Finite Group Databasebeta

← C139×#24808 #48019404

Subgroups — C139×#24808 #48019404

Order 35584.

820 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3069×C139C211yesmaximal, characteristic, complemented
2#3068×C139C211yesmaximal, characteristic
3C2×#471×C139C211yesmaximal, characteristic, complemented
4C2×#471×C139C211yesmaximal, characteristic, complemented
5#2955×C139C211yesmaximal, characteristic, complemented
6#2916×C139C211yesmaximal, characteristic, complemented
7#2070×C139C211yesmaximal, characteristic, complemented
8#2069×C139C211yesmaximal, characteristic, complemented
9#2049×C139C211yesmaximal, characteristic, complemented
10#2048×C139C211yesmaximal, characteristic, complemented
11#1977×C139C211yesmaximal, characteristic, complemented
12#1953×C139C211yesmaximal, characteristic, complemented
13#1903×C139C211yesmaximal, characteristic, complemented
14#1902×C139C211yesmaximal, characteristic, complemented
15#1813×C139C211yesmaximal, characteristic, complemented
16#575×C139C2211yescharacteristic
17C2×#137×C139C2211yescharacteristic
18C2×#137×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
21C22×SD16×C139C2211yescharacteristic
22#568×C139C2211yescharacteristic
23#568×C139C2211yescharacteristic
24C2×#131×C139C2211yescharacteristic
25C2×#131×C139C2211yescharacteristic
26#473×C139—22no—
27#472×C139—22no—
28#471×C139—22no—
29#471×C139—22no—
30#471×C139—22no—
31#471×C139—22no—
32#471×C139—22no—
33#471×C139—22no—
34#444×C139—22no—
35#443×C139—22no—
36#430×C139—22no—
37#430×C139C2211yescharacteristic
38#430×C139C2211yescharacteristic
39#430×C139C2211yescharacteristic
40#430×C139C2211yescharacteristic
41#430×C139C2211yescharacteristic
42C2×#108×C139—22no—
43C2×#108×C139C2211yescharacteristic
44C2×#108×C139C2211yescharacteristic
45C2×#108×C139C2211yescharacteristic
46#421×C139C2211yescharacteristic
47#421×C139C2211yescharacteristic
48#419×C139C2211yescharacteristic
49#418×C139C2211yescharacteristic
50#413×C139C2211yescharacteristic
51#413×C139C2211yescharacteristic
52C2×#101×C139C2211yescharacteristic
53C2×#101×C139C2211yescharacteristic
54C2×#101×C139C2211yescharacteristic
55C2×#100×C139C2211yescharacteristic
56C2×#100×C139C2211yescharacteristic
57C2×#100×C139C2211yescharacteristic
58#405×C139C2211yescharacteristic
59#344×C139C2211yescharacteristic
60#344×C139C2211yescharacteristic
61#338×C139C2211yescharacteristic
62#338×C139C2211yescharacteristic
63C2×#41×C139C2311yescharacteristic
64C2×#41×C139C2311yescharacteristic
65C22×Q8×C139C2311yescharacteristic
66C22×D4×C139C2311yescharacteristic
67#137×C139—21no—
68#137×C139—22no—
69#137×C139—22no—
70#137×C139—22no—
71#137×C139—41no—
72#137×C139D412yes—
73AGL(1,ℤ/8)×C139—21no—
74AGL(1,ℤ/8)×C139—22no—
75AGL(1,ℤ/8)×C139—22no—
76AGL(1,ℤ/8)×C139—22no—
77AGL(1,ℤ/8)×C139—41no—
78AGL(1,ℤ/8)×C139D412yes—
79#135×C139—22no—
80C2×Q16×C139—21no—
81C2×Q16×C139—21no—
82C2×SD16×C139—21no—
83C2×SD16×C139—21no—
84C2×SD16×C139—21no—
85C2×SD16×C139—21no—
86C2×SD16×C139—21no—
87C2×SD16×C139—21no—
88C2×SD16×C139—21no—
89C2×SD16×C139—21no—
90C2×SD16×C139—21no—
91C2×SD16×C139—21no—
92C2×D8×C139—21no—
93C2×D8×C139—21no—
94#131×C139—21no—
