Finite Group Databasebeta

← C139×#25192 #48019788

Subgroups — C139×#25192 #48019788

Order 35584.

1054 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3062×C139C211yesmaximal, characteristic, complemented
2#3045×C139C211yesmaximal, characteristic, complemented
3C2×#453×C139C211yesmaximal, characteristic, complemented
4#3012×C139C211yesmaximal, characteristic, complemented
5C2×#444×C139C211yesmaximal, characteristic, complemented
6#2897×C139C211yesmaximal, characteristic, complemented
7#2063×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2040×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1961×C139C211yesmaximal, characteristic, complemented
12#1938×C139C211yesmaximal, characteristic, complemented
13#1907×C139C211yesmaximal, characteristic, complemented
14#1907×C139C211yesmaximal, characteristic, complemented
15#1860×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C2×#135×C139C2211yescharacteristic
21C2×#131×C139C2211yescharacteristic
22C2×#131×C139C2211yescharacteristic, complemented
23#537×C139C2211yescharacteristic
24#535×C139C2211yescharacteristic, complemented
25C2×#127×C139C2211yescharacteristic
26#520×C139C2211yescharacteristic
27#469×C139—21no—
28#468×C139—21no—
29#466×C139—21no—
30#465×C139—21no—
31#464×C139—21no—
32#463×C139—21no—
33#460×C139—21no—
34#459×C139—21no—
35#453×C139—24no—
36#452×C139—21no—
37#450×C139—21no—
38#449×C139—21no—
39#447×C139—21no—
40#444×C139—24no—
41C2×#108×C139C2211yescharacteristic, complemented
42#428×C139C2211yescharacteristic, complemented
43#424×C139C2211yescharacteristic, complemented
44C2×#104×C139C2211yescharacteristic
45C2×#104×C139C2211yescharacteristic
46C2×#104×C139C2211yescharacteristic, complemented
47#418×C139—21no—
48#418×C139C2211yescharacteristic
49#417×C139—21no—
50#417×C139C2211yescharacteristic
51#417×C139C2211yescharacteristic
52#417×C139C2211yescharacteristic, complemented
53#416×C139—21no—
54#416×C139C2211yescharacteristic
55C2×#102×C139—21no—
56C2×#102×C139C2211yescharacteristic
57C2×#102×C139C2211yescharacteristic
58C2×#102×C139C2211yescharacteristic, complemented
59C2×#102×C139C2211yescharacteristic, complemented
60C2×#100×C139C2211yescharacteristic
61C2×#100×C139C2211yescharacteristic, complemented
62#408×C139C2211yescharacteristic
63C2×#97×C139C2211yescharacteristic, complemented
64#382×C139C2211yescharacteristic, complemented
65#343×C139C2211yescharacteristic, complemented
66#343×C139C2211yescharacteristic, complemented
67#341×C139C2211yescharacteristic, complemented
68#339×C139C2211yescharacteristic, complemented
69H(5,𝔽2)×C139—22no—
70H(5,𝔽2)×C139—22no—
71H(5,𝔽2)×C139—22no—
72H(5,𝔽2)×C139—41no—
73C2×#41×C139—21no—
74C2×#41×C139—21no—
75C2×#41×C139C2311yescharacteristic
76C2×#41×C139C2311yescharacteristic
77C2×#41×C139C2311yescharacteristic
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—41no—
81C22×D4×C139—41no—
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2311yescharacteristic
84AGL(1,ℤ/8)×C139—22no—
85AGL(1,ℤ/8)×C139—22no—
86AGL(1,ℤ/8)×C139—22no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—41no—
89AGL(1,ℤ/8)×C139—41no—
90#135×C139—22no—
91#135×C139—22no—
92C2×Q16×C139D411yescharacteristic, complemented
93C2×SD16×C139—21no—
94C2×SD16×C139—21no—
95C2×SD16×C139—21no—
96C2×SD16×C139D411yescharacteristic, complemented
97C2×SD16×C139D411yescharacteristic, complemented
98C2×D8×C139—21no—
99C2×D8×C139—21no—
100C2×D8×C139—21no—
101C2×D8×C139D411yescharacteristic, complemented
102#131×C139—22no—
103#131×C139—22no—
104#131×C139—41no—
105#131×C139—41no—
106C2×M16×C139—21no—
107C2×M16×C139—21no—
108C2×M16×C139C2311yescharacteristic
109C2×M16×C139C2311yescharacteristic
110C2×M16×C139C2311yescharacteristic
111C2×M16×C139C2311yescharacteristic
112C22×C8×C139—21no—
113C22×C8×C139—21no—
114C22×C8×C139C2311yescharacteristic
