Finite Group Databasebeta

← C139×#8420 #48003016

Subgroups — C139×#8420 #48003016

Order 35584.

1094 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3498×C139C211yesmaximal, characteristic
2#1982×C139C211yesmaximal, characteristic, complemented
3#1806×C139C211yesmaximal, characteristic, complemented
4#1547×C139C211yesmaximal, characteristic, complemented
5#1545×C139C211yesmaximal, characteristic, complemented
6#1502×C139C211yesmaximal, characteristic, complemented
7#1477×C139C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C139—21no—
9#550×C139—21no—
10#550×C139C412yescomplemented
11D42×C139—22no—
12D42×C139—22no—
13D42×C139—21no—
14D42×C139C412yescomplemented
15#535×C139—22no—
16#535×C139—21no—
17#532×C139—21no—
18#532×C139C2211yescharacteristic
19C2×#127×C139—21no—
20C2×#127×C139C2211yescharacteristic
21C4×#41×C139C2211yescharacteristic
22#431×C139C2211yescharacteristic, complemented
23#423×C139C2211yescharacteristic, complemented
24C2×C4⋊C8×C139C2211yescharacteristic, complemented
25C2×#104×C139—21no—
26C2×#102×C139—22no—
27C4×C4⋊C4×C139C2211yescharacteristic, complemented
28#339×C139—21no—
29#332×C139—21no—
30#331×C139—22no—
31#331×C139—21no—
32#327×C139—22no—
33Q8⋊C8×C139—21no—
34D4⋊C8×C139—21no—
35H(5,𝔽2)×C139—42no—
36H(5,𝔽2)×C139—42no—
37H(5,𝔽2)×C139—42no—
38H(5,𝔽2)×C139—42no—
39C2×#41×C139—22no—
40C2×#41×C139—22no—
41C2×#41×C139—21no—
42C2×#41×C139D411yescharacteristic
43C22×D4×C139—22no—
44C22×D4×C139—24no—
45C22×D4×C139—22no—
46C22×D4×C139—22no—
47C22×D4×C139—22no—
48C22×D4×C139—21no—
49C22×D4×C139—21no—
50C22×D4×C139D412yes—
51C2×M16×C139—21no—
52C22×C8×C139—21no—
53C4⋊Q8×C139D411yescharacteristic
54#127×C139—22no—
55#127×C139—22no—
56#127×C139—22no—
57#127×C139—21no—
58#127×C139—21no—
59#127×C139C2×C412yes—
60#127×C139D411yescharacteristic
61#127×C139D412yes—
62#124×C139—22no—
63#124×C139—21no—
64#121×C139—22no—
65#121×C139—24no—
66#121×C139—24no—
67#121×C139—21no—
68#121×C139—22no—
69#121×C139—22no—
70#121×C139—22no—
71#121×C139D412yes—
72#120×C139—24no—
73#120×C139—24no—
74#120×C139—24no—
75C4×Q8×C139C2×C411yescharacteristic
76C4×Q8×C139D411yescharacteristic
77C4×D4×C139—22no—
78C4×D4×C139—21no—
79C4×D4×C139—21no—
80C4×D4×C139—22no—
81C4×D4×C139—21no—
82C4×D4×C139C2×C411yescharacteristic
83C4×D4×C139C2×C412yes—
84C4×D4×C139D411yescharacteristic
85#117×C139—21no—
86#117×C139D411yescharacteristic
87C2×C4⋊C4×C139—21no—
88C2×C42×C139—21no—
89C2×C42×C139—21no—
90C2×C42×C139C2311yescharacteristic
91C4⋊C8×C139—21no—
92C4⋊C8×C139—21no—
93C4⋊C8×C139—21no—
94C4⋊C8×C139—21no—
95C4⋊C8×C139—21no—
96#104×C139—42no—
97#102×C139—44no—
98C22⋊C8×C139—21no—
99C4×C8×C139—21no—
100#95×C139—21no—
101C24×C139—24no—
102C24×C139—22no—
103#41×C139—21no—
104#41×C139—21no—
105#41×C139—44no—
106#41×C139—44no—
107#41×C139—44no—
108#41×C139—44no—
109#41×C139—41no—
110#41×C139—41no—
111#41×C139—41no—
112#41×C139—41no—
113#41×C139D812yes—
114#41×C139SD1612yes—
115C2×Q8×C139—21no—
116C2×Q8×C139C22⋊C411yescharacteristic
117C2×D4×C139—21no—
118C2×D4×C139—24no—
119C2×D4×C139—24no—
120C2×D4×C139—22no—
121C2×D4×C139—24no—
122C2×D4×C139—24no—
123C2×D4×C139—22no—
124C2×D4×C139—22no—
125C2×D4×C139—22no—
126C2×D4×C139—21no—
127C2×D4×C139—22no—
128C2×D4×C139—21no—
129C2×D4×C139—22no—
130C2×D4×C139—44no—
131C2×D4×C139—44no—
132C2×D4×C139—42no—
