Finite Group Databasebeta

← C139×#32997 #48027593

Subgroups — C139×#32997 #48027593

Order 35584.

1326 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C139C211yesmaximal, characteristic, complemented
2#3094×C139C211yesmaximal, characteristic, complemented
3#3006×C139C211yesmaximal, characteristic
4#2504×C139C211yesmaximal, characteristic, complemented
5#1883×C139C214yesmaximal, complemented
6#1860×C139C214yesmaximal, complemented
7#1826×C139C211yesmaximal, characteristic, complemented
8#1821×C139C211yesmaximal, characteristic, complemented
9#1789×C139C211yesmaximal, characteristic, complemented
10C22×#41×C139C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C139C2212yes—
12C2×#121×C139C2211yescharacteristic
13#520×C139—22no—
14#520×C139—22no—
15#520×C139—22no—
16#520×C139C2214yes—
17C2×C4×Q8×C139—21no—
18C2×C4×D4×C139—21no—
19C2×C4×D4×C139—22no—
20C2×#117×C139—21no—
21C2×#117×C139C2211yescharacteristic
22C22×C4⋊C4×C139—21no—
23C22×C4⋊C4×C139C2211yescharacteristic
24#482×C139—22no—
25#481×C139—21no—
26#480×C139—21no—
27#449×C139—22no—
28#448×C139—21no—
29#447×C139—21no—
30#428×C139C2212yescomplemented
31C2×#104×C139C2214yes—
32#418×C139C2212yescomplemented
33#417×C139C2212yes—
34#407×C139C2211yescharacteristic
35#407×C139C2211yescharacteristic
36#397×C139—22no—
37#390×C139C2212yescomplemented
38#386×C139—22no—
39#382×C139C2212yescomplemented
40C4×C22⋊C4×C139C2211yescharacteristic
41#343×C139C2214yescomplemented
42#339×C139C2214yescomplemented
43C2×#41×C139—28no—
44C2×#41×C139—21no—
45C2×#41×C139—21no—
46C2×#41×C139D412yes—
47C2×#41×C139C2312yes—
48C22×Q8×C139D411yescharacteristic
49C22×D4×C139—21no—
50C22×D4×C139—21no—
51C22×D4×C139D411yescharacteristic
52C22×D4×C139C2311yescharacteristic
53C23×C4×C139—21no—
54C23×C4×C139—22no—
55C23×C4×C139D412yes—
56C23×C4×C139C2311yescharacteristic
57AGL(1,ℤ/8)×C139—28no—
58C2×SD16×C139—22no—
59C2×D8×C139—22no—
60C2×M16×C139C2312yes—
61C2×M16×C139C2312yes—
62#121×C139—21no—
63#121×C139—21no—
64#121×C139—21no—
65#121×C139—21no—
66C4×Q8×C139—24no—
67C4×Q8×C139—24no—
68C4×D4×C139—28no—
69C4×D4×C139—24no—
70C4×D4×C139—24no—
71C4×D4×C139—28no—
72#117×C139—24no—
73#117×C139—21no—
74#117×C139—21no—
75#117×C139—24no—
76#117×C139D412yes—
77#117×C139C2312yes—
78C2×C4⋊C4×C139—22no—
79C2×C4⋊C4×C139—24no—
80C2×C4⋊C4×C139—21no—
81C2×C4⋊C4×C139—21no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139—21no—
84C2×C4⋊C4×C139—24no—
85C2×C4⋊C4×C139D412yes—
86C2×C4⋊C4×C139D411yescharacteristic
87C2×C4⋊C4×C139D411yescharacteristic
88C2×C4⋊C4×C139C2311yescharacteristic
89C2×C4⋊C4×C139C2312yes—
90C2×C22⋊C4×C139—22no—
91C2×C22⋊C4×C139—21no—
92C2×C22⋊C4×C139—21no—
93C2×C22⋊C4×C139—21no—
94C2×C22⋊C4×C139—24no—
95C2×C42×C139—22no—
96C2×C42×C139—21no—
97C2×C42×C139C2312yes—
98#107×C139—22no—
99#106×C139—22no—
100#104×C139—28no—
101#103×C139—22no—
102#102×C139—22no—
103#102×C139—22no—
104#102×C139—22no—
105C22⋊C8×C139—21no—
106C22⋊C8×C139—21no—
107C22⋊C8×C139—21no—
108C22⋊C8×C139—21no—
109#95×C139—21no—
110#95×C139—24no—
111C24×C139—21no—
112C24×C139—21no—
113C24×C139C2×D411yescharacteristic
114#41×C139—28no—
