Finite Group Databasebeta

← C139×#24284 #48018880

Subgroups — C139×#24284 #48018880

Order 35584.

1432 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
2C2×#472×C139C211yesmaximal, characteristic, complemented
3C2×#471×C139C211yesmaximal, characteristic, complemented
4#3005×C139C211yesmaximal, characteristic, complemented
5#3003×C139C211yesmaximal, characteristic, complemented
6#2930×C139C211yesmaximal, characteristic, complemented
7#2046×C139C211yesmaximal, characteristic, complemented
8#2045×C139C211yesmaximal, characteristic, complemented
9#2019×C139C211yesmaximal, characteristic, complemented
10#2018×C139C211yesmaximal, characteristic, complemented
11#1978×C139C211yesmaximal, characteristic, complemented
12#1977×C139C211yesmaximal, characteristic, complemented
13#1811×C139C211yesmaximal, characteristic, complemented
14#1785×C139C211yesmaximal, characteristic, complemented
15#1783×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C2×#137×C139C2211yescharacteristic, complemented
19C2×AGL(1,ℤ/8)×C139—24no—
20C2×AGL(1,ℤ/8)×C139—24no—
21C2×AGL(1,ℤ/8)×C139—22no—
22C2×AGL(1,ℤ/8)×C139—22no—
23C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
26C22×SD16×C139C2211yescharacteristic
27C22×SD16×C139C2211yescharacteristic
28C22×D8×C139C2211yescharacteristic
29C22×D8×C139C2211yescharacteristic
30C2×#131×C139C2211yescharacteristic, complemented
31C22×M16×C139C2211yescharacteristic
32#525×C139C2211yescharacteristic
33#472×C139—24no—
34#471×C139—24no—
35#452×C139—22no—
36#450×C139—22no—
37#449×C139—22no—
38#447×C139—22no—
39#436×C139—22no—
40#435×C139—22no—
41C2×#108×C139C2211yescharacteristic, complemented
42C2×#108×C139C2211yescharacteristic, complemented
43#424×C139C2211yescharacteristic, complemented
44#419×C139C2211yescharacteristic, complemented
45#418×C139C2211yescharacteristic
46#418×C139C2211yescharacteristic
47#418×C139C2211yescharacteristic, complemented
48C2×#101×C139C2211yescharacteristic, complemented
49C2×#101×C139C2211yescharacteristic, complemented
50C2×#100×C139C2211yescharacteristic
51C2×#100×C139C2211yescharacteristic
52C2×#100×C139C2211yescharacteristic
53C2×#100×C139C2211yescharacteristic
54C2×#100×C139C2211yescharacteristic, complemented
55C2×#100×C139C2211yescharacteristic, complemented
56#408×C139C2211yescharacteristic, complemented
57#407×C139C2211yescharacteristic
58#407×C139C2211yescharacteristic
59#407×C139C2211yescharacteristic
60#405×C139C2211yescharacteristic, complemented
61#341×C139C2211yescharacteristic, complemented
62#341×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C2×#41×C139C2311yescharacteristic
71C22×Q8×C139C2311yescharacteristic
72C22×D4×C139—22no—
73C22×D4×C139—22no—
74C22×D4×C139—21no—
75C22×D4×C139—22no—
76C22×D4×C139—22no—
77C22×D4×C139—21no—
78C22×D4×C139—41no—
79C22×D4×C139—41no—
80C22×D4×C139C2311yescharacteristic
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139C2311yescharacteristic
85#137×C139—22no—
86#137×C139—41no—
87AGL(1,ℤ/8)×C139—216no—
88AGL(1,ℤ/8)×C139—216no—
89AGL(1,ℤ/8)×C139—22no—
90AGL(1,ℤ/8)×C139—22no—
91AGL(1,ℤ/8)×C139—22no—
92AGL(1,ℤ/8)×C139—41no—
93AGL(1,ℤ/8)×C139—41no—
