Finite Group Databasebeta

← #25101622

Subgroups — #25101622

Order 11008.

1256 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2C4×M16×D43C211yesmaximal, characteristic, complemented
3C4×#13063283C211yesmaximal, characteristic, complemented
4#19135539C211yesmaximal, characteristic, complemented
5#19135538C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19134894C214yesmaximal, complemented
8#104×Dic43C214yesmaximal, complemented
9C43×#1980C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583456C2211yescharacteristic
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583447C411yescharacteristic, complemented
16#14583431—21no—
17#14583431—21no—
18#14583430—21no—
19#14583430—21no—
20#14583428C412yescomplemented
21#14583428C412yescomplemented
22#14583409—21no—
23#14583409—21no—
24#14583406C2212yes—
25#41×Dic43C2212yes—
26C4×#10621900—21no—
27C4×#10621900—21no—
28C2×#13063283—21no—
29C2×C42×D43C2211yescharacteristic
30C2×#13063252C2214yes—
31C4×#10621877C2211yescharacteristic
32#14582851—21no—
33M16×Dic43C2212yes—
34C4×#10621872—21no—
35#97×D43—21no—
36C4×C8×D43—21no—
37C4⋊C4×Dic43—21no—
38C4×C4⋊Dic43C2211yescharacteristic
39C4×(C2×D43)⋊C4C2212yes—
40#14582746—21no—
41#14582744—21no—
42C42×Dic43C2212yes—
43#14582660C2214yes—
44#14582659C2214yes—
45C43×#532C2211yescharacteristic
46C2×#104×C43C2214yes—
47C4×M16×C43C2211yescharacteristic
48C4×C4⋊C4×C43C2211yescharacteristic
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55C2×#10621872—22no—
56M16×D43—24no—
57M16×D43—24no—
58C2×C8×D43—22no—
59#13063325C2×C411yescharacteristic
60#13063325C2×C411yescharacteristic
61#13063318—22no—
62#13063318—22no—
63#13063317C2×C412yes—
64#13063316—21no—
65#13063316—21no—
66#13063312—21no—
67#13063312—21no—
68#13063307—22no—
69#13063307—22no—
70#13063306—22no—
71#13063305—21no—
72#13063305—21no—
73#13063304—21no—
74#13063304—21no—
75#13063301C2×C412yes—
76#13063301C2×C412yes—
77#13063296—21no—
78#13063296—21no—
79#13063296C2×C412yes—
80#13063296C2×C412yes—
81#13063293—22no—
82Q8×Dic43C2×C412yes—
83Q8×Dic43C2×C412yes—
84C4×Dic86—21no—
85C4×Dic86—21no—
86#13063290—21no—
87#13063290—21no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43C2×C412yes—
93D4×Dic43C2×C412yes—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063284—22no—
99#13063284C2312yes—
100#13063283—28no—
101#13063283—21no—
102#13063283—21no—
103#13063281—22no—
104#13063281—22no—
105C2×C4⋊Dic43—21no—
106C2×(C2×D43)⋊C4—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43C2312yes—
113C2×C4×Dic43C2311yescharacteristic
114C42×D43C2×C411yescharacteristic
115C42×D43C2×C411yescharacteristic
116C42×D43C2×C411yescharacteristic
117C42×D43C2×C411yescharacteristic
118C42×D43D411yescharacteristic
119C42×D43D411yescharacteristic
120C42×D43D411yescharacteristic
121C42×D43D411yescharacteristic
122#13063252—28no—
123#13063236—21no—
124#13063235—22no—
125C4×C43⋊C8—21no—
126C8×Dic43—22no—
127C43⋊#95—21no—
128C43⋊#95—22no—
129C2×#41×C43C2312yes—
130C2×M16×C43C2312yes—
131C4⋊Q8×C43C2×C411yescharacteristic
132#127×C43C2×C411yescharacteristic
133#124×C43C2×C412yes—
134#121×C43—21no—
135#121×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C42×C43C2312yes—
140C2×C42×C43C2311yescharacteristic
141#104×C43—28no—
142#97×C43—21no—
143C4×C8×C43—21no—
144#95×C43—21no—
145C23×D43C2×D411yescharacteristic
146#41×C43—24no—
147#41×C43—24no—
148C2×Q8×C43C22×C412yes—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—22no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166#10621900—44no—
167#10621900—44no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—24no—
171C2×C4×D43—42no—
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22⋊C411yescharacteristic
179C2×C4×D43C22⋊C411yescharacteristic
180C2×C4×D43C22×C411yescharacteristic
181C2×C4×D43C22×C411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×C4×D43C2×D411yescharacteristic
184C2×Dic86—21no—
185C2×Dic86—21no—
186M16×C43—22no—
187M16×C43#4114yescomplemented
188C2×C8×C43—22no—
189C4⋊C4×C43—24no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C42×C43—24no—
195C42×C43C22×C411yescharacteristic
196C42×C43C22×C411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207C4⋊Dic43—24no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212C4⋊Dic43C22×C412yes—
213C4⋊Dic43C22×C412yes—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—28no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—24no—
