Finite Group Databasebeta

← #25169788

Subgroups — #25169788

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#19139181C211yesmaximal, characteristic
2#19136138C211yesmaximal, characteristic, complemented
3#19135910C211yesmaximal, characteristic
4#19135838C211yesmaximal, characteristic, complemented
5#19135678C211yesmaximal, characteristic
6#19135452C211yesmaximal, characteristic
7#19135226C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic
9#19135173C211yesmaximal, characteristic, complemented
10#19135154C211yesmaximal, characteristic, complemented
11#19134950C211yesmaximal, characteristic
12#19134950C211yesmaximal, characteristic
13#19134600C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#2365C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063320—21no—
19C2×#13063256C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582826—21no—
32#14582821—21no—
33#14582801C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582791—21no—
38#14582769C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#391C2211yescharacteristic
53C43×#389—21no—
54C43×#387—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C2×#10621884—22no—
61C2×#10621884—22no—
62C2×#10621884—22no—
63C2×#10621884—41no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063320—44no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84#13063256—22no—
85#13063256—41no—
86C4⋊(C43⋊C8)—41no—
87#13063249—22no—
88#13063249—22no—
89#13063249—22no—
90#13063249—41no—
91#13063249—41no—
92#13063249—41no—
93#13063245—22no—
94#13063245—41no—
95C4×C43⋊C8—41no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43C2311yescharacteristic
99C22×Q8×C43C2311yescharacteristic
100C4⋊Q8×C43—22no—
101C4⋊Q8×C43—22no—
102C4×Q8×C43—22no—
103C4×Q8×C43—22no—
104C4×Q8×C43—41no—
105C4×Q8×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43D411yescharacteristic
126#95×C43D411yescharacteristic
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C2×Q8×C43#4112yes—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43SD1614yescomplemented
169C4⋊C4×C43#4112yes—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C42×C43—42no—
178C42×C43—42no—
179#10621884—44no—
180#10621884—44no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—81no—
186(C2×D43)⋊C4—81no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—42no—
194C4⋊Dic43—81no—
195Dic43⋊C4—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×C43C22×D411yescharacteristic
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
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—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43C2×SD1612yes—
253C2×C4×C43C2×SD1612yes—
254C2×C4×C43C2×SD1612yes—
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
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×Dic43—41no—
270D172—41no—
271D172—41no—
272D172—41no—
273D172—41no—
274C43⋊C8—22no—
275C43⋊C8—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#27066—431nomaximal, Sylow
279C22×C43#52511yescharacteristic
280C22×C43#54611yescharacteristic
281C22×C43#55011yescharacteristic
282C22×C43C22×SD1611yescharacteristic
283C22×C43#57511yescharacteristic
284C22×C43#57711yescharacteristic
285C22×C43#57811yescharacteristic
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—22no—
295C4×C43—22no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—42no—
302C4×C43—81no—
303C4×C43#52911yescharacteristic
304C4×C43#53811yescharacteristic
305C4×C43#55111yescharacteristic
306C4×C43#55311yescharacteristic
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310#2512—431no—
311#2365D4311yescharacteristic, complemented
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#246711yescharacteristic
326C2×C43#310311yescharacteristic
327C2×C43#312111yescharacteristic
328C2×C43#329811yescharacteristic
329C2×C43#330711yescharacteristic
330C2×C43#339211yescharacteristic
331C2×C43#340211yescharacteristic
332D43—161no—
333C22×SD16—431no—
334C22×SD16—431no—
335C2×C4⋊Q8C2×D4311yescharacteristic
336C2×#126—861no—
337C2×C4×Q8C2×D4311yescharacteristic
338C2×C4×Q8C2×D4311yescharacteristic
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—861no—
352#396—861no—
353#391C2×D4311yescharacteristic
354#391C2×D4311yescharacteristic
355#390—431no—
356#390—431no—
357#390—431no—
358#389—21no—
359#389—431no—
360#388—861no—
361#387—21no—
362#387—21no—
363#384—431no—
364C4×C4⋊C4—21no—
365C4×C4⋊C4—431no—
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×Q8C22×D4311yescharacteristic
378C22×Q8C22×D4311yescharacteristic
379C22×D4—431no—
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—22no—
391C4⋊Q8—22no—
392#126—1724no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×Q8—41no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22⋊D4311yescharacteristic
408C2×C4⋊C4C22⋊D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
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—21no—
439#95—21no—
440#95—21no—
441#95—861no—
442#95—861no—
443#95C22⋊D4311yescharacteristic
444#95C22⋊D4311yescharacteristic
445C24—861no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8#1062189812yes—
457C2×Q8#1062189812yes—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
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—24no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—3441no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4#1062188414yescomplemented
510C4⋊C4#1062190012yes—
511C22⋊C4—3441no—
512C22⋊C4—3441no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—42no—
525C42—42no—
526C42—1722no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23C22×C22⋊D4311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543D4—1721no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
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×#1062188412yes—
584C2×C4C2×#1062188412yes—
585C2×C4C2×#1062188412yes—
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062190011yescharacteristic
588C2×C4C2×#1062189811yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337111yescharacteristic
592C8—862no—
593C8—1721no—
594C8—1721no—
595C8—1721no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—3441no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22#1458341011yescharacteristic
604C22#1458354311yescharacteristic
605C22#1458356811yescharacteristic
606C22C22×#1062188411yescharacteristic
607C22#1458369711yescharacteristic
608C22#1458370711yescharacteristic
609C22#1458371411yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—3441no—
621C4—3441no—
622C4—3441no—
623C4#1458342911yescharacteristic
624C4#1458348211yescharacteristic
625C4#1458357811yescharacteristic
626C4#1458359511yescharacteristic
627C2—6881no—
628C2#1913864011yescharacteristic
629C2#1914462611yescharacteristic
630C2#1914482411yescharacteristic
631C2#1914646011yescharacteristic
632C2#1914657111yescharacteristic
633C2#1914757211yescharacteristic
634C2#1914767011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2365C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2365D43
hypocenterC43#27066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #19136138C2semidirect
4. #19135838C2semidirect
7. #19135226C2semidirect
9. #19135173C2semidirect
10. #19135154C2semidirect
13. #19134600C2semidirect
14. C4×#13063249C2semidirect
15. C43×#2365C2semidirect
168. C4⋊C4×C43SD16semidirect
311. #2365D43semidirect
376. C43#27066semidirect
509. C4⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191391812
#191361382
#191359102
#191358382
#191356782
#191354522
#191352262
#191352222
#191351732
#191351542
#191349502
#191346002
C4×#130632492
C43×#23652
#2706643