Finite Group Databasebeta

← #25137922

Subgroups — #25137922

Order 11008.

828 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583193C211yesmaximal, characteristic, complemented
2C2×#14582954C211yesmaximal, characteristic
3#19142946C211yesmaximal, characteristic
4#19137125C211yesmaximal, characteristic
5#19136022C211yesmaximal, characteristic
6#19136019C211yesmaximal, characteristic
7#19135794C211yesmaximal, characteristic
8#19135793C211yesmaximal, characteristic
9#19135541C211yesmaximal, characteristic, complemented
10#19135355C211yesmaximal, characteristic, complemented
11#19135335C211yesmaximal, characteristic, complemented
12#19135285C211yesmaximal, characteristic, complemented
13#19135284C211yesmaximal, characteristic, complemented
14#19134599C211yesmaximal, characteristic, complemented
15C43×#1944C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063305C2211yescharacteristic
18C2×#13063303—21no—
19C2×#13063290C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21#14583193—24no—
22#14582954—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×#13063236C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582803—21no—
36#14582797C2211yescharacteristic
37#14582794—21no—
38#14582782—21no—
39#14582770—21no—
40#14582768C2211yescharacteristic
41#14582758—21no—
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47#14582746—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—22no—
70#13063305—22no—
71#13063305—22no—
72#13063303—44no—
73#13063290—22no—
74#13063290—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C42×D43—22no—
94C42×D43—22no—
95#13063258—22no—
96#13063256—22no—
97Dic43⋊C8—22no—
98Dic43⋊C8D414yes—
99#13063250—22no—
100#13063250—22no—
101#13063248—22no—
102#13063248—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105#13063236—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#106×C43—22no—
124#97×C43—22no—
125#95×C43—21no—
126#95×C43—21no—
127C23×D43C2×D411yescharacteristic
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×C4×D43—21no—
143C2×C4×D43—21no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—42no—
160C2×Dic86—42no—
161C2×Dic86—42no—
162C2×Dic86#4112yes—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D412yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43#4112yes—
179C42×C43—21no—
180C42×C43—21no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—42no—
200C4×Dic43—42no—
201C4×Dic43C2×D412yes—
202C4×Dic43#4112yes—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C2×D412yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213C22×D43—21no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43AGL(1,ℤ/8)12yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43#12112yes—
259C2×Dic43#12112yes—
260C2×Dic43#13712yes—
261C2×Dic43#13712yes—
262C4×D43—44no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—44no—
268Dic86—22no—
269Dic86—22no—
270Dic86—41no—
271Dic86—41no—
272Dic86—84no—
273C8×C43—22no—
274C8×C43—41no—
275C43⋊C8—22no—
276C43⋊C8—41no—
277#24711—431nomaximal, Sylow
278C22×C43C2×#12111yescharacteristic
279C22×C43#52511yescharacteristic
280C22×C43#53611yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43C2×#13711yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57511yescharacteristic
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43#54711yescharacteristic
299C4×C43#54811yescharacteristic
300C4×C43#55211yescharacteristic
301C4×C43#55611yescharacteristic
302Dic43—22no—
303Dic43—42no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308Dic43#47014yes—
309C2×#477—431no—
310C2×#432—431no—
311#2857—431no—
312C4×C22⋊Q8—431no—
313#2075—431no—
314#2075—431no—
315#2035—431no—
316#2035—431no—
317#1987—431no—
318#1948—431no—
319#1944—431no—
320#1944D4311yescharacteristic, complemented
321#1935—431no—
322#1935—431no—
323#1803—431no—
324C2×C43#241511yescharacteristic
325C2×C43C2×#47011yescharacteristic
326C2×C43#305511yescharacteristic
327C2×C43#311211yescharacteristic
328C2×C43#311611yescharacteristic
329C2×C43#323711yescharacteristic
330C2×C43#323811yescharacteristic
331D43—42no—
332C2×C4⋊Q8—431no—
333C2×C22⋊Q8—431no—
334C2×C22⋊Q8—861no—
335C2×C4×Q8—431no—
336C22×C42—431no—
337#477—864no—
338#432—864no—
339C2×#107—431no—
340C2×#107C2×D4311yescharacteristic
341C2×#106—431no—
342C2×#106C2×D4311yescharacteristic
