Finite Group Databasebeta

← C139×#25196 #48019792

Subgroups — C139×#25196 #48019792

Order 35584.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3068×C139C211yesmaximal, characteristic, complemented
2#3068×C139C211yesmaximal, characteristic, complemented
3#3019×C139C211yesmaximal, characteristic, complemented
4C2×#453×C139C211yesmaximal, characteristic, complemented
5#2956×C139C211yesmaximal, characteristic, complemented
6#2888×C139C211yesmaximal, characteristic, complemented
7#2069×C139C211yesmaximal, characteristic, complemented
8#2050×C139C211yesmaximal, characteristic, complemented
9#2048×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1965×C139C211yesmaximal, characteristic, complemented
12#1932×C139C211yesmaximal, characteristic, complemented
13#1914×C139C211yesmaximal, characteristic, complemented
14#1903×C139C211yesmaximal, characteristic, complemented
15#1861×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17#575×C139C2211yescharacteristic
18#575×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
22#568×C139C2211yescharacteristic
23#568×C139C2211yescharacteristic
24#568×C139C2211yescharacteristic, complemented
25#535×C139C2211yescharacteristic
26C2×#127×C139C2211yescharacteristic
27#472×C139—22no—
28#472×C139—22no—
29#471×C139—22no—
30#471×C139—22no—
31#455×C139—22no—
32#453×C139—22no—
33#453×C139—22no—
34#453×C139—22no—
35#444×C139—22no—
36#443×C139—22no—
37#430×C139C2211yescharacteristic, complemented
38#430×C139C2211yescharacteristic, complemented
39#430×C139C2211yescharacteristic, complemented
40#423×C139C2211yescharacteristic, complemented
41#421×C139C2211yescharacteristic
42#421×C139C2211yescharacteristic
43C2×#104×C139C2211yescharacteristic
44C2×#104×C139C2211yescharacteristic
45C2×#104×C139C2211yescharacteristic, complemented
46#418×C139C2211yescharacteristic, complemented
47#413×C139—22no—
48#413×C139C2211yescharacteristic
49#413×C139C2211yescharacteristic
50#413×C139C2211yescharacteristic, complemented
51C2×#100×C139—22no—
52C2×#100×C139C2211yescharacteristic
53C2×#100×C139C2211yescharacteristic
54C2×#100×C139C2211yescharacteristic
55C2×#100×C139C2211yescharacteristic
56C2×#100×C139C2211yescharacteristic, complemented
57C2×#100×C139C2211yescharacteristic, complemented
58C4×M16×C139C2211yescharacteristic, complemented
59#344×C139C2211yescharacteristic, complemented
60#344×C139C2211yescharacteristic, complemented
61#339×C139C2211yescharacteristic, complemented
62#338×C139C2211yescharacteristic, complemented
63H(5,𝔽2)×C139—22no—
64H(5,𝔽2)×C139—22no—
65H(5,𝔽2)×C139—41no—
66H(5,𝔽2)×C139—41no—
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×#41×C139C2311yescharacteristic
70C2×#41×C139C2311yescharacteristic
71C2×#41×C139C2311yescharacteristic
72C22×D4×C139—22no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139—22no—
76C22×D4×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78#137×C139—21no—
79#137×C139—21no—
80#137×C139—21no—
81#137×C139D412yescomplemented
82AGL(1,ℤ/8)×C139—21no—
83AGL(1,ℤ/8)×C139—22no—
84AGL(1,ℤ/8)×C139—22no—
85AGL(1,ℤ/8)×C139—21no—
86AGL(1,ℤ/8)×C139—21no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—22no—
89AGL(1,ℤ/8)×C139—41no—
90AGL(1,ℤ/8)×C139—41no—
91AGL(1,ℤ/8)×C139D412yescomplemented
92#135×C139—22no—
93#135×C139—41no—
94C2×SD16×C139—21no—
95C2×SD16×C139—21no—
96C2×SD16×C139—21no—
97C2×D8×C139—21no—
98C2×D8×C139—21no—
99C2×D8×C139—21no—
100#131×C139—22no—
101#131×C139—22no—
102#131×C139—22no—
103#131×C139—22no—
104#131×C139—41no—
105#131×C139—41no—
106C2×M16×C139—22no—
107C2×M16×C139—22no—
108C2×M16×C139—41no—
109C2×M16×C139C2311yescharacteristic
110C2×M16×C139C2311yescharacteristic
111C2×M16×C139C2311yescharacteristic
112C2×M16×C139C2311yescharacteristic
113C2×M16×C139C2311yescharacteristic
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117#127×C139—21no—
118#127×C139—21no—
119#127×C139—21no—
120#127×C139—41no—
121#124×C139—21no—
122#121×C139—41no—
123#120×C139—22no—
124#117×C139C2311yescharacteristic
