Finite Group Databasebeta

← #25169790

Subgroups — #25169790

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#19137651C211yesmaximal, characteristic, complemented
2#19136139C211yesmaximal, characteristic, complemented
3#19135912C211yesmaximal, characteristic
4#19135841C211yesmaximal, characteristic, complemented
5#19135677C211yesmaximal, characteristic
6#19135448C211yesmaximal, characteristic
7#19135229C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic
9#19135170C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134953C211yesmaximal, characteristic
12#19134953C211yesmaximal, characteristic
13#19134597C211yesmaximal, characteristic, complemented
14C4×#13063248C211yesmaximal, characteristic, complemented
15C43×#2512C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C4×C43⋊C8C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582795—21no—
36#14582782—21no—
37#14582782—21no—
38C4⋊C4×Dic43—21no—
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#126×C43—21no—
49C43×#397—21no—
50C43×#396—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#390C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#388—21no—
56C43×#384C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
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
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325—22no—
72#13063325—22no—
73C4×Dic86—22no—
74C4×Dic86—22no—
75C4×Dic86—41no—
76C4×Dic86—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063256—22no—
87#13063256—41no—
88C4⋊(C43⋊C8)—41no—
89#13063248—22no—
90#13063248—22no—
91#13063248—22no—
92#13063248—41no—
93#13063248—41no—
94#13063248—41no—
95#13063246—22no—
96#13063246—41no—
97C4×C43⋊C8—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×D4×C43C2311yescharacteristic
104#126×C43—44no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
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×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
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—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43SD1614yescomplemented
171C22⋊C4×C43—42no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—81no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—42no—
184#10621883—44no—
185#10621883—44no—
186C4⋊Dic43—24no—
187C4⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43#4112yes—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
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—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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—21no—
235C2×C4×C43—21no—
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×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C2×SD1612yes—
246C2×C4×C43C2×SD1612yes—
247C2×C4×C43C2×SD1612yes—
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
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—
266Dic86—22no—
267Dic86—22no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276C43⋊C8—41no—
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—22no—
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43#52911yescharacteristic
303C4×C43#53811yescharacteristic
304C4×C43#55111yescharacteristic
305C4×C43#55311yescharacteristic
306Dic43—42no—
307Dic43—42no—
308Dic43—42no—
309Dic43—81no—
310#2512D4311yescharacteristic
311#2365—431no—
312#2096—431no—
313#2055—431no—
314#2043—431no—
315#2013—431no—
316#1968—431no—
317#1927—431no—
318#1926—431no—
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—21no—
337C2×C4×Q8—431no—
338C2×C4×Q8—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×C4⋊C8—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×C4×C8—431no—
351#397—21no—
352#396—21no—
353#391—431no—
354#391—431no—
355#390C2×D4311yescharacteristic
356#390C2×D4311yescharacteristic
357#390C2×D4311yescharacteristic
358#389—861no—
359#389C2×D4311yescharacteristic
360#388—21no—
361#387—861no—
362#387—861no—
363#384C2×D4311yescharacteristic
364C4×C4⋊C4—431no—
365C4×C4⋊C4—861no—
366C4×C4⋊C4C2×D4311yescharacteristic
367C4×C4⋊C4C2×D4311yescharacteristic
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#336—431no—
373#336—431no—
374#336—431no—
375#336—431no—
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×C8—431no—
389C22×C8—431no—
390C4⋊Q8—862no—
391C4⋊Q8—862no—
392#126—44no—
393C4×Q8—862no—
394C4×Q8—862no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
407C2×C4⋊C4C22⋊D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C42—21no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#106—862no—
425#106—1721no—
426C4⋊C8—1721no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—1721no—
431#103—1721no—
432#103—1721no—
433#102—862no—
434#102—1721no—
435C4×C8—1721no—
436#95—21no—
437#95—21no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95C22⋊D4311yescharacteristic
444#95C22⋊D4311yescharacteristic
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—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—1724no—
479SD16—1724no—
480C2×C8—432no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
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—21no—
498C4⋊C4—41no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4—432no—
503C4⋊C4—864no—
504C4⋊C4—864no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4#1062188314yescomplemented
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—81no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—1722no—
525C42—1722no—
526C42—1722no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C22×C22⋊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—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—862no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—1721no—
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×C4C2×#1062188312yes—
584C2×C4C2×#1062188312yes—
585C2×C4C2×#1062188312yes—
586C2×C4#41×D4311yescharacteristic
587C2×C4#41×D4311yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#1306337111yescharacteristic
591C2×C4#1306337111yescharacteristic
592C8—862no—
593C8—1721no—
594C8—1721no—
595C8—1721no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1458340611yescharacteristic
604C22#1458353711yescharacteristic
605C22#1458356811yescharacteristic
606C22C22×#1062188311yescharacteristic
607C22#1458369711yescharacteristic
608C22#1458371011yescharacteristic
609C22#1458371411yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—3441no—
620C4—1722no—
621C4—1722no—
622C4—1722no—
623C4#1458343211yescharacteristic
624C4#1458348811yescharacteristic
625C4#1458357411yescharacteristic
626C4#1458360011yescharacteristic
627C2—161no—
628C2#1913864211yescharacteristic
629C2#1914462211yescharacteristic
630C2#1914481811yescharacteristic
631C2#1914645411yescharacteristic
632C2#1914656511yescharacteristic
633C2#1914757611yescharacteristic
634C2#1914767011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2512C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2512D43
hypocenterC43#27066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. #19137651C2semidirect
2. #19136139C2semidirect
4. #19135841C2semidirect
7. #19135229C2semidirect
9. #19135170C2semidirect
10. #19135154C2semidirect
13. #19134597C2semidirect
14. C4×#13063248C2semidirect
170. C4⋊C4×C43SD16semidirect
376. C43#27066semidirect
510. C4⋊C4#10621883semidirect

Maximal subgroups

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

subgroupindex
#191376512
#191361392
#191359122
#191358412
#191356772
#191354482
#191352292
#191352192
#191351702
#191351542
#191349532
#191345972
C4×#130632482
C43×#25122
#2706643