Finite Group Databasebeta

← #25165133

Subgroups — #25165133

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139125C211yesmaximal, characteristic, complemented
2#19137660C211yesmaximal, characteristic
3#19136001C211yesmaximal, characteristic, complemented
4#19135965C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic
6#19135280C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135181C211yesmaximal, characteristic, complemented
9#19135177C211yesmaximal, characteristic, complemented
10#19135153C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134858C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2041C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582832—21no—
28#14582831—21no—
29#14582802—21no—
30#14582802C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795—21no—
36#14582782—21no—
37#14582779—21no—
38#14582779—21no—
39#14582768C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#127×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—41no—
66D4×Dic43—41no—
67D4×Dic43—44no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063257—22no—
90#13063256—22no—
91Dic43⋊C8—41no—
92#13063246—22no—
93#13063246—22no—
94#13063246—41no—
95#13063246—41no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43—21no—
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110#127×C43—22no—
111#127×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43C2311yescharacteristic
116#102×C43—22no—
117#102×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120#95×C43—21no—
121C24×C43—21no—
122C24×C43—21no—
123C2×D4×C43—24no—
124C2×D4×C43—24no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—42no—
136C2×D4×C43—42no—
137C2×D4×C43—81no—
138C2×D4×C43—81no—
139C2×D4×C43#4112yes—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—42no—
154C22×Dic43—81no—
155C22×Dic43—81no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—81no—
170C4⋊C4×C43#4112yes—
171C42×C43—21no—
172C42×C43—21no—
173C22⋊Dic43—42no—
174C22⋊Dic43—42no—
175C22⋊Dic43—42no—
176C22⋊Dic43—42no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43—42no—
188C4⋊Dic43—81no—
189C4⋊Dic43SD1614yes—
190C4⋊Dic43#4112yes—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221D4×C43—22no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—48no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—84no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43C2×SD1612yes—
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—21no—
250C2×Dic43—21no—
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—41no—
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—
270C2×Dic43—41no—
271C2×Dic43—84no—
272C2×Dic43—84no—
273C2×Dic43C2×SD1612yes—
274C2×Dic43C2×SD1612yes—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#26754—431nomaximal, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43#52511yescharacteristic
295C22×C43#54611yescharacteristic
296C22×C43#54811yescharacteristic
297C22×C43C22×SD1611yescharacteristic
298C22×C43#57511yescharacteristic
299C22×C43#57611yescharacteristic
300C22×C43#57611yescharacteristic
301C4×C43—22no—
302C4×C43—42no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43#52911yescharacteristic
306C4×C43#53911yescharacteristic
307C4×C43#55211yescharacteristic
308C4×C43#55311yescharacteristic
309Dic43—22no—
310Dic43—22no—
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317#2507—431no—
318#2366—431no—
319#2071—431no—
320#2065—431no—
321#2041—431no—
322#2041D4311yescharacteristic
323#1934—431no—
324#1926—431no—
325#1920—431no—
326#1920—431no—
327#1916—431no—
328#1864—431no—
329#1864—431no—
330#1802—431no—
331C4×#102—431no—
332C2×C43—82no—
333C2×C43—82no—
334C2×C43#246011yescharacteristic
335C2×C43#310111yescharacteristic
336C2×C43#312211yescharacteristic
337C2×C43#329511yescharacteristic
338C2×C43#330911yescharacteristic
339C2×C43#336211yescharacteristic
340C2×C43#337011yescharacteristic
341C2×#127C2×D4311yescharacteristic
342C2×C4×D4—431no—
343C2×C4×D4—431no—
344C2×C4×D4—861no—
345C2×#106—431no—
346C2×#106—431no—
347C2×C4⋊C8—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#102C2×D4311yescharacteristic
353C2×#102C2×D4311yescharacteristic
