Finite Group Databasebeta

← C139×#24473 #48019069

Subgroups — C139×#24473 #48019069

Order 35584.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C139C211yesmaximal, characteristic, complemented
2#3068×C139C211yesmaximal, characteristic, complemented
3#3040×C139C211yesmaximal, characteristic, complemented
4#3021×C139C211yesmaximal, characteristic, complemented
5C2×#454×C139C211yesmaximal, characteristic, complemented
6#2901×C139C211yesmaximal, characteristic, complemented
7#2050×C139C211yesmaximal, characteristic, complemented
8#2049×C139C211yesmaximal, characteristic, complemented
9#2008×C139C211yesmaximal, characteristic, complemented
10#2004×C139C211yesmaximal, characteristic, complemented
11#1906×C139C211yesmaximal, characteristic, complemented
12#1903×C139C211yesmaximal, characteristic, complemented
13#1902×C139C211yesmaximal, characteristic, complemented
14#1861×C139C211yesmaximal, characteristic, complemented
15#1796×C139C211yesmaximal, characteristic, complemented
16#585×C139C2211yescharacteristic
17C2×2−1+4×C139C2211yescharacteristic
18#578×C139—22no—
19#578×C139—22no—
20#577×C139—22no—
21#577×C139—22no—
22#575×C139—22no—
23#575×C139C2211yescharacteristic
24#575×C139C2211yescharacteristic
25C2×#137×C139—22no—
26C2×#137×C139C2211yescharacteristic
27C2×#137×C139C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
31#568×C139C2211yescharacteristic
32#568×C139C2211yescharacteristic
33#535×C139C2211yescharacteristic
34C2×#124×C139C2211yescharacteristic, complemented
35C4×#41×C139C2211yescharacteristic
36#472×C139—22no—
37#471×C139—22no—
38#464×C139—22no—
39#463×C139—22no—
40#454×C139—22no—
41#454×C139—22no—
42#454×C139—22no—
43#453×C139—22no—
44#430×C139C2211yescharacteristic, complemented
45#423×C139C2211yescharacteristic, complemented
46#421×C139—22no—
47#421×C139C2211yescharacteristic
48#421×C139C2211yescharacteristic
49#421×C139C2211yescharacteristic
50#421×C139C2211yescharacteristic
51C2×#104×C139—22no—
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic
54C2×#104×C139C2211yescharacteristic, complemented
55#419×C139C2211yescharacteristic, complemented
56#419×C139C2211yescharacteristic, complemented
57#418×C139C2211yescharacteristic, complemented
58#413×C139C2211yescharacteristic
59#413×C139C2211yescharacteristic, complemented
60C2×#101×C139C2211yescharacteristic, complemented
61C2×#100×C139C2211yescharacteristic, complemented
62#410×C139C2211yescharacteristic, complemented
63#344×C139C2211yescharacteristic, complemented
64#344×C139C2211yescharacteristic, complemented
65#339×C139C2211yescharacteristic, complemented
66#338×C139C2211yescharacteristic, complemented
672−1+4×C139—22no—
682−1+4×C139—22no—
692−1+4×C139—21no—
702−1+4×C139—21no—
712−1+4×C139—22no—
722−1+4×C139—41no—
732−1+4×C139D412yes—
74H(5,𝔽2)×C139—21no—
75H(5,𝔽2)×C139—21no—
76H(5,𝔽2)×C139—41no—
77H(5,𝔽2)×C139D412yes—
78C2×#41×C139—22no—
79C2×#41×C139—22no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—41no—
83C2×#41×C139—41no—
84C2×#41×C139C2311yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C2×#41×C139C2311yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C22×Q8×C139—21no—
89C22×Q8×C139—21no—
90C22×Q8×C139C2311yescharacteristic
91C22×D4×C139C2311yescharacteristic
92#137×C139—24no—
93#137×C139—24no—
94#137×C139—24no—
95#137×C139—22no—
96#137×C139—22no—
97#137×C139—21no—
98#137×C139—22no—
99#137×C139—21no—
100#137×C139—21no—
101#137×C139—22no—
102#137×C139D412yescomplemented
103AGL(1,ℤ/8)×C139—24no—
104AGL(1,ℤ/8)×C139—21no—
105AGL(1,ℤ/8)×C139—21no—
106AGL(1,ℤ/8)×C139—21no—
107AGL(1,ℤ/8)×C139—22no—
108AGL(1,ℤ/8)×C139—22no—
109AGL(1,ℤ/8)×C139—22no—
110AGL(1,ℤ/8)×C139—22no—
111AGL(1,ℤ/8)×C139—22no—
112AGL(1,ℤ/8)×C139—41no—
