Finite Group Databasebeta

← #25116426

Subgroups — #25116426

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583008C211yesmaximal, characteristic
2#19137564C211yesmaximal, characteristic, complemented
3#19137543C211yesmaximal, characteristic, complemented
4#19135470C211yesmaximal, characteristic
5#19135458C211yesmaximal, characteristic
6#19135224C211yesmaximal, characteristic, complemented
7#19135223C211yesmaximal, characteristic, complemented
8#19135214C211yesmaximal, characteristic, complemented
9#19134762C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134493C211yesmaximal, characteristic, complemented
13#19134483C211yesmaximal, characteristic, complemented
14#19134468C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063281—21no—
20#14583008C418yescomplemented
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582793—21no—
37#14582790—21no—
38#14582788—21no—
39#14582787—21no—
40#14582768C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582761—21no—
43#14582757—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C2×#10621882—22no—
64C2×#10621882—22no—
65C2×#10621882C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68D4×Dic43—22no—
69D4×Dic43C2×C414yes—
70#13063287—22no—
71#13063287C2×C414yes—
72#13063281—44no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4D411yescharacteristic
79C2×Dic43⋊C4D411yescharacteristic
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—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×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063258—22no—
94#13063257—41no—
95#13063256—22no—
96#13063256C2×C414yes—
97Dic43⋊C8—22no—
98#13063247—41no—
99#13063247C2×C414yes—
100#13063246—41no—
101#13063245—41no—
102#13063236—22no—
103#13063235C2×C414yes—
104C8×Dic43—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×D4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120C2×C42×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#107×C43—41no—
123#102×C43—41no—
124#102×C43C2×C414yes—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43C22×C412yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C22×C412yes—
156C2×C4×D43—24no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C22×C412yes—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C22×C412yes—
171C22⋊C4×C43—42no—
172C22⋊C4×C43—81no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—81no—
176C22⋊Dic43—24no—
177C22⋊Dic43—42no—
178C22⋊Dic43—81no—
179#10621882—28no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—42no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C412yes—
191Dic43⋊C4—22no—
192Dic43⋊C4—41no—
193Dic43⋊C4—42no—
194Dic43⋊C4—81no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C4×Dic43—81no—
200C4×Dic43C22×C412yes—
201C4×Dic43#4112yes—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C22×C412yes—
206C2×C43⋊C8#4112yes—
207C2×C43⋊C8#4112yes—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—22no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43C23×C411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
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—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—48no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43C4×D412yes—
268C2×Dic43C4×D412yes—
269C2×Dic43AGL(1,ℤ/8)12yes—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—84no—
275C8×C43—22no—
276C8×C43—41no—
277C43⋊C8—41no—
278C43⋊C8#11714yescomplemented
279#22817—431nomaximal, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C2×C4×D411yescharacteristic
288C22×C43#54711yescharacteristic
289C22×C43#55011yescharacteristic
290C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C43#57511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—81no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—42no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43C2×#11711yescharacteristic
307C4×C43#52011yescharacteristic
308C4×C43#55511yescharacteristic
309C4×C43#55611yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—42no—
315Dic43—81no—
316Dic43—81no—
317C2×#442—431no—
318#2357—431no—
319#2354—431no—
320#1972—431no—
321#1970—431no—
322#1926—431no—
323#1926—431no—
324#1925—431no—
325#1925D4311yescharacteristic, complemented
326#1847—431no—
327#1804—431no—
328#1802—431no—
329#1776—431no—
330C4×#106—431no—
331#1771—431no—
332C2×C43—82no—
333C2×C43#235411yescharacteristic
334C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C43#294611yescharacteristic
336C2×C43#334511yescharacteristic
337C2×C43#334711yescharacteristic
338C2×C43#339911yescharacteristic
339C2×C43#340111yescharacteristic
340D43—82no—
341C22×D8—431no—
342C2×C4×D4—431no—
343C2×C4×D4—431no—
344C2×#117—861no—
345#442—438no—
346C2×#107—431no—
347C2×#107C2×D4311yescharacteristic
348C2×#106—431no—
349C2×#106—431no—
350C2×#106—431no—
351C2×C4⋊C8—431no—
