Finite Group Databasebeta

← C139×#26500 #48021096

Subgroups — C139×#26500 #48021096

Order 35584.

698 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3163×C139C211yesmaximal, characteristic, complemented
2#3082×C139C211yesmaximal, characteristic, complemented
3#3081×C139C211yesmaximal, characteristic
4#2949×C139C211yesmaximal, characteristic
5#2064×C139C211yesmaximal, characteristic, complemented
6#2063×C139C211yesmaximal, characteristic
7#2028×C139C211yesmaximal, characteristic, complemented
8#2027×C139C211yesmaximal, characteristic
9#1977×C139C211yesmaximal, characteristic
10#1968×C139C211yesmaximal, characteristic
11#1951×C139C211yesmaximal, characteristic, complemented
12#1945×C139C211yesmaximal, characteristic, complemented
13#1857×C139C211yesmaximal, characteristic, complemented
14#1856×C139C211yesmaximal, characteristic
15#1772×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17#544×C139C2211yescharacteristic
18#544×C139C2211yescharacteristic
19#519×C139C2211yescharacteristic
20#518×C139C2211yescharacteristic
21#501×C139—21no—
22#501×C139—21no—
23#499×C139—21no—
24#498×C139—21no—
25#479×C139—21no—
26#479×C139—21no—
27#478×C139—21no—
28#478×C139—21no—
29#477×C139—21no—
30#476×C139—21no—
31#475×C139—21no—
32#474×C139—21no—
33#440×C139—21no—
34#440×C139—21no—
35C4×SD16×C139—21no—
36C4×SD16×C139—21no—
37C2×#108×C139C2211yescharacteristic
38C2×#108×C139C2211yescharacteristic
39#428×C139C2211yescharacteristic
40#428×C139C2211yescharacteristic
41#428×C139C2211yescharacteristic
42#428×C139C2211yescharacteristic
43#427×C139C2211yescharacteristic
44#427×C139C2211yescharacteristic
45C2×#106×C139C2211yescharacteristic
46#424×C139C2211yescharacteristic
47#424×C139C2211yescharacteristic
48#419×C139C2211yescharacteristic
49#419×C139C2211yescharacteristic
50#418×C139C2211yescharacteristic
51#418×C139C2211yescharacteristic
52C2×#103×C139C2211yescharacteristic
53C2×#102×C139C2211yescharacteristic
54C2×#101×C139C2211yescharacteristic
55C2×#100×C139C2211yescharacteristic
56#405×C139C2211yescharacteristic
57#405×C139C2211yescharacteristic
58C2×C4×C8×C139C2211yescharacteristic
59#391×C139C2211yescharacteristic
60#390×C139C2211yescharacteristic
61#343×C139C2211yescharacteristic
62#343×C139C2211yescharacteristic
63#339×C139C2211yescharacteristic
64#339×C139C2211yescharacteristic
65#339×C139C2211yescharacteristic
66#339×C139C2211yescharacteristic
67C22×Q8×C139C2311yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×SD16×C139—22no—
72C2×SD16×C139Q814yescomplemented
73C2×M16×C139C2311yescharacteristic
74C2×M16×C139C2311yescharacteristic
75C2×M16×C139C2311yescharacteristic
76C2×M16×C139C2311yescharacteristic
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C4⋊Q8×C139—21no—
80C4⋊Q8×C139—21no—
81C4⋊Q8×C139—21no—
82C4⋊Q8×C139—21no—
83#125×C139—21no—
84#125×C139—21no—
85#125×C139—21no—
86#125×C139—21no—
87C22⋊Q8×C139—41no—
88C22⋊Q8×C139—41no—
89C4×Q8×C139—21no—
90C4×Q8×C139—21no—
91C4×Q8×C139—21no—
92C4×Q8×C139—21no—
93C4×D4×C139—21no—
94C4×D4×C139—21no—
95C4×D4×C139—21no—
96C4×D4×C139—21no—
97#117×C139—41no—
98#117×C139C2311yescharacteristic
99#117×C139C2311yescharacteristic
100#117×C139C2311yescharacteristic
101#117×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C22⋊C4×C139—41no—
105C2×C22⋊C4×C139—41no—
106C2×C42×C139C2311yescharacteristic
107#108×C139—22no—
108#108×C139—22no—
109#107×C139—21no—
110#107×C139—21no—
111#107×C139—21no—
112#107×C139—21no—
113#107×C139D411yescharacteristic
114#107×C139D411yescharacteristic
115#107×C139D411yescharacteristic
116#107×C139D411yescharacteristic
117#106×C139—21no—
118#106×C139—21no—
119#106×C139—21no—
