Finite Group Databasebeta

← C139×#33540 #48028136

Subgroups — C139×#33540 #48028136

Order 35584.

1078 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×#578×C139C211yesmaximal, characteristic, complemented
2#3414×C139C211yesmaximal, characteristic, complemented
3C2×#510×C139C211yesmaximal, characteristic, complemented
4#3067×C139C211yesmaximal, characteristic, complemented
5#2195×C139C214yesmaximal, complemented
6#2193×C139C214yesmaximal, complemented
7C2×#362×C139C211yesmaximal, characteristic, complemented
8#2143×C139C211yesmaximal, characteristic, complemented
9#2117×C139C211yesmaximal, characteristic, complemented
10C2×2−1+4×C139—21no—
11#578×C139—22no—
12#578×C139—22no—
13#578×C139—22no—
14#578×C139C2214yes—
15#575×C139—21no—
16C2×#137×C139—22no—
17C2×#137×C139—21no—
18C2×#135×C139—21no—
19C2×#135×C139C2211yescharacteristic
20C2×#135×C139C2211yescharacteristic
21C22×Q16×C139—21no—
22C22×Q16×C139C2211yescharacteristic
23C2×#131×C139C2211yescharacteristic
24#510×C139—22no—
25#510×C139—22no—
26#510×C139—21no—
27#510×C139C2212yescomplemented
28#509×C139—21no—
29#509×C139C2212yescomplemented
30#508×C139—22no—
31C2×Q32×C139C2212yescomplemented
32C2×SD32×C139C2212yescomplemented
33C2×M32×C139C2211yescharacteristic
34C2×M32×C139C2211yescharacteristic
35#473×C139C2212yescomplemented
36#472×C139C2212yescomplemented
37#471×C139—22no—
38C2×#108×C139C2211yescharacteristic
39#413×C139—21no—
40#362×C139C2214yescomplemented
41#359×C139C2214yescomplemented
42#350×C139C2214yescomplemented
432−1+4×C139—24no—
442−1+4×C139—24no—
452−1+4×C139—42no—
462−1+4×C139—42no—
47C2×#41×C139—22no—
48C2×#41×C139—21no—
49C2×#41×C139—21no—
50C2×#41×C139—42no—
51C2×#41×C139—41no—
52C2×#41×C139D411yescharacteristic
53C22×Q8×C139—22no—
54C22×Q8×C139—21no—
55C22×Q8×C139—41no—
56#137×C139—24no—
57#137×C139—28no—
58#137×C139—28no—
59#137×C139—22no—
60#137×C139—24no—
61#137×C139—41no—
62AGL(1,ℤ/8)×C139—22no—
63AGL(1,ℤ/8)×C139—41no—
64#135×C139—24no—
65#135×C139—24no—
66#135×C139—21no—
67#135×C139—21no—
68#135×C139—21no—
69#135×C139—21no—
70#135×C139—21no—
71#135×C139—21no—
72#135×C139—42no—
73#135×C139D412yes—
74#135×C139C2312yes—
75C2×Q16×C139—22no—
76C2×Q16×C139—24no—
77C2×Q16×C139—24no—
78C2×Q16×C139—21no—
79C2×Q16×C139—21no—
80C2×Q16×C139—21no—
81C2×Q16×C139D411yescharacteristic
82C2×Q16×C139D412yes—
83C2×Q16×C139D412yes—
84C2×Q16×C139C2311yescharacteristic
85C2×Q16×C139C2312yes—
86C2×SD16×C139—22no—
87C2×SD16×C139—21no—
88C2×SD16×C139—21no—
89C2×D8×C139D411yescharacteristic
90C2×D8×C139C2311yescharacteristic
91#131×C139—21no—
92#131×C139—21no—
93#131×C139D412yes—
94#131×C139C2312yes—
95C2×M16×C139—21no—
96C2×M16×C139—21no—
97C2×M16×C139D411yescharacteristic
98C22×C8×C139—21no—
99C22×C8×C139C2311yescharacteristic
100Q32×C139—24no—
101Q32×C139—22no—
102SD32×C139—24no—
103SD32×C139—22no—
104SD32×C139—22no—
105D16×C139—22no—
106M32×C139—21no—
107M32×C139—21no—
108M32×C139—21no—
109M32×C139C2312yes—
110C2×C16×C139—21no—
111C2×C16×C139C2312yes—
112#108×C139—21no—
113#108×C139C2312yes—
114#101×C139—22no—
115#100×C139—22no—
116#41×C139—21no—
117#41×C139—21no—
118#41×C139—28no—
119#41×C139—22no—
120#41×C139—22no—
121#41×C139—44no—
122#41×C139—48no—
123#41×C139—48no—
124#41×C139—44no—
125#41×C139—44no—
126#41×C139—41no—
127#41×C139—41no—
128#41×C139—41no—
129#41×C139—41no—
130#41×C139—41no—
131#41×C139—41no—
132#41×C139D812yes—
133#41×C139C2×D412yes—