95#131×C139—21no—
96#131×C139—22no—
97#131×C139—22no—
98#131×C139—21no—
99#131×C139—21no—
100#131×C139—21no—
101#131×C139—21no—
102#131×C139—41no—
103#131×C139—41no—
104#131×C139D412yes—
105#131×C139D412yes—
106C2×M16×C139—21no—
107C2×M16×C139—21no—
108C2×M16×C139—22no—
109C2×M16×C139—22no—
110C2×M16×C139C2311yescharacteristic
111C2×M16×C139C2311yescharacteristic
112C2×M16×C139C2311yescharacteristic
113C2×M16×C139C2311yescharacteristic
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C22×C8×C139—21no—
120C22×C8×C139—21no—
121C22×C8×C139C2311yescharacteristic
122#117×C139C2311yescharacteristic
123#108×C139—22no—
124#108×C139—22no—
125#108×C139—22no—
126#108×C139—22no—
127#108×C139—22no—
128#108×C139—21no—
129#108×C139—21no—
130#108×C139—21no—
131#108×C139—21no—
132#108×C139D412yes—
133#108×C139D412yes—
134#104×C139—22no—
135#104×C139—22no—
136#103×C139—41no—
137#102×C139—41no—
138#101×C139—21no—
139#101×C139—21no—
140#101×C139—22no—
141#101×C139—22no—
142#101×C139—22no—
143#100×C139—21no—
144#100×C139—21no—
145#100×C139—22no—
146#100×C139—22no—
147#100×C139—22no—
148#97×C139—21no—
149C4×C8×C139—21no—
150C24×C139—21no—
151#41×C139—21no—
152#41×C139—21no—
153#41×C139—21no—
154#41×C139—21no—
155#41×C139—21no—
156#41×C139—21no—
157#41×C139C2×D412yes—
158#41×C139C2×D412yes—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139C2×D411yescharacteristic
166C2×Q8×C139#4111yescharacteristic
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139C2×D411yescharacteristic
176C2×D4×C139#4111yescharacteristic
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—21no—
180C22×C4×C139C2411yescharacteristic
181Q16×C139—22no—
182Q16×C139—42no—
183Q16×C139—42no—
184SD16×C139—22no—
185SD16×C139—22no—
186SD16×C139—42no—
187SD16×C139—42no—
188SD16×C139—42no—
189SD16×C139—42no—
190SD16×C139—41no—
191SD16×C139—41no—
192SD16×C139—41no—
193SD16×C139—41no—
194D8×C139—22no—
195D8×C139—42no—
196D8×C139—42no—
197M16×C139—21no—
198M16×C139—21no—
199M16×C139—21no—
200M16×C139—21no—
201M16×C139—22no—
202M16×C139—22no—
203M16×C139—21no—
204M16×C139—21no—
205M16×C139—21no—
206M16×C139—21no—
207M16×C139—21no—
208M16×C139—21no—
209M16×C139—21no—
210M16×C139—21no—
211M16×C139—21no—
212M16×C139—21no—
213M16×C139—42no—
214M16×C139—42no—
215M16×C139—41no—
216M16×C139—41no—
217M16×C139C2×D412yes—
218M16×C139C2×D412yes—
219M16×C139C2×D412yes—
220M16×C139C2×D412yes—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—22no—
226C2×C8×C139—22no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—42no—
233C2×C8×C139—42no—
234C2×C8×C139—41no—
235C2×C8×C139—41no—
236C2×C8×C139C2×D411yescharacteristic
237C2×C8×C139C2×D411yescharacteristic
238C2×C8×C139C2×D411yescharacteristic
239C2×C8×C139C2×D411yescharacteristic
240C2×C8×C139#4111yescharacteristic
241C2×C8×C139#4111yescharacteristic
242C4⋊C4×C139—21no—
243C22⋊C4×C139—21no—
244C42×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—41no—
248C23×C139—41no—
249C23×C139—41no—
250C23×C139—161no—
251C23×C1392−1+411yescharacteristic
252Q8×C139—21no—
253Q8×C139—21no—
254Q8×C139—21no—
255Q8×C139—41no—
256Q8×C139—41no—
257Q8×C139—41no—
258Q8×C139—41no—
