Finite Group Databasebeta

← #25104604

Subgroups — #25104604

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583244C211yesmaximal, characteristic
2#19137339C211yesmaximal, characteristic, complemented
3#19137317C211yesmaximal, characteristic
4#19135566C211yesmaximal, characteristic, complemented
5#19135417C211yesmaximal, characteristic
6#19135294C211yesmaximal, characteristic, complemented
7#19135290C211yesmaximal, characteristic, complemented
8#19135279C211yesmaximal, characteristic, complemented
9#19135275C211yesmaximal, characteristic, complemented
10#19134724C211yesmaximal, characteristic, complemented
11#19134421C211yesmaximal, characteristic, complemented
12C4×#13063245C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134283C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583244C418yescomplemented
20C2×#13063247C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582805—21no—
32#14582803—21no—
33#14582802C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582786—21no—
38#14582783—21no—
39#14582778—21no—
40#14582778—21no—
41#14582775—21no—
42#14582775—21no—
43#14582764C2211yescharacteristic
44#14582764C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582745C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063324—22no—
68#13063324C2×C414yescomplemented
69#13063321—22no—
70#13063321C2×C414yes—
71C4×D172—22no—
72C4×D172—22no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063247—22no—
88#13063247C2×C414yescomplemented
89#13063246—22no—
90#13063246C2×C414yescomplemented
91#13063245—22no—
92#13063245C2×C414yescomplemented
93#13063235—22no—
94#13063235—22no—
95C4×C43⋊C8—22no—
96C8×Dic43—22no—
97C8×Dic43C2×C414yescomplemented
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C43⋊#95D411yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yescomplemented
123#97×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C23×D43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—24no—
143C2×C22⋊D43—24no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C2×C22⋊D43—81no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C22×C412yes—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×Dic86—24no—
165C2×Dic86—81no—
166C2×Dic86—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C22×C412yes—
172C2×C8×C43#4112yes—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C412yes—
179C22⋊C4×C43—42no—
180C42×C43—81no—
181C42×C43#4112yes—
182C42×C43#4112yes—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—81no—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—81no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C4×Dic43C22×C412yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C412yes—
207C2×C43⋊C8#4112yes—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—84no—
241C2×C4×C43#12412yes—
242C2×C4×C43#12412yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C22⋊D43—84no—
250C22⋊D43—84no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43C4×D412yes—
271C2×Dic43C4×D412yes—
272D172—22no—
273D172—22no—
274D172—41no—
275D172—41no—
276C4×D43—84no—
277Dic86—84no—
278C8×C43—22no—
279C8×C43—22no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282#21644—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43C2×#12411yescharacteristic
292C22×C43#53211yescharacteristic
293C22×C43#57611yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57711yescharacteristic
296C22×C43#57711yescharacteristic
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—22no—
305C4×C43—22no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C4×#4111yescharacteristic
310C4×C43C4×#4111yescharacteristic
311C4×C43#52911yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—41no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#486—431no—
321#2331—431no—
322#2328—431no—
323#1993—431no—
324#1961—431no—
325#1936—431no—
326#1936—431no—
327#1934—431no—
328#1934—431no—
329#1835—431no—
330#1762—431no—
331#1762D4311yescharacteristic, complemented
332C4×#102—431no—
333C4×#102—431no—
334#1726—431no—
335C2×C43—82no—
336C2×C43C4×#12411yescharacteristic
337C2×C43#294811yescharacteristic
338C2×C43#294911yescharacteristic
339C2×C43#313611yescharacteristic
340C2×C43#313611yescharacteristic
341C2×C43#317911yescharacteristic
342C2×C43#317911yescharacteristic
343D43—82no—
344C2×C4⋊Q8—431no—
345C2×#127—431no—
346C2×C4×D4—431no—
347C2×C4×D4C2×D4311yescharacteristic
348#486—438no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102C2×D4311yescharacteristic
356C2×#102C2×D4311yescharacteristic
357C2×#97—431no—