223C4×Dic43—44no—
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22⋊C411yescharacteristic
229C4×Dic43C22⋊C411yescharacteristic
230C4×Dic43C22⋊C411yescharacteristic
231C4×Dic43C22⋊C411yescharacteristic
232C4×Dic43C22×C411yescharacteristic
233C4×Dic43C22×C411yescharacteristic
234C4×Dic43C2×D411yescharacteristic
235C4×Dic43C2×D411yescharacteristic
236#10621877—22no—
237#10621877#4114yescomplemented
238C2×C43⋊C8—22no—
239#10621872—28no—
240C8×D43—28no—
241C23×C43—22no—
242C23×C43C22×D411yescharacteristic
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—22no—
246C22×D43—41no—
247C22×D43C2×C22⋊C411yescharacteristic
248C22×D43C2×C22⋊C411yescharacteristic
249Q8×C43—24no—
250D4×C43—24no—
251D4×C43—42no—
252D4×C43—42no—
253D4×C43—42no—
254D4×C43—42no—
255C2×C4×C43—22no—
256C2×C4×C43—24no—
257C2×C4×C43—22no—
258C2×C4×C43—41no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—44no—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C23×C411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4112yes—
269C2×C4×C43C2×#4112yes—
270C22⋊D43—44no—
271C22⋊D43—44no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—24no—
277C2×Dic43—22no—
278C2×Dic43—22no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—44no—
282C2×Dic43—44no—
283C2×Dic43C2×C22⋊C411yescharacteristic
284C2×Dic43C2×C22⋊C411yescharacteristic
285C2×Dic43C2×C22⋊C411yescharacteristic
286C2×Dic43C2×C22⋊C411yescharacteristic
287C2×Dic43C2×C22⋊C411yescharacteristic
288C2×Dic43C2×C22⋊C411yescharacteristic
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—41no—
299C4×D43—41no—
300C4×D43#10414yescomplemented
301Dic86—42no—
302Dic86—42no—
303C8×C43—24no—
304C43⋊C8—24no—
305#21382—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43C22×C22⋊C411yescharacteristic
312C22×C43#53211yescharacteristic
313C22×C43#53211yescharacteristic
314C2×D43—21no—
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—21no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43C2×#10412yes—
322C4×C43—21no—
323C4×C43—21no—
324C4×C43—21no—
325C4×C43—44no—
326C4×C43—42no—
327C4×C43C2×#10412yes—
328C4×C43C4×#4112yes—
329C4×C43#52512yes—
330Dic43—21no—
331Dic43—21no—
332Dic43—21no—
333Dic43—21no—
334Dic43—44no—
335Dic43—42no—
336Dic43—42no—
337Dic43C2×#10412yes—
338Dic43#42112yes—
339#3444—431no—
340C2×C4×M16—431no—
341C4×#117—431no—
342#1986—431no—
343#1986—431no—
344#1980—431no—
345#1980D4311yescharacteristic, complemented
346#1871—434no—
347C4×#104—434no—
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—82no—
351C2×C43#229711yescharacteristic
352C2×C43C22×#10411yescharacteristic
353C2×C43C2×#42111yescharacteristic
354D43—22no—
355D43—41no—
356C22×M16—432no—
357#533—431no—
358#533—431no—
359#533—431no—
360#532—431no—
361#532—431no—
362#532C2×D4311yescharacteristic
363#529—432no—
364#529—432no—
365#529—861no—
366#529—861no—
367#529—861no—
368#529—861no—
369#525—432no—
370#525—861no—
371#525—861no—
372C4×#41—432no—
373C4×#41—861no—
374C4×#41—861no—
375C2×#117—861no—
376C22×C42—431no—
377C2×#104—434no—
378C2×#104C2×D4314yes—
379C4×M16—432no—
380C4×M16—431no—
381C4×M16—861no—
382C4×M16—861no—
383C4×M16C2×D4311yescharacteristic
384C2×#97—861no—
385C2×C4×C8—861no—
386C4×C4⋊C4—431no—
387C4×C4⋊C4—861no—
388C4×C4⋊C4C2×D4311yescharacteristic
389C4×C22⋊C4—432no—
390C4×C22⋊C4—861no—
391#376—861no—
392C43—432no—
393#339—434no—
394#339—434no—
395C43#2138211yescharacteristic, complemented, Sylow
396C2×#41—861no—
397C2×#41—861no—
398C2×#41C22×D4312yes—
399C23×C4—431no—
400C23×C4—431no—
401C23×C4—431no—
402C2×M16—432no—
403C2×M16—862no—
404C2×M16—864no—
405C2×M16—864no—
406C2×M16C22×D4312yes—
407C22×C8—862no—
408C4⋊Q8—431no—
409C4⋊Q8—431no—
410C4⋊Q8C4×D4311yescharacteristic
411#127C4×D4311yescharacteristic
412#126—862no—
413#126—862no—
414#125—432no—
415#125—861no—
416#125—861no—
417#124—861no—
418#124—861no—
419#124C4×D4312yes—
420#123—862no—
421#123—862no—
422#123—862no—
423C22⋊Q8—432no—
424C22⋊Q8—432no—
425C22⋊Q8—861no—
426C22⋊Q8—861no—
427C22⋊Q8—861no—
428C22⋊Q8—861no—
429#121—21no—
430#121—21no—
431#121—432no—
432#121—432no—
433#121—861no—
434#121—861no—
435#120—862no—
436C4×Q8—432no—
437C4×Q8—432no—
438C4×Q8—861no—
439C4×Q8—861no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—432no—
445C4×D4—432no—
446C4×D4—861no—
447C4×D4—861no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—862no—
451C4×D4—862no—
