Finite Group Databasebeta

← #25159692

Subgroups — #25159692

Order 11008.

848 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
1C2×#14583201C211yesmaximal, characteristic
2#19138450C211yesmaximal, characteristic, complemented
3#19137500C211yesmaximal, characteristic
4#19136145C211yesmaximal, characteristic, complemented
5#19136080C211yesmaximal, characteristic, complemented
6#19135974C211yesmaximal, characteristic, complemented
7#19135935C211yesmaximal, characteristic, complemented
8#19135323C211yesmaximal, characteristic, complemented
9#19135152C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic
11#19134931C211yesmaximal, characteristic
12#19134858C211yesmaximal, characteristic
13#19134849C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, characteristic
15C2×C4×SD16×C43C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583201—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29#14582838—21no—
30#14582832—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797—21no—
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582783—21no—
39#14582772—21no—
40#14582771—21no—
41#14582764C2211yescharacteristic
42#14582757—21no—
43C4×Dic43⋊C4C2211yescharacteristic
44C2×C43⋊#95—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C4×SD16×C43—24no—
57C2×#106×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063316—22no—
66#13063316—41no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063258—22no—
88#13063258—41no—
89#13063257—22no—
90#13063257—22no—
91Dic43⋊C8—22no—
92#13063249—22no—
93#13063249—41no—
94#13063246—22no—
95#13063246—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43Q814yes—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×Q8×C43—22no—
117C4×Q8×C43—41no—
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#106×C43—22no—
127#103×C43—22no—
128#102×C43D414yes—
129C4×C8×C43—22no—
130C24×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43C2×Q812yes—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43C2×Q812yes—
142C2×D4×C43#4112yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—24no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—81no—
160C22×Dic43—81no—
161C22×Dic43—81no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166SD16×C43—28no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C2×C8×C43C2×Q812yes—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43C2×D412yes—
178C22⋊C4×C43—42no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—42no—
182C22⋊Dic43—24no—
183C22⋊Dic43—42no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192C4⋊Dic43—42no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—22no—
195Dic43⋊C4—41no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43C22⋊Q814yes—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
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×C43—84no—
241C2×C4×C43#13512yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43H(5,𝔽2)11yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
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×Dic43—84no—
273C2×Dic43—84no—
274C8×C43—22no—
275C8×C43—22no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278#26378—431nomaximal, Sylow
279C22×C43—24no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43#52511yescharacteristic
287C22×C43D4211yescharacteristic
288C22×C43D4×Q811yescharacteristic
289C22×C43C2×#13511yescharacteristic
290C22×C43#57511yescharacteristic
291C22×C43#57711yescharacteristic
292C22×C43#57711yescharacteristic
293C4×C43—22no—
294C4×C43—42no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—81no—
298C4×C43C2×C22⋊Q811yescharacteristic
299C4×C43#53911yescharacteristic
300C4×C43#54711yescharacteristic
301C4×C43#55411yescharacteristic
302Dic43—41no—
303Dic43—41no—
304Dic43—42no—
305Dic43—41no—
306Dic43—41no—
307Dic43—81no—
308Dic43—81no—
309Dic43—81no—
310C2×#478—431no—
311C2×C4×SD16D4311yescharacteristic
312#2453—431no—
313#2349—431no—
314#2097—431no—
315#2085—431no—
316#2066—431no—
317#2059—431no—
318#1941—431no—
319#1916—431no—
320#1877—431no—
321#1877—431no—
322#1864—431no—
323#1863—431no—
324#1862—431no—
325C2×C43—44no—
326C2×C43#244911yescharacteristic
327C2×C43#310211yescharacteristic
328C2×C43#312311yescharacteristic
329C2×C43#326711yescharacteristic
330C2×C43#328211yescharacteristic
331C2×C43#338111yescharacteristic
332C2×C43#338811yescharacteristic
333C22×SD16C2×D4311yescharacteristic
334C2×#125—431no—
335C2×C4×Q8C2×D4311yescharacteristic
336C2×C4×D4—431no—
337C2×C4×D4—431no—
338C2×C4×D4C2×D4311yescharacteristic
339#478—864no—
340C4×SD16—24no—
341C2×#107—431no—
342C2×#107—431no—
343C2×#106—431no—
344C2×#106—431no—
345C2×#106C2×D4311yescharacteristic