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×#97—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#390—431no—
362#390—431no—
363#390—431no—
364#390C2×D4311yescharacteristic
365#388—861no—
366#388—861no—
367#388—861no—
368#388—861no—
369#384—431no—
370#382—431no—
371#381—861no—
372#380—861no—
373C4×C4⋊C4—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—431no—
377C4×C4⋊C4C2×D4311yescharacteristic
378C4×C22⋊C4—861no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340C2×D4311yescharacteristic
383#336—431no—
384#336C2×D4311yescharacteristic
385C43#2281711yescharacteristic, complemented, Sylow
386C22×D4—431no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—861no—
389C23×C4—861no—
390C2×D8—434no—
391C2×D8—862no—
392C2×D8—862no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4×D4—434no—
398C4×D4—434no—
399C4×D4—862no—
400C4×D4—862no—
401#117—1724no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—431no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—861no—
417C2×C22⋊C4—861no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—21no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#107—41no—
430#107—862no—
431#106—434no—
432#106—862no—
433#106—1721no—
434C4⋊C8—862no—
435#102—41no—
436#102—434no—
437#102—1721no—
438#102—1721no—
439#102—1721no—
440#102C4×D4314yes—
441#97—434no—
442#97—862no—
443C4×C8—862no—
444#95—21no—
445#95—431no—
446#95—431no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—21no—
453C24—861no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—432no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4C2×C4×D4312yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—864no—
474C22×C4—864no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—3441no—
479C22×C4—3441no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485D8—868no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—432no—
492C2×C8—432no—
493C2×C8—432no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8C2×C4×D4312yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—432no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—3441no—
511C4⋊C4—1721no—
512C4⋊C4—1722no—
513C4⋊C4C2×C4×D4312yes—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—864no—
517C22⋊C4—864no—
518C22⋊C4—3441no—
519C22⋊C4—3441no—
520C22⋊C4—3441no—
521C22⋊C4—1722no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C42—21no—
525C42—21no—
526C42—81no—
527C42—432no—
528C42—432no—
529C42—861no—
530C42—861no—
531C42—3441no—
532C42—1722no—
533C42—1722no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—862no—
542C23—1721no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23—1721no—
548C23C2×D4×D4311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—862no—
554D4—862no—
555D4—1721no—
556D4—1721no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—3444no—
586C2×C4—1728no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4C22×C4×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4#41×D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4#1306337011yescharacteristic
600C2×C4#1306337211yescharacteristic
601C8—22no—
602C8—41no—
603C8—434no—
604C8—1721no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—3441no—
616C22—1722no—
617C22—1722no—
618C22—1722no—
619C22C4×D4×D4311yescharacteristic
620C22#1458354711yescharacteristic
621C22#1458356711yescharacteristic
622C22AGL(1,ℤ/8)×D4311yescharacteristic
623C22#1458369811yescharacteristic
624C22#1458370011yescharacteristic
625C22#1458370611yescharacteristic
626C4—41no—
627C4—41no—
628C4—42no—
629C4—81no—
630C4—81no—
631C4—862no—
632C4—862no—
633C4—862no—
634C4—3441no—
635C4—3441no—
636C4—1721no—
637C4—1722no—
638C4#117×D4311yescharacteristic
639C4#1458337811yescharacteristic
640C4#1458361111yescharacteristic
641C4#1458361611yescharacteristic
642C2—82no—
643C2—3442no—
644C2#1913754111yescharacteristic
645C2#1914340011yescharacteristic
646C2#1914342011yescharacteristic
647C2#1914706811yescharacteristic
648C2#1914709811yescharacteristic
649C2#1914764011yescharacteristic
650C2#1914766411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#22817
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #19137564C2semidirect
3. #19137543C2semidirect
6. #19135224C2semidirect
7. #19135223C2semidirect
8. #19135214C2semidirect
9. #19134762C2semidirect
10. #19134603C2semidirect
11. #19134594C2semidirect
12. #19134493C2semidirect
13. #19134483C2semidirect
14. #19134468C2semidirect
15. C43×#1925C2semidirect
20. #14583008C4semidirect
278. C43⋊C8#117semidirect
325. #1925D43semidirect
385. C43#22817semidirect

Maximal subgroups

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

subgroupindex
C2×#145830082
#191375642
#191375432
#191354702
#191354582
#191352242
#191352232
#191352142
#191347622
#191346032
#191345942
#191344932
#191344832
#191344682
C43×#19252
#2281743