115C22×C8×C139C2311yescharacteristic
116#127×C139—21no—
117#127×C139—22no—
118#127×C139—22no—
119#124×C139—21no—
120C22⋊Q8×C139—21no—
121C22⋊Q8×C139—21no—
122#121×C139—21no—
123#121×C139—21no—
124#121×C139—21no—
125#121×C139—21no—
126#121×C139—41no—
127#120×C139—41no—
128C4×Q8×C139—21no—
129C4×D4×C139—21no—
130C4×D4×C139—41no—
131#117×C139—21no—
132#117×C139C2311yescharacteristic
133C2×C4⋊C4×C139—21no—
134C2×C4⋊C4×C139C2311yescharacteristic
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C42×C139C2311yescharacteristic
137#108×C139—22no—
138#107×C139—21no—
139#106×C139—21no—
140C4⋊C8×C139—21no—
141C4⋊C8×C139—21no—
142#104×C139—22no—
143#104×C139—22no—
144#104×C139D414yescomplemented
145#103×C139—21no—
146#103×C139—21no—
147#103×C139—21no—
148#103×C139D411yescharacteristic, complemented
149#103×C139D411yescharacteristic, complemented
150#102×C139—21no—
151#102×C139—21no—
152#102×C139—21no—
153#102×C139—21no—
154#102×C139—21no—
155#102×C139—21no—
156#102×C139—21no—
157#102×C139—21no—
158#102×C139—21no—
159#102×C139—21no—
160#102×C139—21no—
161#102×C139—21no—
162#102×C139—21no—
163#102×C139D411yescharacteristic, complemented
164#102×C139D411yescharacteristic, complemented
165#100×C139—22no—
166#100×C139—41no—
167C22⋊C8×C139—21no—
168C22⋊C8×C139—21no—
169#97×C139—22no—
170#95×C139—41no—
171C24×C139—21no—
172C24×C139—21no—
173C24×C139—41no—
174#41×C139—21no—
175#41×C139—21no—
176#41×C139—24no—
177#41×C139—21no—
178#41×C139—21no—
179#41×C139—21no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—21no—
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—42no—
186#41×C139—42no—
187#41×C139—42no—
188#41×C139C2×D412yes—
189#41×C139#4112yes—
190C2×Q8×C139C2×D411yescharacteristic
191C2×Q8×C139C2×D411yescharacteristic
192C2×Q8×C139C2×D411yescharacteristic
193C2×D4×C139—21no—
194C2×D4×C139—24no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—42no—
209C2×D4×C139—41no—
210C2×D4×C139—41no—
211C2×D4×C139—44no—
212C2×D4×C139—41no—
213C2×D4×C139—41no—
214C2×D4×C139—42no—
215C2×D4×C139—44no—
216C2×D4×C139—44no—
217C2×D4×C139—42no—
218C2×D4×C139—41no—
219C2×D4×C139—82no—
220C2×D4×C139—82no—
221C2×D4×C139C2×D411yescharacteristic
222C2×D4×C139C2×D411yescharacteristic
223C2×D4×C139C2×D411yescharacteristic
224C2×D4×C139#4112yes—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—41no—
232C22×C4×C139—41no—
233C22×C4×C139C2411yescharacteristic
234Q16×C139—22no—
235SD16×C139—22no—
236SD16×C139—22no—
237SD16×C139—42no—
238SD16×C139—42no—
239SD16×C139—42no—
240D8×C139—22no—
241D8×C139—42no—
242D8×C139—42no—
243D8×C139—42no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—42no—
252M16×C139—42no—
253M16×C139C2×D412yes—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—42no—
263C2×C8×C139—42no—
264C2×C8×C139C2×D411yescharacteristic
265C2×C8×C139C2×D411yescharacteristic
266C2×C8×C139C2×D411yescharacteristic
267C2×C8×C139C2×D411yescharacteristic
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—41no—
273C4⋊C4×C139—41no—
274C4⋊C4×C139C2×D411yescharacteristic
275C4⋊C4×C139C2×D411yescharacteristic
276C22⋊C4×C139—21no—
277C22⋊C4×C139—41no—
278C22⋊C4×C139—41no—
279C22⋊C4×C139—41no—
280C22⋊C4×C139—41no—
281C22⋊C4×C139—41no—
282C42×C139—21no—
283C42×C139—21no—
284C42×C139—41no—
285C42×C139C2×D412yes—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—22no—
290C23×C139—44no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—81no—
297C23×C139—81no—
298C23×C139—81no—
299C23×C139—81no—
300C23×C139—161no—
301C23×C139—161no—
302C23×C139H(5,𝔽2)11yescharacteristic
303Q8×C139—21no—
304Q8×C139—21no—
305Q8×C139—21no—
306Q8×C139—21no—
307Q8×C139—21no—
308Q8×C139#12112yes—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—21no—
312D4×C139—21no—
313D4×C139—22no—
314D4×C139—21no—
315D4×C139—21no—
316D4×C139—21no—
317D4×C139—22no—
318D4×C139—44no—
