Finite Group Databasebeta

← #25146302

Subgroups — #25146302

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583028C211yesmaximal, characteristic, complemented
2#19139949C211yesmaximal, characteristic
3#19139811C211yesmaximal, characteristic, complemented
4#19135988C211yesmaximal, characteristic, complemented
5#19135974C211yesmaximal, characteristic, complemented
6#19135908C211yesmaximal, characteristic
7#19135908C211yesmaximal, characteristic
8#19135478C211yesmaximal, characteristic
9#19135451C211yesmaximal, characteristic
10#19135416C211yesmaximal, characteristic, complemented
11#19135365C211yesmaximal, characteristic, complemented
12#19135282C211yesmaximal, characteristic, complemented
13#19135268C211yesmaximal, characteristic, complemented
14#19134420C211yesmaximal, characteristic
15C2×C43×#461C211yesmaximal, characteristic
16C2×C4×Dic86C2211yescharacteristic
17#14583028—24no—
18C2×#13063259C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582837—21no—
32#14582837—21no—
33#14582835—21no—
34#14582811—21no—
35#14582806C2211yescharacteristic
36#14582806C2211yescharacteristic
37#14582806C2211yescharacteristic
38#14582806C2211yescharacteristic
39#14582804—21no—
40#14582802C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582772—21no—
45#14582772—21no—
46#14582765C2211yescharacteristic
47#14582764—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×SD16×C43C2211yescharacteristic
55C2×C4⋊Q8×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#461—24no—
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C22×Dic86D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C4×Dic86—22no—
65C4×Dic86—22no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4D411yescharacteristic
74C2×Dic43⋊C4D411yescharacteristic
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063259—41no—
83#13063257—41no—
84Dic43⋊C8—22no—
85Dic43⋊C8—22no—
86#13063249—22no—
87#13063249—22no—
88#13063249—41no—
89#13063249—41no—
90#13063246—22no—
91#13063246—22no—
92#13063236—22no—
93#13063235—22no—
94C8×Dic43—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
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⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43—22no—
115C2×SD16×C43—22no—
116C2×SD16×C43—41no—
117C2×SD16×C43—41no—
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C4⋊Q8×C43—22no—
121C4⋊Q8×C43—22no—
122C4×D4×C43—22no—
123C4×D4×C43—22no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43D414yes—
130#103×C43—22no—
131#103×C43—22no—
132C24×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—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43#4112yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—42no—
155C22×C4×C43—81no—
156C22×C4×C43—81no—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×Dic86—22no—
169C2×Dic86—22no—
170C2×Dic86—41no—
171SD16×C43—44no—
172SD16×C43—44no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D412yes—
178C2×C8×C43C2×D412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C22⋊C4×C43—42no—
184C42×C43C2×D412yes—
185C42×C43#4112yes—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189C22⋊Dic43—81no—
190C4⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—81no—
202Dic43⋊C4—81no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—21no—
207C4×Dic43—42no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8#4112yes—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—41no—
233D4×C43—41no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
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×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—84no—
248C2×C4×C43#12112yes—
249C2×C4×C43#12112yes—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43#13712yes—
280Dic86—44no—
281C8×C43—22no—
282C8×C43—22no—
283C43⋊C8—22no—
284C43⋊C8—41no—
285#25308—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×#12111yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43#55011yescharacteristic
296C22×C43C2×#13711yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43#52911yescharacteristic
306C4×C43#54211yescharacteristic
307C4×C43#54611yescharacteristic
308C4×C43#54811yescharacteristic
309Dic43—22no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43—81no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317C2×#461D4311yescharacteristic
318C2×#446—431no—
319#2580—431no—
320#2568—431no—
321#2068—431no—
322#2066—431no—
323#2055—431no—
324#2055—431no—
325#1973—431no—
326#1968—431no—
327#1960—431no—
328#1949—431no—
329#1935—431no—
330#1933—431no—
331#1762—431no—
332C2×C43—82no—