120#106×C139—21no—
121#106×C139—21no—
122#106×C139—21no—
123#106×C139D411yescharacteristic
124#106×C139D411yescharacteristic
125#106×C139D411yescharacteristic
126#106×C139D411yescharacteristic
127C4⋊C8×C139—21no—
128C4⋊C8×C139—21no—
129C4⋊C8×C139—21no—
130C4⋊C8×C139—21no—
131#103×C139—21no—
132#103×C139—21no—
133#103×C139—21no—
134#103×C139—21no—
135#103×C139—21no—
136#103×C139—21no—
137#102×C139—21no—
138#102×C139—21no—
139#102×C139—21no—
140#102×C139—21no—
141#102×C139—21no—
142#102×C139—21no—
143#101×C139—22no—
144#100×C139—22no—
145#97×C139—21no—
146#97×C139—21no—
147C4×C8×C139—21no—
148C4×C8×C139—21no—
149C4×C8×C139—22no—
150#95×C139—41no—
151C24×C139—21no—
152C2×Q8×C139—21no—
153C2×Q8×C139—21no—
154C2×Q8×C139—21no—
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—41no—
158C2×Q8×C139—41no—
159C2×Q8×C139C2×Q812yes—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139C2×Q812yes—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—41no—
171C22×C4×C139—41no—
172C22×C4×C139C2411yescharacteristic
173SD16×C139—24no—
174SD16×C139—24no—
175M16×C139—21no—
176M16×C139—21no—
177M16×C139—21no—
178M16×C139—21no—
179M16×C139—21no—
180M16×C139—21no—
181M16×C139—21no—
182M16×C139#4112yes—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139C2×D411yescharacteristic
190C2×C8×C139C2×D411yescharacteristic
191C2×C8×C139C2×D411yescharacteristic
192C2×C8×C139C2×D411yescharacteristic
193C2×C8×C139C2×Q812yes—
194C2×C8×C139#4112yes—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—41no—
200C4⋊C4×C139—41no—
201C4⋊C4×C139—41no—
202C4⋊C4×C139—41no—
203C4⋊C4×C139—41no—
204C4⋊C4×C139—41no—
205C4⋊C4×C139—41no—
206C4⋊C4×C139—41no—
207C4⋊C4×C139C2×D411yescharacteristic
208C4⋊C4×C139C2×D411yescharacteristic
209C4⋊C4×C139C2×D411yescharacteristic
210C4⋊C4×C139C2×D411yescharacteristic
211C4⋊C4×C139C2×D411yescharacteristic
212C4⋊C4×C139C2×D411yescharacteristic
213C4⋊C4×C139C2×D411yescharacteristic
214C4⋊C4×C139C2×D411yescharacteristic
215C22⋊C4×C139—21no—
216C22⋊C4×C139—21no—
217C22⋊C4×C139—21no—
218C22⋊C4×C139—21no—
219C22⋊C4×C139—41no—
220C22⋊C4×C139—41no—
221C22⋊C4×C139—82no—
222C42×C139—21no—
223C42×C139—21no—
224C42×C139—21no—
225C42×C139—21no—
226C42×C139—21no—
227C42×C139—21no—
228C42×C139—41no—
229C42×C139—41no—
230C23×C139—22no—
231C23×C139—41no—
232C23×C139—41no—
233C23×C139—81no—
234C23×C139—81no—
235C23×C139H(5,𝔽2)11yescharacteristic
236Q8×C139—22no—
237Q8×C139—22no—
238Q8×C139—41no—
239Q8×C139—41no—
240Q8×C139—161no—
241Q8×C139—161no—
242D4×C139—22no—
243D4×C139—22no—
244D4×C139—41no—
245D4×C139—41no—
246C2×C4×C139—22no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—22no—
256C2×C4×C139—41no—
257C2×C4×C139—41no—
258C2×C4×C139—41no—
259C2×C4×C139—41no—
260C2×C4×C139—41no—
261C2×C4×C139—41no—
262C2×C4×C139—81no—
263C2×C4×C139—81no—
264C2×C4×C139—161no—
265C2×C4×C139—161no—
266C2×C4×C139C22×D411yescharacteristic
267C2×C4×C139C22×D411yescharacteristic
268C2×C4×C139C22×Q811yescharacteristic
269C2×C4×C139C2×#4111yescharacteristic
270C2×C4×C139C2×#4111yescharacteristic
271C2×C4×C1392−1+411yescharacteristic
272C8×C139—21no—
273C8×C139—21no—
274C8×C139—22no—
275C8×C139—41no—
276C8×C139—41no—
277C8×C139—41no—
278C8×C139C22⋊Q812yes—
279C8×C139C22⋊Q812yes—
280C22×C139—21no—
281C22×C139—21no—
282C22×C139—42no—
283C22×C139—82no—
284C22×C139—81no—
285C22×C139—81no—
286C22×C139—161no—
287C22×C139#54211yescharacteristic
288C22×C139D4211yescharacteristic
289C22×C139#55411yescharacteristic
290C4×C139—42no—
291C4×C139—42no—
292C4×C139—41no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—41no—
296C4×C139—41no—
297C4×C139—41no—
298C4×C139—41no—
299C4×C139—41no—
