Finite Group Databasebeta

← #25200597

Subgroups — #25200597

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142963C211yesmaximal, characteristic
2C4×#13063323C211yesmaximal, characteristic, complemented
3#19136074C211yesmaximal, characteristic, complemented
4#19136002C211yesmaximal, characteristic
5#19135840C211yesmaximal, characteristic, complemented
6#19135679C211yesmaximal, characteristic
7#19135447C211yesmaximal, characteristic
8#19135446C211yesmaximal, characteristic
9#19135269C211yesmaximal, characteristic, complemented
10#19135268C211yesmaximal, characteristic, complemented
11#19134950C211yesmaximal, characteristic
12#19134949C211yesmaximal, characteristic
13#19134862C211yesmaximal, characteristic, complemented
14#19134339C211yesmaximal, characteristic, complemented
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063320—21no—
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582804C2211yescharacteristic
32#14582801C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582794—21no—
38#14582794—21no—
39#14582791—21no—
40#14582789—21no—
41#14582788—21no—
42#14582768C2211yescharacteristic
43C4×Dic43⋊C4—21no—
44C4×Dic43⋊C4—21no—
45C42×Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C2×#10621873—22no—
62C2×#10621873—22no—
63C2×#10621873—41no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063323—22no—
70#13063323—22no—
71#13063320—44no—
72C4×Dic86—41no—
73C4×Dic86—41no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063256—41no—
97#13063250—22no—
98#13063249—22no—
99#13063248—22no—
100#13063248—41no—
101#13063247—41no—
102#13063245—41no—
103C8×Dic43—22no—
104C8×Dic43—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×Q8×C43—41no—
115C4×Q8×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#106×C43—41no—
124#103×C43—22no—
125#103×C43—41no—
126#95×C43—21no—
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86#4112yes—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177#10621884—44no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—42no—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—22no—
200C4×Dic43—22no—
201C4×Dic43—41no—
202C4×Dic43—42no—
203C4×Dic43SD1614yescomplemented
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8#4112yes—
210#10621873—44no—
211C23×C43C22×D411yescharacteristic
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—41no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
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×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C2×SD1612yes—
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43C2×SD1612yes—
265C2×Dic43C2×SD1612yes—
266C2×Dic43#13512yes—
267C2×Dic43#13712yes—
268D172—41no—
269D172—41no—
270D172—41no—
271D172—41no—
272Dic86—22no—
273Dic86—22no—
274Dic86—41no—
275Dic86—41no—
276C8×C43—22no—
277C8×C43—41no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280#29494—431nomaximal, Sylow
281C22×C43#52511yescharacteristic
282C22×C43#53211yescharacteristic
283C22×C43#53511yescharacteristic
284C22×C43C22×SD1611yescharacteristic
285C22×C43C2×#13511yescharacteristic
286C22×C43C2×#13711yescharacteristic
287C22×C43#57511yescharacteristic
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—81no—
295C4×C43—22no—
296C4×C43—42no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43#55111yescharacteristic
302C4×C43#55111yescharacteristic
303C4×C43#55311yescharacteristic
304C4×C43#55311yescharacteristic
305Dic43—22no—
306Dic43—22no—
307Dic43—22no—
308Dic43—22no—
309Dic43—42no—
310Dic43—81no—
311Dic43—81no—
312#2860—431no—
313C4×C4⋊Q8—431no—
314#2084—431no—
315#2071—431no—
316#2043—431no—
317#2013—431no—
318#1968—431no—
319#1968—431no—
320#1933—431no—
321#1933—431no—
322#1880—431no—
323#1880—431no—
324#1865—431no—
325#1865D4311yescharacteristic, complemented
326#1744—431no—
327C2×C43#260311yescharacteristic
328C2×C43#310311yescharacteristic
329C2×C43#310811yescharacteristic
330C2×C43#316711yescharacteristic
331C2×C43#318111yescharacteristic
332C2×C43#320611yescharacteristic
333C2×C43#321211yescharacteristic
334D43—161no—
335C22×SD16—431no—
336C22×SD16—431no—
337C2×C4⋊Q8—431no—
338C2×#126—861no—
339C2×C4×Q8—431no—
340C2×C4×Q8C2×D4311yescharacteristic
341C2×#106—431no—
342C2×#106C2×D4311yescharacteristic
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103C2×D4311yescharacteristic
348C2×#103C2×D4311yescharacteristic
349C2×#102—431no—
350C2×#102—431no—
351C2×C4×C8—431no—
352C2×C4×C8—431no—
353#391—431no—
354#391—431no—
355#390—431no—