346C2×C4⋊C8—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#103C2×D4311yescharacteristic
350C2×#102—431no—
351C2×#102—431no—
352C2×#102C2×D4311yescharacteristic
353C2×C4×C8C2×D4311yescharacteristic
354#400—861no—
355#398—861no—
356#391—431no—
357#391—431no—
358#389—431no—
359#389—431no—
360#389—431no—
361#389—431no—
362#389—861no—
363#387—861no—
364#385—861no—
365#385—861no—
366#382—431no—
367#380—861no—
368C4×C4⋊C4—431no—
369C2×#95—861no—
370#340—431no—
371#340—431no—
372#340—431no—
373#340—431no—
374#336—431no—
375#336—431no—
376#336—431no—
377#336—431no—
378C43#2637811yescharacteristic, complemented, Sylow
379C22×Q8C22×D4311yescharacteristic
380C22×D4C22×D4311yescharacteristic
381C23×C4—21no—
382C23×C4—861no—
383C23×C4—861no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16Dic8614yes—
387C22×C8—431no—
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391#125—862no—
392#125—1721no—
393C4×Q8—22no—
394C4×Q8—41no—
395C4×D4—22no—
396C4×D4—41no—
397C4×D4—862no—
398C4×D4—862no—
399C4×D4—862no—
400C4×D4—1721no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—861no—
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—21no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C42—21no—
420C2×C42—431no—
421C2×C42—431no—
422C2×C42C22×D4311yescharacteristic
423#107—862no—
424#107—1721no—
425#106—22no—
426#106—862no—
427#106—862no—
428C4⋊C8—862no—
429#103—22no—
430#103—862no—
431#103—1721no—
432#102—862no—
433#102—862no—
434#102C22⋊D4314yes—
435C4×C8—22no—
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—
445#95—861no—
446#95—861no—
447#95—861no—
448C24—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×Dic8612yes—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×Dic8612yes—
459C2×D4#1062189812yes—
460C2×D4C2×C22⋊D4312yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—81no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—864no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3441no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—28no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8C2×Dic8612yes—
496C2×C8C2×C22⋊D4312yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—432no—
502C4⋊C4—862no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—3441no—
512C4⋊C4—1721no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4C2×C22⋊D4312yes—
518C22⋊C4—42no—
519C22⋊C4—864no—
520C22⋊C4—1722no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—861no—
525C42—861no—
526C42—861no—
527C42—861no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23C2×D4×D4311yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—41no—
539Q8—41no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4#1306330414yes—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—862no—
562C2×C4—861no—
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—3444no—
573C2×C4—3444no—
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×C4#1306334612yes—
586C2×C4C22×C22⋊D4311yescharacteristic
587C2×C4C22×Dic8611yescharacteristic
588C2×C4#41×D4311yescharacteristic
589C2×C4C2×#1062189811yescharacteristic
590C2×C4#1306337011yescharacteristic
591C2×C4#1306337211yescharacteristic
592C8—22no—
593C8—22no—
594C8—1721no—
595C8—1721no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22#1458340811yescharacteristic
604C22D4×C22⋊D4311yescharacteristic
605C22D4×Dic8611yescharacteristic
606C22C2×#1306334611yescharacteristic
607C22#1458369611yescharacteristic
608C22#1458370511yescharacteristic
609C22#1458370611yescharacteristic
610C4—22no—
611C4—42no—
612C4—41no—
613C4—42no—
614C4—81no—
615C4—3441no—
616C4—3441no—
617C4—3441no—
618C4—1721no—
619C4—1721no—
620C4—1721no—
621C4—1722no—
622C4—1721no—
623C4C2×#1306330411yescharacteristic
624C4#1458349111yescharacteristic
625C4#1458354811yescharacteristic
626C4#1458360811yescharacteristic
627C2—44no—
628C2#1913839811yescharacteristic
629C2#1914461711yescharacteristic
630C2#1914484411yescharacteristic
631C2#1914612011yescharacteristic
632C2#1914630211yescharacteristic
633C2#1914746811yescharacteristic
634C2#1914753611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×C4×SD16D43
hypocenterC43#26378
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #19138450C2semidirect
4. #19136145C2semidirect
5. #19136080C2semidirect
6. #19135974C2semidirect
7. #19135935C2semidirect
8. #19135323C2semidirect
9. #19135152C2semidirect
13. #19134849C2semidirect
378. C43#26378semidirect

Maximal subgroups

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

subgroupindex
C2×#145832012
#191384502
#191375002
#191361452
#191360802
#191359742
#191359352
#191353232
#191351522
#191349312
#191348582
#191348492
#191348422
C2×C4×SD16×C432
#2637843