Finite Group Databasebeta

← C139×#9241 #48003837

Subgroups — C139×#9241 #48003837

Order 35584.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C139C211yesmaximal, characteristic
2#2880×C139C211yesmaximal, characteristic, complemented
3#1789×C139C211yesmaximal, characteristic, complemented
4#1507×C139C211yesmaximal, characteristic, complemented
5#1471×C139C211yesmaximal, characteristic, complemented
6#1293×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C22×#41×C139C2211yescharacteristic
9C22×SD16×C139C411yescharacteristic, complemented
10C22×D8×C139C411yescharacteristic, complemented
11C2×#131×C139—21no—
12C2×#121×C139C2211yescharacteristic
13#449×C139—21no—
14#449×C139—21no—
15#449×C139—21no—
16#449×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#327×C139—22no—
31#323×C139—21no—
32#323×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×D4×C139—21no—
43C22×D4×C139—21no—
44C22×D4×C139C2×C411yescharacteristic
45C22×D4×C139C2×C411yescharacteristic
46C23×C4×C139—21no—
47C23×C4×C139C2311yescharacteristic
48C2×SD16×C139—21no—
49C2×SD16×C139—21no—
50C2×SD16×C139—42no—
51C2×D8×C139—21no—
52C2×D8×C139—21no—
53C2×D8×C139—42no—
54#131×C139—42no—
55#131×C139—42no—
56C2×M16×C139—22no—
57C2×M16×C139—21no—
58C2×M16×C139—21no—
59C22×C8×C139—22no—
60C22×C8×C139—21no—
61C22×C8×C139C2×C411yescharacteristic
62C22×C8×C139C2×C411yescharacteristic
63#121×C139—21no—
64#121×C139—21no—
65#121×C139—21no—
66#121×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—21no—
91C24×C139#4111yescharacteristic
92#41×C139—22no—
93#41×C139—22no—
94#41×C139—22no—
95#41×C139—22no—
96#41×C139—41no—
97#41×C139—41no—
98#41×C139—41no—
99#41×C139—41no—
100#41×C139—44no—
101#41×C139—44no—
102C2×Q8×C139—21no—
103C2×Q8×C139—22no—
104C2×Q8×C139—41no—
105C2×Q8×C139C22⋊C411yescharacteristic
106C2×Q8×C139C22⋊C411yescharacteristic
107C2×D4×C139—21no—
108C2×D4×C139—22no—
109C2×D4×C139—21no—
110C2×D4×C139—21no—
111C2×D4×C139—21no—
112C2×D4×C139—21no—
113C2×D4×C139—21no—
114C2×D4×C139—21no—
115C2×D4×C139—41no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—44no—
119C2×D4×C139—41no—
120C2×D4×C139—41no—
121C2×D4×C139—82no—
122C2×D4×C139C22⋊C411yescharacteristic
123C2×D4×C139C22⋊C411yescharacteristic
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—41no—
131C22×C4×C139—41no—
132C22×C4×C139—44no—
133C22×C4×C139—41no—
134C22×C4×C139C22×C411yescharacteristic
135C22×C4×C139C2×D411yescharacteristic
136C22×C4×C139C2×D411yescharacteristic
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139#4111yescharacteristic
140SD16×C139—42no—
141SD16×C139—42no—
142D8×C139—42no—
143D8×C139—42no—
144M16×C139—44no—
145M16×C139—41no—
146M16×C139—41no—
147M16×C139—41no—
148M16×C139—41no—
149C2×C8×C139—21no—
150C2×C8×C139—21no—
151C2×C8×C139—21no—
152C2×C8×C139—22no—
153C2×C8×C139—21no—
154C2×C8×C139—44no—
155C2×C8×C139—41no—
156C2×C8×C139—41no—
157C2×C8×C139—41no—
158C2×C8×C139—41no—
159C2×C8×C139—41no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—21no—
162C22⋊C4×C139—22no—
163C22⋊C4×C139—41no—
164C22⋊C4×C139—41no—
165C22⋊C4×C139—41no—
166C42×C139—41no—
167C42×C139—41no—
168C23×C139—21no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—21no—
172C23×C139—41no—
173C23×C139—41no—
174C23×C139—42no—
175C23×C139—41no—
176C23×C139—41no—
177C23×C139—41no—
178C23×C139—41no—
179C23×C139—41no—
180C23×C139—81no—
181C23×C139—81no—
182C23×C139—81no—
183C23×C139C4×D411yescharacteristic
184C23×C139#12111yescharacteristic
185C23×C139#12311yescharacteristic
186Q8×C139—21no—
187Q8×C139—21no—
188Q8×C139—21no—
189Q8×C139—42no—
190Q8×C139#9912yes—
191D4×C139—24no—
192D4×C139—21no—
193D4×C139—21no—
194D4×C139—21no—
195D4×C139—42no—
196D4×C139—42no—
197D4×C139—42no—
198D4×C139—42no—
199D4×C139—41no—
200D4×C139—41no—
201D4×C139—81no—
202D4×C139—82no—
203D4×C139—82no—
204D4×C139#9912yes—
205C2×C4×C139—24no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—41no—
217C2×C4×C139—42no—
218C2×C4×C139—42no—
219C2×C4×C139—42no—
220C2×C4×C139—42no—
221C2×C4×C139—42no—
222C2×C4×C139—41no—
223C2×C4×C139—81no—
224C2×C4×C139—81no—
225C2×C4×C139—81no—
226C2×C4×C139C2×C22⋊C411yescharacteristic
227C2×C4×C139C4×D411yescharacteristic
228C2×C4×C139#12011yescharacteristic
229C2×C4×C139#12111yescharacteristic
230C8×C139—41no—
231C8×C139—42no—
232C8×C139—41no—
233C8×C139—41no—
234C8×C139—41no—
235C8×C139—81no—
236C22×C139—21no—
237C22×C139—21no—
238C22×C139—21no—
239C22×C139—21no—
240C22×C139—21no—
241C22×C139—21no—
242C22×C139—22no—
243C22×C139—21no—
244C22×C139—21no—
245C22×C139—41no—
246C22×C139—41no—
247C22×C139—41no—
248C22×C139—41no—
249C22×C139—41no—
250C22×C139—81no—
251C22×C139—81no—
