Finite Group Databasebeta

← #25169789

Subgroups — #25169789

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139179C211yesmaximal, characteristic
2#19137655C211yesmaximal, characteristic, complemented
3#19136136C211yesmaximal, characteristic, complemented
4#19135908C211yesmaximal, characteristic
5#19135838C211yesmaximal, characteristic, complemented
6#19135451C211yesmaximal, characteristic
7#19135232C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic
9#19135174C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134952C211yesmaximal, characteristic
12#19134952C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#2013C211yesmaximal, characteristic
16C2×#13063318—21no—
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582827—21no—
30#14582822—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798—21no—
36#14582797C2211yescharacteristic
37#14582793—21no—
38#14582785—21no—
39#14582785—21no—
40#14582768C2211yescharacteristic
41C4⋊C4×Dic43—21no—
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4⋊Q8×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C43⋊C8C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61#13063318—44no—
62Q8×Dic43—22no—
63Q8×Dic43—22no—
64Q8×Dic43—41no—
65Q8×Dic43—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063257—22no—
88#13063256—41no—
89Dic43⋊C8—41no—
90#13063249—22no—
91#13063249—22no—
92#13063249—41no—
93#13063249—41no—
94#13063246—22no—
95#13063246—41no—
96C8×Dic43—41no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C2×SD16×C43—22no—
110C2×SD16×C43—22no—
111C2×SD16×C43—22no—
112C2×SD16×C43—41no—
113C2×SD16×C43—41no—
114C2×SD16×C43—41no—
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43—22no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—22no—
126#103×C43—41no—
127C24×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×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#4112yes—
139C2×Q8×C43#4112yes—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160SD16×C43—44no—
161SD16×C43—44no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—42no—
177C22⋊Dic43—42no—
178C22⋊Dic43—42no—
179C22⋊Dic43—81no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43—42no—
189C4⋊Dic43—42no—
190C4⋊Dic43SD1614yescomplemented
191C4⋊Dic43#4112yes—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
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—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217Q8×C43—22no—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—41no—
224Q8×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43C2×SD1612yes—
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
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—41no—
272C2×Dic43C2×SD1612yes—
273C2×Dic43C2×SD1612yes—
274C8×C43—22no—
275C8×C43—41no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#27066—431nomaximal, Sylow
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43#52511yescharacteristic
287C22×C43#54611yescharacteristic
288C22×C43#55011yescharacteristic
289C22×C43C22×SD1611yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57811yescharacteristic
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—42no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43#52911yescharacteristic
299C4×C43#53811yescharacteristic
300C4×C43#55111yescharacteristic
301C4×C43#55311yescharacteristic
302Dic43—22no—
303Dic43—22no—
304Dic43—41no—
305Dic43—41no—
306Dic43—42no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310#2512—431no—
311#2365—431no—
312#2096—431no—
313#2055—431no—
314#2043—431no—
315#2013D4311yescharacteristic
316#1968—431no—
317#1927—431no—
318#1926—431no—
319#1919—431no—
320#1916—431no—
321#1880—431no—
322#1880—431no—
323#1803—431no—
324C4×#103—431no—
325C2×C43—161no—
326C2×C43#246711yescharacteristic
327C2×C43#310311yescharacteristic
328C2×C43#312111yescharacteristic
329C2×C43#329811yescharacteristic
330C2×C43#330711yescharacteristic
331C2×C43#339211yescharacteristic
332C2×C43#340211yescharacteristic
333C22×SD16C2×D4311yescharacteristic
334C22×SD16C2×D4311yescharacteristic
335C2×C4⋊Q8C2×D4311yescharacteristic
336C2×#126—861no—
337C2×C4×Q8—431no—
338C2×C4×Q8—431no—
339C2×#106—431no—
340C2×#106—431no—
341C2×C4⋊C8—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#103—431no—
345C2×#103—431no—
346C2×#103C2×D4311yescharacteristic
