Finite Group Databasebeta

← #25169841

Subgroups — #25169841

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139193C211yesmaximal, characteristic
2#19137649C211yesmaximal, characteristic, complemented
3#19136141C211yesmaximal, characteristic, complemented
4#19135908C211yesmaximal, characteristic
5#19135840C211yesmaximal, characteristic, complemented
6#19135676C211yesmaximal, characteristic
7#19135448C211yesmaximal, characteristic
8#19135237C211yesmaximal, characteristic, complemented
9#19135217C211yesmaximal, characteristic
10#19135183C211yesmaximal, characteristic, complemented
11#19135150C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic
13#19134609C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063323C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582827—21no—
30#14582824—21no—
31#14582806C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582794—21no—
37#14582793—21no—
38#14582792—21no—
39#14582783—21no—
40#14582780—21no—
41#14582764C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063323—22no—
66#13063323—22no—
67#13063290—22no—
68#13063290—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063259—41no—
88#13063256—22no—
89Dic43⋊C8—41no—
90#13063250—22no—
91#13063250—41no—
92#13063249—22no—
93#13063249—22no—
94#13063248—41no—
95#13063246—41no—
96C4×C43⋊C8—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C2×SD16×C43—22no—
111C2×SD16×C43—41no—
112C2×SD16×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C4×Q8×C43—22no—
116C4×Q8×C43—41no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#103×C43—41no—
125#102×C43—22no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
159SD16×C43—44no—
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—42no—
170C4⋊C4×C43#4112yes—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—81no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179C22⋊Dic43—81no—
180#10621883—44no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—81no—
188Dic43⋊C4—24no—
189Dic43⋊C4—24no—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8#4112yes—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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×C43—41no—
236C2×C4×C43#13712yes—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
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×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43#13512yes—
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—41no—
272C8×C43—41no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275#27069—431nomaximal, Sylow
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43#52511yescharacteristic
284C22×C43#54611yescharacteristic
285C22×C43#55011yescharacteristic
286C22×C43C2×#13511yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57711yescharacteristic
289C22×C43#57711yescharacteristic
290C4×C43—22no—
291C4×C43—42no—
292C4×C43—41no—
293C4×C43—42no—
294C4×C43—81no—
295C4×C43#52911yescharacteristic
296C4×C43#53811yescharacteristic
297C4×C43#55111yescharacteristic
298C4×C43#55311yescharacteristic
299Dic43—22no—
300Dic43—41no—
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
307#2513—431no—
308#2365—431no—
309#2097—431no—
310#2055—431no—
311#2043—431no—
312#2013—431no—
313#1968—431no—
314#1928—431no—
315#1925—431no—
316#1920—431no—
317#1916—431no—
318#1880—431no—
319#1880D4311yescharacteristic
320#1805—431no—
321C4×#103—431no—
322C2×C43—161no—
323C2×C43#246711yescharacteristic
324C2×C43#310811yescharacteristic
325C2×C43#312611yescharacteristic
326C2×C43#330311yescharacteristic
327C2×C43#332011yescharacteristic
328C2×C43#339411yescharacteristic
329C2×C43#340011yescharacteristic
330C22×SD16—431no—
331C22×SD16C2×D4311yescharacteristic
332C2×C4⋊Q8—431no—
333C2×C4×Q8—431no—
334C2×C4×Q8C2×D4311yescharacteristic
335C2×#107—431no—
336C2×#106—431no—
337C2×C4⋊C8—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103C2×D4311yescharacteristic
344C2×#102—431no—
345C2×#102C2×D4311yescharacteristic
346C2×C4×C8—431no—
347#397—861no—
348#397—861no—
349#391—431no—
350#391—431no—
351#390—431no—
352#390—431no—
353#390C2×D4311yescharacteristic
354#389—431no—
355#389—861no—
356#388—861no—
357#388—861no—
358#387—861no—
359#387—861no—
360#382—431no—
361C4×C4⋊C4—431no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4—861no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336—431no—
371#336—431no—
372#336C2×D4311yescharacteristic
373C43#2706911yescharacteristic, complemented, Sylow
374C22×Q8—431no—
375C22×Q8C22×D4311yescharacteristic
376C22×D4C22×D4311yescharacteristic
377C2×SD16—22no—
378C2×SD16—41no—
379C2×SD16—41no—
380C2×SD16—862no—
381C2×SD16—862no—
382C2×SD16—1721no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C4⋊Q8—862no—
388C4⋊Q8—862no—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×Q8—862no—
392C4×Q8—1721no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—21no—
412C2×C42—431no—
413C2×C42—431no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418#107—1721no—
419#106—862no—
420C4⋊C8—1721no—
421#103—41no—
422#103—862no—
423#103—862no—
424#103—862no—
425#103—1721no—
426#103—1721no—
427#102—22no—
428#102—1721no—
429C4×C8—1721no—
430#95—431no—
431#95—431no—
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—
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—432no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8#1062189812yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4D4×D4311yescharacteristic
472C22×C4D4×D4311yescharacteristic
473C22×C4C23×D4311yescharacteristic
474SD16—44no—
475SD16—1724no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—432no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—862no—
493C4⋊C4—864no—
494C4⋊C4—864no—
495C4⋊C4—862no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—3441no—
503C4⋊C4—1722no—
504C4⋊C4#1062190012yes—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—3441no—
508C22⋊C4—3441no—
509C22⋊C4—3441no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42—3441no—
519C42—1722no—
520C42—1722no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23C2×D4×D4311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533Q8—862no—
534Q8—862no—
535Q8—1721no—
536Q8—1721no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
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—862no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—1721no—
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#1306335412yes—
580C2×C4#41×D4311yescharacteristic
581C2×C4#41×D4311yescharacteristic
582C2×C4C2×#1062190011yescharacteristic
583C2×C4C2×#1062189811yescharacteristic
584C2×C4#1306337011yescharacteristic
585C2×C4#1306337011yescharacteristic
586C8—41no—
587C8—41no—
588C8—862no—
589C8—1721no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#1458340811yescharacteristic
598C22#1458353611yescharacteristic
599C22#1458356711yescharacteristic
600C22#135×D4311yescharacteristic
601C22C2×#1306335411yescharacteristic
602C22#1458370811yescharacteristic
603C22#1458370911yescharacteristic
604C4—22no—
605C4—41no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—862no—
610C4—3441no—
611C4—3441no—
612C4—3441no—
613C4—1721no—
614C4—1721no—
615C4—1722no—
616C4—1721no—
617C4#1458342911yescharacteristic
618C4#1458348711yescharacteristic
619C4#1458357711yescharacteristic
620C4#1458359611yescharacteristic
621C2—161no—
622C2#1913864811yescharacteristic
623C2#1914467311yescharacteristic
624C2#1914488511yescharacteristic
625C2#1914651611yescharacteristic
626C2#1914677011yescharacteristic
627C2#1914758611yescharacteristic
628C2#1914764711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1880D43
hypocenterC43#27069
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. #19137649C2semidirect
3. #19136141C2semidirect
5. #19135840C2semidirect
8. #19135237C2semidirect
10. #19135183C2semidirect
11. #19135150C2semidirect
13. #19134609C2semidirect
14. C4×#13063249C2semidirect
373. C43#27069semidirect

Maximal subgroups

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

subgroupindex
#191391932
#191376492
#191361412
#191359082
#191358402
#191356762
#191354482
#191352372
#191352172
#191351832
#191351502
#191349472
#191346092
C4×#130632492
C43×#18802
#2706943