Finite Group Databasebeta

← C139×#9963 #48004559

Subgroups — C139×#9963 #48004559

Order 35584.

1046 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C139C211yesmaximal, characteristic, complemented
2C2×#447×C139C211yesmaximal, characteristic
3#2639×C139C211yesmaximal, characteristic, complemented
4C2×#328×C139C211yesmaximal, characteristic, complemented
5C2×#327×C139C211yesmaximal, characteristic, complemented
6#1438×C139C211yesmaximal, characteristic, complemented
7#1280×C139C211yesmaximal, characteristic, complemented
8C23×D4×C139C2211yescharacteristic
9C22×SD16×C139—21no—
10C22×D8×C139—21no—
11C2×C22⋊Q8×C139C2211yescharacteristic
12C2×#121×C139C2211yescharacteristic
13C22×C22⋊C4×C139—22no—
14#450×C139—22no—
15#450×C139—22no—
16#447×C139—22no—
17#447×C139—22no—
18C2×#102×C139—21no—
19C2×#102×C139—21no—
20C2×C22⋊C8×C139C2211yescharacteristic
21C2×C22⋊C8×C139C2211yescharacteristic
22#400×C139—21no—
23#397×C139—21no—
24#394×C139—21no—
25#393×C139—21no—
26#386×C139—22no—
27C2×#95×C139C2211yescharacteristic
28C2×#95×C139C2211yescharacteristic
29#328×C139—22no—
30#327×C139—22no—
31C25×C139—21no—
32C22×Q8×C139D411yescharacteristic
33C22×D4×C139—21no—
34C22×D4×C139—21no—
35C22×D4×C139—21no—
36C22×D4×C139—21no—
37C22×D4×C139—21no—
38C22×D4×C139—21no—
39C22×D4×C139—44no—
40C22×D4×C139D412yes—
41C22×D4×C139D411yescharacteristic
42C23×C4×C139—21no—
43C23×C4×C139D412yes—
44C23×C4×C139C2311yescharacteristic
45C2×SD16×C139—24no—
46C2×SD16×C139—44no—
47C2×D8×C139—24no—
48C2×D8×C139—44no—
49C22×C8×C139—21no—
50C22×C8×C139—21no—
51C22⋊Q8×C139—21no—
52C22⋊Q8×C139—21no—
53C22⋊Q8×C139—21no—
54C22⋊Q8×C139—21no—
55#121×C139—21no—
56#121×C139—21no—
57#121×C139—21no—
58#121×C139—21no—
59C2×C4⋊C4×C139—21no—
60C2×C4⋊C4×C139D411yescharacteristic
61C2×C4⋊C4×C139D411yescharacteristic
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139—21no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139—44no—
67C2×C22⋊C4×C139—44no—
68C2×C22⋊C4×C139—44no—
69#102×C139—24no—
70#102×C139—24no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139—21no—
73C22⋊C8×C139D412yes—
74C22⋊C8×C139D412yes—
75#95×C139—22no—
76#95×C139—22no—
77#95×C139—21no—
78#95×C139—21no—
79#95×C139—21no—
80#95×C139—21no—
81C24×C139—24no—
82C24×C139—22no—
83C24×C139—21no—
84C24×C139—42no—
85C24×C139—42no—
86C24×C139—42no—
87C24×C139—41no—
88C24×C139—41no—
89C24×C139—42no—
90C24×C139—42no—
91C24×C139C2×D411yescharacteristic
92C2×Q8×C139—21no—
93C2×Q8×C139—21no—
94C2×Q8×C139—42no—
95C2×D4×C139—24no—
96C2×D4×C139—24no—
97C2×D4×C139—22no—
98C2×D4×C139—22no—
99C2×D4×C139—21no—
100C2×D4×C139—21no—
101C2×D4×C139—42no—
102C2×D4×C139—42no—
103C2×D4×C139—42no—
104C2×D4×C139—44no—
105C2×D4×C139—44no—
106C2×D4×C139—44no—
107C2×D4×C139—44no—
108C2×D4×C139—41no—
109C2×D4×C139—41no—
110C2×D4×C139—42no—
111C2×D4×C139—42no—
112C2×D4×C139—41no—
113C2×D4×C139—41no—
114C22×C4×C139—22no—
115C22×C4×C139—22no—
116C22×C4×C139—21no—
117C22×C4×C139—21no—
118C22×C4×C139—21no—
119C22×C4×C139—22no—
120C22×C4×C139—22no—
121C22×C4×C139—42no—
122C22×C4×C139—42no—
123C22×C4×C139—42no—
124C22×C4×C139—42no—
125C22×C4×C139—41no—
126C22×C4×C139—41no—
127C22×C4×C139—42no—
128C22×C4×C139C2×D411yescharacteristic
129C22×C4×C139C2×D411yescharacteristic
130C22×C4×C139C2×D411yescharacteristic
131C22×C4×C139C2×D411yescharacteristic
132C22×C4×C139C2×D411yescharacteristic
133C22×C4×C139#4111yescharacteristic
134SD16×C139—48no—
135D8×C139—48no—
136C2×C8×C139—22no—
137C2×C8×C139—22no—
138C2×C8×C139—42no—
139C2×C8×C139—42no—
140C4⋊C4×C139—21no—
141C4⋊C4×C139—21no—
142C4⋊C4×C139—21no—
143C4⋊C4×C139—21no—
144C4⋊C4×C139—41no—
145C4⋊C4×C139—41no—
146C22⋊C4×C139—416no—
147C22⋊C4×C139—41no—
148C22⋊C4×C139—41no—
149C22⋊C4×C139—41no—
150C22⋊C4×C139—41no—
151C22⋊C4×C139—82no—