113AGL(1,ℤ/8)×C139D412yescomplemented
114#135×C139—24no—
115#135×C139—24no—
116#135×C139—22no—
117#135×C139—22no—
118C2×Q16×C139—24no—
119C2×Q16×C139—21no—
120C2×Q16×C139D412yescomplemented
121C2×SD16×C139—24no—
122C2×SD16×C139—21no—
123C2×SD16×C139—21no—
124C2×SD16×C139—21no—
125C2×SD16×C139—21no—
126C2×SD16×C139D412yescomplemented
127C2×D8×C139—21no—
128C2×D8×C139—21no—
129C2×D8×C139—21no—
130#131×C139—22no—
131#131×C139—22no—
132#131×C139—22no—
133#131×C139—41no—
134C2×M16×C139—22no—
135C2×M16×C139—22no—
136C2×M16×C139C2311yescharacteristic
137C2×M16×C139C2311yescharacteristic
138C2×M16×C139C2311yescharacteristic
139C2×M16×C139C2311yescharacteristic
140C2×M16×C139C2311yescharacteristic
141C2×M16×C139C2311yescharacteristic
142#127×C139—21no—
143#124×C139—21no—
144#124×C139—22no—
145#124×C139—21no—
146#124×C139—21no—
147#121×C139—41no—
148#120×C139—41no—
149C4×Q8×C139—21no—
150C4×D4×C139—21no—
151C4×D4×C139—41no—
152#117×C139—21no—
153#117×C139C2311yescharacteristic
154#117×C139C2311yescharacteristic
155C2×C22⋊C4×C139—41no—
156C2×C42×C139—21no—
157C2×C42×C139C2311yescharacteristic
158#108×C139—22no—
159C4⋊C8×C139—22no—
160#104×C139—22no—
161#104×C139—22no—
162#104×C139—22no—
163#104×C139—22no—
164#104×C139—21no—
165#104×C139—21no—
166#104×C139—21no—
167#104×C139—21no—
168#104×C139D412yescomplemented
169#104×C139D412yescomplemented
170#103×C139—22no—
171#103×C139—41no—
172#102×C139—22no—
173#101×C139—21no—
174#101×C139—21no—
175#101×C139—22no—
176#100×C139—21no—
177#100×C139—21no—
178#100×C139—22no—
179#99×C139—41no—
180C24×C139—21no—
181#41×C139—21no—
182#41×C139—21no—
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—24no—
186#41×C139—22no—
187#41×C139—22no—
188#41×C139—22no—
189#41×C139—22no—
190#41×C139—21no—
191#41×C139—21no—
192#41×C139—21no—
193#41×C139—21no—
194#41×C139—21no—
195#41×C139—21no—
196#41×C139—21no—
197#41×C139—21no—
198#41×C139—42no—
199#41×C139—42no—
200#41×C139—42no—
201#41×C139—42no—
202#41×C139—42no—
203#41×C139—44no—
204#41×C139—42no—
205#41×C139—41no—
206#41×C139—41no—
207#41×C139—44no—
208#41×C139—42no—
209#41×C139C2×D412yes—
210#41×C139C2×D412yes—
211#41×C139C2×D412yes—
212#41×C139C2×D412yes—
213C2×Q8×C139—21no—
214C2×Q8×C139—24no—
215C2×Q8×C139—22no—
216C2×Q8×C139—22no—
217C2×Q8×C139—21no—
218C2×Q8×C139—21no—
219C2×Q8×C139—21no—
220C2×Q8×C139—21no—
221C2×Q8×C139—41no—
222C2×Q8×C139—42no—
223C2×Q8×C139—42no—
224C2×Q8×C139—41no—
225C2×Q8×C139—42no—
226C2×Q8×C139C2×D411yescharacteristic
227C2×Q8×C139C2×D411yescharacteristic
228C2×Q8×C139C2×D412yes—
229C2×Q8×C139C2×D411yescharacteristic
230C2×Q8×C139#4111yescharacteristic
231C2×D4×C139—21no—
232C2×D4×C139—21no—
233C2×D4×C139—22no—
234C2×D4×C139—22no—
235C2×D4×C139—21no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—21no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—21no—
243C2×D4×C139—42no—
244C2×D4×C139—41no—
245C2×D4×C139—42no—
246C2×D4×C139—42no—
247C2×D4×C139—41no—
248C2×D4×C139—42no—
249C2×D4×C139C2×D411yescharacteristic
250C2×D4×C139C2×D411yescharacteristic
251C2×D4×C139C2×D411yescharacteristic
252C2×D4×C139#4111yescharacteristic
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—42no—
260C22×C4×C139—41no—
261C22×C4×C139—41no—
262C22×C4×C139—41no—
263C22×C4×C139C2411yescharacteristic
264Q16×C139—24no—
265Q16×C139—22no—
266Q16×C139—22no—
267Q16×C139—24no—
268SD16×C139—24no—
269SD16×C139—22no—
270SD16×C139—22no—
271SD16×C139—22no—
272SD16×C139—22no—
273SD16×C139—24no—
274SD16×C139—42no—
275SD16×C139—42no—
276SD16×C139—42no—
277D8×C139—22no—
278D8×C139—22no—
279D8×C139—42no—
280D8×C139—42no—
281D8×C139—42no—
282M16×C139—24no—
283M16×C139—21no—
284M16×C139—21no—
285M16×C139—21no—
286M16×C139—21no—