347C2×#103C2×D4311yescharacteristic
348C2×#102—431no—
349C2×#102—431no—
350C2×C4×C8—431no—
351#397—861no—
352#396—861no—
353#391—431no—
354#391—431no—
355#390—431no—
356#390—431no—
357#390C2×D4311yescharacteristic
358#389—431no—
359#389—861no—
360#388—861no—
361#387—861no—
362#387—861no—
363#384—431no—
364C4×C4⋊C4—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—861no—
368#340—431no—
369#340—431no—
370#340—431no—
371#340—431no—
372#336—431no—
373#336—431no—
374#336—431no—
375#336C2×D4311yescharacteristic
376C43#2706611yescharacteristic, complemented, Sylow
377C22×Q8C22×D4311yescharacteristic
378C22×Q8C22×D4311yescharacteristic
379C22×D4C22×D4311yescharacteristic
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C2×SD16—41no—
385C2×SD16—41no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392#126—1724no—
393C4×Q8—862no—
394C4×Q8—862no—
395C4×Q8—1721no—
396C4×Q8—1721no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
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×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—861no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—861no—
420C2×C42—861no—
421C2×C42—861no—
422C2×C42—861no—
423C2×C42C22×D4311yescharacteristic
424#106—862no—
425#106—1721no—
426C4⋊C8—1721no—
427#103—22no—
428#103—41no—
429#103—862no—
430#103—862no—
431#103—1721no—
432#103—1721no—
433#102—862no—
434#102—1721no—
435C4×C8—1721no—
436#95—431no—
437#95—431no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444#95—861no—
445C24—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8#1062190012yes—
457C2×Q8#1062190012yes—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—44no—
479SD16—44no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8#1062190012yes—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—434no—
497C4⋊C4—432no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—3441no—
506C4⋊C4—1721no—
507C4⋊C4—1722no—
508C4⋊C4—1722no—
509C4⋊C4—1722no—
510C4⋊C4—1722no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—3441no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—21no—
518C42—21no—
519C42—861no—
520C42—861no—
521C42—861no—
522C42—861no—
523C42—1722no—
524C42—1722no—
525C42—1722no—
526C42—1722no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×D4×D4311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—432no—
562C2×C4—432no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—862no—
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×C4—1721no—
585C2×C4SD16×D4312yes—
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062190011yescharacteristic
588C2×C4C2×#1062190011yescharacteristic
589C2×C4C2×#1062190011yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337011yescharacteristic
592C8—22no—
593C8—41no—
594C8—1721no—
595C8—1721no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1458340511yescharacteristic
604C22#1458354611yescharacteristic
605C22#1458356911yescharacteristic
606C22C2×SD16×D4311yescharacteristic
607C22#1458369811yescharacteristic
608C22#1458370511yescharacteristic
609C22#1458371511yescharacteristic
610C4—22no—
611C4—42no—
612C4—42no—
613C4—41no—
614C4—81no—
615C4—862no—
616C4—862no—
617C4—3441no—
618C4—3441no—
619C4—3441no—
620C4—1721no—
621C4—1721no—
622C4—1722no—
623C4#1458343011yescharacteristic
624C4#1458348411yescharacteristic
625C4#1458358011yescharacteristic
626C4#1458359211yescharacteristic
627C2—161no—
628C2#1913864111yescharacteristic
629C2#1914462111yescharacteristic
630C2#1914481711yescharacteristic
631C2#1914646311yescharacteristic
632C2#1914657811yescharacteristic
633C2#1914757311yescharacteristic
634C2#1914767111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2013C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2013D43
hypocenterC43#27066
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #19137655C2semidirect
3. #19136136C2semidirect
5. #19135838C2semidirect
7. #19135232C2semidirect
9. #19135174C2semidirect
10. #19135151C2semidirect
13. #19134598C2semidirect
14. #103×Dic43C2semidirect
190. C4⋊Dic43SD16semidirect
376. C43#27066semidirect

Maximal subgroups

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

subgroupindex
#191391792
#191376552
#191361362
#191359082
#191358382
#191354512
#191352322
#191352192
#191351742
#191351512
#191349522
#191345982
#103×Dic432
C43×#20132
#2706643