Finite Group Databasebeta

← #25116332

Subgroups — #25116332

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic43C211yesmaximal, characteristic
2#19137567C211yesmaximal, characteristic
3#19137559C211yesmaximal, characteristic, complemented
4#19135451C211yesmaximal, characteristic
5#19135239C211yesmaximal, characteristic, complemented
6#19135233C211yesmaximal, characteristic, complemented
7#19135218C211yesmaximal, characteristic
8#19135212C211yesmaximal, characteristic
9#19134756C211yesmaximal, characteristic, complemented
10#19134608C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic
12#106×Dic43C211yesmaximal, characteristic, complemented
13C4×#13063257C211yesmaximal, characteristic, complemented
14C8×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18SD16×Dic43C418yescomplemented
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582793—21no—
33#14582787—21no—
34#14582784—21no—
35#14582782—21no—
36#14582766—21no—
37#14582764C2211yescharacteristic
38#14582764C2211yescharacteristic
39#14582760—21no—
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C22⋊C4×Dic43—21no—
46#14582744—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63Q8×Dic43—22no—
64Q8×Dic43C2×C414yes—
65D4×Dic43—22no—
66D4×Dic43C2×C414yes—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4D411yescharacteristic
73C2×Dic43⋊C4D411yescharacteristic
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063258—41no—
85#13063258—41no—
86#13063257—22no—
87#13063257C2×C414yes—
88Dic43⋊C8—22no—
89#13063249—41no—
90#13063249C2×C414yes—
91#13063246—41no—
92#13063246C2×C414yes—
93C8×Dic43—22no—
94C8×Dic43C2×C414yes—
95C43⋊#95—21no—
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⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C2×SD16×C43—22no—
110C2×SD16×C43—22no—
111C2×SD16×C43C2×C414yes—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#106×C43—22no—
120#103×C43—41no—
121#102×C43—41no—
122C4×C8×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125C24×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C22×C412yes—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43C22×C412yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—81no—
150C22×Dic43—81no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155SD16×C43—28no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C22×C412yes—
160C2×C8×C43#4112yes—
161C2×C8×C43#4112yes—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C22⋊Dic43—24no—
171C22⋊Dic43—42no—
172C22⋊Dic43—81no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C412yes—
181C4⋊Dic43C22×C412yes—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—24no—
187C4×Dic43—42no—
188C4×Dic43—42no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C4×Dic43C22×C412yes—
192C4×Dic43#4112yes—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C412yes—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43C22×D411yescharacteristic
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
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#13512yes—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—84no—
258C2×Dic43C4×D412yes—
259C2×Dic43C4×D412yes—
260C2×Dic43#13512yes—
261C8×C43—41no—
262C8×C43#11714yes—
263C43⋊C8—22no—
264C43⋊C8—41no—
265#22806—431nomaximal, Sylow
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43C2×C4×D411yescharacteristic
274C22×C43#54711yescharacteristic
275C22×C43#55011yescharacteristic
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43#57711yescharacteristic
279C22×C43#57711yescharacteristic
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43C2×#11711yescharacteristic
286C4×C43#52011yescharacteristic
287C4×C43#55511yescharacteristic
288C4×C43#55611yescharacteristic
289Dic43—22no—
290Dic43—22no—
291Dic43—22no—
292Dic43—41no—
293Dic43—42no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297C2×C4×SD16—431no—
298#2357—431no—
299#2356—431no—
300#1968—431no—
301#1968D4311yescharacteristic
302#1928—431no—
303#1928—431no—
304#1925—431no—
305#1925—431no—
306#1846—431no—
307#1805—431no—
308#1804—431no—
309C4×#106—431no—
310C4×#106—431no—
311C8×C4⋊C4—431no—
312C2×C43—82no—
313C2×C43#235411yescharacteristic
314C2×C43C4×#13511yescharacteristic
315C2×C43#294911yescharacteristic
316C2×C43#333711yescharacteristic
317C2×C43#333711yescharacteristic
318C2×C43#339411yescharacteristic
319C2×C43#339411yescharacteristic