333C2×C43#242611yescharacteristic
334C2×C43#305611yescharacteristic
335C2×C43#305711yescharacteristic
336C2×C43#337211yescharacteristic
337C2×C43#337611yescharacteristic
338C2×C43#340011yescharacteristic
339C2×C43#340111yescharacteristic
340C22×SD16C2×D4311yescharacteristic
341C22×SD16C2×D4311yescharacteristic
342C2×C4⋊Q8C2×D4311yescharacteristic
343C2×C4×Q8—431no—
344C2×C4×D4C2×D4311yescharacteristic
345#461—24no—
346#446—864no—
347C2×#107—431no—
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×C4⋊C8C2×D4311yescharacteristic
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103C2×D4311yescharacteristic
357C2×#103C2×D4311yescharacteristic
358C2×#102—431no—
359C2×#102—431no—
360C2×#97—431no—
361C2×#97—431no—
362C2×C4×C8—431no—
363#400—861no—
364#400—861no—
365#399—861no—
366#393—861no—
367#391—431no—
368#391—431no—
369#391—431no—
370#391—431no—
371#391—861no—
372#390—431no—
373#390—431no—
374#389—431no—
375#389—431no—
376#385—861no—
377#385—861no—
378#382—431no—
379#382—861no—
380C4×C4⋊C4—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385C43#2530811yescharacteristic, complemented, Sylow
386C22×Q8—431no—
387C22×Q8C22×D4311yescharacteristic
388C22×Q8C22×D4311yescharacteristic
389C22×D4C22×D4311yescharacteristic
390C23×C4—21no—
391C2×SD16—22no—
392C2×SD16—22no—
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16—41no—
396C2×SD16—41no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C4⋊Q8—22no—
402C4⋊Q8—22no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×D4—22no—
406C4×D4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#107—1721no—
429#106—1721no—
430C4⋊C8—862no—
431C4⋊C8—862no—
432C4⋊C8C22⋊D4314yes—
433#103—22no—
434#103—22no—
435#103—862no—
436#103—862no—
437#103—1721no—
438#103—1721no—
439#102—862no—
440#102—862no—
441#97—862no—
442#97—862no—
443C4×C8—862no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8—1721no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4#1062190012yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496SD16—44no—
497SD16—44no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—432no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8C2×C22⋊D4312yes—
509C2×C8C2×C22⋊D4312yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—3441no—
527C22⋊C4—42no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1722no—
537C42#1062190012yes—
538C42C2×C22⋊D4312yes—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C2×D4×D4311yescharacteristic
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—1724no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
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—84no—
574C2×C4—432no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4#1306329612yes—
599C2×C4#1306329612yes—
600C2×C4C22×C22⋊D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4C2×#1062190011yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4#1306337011yescharacteristic
605C2×C4#1306337211yescharacteristic
606C8—22no—
607C8—22no—
608C8—862no—
609C8—1721no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22C2×#1306329611yescharacteristic
618C22#1458355511yescharacteristic
619C22#1458356711yescharacteristic
620C22#137×D4311yescharacteristic
621C22#1458369811yescharacteristic
622C22#1458370511yescharacteristic
623C22#1458370511yescharacteristic
624C4—22no—
625C4—22no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—862no—
630C4—3441no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—1721no—
635C4—1721no—
636C4—1721no—
637C4#1458343011yescharacteristic
638C4#1458351611yescharacteristic
639C4#1458354311yescharacteristic
640C4#1458355611yescharacteristic
641C2—82no—
642C2#1913815711yescharacteristic
643C2#1914421911yescharacteristic
644C2#1914423011yescharacteristic
645C2#1914737111yescharacteristic
646C2#1914741511yescharacteristic
647C2#1914764311yescharacteristic
648C2#1914766811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#461C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#461D43
hypocenterC43#25308
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#14583028C2semidirect
3. #19139811C2semidirect
4. #19135988C2semidirect
5. #19135974C2semidirect
10. #19135416C2semidirect
11. #19135365C2semidirect
12. #19135282C2semidirect
13. #19135268C2semidirect
385. C43#25308semidirect

Maximal subgroups

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

subgroupindex
C2×#145830282
#191399492
#191398112
#191359882
#191359742
#191359082
#191354782
#191354512
#191354162
#191353652
#191352822
#191352682
#191344202
C2×C43×#4612
#2530843