343C2×C4⋊C8—431no—
344C2×C4⋊C8—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×C22⋊C8—431no—
350C2×C22⋊C8—431no—
351C2×#97—431no—
352C2×#97C2×D4311yescharacteristic
353#391—431no—
354#391—861no—
355#389—431no—
356#389—861no—
357#389C2×D4311yescharacteristic
358#389C2×D4311yescharacteristic
359#387—861no—
360#385—861no—
361#384—431no—
362#380—431no—
363#380—431no—
364#380—431no—
365#380—861no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—861no—
368C4×C22⋊C4—861no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340C2×D4311yescharacteristic
376#340C2×D4311yescharacteristic
377C43#2471111yescharacteristic, complemented, Sylow
378C22×Q8—431no—
379C22×Q8—861no—
380C23×C4—431no—
381C23×C4—431no—
382C23×C4—431no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387C4⋊Q8—862no—
388C4⋊Q8—862no—
389C22⋊Q8—862no—
390C22⋊Q8—862no—
391C22⋊Q8—1724no—
392C4×Q8—862no—
393C4×Q8—862no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C42—431no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—862no—
417C2×C42—862no—
418C2×C42—861no—
419C2×C42—861no—
420C2×C42C22×D4311yescharacteristic
421#107—22no—
422#107—862no—
423#106—22no—
424#106—862no—
425C4⋊C8—434no—
426C4⋊C8—862no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—862no—
431C22⋊C8—862no—
432C22⋊C8—862no—
433#97—22no—
434#97—862no—
435#95—21no—
436#95—21no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444C24—431no—
445C2×Q8—432no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—1722no—
452C2×Q8—1722no—
453C2×Q8—1722no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—1721no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—432no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8D4×D4312yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—864no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C4⋊C4—1722no—
512C4⋊C4—1722no—
513C4⋊C4#1062189812yes—
514C22⋊C4—864no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C42—21no—
519C42—21no—
520C42—432no—
521C42—432no—
522C42—862no—
523C42—862no—
524C42—1722no—
525C42—1722no—
526C23—432no—
527C23—861no—
528C23—861no—
529C23—861no—
530C23—861no—
531C23—861no—
532C23—861no—
533C23C2×D4×D4311yescharacteristic
534Q8—862no—
535Q8—862no—
536Q8—3444no—
537Q8—1721no—
538Q8—1721no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—862no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—1724no—
568C2×C4—1724no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
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×C4—1721no—
584C2×C4C2×D4×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062189811yescharacteristic
588C2×C4#1306337311yescharacteristic
589C2×C4#1306337311yescharacteristic
590C8—22no—
591C8—41no—
592C8—862no—
593C8—1721no—
594C22—862no—
595C22—862no—
596C22—862no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22#121×D4311yescharacteristic
602C22#1458340811yescharacteristic
603C22#1458347411yescharacteristic
604C22AGL(1,ℤ/8)×D4311yescharacteristic
605C22#137×D4311yescharacteristic
606C22#137×D4311yescharacteristic
607C22#1458369511yescharacteristic
608C4—41no—
609C4—41no—
610C4—42no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—434no—
615C4—862no—
616C4—3441no—
617C4—3441no—
618C4—3441no—
619C4—1721no—
620C4—1722no—
621C4#1458355011yescharacteristic
622C4#1458355911yescharacteristic
623C4#1458358111yescharacteristic
624C4#1458362111yescharacteristic
625C2—1722no—
626C2#1913802311yescharacteristic
627C2#470×D4311yescharacteristic
628C2#1914421311yescharacteristic
629C2#1914471511yescharacteristic
630C2#1914475311yescharacteristic
631C2#1914581011yescharacteristic
632C2#1914581711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1944D43
hypocenterC43#24711
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
1. C2×#14583193C2semidirect
9. #19135541C2semidirect
10. #19135355C2semidirect
11. #19135335C2semidirect
12. #19135285C2semidirect
13. #19135284C2semidirect
14. #19134599C2semidirect
15. C43×#1944C2semidirect
320. #1944D43semidirect
377. C43#24711semidirect

Maximal subgroups

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

subgroupindex
C2×#145831932
C2×#145829542
#191429462
#191371252
#191360222
#191360192
#191357942
#191357932
#191355412
#191353552
#191353352
#191352852
#191352842
#191345992
C43×#19442
#2471143