452C4×D4—862no—
453C4×D4—862no—
454#117—432no—
455#117—862no—
456#117—862no—
457#117—862no—
458#117—861no—
459#117—861no—
460#117—868no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—861no—
463C2×C22⋊C4—862no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—431no—
469C2×C42—431no—
470C2×C42—431no—
471C2×C42—431no—
472C2×C42—431no—
473C2×C42—431no—
474C2×C42—431no—
475C2×C42—432no—
476C2×C42—862no—
477C2×C42—862no—
478C2×C42—862no—
479C2×C42C22×D4312yes—
480C2×C42C22×D4311yescharacteristic
481#104—28no—
482#104—868no—
483#97—21no—
484#97—862no—
485#97—861no—
486C4×C8—21no—
487C4×C8—862no—
488C4×C8—861no—
489#95—21no—
490#95—862no—
491#95—861no—
492C24—431no—
493#41—24no—
494#41—24no—
495#41—1724no—
496#41—1724no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8C2×C4×D4312yes—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—862no—
504C2×D4—862no—
505C2×D4C2×C4×D4312yes—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—864no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—1722no—
530C22×C4D4×D4311yescharacteristic
531C22×C4D4×D4311yescharacteristic
532C22×C4C23×D4311yescharacteristic
533M16—22no—
534M16—434no—
535M16—868no—
536M16—862no—
537M16#1062190014yescomplemented
538C2×C8—22no—
539C2×C8—868no—
540C2×C8—862no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—432no—
545C4⋊C4—432no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4—862no—
549C4⋊C4—862no—
550C4⋊C4—864no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—862no—
558C22⋊C4—862no—
559C22⋊C4—868no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—862no—
565C42—24no—
566C42—431no—
567C42—431no—
568C42—431no—
569C42—431no—
570C42—431no—
571C42—431no—
572C42—431no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—862no—
579C42—862no—
580C42—868no—
581C42—862no—
582C42—864no—
583C42—1724no—
584C42C2×C4×D4311yescharacteristic
585C42C2×C4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C42D4×D4311yescharacteristic
588C23—22no—
589C23—431no—
590C23—431no—
591C23—862no—
592C23—861no—
593C23—861no—
594C23—1721no—
595C23C2×D4×D4311yescharacteristic
596Q8—24no—
597Q8—1722no—
598Q8—1722no—
599D4—24no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604D4—1724no—
605D4—1724no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—44no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—434no—
616C2×C4—431no—
617C2×C4—431no—
618C2×C4—431no—
619C2×C4—431no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—864no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1724no—
639C2×C4—1724no—
640C2×C4—1722no—
641C2×C4—1722no—
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22⋊C4×D4311yescharacteristic
645C2×C4C22⋊C4×D4311yescharacteristic
646C2×C4C22×C4×D4311yescharacteristic
647C2×C4C2×D4×D4311yescharacteristic
648C2×C4#41×D4312yes—
649C2×C4C2×#1062190012yes—
650C8—24no—
651C8—864no—
652C22—21no—
653C22—21no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—432no—
658C22—861no—
659C22—861no—
660C22—861no—
661C22—861no—
662C22—861no—
663C22—1722no—
664C22—1722no—
665C22C2×C22⋊C4×D4311yescharacteristic
666C22#1458344711yescharacteristic
667C22#1458344811yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—44no—
672C4—42no—
673C4—432no—
674C4—432no—
675C4—861no—
676C4—861no—
677C4—861no—
678C4—861no—
679C4—1724no—
680C4—1722no—
681C4—1722no—
682C4#104×D4312yes—
683C4C4×#1062190012yes—
684C4#1458340912yes—
685C2—21no—
686C2—21no—
687C2—82no—
688C2—862no—
689C2—1721no—
690C2#1913708211yescharacteristic
691C2C2×#104×D4311yescharacteristic
692C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1980C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1980D43
hypocenterC43#21382
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. C4×M16×D43C2semidirect
3. C4×#13063283C2semidirect
4. #19135539C2semidirect
5. #19135538C2semidirect
6. #19135515C2semidirect
7. #19134894C2semidirect
8. #104×Dic43C2semidirect
9. C43×#1980C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
14. #14583447C4semidirect
15. #14583447C4semidirect
20. #14583428C4semidirect
21. #14583428C4semidirect
187. M16×C43#41semidirect
237. #10621877#41semidirect
300. C4×D43#104semidirect
345. #1980D43semidirect
395. C43#21382semidirect
537. M16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478902
C4×M16×D432
C4×#130632832
#191355392
#191355382
#191355152
#191348942
#104×Dic432
C43×#19802
#2138243