133C2×D4×C139—42no—
134C2×D4×C139—48no—
135C2×D4×C139—48no—
136C2×D4×C139—44no—
137C2×D4×C139—44no—
138C2×D4×C139—41no—
139C2×D4×C139—41no—
140C2×D4×C139—41no—
141C2×D4×C139—41no—
142C2×D4×C139—82no—
143C2×D4×C139—84no—
144C2×D4×C139—82no—
145C2×D4×C139—82no—
146C2×D4×C139C22⋊C411yescharacteristic
147C2×D4×C139C22⋊C412yes—
148C2×D4×C139C22⋊C414yes—
149C22×C4×C139—21no—
150C22×C4×C139—24no—
151C22×C4×C139—21no—
152C22×C4×C139—22no—
153C22×C4×C139—21no—
154C22×C4×C139—41no—
155C22×C4×C139C2×D411yescharacteristic
156C22×C4×C139C2×D411yescharacteristic
157C22×C4×C139C2×D411yescharacteristic
158M16×C139—41no—
159M16×C139—41no—
160C2×C8×C139—42no—
161C2×C8×C139—41no—
162C2×C8×C139—41no—
163C2×C8×C139—41no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—21no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—22no—
168C4⋊C4×C139—41no—
169C4⋊C4×C139C22⋊C411yescharacteristic
170C4⋊C4×C139C22⋊C411yescharacteristic
171C4⋊C4×C139C22⋊C412yes—
172C22⋊C4×C139—24no—
173C22⋊C4×C139—24no—
174C22⋊C4×C139—21no—
175C22⋊C4×C139—21no—
176C22⋊C4×C139—22no—
177C22⋊C4×C139—21no—
178C22⋊C4×C139—22no—
179C42×C139—21no—
180C42×C139—21no—
181C42×C139—21no—
182C42×C139—41no—
183C42×C139—41no—
184C42×C139C22×C411yescharacteristic
185C42×C139C2×D411yescharacteristic
186C42×C139C2×D411yescharacteristic
187C42×C139C2×D411yescharacteristic
188C23×C139—21no—
189C23×C139—24no—
190C23×C139—22no—
191C23×C139—48no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—82no—
195C23×C139—82no—
196C23×C139—84no—
197C23×C139—84no—
198C23×C139#12011yescharacteristic
199Q8×C139—21no—
200Q8×C139—41no—
201Q8×C139—41no—
202Q8×C139#10212yescomplemented
203D4×C139—22no—
204D4×C139—22no—
205D4×C139—21no—
206D4×C139—44no—
207D4×C139—42no—
208D4×C139—48no—
209D4×C139—44no—
210D4×C139—48no—
211D4×C139—42no—
212D4×C139—42no—
213D4×C139—42no—
214D4×C139—42no—
215D4×C139—41no—
216D4×C139—42no—
217D4×C139—41no—
218D4×C139—42no—
219D4×C139—42no—
220D4×C139—41no—
221D4×C139—42no—
222D4×C139—41no—
223D4×C139—82no—
224D4×C139—84no—
225D4×C139—84no—
226D4×C139#10212yescomplemented
227C2×C4×C139—21no—
228C2×C4×C139—22no—
229C2×C4×C139—22no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—22no—
235C2×C4×C139—41no—
236C2×C4×C139—48no—
237C2×C4×C139—42no—
238C2×C4×C139—42no—
239C2×C4×C139—42no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—42no—
243C2×C4×C139—81no—
244C2×C4×C139—81no—
245C2×C4×C139C2×C22⋊C411yescharacteristic
246C2×C4×C139C2×C22⋊C411yescharacteristic
247C2×C4×C139C2×C22⋊C411yescharacteristic
248C2×C4×C139#12011yescharacteristic
249C2×C4×C139#12011yescharacteristic
250C2×C4×C139#12011yescharacteristic
251C2×C4×C139C2×D811yescharacteristic
252C2×C4×C139C2×SD1611yescharacteristic
253C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
254C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
255C8×C139—81no—
256C8×C139—81no—
257C8×C139—81no—
258C22×C139—21no—
259C22×C139—21no—
260C22×C139—22no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139—44no—
264C22×C139—42no—
265C22×C139—44no—
266C22×C139—42no—
267C22×C139—44no—
268C22×C139—42no—
269C22×C139—162no—
270C22×C139—162no—
271C22×C139—168no—
272C22×C139#37911yescharacteristic
273C22×C139#44711yescharacteristic
274C22×C139#45011yescharacteristic
275C4×C139—21no—
276C4×C139—21no—
277C4×C139—21no—
278C4×C139—22no—