319D4×C139—44no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—88no—
331D4×C139—161no—
332D4×C139—161no—
333D4×C139—161no—
334D4×C139#12112yes—
335C2×C4×C139—21no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—22no—
343C2×C4×C139—44no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—81no—
353C2×C4×C139—81no—
354C2×C4×C139—161no—
355C2×C4×C139C22×D411yescharacteristic
356C2×C4×C139C22×D411yescharacteristic
357C2×C4×C139C22×D411yescharacteristic
358C2×C4×C139C2×#4111yescharacteristic
359C2×C4×C139C2×#4111yescharacteristic
360C2×C4×C139H(5,𝔽2)11yescharacteristic
361C8×C139—21no—
362C8×C139—21no—
363C8×C139—21no—
364C8×C139—21no—
365C8×C139—22no—
366C8×C139—41no—
367C8×C139—41no—
368C8×C139—41no—
369C22×C139—21no—
370C22×C139—21no—
371C22×C139—22no—
372C22×C139—41no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—42no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—41no—
379C22×C139—41no—
380C22×C139—41no—
381C22×C139—82no—
382C22×C139—82no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—161no—
389C22×C139—161no—
390C22×C139—164no—
391C22×C139#53811yescharacteristic
392C22×C139D4211yescharacteristic
393C22×C139#54611yescharacteristic
394C4×C139—22no—
395C4×C139—42no—
396C4×C139—41no—
397C4×C139—41no—
398C4×C139—41no—
399C4×C139—41no—
400C4×C139—81no—
401C4×C139—81no—
402C4×C139C2×#12111yescharacteristic
403C4×C139#52511yescharacteristic
404C4×C139D4211yescharacteristic
405C4×C139#54611yescharacteristic
406C2×C139—21no—
407C2×C139—21no—
408C2×C139—42no—
409C2×C139—81no—
410C2×C139—81no—
411C2×C139—82no—
412C2×C139—161no—
413C2×C139#242411yescharacteristic
414C2×C139#328811yescharacteristic
415C2×C139#328811yescharacteristic
416#25192C13911yesmaximal, characteristic, direct product factor, Sylow
417C139#2519211yescharacteristic, direct product factor, Sylow
418#3062C2×C13911yescharacteristic, complemented
419#3045C2×C13911yescharacteristic, complemented
420C2×#453C2×C13911yescharacteristic, complemented
421#3012C2×C13911yescharacteristic, complemented
422C2×#444C2×C13911yescharacteristic, complemented
423#2897C2×C13911yescharacteristic, complemented
424#2063C2×C13911yescharacteristic, complemented
425#2051C2×C13911yescharacteristic, complemented
426#2040C2×C13911yescharacteristic, complemented
427#2002C2×C13911yescharacteristic, complemented
428#1961C2×C13911yescharacteristic, complemented
429#1938C2×C13911yescharacteristic, complemented
430#1907C2×C13911yescharacteristic, complemented
431#1907C2×C13911yescharacteristic, complemented
432#1860C2×C13911yescharacteristic, complemented
433C2×H(5,𝔽2)C22×C13911yescharacteristic
434C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
435C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
436C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
437C2×#135C22×C13911yescharacteristic
438C2×#131C22×C13911yescharacteristic
439C2×#131C22×C13911yescharacteristic, complemented
440#537C22×C13911yescharacteristic
441#535C22×C13911yescharacteristic, complemented
442C2×#127C22×C13911yescharacteristic
443#520C22×C13911yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#444—24no—
458C2×#108C22×C13911yescharacteristic, complemented
459#428C22×C13911yescharacteristic, complemented
460#424C22×C13911yescharacteristic, complemented
461C2×#104C22×C13911yescharacteristic
462C2×#104C22×C13911yescharacteristic
463C2×#104C22×C13911yescharacteristic, complemented
464#418—21no—
465#418C22×C13911yescharacteristic
466#417—21no—
467#417C22×C13911yescharacteristic
468#417C22×C13911yescharacteristic
469#417C22×C13911yescharacteristic, complemented
470#416—21no—
471#416C22×C13911yescharacteristic
472C2×#102—21no—
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic, complemented
476C2×#102C22×C13911yescharacteristic, complemented
477C2×#100C22×C13911yescharacteristic
478C2×#100C22×C13911yescharacteristic, complemented
