Finite Group Databasebeta

← C139×#12690 #48007286

Subgroups — C139×#12690 #48007286

Order 35584.

1228 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C139C211yesmaximal, characteristic
2C2×#352×C139C212yesmaximal, complemented
3C2×AΣL(1,𝔽16)×C139C212yesmaximal, complemented
4#1783×C139C211yesmaximal, characteristic, complemented
5#1781×C139C211yesmaximal, characteristic, complemented
6C23×D4×C139C411yescharacteristic, complemented
7C23×D4×C139C2211yescharacteristic
8#534×C139—24no—
9#534×C139—24no—
10C2×#123×C139—21no—
11C2×#123×C139C411yescharacteristic, complemented
12C2×#123×C139C2211yescharacteristic
13C2×#121×C139—21no—
14C2×#121×C139—21no—
15C2×#120×C139—21no—
16C2×#120×C139C411yescharacteristic, complemented
17C2×#120×C139C2211yescharacteristic
18C22×C22⋊C4×C139C411yescharacteristic, complemented
19C2×#100×C139—21no—
20C2×#100×C139C2212yes—
21C2×#99×C139—21no—
22C2×#99×C139C2212yes—
23#407×C139—21no—
24#379×C139—21no—
25#352×C139—24no—
26AΣL(1,𝔽16)×C139—24no—
27C25×C139C2×C411yescharacteristic
28C25×C139C2×C411yescharacteristic
29C25×C139D411yescharacteristic
30C22×D4×C139—21no—
31C22×D4×C139—21no—
32C22×D4×C139—22no—
33C22×D4×C139—21no—
34C22×D4×C139—21no—
35C22×D4×C139—22no—
36C22×D4×C139—22no—
37C22×D4×C139—22no—
38C22×D4×C139—42no—
39C22×D4×C139—42no—
40C22×D4×C139—42no—
41C22×D4×C139—42no—
42C22×D4×C139C2×C411yescharacteristic
43C22×D4×C139D411yescharacteristic
44C22×D4×C139D411yescharacteristic
45C22×D4×C139C2311yescharacteristic
46C23×C4×C139—21no—
47C23×C4×C139C2×C411yescharacteristic
48C23×C4×C139D411yescharacteristic
49C2×M16×C139—22no—
50#123×C139—28no—
51#123×C139—22no—
52#123×C139—22no—
53#123×C139—22no—
54#123×C139D414yes—
55#121×C139—28no—
56#121×C139—28no—
57#120×C139—28no—
58#120×C139—22no—
59#120×C139—22no—
60#120×C139—22no—
61#120×C139D414yes—
62C2×C4⋊C4×C139—21no—
63C2×C4⋊C4×C139—21no—
64C2×C22⋊C4×C139—21no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—21no—
67C2×C22⋊C4×C139—21no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—22no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—22no—
72C2×C22⋊C4×C139—42no—
73C2×C22⋊C4×C139C2×C411yescharacteristic
74C2×C22⋊C4×C139C2×C411yescharacteristic
75#100×C139—22no—
76#100×C139—22no—
77#100×C139—42no—
78#99×C139—22no—
79#99×C139—22no—
80#99×C139—42no—
81C22⋊C8×C139—42no—
82C24×C139—22no—
83C24×C139—22no—
84C24×C139—21no—
85C24×C139—21no—
86C24×C139—21no—
87C24×C139—22no—
88C24×C139—21no—
89C24×C139—22no—
90C24×C139—41no—
91C24×C139—41no—
92C24×C139—41no—
93C24×C139—82no—
94C24×C139—82no—
95C24×C139—82no—
96C24×C139C22⋊C411yescharacteristic
97C24×C139C22⋊C411yescharacteristic
98C24×C139C22⋊C411yescharacteristic
99C24×C139C22⋊C412yescomplemented
100C24×C139C22×C411yescharacteristic
101C24×C139C2×D411yescharacteristic
102C2×D4×C139—24no—
103C2×D4×C139—24no—
104C2×D4×C139—22no—
105C2×D4×C139—22no—
106C2×D4×C139—21no—
107C2×D4×C139—21no—
108C2×D4×C139—22no—
109C2×D4×C139—24no—
110C2×D4×C139—24no—
111C2×D4×C139—22no—
112C2×D4×C139—41no—
113C2×D4×C139—41no—
114C2×D4×C139—41no—
115C2×D4×C139—41no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—48no—
119C2×D4×C139—48no—
120C2×D4×C139—48no—
121C2×D4×C139—42no—
122C2×D4×C139—42no—
123C2×D4×C139—48no—
124C2×D4×C139—42no—
125C2×D4×C139—42no—
126C2×D4×C139—82no—
127C2×D4×C139—82no—
128C2×D4×C139C2×D412yes—
129C2×D4×C139C2×D412yes—
130C22×C4×C139—22no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—21no—
134C22×C4×C139—21no—
135C22×C4×C139—24no—
136C22×C4×C139—22no—
137C22×C4×C139—41no—
138C22×C4×C139—41no—
139C22×C4×C139—41no—
140C22×C4×C139—42no—
141C22×C4×C139—82no—
142C22×C4×C139C22⋊C411yescharacteristic
143C22×C4×C139C22⋊C412yescomplemented
144C22×C4×C139C2×D411yescharacteristic
145M16×C139—42no—
146M16×C139—42no—
147C2×C8×C139—42no—