358C2×#97—431no—
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8—431no—
361C2×C4×C8—431no—
362C2×C4×C8—431no—
363#391—861no—
364#391—861no—
365#390—431no—
366#390—431no—
367#389—431no—
368#389—431no—
369#387—861no—
370#387—861no—
371#386—861no—
372#386—861no—
373#386—861no—
374#386—861no—
375#382—431no—
376#382—431no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4C2×D4311yescharacteristic
379#376—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388C43#2164411yescharacteristic, complemented, Sylow
389C22×Q8—861no—
390C22×D4—431no—
391C22×D4—861no—
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—861no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C4⋊Q8—434no—
401C4⋊Q8—862no—
402#127—434no—
403#127—862no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—862no—
407C4×D4—862no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C42—21no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#102—22no—
429#102—434no—
430#102—434no—
431#102—434no—
432#102—862no—
433#102—862no—
434#102—862no—
435#102C4×D4314yescomplemented
436#97—22no—
437#97—862no—
438#97—862no—
439C4×C8—434no—
440C4×C8—862no—
441C4×C8—862no—
442#95—21no—
443#95—431no—
444#95—431no—
445#95—431no—
446#95—431no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—861no—
456C2×Q8—864no—
457C2×Q8—3441no—
458C2×Q8—3441no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—432no—
465C2×D4—864no—
466C2×D4—864no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4—3441no—
475C2×D4—3441no—
476C2×D4C2×C4×D4312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—3441no—
491C22×C4—3441no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—432no—
501C2×C8—432no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8C2×C4×D4312yes—
507C2×C8#1062189812yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—864no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4C2×C4×D4312yes—
523C22⋊C4—42no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—1722no—
529C42—81no—
530C42—432no—
531C42—432no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C42#1062189812yes—
536C42#1062190012yes—
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—862no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23C2×D4×D4311yescharacteristic
552Q8—3444no—
553D4—22no—
554D4—22no—
555D4—41no—
556D4—41no—
557D4—862no—
558D4—862no—
559D4—3444no—
560D4—3444no—
561D4—1721no—
562D4—1721no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—3444no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4#1306331112yes—
600C2×C4#1306331112yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4C2×#1062190011yescharacteristic
605C2×C4C2×#1062189811yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C8—22no—
608C8—22no—
609C8—862no—
610C8—862no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C4×D4×D4311yescharacteristic
626C22C2×#1306331111yescharacteristic
627C22#1458344611yescharacteristic
628C22#1458370311yescharacteristic
629C22#1458370311yescharacteristic
630C22#1458370811yescharacteristic
631C22#1458370911yescharacteristic
632C4—22no—
633C4—22no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—3441no—
640C4—3441no—
641C4—1722no—
642C4—1721no—
643C4—1721no—
644C4C4×#1062190011yescharacteristic
645C4C4×#1062189811yescharacteristic
646C4#1458342711yescharacteristic
647C4#1458342911yescharacteristic
648C2—82no—
649C2—3442no—
650C2C4×#1306331111yescharacteristic
651C2#1914344411yescharacteristic
652C2#1914345111yescharacteristic
653C2#1914494511yescharacteristic
654C2#1914495211yescharacteristic
655C2#1914527611yescharacteristic
656C2#1914528411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#21644
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #19137339C2semidirect
4. #19135566C2semidirect
6. #19135294C2semidirect
7. #19135290C2semidirect
8. #19135279C2semidirect
9. #19135275C2semidirect
10. #19134724C2semidirect
11. #19134421C2semidirect
12. C4×#13063245C2semidirect
13. C4×#13063246C2semidirect
14. #19134283C2semidirect
15. C43×#1762C2semidirect
19. #14583244C4semidirect
68. #13063324C2×C4semidirect
88. #13063247C2×C4semidirect
90. #13063246C2×C4semidirect
92. #13063245C2×C4semidirect
97. C8×Dic43C2×C4semidirect
122. #102×C43C2×C4semidirect
331. #1762D43semidirect
388. C43#21644semidirect
435. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832442
#191373392
#191373172
#191355662
#191354172
#191352942
#191352902
#191352792
#191352752
#191347242
#191344212
C4×#130632452
C4×#130632462
#191342832
C43×#17622
#2164443