279C4×C139—41no—
280C4×C139—41no—
281C4×C139—42no—
282C4×C139—82no—
283C4×C139C2×#10211yescharacteristic
284C4×C139#41811yescharacteristic
285C4×C139#44711yescharacteristic
286C4×C139#45011yescharacteristic
287C4×C139#45311yescharacteristic
288C4×C139#45511yescharacteristic
289C2×C139—21no—
290C2×C139—21no—
291C2×C139—42no—
292C2×C139—84no—
293C2×C139—82no—
294C2×C139#178611yescharacteristic
295C2×C139#179211yescharacteristic
296C2×C139#179511yescharacteristic
297#8420C13911yesmaximal, characteristic, direct product factor, Sylow
298C139#842011yescharacteristic, direct product factor, Sylow
299#3498C2×C13911yescharacteristic
300#1982C2×C13911yescharacteristic, complemented
301#1806C2×C13911yescharacteristic, complemented
302#1547C2×C13911yescharacteristic, complemented
303#1545C2×C13911yescharacteristic, complemented
304#1502C2×C13911yescharacteristic, complemented
305#1477C2×C13911yescharacteristic, complemented
306C2×H(5,𝔽2)—21no—
307#550—21no—
308#550C4×C13912yescomplemented
309D42—22no—
310D42—22no—
311D42—21no—
312D42C4×C13912yescomplemented
313#535—22no—
314#535—21no—
315#532—21no—
316#532C22×C13911yescharacteristic
317C2×#127—21no—
318C2×#127C22×C13911yescharacteristic
319C4×#41C22×C13911yescharacteristic
320#431C22×C13911yescharacteristic, complemented
321#423C22×C13911yescharacteristic, complemented
322C2×C4⋊C8C22×C13911yescharacteristic, complemented
323C2×#104—21no—
324C2×#102—22no—
325C4×C4⋊C4C22×C13911yescharacteristic, complemented
326#339—21no—
327#332—21no—
328#331—22no—
329#331—21no—
330#327—22no—
331Q8⋊C8—21no—
332D4⋊C8—21no—
333H(5,𝔽2)—42no—
334H(5,𝔽2)—42no—
335H(5,𝔽2)—42no—
336H(5,𝔽2)—42no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—21no—
340C2×#41D4×C13911yescharacteristic
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4D4×C13912yes—
349C2×M16—21no—
350C22×C8—21no—
351C4⋊Q8D4×C13911yescharacteristic
352#127—22no—
353#127—22no—
354#127—22no—
355#127—21no—
356#127—21no—
357#127C2×C4×C13912yes—
358#127D4×C13911yescharacteristic
359#127D4×C13912yes—
360#124—22no—
361#124—21no—
362#121—22no—
363#121—24no—
364#121—24no—
365#121—21no—
366#121—22no—
367#121—22no—
368#121—22no—
369#121D4×C13912yes—
370#120—24no—
371#120—24no—
372#120—24no—
373C4×Q8C2×C4×C13911yescharacteristic
374C4×Q8D4×C13911yescharacteristic
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4C2×C4×C13911yescharacteristic
381C4×D4C2×C4×C13912yes—
382C4×D4D4×C13911yescharacteristic
383#117—21no—
384#117D4×C13911yescharacteristic
385C2×C4⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42C23×C13911yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394#104—42no—
395#102—44no—
396C22⋊C8—21no—
397C4×C8—21no—
398#95—21no—
399C24—24no—
400C24—22no—
401#41—21no—
402#41—21no—
403#41—44no—
404#41—44no—
405#41—44no—
406#41—44no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41D8×C13912yes—
412#41SD16×C13912yes—
413C2×Q8—21no—
414C2×Q8C22⋊C4×C13911yescharacteristic
415C2×D4—21no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—82no—
441C2×D4—84no—
442C2×D4—82no—
443C2×D4—82no—
444C2×D4C22⋊C4×C13911yescharacteristic
445C2×D4C22⋊C4×C13912yes—
446C2×D4C22⋊C4×C13914yes—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4C2×D4×C13911yescharacteristic
454C22×C4C2×D4×C13911yescharacteristic
455C22×C4C2×D4×C13911yescharacteristic
