Finite Group Databasebeta

← #25200618

Subgroups — #25200618

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142978C211yesmaximal, characteristic, complemented
2#19137142C211yesmaximal, characteristic
3#19136082C211yesmaximal, characteristic, complemented
4#19136017C211yesmaximal, characteristic, complemented
5#19135834C211yesmaximal, characteristic
6#19135691C211yesmaximal, characteristic
7#19135456C211yesmaximal, characteristic, complemented
8#19135448C211yesmaximal, characteristic
9#19135270C211yesmaximal, characteristic, complemented
10#19134937C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic
12#19134864C211yesmaximal, characteristic, complemented
13#19134844C211yesmaximal, characteristic
14#19134340C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582787—21no—
37#14582787—21no—
38#14582785—21no—
39#14582782—21no—
40#14582780—21no—
41#14582766—21no—
42#14582764C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45C42×Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×C4×C8×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43—21no—
62C2×Dic172—22no—
63C2×Dic172—22no—
64C2×Dic172—41no—
65C2×#10621883—22no—
66C2×#10621883—22no—
67C2×#10621883—41no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063312—22no—
71#13063312—22no—
72#13063290—41no—
73#13063290—41no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—41no—
92#13063256—41no—
93#13063250—41no—
94#13063250—41no—
95#13063248—22no—
96#13063248—22no—
97#13063248—41no—
98#13063246—41no—
99C4×C43⋊C8—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#102×C43—22no—
123#102×C43—22no—
124C4×C8×C43—22no—
125#95×C43—21no—
126C24×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
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—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C42×C43—21no—
178C42×C43—21no—
179C22⋊Dic43—24no—
180C22⋊Dic43—24no—
181C22⋊Dic43—42no—
182#10621883—44no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—22no—
197C4×Dic43—41no—
198C4×Dic43—42no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8#4112yes—
205Dic172—44no—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214D4×C43—22no—
215D4×C43—22no—
216D4×C43—41no—
217D4×C43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43#13512yes—
232C2×C4×C43#13712yes—
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
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—84no—
263C2×Dic43#13512yes—
264Dic86—22no—
265Dic86—22no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276#29496—431nomaximal, Sylow
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43#52511yescharacteristic
285C22×C43#53211yescharacteristic
286C22×C43#53511yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C22×C43#57511yescharacteristic
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#55111yescharacteristic
297C4×C43#55111yescharacteristic
298C4×C43#55311yescharacteristic
299C4×C43#55311yescharacteristic
300Dic43—22no—
301Dic43—41no—
302Dic43—41no—
303Dic43—42no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308#2863—431no—
309C4×#124—431no—
310#2085—431no—
311#2074—431no—
312#2042—431no—
313#2015—431no—
314#1969—431no—
315#1968—431no—
316#1934D4311yescharacteristic
317#1933—431no—
318#1878—431no—
319#1877—431no—
320#1865—431no—
321#1862—431no—
322#1744—431no—
323C2×C43—82no—
324C2×C43#260311yescharacteristic
325C2×C43#310211yescharacteristic
326C2×C43#310711yescharacteristic
327C2×C43#316811yescharacteristic
328C2×C43#318111yescharacteristic
329C2×C43#321011yescharacteristic
330C2×C43#321111yescharacteristic
331C22×Q16—431no—
332C22×SD16—431no—
333C2×#124—431no—
334C2×C4×Q8—431no—
335C2×C4×D4—431no—
336C2×#107—431no—
337C2×#106—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#102—431no—
344C2×#102C2×D4311yescharacteristic
345C2×#102C2×D4311yescharacteristic
346C2×C4×C8—431no—
347C2×C4×C8C2×D4311yescharacteristic
348#391—431no—
349#391—431no—
350#391—431no—
351#391—431no—
352#390C2×D4311yescharacteristic
353#389—431no—
354#389—431no—
355#389C2×D4311yescharacteristic
356#388—861no—
357#388—861no—
358#387—861no—
359#387—861no—
360#387—861no—
361#383—861no—
362#382—431no—
363C4×C22⋊C4—861no—
364C4×C22⋊C4—861no—
365C43—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#340C2×D4311yescharacteristic
370#336—431no—
371#336—431no—
372#336—431no—
373#336—431no—
374C43#2949611yescharacteristic, complemented, Sylow
375C22×Q8—431no—
376C22×Q8—431no—
377C22×D4C22×D4311yescharacteristic
378C23×C4—861no—
379C2×Q16—862no—
380C2×Q16—862no—
381C2×Q16—1721no—
382C2×SD16—862no—
383C2×SD16—862no—
384C2×SD16—1721no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389#124—862no—
390#124—862no—
391C4×Q8—1721no—
392C4×Q8—1721no—
393C4×D4—1721no—
394C4×D4—1721no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417#107—1721no—
418#106—1721no—
419#103—862no—
420#103—862no—
421#103—1721no—
422#103—1721no—
423#103—1721no—
424#102—22no—
425#102—22no—
426#102—1721no—
427C4×C8—22no—
428C4×C8—862no—
429#95—21no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—21no—
443C2×Q8—432no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4#1062189812yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478Q16—1724no—
479SD16—1724no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8#1062190012yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—862no—
514C42—862no—
515C42—862no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42—861no—
520C42—1721no—
521C42—1722no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C2×D4×D4311yescharacteristic
530Q8—862no—
531Q8—862no—
532Q8—1721no—
533Q8—1721no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—432no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—862no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—3444no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4#1306334412yes—
581C2×C4#1306335412yes—
582C2×C4#41×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4C2×#1062190011yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337111yescharacteristic
587C2×C4#1306337111yescharacteristic
588C8—22no—
589C8—41no—
590C8—862no—
591C8—1721no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1458340811yescharacteristic
600C22#1458344411yescharacteristic
601C22#1458346711yescharacteristic
602C22#135×D4311yescharacteristic
603C22C2×#1306334411yescharacteristic
604C22C2×#1306335411yescharacteristic
605C22#1458369611yescharacteristic
606C4—22no—
607C4—22no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—862no—
612C4—3441no—
613C4—3441no—
614C4—3441no—
615C4—1721no—
616C4—1722no—
617C4—1721no—
618C4—1721no—
619C4#1458357211yescharacteristic
620C4#1458357311yescharacteristic
621C4#1458359511yescharacteristic
622C4#1458360011yescharacteristic
623C2—82no—
624C2#1914022011yescharacteristic
625C2#1914460911yescharacteristic
626C2#1914466211yescharacteristic
627C2#1914516011yescharacteristic
628C2#1914529711yescharacteristic
629C2#1914555211yescharacteristic
630C2#1914556111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1934D43
hypocenterC43#29496
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
1. #19142978C2semidirect
3. #19136082C2semidirect
4. #19136017C2semidirect
7. #19135456C2semidirect
9. #19135270C2semidirect
10. #19134937C2semidirect
12. #19134864C2semidirect
14. #19134340C2semidirect
374. C43#29496semidirect

Maximal subgroups

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

subgroupindex
#191429782
#191371422
#191360822
#191360172
#191358342
#191356912
#191354562
#191354482
#191352702
#191349372
#191349272
#191348642
#191348442
#191343402
C43×#19342
#2949643