Finite Group Databasebeta

← #25116333

Subgroups — #25116333

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×#14582984C211yesmaximal, characteristic
2#19137564C211yesmaximal, characteristic
3#19137559C211yesmaximal, characteristic, complemented
4#19135452C211yesmaximal, characteristic
5#19135446C211yesmaximal, characteristic
6#19135238C211yesmaximal, characteristic, complemented
7#19135216C211yesmaximal, characteristic
8#19135214C211yesmaximal, characteristic
9#19134758C211yesmaximal, characteristic, complemented
10#19134608C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic
12C4×#13063256C211yesmaximal, characteristic, complemented
13#19134483C211yesmaximal, characteristic, complemented
14#19134456C211yesmaximal, characteristic, complemented
15C43×#1928C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14582984C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582801C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582790—21no—
36#14582788—21no—
37#14582784—21no—
38#14582782—21no—
39#14582766—21no—
40#14582764C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582761—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4×Dic43⋊C4C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47C4×(C2×D43)⋊C4—21no—
48#14582744—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C2×#10621884—22no—
63C2×#10621884—22no—
64C2×#10621884C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—22no—
68Q8×Dic43C2×C414yes—
69#13063287—22no—
70#13063287C2×C414yes—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4D411yescharacteristic
76C2×Dic43⋊C4D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063259—41no—
89#13063256—22no—
90#13063256—22no—
91#13063256C2×C414yes—
92Dic43⋊C8—22no—
93#13063249—41no—
94#13063247—41no—
95#13063247C2×C414yes—
96#13063245—41no—
97C4×C43⋊C8—22no—
98C8×Dic43—22no—
99C8×Dic43C2×C414yes—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C22×Q8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119#107×C43—41no—
120#103×C43—41no—
121#103×C43C2×C414yes—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—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—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22×C412yes—
152C2×C4×D43—24no—
153C2×C4×D43—81no—
154C2×C4×D43—81no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C22×C412yes—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C22×C412yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—81no—
170#10621884—28no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—81no—
175(C2×D43)⋊C4—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—24no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C412yes—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—24no—
188C4×Dic43—42no—
189C4×Dic43—42no—
190C4×Dic43—81no—
191C4×Dic43C22×C412yes—
192C4×Dic43#4112yes—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C22×C412yes—
197C2×C43⋊C8#4112yes—
198C2×C43⋊C8#4112yes—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207Q8×C43—22no—
208Q8×C43—22no—
209Q8×C43—41no—
210Q8×C43—41no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
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#13512yes—
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×C4×C432−1+411yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43C4×D412yes—
254C2×Dic43C4×D412yes—
255C2×Dic43#13512yes—
256D172—22no—
257D172—22no—
258D172—41no—
259D172—41no—
260C4×D43—84no—
261C8×C43—22no—
262C8×C43—41no—
263C43⋊C8—41no—
264C43⋊C8#11714yes—
265#22806—431nomaximal, Sylow
266C22×C43C2×C4×D411yescharacteristic
267C22×C43#54711yescharacteristic
268C22×C43#55011yescharacteristic
269C22×C43C2×#13511yescharacteristic
270C22×C43C2×#13511yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C4×C43—22no—
281C4×C43—41no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43C2×#11711yescharacteristic
287C4×C43#52011yescharacteristic
288C4×C43#55511yescharacteristic
289C4×C43#55611yescharacteristic
290Dic43—22no—
291Dic43—22no—
292Dic43—22no—
293Dic43—41no—
294Dic43—42no—
295Dic43—81no—
296Dic43—81no—
297C2×C4×SD16—431no—
298#2357—431no—
299#2356—431no—
300#1968—431no—
301#1968—431no—
302#1928—431no—
303#1928D4311yescharacteristic, complemented
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#235411yescharacteristic
313C2×C43C4×#13511yescharacteristic
314C2×C43#294911yescharacteristic
315C2×C43#333711yescharacteristic
316C2×C43#333711yescharacteristic