94AGL(1,ℤ/8)×C139—41no—
95C2×Q16×C139—21no—
96C2×SD16×C139—22no—
97C2×SD16×C139—22no—
98C2×SD16×C139—21no—
99C2×SD16×C139—21no—
100C2×SD16×C139—21no—
101C2×SD16×C139—21no—
102C2×SD16×C139—22no—
103C2×SD16×C139—21no—
104C2×SD16×C139—21no—
105C2×SD16×C139—22no—
106C2×SD16×C139D414yescomplemented
107C2×D8×C139—22no—
108C2×D8×C139—22no—
109C2×D8×C139—21no—
110C2×D8×C139—21no—
111C2×D8×C139—21no—
112C2×D8×C139—22no—
113C2×D8×C139—21no—
114C2×D8×C139—21no—
115C2×D8×C139—22no—
116C2×D8×C139D414yescomplemented
117#131×C139—22no—
118#131×C139—22no—
119C2×M16×C139—22no—
120C2×M16×C139—22no—
121C2×M16×C139—21no—
122C2×M16×C139D412yes—
123C2×M16×C139D412yes—
124C2×M16×C139C2311yescharacteristic
125C2×M16×C139C2311yescharacteristic
126C2×M16×C139C2311yescharacteristic
127C2×M16×C139C2311yescharacteristic
128C2×M16×C139C2311yescharacteristic
129C2×M16×C139C2311yescharacteristic
130C22×C8×C139—21no—
131C22×C8×C139C2311yescharacteristic
132C22×C8×C139C2311yescharacteristic
133#123×C139—21no—
134C22⋊Q8×C139D412yes—
135#121×C139D412yes—
136#120×C139—21no—
137C4×D4×C139—22no—
138#117×C139C2311yescharacteristic
139#108×C139—22no—
140#108×C139—22no—
141C4⋊C8×C139—22no—
142#103×C139—22no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139—22no—
146#101×C139—22no—
147#101×C139—41no—
148#100×C139—22no—
149#100×C139—22no—
150#100×C139—22no—
151#100×C139—41no—
152#100×C139—41no—
153#100×C139—41no—
154C22⋊C8×C139—22no—
155C22⋊C8×C139—22no—
156C22⋊C8×C139—22no—
157C22⋊C8×C139—22no—
158#97×C139—21no—
159C4×C8×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—42no—
164C24×C139—42no—
165C24×C139—42no—
166C24×C139—84no—
167C24×C139#4111yescharacteristic
168#41×C139—28no—
169#41×C139—21no—
170#41×C139—21no—
171#41×C139—21no—
172#41×C139—21no—
173#41×C139—44no—
174#41×C139—44no—
175#41×C139—44no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
181C2×Q8×C139C2×D412yes—
182C2×Q8×C139C2×D411yescharacteristic
183C2×D4×C139—28no—
184C2×D4×C139—21no—
185C2×D4×C139—22no—
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—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
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—44no—
202C2×D4×C139—44no—
203C2×D4×C139—42no—
204C2×D4×C139—42no—
205C2×D4×C139—42no—
206C2×D4×C139—44no—
207C2×D4×C139—42no—
208C2×D4×C139—42no—
209C2×D4×C139—42no—
210C2×D4×C139C2×D412yes—
211C2×D4×C139C2×D412yes—
212C2×D4×C139C2×D412yes—
213C2×D4×C139C2×D411yescharacteristic
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—42no—
221C22×C4×C139—42no—
222C22×C4×C139—42no—
223C22×C4×C139C2×D412yes—
224C22×C4×C139C2×D412yes—
225C22×C4×C139#4111yescharacteristic
226C22×C4×C139C2411yescharacteristic
227Q16×C139—42no—
228SD16×C139—28no—
229SD16×C139—24no—
230SD16×C139—24no—
231SD16×C139—42no—
232SD16×C139—42no—
233SD16×C139—42no—
234SD16×C139—42no—
235D8×C139—28no—
236D8×C139—24no—
237D8×C139—24no—
238D8×C139—42no—
239D8×C139—42no—
240D8×C139—42no—
241M16×C139—24no—
242M16×C139—24no—
243M16×C139—21no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—21no—
254M16×C139—21no—
255M16×C139—42no—
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—21no—