148C4⋊C4×C139—24no—
149C4⋊C4×C139—24no—
150C22⋊C4×C139—24no—
151C22⋊C4×C139—24no—
152C22⋊C4×C139—24no—
153C22⋊C4×C139—21no—
154C22⋊C4×C139—21no—
155C22⋊C4×C139—24no—
156C22⋊C4×C139—24no—
157C22⋊C4×C139—42no—
158C22⋊C4×C139—42no—
159C22⋊C4×C139—84no—
160C22⋊C4×C139C22⋊C412yescomplemented
161C22⋊C4×C139C22⋊C412yescomplemented
162C23×C139—24no—
163C23×C139—24no—
164C23×C139—21no—
165C23×C139—21no—
166C23×C139—21no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—21no—
172C23×C139—21no—
173C23×C139—22no—
174C23×C139—21no—
175C23×C139—21no—
176C23×C139—42no—
177C23×C139—44no—
178C23×C139—42no—
179C23×C139—42no—
180C23×C139—42no—
181C23×C139—42no—
182C23×C139—44no—
183C23×C139—42no—
184C23×C139—42no—
185C23×C139—42no—
186C23×C139—42no—
187C23×C139—41no—
188C23×C139—41no—
189C23×C139—82no—
190C23×C139—82no—
191C23×C139—82no—
192C23×C139—82no—
193C23×C139—84no—
194C23×C139—82no—
195C23×C139—82no—
196C23×C139—82no—
197C23×C139—84no—
198C23×C139—84no—
199C23×C139—84no—
200C23×C139—84no—
201C23×C139#9912yes—
202C23×C139#9912yes—
203C23×C139C2×C22⋊C411yescharacteristic
204C23×C139C2×C22⋊C411yescharacteristic
205C23×C139C2×C22⋊C411yescharacteristic
206C23×C139#12012yes—
207D4×C139—42no—
208D4×C139—42no—
209D4×C139—44no—
210D4×C139—44no—
211D4×C139—42no—
212D4×C139—42no—
213D4×C139—48no—
214D4×C139—48no—
215D4×C139—84no—
216D4×C139—84no—
217C2×C4×C139—21no—
218C2×C4×C139—21no—
219C2×C4×C139—22no—
220C2×C4×C139—22no—
221C2×C4×C139—21no—
222C2×C4×C139—22no—
223C2×C4×C139—21no—
224C2×C4×C139—21no—
225C2×C4×C139—44no—
226C2×C4×C139—42no—
227C2×C4×C139—42no—
228C2×C4×C139—42no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—42no—
232C2×C4×C139—84no—
233C2×C4×C139—82no—
234C2×C4×C139—84no—
235C2×C4×C139#12012yes—
236C8×C139—82no—
237C22×C139—22no—
238C22×C139—22no—
239C22×C139—22no—
240C22×C139—22no—
241C22×C139—21no—
242C22×C139—21no—
243C22×C139—22no—
244C22×C139—22no—
245C22×C139—42no—
246C22×C139—41no—
247C22×C139—41no—
248C22×C139—42no—
249C22×C139—42no—
250C22×C139—42no—
251C22×C139—42no—
252C22×C139—42no—
253C22×C139—42no—
254C22×C139—42no—
255C22×C139—42no—
256C22×C139—42no—
257C22×C139—42no—
258C22×C139—42no—
259C22×C139—42no—
260C22×C139—41no—
261C22×C139—42no—
262C22×C139—81no—
263C22×C139—81no—
264C22×C139—82no—
265C22×C139—84no—
266C22×C139—84no—
267C22×C139—88no—
268C22×C139—84no—
269C22×C139—84no—
270C22×C139—82no—
271C22×C139#37911yescharacteristic
272C22×C139C2×#9911yescharacteristic
273C22×C139C2×#9911yescharacteristic
274C4×C139—22no—
275C4×C139—42no—
276C4×C139—42no—
277C4×C139—41no—
278C4×C139—42no—
279C4×C139—162no—
280C2×C139—21no—
281C2×C139—21no—
282C2×C139—42no—
283C2×C139—42no—
284C2×C139—42no—
285C2×C139—41no—
286C2×C139—41no—
287C2×C139—81no—
288C2×C139—82no—
289C2×C139#178111yescharacteristic
290C2×C139#212112yes—
291#12690C13911yesmaximal, characteristic, direct product factor, Sylow
292C139#1269011yescharacteristic, direct product factor, Sylow
293C2×#534C2×C13911yescharacteristic
294C2×#352C2×C13912yescomplemented
295C2×AΣL(1,𝔽16)C2×C13912yescomplemented
296#1783C2×C13911yescharacteristic, complemented
297#1781C2×C13911yescharacteristic, complemented
298C23×D4C4×C13911yescharacteristic, complemented
299C23×D4C22×C13911yescharacteristic
300#534—24no—
301#534—24no—
302C2×#123—21no—
303C2×#123C4×C13911yescharacteristic, complemented
304C2×#123C22×C13911yescharacteristic
305C2×#121—21no—
306C2×#121—21no—
307C2×#120—21no—
308C2×#120C4×C13911yescharacteristic, complemented
309C2×#120C22×C13911yescharacteristic
310C22×C22⋊C4C4×C13911yescharacteristic, complemented
311C2×#100—21no—
312C2×#100C22×C13912yes—
313C2×#99—21no—
314C2×#99C22×C13912yes—
315#407—21no—
316#379—21no—
317#352—24no—
318AΣL(1,𝔽16)—24no—
319C25C2×C4×C13911yescharacteristic
320C25C2×C4×C13911yescharacteristic