152C22⋊C4×C139—82no—
153C23×C139—21no—
154C23×C139—21no—
155C23×C139—22no—
156C23×C139—24no—
157C23×C139—44no—
158C23×C139—44no—
159C23×C139—42no—
160C23×C139—44no—
161C23×C139—44no—
162C23×C139—44no—
163C23×C139—44no—
164C23×C139—42no—
165C23×C139—44no—
166C23×C139—44no—
167C23×C139—41no—
168C23×C139—42no—
169C23×C139—41no—
170C23×C139—41no—
171C23×C139—42no—
172C23×C139—82no—
173C23×C139—82no—
174C23×C139—82no—
175C23×C139—82no—
176C23×C139—82no—
177C23×C139—82no—
178C23×C139—81no—
179C23×C139—81no—
180C23×C139—81no—
181C23×C139—81no—
182C23×C139#12011yescharacteristic
183C23×C139#12111yescharacteristic
184C23×C139#12711yescharacteristic
185C23×C139#13512yes—
186C23×C139AGL(1,ℤ/8)12yes—
187Q8×C139—42no—
188Q8×C139—81no—
189D4×C139—24no—
190D4×C139—24no—
191D4×C139—42no—
192D4×C139—42no—
193D4×C139—44no—
194D4×C139—44no—
195D4×C139—42no—
196D4×C139—81no—
197D4×C139—82no—
198D4×C139—81no—
199D4×C139—81no—
200C2×C4×C139—22no—
201C2×C4×C139—22no—
202C2×C4×C139—41no—
203C2×C4×C139—41no—
204C2×C4×C139—41no—
205C2×C4×C139—41no—
206C2×C4×C139—44no—
207C2×C4×C139—44no—
208C2×C4×C139—42no—
209C2×C4×C139—41no—
210C2×C4×C139—41no—
211C2×C4×C139—41no—
212C2×C4×C139—42no—
213C2×C4×C139—42no—
214C2×C4×C139—41no—
215C2×C4×C139—42no—
216C2×C4×C139—41no—
217C2×C4×C139—42no—
218C2×C4×C139—42no—
219C2×C4×C139—82no—
220C2×C4×C139—81no—
221C2×C4×C139—81no—
222C2×C4×C139—82no—
223C2×C4×C139#12011yescharacteristic
224C2×C4×C139#12011yescharacteristic
225C2×C4×C139#12111yescharacteristic
226C2×C4×C139#12111yescharacteristic
227C8×C139—42no—
228C8×C139—42no—
229C22×C139—22no—
230C22×C139—22no—
231C22×C139—22no—
232C22×C139—22no—
233C22×C139—21no—
234C22×C139—21no—
235C22×C139—21no—
236C22×C139—21no—
237C22×C139—48no—
238C22×C139—44no—
239C22×C139—84no—
240C22×C139—84no—
241C22×C139—84no—
242C22×C139—84no—
243C22×C139—84no—
244C22×C139—82no—
245C22×C139—82no—
246C22×C139—82no—
247C22×C139—82no—
248C22×C139—81no—
249C22×C139—81no—
250C22×C139—81no—
251C22×C139#39211yescharacteristic
252C22×C139#44912yes—
253C22×C139#45311yescharacteristic
254C22×C139#45411yescharacteristic
255C22×C139B(4,𝔽2)12yes—
256C22×C139#46312yes—
257C22×C139#49511yescharacteristic
258C22×C139#49611yescharacteristic
259C4×C139—21no—
260C4×C139—21no—
261C4×C139—21no—
262C4×C139—21no—
263C4×C139—82no—
264C4×C139—82no—
265C4×C139—81no—
266C4×C139—81no—
267C4×C139—81no—
268C2×C139—21no—
269C2×C139—22no—
270C2×C139—21no—
271C2×C139—84no—
272C2×C139—161no—
273C2×C139#159712yes—
274C2×C139#160012yes—
275C2×C139#200611yescharacteristic
276C2×C139#201211yescharacteristic
277C2×C139#202111yescharacteristic
278#9963C13911yesmaximal, characteristic, direct product factor, Sylow
279C139#996311yescharacteristic, direct product factor, Sylow
280C2×#450C2×C13911yescharacteristic, complemented
281C2×#447C2×C13911yescharacteristic
282#2639C2×C13911yescharacteristic, complemented
283C2×#328C2×C13911yescharacteristic, complemented
284C2×#327C2×C13911yescharacteristic, complemented
285#1438C2×C13911yescharacteristic, complemented
286#1280C2×C13911yescharacteristic, complemented
287C23×D4C22×C13911yescharacteristic
288C22×SD16—21no—
289C22×D8—21no—
290C2×C22⋊Q8C22×C13911yescharacteristic
291C2×#121C22×C13911yescharacteristic
292C22×C22⋊C4—22no—
293#450—22no—
294#450—22no—
295#447—22no—
296#447—22no—
297C2×#102—21no—
298C2×#102—21no—
299C2×C22⋊C8C22×C13911yescharacteristic
300C2×C22⋊C8C22×C13911yescharacteristic
301#400—21no—
302#397—21no—
303#394—21no—
304#393—21no—
305#386—22no—
306C2×#95C22×C13911yescharacteristic
307C2×#95C22×C13911yescharacteristic
308#328—22no—
309#327—22no—
310C25—21no—
311C22×Q8D4×C13911yescharacteristic
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—44no—
319C22×D4D4×C13911yescharacteristic