300C4×C139—81no—
301C4×C139—81no—
302C4×C139C2×C22⋊Q811yescharacteristic
303C4×C139#53211yescharacteristic
304C4×C139#54811yescharacteristic
305C4×C139D4×Q811yescharacteristic
306C2×C139—21no—
307C2×C139—21no—
308C2×C139—82no—
309C2×C139#245211yescharacteristic
310C2×C139#329011yescharacteristic
311C2×C139#329111yescharacteristic
312#26500C13911yesmaximal, characteristic, direct product factor, Sylow
313C139#2650011yescharacteristic, direct product factor, Sylow
314#3163C2×C13911yescharacteristic, complemented
315#3082C2×C13911yescharacteristic, complemented
316#3081C2×C13911yescharacteristic
317#2949C2×C13911yescharacteristic
318#2064C2×C13911yescharacteristic, complemented
319#2063C2×C13911yescharacteristic
320#2028C2×C13911yescharacteristic, complemented
321#2027C2×C13911yescharacteristic
322#1977C2×C13911yescharacteristic
323#1968C2×C13911yescharacteristic
324#1951C2×C13911yescharacteristic, complemented
325#1945C2×C13911yescharacteristic, complemented
326#1857C2×C13911yescharacteristic, complemented
327#1856C2×C13911yescharacteristic
328#1772C2×C13911yescharacteristic, complemented
329C22×SD16C22×C13911yescharacteristic
330#544C22×C13911yescharacteristic
331#544C22×C13911yescharacteristic
332#519C22×C13911yescharacteristic
333#518C22×C13911yescharacteristic
334#501—21no—
335#501—21no—
336#499—21no—
337#498—21no—
338#479—21no—
339#479—21no—
340#478—21no—
341#478—21no—
342#477—21no—
343#476—21no—
344#475—21no—
345#474—21no—
346#440—21no—
347#440—21no—
348C4×SD16—21no—
349C4×SD16—21no—
350C2×#108C22×C13911yescharacteristic
351C2×#108C22×C13911yescharacteristic
352#428C22×C13911yescharacteristic
353#428C22×C13911yescharacteristic
354#428C22×C13911yescharacteristic
355#428C22×C13911yescharacteristic
356#427C22×C13911yescharacteristic
357#427C22×C13911yescharacteristic
358C2×#106C22×C13911yescharacteristic
359#424C22×C13911yescharacteristic
360#424C22×C13911yescharacteristic
361#419C22×C13911yescharacteristic
362#419C22×C13911yescharacteristic
363#418C22×C13911yescharacteristic
364#418C22×C13911yescharacteristic
365C2×#103C22×C13911yescharacteristic
366C2×#102C22×C13911yescharacteristic
367C2×#101C22×C13911yescharacteristic
368C2×#100C22×C13911yescharacteristic
369#405C22×C13911yescharacteristic
370#405C22×C13911yescharacteristic
371C2×C4×C8C22×C13911yescharacteristic
372#391C22×C13911yescharacteristic
373#390C22×C13911yescharacteristic
374#343C22×C13911yescharacteristic
375#343C22×C13911yescharacteristic
376#339C22×C13911yescharacteristic
377#339C22×C13911yescharacteristic
378#339C22×C13911yescharacteristic
379#339C22×C13911yescharacteristic
380C22×Q8C23×C13911yescharacteristic
381C22×D4C23×C13911yescharacteristic
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—22no—
385C2×SD16Q8×C13914yescomplemented
386C2×M16C23×C13911yescharacteristic
387C2×M16C23×C13911yescharacteristic
388C2×M16C23×C13911yescharacteristic
389C2×M16C23×C13911yescharacteristic
390C22×C8C23×C13911yescharacteristic
391C22×C8C23×C13911yescharacteristic
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396#125—21no—
397#125—21no—
398#125—21no—
399#125—21no—
400C22⋊Q8—41no—
401C22⋊Q8—41no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410#117—41no—
411#117C23×C13911yescharacteristic
412#117C23×C13911yescharacteristic
413#117C23×C13911yescharacteristic
414#117C23×C13911yescharacteristic
415C2×C4⋊C4C23×C13911yescharacteristic
416C2×C4⋊C4C23×C13911yescharacteristic
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C42C23×C13911yescharacteristic
420#108—22no—
421#108—22no—
422#107—21no—
423#107—21no—
424#107—21no—
425#107—21no—
426#107D4×C13911yescharacteristic
427#107D4×C13911yescharacteristic