134C2×Q8×C139—28no—
135C2×Q8×C139—22no—
136C2×Q8×C139—21no—
137C2×Q8×C139—22no—
138C2×Q8×C139—22no—
139C2×Q8×C139—21no—
140C2×Q8×C139—42no—
141C2×Q8×C139—44no—
142C2×Q8×C139—44no—
143C2×Q8×C139—44no—
144C2×Q8×C139—41no—
145C2×Q8×C139—41no—
146C2×Q8×C139—41no—
147C2×Q8×C139D811yescharacteristic
148C2×D4×C139—21no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—42no—
152C2×D4×C139—41no—
153C2×D4×C139—41no—
154C2×D4×C139D811yescharacteristic
155C22×C4×C139—21no—
156C22×C4×C139—42no—
157C22×C4×C139—42no—
158C22×C4×C139—41no—
159C22×C4×C139—41no—
160C22×C4×C139—41no—
161C22×C4×C139C2×D411yescharacteristic
162Q16×C139—28no—
163Q16×C139—21no—
164Q16×C139—22no—
165Q16×C139—22no—
166Q16×C139—22no—
167Q16×C139—21no—
168Q16×C139—21no—
169Q16×C139—42no—
170Q16×C139C2×D412yes—
171Q16×C139C2×D414yes—
172SD16×C139—28no—
173SD16×C139—22no—
174SD16×C139—22no—
175SD16×C139—42no—
176SD16×C139—42no—
177SD16×C139—41no—
178SD16×C139—41no—
179D8×C139—21no—
180D8×C139—21no—
181D8×C139—21no—
182D8×C139—42no—
183D8×C139C2×D412yes—
184M16×C139—21no—
185M16×C139—22no—
186M16×C139—22no—
187M16×C139—22no—
188M16×C139—41no—
189M16×C139C2×D412yes—
190C2×C8×C139—21no—
191C2×C8×C139—22no—
192C2×C8×C139—22no—
193C2×C8×C139—41no—
194C2×C8×C139C2×D411yescharacteristic
195C2×C8×C139C2×D411yescharacteristic
196C2×C8×C139C2×D411yescharacteristic
197C2×C8×C139C2×D411yescharacteristic
198C2×C8×C139C2×D411yescharacteristic
199C2×C8×C139C2411yescharacteristic
200C16×C139—22no—
201C16×C139—22no—
202C23×C139—21no—
203C23×C139—41no—
204C23×C139—41no—
205C23×C139AGL(1,ℤ/8)11yescharacteristic
206Q8×C139—21no—
207Q8×C139—24no—
208Q8×C139—22no—
209Q8×C139—48no—
210Q8×C139—42no—
211Q8×C139—41no—
212Q8×C139—42no—
213Q8×C139—42no—
214Q8×C139—41no—
215Q8×C139—41no—
216Q8×C139C2×D812yes—
217D4×C139—22no—
218D4×C139—22no—
219D4×C139—22no—
220D4×C139—21no—
221D4×C139—48no—
222D4×C139—42no—
223D4×C139—42no—
224D4×C139—41no—
225D4×C139—41no—
226D4×C139—41no—
227D4×C139—81no—
228D4×C139—81no—
229D4×C139C2×D812yes—
230C2×C4×C139—21no—
231C2×C4×C139—22no—
232C2×C4×C139—22no—
233C2×C4×C139—48no—
234C2×C4×C139—48no—
235C2×C4×C139—42no—
236C2×C4×C139—42no—
237C2×C4×C139—41no—
238C2×C4×C139—42no—
239C2×C4×C139—42no—
240C2×C4×C139—42no—
241C2×C4×C139—41no—
242C2×C4×C139—81no—
243C2×C4×C139—81no—
244C2×C4×C139#12011yescharacteristic
245C2×C4×C139#12011yescharacteristic
246C2×C4×C139C2×D811yescharacteristic
247C2×C4×C139C2×D811yescharacteristic
248C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
249C2×C4×C139C22×D411yescharacteristic
250C8×C139—22no—
251C8×C139—42no—
252C8×C139#12011yescharacteristic
253C8×C139#12011yescharacteristic
254C8×C139C22×D411yescharacteristic
255C8×C139C22×D411yescharacteristic
256C22×C139—22no—
257C22×C139—41no—
258C22×C139—42no—
259C22×C139—42no—
260C22×C139—82no—
261C22×C139—81no—
262C22×C139—161no—
263C22×C139#44711yescharacteristic
264C22×C139#44711yescharacteristic
265C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
266C4×C139—22no—
267C4×C139—44no—
268C4×C139—42no—
269C4×C139—81no—
270C4×C139#44711yescharacteristic
271C4×C139#44711yescharacteristic
272C4×C139C2×#12011yescharacteristic
273C4×C139C22×D811yescharacteristic
274C2×C139—21no—
275C2×C139—21no—
276C2×C139—21no—
277C2×C139—42no—
278C2×C139—82no—
279C2×C139—161no—
280C2×C139C2×#44711yescharacteristic
281#33540C13911yesmaximal, characteristic, direct product factor, Sylow
