Finite Group Databasebeta

← C139×#9239 #48003835

Subgroups — C139×#9239 #48003835

Order 35584.

686 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C139C211yesmaximal, characteristic
2#2880×C139C211yesmaximal, characteristic
3#1789×C139C211yesmaximal, characteristic
4#1508×C139C211yesmaximal, characteristic, complemented
5#1472×C139C211yesmaximal, characteristic, complemented
6#1293×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C22×#41×C139C2211yescharacteristic
9C22×Q16×C139C411yescharacteristic, complemented
10C22×SD16×C139C411yescharacteristic, complemented
11C2×#131×C139—21no—
12C2×C22⋊Q8×C139C2211yescharacteristic
13#452×C139—21no—
14#452×C139—21no—
15#452×C139—21no—
16#452×C139—21no—
17C2×#104×C139—21no—
18C2×#104×C139—21no—
19C2×#103×C139C411yescharacteristic, complemented
20C2×#102×C139C411yescharacteristic, complemented
21#408×C139—21no—
22#408×C139—22no—
23#407×C139—21no—
24#407×C139C2211yescharacteristic
25#407×C139C2211yescharacteristic
26C2×C22⋊C8×C139—21no—
27C2×C22⋊C8×C139C2211yescharacteristic
28C2×C22⋊C8×C139C2211yescharacteristic
29C4×C22⋊C4×C139C2211yescharacteristic
30#328×C139—22no—
31#324×C139—21no—
32#324×C139—21no—
33C2×#41×C139—21no—
34C2×#41×C139—21no—
35C2×#41×C139—42no—
36C2×#41×C139—42no—
37C2×#41×C139D411yescharacteristic
38C2×#41×C139D411yescharacteristic
39C2×#41×C139D411yescharacteristic
40C2×#41×C139D411yescharacteristic
41C22×Q8×C139C2×C411yescharacteristic
42C22×Q8×C139C2×C411yescharacteristic
43C22×D4×C139—21no—
44C22×D4×C139C2×C411yescharacteristic
45C23×C4×C139—21no—
46C23×C4×C139C2311yescharacteristic
47C2×Q16×C139—21no—
48C2×Q16×C139—21no—
49C2×Q16×C139—42no—
50C2×SD16×C139—21no—
51C2×SD16×C139—21no—
52C2×SD16×C139—42no—
53#131×C139—42no—
54#131×C139—42no—
55C2×M16×C139—22no—
56C2×M16×C139—21no—
57C2×M16×C139—21no—
58C22×C8×C139—22no—
59C22×C8×C139—21no—
60C22×C8×C139C2×C411yescharacteristic
61C22×C8×C139C2×C411yescharacteristic
62C22⋊Q8×C139—21no—
63C22⋊Q8×C139—21no—
64C22⋊Q8×C139—21no—
65C22⋊Q8×C139—21no—
66C2×C4⋊C4×C139—21no—
67C2×C4⋊C4×C139C2×C411yescharacteristic
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C42×C139—21no—
71#104×C139—42no—
72#104×C139—42no—
73#103×C139—21no—
74#103×C139—21no—
75#102×C139—21no—
76#102×C139—21no—
77C22⋊C8×C139—22no—
78C22⋊C8×C139—22no—
79C22⋊C8×C139—21no—
80C22⋊C8×C139—21no—
81C22⋊C8×C139—21no—
82C22⋊C8×C139—21no—
83C22⋊C8×C139—21no—
84C22⋊C8×C139—21no—
85C22⋊C8×C139D411yescharacteristic
86C22⋊C8×C139D411yescharacteristic
87C22⋊C8×C139D412yes—
88#95×C139—21no—
89C24×C139—21no—
90C24×C139#4111yescharacteristic
91#41×C139—22no—
92#41×C139—22no—
93#41×C139—22no—
94#41×C139—22no—
95#41×C139—41no—
96#41×C139—41no—
97#41×C139—41no—
98#41×C139—41no—
99#41×C139—44no—
100#41×C139—44no—
101C2×Q8×C139—21no—
102C2×Q8×C139—22no—
103C2×Q8×C139—21no—
104C2×Q8×C139—21no—
105C2×Q8×C139—41no—
106C2×Q8×C139—41no—
107C2×Q8×C139—41no—
108C2×Q8×C139C22⋊C411yescharacteristic
109C2×Q8×C139C22⋊C411yescharacteristic
110C2×D4×C139—21no—
111C2×D4×C139—22no—
112C2×D4×C139—21no—
113C2×D4×C139—21no—
114C2×D4×C139—21no—
115C2×D4×C139—21no—
116C2×D4×C139—41no—
117C2×D4×C139—44no—
118C2×D4×C139C22⋊C411yescharacteristic
119C2×D4×C139C22⋊C411yescharacteristic
120C22×C4×C139—21no—
121C22×C4×C139—21no—
122C22×C4×C139—21no—
123C22×C4×C139—21no—
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—41no—
128C22×C4×C139—41no—
129C22×C4×C139—44no—
130C22×C4×C139—41no—
131C22×C4×C139C22×C411yescharacteristic
132C22×C4×C139C2×D411yescharacteristic
133C22×C4×C139C2×D411yescharacteristic
134C22×C4×C139C2×D411yescharacteristic
135C22×C4×C139C2×D411yescharacteristic
136C22×C4×C139#4111yescharacteristic
137Q16×C139—42no—
138Q16×C139—42no—
139SD16×C139—42no—
140SD16×C139—42no—
141M16×C139—44no—
142M16×C139—41no—
143M16×C139—41no—
144M16×C139—41no—
