Finite Group Databasebeta

← C139×#25188 #48019784

Subgroups — C139×#25188 #48019784

Order 35584.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 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×#443×C139C211yesmaximal, characteristic, complemented
6#2897×C139C211yesmaximal, characteristic, complemented
7#2063×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2039×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1957×C139C211yesmaximal, characteristic, complemented
12#1937×C139C211yesmaximal, characteristic, complemented
13#1907×C139C211yesmaximal, characteristic, complemented
14#1907×C139C211yesmaximal, characteristic, complemented
15#1859×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#443×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×C4×C8×C139C2211yescharacteristic, complemented
64#384×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×C139—41no—
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C4⋊C4×C139C2311yescharacteristic
137C2×C42×C139C2311yescharacteristic
138#108×C139—22no—
139#107×C139—21no—
140#106×C139—21no—
141C4⋊C8×C139—21no—
142C4⋊C8×C139—21no—
143#104×C139—22no—
144#104×C139—22no—
145#104×C139D414yescomplemented
146#103×C139—21no—
147#103×C139—21no—
148#103×C139—21no—
149#103×C139D411yescharacteristic, complemented
150#103×C139D411yescharacteristic, complemented
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×C139—21no—
164#102×C139D411yescharacteristic, complemented
165#102×C139D411yescharacteristic, complemented
166#100×C139—22no—
167#100×C139—41no—
168C22⋊C8×C139—21no—
169C22⋊C8×C139—21no—
170C4×C8×C139—22no—
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×C139—82no—
275C4⋊C4×C139C2×D411yescharacteristic
276C4⋊C4×C139C2×D411yescharacteristic
277C22⋊C4×C139—21no—
278C22⋊C4×C139—41no—
279C22⋊C4×C139—41no—
280C22⋊C4×C139—41no—
281C22⋊C4×C139—41no—
282C22⋊C4×C139—41no—
283C42×C139—21no—
284C42×C139—21no—
285C42×C139—41no—
286C42×C139C2×D412yes—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—22no—
291C23×C139—44no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—81no—
298C23×C139—81no—
299C23×C139—81no—
300C23×C139—81no—
301C23×C139—161no—
302C23×C139—161no—
303C23×C139H(5,𝔽2)11yescharacteristic
304Q8×C139—21no—
305Q8×C139—21no—
306Q8×C139—21no—
307Q8×C139—21no—
308Q8×C139—21no—
309Q8×C139#12112yes—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—21no—
313D4×C139—21no—
314D4×C139—22no—
315D4×C139—21no—
316D4×C139—21no—
317D4×C139—21no—
318D4×C139—22no—
319D4×C139—44no—
320D4×C139—44no—
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—41no—
331D4×C139—88no—
332D4×C139—161no—
333D4×C139—161no—
334D4×C139—161no—
335D4×C139#12112yes—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—21no—
339C2×C4×C139—22no—
340C2×C4×C139—22no—
341C2×C4×C139—22no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—44no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—81no—
354C2×C4×C139—81no—
355C2×C4×C139—161no—
356C2×C4×C139C22×D411yescharacteristic
357C2×C4×C139C22×D411yescharacteristic
358C2×C4×C139C22×D411yescharacteristic
359C2×C4×C139C2×#4111yescharacteristic
360C2×C4×C139C2×#4111yescharacteristic
361C2×C4×C139H(5,𝔽2)11yescharacteristic
362C8×C139—21no—
363C8×C139—21no—
364C8×C139—21no—
365C8×C139—21no—
366C8×C139—22no—
367C8×C139—41no—
368C8×C139—41no—
369C8×C139—41no—
370C22×C139—21no—
371C22×C139—21no—
372C22×C139—22no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—42no—
377C22×C139—41no—
378C22×C139—41no—
379C22×C139—41no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—82no—
383C22×C139—82no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—161no—
390C22×C139—161no—
391C22×C139—164no—
392C22×C139#53811yescharacteristic
393C22×C139D4211yescharacteristic
394C22×C139#54611yescharacteristic
395C4×C139—24no—
396C4×C139—22no—
397C4×C139—41no—
398C4×C139—41no—
399C4×C139—41no—
400C4×C139—41no—
401C4×C139—81no—
402C4×C139—81no—
403C4×C139C2×#12111yescharacteristic