320C22×SD16C2×D4311yescharacteristic
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C4×SD16—438no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#106—431no—
327C2×#106—431no—
328C2×#106C2×D4311yescharacteristic
329C2×C4⋊C8—431no—
330C2×#103—431no—
331C2×#103—431no—
332C2×#103C2×D4311yescharacteristic
333C2×#102—431no—
334C2×#102—431no—
335C2×#102C2×D4311yescharacteristic
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8C2×D4311yescharacteristic
339#391—431no—
340#391C2×D4311yescharacteristic
341#390—431no—
342#390C2×D4311yescharacteristic
343#388—861no—
344#388—861no—
345#387—861no—
346#387—861no—
347#383—861no—
348#382—431no—
349#382—431no—
350#381—861no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C22⋊C4—861no—
357#376—861no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#336—431no—
363#336—431no—
364C43#2280611yescharacteristic, complemented, Sylow
365C22×Q8C22×D4311yescharacteristic
366C22×D4C22×D4311yescharacteristic
367C23×C4—861no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C4×D4314yes—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4×Q8—434no—
376C4×Q8—862no—
377C4×D4—434no—
378C4×D4—862no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—1721no—
402#107—1721no—
403#106—22no—
404#106—434no—
405#106—862no—
406C4⋊C8—862no—
407#103—41no—
408#103—434no—
409#103—1721no—
410#102—41no—
411#102—434no—
412#102—1721no—
413C4×C8—22no—
414C4×C8—434no—
415C4×C8—862no—
416#95—21no—
417#95—21no—
418#95—431no—
419#95—431no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428#95—861no—
429#95—861no—
430C24—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4312yes—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C2×C4×D4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—864no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—3441no—
456C22×C4—3441no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460SD16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—432no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8C2×C4×D4312yes—
471C2×C8#1062190012yes—
472C2×C8#1062190012yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—432no—
478C4⋊C4—432no—
479C4⋊C4—862no—
480C4⋊C4—864no—
481C4⋊C4—862no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C22⋊C4—864no—
491C22⋊C4—3441no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—432no—
496C42—432no—
497C42—864no—
498C42—861no—
499C42—861no—
500C42—3441no—
501C42—3441no—
502C42—1722no—
503C42—1722no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D4311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—3444no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306334612yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4C2×#1062190011yescharacteristic
563C2×C4C2×#1062190011yescharacteristic
564C2×C4#1306337011yescharacteristic
565C2×C4#1306337211yescharacteristic
566C8—41no—
567C8—862no—
568C8—1721no—
569C8#1306328114yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C4×D4×D4311yescharacteristic
578C22#1458354911yescharacteristic
579C22#1458356911yescharacteristic
580C22#135×D4311yescharacteristic
581C22C2×#1306334611yescharacteristic
582C22#1458370511yescharacteristic
583C22#1458370611yescharacteristic
584C4—22no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—862no—
590C4—862no—
591C4—862no—
592C4—3441no—
593C4—3441no—
594C4—1722no—
595C4—1722no—
596C4—1721no—
597C4C2×#1306328111yescharacteristic
598C4#1458337811yescharacteristic
599C4#1458361311yescharacteristic
600C4#1458361811yescharacteristic
601C2—82no—
602C2#1913754311yescharacteristic
603C2C4×#1306334611yescharacteristic
604C2#1914344911yescharacteristic
605C2#1914696911yescharacteristic
606C2#1914698011yescharacteristic
607C2#1914758811yescharacteristic
608C2#1914759611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1968D43
hypocenterC43#22806
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
3. #19137559C2semidirect
5. #19135239C2semidirect
6. #19135233C2semidirect
9. #19134756C2semidirect
10. #19134608C2semidirect
12. #106×Dic43C2semidirect
13. C4×#13063257C2semidirect
14. C8×Dic43⋊C4C2semidirect
18. SD16×Dic43C4semidirect
364. C43#22806semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic432
#191375672
#191375592
#191354512
#191352392
#191352332
#191352182
#191352122
#191347562
#191346082
#191346032
#106×Dic432
C4×#130632572
C8×Dic43⋊C42
C43×#19682
#2280643