145M16×C139—41no—
146C2×C8×C139—21no—
147C2×C8×C139—21no—
148C2×C8×C139—21no—
149C2×C8×C139—22no—
150C2×C8×C139—21no—
151C2×C8×C139—44no—
152C2×C8×C139—41no—
153C2×C8×C139—41no—
154C2×C8×C139—41no—
155C2×C8×C139—41no—
156C2×C8×C139—41no—
157C4⋊C4×C139—21no—
158C4⋊C4×C139—21no—
159C4⋊C4×C139—41no—
160C4⋊C4×C139—41no—
161C22⋊C4×C139—22no—
162C22⋊C4×C139—41no—
163C22⋊C4×C139—41no—
164C22⋊C4×C139—41no—
165C42×C139—41no—
166C42×C139—41no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—41no—
172C23×C139—41no—
173C23×C139—42no—
174C23×C139—41no—
175C23×C139—41no—
176C23×C139—81no—
177C23×C139C4×D411yescharacteristic
178C23×C139#12111yescharacteristic
179C23×C139#12311yescharacteristic
180Q8×C139—21no—
181Q8×C139—21no—
182Q8×C139—21no—
183Q8×C139—42no—
184Q8×C139—41no—
185Q8×C139—41no—
186Q8×C139—81no—
187Q8×C139#9912yes—
188D4×C139—24no—
189D4×C139—21no—
190D4×C139—21no—
191D4×C139—21no—
192D4×C139—42no—
193D4×C139—42no—
194D4×C139—42no—
195D4×C139—42no—
196D4×C139#9912yes—
197C2×C4×C139—24no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—21no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—21no—
206C2×C4×C139—41no—
207C2×C4×C139—41no—
208C2×C4×C139—41no—
209C2×C4×C139—42no—
210C2×C4×C139—42no—
211C2×C4×C139—42no—
212C2×C4×C139—42no—
213C2×C4×C139—42no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—41no—
217C2×C4×C139—41no—
218C2×C4×C139—81no—
219C2×C4×C139—81no—
220C2×C4×C139—81no—
221C2×C4×C139C2×C22⋊C411yescharacteristic
222C2×C4×C139C4×D411yescharacteristic
223C2×C4×C139#12011yescharacteristic
224C2×C4×C139#12111yescharacteristic
225C8×C139—41no—
226C8×C139—42no—
227C8×C139—41no—
228C8×C139—41no—
229C8×C139—41no—
230C8×C139—81no—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—21no—
235C22×C139—21no—
236C22×C139—21no—
237C22×C139—22no—
238C22×C139—21no—
239C22×C139—21no—
240C22×C139—41no—
241C22×C139—41no—
242C22×C139—41no—
243C22×C139—41no—
244C22×C139—41no—
245C22×C139—81no—
246C22×C139—81no—
247C22×C139—82no—
248C22×C139—82no—
249C22×C139#38611yescharacteristic
250C22×C139#44311yescharacteristic
251C22×C139#44411yescharacteristic
252C4×C139—21no—
253C4×C139—21no—
254C4×C139—22no—
255C4×C139—21no—
256C4×C139—41no—
257C4×C139—82no—
258C4×C139—81no—
259C4×C139—81no—
260C4×C139C2×#9911yescharacteristic
261C4×C139C2×#9911yescharacteristic
262C2×C139—21no—
263C2×C139—21no—
264C2×C139—41no—
265C2×C139—41no—
266C2×C139—42no—
267C2×C139—81no—
268C2×C139#187611yescharacteristic
269C2×C139#189811yescharacteristic
270C2×C139#190211yescharacteristic
271#9239C13911yesmaximal, characteristic, direct product factor, Sylow
272C139#923911yescharacteristic, direct product factor, Sylow
273C2×#452C2×C13911yescharacteristic
274#2880C2×C13911yescharacteristic
275#1789C2×C13911yescharacteristic
276#1508C2×C13911yescharacteristic, complemented
277#1472C2×C13911yescharacteristic, complemented
278#1293C2×C13911yescharacteristic, complemented
279#1282C2×C13911yescharacteristic, complemented
280C22×#41C22×C13911yescharacteristic
281C22×Q16C4×C13911yescharacteristic, complemented
282C22×SD16C4×C13911yescharacteristic, complemented
283C2×#131—21no—
284C2×C22⋊Q8C22×C13911yescharacteristic
285#452—21no—
286#452—21no—
287#452—21no—
288#452—21no—
289C2×#104—21no—
290C2×#104—21no—
291C2×#103C4×C13911yescharacteristic, complemented
292C2×#102C4×C13911yescharacteristic, complemented
293#408—21no—
294#408—22no—
295#407—21no—
296#407C22×C13911yescharacteristic
297#407C22×C13911yescharacteristic
298C2×C22⋊C8—21no—
299C2×C22⋊C8C22×C13911yescharacteristic
300C2×C22⋊C8C22×C13911yescharacteristic
301C4×C22⋊C4C22×C13911yescharacteristic
302#328—22no—
303#324—21no—
304#324—21no—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—42no—
308C2×#41—42no—
309C2×#41D4×C13911yescharacteristic
310C2×#41D4×C13911yescharacteristic
