Finite Group Databasebeta

← #25199478

Subgroups — #25199478

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137123C211yesmaximal, characteristic
2#19137123C211yesmaximal, characteristic
3#19135798C211yesmaximal, characteristic
4#19135791C211yesmaximal, characteristic
5#19135605C211yesmaximal, characteristic
6#19135234C211yesmaximal, characteristic, complemented
7#19135227C211yesmaximal, characteristic, complemented
8#19135171C211yesmaximal, characteristic, complemented
9#19135164C211yesmaximal, characteristic, complemented
10#19134937C211yesmaximal, characteristic, complemented
11#19134937C211yesmaximal, characteristic, complemented
12#19134860C211yesmaximal, characteristic, complemented
13#19134860C211yesmaximal, characteristic, complemented
14#19134661C211yesmaximal, characteristic
15C43×#2077C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582804C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582781—21no—
36#14582781—21no—
37#14582771—21no—
38#14582771—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41#14582750—21no—
42#14582750—21no—
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#380C2211yescharacteristic
55C43×#380C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C2×Dic172—22no—
64C2×Dic172—22no—
65C2×Dic172—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063304—22no—
69#13063304—22no—
70#13063304—22no—
71#13063304—22no—
72#13063290—41no—
73#13063290—41no—
74#13063290—41no—
75#13063290—41no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—41no—
91C2×C4×Dic43—41no—
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063256—22no—
98#13063250—22no—
99#13063250—22no—
100#13063248—22no—
101#13063248—22no—
102#13063248—41no—
103#13063248—41no—
104C22⋊(C43⋊C8)—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C23×C4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122#106×C43—41no—
123C22⋊C8×C43—41no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—41no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86#4112yes—
164C2×Dic86#4112yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×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—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—42no—
181C22⋊Dic43—24no—
182C22⋊Dic43—24no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43#4112yes—
186C4⋊Dic43#4112yes—
187Dic43⋊C4—24no—
188Dic43⋊C4—24no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43—41no—
199C4×Dic43—42no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209Dic172—44no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43#13712yes—
217C23×C43C22×D411yescharacteristic
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
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×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43H(5,𝔽2)11yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—44no—
258C2×Dic43—44no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43#13512yes—
268C2×Dic43#13712yes—
269Dic86—22no—
270Dic86—22no—
271Dic86—22no—
272Dic86—22no—
273Dic86—41no—
274Dic86—41no—
275Dic86—41no—
276Dic86—41no—
277C8×C43—41no—
278C8×C43—41no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#29417—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43#52511yescharacteristic
290C22×C43#52511yescharacteristic
291C22×C43#53411yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43C2×#13711yescharacteristic
295C22×C43#57511yescharacteristic
296C4×C43—41no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43#55111yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55311yescharacteristic
304C4×C43#55911yescharacteristic
305Dic43—22no—
306Dic43—22no—
307Dic43—42no—
308Dic43—42no—
309Dic43—42no—
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313C4×C22⋊Q8—431no—
314C4×C22⋊Q8—431no—
315#2077D4311yescharacteristic
316#2036—431no—
317#2035—431no—
318#2001—431no—
319#1928—431no—
320#1927—431no—
321#1919—431no—
322#1918—431no—
323#1878—431no—
324#1878—431no—
325#1865—431no—
326#1865—431no—
327#1817—431no—
328C2×C43—42no—
329C2×C43#260011yescharacteristic
330C2×C43#310211yescharacteristic
331C2×C43#310711yescharacteristic
332C2×C43#311311yescharacteristic
333C2×C43#311711yescharacteristic
334C2×C43#319011yescharacteristic
335C2×C43#319611yescharacteristic
336C22×Q16—431no—
337C2×C22⋊Q8—431no—
338C2×C22⋊Q8—431no—
339C2×C4×Q8—431no—
340C2×C4×Q8—431no—