287M16×C139—21no—
288M16×C139—21no—
289M16×C139—21no—
290M16×C139—21no—
291M16×C139—21no—
292M16×C139—21no—
293M16×C139—42no—
294M16×C139C2×D412yes—
295M16×C139C2×D412yes—
296C2×C8×C139—24no—
297C2×C8×C139—21no—
298C2×C8×C139—21no—
299C2×C8×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139—21no—
302C2×C8×C139—42no—
303C2×C8×C139C2×D412yes—
304C4⋊C4×C139—21no—
305C4⋊C4×C139—21no—
306C4⋊C4×C139—41no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—42no—
310C22⋊C4×C139—42no—
311C22⋊C4×C139—41no—
312C22⋊C4×C139—42no—
313C42×C139—21no—
314C42×C139—21no—
315C42×C139—21no—
316C42×C139—41no—
317C42×C139C2×D411yescharacteristic
318C42×C139C2×D411yescharacteristic
319C23×C139—21no—
320C23×C139—21no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—42no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—82no—
328C23×C139H(5,𝔽2)11yescharacteristic
329Q8×C139—21no—
330Q8×C139—21no—
331Q8×C139—21no—
332Q8×C139—22no—
333Q8×C139—21no—
334Q8×C139—21no—
335Q8×C139—21no—
336Q8×C139—22no—
337Q8×C139—42no—
338Q8×C139—44no—
339Q8×C139—41no—
340Q8×C139—41no—
341Q8×C139#12012yes—
342Q8×C139#12112yes—
343D4×C139—22no—
344D4×C139—22no—
345D4×C139—22no—
346D4×C139—22no—
347D4×C139—21no—
348D4×C139—21no—
349D4×C139—21no—
350D4×C139—21no—
351D4×C139—21no—
352D4×C139—21no—
353D4×C139—42no—
354D4×C139—42no—
355D4×C139—42no—
356D4×C139—44no—
357D4×C139—41no—
358D4×C139—41no—
359D4×C139—41no—
360D4×C139—41no—
361D4×C139—41no—
362D4×C139—41no—
363D4×C139—41no—
364D4×C139—41no—
365D4×C139—162no—
366D4×C139#12012yes—
367D4×C139#12112yes—
368C2×C4×C139—21no—
369C2×C4×C139—21no—
370C2×C4×C139—22no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—22no—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—21no—
377C2×C4×C139—22no—
378C2×C4×C139—21no—
379C2×C4×C139—42no—
380C2×C4×C139—42no—
381C2×C4×C139—42no—
382C2×C4×C139—44no—
383C2×C4×C139—44no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—81no—
393C2×C4×C139—82no—
394C2×C4×C139C22×D411yescharacteristic
395C2×C4×C139C22×D411yescharacteristic
396C2×C4×C139C22×D411yescharacteristic
397C2×C4×C139C22×D411yescharacteristic
398C2×C4×C139C2×#4111yescharacteristic
399C2×C4×C139H(5,𝔽2)11yescharacteristic
400C8×C139—22no—
401C8×C139—22no—
402C8×C139—22no—
403C8×C139—41no—
404C8×C139—41no—
405C8×C139—41no—
406C22×C139—22no—
407C22×C139—22no—
408C22×C139—41no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139—81no—
414C22×C139—81no—
415C22×C139—82no—
416C22×C139—82no—
417C22×C139—81no—
418C22×C139—161no—
419C22×C139—162no—
420C22×C139#53411yescharacteristic
421C22×C139D4211yescharacteristic
422C22×C139#54611yescharacteristic
423C4×C139—22no—
424C4×C139—22no—
425C4×C139—41no—
426C4×C139—41no—
427C4×C139—41no—
428C4×C139—42no—
429C4×C139—41no—
430C4×C139—81no—
431C4×C139—81no—
432C4×C139C2×#12011yescharacteristic
433C4×C139C2×#12111yescharacteristic
434C4×C139D4211yescharacteristic
435C4×C139#54611yescharacteristic
436C2×C139—21no—
437C2×C139—21no—
438C2×C139—21no—
439C2×C139—42no—
440C2×C139—42no—
441C2×C139—81no—
442C2×C139—81no—
443C2×C139—161no—
444C2×C139#241011yescharacteristic
445#24473C13911yesmaximal, characteristic, direct product factor, Sylow
446C139#2447311yescharacteristic, direct product factor, Sylow
447#3586C2×C13911yescharacteristic, complemented
448#3068C2×C13911yescharacteristic, complemented
449#3040C2×C13911yescharacteristic, complemented
450#3021C2×C13911yescharacteristic, complemented
451C2×#454C2×C13911yescharacteristic, complemented
452#2901C2×C13911yescharacteristic, complemented
453#2050C2×C13911yescharacteristic, complemented
454#2049C2×C13911yescharacteristic, complemented
455#2008C2×C13911yescharacteristic, complemented