354C2×#102C2×D4311yescharacteristic
355C2×#102C2×D4311yescharacteristic
356C2×C4×C8—431no—
357#398—861no—
358#398—861no—
359#390—431no—
360#390—431no—
361#390—861no—
362#389—431no—
363#389—431no—
364#389—431no—
365#389—861no—
366#389C2×D4311yescharacteristic
367#387—861no—
368#386—861no—
369#386—861no—
370#384—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—431no—
373C4×C4⋊C4—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#336—431no—
381#336—431no—
382#336—431no—
383#336C2×D4311yescharacteristic
384C43#2675411yescharacteristic, complemented, Sylow
385C22×D4—21no—
386C22×D4—21no—
387C22×D4C22×D4311yescharacteristic
388C22×D4C22×D4311yescharacteristic
389C23×C4—861no—
390C23×C4—861no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395#127—22no—
396#127—22no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—1721no—
400C4×D4—1721no—
401C4×D4—1724no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42C22×D4311yescharacteristic
427#106—862no—
428#106—862no—
429C4⋊C8—1721no—
430#102—22no—
431#102—22no—
432#102—22no—
433#102—22no—
434#102—862no—
435#102—862no—
436#102—1721no—
437#102—1721no—
438C4×C8—1721no—
439#95—21no—
440#95—431no—
441#95—431no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24—21no—
448C24—21no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4#1062190012yes—
466C2×D4#1062190012yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4D4×D4311yescharacteristic
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—81no—
502C4⋊C4—434no—
503C4⋊C4—432no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—3441no—
512C4⋊C4—3441no—
513C4⋊C4—3441no—
514C4⋊C4—3441no—
515C4⋊C4—1721no—
516C4⋊C4—1722no—
517C4⋊C4#1062190012yes—
518C22⋊C4—3441no—
519C22⋊C4—3441no—
520C22⋊C4—1722no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C42—21no—
525C42—21no—
526C42—861no—
527C42—861no—
528C42—861no—
529C42—861no—
530C42—3441no—
531C42—1722no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C2×D4×D4311yescharacteristic
547D4—22no—
548D4—22no—
549D4—22no—
550D4—22no—
551D4—48no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—862no—
581C2×C4—3444no—
582C2×C4—3444no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
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×C4SD16×D4312yes—
595C2×C4#41×D4311yescharacteristic
596C2×C4C2×#1062190011yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4C2×#1062190011yescharacteristic
599C2×C4#1306337111yescharacteristic
600C2×C4#1306337211yescharacteristic
601C8—41no—
602C8—41no—
603C8—1721no—
604C8—1721no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#1458340511yescharacteristic
620C22#1458354211yescharacteristic
621C22#1458355511yescharacteristic
622C22C2×SD16×D4311yescharacteristic
623C22#1458369511yescharacteristic
624C22#1458370011yescharacteristic
625C22#1458370311yescharacteristic
626C4—22no—
627C4—42no—
628C4—41no—
629C4—81no—
630C4—862no—
631C4—862no—
632C4—3441no—
633C4—3441no—
634C4—3441no—
635C4—1721no—
636C4—1721no—
637C4—1722no—
638C4#1458343011yescharacteristic
639C4#1458349311yescharacteristic
640C4#1458358611yescharacteristic
641C4#1458360111yescharacteristic
642C2—82no—
643C2—82no—
644C2#1913854211yescharacteristic
645C2#1914459811yescharacteristic
646C2#1914483211yescharacteristic
647C2#1914641811yescharacteristic
648C2#1914660011yescharacteristic
649C2#1914726111yescharacteristic
650C2#1914734111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2041C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#2041D43
hypocenterC43#26754
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
1. #19139125C2semidirect
3. #19136001C2semidirect
4. #19135965C2semidirect
6. #19135280C2semidirect
7. #19135225C2semidirect
8. #19135181C2semidirect
9. #19135177C2semidirect
10. #19135153C2semidirect
11. #19134858C2semidirect
12. #19134858C2semidirect
13. #19134593C2semidirect
14. #102×Dic43C2semidirect
384. C43#26754semidirect

Maximal subgroups

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

subgroupindex
#191391252
#191376602
#191360012
#191359652
#191358262
#191352802
#191352252
#191351812
#191351772
#191351532
#191348582
#191345932
#102×Dic432
C43×#20412
#2675443