356#390—431no—
357#390—431no—
358#389—431no—
359#389—431no—
360#389—861no—
361#389—861no—
362#389C2×D4311yescharacteristic
363#388—861no—
364#388—861no—
365#388—861no—
366#384—431no—
367C4×C4⋊C4—861no—
368C4×C4⋊C4—861no—
369C43—431no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340C2×D4311yescharacteristic
374#336—431no—
375#336—431no—
376#336—431no—
377#336C2×D4311yescharacteristic
378C43#2949411yescharacteristic, complemented, Sylow
379C22×Q8—431no—
380C22×Q8C22×D4311yescharacteristic
381C22×D4—431no—
382C2×SD16—862no—
383C2×SD16—862no—
384C2×SD16—862no—
385C2×SD16—862no—
386C2×SD16—1721no—
387C2×SD16—1721no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392C4⋊Q8—862no—
393C4⋊Q8—862no—
394#126—1724no—
395C4×Q8—41no—
396C4×Q8—41no—
397C4×Q8—1721no—
398C4×Q8—1721no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C4⋊C4C22×D4311yescharacteristic
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—21no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428#106—41no—
429#106—1721no—
430#103—22no—
431#103—41no—
432#103—862no—
433#103—862no—
434#103—862no—
435#103—1721no—
436#102—1721no—
437#102—1721no—
438C4×C8—862no—
439C4×C8—862no—
440#95—21no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445#95—861no—
446#95—861no—
447C24—861no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×Q8#1062190212yes—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—861no—
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—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480SD16—1724no—
481SD16—1724no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—432no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8#1062189812yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—864no—
503C4⋊C4—864no—
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—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C22⋊C4—1722no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—434no—
523C42—862no—
524C42—862no—
525C42—861no—
526C42—861no—
527C42—861no—
528C42—861no—
529C42—1721no—
530C42—1722no—
531C23—1721no—
532C23—1721no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23C2×D4×D4311yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—41no—
542Q8—41no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547D4—1721no—
548D4—1721no—
549D4—1721no—
550D4—1721no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
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—41no—
567C2×C4—41no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—432no—
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—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4SD16×D4312yes—
590C2×C4#41×D4311yescharacteristic
591C2×C4#41×D4311yescharacteristic
592C2×C4C2×#1062189811yescharacteristic
593C2×C4C2×#1062190211yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337011yescharacteristic
596C8—22no—
597C8—41no—
598C8—862no—
599C8—1721no—
600C22—3441no—
601C22—3441no—
602C22—3441no—
603C22—3441no—
604C22—3441no—
605C22—3441no—
606C22—3441no—
607C22#1458341211yescharacteristic
608C22#1458344611yescharacteristic
609C22#1458346411yescharacteristic
610C22C2×SD16×D4311yescharacteristic
611C22#135×D4311yescharacteristic
612C22#137×D4311yescharacteristic
613C22#1458369811yescharacteristic
614C4—22no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—862no—
621C4—862no—
622C4—862no—
623C4—862no—
624C4—3441no—
625C4—3441no—
626C4—1722no—
627C4#1458357611yescharacteristic
628C4#1458357811yescharacteristic
629C4#1458359411yescharacteristic
630C4#1458359711yescharacteristic
631C2—6881no—
632C2#1914022111yescharacteristic
633C2#1914462811yescharacteristic
634C2#1914468011yescharacteristic
635C2#1914515111yescharacteristic
636C2#1914530211yescharacteristic
637C2#1914551811yescharacteristic
638C2#1914557411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1865D43
hypocenterC43#29494
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
2. C4×#13063323C2semidirect
3. #19136074C2semidirect
5. #19135840C2semidirect
9. #19135269C2semidirect
10. #19135268C2semidirect
13. #19134862C2semidirect
14. #19134339C2semidirect
15. C43×#1865C2semidirect
203. C4×Dic43SD16semidirect
325. #1865D43semidirect
378. C43#29494semidirect

Maximal subgroups

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

subgroupindex
#191429632
C4×#130633232
#191360742
#191360022
#191358402
#191356792
#191354472
#191354462
#191352692
#191352682
#191349502
#191349492
#191348622
#191343392
C43×#18652
#2949443