341C22×C42—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106C2×D4311yescharacteristic
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#103—431no—
350C2×#103—431no—
351C2×C22⋊C8—431no—
352C2×C22⋊C8C2×D4311yescharacteristic
353#391—431no—
354#391—431no—
355#389—431no—
356#389—431no—
357#387—861no—
358#387—861no—
359#385—861no—
360#385—861no—
361#380C2×D4311yescharacteristic
362#380C2×D4311yescharacteristic
363C4×C4⋊C4—431no—
364C4×C4⋊C4—431no—
365C4×C4⋊C4—861no—
366C4×C4⋊C4—861no—
367C4×C22⋊C4—861no—
368C4×C22⋊C4—861no—
369#340—431no—
370#340—431no—
371#340—431no—
372#340C2×D4311yescharacteristic
373#340C2×D4311yescharacteristic
374#340C2×D4311yescharacteristic
375#336—431no—
376#336—431no—
377#336—431no—
378#336—431no—
379C43#2941711yescharacteristic, complemented, Sylow
380C22×Q8—431no—
381C22×Q8—431no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4C22×D4311yescharacteristic
385C2×Q16—862no—
386C2×Q16—862no—
387C2×Q16—1721no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396C4×Q8—1721no—
397C4×Q8—1721no—
398C4×Q8—1721no—
399C4×Q8—1721no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4C22×D4311yescharacteristic
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C42—431no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—431no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42—861no—
424C2×C42—1721no—
425C2×C42—1721no—
426#107—862no—
427#106—41no—
428#106—862no—
429#103—862no—
430#103—862no—
431#103—862no—
432#103—862no—
433#103—1721no—
434#103—1721no—
435C22⋊C8—41no—
436C22⋊C8—1721no—
437#95—21no—
438#95—21no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24D4×D4311yescharacteristic
448C2×Q8—432no—
449C2×Q8—432no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8—861no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—431no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4—1721no—
484C22×C4D4×D4311yescharacteristic
485C22×C4C23×D4311yescharacteristic
486Q16—1724no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—432no—
508C4⋊C4—432no—
509C4⋊C4—864no—
510C4⋊C4—864no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C42—861no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—1721no—
526C42—1721no—
527C42—1722no—
528C42—1722no—
529C42—1722no—
530C42—1722no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#1306335412yes—
538C23C2×D4×D4311yescharacteristic
539Q8—862no—
540Q8—862no—
541Q8—862no—
542Q8—862no—
543Q8—1721no—
544Q8—1721no—
545Q8—1721no—
546Q8—1721no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—432no—
567C2×C4—432no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—1724no—
583C2×C4—1724no—
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#41×D4311yescharacteristic
593C2×C4#41×D4311yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#1306337011yescharacteristic
597C2×C4#1306337111yescharacteristic
598C8—41no—
599C8—41no—
600C8—1721no—
601C8—1721no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22#1458340711yescharacteristic
610C22#1458340711yescharacteristic
611C22#1458345711yescharacteristic
612C22#135×D4311yescharacteristic
613C22#137×D4311yescharacteristic
614C22C2×#1306335411yescharacteristic
615C22#1458369511yescharacteristic
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—862no—
622C4—862no—
623C4—1722no—
624C4—1722no—
625C4—1721no—
626C4—1722no—
627C4—1721no—
628C4—1722no—
629C4#1458357911yescharacteristic
630C4#1458360011yescharacteristic
631C4#1458360011yescharacteristic
632C4#1458363311yescharacteristic
633C2—42no—
634C2#1914018311yescharacteristic
635C2#1914460811yescharacteristic
636C2#1914466111yescharacteristic
637C2#1914472211yescharacteristic
638C2#1914476311yescharacteristic
639C2#1914537111yescharacteristic
640C2#1914542011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2077C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2077D43
hypocenterC43#29417
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
6. #19135234C2semidirect
7. #19135227C2semidirect
8. #19135171C2semidirect
9. #19135164C2semidirect
10. #19134937C2semidirect
11. #19134937C2semidirect
12. #19134860C2semidirect
13. #19134860C2semidirect
379. C43#29417semidirect

Maximal subgroups

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

subgroupindex
#191371232
#191357982
#191357912
#191356052
#191352342
#191352272
#191351712
#191351642
#191349372
#191348602
#191346612
C43×#20772
#2941743