456#2004C2×C13911yescharacteristic, complemented
457#1906C2×C13911yescharacteristic, complemented
458#1903C2×C13911yescharacteristic, complemented
459#1902C2×C13911yescharacteristic, complemented
460#1861C2×C13911yescharacteristic, complemented
461#1796C2×C13911yescharacteristic, complemented
462#585C22×C13911yescharacteristic
463C2×2−1+4C22×C13911yescharacteristic
464#578—22no—
465#578—22no—
466#577—22no—
467#577—22no—
468#575—22no—
469#575C22×C13911yescharacteristic
470#575C22×C13911yescharacteristic
471C2×#137—22no—
472C2×#137C22×C13911yescharacteristic
473C2×#137C22×C13911yescharacteristic
474C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
475C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
476C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
477#568C22×C13911yescharacteristic
478#568C22×C13911yescharacteristic
479#535C22×C13911yescharacteristic
480C2×#124C22×C13911yescharacteristic, complemented
481C4×#41C22×C13911yescharacteristic
482#472—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#454—22no—
487#454—22no—
488#454—22no—
489#453—22no—
490#430C22×C13911yescharacteristic, complemented
491#423C22×C13911yescharacteristic, complemented
492#421—22no—
493#421C22×C13911yescharacteristic
494#421C22×C13911yescharacteristic
495#421C22×C13911yescharacteristic
496#421C22×C13911yescharacteristic
497C2×#104—22no—
498C2×#104C22×C13911yescharacteristic
499C2×#104C22×C13911yescharacteristic
500C2×#104C22×C13911yescharacteristic, complemented
501#419C22×C13911yescharacteristic, complemented
502#419C22×C13911yescharacteristic, complemented
503#418C22×C13911yescharacteristic, complemented
504#413C22×C13911yescharacteristic
505#413C22×C13911yescharacteristic, complemented
506C2×#101C22×C13911yescharacteristic, complemented
507C2×#100C22×C13911yescharacteristic, complemented
508#410C22×C13911yescharacteristic, complemented
509#344C22×C13911yescharacteristic, complemented
510#344C22×C13911yescharacteristic, complemented
511#339C22×C13911yescharacteristic, complemented
512#338C22×C13911yescharacteristic, complemented
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C13912yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C13912yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C13911yescharacteristic
531C2×#41C23×C13911yescharacteristic
532C2×#41C23×C13911yescharacteristic
533C2×#41C23×C13911yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C13911yescharacteristic
537C22×D4C23×C13911yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C13912yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C13912yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C13912yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C13912yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C13911yescharacteristic
583C2×M16C23×C13911yescharacteristic
584C2×M16C23×C13911yescharacteristic
585C2×M16C23×C13911yescharacteristic
586C2×M16C23×C13911yescharacteristic
587C2×M16C23×C13911yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C13911yescharacteristic
600#117C23×C13911yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C13911yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C13912yescomplemented
615#104D4×C13912yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C13912yes—
656#41C2×D4×C13912yes—
657#41C2×D4×C13912yes—
658#41C2×D4×C13912yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C13911yescharacteristic
673C2×Q8C2×D4×C13911yescharacteristic
674C2×Q8C2×D4×C13912yes—
675C2×Q8C2×D4×C13911yescharacteristic
676C2×Q8#41×C13911yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C13911yescharacteristic
696C2×D4C2×D4×C13911yescharacteristic
697C2×D4C2×D4×C13911yescharacteristic