259Q8×C139#12112yes—
260D4×C139—22no—
261D4×C139—22no—
262D4×C139—21no—
263D4×C139—21no—
264D4×C139—21no—
265D4×C139—41no—
266D4×C139—41no—
267D4×C139—41no—
268D4×C139—41no—
269D4×C139—41no—
270D4×C139—41no—
271D4×C139#12112yes—
272C2×C4×C139—21no—
273C2×C4×C139—22no—
274C2×C4×C139—22no—
275C2×C4×C139—21no—
276C2×C4×C139—41no—
277C2×C4×C139—41no—
278C2×C4×C139—41no—
279C2×C4×C139—41no—
280C2×C4×C139—41no—
281C2×C4×C139—41no—
282C2×C4×C139C22×D411yescharacteristic
283C2×C4×C139C22×D411yescharacteristic
284C2×C4×C139C22×D411yescharacteristic
285C2×C4×C139C2×#4111yescharacteristic
286C2×C4×C139C2×#4111yescharacteristic
287C2×C4×C139H(5,𝔽2)11yescharacteristic
288C8×C139—22no—
289C8×C139—22no—
290C8×C139—22no—
291C8×C139—22no—
292C8×C139—41no—
293C8×C139—41no—
294C8×C139—41no—
295C8×C139—41no—
296C8×C139—41no—
297C8×C139#12111yescharacteristic
298C8×C139#12111yescharacteristic
299C8×C139#12111yescharacteristic
300C8×C139#12111yescharacteristic
301C22×C139—22no—
302C22×C139—41no—
303C22×C139—41no—
304C22×C139—81no—
305C22×C139—81no—
306C22×C139—81no—
307C22×C139—161no—
308C22×C139—161no—
309C22×C139—161no—
310C22×C139#53711yescharacteristic
311C22×C139#54711yescharacteristic
312C22×C139#54811yescharacteristic
313C4×C139—22no—
314C4×C139—41no—
315C4×C139—81no—
316C4×C139—81no—
317C4×C139C2×#12111yescharacteristic
318C4×C139C2×#12111yescharacteristic
319C4×C139D4211yescharacteristic
320C4×C139#55311yescharacteristic
321C2×C139—21no—
322C2×C139—21no—
323C2×C139—21no—
324C2×C139—42no—
325C2×C139—81no—
326C2×C139—161no—
327C2×C139#241611yescharacteristic
328#24808C13911yesmaximal, characteristic, direct product factor, Sylow
329C139#2480811yescharacteristic, direct product factor, Sylow
330#3069C2×C13911yescharacteristic, complemented
331#3068C2×C13911yescharacteristic
332C2×#471C2×C13911yescharacteristic, complemented
333C2×#471C2×C13911yescharacteristic, complemented
334#2955C2×C13911yescharacteristic, complemented
335#2916C2×C13911yescharacteristic, complemented
336#2070C2×C13911yescharacteristic, complemented
337#2069C2×C13911yescharacteristic, complemented
338#2049C2×C13911yescharacteristic, complemented
339#2048C2×C13911yescharacteristic, complemented
340#1977C2×C13911yescharacteristic, complemented
341#1953C2×C13911yescharacteristic, complemented
342#1903C2×C13911yescharacteristic, complemented
343#1902C2×C13911yescharacteristic, complemented
344#1813C2×C13911yescharacteristic, complemented
345#575C22×C13911yescharacteristic
346C2×#137C22×C13911yescharacteristic
347C2×#137C22×C13911yescharacteristic
348C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
349C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
350C22×SD16C22×C13911yescharacteristic
351#568C22×C13911yescharacteristic
352#568C22×C13911yescharacteristic
353C2×#131C22×C13911yescharacteristic
354C2×#131C22×C13911yescharacteristic
355#473—22no—
356#472—22no—
357#471—22no—
358#471—22no—
359#471—22no—
360#471—22no—
361#471—22no—
362#471—22no—
363#444—22no—
364#443—22no—
365#430—22no—
366#430C22×C13911yescharacteristic
367#430C22×C13911yescharacteristic
368#430C22×C13911yescharacteristic
369#430C22×C13911yescharacteristic