125C2×C42×C139C2311yescharacteristic
126#108×C139—22no—
127#108×C139—22no—
128#108×C139—22no—
129C4⋊C8×C139—41no—
130#104×C139—22no—
131#104×C139—22no—
132#104×C139—21no—
133#104×C139—21no—
134#104×C139—21no—
135#104×C139—21no—
136#104×C139D412yescomplemented
137#104×C139D412yescomplemented
138#102×C139—41no—
139#101×C139—21no—
140#101×C139—21no—
141#101×C139D412yescomplemented
142#100×C139—21no—
143#100×C139—21no—
144#100×C139—22no—
145#100×C139—22no—
146#100×C139—22no—
147#100×C139—22no—
148#100×C139—22no—
149#100×C139—22no—
150#100×C139D412yescomplemented
151#97×C139—21no—
152C4×C8×C139—21no—
153C24×C139—22no—
154C24×C139—21no—
155C24×C139#4112yes—
156#41×C139—21no—
157#41×C139—21no—
158#41×C139—21no—
159#41×C139—21no—
160#41×C139—21no—
161#41×C139—21no—
162#41×C139—21no—
163#41×C139—21no—
164#41×C139—21no—
165#41×C139—21no—
166#41×C139—42no—
167#41×C139—42no—
168#41×C139—42no—
169#41×C139—42no—
170#41×C139C2×D412yes—
171#41×C139C2×D412yes—
172C2×Q8×C139C2×D411yescharacteristic
173C2×Q8×C139C2×D411yescharacteristic
174C2×Q8×C139#4111yescharacteristic
175C2×D4×C139—21no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—21no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—44no—
197C2×D4×C139—44no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—84no—
202C2×D4×C139C2×D411yescharacteristic
203C2×D4×C139C2×D411yescharacteristic
204C2×D4×C139#4111yescharacteristic
205C22×C4×C139—21no—
206C22×C4×C139—22no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139C2411yescharacteristic
211Q16×C139—22no—
212Q16×C139—41no—
213SD16×C139—22no—
214SD16×C139—22no—
215SD16×C139—42no—
216SD16×C139—42no—
217SD16×C139—41no—
218SD16×C139—41no—
219SD16×C139—42no—
220D8×C139—22no—
221D8×C139—42no—
222D8×C139—42no—
223D8×C139—41no—
224D8×C139—42no—
225M16×C139—21no—
226M16×C139—21no—
227M16×C139—21no—
228M16×C139—21no—
229M16×C139—21no—
230M16×C139—21no—
231M16×C139—21no—
232M16×C139—21no—
233M16×C139—21no—
234M16×C139—21no—
235M16×C139—21no—
236M16×C139—21no—
237M16×C139—42no—
238M16×C139—42no—
239M16×C139—42no—
240M16×C139C2×D412yes—
241M16×C139C2×D412yes—
242M16×C139C2×D412yes—
243M16×C139C2×D412yes—
244C2×C8×C139—21no—
245C2×C8×C139—21no—
246C2×C8×C139—21no—
247C2×C8×C139—21no—
248C2×C8×C139—21no—
249C2×C8×C139—21no—
250C2×C8×C139—21no—
251C2×C8×C139—21no—
252C2×C8×C139—42no—
253C2×C8×C139—42no—
254C2×C8×C139—42no—
255C4⋊C4×C139—21no—
256C22⋊C4×C139—21no—
257C22⋊C4×C139—42no—
258C42×C139—21no—
259C42×C139—21no—
260C42×C139C2×D411yescharacteristic
261C42×C139C2×D411yescharacteristic
262C23×C139—21no—
263C23×C139—22no—
264C23×C139—21no—
265C23×C139—22no—
266C23×C139—21no—
267C23×C139—22no—
268C23×C139—44no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—82no—
273C23×C139—82no—
274C23×C139—162no—
275C23×C139C2×#4111yescharacteristic
276Q8×C139—21no—
277Q8×C139—21no—
278Q8×C139—21no—
279Q8×C139—21no—
280Q8×C139—21no—
281Q8×C139#12112yes—
282D4×C139—22no—
283D4×C139—22no—
284D4×C139—21no—
285D4×C139—21no—
286D4×C139—21no—
287D4×C139—21no—
288D4×C139—21no—
289D4×C139—44no—
290D4×C139—44no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—41no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—84no—
304D4×C139—84no—
305D4×C139—162no—
306D4×C139#12112yes—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—22no—
310C2×C4×C139—22no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
314C2×C4×C139—44no—
315C2×C4×C139—42no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139C22×D411yescharacteristic
322C2×C4×C139C22×D411yescharacteristic
323C2×C4×C139C22×D411yescharacteristic
324C2×C4×C139C2×#4111yescharacteristic
325C2×C4×C139H(5,𝔽2)11yescharacteristic
326C2×C4×C139H(5,𝔽2)11yescharacteristic
327C8×C139—22no—
328C8×C139—22no—
329C8×C139—22no—
330C8×C139—22no—
331C8×C139—41no—
332C8×C139—41no—
333C8×C139—41no—
334C8×C139—41no—
335C22×C139—22no—
336C22×C139—41no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139—42no—
340C22×C139—81no—
341C22×C139—82no—
342C22×C139—81no—
343C22×C139—82no—
344C22×C139—82no—