115#41×C139—28no—
116#41×C139—24no—
117#41×C139—24no—
118#41×C139—24no—
119#41×C139#4118yes—
120C2×Q8×C139—24no—
121C2×Q8×C139—21no—
122C2×Q8×C139C2×D412yes—
123C2×D4×C139—28no—
124C2×D4×C139—22no—
125C2×D4×C139—22no—
126C2×D4×C139—24no—
127C2×D4×C139—21no—
128C2×D4×C139—21no—
129C2×D4×C139—21no—
130C2×D4×C139—24no—
131C2×D4×C139—44no—
132C2×D4×C139—41no—
133C2×D4×C139—41no—
134C2×D4×C139C2×D412yes—
135C22×C4×C139—28no—
136C22×C4×C139—21no—
137C22×C4×C139—22no—
138C22×C4×C139—22no—
139C22×C4×C139—24no—
140C22×C4×C139—21no—
141C22×C4×C139—22no—
142C22×C4×C139—21no—
143C22×C4×C139—28no—
144C22×C4×C139—22no—
145C22×C4×C139—21no—
146C22×C4×C139—22no—
147C22×C4×C139—82no—
148C22×C4×C139—84no—
149C22×C4×C139C2×D411yescharacteristic
150C22×C4×C139C2×D411yescharacteristic
151C22×C4×C139C2×D411yescharacteristic
152C22×C4×C139C2×D411yescharacteristic
153C22×C4×C139C2×D411yescharacteristic
154C22×C4×C139C2×D414yes—
155C22×C4×C139C2411yescharacteristic
156SD16×C139—44no—
157D8×C139—44no—
158M16×C139—24no—
159M16×C139—24no—
160C2×C8×C139—22no—
161C2×C8×C139—22no—
162C4⋊C4×C139—28no—
163C4⋊C4×C139—22no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—22no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—22no—
168C4⋊C4×C139—22no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—21no—
171C4⋊C4×C139C2×D412yes—
172C4⋊C4×C139C2×D412yes—
173C22⋊C4×C139—28no—
174C22⋊C4×C139—22no—
175C22⋊C4×C139—22no—
176C22⋊C4×C139—42no—
177C22⋊C4×C139—41no—
178C22⋊C4×C139—41no—
179C22⋊C4×C139—84no—
180C42×C139—28no—
181C42×C139—22no—
182C42×C139—22no—
183C42×C139—24no—
184C23×C139—24no—
185C23×C139—22no—
186C23×C139—22no—
187C23×C139—22no—
188C23×C139—41no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—42no—
192C23×C139—42no—
193C23×C139—41no—
194C23×C139—42no—
195C23×C139#12011yescharacteristic
196C23×C139#12011yescharacteristic
197C23×C139C22×D411yescharacteristic
198Q8×C139—24no—
199Q8×C139—22no—
200Q8×C139#12314yes—
201D4×C139—28no—
202D4×C139—24no—
203D4×C139—28no—
204D4×C139—22no—
205D4×C139—42no—
206D4×C139—42no—
207D4×C139—82no—
208D4×C139—82no—
209D4×C139#12314yes—
210C2×C4×C139—24no—
211C2×C4×C139—28no—
212C2×C4×C139—22no—
213C2×C4×C139—22no—
214C2×C4×C139—22no—
215C2×C4×C139—22no—
216C2×C4×C139—22no—
217C2×C4×C139—28no—
218C2×C4×C139—22no—
219C2×C4×C139—22no—
220C2×C4×C139—24no—
221C2×C4×C139—22no—
222C2×C4×C139—44no—
223C2×C4×C139—42no—
224C2×C4×C139—42no—
225C2×C4×C139—44no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—42no—
229C2×C4×C139—41no—
230C2×C4×C139—42no—
231C2×C4×C139—82no—
232C2×C4×C139—88no—
233C2×C4×C139#12011yescharacteristic
234C2×C4×C139#12011yescharacteristic
235C2×C4×C139C22×D411yescharacteristic
236C2×C4×C139C22×D411yescharacteristic
237C2×C4×C139C2×#4114yes—
238C8×C139—42no—
239C8×C139—42no—
240C22×C139—21no—
241C22×C139—21no—
242C22×C139—21no—
243C22×C139—21no—
244C22×C139—21no—
245C22×C139—24no—
246C22×C139—21no—
247C22×C139—21no—
248C22×C139—44no—
249C22×C139—48no—
250C22×C139—42no—
251C22×C139—42no—
252C22×C139—84no—
253C22×C139—81no—
254C22×C139—81no—
255C22×C139—81no—
256C22×C139#45412yes—
257C22×C139C2×#12011yescharacteristic