317C2×C43#339411yescharacteristic
318C2×C43#339411yescharacteristic
319D43—82no—
320C22×SD16—431no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C4×SD16—438no—
324C2×#107—431no—
325C2×#107C2×D4311yescharacteristic
326C2×#106—431no—
327C2×#106—431no—
328C2×#106—431no—
329C2×C4⋊C8—431no—
330C2×#103—431no—
331C2×#103C2×D4311yescharacteristic
332C2×#103C2×D4311yescharacteristic
333C2×#102—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×C4×C8—431no—
337C2×C4×C8—431no—
338C2×C4×C8—431no—
339#391—431no—
340#391C2×D4311yescharacteristic
341#390—431no—
342#390—431no—
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⋊C4C2×D4311yescharacteristic
356C4×C22⋊C4—861no—
357#376—861no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#336—431no—
363#336C2×D4311yescharacteristic
364C43#2280611yescharacteristic, complemented, Sylow
365C22×Q8C22×D4311yescharacteristic
366C22×D4—431no—
367C23×C4—861no—
368C2×SD16—434no—
369C2×SD16—862no—
370C2×SD16—862no—
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—861no—
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—21no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—861no—
397C2×C42—861no—
398C2×C42—861no—
399C2×C42—861no—
400C2×C42C22×D4311yescharacteristic
401#107—41no—
402#107—1721no—
403#106—434no—
404#106—862no—
405#106—862no—
406C4⋊C8—862no—
407#103—41no—
408#103—1721no—
409#103C4×D4314yes—
410#102—434no—
411#102—1721no—
412#102—1721no—
413C4×C8—434no—
414C4×C8—862no—
415C4×C8—862no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—431no—
420#95—431no—
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—861no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C2×C4×D4312yes—
437C2×D4—432no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—864no—
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—868no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—432no—
467C2×C8—432no—
468C2×C8—432no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8C2×C4×D4312yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
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⋊C4C2×C4×D4312yes—
488C22⋊C4—864no—
489C22⋊C4—3441no—
490C22⋊C4—3441no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—81no—
496C42—432no—
497C42—432no—
498C42—864no—
499C42—861no—
500C42—861no—
501C42—3441no—
502C42—1722no—
503C42—1722no—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23C2×D4×D4311yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—862no—
517D4—862no—
518D4—1721no—
519D4—1721no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—3444no—
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#1306334812yes—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#1306337011yescharacteristic
565C2×C4#1306337211yescharacteristic
566C8—22no—
567C8—41no—
568C8—434no—
569C8—1721no—
570C22—3441no—
571C22—3441no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22—1722no—
576C22—1722no—
577C22C4×D4×D4311yescharacteristic
578C22#1458354711yescharacteristic
579C22#1458356711yescharacteristic
580C22#135×D4311yescharacteristic
581C22C2×#1306334811yescharacteristic
582C22#1458370811yescharacteristic
583C22#1458370911yescharacteristic
584C4—22no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—862no—
591C4—862no—
592C4—862no—
593C4—3441no—
594C4—3441no—
595C4—1722no—
596C4—1721no—
597C4#117×D4311yescharacteristic
598C4#1458337811yescharacteristic
599C4#1458361111yescharacteristic
600C4#1458361611yescharacteristic
601C2—3442no—
602C2#1913754111yescharacteristic
603C2C4×#1306334811yescharacteristic
604C2#1914345111yescharacteristic
605C2#1914697211yescharacteristic
606C2#1914697711yescharacteristic
607C2#1914759011yescharacteristic
608C2#1914759411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1928C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1928D43
hypocenterC43#22806
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
3. #19137559C2semidirect
6. #19135238C2semidirect
9. #19134758C2semidirect
10. #19134608C2semidirect
12. C4×#13063256C2semidirect
13. #19134483C2semidirect
14. #19134456C2semidirect
15. C43×#1928C2semidirect
19. #14582984C4semidirect
303. #1928D43semidirect
364. C43#22806semidirect

Maximal subgroups

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

subgroupindex
C2×#145829842
#191375642
#191375592
#191354522
#191354462
#191352382
#191352162
#191352142
#191347582
#191346082
#191346042
C4×#130632562
#191344832
#191344562
C43×#19282
#2280643