252C22×C139—82no—
253C22×C139—82no—
254C22×C139—81no—
255C22×C139—81no—
256C22×C139—81no—
257C22×C139—161no—
258C22×C139—161no—
259C22×C139#38611yescharacteristic
260C22×C139#44311yescharacteristic
261C22×C139#44411yescharacteristic
262C4×C139—21no—
263C4×C139—21no—
264C4×C139—22no—
265C4×C139—21no—
266C4×C139—41no—
267C4×C139—82no—
268C4×C139—81no—
269C4×C139C2×#9911yescharacteristic
270C4×C139C2×#9911yescharacteristic
271C2×C139—21no—
272C2×C139—21no—
273C2×C139—41no—
274C2×C139—41no—
275C2×C139—42no—
276C2×C139—81no—
277C2×C139—161no—
278C2×C139#187611yescharacteristic
279C2×C139#189811yescharacteristic
280C2×C139#190311yescharacteristic
281#9241C13911yesmaximal, characteristic, direct product factor, Sylow
282C139#924111yescharacteristic, direct product factor, Sylow
283C2×#449C2×C13911yescharacteristic
284#2880C2×C13911yescharacteristic, complemented
285#1789C2×C13911yescharacteristic, complemented
286#1507C2×C13911yescharacteristic, complemented
287#1471C2×C13911yescharacteristic, complemented
288#1293C2×C13911yescharacteristic, complemented
289#1282C2×C13911yescharacteristic, complemented
290C22×#41C22×C13911yescharacteristic
291C22×SD16C4×C13911yescharacteristic, complemented
292C22×D8C4×C13911yescharacteristic, complemented
293C2×#131—21no—
294C2×#121C22×C13911yescharacteristic
295#449—21no—
296#449—21no—
297#449—21no—
298#449—21no—
299C2×#104—21no—
300C2×#104—21no—
301C2×#103C4×C13911yescharacteristic, complemented
302C2×#102C4×C13911yescharacteristic, complemented
303#408—21no—
304#408—22no—
305#407—21no—
306#407C22×C13911yescharacteristic
307#407C22×C13911yescharacteristic
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C13911yescharacteristic
310C2×C22⋊C8C22×C13911yescharacteristic
311C4×C22⋊C4C22×C13911yescharacteristic
312#327—22no—
313#323—21no—
314#323—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C13911yescharacteristic
320C2×#41D4×C13911yescharacteristic
321C2×#41D4×C13911yescharacteristic
322C2×#41D4×C13911yescharacteristic
323C22×Q8C2×C4×C13911yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C13911yescharacteristic
327C22×D4C2×C4×C13911yescharacteristic
328C23×C4—21no—
329C23×C4C23×C13911yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C13911yescharacteristic
344C22×C8C2×C4×C13911yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C13911yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C13911yescharacteristic
368C22⋊C8D4×C13911yescharacteristic
369C22⋊C8D4×C13912yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C13911yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C13911yescharacteristic
388C2×Q8C22⋊C4×C13911yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C13911yescharacteristic
405C2×D4C22⋊C4×C13911yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C13911yescharacteristic
417C22×C4C2×D4×C13911yescharacteristic
418C22×C4C2×D4×C13911yescharacteristic
419C22×C4C2×D4×C13911yescharacteristic
420C22×C4C2×D4×C13911yescharacteristic
421C22×C4#41×C13911yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C13911yescharacteristic
466C23#121×C13911yescharacteristic
467C23#123×C13911yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C13912yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C13912yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C13911yescharacteristic
509C2×C4C4×D4×C13911yescharacteristic
510C2×C4#120×C13911yescharacteristic
511C2×C4#121×C13911yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#386×C13911yescharacteristic
542C22#443×C13911yescharacteristic
543C22#444×C13911yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C13911yescharacteristic
552C4C2×#99×C13911yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2#1876×C13911yescharacteristic
561C2#1898×C13911yescharacteristic
562C2#1903×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#449×C139C2
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
2. #2880×C139C2semidirect
3. #1789×C139C2semidirect
4. #1507×C139C2semidirect
5. #1471×C139C2semidirect
6. #1293×C139C2semidirect
7. #1282×C139C2semidirect
9. C22×SD16×C139C4semidirect
10. C22×D8×C139C4semidirect
19. C2×#103×C139C4semidirect
20. C2×#102×C139C4semidirect
281. #9241C139direct (N × H)
282. C139#9241direct (N × H)
284. #2880C2×C139semidirect
285. #1789C2×C139semidirect
286. #1507C2×C139semidirect
287. #1471C2×C139semidirect
288. #1293C2×C139semidirect
289. #1282C2×C139semidirect
291. C22×SD16C4×C139semidirect
292. C22×D8C4×C139semidirect
301. C2×#103C4×C139semidirect
302. C2×#102C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1392
#2880×C1392
#1789×C1392
#1507×C1392
#1471×C1392
#1293×C1392
#1282×C1392
#9241139