321C25D4×C13911yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4C2×C4×C13911yescharacteristic
335C22×D4D4×C13911yescharacteristic
336C22×D4D4×C13911yescharacteristic
337C22×D4C23×C13911yescharacteristic
338C23×C4—21no—
339C23×C4C2×C4×C13911yescharacteristic
340C23×C4D4×C13911yescharacteristic
341C2×M16—22no—
342#123—28no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123D4×C13914yes—
347#121—28no—
348#121—28no—
349#120—28no—
350#120—22no—
351#120—22no—
352#120—22no—
353#120D4×C13914yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4C2×C4×C13911yescharacteristic
366C2×C22⋊C4C2×C4×C13911yescharacteristic
367#100—22no—
368#100—22no—
369#100—42no—
370#99—22no—
371#99—22no—
372#99—42no—
373C22⋊C8—42no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—82no—
386C24—82no—
387C24—82no—
388C24C22⋊C4×C13911yescharacteristic
389C24C22⋊C4×C13911yescharacteristic
390C24C22⋊C4×C13911yescharacteristic
391C24C22⋊C4×C13912yescomplemented
392C24C22×C4×C13911yescharacteristic
393C24C2×D4×C13911yescharacteristic
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—48no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4C2×D4×C13912yes—
421C2×D4C2×D4×C13912yes—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—82no—
434C22×C4C22⋊C4×C13911yescharacteristic
435C22×C4C22⋊C4×C13912yescomplemented
436C22×C4C2×D4×C13911yescharacteristic
437M16—42no—
438M16—42no—
439C2×C8—42no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—84no—
452C22⋊C4C22⋊C4×C13912yescomplemented
453C22⋊C4C22⋊C4×C13912yescomplemented
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—42no—
469C23—44no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—82no—
482C23—82no—
483C23—82no—
484C23—82no—
485C23—84no—
486C23—82no—
487C23—82no—
488C23—82no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23#99×C13912yes—
494C23#99×C13912yes—
495C23C2×C22⋊C4×C13911yescharacteristic
496C23C2×C22⋊C4×C13911yescharacteristic
497C23C2×C22⋊C4×C13911yescharacteristic
498C23#120×C13912yes—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—48no—
507D4—84no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—82no—
526C2×C4—84no—
527C2×C4#120×C13912yes—
528C8—82no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—82no—
557C22—84no—
558C22—84no—
559C22—88no—
560C22—84no—
561C22—84no—
562C22—82no—
563C22#379×C13911yescharacteristic
564C22C2×#99×C13911yescharacteristic
565C22C2×#99×C13911yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—162no—
572C2—21no—
573C2—21no—
574C2—42no—
575C2—42no—
576C2—41no—
577C2—41no—
578C2—42no—
579C2—81no—
580C2—82no—
581C2#1781×C13911yescharacteristic
582C2#2121×C13912yes—
subgroupG/H
center, socleC22×C139C2×#99
commutatorC24C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radicalC2×#534×C139C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C24×C139 ◁ C23×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#352×C139C2semidirect
3. C2×AΣL(1,𝔽16)×C139C2semidirect
4. #1783×C139C2semidirect
5. #1781×C139C2semidirect
6. C23×D4×C139C4semidirect
11. C2×#123×C139C4semidirect
16. C2×#120×C139C4semidirect
18. C22×C22⋊C4×C139C4semidirect
99. C24×C139C22⋊C4semidirect
143. C22×C4×C139C22⋊C4semidirect
160. C22⋊C4×C139C22⋊C4semidirect
161. C22⋊C4×C139C22⋊C4semidirect
291. #12690C139direct (N × H)
292. C139#12690direct (N × H)
294. C2×#352C2×C139semidirect
295. C2×AΣL(1,𝔽16)C2×C139semidirect
296. #1783C2×C139semidirect
297. #1781C2×C139semidirect
298. C23×D4C4×C139semidirect
303. C2×#123C4×C139semidirect
308. C2×#120C4×C139semidirect
310. C22×C22⋊C4C4×C139semidirect
391. C24C22⋊C4×C139semidirect
435. C22×C4C22⋊C4×C139semidirect
452. C22⋊C4C22⋊C4×C139semidirect
453. C22⋊C4C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1392
C2×#352×C1392
C2×AΣL(1,𝔽16)×C1392
#1783×C1392
#1781×C1392
#12690139