258C22×C139#52512yes—
259C4×C139—21no—
260C4×C139—24no—
261C4×C139—21no—
262C4×C139—42no—
263C4×C139—44no—
264C4×C139—42no—
265C4×C139—82no—
266C4×C139—81no—
267C4×C139C2×#12312yes—
268C4×C139#52512yes—
269C2×C139—22no—
270C2×C139—22no—
271C2×C139—41no—
272C2×C139—44no—
273C2×C139—161no—
274C2×C139#284911yescharacteristic
275C2×C139C2×#45411yescharacteristic
276C2×C139#301911yescharacteristic
277#32997C13911yesmaximal, characteristic, direct product factor, Sylow
278C139#3299711yescharacteristic, direct product factor, Sylow
279C2×#520C2×C13911yescharacteristic, complemented
280#3094C2×C13911yescharacteristic, complemented
281#3006C2×C13911yescharacteristic
282#2504C2×C13911yescharacteristic, complemented
283#1883C2×C13914yescomplemented
284#1860C2×C13914yescomplemented
285#1826C2×C13911yescharacteristic, complemented
286#1821C2×C13911yescharacteristic, complemented
287#1789C2×C13911yescharacteristic, complemented
288C22×#41C22×C13911yescharacteristic
289C2×AGL(1,ℤ/8)C22×C13912yes—
290C2×#121C22×C13911yescharacteristic
291#520—22no—
292#520—22no—
293#520—22no—
294#520C22×C13914yes—
295C2×C4×Q8—21no—
296C2×C4×D4—21no—
297C2×C4×D4—22no—
298C2×#117—21no—
299C2×#117C22×C13911yescharacteristic
300C22×C4⋊C4—21no—
301C22×C4⋊C4C22×C13911yescharacteristic
302#482—22no—
303#481—21no—
304#480—21no—
305#449—22no—
306#448—21no—
307#447—21no—
308#428C22×C13912yescomplemented
309C2×#104C22×C13914yes—
310#418C22×C13912yescomplemented
311#417C22×C13912yes—
312#407C22×C13911yescharacteristic
313#407C22×C13911yescharacteristic
314#397—22no—
315#390C22×C13912yescomplemented
316#386—22no—
317#382C22×C13912yescomplemented
318C4×C22⋊C4C22×C13911yescharacteristic
319#343C22×C13914yescomplemented
320#339C22×C13914yescomplemented
321C2×#41—28no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41D4×C13912yes—
325C2×#41C23×C13912yes—
326C22×Q8D4×C13911yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4D4×C13911yescharacteristic
330C22×D4C23×C13911yescharacteristic
331C23×C4—21no—
332C23×C4—22no—
333C23×C4D4×C13912yes—
334C23×C4C23×C13911yescharacteristic
335AGL(1,ℤ/8)—28no—
336C2×SD16—22no—
337C2×D8—22no—
338C2×M16C23×C13912yes—
339C2×M16C23×C13912yes—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×D4—28no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—28no—
350#117—24no—
351#117—21no—
352#117—21no—
353#117—24no—
354#117D4×C13912yes—
355#117C23×C13912yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4D4×C13912yes—
364C2×C4⋊C4D4×C13911yescharacteristic
365C2×C4⋊C4D4×C13911yescharacteristic
366C2×C4⋊C4C23×C13911yescharacteristic
367C2×C4⋊C4C23×C13912yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C42—22no—
374C2×C42—21no—
375C2×C42C23×C13912yes—
376#107—22no—
377#106—22no—
378#104—28no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387#95—21no—
388#95—24no—
389C24—21no—
390C24—21no—
391C24C2×D4×C13911yescharacteristic
392#41—28no—
393#41—28no—
394#41—24no—
395#41—24no—
396#41—24no—
397#41#41×C13918yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8C2×D4×C13912yes—
401C2×D4—28no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—24no—
