#14582793—21no—
38#14582792—21no—
39#14582787—21no—
40#14582768C2211yescharacteristic
41#14582750—21no—
42#14582750—21no—
43C42×Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063323—22no—
66#13063323—22no—
67#13063318—44no—
68Q8×Dic43—41no—
69Q8×Dic43—41no—
70#13063290—41no—
71#13063290—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063258—41no—
97#13063250—22no—
98#13063250—22no—
99#13063249—22no—
100#13063249—22no—
101#13063248—41no—
102#13063246—41no—
103#13063236—22no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—41no—
122#103×C43—41no—
123#102×C43—41no—
124#97×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86#4112yes—
160SD16×C43—44no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—42no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—42no—
178C22⋊Dic43—42no—
179#10621883—44no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—42no—
188Dic43⋊C4—24no—
189Dic43⋊C4—24no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43—41no—
203C4×Dic43—42no—
204C4×Dic43—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8#4112yes—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C22×D411yescharacteristic
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43AGL(1,ℤ/8)12yes—
270C2×Dic43#13712yes—
271C2×Dic43#13712yes—
272Dic86—22no—
273Dic86—22no—
274Dic86—41no—
275Dic86—41no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280#29500—431nomaximal, Sylow
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43#52511yescharacteristic
289C22×C43#53211yescharacteristic
290C22×C43#53511yescharacteristic
291C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C43C2×#13711yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57511yescharacteristic
295C4×C43—42no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#55111yescharacteristic
301C4×C43#55111yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55311yescharacteristic
304Dic43—22no—
305Dic43—22no—
306Dic43—22no—
307Dic43—42no—
308Dic43—41no—
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312#2860—431no—
313C4×C4⋊Q8—431no—
314#2083—431no—
315#2071—431no—
316#2043—431no—
317#2013—431no—
318#1973—431no—
319#1973D4311yescharacteristic
320#1935—431no—
321#1935—431no—
322#1880—431no—
323#1880—431no—
324#1863—431no—
325#1863—431no—
326#1745—431no—
327C2×C43—161no—
328C2×C43#260311yescharacteristic
329C2×C43#311211yescharacteristic
330C2×C43#311711yescharacteristic
331C2×C43#317211yescharacteristic
332C2×C43#318211yescharacteristic
333C2×C43#321411yescharacteristic
334C2×C43#321811yescharacteristic
335C22×SD16—431no—
336C22×SD16C2×D4311yescharacteristic
337C2×C4⋊Q8—431no—
338C2×#126—861no—
339C2×C4×Q8—431no—
340C2×C4×Q8—431no—
341C2×#107—431no—
342C2×#107C2×D4311yescharacteristic
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#103C2×D4311yescharacteristic
349C2×#102—431no—
350C2×#102C2×D4311yescharacteristic
351C2×#97—431no—
352C2×#97C2×D4311yescharacteristic
353#391—431no—
354#391C2×D4311yescharacteristic
355#390—431no—
356#390—431no—
357#390C2×D4311yescharacteristic
358#389—431no—
359#389—431no—
360#389—431no—
361#389—861no—
362#389—861no—
363#388—861no—
364#388—861no—
365#388—861no—
366#384—431no—
367C4×C4⋊C4—861no—
368C4×C4⋊C4—861no—
369C43—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336—431no—
375#336—431no—
376#336—431no—
377#336—431no—
378C43#2950011yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×Q8C22×D4311yescharacteristic
381C22×D4C22×D4311yescharacteristic
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—41no—
385C2×SD16—862no—
386C2×SD16—862no—
387C2×SD16—1721no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C4⋊Q8—862no—
393C4⋊Q8—862no—
394#126—1724no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C4×Q8—1721no—
398C4×Q8—1721no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
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⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—431no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#107—41no—
429#107—1721no—
430#103—41no—
431#103—862no—
432#103—862no—
433#103—862no—
434#103—862no—
435#103—1721no—
436#102—41no—
437#102—1721no—
438#97—22no—
439#97—862no—
440#95—21no—
441#95—21no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8#1062189812yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480SD16—44no—
481SD16—1724no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—432no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8#1062190012yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—864no—
499C4⋊C4—864no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—862no—
522C42—862no—
523C42—862no—
524C42—861no—
525C42—861no—
526C42—861no—
527C42—861no—
528C42—1721no—
529C42—1722no—
530C42—1722no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C2×D4×D4311yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—41no—
542Q8—41no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—432no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4#41×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337011yescharacteristic
596C8—22no—
597C8—41no—
598C8—862no—
599C8—1721no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1458340811yescharacteristic
608C22#1458344411yescharacteristic
609C22#1458346211yescharacteristic
610C22AGL(1,ℤ/8)×D4311yescharacteristic
611C22#137×D4311yescharacteristic
612C22#137×D4311yescharacteristic
613C22#1458369511yescharacteristic
614C4—41no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—862no—
620C4—862no—
621C4—862no—
622C4—3441no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4—1722no—
627C4#1458357511yescharacteristic
628C4#1458357911yescharacteristic
629C4#1458359611yescharacteristic
630C4#1458359811yescharacteristic
631C2—161no—
632C2#1914021811yescharacteristic
633C2#1914471511yescharacteristic
634C2#1914476411yescharacteristic
635C2#1914519411yescharacteristic
636C2#1914530811yescharacteristic
637C2#1914558511yescharacteristic
638C2#1914561811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1973C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1973D43
hypocenterC43#29500
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. #19137164C2semidirect
3. #19136069C2semidirect
5. #19135840C2semidirect
8. #19135288C2semidirect
9. #19135285C2semidirect
12. #19134847C2semidirect
13. #19134846C2semidirect
14. #19134343C2semidirect
378. C43#29500semidirect

Maximal subgroups

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

subgroupindex
#191429592
#191371642
#191360692
#191360012
#191358402
#191356762
#191354752
#191352882
#191352852
#191349522
#191349472
#191348472
#191348462
#191343432
C43×#19732
#2950043