345C22×C139—81no—
346C22×C139—82no—
347C22×C139—81no—
348C22×C139—161no—
349C22×C139—161no—
350C22×C139—164no—
351C22×C139#52511yescharacteristic
352C22×C139#54611yescharacteristic
353C22×C139#54611yescharacteristic
354C4×C139—22no—
355C4×C139—22no—
356C4×C139—41no—
357C4×C139—41no—
358C4×C139—41no—
359C4×C139—81no—
360C4×C139C2×#12111yescharacteristic
361C4×C139#53811yescharacteristic
362C4×C139D4211yescharacteristic
363C4×C139D4211yescharacteristic
364C2×C139—21no—
365C2×C139—21no—
366C2×C139—21no—
367C2×C139—42no—
368C2×C139—81no—
369C2×C139—82no—
370C2×C139—81no—
371C2×C139—161no—
372C2×C139#242411yescharacteristic
373#25196C13911yesmaximal, characteristic, direct product factor, Sylow
374C139#2519611yescharacteristic, direct product factor, Sylow
375#3068C2×C13911yescharacteristic, complemented
376#3068C2×C13911yescharacteristic, complemented
377#3019C2×C13911yescharacteristic, complemented
378C2×#453C2×C13911yescharacteristic, complemented
379#2956C2×C13911yescharacteristic, complemented
380#2888C2×C13911yescharacteristic, complemented
381#2069C2×C13911yescharacteristic, complemented
382#2050C2×C13911yescharacteristic, complemented
383#2048C2×C13911yescharacteristic, complemented
384#2002C2×C13911yescharacteristic, complemented
385#1965C2×C13911yescharacteristic, complemented
386#1932C2×C13911yescharacteristic, complemented
387#1914C2×C13911yescharacteristic, complemented
388#1903C2×C13911yescharacteristic, complemented
389#1861C2×C13911yescharacteristic, complemented
390C2×H(5,𝔽2)C22×C13911yescharacteristic
391#575C22×C13911yescharacteristic
392#575C22×C13911yescharacteristic
393C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
394C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
395C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
396#568C22×C13911yescharacteristic
397#568C22×C13911yescharacteristic
398#568C22×C13911yescharacteristic, complemented
399#535C22×C13911yescharacteristic
400C2×#127C22×C13911yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C13911yescharacteristic, complemented
412#430C22×C13911yescharacteristic, complemented
413#430C22×C13911yescharacteristic, complemented
414#423C22×C13911yescharacteristic, complemented
415#421C22×C13911yescharacteristic
416#421C22×C13911yescharacteristic
417C2×#104C22×C13911yescharacteristic
418C2×#104C22×C13911yescharacteristic
419C2×#104C22×C13911yescharacteristic, complemented
420#418C22×C13911yescharacteristic, complemented
421#413—22no—
422#413C22×C13911yescharacteristic
423#413C22×C13911yescharacteristic
424#413C22×C13911yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C13911yescharacteristic
427C2×#100C22×C13911yescharacteristic
428C2×#100C22×C13911yescharacteristic
429C2×#100C22×C13911yescharacteristic
430C2×#100C22×C13911yescharacteristic, complemented
431C2×#100C22×C13911yescharacteristic, complemented
432C4×M16C22×C13911yescharacteristic, complemented
433#344C22×C13911yescharacteristic, complemented
434#344C22×C13911yescharacteristic, complemented
435#339C22×C13911yescharacteristic, complemented
436#338C22×C13911yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C13911yescharacteristic
444C2×#41C23×C13911yescharacteristic
445C2×#41C23×C13911yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C13911yescharacteristic
451C22×D4C23×C13911yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C13912yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C13912yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C13911yescharacteristic
484C2×M16C23×C13911yescharacteristic
485C2×M16C23×C13911yescharacteristic
486C2×M16C23×C13911yescharacteristic
487C2×M16C23×C13911yescharacteristic
488C2×M16C23×C13911yescharacteristic
489C2×M16C23×C13911yescharacteristic
490C2×M16C23×C13911yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C13911yescharacteristic
499C2×C42C23×C13911yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C13912yescomplemented