409C2×D4—44no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C2×D4×C13912yes—
413C22×C4—28no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—28no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—82no—
426C22×C4—84no—
427C22×C4C2×D4×C13911yescharacteristic
428C22×C4C2×D4×C13911yescharacteristic
429C22×C4C2×D4×C13911yescharacteristic
430C22×C4C2×D4×C13911yescharacteristic
431C22×C4C2×D4×C13911yescharacteristic
432C22×C4C2×D4×C13914yes—
433C22×C4C24×C13911yescharacteristic
434SD16—44no—
435D8—44no—
436M16—24no—
437M16—24no—
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—28no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4C2×D4×C13912yes—
450C4⋊C4C2×D4×C13912yes—
451C22⋊C4—28no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—84no—
458C42—28no—
459C42—22no—
460C42—22no—
461C42—24no—
462C23—24no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23#120×C13911yescharacteristic
474C23#120×C13911yescharacteristic
475C23C22×D4×C13911yescharacteristic
476Q8—24no—
477Q8—22no—
478Q8#123×C13914yes—
479D4—28no—
480D4—24no—
481D4—28no—
482D4—22no—
483D4—42no—
484D4—42no—
485D4—82no—
486D4—82no—
487D4#123×C13914yes—
488C2×C4—24no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—28no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—88no—
511C2×C4#120×C13911yescharacteristic
512C2×C4#120×C13911yescharacteristic
513C2×C4C22×D4×C13911yescharacteristic
514C2×C4C22×D4×C13911yescharacteristic
515C2×C4C2×#41×C13914yes—
516C8—42no—
517C8—42no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—24no—
524C22—21no—
525C22—21no—
526C22—44no—
527C22—48no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22#454×C13912yes—
535C22C2×#120×C13911yescharacteristic
536C22#525×C13912yes—
537C4—21no—
538C4—24no—
539C4—21no—
540C4—42no—
541C4—44no—
542C4—42no—
543C4—82no—
544C4—81no—
545C4C2×#123×C13912yes—
546C4#525×C13912yes—
547C2—22no—
548C2—22no—
549C2—41no—
550C2—44no—
551C2—161no—
552C2#2849×C13911yescharacteristic
553C2C2×#454×C13911yescharacteristic
554C2#3019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3006×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#520×C139C2semidirect
2. #3094×C139C2semidirect
4. #2504×C139C2semidirect
5. #1883×C139C2semidirect
6. #1860×C139C2semidirect
7. #1826×C139C2semidirect
8. #1821×C139C2semidirect
9. #1789×C139C2semidirect
30. #428×C139C22semidirect
32. #418×C139C22semidirect
37. #390×C139C22semidirect
39. #382×C139C22semidirect
41. #343×C139C22semidirect
42. #339×C139C22semidirect
277. #32997C139direct (N × H)
278. C139#32997direct (N × H)
279. C2×#520C2×C139semidirect
280. #3094C2×C139semidirect
282. #2504C2×C139semidirect
283. #1883C2×C139semidirect
284. #1860C2×C139semidirect
285. #1826C2×C139semidirect
286. #1821C2×C139semidirect
287. #1789C2×C139semidirect
308. #428C22×C139semidirect
310. #418C22×C139semidirect
315. #390C22×C139semidirect
317. #382C22×C139semidirect
319. #343C22×C139semidirect
320. #339C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1392
#3094×C1392
#3006×C1392
#2504×C1392
#1883×C1392
#1860×C1392
#1826×C1392
#1821×C1392
#1789×C1392
#32997139