370#430C22×C13911yescharacteristic
371C2×#108—22no—
372C2×#108C22×C13911yescharacteristic
373C2×#108C22×C13911yescharacteristic
374C2×#108C22×C13911yescharacteristic
375#421C22×C13911yescharacteristic
376#421C22×C13911yescharacteristic
377#419C22×C13911yescharacteristic
378#418C22×C13911yescharacteristic
379#413C22×C13911yescharacteristic
380#413C22×C13911yescharacteristic
381C2×#101C22×C13911yescharacteristic
382C2×#101C22×C13911yescharacteristic
383C2×#101C22×C13911yescharacteristic
384C2×#100C22×C13911yescharacteristic
385C2×#100C22×C13911yescharacteristic
386C2×#100C22×C13911yescharacteristic
387#405C22×C13911yescharacteristic
388#344C22×C13911yescharacteristic
389#344C22×C13911yescharacteristic
390#338C22×C13911yescharacteristic
391#338C22×C13911yescharacteristic
392C2×#41C23×C13911yescharacteristic
393C2×#41C23×C13911yescharacteristic
394C22×Q8C23×C13911yescharacteristic
395C22×D4C23×C13911yescharacteristic
396#137—21no—
397#137—22no—
398#137—22no—
399#137—22no—
400#137—41no—
401#137D4×C13912yes—
402AGL(1,ℤ/8)—21no—
403AGL(1,ℤ/8)—22no—
404AGL(1,ℤ/8)—22no—
405AGL(1,ℤ/8)—22no—
406AGL(1,ℤ/8)—41no—
407AGL(1,ℤ/8)D4×C13912yes—
408#135—22no—
409C2×Q16—21no—
410C2×Q16—21no—
411C2×SD16—21no—
412C2×SD16—21no—
413C2×SD16—21no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×SD16—21no—
421C2×D8—21no—
422C2×D8—21no—
423#131—21no—
424#131—21no—
425#131—22no—
426#131—22no—
427#131—21no—
428#131—21no—
429#131—21no—
430#131—21no—
431#131—41no—
432#131—41no—
433#131D4×C13912yes—
434#131D4×C13912yes—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16C23×C13911yescharacteristic
440C2×M16C23×C13911yescharacteristic
441C2×M16C23×C13911yescharacteristic
442C2×M16C23×C13911yescharacteristic
443C2×M16C23×C13911yescharacteristic
444C2×M16C23×C13911yescharacteristic
445C2×M16C23×C13911yescharacteristic
446C2×M16C23×C13911yescharacteristic
447C2×M16C23×C13911yescharacteristic
448C22×C8—21no—
449C22×C8—21no—
450C22×C8C23×C13911yescharacteristic
451#117C23×C13911yescharacteristic
452#108—22no—
453#108—22no—
454#108—22no—
455#108—22no—
456#108—22no—
457#108—21no—
458#108—21no—
459#108—21no—
460#108—21no—
461#108D4×C13912yes—
462#108D4×C13912yes—
463#104—22no—
464#104—22no—
465#103—41no—
466#102—41no—
467#101—21no—
468#101—21no—
469#101—22no—
470#101—22no—
471#101—22no—
472#100—21no—
473#100—21no—
474#100—22no—
475#100—22no—
476#100—22no—
477#97—21no—
478C4×C8—21no—
479C24—21no—
480#41—21no—
481#41—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486#41C2×D4×C13912yes—
487#41C2×D4×C13912yes—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D4×C13911yescharacteristic
495C2×Q8#41×C13911yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C2×D4×C13911yescharacteristic
505C2×D4#41×C13911yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4C24×C13911yescharacteristic
510Q16—22no—
511Q16—42no—
512Q16—42no—
513SD16—22no—
514SD16—22no—
515SD16—42no—
516SD16—42no—
517SD16—42no—
518SD16—42no—
519SD16—41no—
520SD16—41no—
521SD16—41no—
522SD16—41no—
523D8—22no—
524D8—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—22no—
531M16—22no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—21no—