404C4×C139#52511yescharacteristic
405C4×C139D4211yescharacteristic
406C4×C139#54611yescharacteristic
407C2×C139—21no—
408C2×C139—21no—
409C2×C139—42no—
410C2×C139—81no—
411C2×C139—81no—
412C2×C139—82no—
413C2×C139—161no—
414C2×C139#242411yescharacteristic
415C2×C139#329111yescharacteristic
416C2×C139#329211yescharacteristic
417#25188C13911yesmaximal, characteristic, direct product factor, Sylow
418C139#2518811yescharacteristic, direct product factor, Sylow
419#3062C2×C13911yescharacteristic, complemented
420#3045C2×C13911yescharacteristic, complemented
421C2×#453C2×C13911yescharacteristic, complemented
422#3012C2×C13911yescharacteristic, complemented
423C2×#443C2×C13911yescharacteristic, complemented
424#2897C2×C13911yescharacteristic, complemented
425#2063C2×C13911yescharacteristic, complemented
426#2051C2×C13911yescharacteristic, complemented
427#2039C2×C13911yescharacteristic, complemented
428#2002C2×C13911yescharacteristic, complemented
429#1957C2×C13911yescharacteristic, complemented
430#1937C2×C13911yescharacteristic, complemented
431#1907C2×C13911yescharacteristic, complemented
432#1907C2×C13911yescharacteristic, complemented
433#1859C2×C13911yescharacteristic, complemented
434C2×H(5,𝔽2)C22×C13911yescharacteristic
435C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
436C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
437C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
438C2×#135C22×C13911yescharacteristic
439C2×#131C22×C13911yescharacteristic
440C2×#131C22×C13911yescharacteristic, complemented
441#537C22×C13911yescharacteristic
442#535C22×C13911yescharacteristic, complemented
443C2×#127C22×C13911yescharacteristic
444#520C22×C13911yescharacteristic
445#469—21no—
446#468—21no—
447#466—21no—
448#465—21no—
449#464—21no—
450#463—21no—
451#460—21no—
452#459—21no—
453#453—24no—
454#452—21no—
455#450—21no—
456#449—21no—
457#447—21no—
458#443—24no—
459C2×#108C22×C13911yescharacteristic, complemented
460#428C22×C13911yescharacteristic, complemented
461#424C22×C13911yescharacteristic, complemented
462C2×#104C22×C13911yescharacteristic
463C2×#104C22×C13911yescharacteristic
464C2×#104C22×C13911yescharacteristic, complemented
465#418—21no—
466#418C22×C13911yescharacteristic
467#417—21no—
468#417C22×C13911yescharacteristic
469#417C22×C13911yescharacteristic
470#417C22×C13911yescharacteristic, complemented
471#416—21no—
472#416C22×C13911yescharacteristic
473C2×#102—21no—
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic, complemented
477C2×#102C22×C13911yescharacteristic, complemented
478C2×#100C22×C13911yescharacteristic
479C2×#100C22×C13911yescharacteristic, complemented
480#408C22×C13911yescharacteristic
481C2×C4×C8C22×C13911yescharacteristic, complemented
482#384C22×C13911yescharacteristic, complemented
483#343C22×C13911yescharacteristic, complemented
484#343C22×C13911yescharacteristic, complemented
485#341C22×C13911yescharacteristic, complemented
486#339C22×C13911yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C13911yescharacteristic
494C2×#41C23×C13911yescharacteristic
495C2×#41C23×C13911yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C13911yescharacteristic
501C22×D4C23×C13911yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C13911yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C13911yescharacteristic, complemented
515C2×SD16D4×C13911yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C13911yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C13911yescharacteristic
527C2×M16C23×C13911yescharacteristic
528C2×M16C23×C13911yescharacteristic
529C2×M16C23×C13911yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C13911yescharacteristic
533C22×C8C23×C13911yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C13911yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C42C23×C13911yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C13914yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C13911yescharacteristic, complemented