479#408C22×C13911yescharacteristic
480C2×#97C22×C13911yescharacteristic, complemented
481#382C22×C13911yescharacteristic, complemented
482#343C22×C13911yescharacteristic, complemented
483#343C22×C13911yescharacteristic, complemented
484#341C22×C13911yescharacteristic, complemented
485#339C22×C13911yescharacteristic, complemented
486H(5,𝔽2)—22no—
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—41no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41C23×C13911yescharacteristic
493C2×#41C23×C13911yescharacteristic
494C2×#41C23×C13911yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C13911yescharacteristic
500C22×D4C23×C13911yescharacteristic
501AGL(1,ℤ/8)—22no—
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—41no—
506AGL(1,ℤ/8)—41no—
507#135—22no—
508#135—22no—
509C2×Q16D4×C13911yescharacteristic, complemented
510C2×SD16—21no—
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16D4×C13911yescharacteristic, complemented
514C2×SD16D4×C13911yescharacteristic, complemented
515C2×D8—21no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8D4×C13911yescharacteristic, complemented
519#131—22no—
520#131—22no—
521#131—41no—
522#131—41no—
523C2×M16—21no—
524C2×M16—21no—
525C2×M16C23×C13911yescharacteristic
526C2×M16C23×C13911yescharacteristic
527C2×M16C23×C13911yescharacteristic
528C2×M16C23×C13911yescharacteristic
529C22×C8—21no—
530C22×C8—21no—
531C22×C8C23×C13911yescharacteristic
532C22×C8C23×C13911yescharacteristic
533#127—21no—
534#127—22no—
535#127—22no—
536#124—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539#121—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—41no—
544#120—41no—
545C4×Q8—21no—
546C4×D4—21no—
547C4×D4—41no—
548#117—21no—
549#117C23×C13911yescharacteristic
550C2×C4⋊C4—21no—
551C2×C4⋊C4C23×C13911yescharacteristic
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C42C23×C13911yescharacteristic
554#108—22no—
555#107—21no—
556#106—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559#104—22no—
560#104—22no—
561#104D4×C13914yescomplemented
562#103—21no—
563#103—21no—
564#103—21no—
565#103D4×C13911yescharacteristic, complemented
566#103D4×C13911yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102D4×C13911yescharacteristic, complemented
581#102D4×C13911yescharacteristic, complemented
582#100—22no—
583#100—41no—
584C22⋊C8—21no—
585C22⋊C8—21no—
586#97—22no—
587#95—41no—
588C24—21no—
589C24—21no—
590C24—41no—
591#41—21no—
592#41—21no—
593#41—24no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41C2×D4×C13912yes—
606#41#41×C13912yes—
607C2×Q8C2×D4×C13911yescharacteristic
608C2×Q8C2×D4×C13911yescharacteristic
609C2×Q8C2×D4×C13911yescharacteristic
610C2×D4—21no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4—44no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—41no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C13911yescharacteristic
639C2×D4C2×D4×C13911yescharacteristic
640C2×D4C2×D4×C13911yescharacteristic
641C2×D4#41×C13912yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C13911yescharacteristic
651Q16—22no—
652SD16—22no—
653SD16—22no—
654SD16—42no—
655SD16—42no—
656SD16—42no—
657D8—22no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16—42no—
670M16C2×D4×C13912yes—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—42no—
681C2×C8C2×D4×C13911yescharacteristic
682C2×C8C2×D4×C13911yescharacteristic
683C2×C8C2×D4×C13911yescharacteristic
684C2×C8C2×D4×C13911yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—41no—
690C4⋊C4—41no—
691C4⋊C4C2×D4×C13911yescharacteristic
692C4⋊C4C2×D4×C13911yescharacteristic
693C22⋊C4—21no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—41no—
702C42C2×D4×C13912yes—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—161no—
718C23—161no—
719C23H(5,𝔽2)×C13911yescharacteristic
720Q8—21no—
721Q8—21no—