320C22×D4D4×C13912yes—
321C23×C4—21no—
322C23×C4D4×C13912yes—
323C23×C4C23×C13911yescharacteristic
324C2×SD16—24no—
325C2×SD16—44no—
326C2×D8—24no—
327C2×D8—44no—
328C22×C8—21no—
329C22×C8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4D4×C13911yescharacteristic
340C2×C4⋊C4D4×C13911yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348#102—24no—
349#102—24no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8D4×C13912yes—
353C22⋊C8D4×C13912yes—
354#95—22no—
355#95—22no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360C24—24no—
361C24—22no—
362C24—21no—
363C24—42no—
364C24—42no—
365C24—42no—
366C24—41no—
367C24—41no—
368C24—42no—
369C24—42no—
370C24C2×D4×C13911yescharacteristic
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—42no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—41no—
392C2×D4—41no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—42no—
407C22×C4C2×D4×C13911yescharacteristic
408C22×C4C2×D4×C13911yescharacteristic
409C22×C4C2×D4×C13911yescharacteristic
410C22×C4C2×D4×C13911yescharacteristic
411C22×C4C2×D4×C13911yescharacteristic
412C22×C4#41×C13911yescharacteristic
413SD16—48no—
414D8—48no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—42no—
418C2×C8—42no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C22⋊C4—416no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—82no—
431C22⋊C4—82no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—24no—
436C23—44no—
437C23—44no—
438C23—42no—
439C23—44no—
440C23—44no—
441C23—44no—
442C23—44no—
443C23—44no—
444C23—44no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—42no—
450C23—41no—
451C23—82no—
452C23—82no—
453C23—82no—
454C23—82no—
455C23—82no—
456C23—82no—
457C23—81no—
458C23—81no—
459C23—81no—
460C23—81no—
461C23#120×C13911yescharacteristic
462C23#121×C13911yescharacteristic
463C23#127×C13911yescharacteristic
464C23#135×C13912yes—
465C23AGL(1,ℤ/8)×C13912yes—
466Q8—42no—
467Q8—81no—
468D4—24no—
469D4—24no—
470D4—42no—
471D4—42no—
472D4—44no—
473D4—44no—
474D4—42no—
475D4—81no—
476D4—82no—
477D4—81no—
478D4—81no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—81no—
499C2×C4—82no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4#120×C13911yescharacteristic
503C2×C4#120×C13911yescharacteristic
504C2×C4#121×C13911yescharacteristic
505C2×C4#121×C13911yescharacteristic
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—48no—
517C22—44no—
518C22—84no—
519C22—84no—
520C22—84no—
521C22—82no—
522C22—82no—
523C22—84no—
524C22—84no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—82no—
529C22—82no—
530C22#392×C13911yescharacteristic
531C22#449×C13912yes—
532C22#453×C13911yescharacteristic
533C22#454×C13911yescharacteristic
534C22B(4,𝔽2)×C13912yes—
535C22#463×C13912yes—
536C22#495×C13911yescharacteristic
537C22#496×C13911yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—82no—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—84no—
551C2—161no—
552C2#1597×C13912yes—
553C2#1600×C13912yes—
554C2#2006×C13911yescharacteristic
555C2#2012×C13911yescharacteristic
556C2#2021×C13911yescharacteristic
subgroupG/H
center, socleC23×C139#120
commutator, Frattini, cosocleC23×C4C23×C139
prime radicalC2×#447×C139C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#450×C139C2semidirect
3. #2639×C139C2semidirect
4. C2×#328×C139C2semidirect
5. C2×#327×C139C2semidirect
6. #1438×C139C2semidirect
7. #1280×C139C2semidirect
278. #9963C139direct (N × H)
279. C139#9963direct (N × H)
280. C2×#450C2×C139semidirect
282. #2639C2×C139semidirect
283. C2×#328C2×C139semidirect
284. C2×#327C2×C139semidirect
285. #1438C2×C139semidirect
286. #1280C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1392
C2×#447×C1392
#2639×C1392
C2×#328×C1392
C2×#327×C1392
#1438×C1392
#1280×C1392
#9963139