568#103D4×C13911yescharacteristic, complemented
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#102—21no—
581#102—21no—
582#102D4×C13911yescharacteristic, complemented
583#102D4×C13911yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C13912yes—
607#41#41×C13912yes—
608C2×Q8C2×D4×C13911yescharacteristic
609C2×Q8C2×D4×C13911yescharacteristic
610C2×Q8C2×D4×C13911yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
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—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C13911yescharacteristic
640C2×D4C2×D4×C13911yescharacteristic
641C2×D4C2×D4×C13911yescharacteristic
642C2×D4#41×C13912yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C13911yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C13912yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C13911yescharacteristic
683C2×C8C2×D4×C13911yescharacteristic
684C2×C8C2×D4×C13911yescharacteristic
685C2×C8C2×D4×C13911yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C13911yescharacteristic
694C4⋊C4C2×D4×C13911yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C13912yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C13911yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C13912yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C13912yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C13911yescharacteristic
775C2×C4C22×D4×C13911yescharacteristic
776C2×C4C22×D4×C13911yescharacteristic
777C2×C4C2×#41×C13911yescharacteristic
778C2×C4C2×#41×C13911yescharacteristic
779C2×C4H(5,𝔽2)×C13911yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C13911yescharacteristic
811C22D42×C13911yescharacteristic
812C22#546×C13911yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C13911yescharacteristic
822C4#525×C13911yescharacteristic
823C4D42×C13911yescharacteristic
824C4#546×C13911yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2#2424×C13911yescharacteristic
833C2#3291×C13911yescharacteristic
834C2#3292×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×#443×C139C2semidirect
6. #2897×C139C2semidirect
7. #2063×C139C2semidirect
8. #2051×C139C2semidirect
9. #2039×C139C2semidirect
10. #2002×C139C2semidirect
11. #1957×C139C2semidirect
12. #1937×C139C2semidirect
13. #1907×C139C2semidirect
14. #1907×C139C2semidirect
15. #1859×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×C4×C8×C139C22semidirect
64. #384×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
145. #104×C139D4semidirect
149. #103×C139D4semidirect
150. #103×C139D4semidirect
164. #102×C139D4semidirect
165. #102×C139D4semidirect
417. #25188C139direct (N × H)
418. C139#25188direct (N × H)
419. #3062C2×C139semidirect
420. #3045C2×C139semidirect
421. C2×#453C2×C139semidirect
422. #3012C2×C139semidirect
423. C2×#443C2×C139semidirect
424. #2897C2×C139semidirect
425. #2063C2×C139semidirect
426. #2051C2×C139semidirect
427. #2039C2×C139semidirect
428. #2002C2×C139semidirect
429. #1957C2×C139semidirect
430. #1937C2×C139semidirect
431. #1907C2×C139semidirect
432. #1907C2×C139semidirect
433. #1859C2×C139semidirect
440. C2×#131C22×C139semidirect
442. #535C22×C139semidirect
459. C2×#108C22×C139semidirect
460. #428C22×C139semidirect
461. #424C22×C139semidirect
464. C2×#104C22×C139semidirect
470. #417C22×C139semidirect
476. C2×#102C22×C139semidirect
477. C2×#102C22×C139semidirect
479. C2×#100C22×C139semidirect
481. C2×C4×C8C22×C139semidirect
482. #384C22×C139semidirect
483. #343C22×C139semidirect
484. #343C22×C139semidirect
485. #341C22×C139semidirect
486. #339C22×C139semidirect
510. C2×Q16D4×C139semidirect
514. C2×SD16D4×C139semidirect
515. C2×SD16D4×C139semidirect
519. C2×D8D4×C139semidirect
563. #104D4×C139semidirect
567. #103D4×C139semidirect
568. #103D4×C139semidirect
582. #102D4×C139semidirect
583. #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×#443×C1392
#2897×C1392
#2063×C1392
#2051×C1392
#2039×C1392
#2002×C1392
#1957×C1392
#1937×C1392
#1907×C1392
#1859×C1392
#25188139