511#104D4×C13912yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C13912yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C13912yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C13912yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C13912yes—
545#41C2×D4×C13912yes—
546C2×Q8C2×D4×C13911yescharacteristic
547C2×Q8C2×D4×C13911yescharacteristic
548C2×Q8#41×C13911yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C13911yescharacteristic
577C2×D4C2×D4×C13911yescharacteristic
578C2×D4#41×C13911yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C13911yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C13912yes—
615M16C2×D4×C13912yes—
616M16C2×D4×C13912yes—
617M16C2×D4×C13912yes—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C13911yescharacteristic
635C42C2×D4×C13911yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C13911yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C13912yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C13912yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C13911yescharacteristic
696C2×C4C22×D4×C13911yescharacteristic
697C2×C4C22×D4×C13911yescharacteristic
698C2×C4C2×#41×C13911yescharacteristic
699C2×C4H(5,𝔽2)×C13911yescharacteristic
700C2×C4H(5,𝔽2)×C13911yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C13911yescharacteristic
726C22#546×C13911yescharacteristic
727C22#546×C13911yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C13911yescharacteristic
735C4#538×C13911yescharacteristic
736C4D42×C13911yescharacteristic
737C4D42×C13911yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2#2424×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2424
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. #3068×C139C2semidirect
2. #3068×C139C2semidirect
3. #3019×C139C2semidirect
4. C2×#453×C139C2semidirect
5. #2956×C139C2semidirect
6. #2888×C139C2semidirect
7. #2069×C139C2semidirect
8. #2050×C139C2semidirect
9. #2048×C139C2semidirect
10. #2002×C139C2semidirect
11. #1965×C139C2semidirect
12. #1932×C139C2semidirect
13. #1914×C139C2semidirect
14. #1903×C139C2semidirect
15. #1861×C139C2semidirect
21. C2×AGL(1,ℤ/8)×C139C22semidirect
24. #568×C139C22semidirect
37. #430×C139C22semidirect
38. #430×C139C22semidirect
39. #430×C139C22semidirect
40. #423×C139C22semidirect
45. C2×#104×C139C22semidirect
46. #418×C139C22semidirect
50. #413×C139C22semidirect
56. C2×#100×C139C22semidirect
57. C2×#100×C139C22semidirect
58. C4×M16×C139C22semidirect
59. #344×C139C22semidirect
60. #344×C139C22semidirect
61. #339×C139C22semidirect
62. #338×C139C22semidirect
81. #137×C139D4semidirect
91. AGL(1,ℤ/8)×C139D4semidirect
136. #104×C139D4semidirect
137. #104×C139D4semidirect
141. #101×C139D4semidirect
150. #100×C139D4semidirect
373. #25196C139direct (N × H)
374. C139#25196direct (N × H)
375. #3068C2×C139semidirect
376. #3068C2×C139semidirect
377. #3019C2×C139semidirect
378. C2×#453C2×C139semidirect
379. #2956C2×C139semidirect
380. #2888C2×C139semidirect
381. #2069C2×C139semidirect
382. #2050C2×C139semidirect
383. #2048C2×C139semidirect
384. #2002C2×C139semidirect
385. #1965C2×C139semidirect
386. #1932C2×C139semidirect
387. #1914C2×C139semidirect
388. #1903C2×C139semidirect
389. #1861C2×C139semidirect
395. C2×AGL(1,ℤ/8)C22×C139semidirect
398. #568C22×C139semidirect
411. #430C22×C139semidirect
412. #430C22×C139semidirect
413. #430C22×C139semidirect
414. #423C22×C139semidirect
419. C2×#104C22×C139semidirect
420. #418C22×C139semidirect
424. #413C22×C139semidirect
430. C2×#100C22×C139semidirect
431. C2×#100C22×C139semidirect
432. C4×M16C22×C139semidirect
433. #344C22×C139semidirect
434. #344C22×C139semidirect
435. #339C22×C139semidirect
436. #338C22×C139semidirect
455. #137D4×C139semidirect
465. AGL(1,ℤ/8)D4×C139semidirect
510. #104D4×C139semidirect
511. #104D4×C139semidirect
515. #101D4×C139semidirect
524. #100D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3068×C1392
#3019×C1392
C2×#453×C1392
#2956×C1392
#2888×C1392
#2069×C1392
#2050×C1392
#2048×C1392
#2002×C1392
#1965×C1392
#1932×C1392
#1914×C1392
#1903×C1392
#1861×C1392
#25196139