282C139#3354011yescharacteristic, direct product factor, Sylow
283C2×#578C2×C13911yescharacteristic, complemented
284#3414C2×C13911yescharacteristic, complemented
285C2×#510C2×C13911yescharacteristic, complemented
286#3067C2×C13911yescharacteristic, complemented
287#2195C2×C13914yescomplemented
288#2193C2×C13914yescomplemented
289C2×#362C2×C13911yescharacteristic, complemented
290#2143C2×C13911yescharacteristic, complemented
291#2117C2×C13911yescharacteristic, complemented
292C2×2−1+4—21no—
293#578—22no—
294#578—22no—
295#578—22no—
296#578C22×C13914yes—
297#575—21no—
298C2×#137—22no—
299C2×#137—21no—
300C2×#135—21no—
301C2×#135C22×C13911yescharacteristic
302C2×#135C22×C13911yescharacteristic
303C22×Q16—21no—
304C22×Q16C22×C13911yescharacteristic
305C2×#131C22×C13911yescharacteristic
306#510—22no—
307#510—22no—
308#510—21no—
309#510C22×C13912yescomplemented
310#509—21no—
311#509C22×C13912yescomplemented
312#508—22no—
313C2×Q32C22×C13912yescomplemented
314C2×SD32C22×C13912yescomplemented
315C2×M32C22×C13911yescharacteristic
316C2×M32C22×C13911yescharacteristic
317#473C22×C13912yescomplemented
318#472C22×C13912yescomplemented
319#471—22no—
320C2×#108C22×C13911yescharacteristic
321#413—21no—
322#362C22×C13914yescomplemented
323#359C22×C13914yescomplemented
324#350C22×C13914yescomplemented
3252−1+4—24no—
3262−1+4—24no—
3272−1+4—42no—
3282−1+4—42no—
329C2×#41—22no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—42no—
333C2×#41—41no—
334C2×#41D4×C13911yescharacteristic
335C22×Q8—22no—
336C22×Q8—21no—
337C22×Q8—41no—
338#137—24no—
339#137—28no—
340#137—28no—
341#137—22no—
342#137—24no—
343#137—41no—
344AGL(1,ℤ/8)—22no—
345AGL(1,ℤ/8)—41no—
346#135—24no—
347#135—24no—
348#135—21no—
349#135—21no—
350#135—21no—
351#135—21no—
352#135—21no—
353#135—21no—
354#135—42no—
355#135D4×C13912yes—
356#135C23×C13912yes—
357C2×Q16—22no—
358C2×Q16—24no—
359C2×Q16—24no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16D4×C13911yescharacteristic
364C2×Q16D4×C13912yes—
365C2×Q16D4×C13912yes—
366C2×Q16C23×C13911yescharacteristic
367C2×Q16C23×C13912yes—
368C2×SD16—22no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8D4×C13911yescharacteristic
372C2×D8C23×C13911yescharacteristic
373#131—21no—
374#131—21no—
375#131D4×C13912yes—
376#131C23×C13912yes—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16D4×C13911yescharacteristic
380C22×C8—21no—
381C22×C8C23×C13911yescharacteristic
382Q32—24no—
383Q32—22no—
384SD32—24no—
385SD32—22no—
386SD32—22no—
387D16—22no—
388M32—21no—
389M32—21no—
390M32—21no—
391M32C23×C13912yes—
392C2×C16—21no—
393C2×C16C23×C13912yes—
394#108—21no—
395#108C23×C13912yes—
396#101—22no—
397#100—22no—
398#41—21no—
399#41—21no—
400#41—28no—
401#41—22no—
402#41—22no—
403#41—44no—
404#41—48no—
405#41—48no—
406#41—44no—
407#41—44no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41D8×C13912yes—
415#41C2×D4×C13912yes—
416C2×Q8—28no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—42no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8D8×C13911yescharacteristic
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4D8×C13911yescharacteristic
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C2×D4×C13911yescharacteristic
444Q16—28no—
445Q16—21no—
446Q16—22no—
447Q16—22no—
448Q16—22no—
449Q16—21no—
450Q16—21no—
451Q16—42no—
452Q16C2×D4×C13912yes—
453Q16C2×D4×C13914yes—
454SD16—28no—
455SD16—22no—