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8#121×C13912yes—
726D4—22no—
727D4—22no—
728D4—21no—
729D4—21no—
730D4—22no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—22no—
735D4—44no—
736D4—44no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—88no—
748D4—161no—
749D4—161no—
750D4—161no—
751D4#121×C13912yes—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—161no—
772C2×C4C22×D4×C13911yescharacteristic
773C2×C4C22×D4×C13911yescharacteristic
774C2×C4C22×D4×C13911yescharacteristic
775C2×C4C2×#41×C13911yescharacteristic
776C2×C4C2×#41×C13911yescharacteristic
777C2×C4H(5,𝔽2)×C13911yescharacteristic
778C8—21no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—161no—
806C22—161no—
807C22—164no—
808C22#538×C13911yescharacteristic
809C22D42×C13911yescharacteristic
810C22#546×C13911yescharacteristic
811C4—22no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4C2×#121×C13911yescharacteristic
820C4#525×C13911yescharacteristic
821C4D42×C13911yescharacteristic
822C4#546×C13911yescharacteristic
823C2—21no—
824C2—21no—
825C2—42no—
826C2—81no—
827C2—81no—
828C2—82no—
829C2—161no—
830C2#2424×C13911yescharacteristic
831C2#3288×C13911yescharacteristic
832C2#3288×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC22×C4C24×C139
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. #3062×C139C2semidirect
2. #3045×C139C2semidirect
3. C2×#453×C139C2semidirect
4. #3012×C139C2semidirect
5. C2×#444×C139C2semidirect
6. #2897×C139C2semidirect
7. #2063×C139C2semidirect
8. #2051×C139C2semidirect
9. #2040×C139C2semidirect
10. #2002×C139C2semidirect
11. #1961×C139C2semidirect
12. #1938×C139C2semidirect
13. #1907×C139C2semidirect
14. #1907×C139C2semidirect
15. #1860×C139C2semidirect
22. C2×#131×C139C22semidirect
24. #535×C139C22semidirect
41. C2×#108×C139C22semidirect
42. #428×C139C22semidirect
43. #424×C139C22semidirect
46. C2×#104×C139C22semidirect
52. #417×C139C22semidirect
58. C2×#102×C139C22semidirect
59. C2×#102×C139C22semidirect
61. C2×#100×C139C22semidirect
63. C2×#97×C139C22semidirect
64. #382×C139C22semidirect
65. #343×C139C22semidirect
66. #343×C139C22semidirect
67. #341×C139C22semidirect
68. #339×C139C22semidirect
92. C2×Q16×C139D4semidirect
96. C2×SD16×C139D4semidirect
97. C2×SD16×C139D4semidirect
101. C2×D8×C139D4semidirect
144. #104×C139D4semidirect
148. #103×C139D4semidirect
149. #103×C139D4semidirect
163. #102×C139D4semidirect
164. #102×C139D4semidirect
416. #25192C139direct (N × H)
417. C139#25192direct (N × H)
418. #3062C2×C139semidirect
419. #3045C2×C139semidirect
420. C2×#453C2×C139semidirect
421. #3012C2×C139semidirect
422. C2×#444C2×C139semidirect
423. #2897C2×C139semidirect
424. #2063C2×C139semidirect
425. #2051C2×C139semidirect
426. #2040C2×C139semidirect
427. #2002C2×C139semidirect
428. #1961C2×C139semidirect
429. #1938C2×C139semidirect
430. #1907C2×C139semidirect
431. #1907C2×C139semidirect
432. #1860C2×C139semidirect
439. C2×#131C22×C139semidirect
441. #535C22×C139semidirect
458. C2×#108C22×C139semidirect
459. #428C22×C139semidirect
460. #424C22×C139semidirect
463. C2×#104C22×C139semidirect
469. #417C22×C139semidirect
475. C2×#102C22×C139semidirect
476. C2×#102C22×C139semidirect
478. C2×#100C22×C139semidirect
480. C2×#97C22×C139semidirect
481. #382C22×C139semidirect
482. #343C22×C139semidirect
483. #343C22×C139semidirect
484. #341C22×C139semidirect
485. #339C22×C139semidirect
509. C2×Q16D4×C139semidirect
513. C2×SD16D4×C139semidirect
514. C2×SD16D4×C139semidirect
518. C2×D8D4×C139semidirect
561. #104D4×C139semidirect
565. #103D4×C139semidirect
566. #103D4×C139semidirect
580. #102D4×C139semidirect
581. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3062×C1392
#3045×C1392
C2×#453×C1392
#3012×C1392
C2×#444×C1392
#2897×C1392
#2063×C1392
#2051×C1392
#2040×C1392
#2002×C1392
#1961×C1392
#1938×C1392
#1907×C1392
#1860×C1392
#25192139