311C2×#41D4×C13911yescharacteristic
312C2×#41D4×C13911yescharacteristic
313C22×Q8C2×C4×C13911yescharacteristic
314C22×Q8C2×C4×C13911yescharacteristic
315C22×D4—21no—
316C22×D4C2×C4×C13911yescharacteristic
317C23×C4—21no—
318C23×C4C23×C13911yescharacteristic
319C2×Q16—21no—
320C2×Q16—21no—
321C2×Q16—42no—
322C2×SD16—21no—
323C2×SD16—21no—
324C2×SD16—42no—
325#131—42no—
326#131—42no—
327C2×M16—22no—
328C2×M16—21no—
329C2×M16—21no—
330C22×C8—22no—
331C22×C8—21no—
332C22×C8C2×C4×C13911yescharacteristic
333C22×C8C2×C4×C13911yescharacteristic
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4C2×C4×C13911yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C42—21no—
343#104—42no—
344#104—42no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8D4×C13911yescharacteristic
358C22⋊C8D4×C13911yescharacteristic
359C22⋊C8D4×C13912yes—
360#95—21no—
361C24—21no—
362C24#41×C13911yescharacteristic
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—41no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—44no—
372#41—44no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8C22⋊C4×C13911yescharacteristic
381C2×Q8C22⋊C4×C13911yescharacteristic
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4C22⋊C4×C13911yescharacteristic
391C2×D4C22⋊C4×C13911yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—44no—
402C22×C4—41no—
403C22×C4C22×C4×C13911yescharacteristic
404C22×C4C2×D4×C13911yescharacteristic
405C22×C4C2×D4×C13911yescharacteristic
406C22×C4C2×D4×C13911yescharacteristic
407C22×C4C2×D4×C13911yescharacteristic
408C22×C4#41×C13911yescharacteristic
409Q16—42no—
410Q16—42no—
411SD16—42no—
412SD16—42no—
413M16—44no—
414M16—41no—
415M16—41no—
416M16—41no—
417M16—41no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—21no—
423C2×C8—44no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C42—41no—
438C42—41no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—81no—
449C23C4×D4×C13911yescharacteristic
450C23#121×C13911yescharacteristic
451C23#123×C13911yescharacteristic
452Q8—21no—
453Q8—21no—
454Q8—21no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—81no—
459Q8#99×C13912yes—
460D4—24no—
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4#99×C13912yes—
469C2×C4—24no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4C2×C22⋊C4×C13911yescharacteristic
494C2×C4C4×D4×C13911yescharacteristic
495C2×C4#120×C13911yescharacteristic
496C2×C4#121×C13911yescharacteristic
497C8—41no—
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—81no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—81no—
518C22—81no—
519C22—82no—
520C22—82no—
521C22#386×C13911yescharacteristic
522C22#443×C13911yescharacteristic
523C22#444×C13911yescharacteristic
524C4—21no—
525C4—21no—
526C4—22no—
527C4—21no—
528C4—41no—
529C4—82no—
530C4—81no—
531C4—81no—
532C4C2×#99×C13911yescharacteristic
533C4C2×#99×C13911yescharacteristic
534C2—21no—
535C2—21no—
536C2—41no—
537C2—41no—
538C2—42no—
539C2—81no—
540C2#1876×C13911yescharacteristic
541C2#1898×C13911yescharacteristic
542C2#1902×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC22×#41×C139C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1508×C139C2semidirect
5. #1472×C139C2semidirect
6. #1293×C139C2semidirect
7. #1282×C139C2semidirect
9. C22×Q16×C139C4semidirect
10. C22×SD16×C139C4semidirect
19. C2×#103×C139C4semidirect
20. C2×#102×C139C4semidirect
271. #9239C139direct (N × H)
272. C139#9239direct (N × H)
276. #1508C2×C139semidirect
277. #1472C2×C139semidirect
278. #1293C2×C139semidirect
279. #1282C2×C139semidirect
281. C22×Q16C4×C139semidirect
282. C22×SD16C4×C139semidirect
291. C2×#103C4×C139semidirect
292. C2×#102C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C1392
#2880×C1392
#1789×C1392
#1508×C1392
#1472×C1392
#1293×C1392
#1282×C1392
#9239139