456M16—41no—
457M16—41no—
458C2×C8—42no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4C22⋊C4×C13911yescharacteristic
468C4⋊C4C22⋊C4×C13911yescharacteristic
469C4⋊C4C22⋊C4×C13912yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42C22×C4×C13911yescharacteristic
483C42C2×D4×C13911yescharacteristic
484C42C2×D4×C13911yescharacteristic
485C42C2×D4×C13911yescharacteristic
486C23—21no—
487C23—24no—
488C23—22no—
489C23—48no—
490C23—42no—
491C23—42no—
492C23—82no—
493C23—82no—
494C23—84no—
495C23—84no—
496C23#120×C13911yescharacteristic
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8#102×C13912yescomplemented
501D4—22no—
502D4—22no—
503D4—21no—
504D4—44no—
505D4—42no—
506D4—48no—
507D4—44no—
508D4—48no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—41no—
514D4—42no—
515D4—41no—
516D4—42no—
517D4—42no—
518D4—41no—
519D4—42no—
520D4—41no—
521D4—82no—
522D4—84no—
523D4—84no—
524D4#102×C13912yescomplemented
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4C2×C22⋊C4×C13911yescharacteristic
544C2×C4C2×C22⋊C4×C13911yescharacteristic
545C2×C4C2×C22⋊C4×C13911yescharacteristic
546C2×C4#120×C13911yescharacteristic
547C2×C4#120×C13911yescharacteristic
548C2×C4#120×C13911yescharacteristic
549C2×C4C2×D8×C13911yescharacteristic
550C2×C4C2×SD16×C13911yescharacteristic
551C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
552C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
553C8—81no—
554C8—81no—
555C8—81no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—44no—
562C22—42no—
563C22—44no—
564C22—42no—
565C22—44no—
566C22—42no—
567C22—162no—
568C22—162no—
569C22—168no—
570C22#379×C13911yescharacteristic
571C22#447×C13911yescharacteristic
572C22#450×C13911yescharacteristic
573C4—22no—
574C4—21no—
575C4—21no—
576C4—21no—
577C4—42no—
578C4—41no—
579C4—41no—
580C4—82no—
581C4C2×#102×C13911yescharacteristic
582C4#418×C13911yescharacteristic
583C4#447×C13911yescharacteristic
584C4#450×C13911yescharacteristic
585C4#453×C13911yescharacteristic
586C4#455×C13911yescharacteristic
587C2—21no—
588C2—21no—
589C2—42no—
590C2—84no—
591C2—82no—
592C2#1786×C13911yescharacteristic
593C2#1792×C13911yescharacteristic
594C2#1795×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3498×C139C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1982×C139C2semidirect
3. #1806×C139C2semidirect
4. #1547×C139C2semidirect
5. #1545×C139C2semidirect
6. #1502×C139C2semidirect
7. #1477×C139C2semidirect
10. #550×C139C4semidirect
14. D42×C139C4semidirect
22. #431×C139C22semidirect
23. #423×C139C22semidirect
24. C2×C4⋊C8×C139C22semidirect
27. C4×C4⋊C4×C139C22semidirect
202. Q8×C139#102semidirect
226. D4×C139#102semidirect
297. #8420C139direct (N × H)
298. C139#8420direct (N × H)
300. #1982C2×C139semidirect
301. #1806C2×C139semidirect
302. #1547C2×C139semidirect
303. #1545C2×C139semidirect
304. #1502C2×C139semidirect
305. #1477C2×C139semidirect
308. #550C4×C139semidirect
312. D42C4×C139semidirect
320. #431C22×C139semidirect
321. #423C22×C139semidirect
322. C2×C4⋊C8C22×C139semidirect
325. C4×C4⋊C4C22×C139semidirect
500. Q8#102×C139semidirect
524. D4#102×C139semidirect

Maximal subgroups

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

subgroupindex
#3498×C1392
#1982×C1392
#1806×C1392
#1547×C1392
#1545×C1392
#1502×C1392
#1477×C1392
#8420139