428#107D4×C13911yescharacteristic
429#107D4×C13911yescharacteristic
430#106—21no—
431#106—21no—
432#106—21no—
433#106—21no—
434#106—21no—
435#106—21no—
436#106D4×C13911yescharacteristic
437#106D4×C13911yescharacteristic
438#106D4×C13911yescharacteristic
439#106D4×C13911yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444#103—21no—
445#103—21no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—21no—
456#101—22no—
457#100—22no—
458#97—21no—
459#97—21no—
460C4×C8—21no—
461C4×C8—21no—
462C4×C8—22no—
463#95—41no—
464C24—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8C2×Q8×C13912yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×Q8×C13912yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4C24×C13911yescharacteristic
486SD16—24no—
487SD16—24no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16#41×C13912yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8C2×D4×C13911yescharacteristic
503C2×C8C2×D4×C13911yescharacteristic
504C2×C8C2×D4×C13911yescharacteristic
505C2×C8C2×D4×C13911yescharacteristic
506C2×C8C2×Q8×C13912yes—
507C2×C8#41×C13912yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4C2×D4×C13911yescharacteristic
521C4⋊C4C2×D4×C13911yescharacteristic
522C4⋊C4C2×D4×C13911yescharacteristic
523C4⋊C4C2×D4×C13911yescharacteristic
524C4⋊C4C2×D4×C13911yescharacteristic
525C4⋊C4C2×D4×C13911yescharacteristic
526C4⋊C4C2×D4×C13911yescharacteristic
527C4⋊C4C2×D4×C13911yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—82no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—41no—
542C42—41no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—81no—
547C23—81no—
548C23H(5,𝔽2)×C13911yescharacteristic
549Q8—22no—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—161no—
554Q8—161no—
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—161no—
578C2×C4—161no—
579C2×C4C22×D4×C13911yescharacteristic
580C2×C4C22×D4×C13911yescharacteristic
581C2×C4C22×Q8×C13911yescharacteristic
582C2×C4C2×#41×C13911yescharacteristic
583C2×C4C2×#41×C13911yescharacteristic
584C2×C42−1+4×C13911yescharacteristic
585C8—21no—
586C8—21no—
587C8—22no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8C22⋊Q8×C13912yes—
592C8C22⋊Q8×C13912yes—
593C22—21no—
594C22—21no—
595C22—42no—
596C22—82no—
597C22—81no—
598C22—81no—
599C22—161no—
600C22#542×C13911yescharacteristic
601C22D42×C13911yescharacteristic
602C22#554×C13911yescharacteristic
603C4—42no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—42no—
613C4—81no—
614C4—81no—
615C4C2×C22⋊Q8×C13911yescharacteristic
616C4#532×C13911yescharacteristic
617C4#548×C13911yescharacteristic
618C4D4×Q8×C13911yescharacteristic
619C2—21no—
620C2—21no—
621C2—82no—
622C2#2452×C13911yescharacteristic
623C2#3290×C13911yescharacteristic
624C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3163×C139C2semidirect
2. #3082×C139C2semidirect
5. #2064×C139C2semidirect
7. #2028×C139C2semidirect
11. #1951×C139C2semidirect
12. #1945×C139C2semidirect
13. #1857×C139C2semidirect
15. #1772×C139C2semidirect
72. C2×SD16×C139Q8semidirect
312. #26500C139direct (N × H)
313. C139#26500direct (N × H)
314. #3163C2×C139semidirect
315. #3082C2×C139semidirect
318. #2064C2×C139semidirect
320. #2028C2×C139semidirect
324. #1951C2×C139semidirect
325. #1945C2×C139semidirect
326. #1857C2×C139semidirect
328. #1772C2×C139semidirect
385. C2×SD16Q8×C139semidirect

Maximal subgroups

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

subgroupindex
#3163×C1392
#3082×C1392
#3081×C1392
#2949×C1392
#2064×C1392
#2063×C1392
#2028×C1392
#2027×C1392
#1977×C1392
#1968×C1392
#1951×C1392
#1945×C1392
#1857×C1392
#1856×C1392
#1772×C1392
#26500139