539M16—21no—
540M16—21no—
541M16—21no—
542M16—42no—
543M16—42no—
544M16—41no—
545M16—41no—
546M16C2×D4×C13912yes—
547M16C2×D4×C13912yes—
548M16C2×D4×C13912yes—
549M16C2×D4×C13912yes—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—42no—
562C2×C8—42no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8C2×D4×C13911yescharacteristic
566C2×C8C2×D4×C13911yescharacteristic
567C2×C8C2×D4×C13911yescharacteristic
568C2×C8C2×D4×C13911yescharacteristic
569C2×C8#41×C13911yescharacteristic
570C2×C8#41×C13911yescharacteristic
571C4⋊C4—21no—
572C22⋊C4—21no—
573C42—21no—
574C23—21no—
575C23—21no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—161no—
580C232−1+4×C13911yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8#121×C13912yes—
589D4—22no—
590D4—22no—
591D4—21no—
592D4—21no—
593D4—21no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4#121×C13912yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C22×D4×C13911yescharacteristic
612C2×C4C22×D4×C13911yescharacteristic
613C2×C4C22×D4×C13911yescharacteristic
614C2×C4C2×#41×C13911yescharacteristic
615C2×C4C2×#41×C13911yescharacteristic
616C2×C4H(5,𝔽2)×C13911yescharacteristic
617C8—22no—
618C8—22no—
619C8—22no—
620C8—22no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#121×C13911yescharacteristic
627C8#121×C13911yescharacteristic
628C8#121×C13911yescharacteristic
629C8#121×C13911yescharacteristic
630C22—22no—
631C22—41no—
632C22—41no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—161no—
637C22—161no—
638C22—161no—
639C22#537×C13911yescharacteristic
640C22#547×C13911yescharacteristic
641C22#548×C13911yescharacteristic
642C4—22no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4C2×#121×C13911yescharacteristic
647C4C2×#121×C13911yescharacteristic
648C4D42×C13911yescharacteristic
649C4#553×C13911yescharacteristic
650C2—21no—
651C2—21no—
652C2—21no—
653C2—42no—
654C2—81no—
655C2—161no—
656C2#2416×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2416
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3068×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3069×C139C2semidirect
3. C2×#471×C139C2semidirect
4. C2×#471×C139C2semidirect
5. #2955×C139C2semidirect
6. #2916×C139C2semidirect
7. #2070×C139C2semidirect
8. #2069×C139C2semidirect
9. #2049×C139C2semidirect
10. #2048×C139C2semidirect
11. #1977×C139C2semidirect
12. #1953×C139C2semidirect
13. #1903×C139C2semidirect
14. #1902×C139C2semidirect
15. #1813×C139C2semidirect
328. #24808C139direct (N × H)
329. C139#24808direct (N × H)
330. #3069C2×C139semidirect
332. C2×#471C2×C139semidirect
333. C2×#471C2×C139semidirect
334. #2955C2×C139semidirect
335. #2916C2×C139semidirect
336. #2070C2×C139semidirect
337. #2069C2×C139semidirect
338. #2049C2×C139semidirect
339. #2048C2×C139semidirect
340. #1977C2×C139semidirect
341. #1953C2×C139semidirect
342. #1903C2×C139semidirect
343. #1902C2×C139semidirect
344. #1813C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3069×C1392
#3068×C1392
C2×#471×C1392
#2955×C1392
#2916×C1392
#2070×C1392
#2069×C1392
#2049×C1392
#2048×C1392
#1977×C1392
#1953×C1392
#1903×C1392
#1902×C1392
#1813×C1392
#24808139