698C2×D4#41×C13911yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C13911yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C13912yes—
741M16C2×D4×C13912yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C13912yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C13911yescharacteristic
764C42C2×D4×C13911yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C13911yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C13912yes—
788Q8#121×C13912yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C13912yes—
813D4#121×C13912yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—82no—
840C2×C4C22×D4×C13911yescharacteristic
841C2×C4C22×D4×C13911yescharacteristic
842C2×C4C22×D4×C13911yescharacteristic
843C2×C4C22×D4×C13911yescharacteristic
844C2×C4C2×#41×C13911yescharacteristic
845C2×C4H(5,𝔽2)×C13911yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22#534×C13911yescharacteristic
867C22D42×C13911yescharacteristic
868C22#546×C13911yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C13911yescharacteristic
879C4C2×#121×C13911yescharacteristic
880C4D42×C13911yescharacteristic
881C4#546×C13911yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2#2410×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2410
commutator, Frattini, cosocleC22×C4C24×C139
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. #3586×C139C2semidirect
2. #3068×C139C2semidirect
3. #3040×C139C2semidirect
4. #3021×C139C2semidirect
5. C2×#454×C139C2semidirect
6. #2901×C139C2semidirect
7. #2050×C139C2semidirect
8. #2049×C139C2semidirect
9. #2008×C139C2semidirect
10. #2004×C139C2semidirect
11. #1906×C139C2semidirect
12. #1903×C139C2semidirect
13. #1902×C139C2semidirect
14. #1861×C139C2semidirect
15. #1796×C139C2semidirect
30. C2×AGL(1,ℤ/8)×C139C22semidirect
34. C2×#124×C139C22semidirect
44. #430×C139C22semidirect
45. #423×C139C22semidirect
54. C2×#104×C139C22semidirect
55. #419×C139C22semidirect
56. #419×C139C22semidirect
57. #418×C139C22semidirect
59. #413×C139C22semidirect
60. C2×#101×C139C22semidirect
61. C2×#100×C139C22semidirect
62. #410×C139C22semidirect
63. #344×C139C22semidirect
64. #344×C139C22semidirect
65. #339×C139C22semidirect
66. #338×C139C22semidirect
102. #137×C139D4semidirect
113. AGL(1,ℤ/8)×C139D4semidirect
120. C2×Q16×C139D4semidirect
126. C2×SD16×C139D4semidirect
168. #104×C139D4semidirect
169. #104×C139D4semidirect
445. #24473C139direct (N × H)
446. C139#24473direct (N × H)
447. #3586C2×C139semidirect
448. #3068C2×C139semidirect
449. #3040C2×C139semidirect
450. #3021C2×C139semidirect
451. C2×#454C2×C139semidirect
452. #2901C2×C139semidirect
453. #2050C2×C139semidirect
454. #2049C2×C139semidirect
455. #2008C2×C139semidirect
456. #2004C2×C139semidirect
457. #1906C2×C139semidirect
458. #1903C2×C139semidirect
459. #1902C2×C139semidirect
460. #1861C2×C139semidirect
461. #1796C2×C139semidirect
476. C2×AGL(1,ℤ/8)C22×C139semidirect
480. C2×#124C22×C139semidirect
490. #430C22×C139semidirect
491. #423C22×C139semidirect
500. C2×#104C22×C139semidirect
501. #419C22×C139semidirect
502. #419C22×C139semidirect
503. #418C22×C139semidirect
505. #413C22×C139semidirect
506. C2×#101C22×C139semidirect
507. C2×#100C22×C139semidirect
508. #410C22×C139semidirect
509. #344C22×C139semidirect
510. #344C22×C139semidirect
511. #339C22×C139semidirect
512. #338C22×C139semidirect
548. #137D4×C139semidirect
559. AGL(1,ℤ/8)D4×C139semidirect
566. C2×Q16D4×C139semidirect
572. C2×SD16D4×C139semidirect
614. #104D4×C139semidirect
615. #104D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3586×C1392
#3068×C1392
#3040×C1392
#3021×C1392
C2×#454×C1392
#2901×C1392
#2050×C1392
#2049×C1392
#2008×C1392
#2004×C1392
#1906×C1392
#1903×C1392
#1902×C1392
#1861×C1392
#1796×C1392
#24473139