456SD16—22no—
457SD16—42no—
458SD16—42no—
459SD16—41no—
460SD16—41no—
461D8—21no—
462D8—21no—
463D8—21no—
464D8—42no—
465D8C2×D4×C13912yes—
466M16—21no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—41no—
471M16C2×D4×C13912yes—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8C2×D4×C13911yescharacteristic
477C2×C8C2×D4×C13911yescharacteristic
478C2×C8C2×D4×C13911yescharacteristic
479C2×C8C2×D4×C13911yescharacteristic
480C2×C8C2×D4×C13911yescharacteristic
481C2×C8C24×C13911yescharacteristic
482C16—22no—
483C16—22no—
484C23—21no—
485C23—41no—
486C23—41no—
487C23AGL(1,ℤ/8)×C13911yescharacteristic
488Q8—21no—
489Q8—24no—
490Q8—22no—
491Q8—48no—
492Q8—41no—
493Q8—42no—
494Q8—42no—
495Q8—42no—
496Q8—41no—
497Q8—41no—
498Q8C2×D8×C13912yes—
499D4—22no—
500D4—22no—
501D4—21no—
502D4—22no—
503D4—48no—
504D4—42no—
505D4—42no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—81no—
511D4C2×D8×C13912yes—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—48no—
516C2×C4—48no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4#120×C13911yescharacteristic
527C2×C4#120×C13911yescharacteristic
528C2×C4C2×D8×C13911yescharacteristic
529C2×C4C2×D8×C13911yescharacteristic
530C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
531C2×C4C22×D4×C13911yescharacteristic
532C8—22no—
533C8—42no—
534C8#120×C13911yescharacteristic
535C8#120×C13911yescharacteristic
536C8C22×D4×C13911yescharacteristic
537C8C22×D4×C13911yescharacteristic
538C22—22no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—82no—
543C22—81no—
544C22—161no—
545C22#447×C13911yescharacteristic
546C22#447×C13911yescharacteristic
547C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
548C4—22no—
549C4—44no—
550C4—42no—
551C4—81no—
552C4#447×C13911yescharacteristic
553C4#447×C13911yescharacteristic
554C4C2×#120×C13911yescharacteristic
555C4C22×D8×C13911yescharacteristic
556C2—21no—
557C2—21no—
558C2—21no—
559C2—42no—
560C2—82no—
561C2—161no—
562C2C2×#447×C13911yescharacteristic
subgroupG/H
center, socleC2×C139C2×#447
commutator, Frattini, cosocleC2×C8C24×C139
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ C2×#131×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#578×C139C2semidirect
2. #3414×C139C2semidirect
3. C2×#510×C139C2semidirect
4. #3067×C139C2semidirect
5. #2195×C139C2semidirect
6. #2193×C139C2semidirect
7. C2×#362×C139C2semidirect
8. #2143×C139C2semidirect
9. #2117×C139C2semidirect
27. #510×C139C22semidirect
29. #509×C139C22semidirect
31. C2×Q32×C139C22semidirect
32. C2×SD32×C139C22semidirect
35. #473×C139C22semidirect
36. #472×C139C22semidirect
40. #362×C139C22semidirect
41. #359×C139C22semidirect
42. #350×C139C22semidirect
281. #33540C139direct (N × H)
282. C139#33540direct (N × H)
283. C2×#578C2×C139semidirect
284. #3414C2×C139semidirect
285. C2×#510C2×C139semidirect
286. #3067C2×C139semidirect
287. #2195C2×C139semidirect
288. #2193C2×C139semidirect
289. C2×#362C2×C139semidirect
290. #2143C2×C139semidirect
291. #2117C2×C139semidirect
309. #510C22×C139semidirect
311. #509C22×C139semidirect
313. C2×Q32C22×C139semidirect
314. C2×SD32C22×C139semidirect
317. #473C22×C139semidirect
318. #472C22×C139semidirect
322. #362C22×C139semidirect
323. #359C22×C139semidirect
324. #350C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C1392
#3414×C1392
C2×#510×C1392
#3067×C1392
#2195×C1392
#2193×C1392
C2×#362×C1392
#2143×C1392
#2117×C1392
#33540139