263C2×C8×C139—21no—
264C2×C8×C139—42no—
265C2×C8×C139C2×D412yes—
266C2×C8×C139C2×D411yescharacteristic
267C2×C8×C139C2×D411yescharacteristic
268C2×C8×C139C2×D412yes—
269C2×C8×C139C2×D412yes—
270C4⋊C4×C139—22no—
271C4⋊C4×C139C2×D412yes—
272C22⋊C4×C139—22no—
273C22⋊C4×C139—21no—
274C22⋊C4×C139—22no—
275C42×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—22no—
280C23×C139—22no—
281C23×C139—22no—
282C23×C139—42no—
283C23×C139—48no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—82no—
291C23×C139—82no—
292C23×C139—82no—
293C23×C139—84no—
294C23×C139—84no—
295C23×C139—88no—
296C23×C139—88no—
297C23×C139#12112yes—
298C23×C139C2×#4111yescharacteristic
299Q8×C139—22no—
300Q8×C139—21no—
301Q8×C139—21no—
302Q8×C139—22no—
303Q8×C139—41no—
304Q8×C139—41no—
305D4×C139—22no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—21no—
309D4×C139—21no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—48no—
314D4×C139—48no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—82no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—22no—
327C2×C4×C139—22no—
328C2×C4×C139—22no—
329C2×C4×C139—22no—
330C2×C4×C139—22no—
331C2×C4×C139—21no—
332C2×C4×C139—22no—
333C2×C4×C139—48no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139#12112yes—
339C2×C4×C139C22×D411yescharacteristic
340C2×C4×C139C22×D411yescharacteristic
341C2×C4×C139C22×D411yescharacteristic
342C2×C4×C139C22×D411yescharacteristic
343C2×C4×C139H(5,𝔽2)11yescharacteristic
344C2×C4×C139H(5,𝔽2)11yescharacteristic
345C8×C139—22no—
346C8×C139—41no—
347C8×C139—41no—
348C8×C139—41no—
349C8×C139—41no—
350C8×C139—41no—
351C8×C139—41no—
352C8×C139#12012yes—
353C8×C139#12012yes—
354C22×C139—22no—
355C22×C139—22no—
356C22×C139—22no—
357C22×C139—22no—
358C22×C139—42no—
359C22×C139—42no—
360C22×C139—42no—
361C22×C139—41no—
362C22×C139—42no—
363C22×C139—42no—
364C22×C139—42no—
365C22×C139—82no—
366C22×C139—82no—
367C22×C139—82no—
368C22×C139—82no—
369C22×C139—82no—
370C22×C139—82no—
371C22×C139—816no—
372C22×C139—82no—
373C22×C139—82no—
374C22×C139—82no—
375C22×C139C2×#12111yescharacteristic
376C22×C139#54611yescharacteristic
377C22×C139#54611yescharacteristic
378C4×C139—22no—
379C4×C139—42no—
380C4×C139—41no—
381C4×C139—42no—
382C4×C139C2×#12011yescharacteristic
383C4×C139#53511yescharacteristic
384C4×C139D4211yescharacteristic
385C4×C139D4211yescharacteristic
386C2×C139—21no—
387C2×C139—21no—
388C2×C139—42no—
389C2×C139—81no—
390C2×C139—82no—
391C2×C139—82no—
392C2×C139—82no—
393C2×C139#240811yescharacteristic
394C2×C139#306812yes—
395#24284C13911yesmaximal, characteristic, direct product factor, Sylow
396C139#2428411yescharacteristic, direct product factor, Sylow
397C22×AGL(1,ℤ/8)C2×C13911yescharacteristic, complemented
398C2×#472C2×C13911yescharacteristic, complemented
399C2×#471C2×C13911yescharacteristic, complemented
400#3005C2×C13911yescharacteristic, complemented
401#3003C2×C13911yescharacteristic, complemented
402#2930C2×C13911yescharacteristic, complemented
403#2046C2×C13911yescharacteristic, complemented
404#2045C2×C13911yescharacteristic, complemented
405#2019C2×C13911yescharacteristic, complemented
406#2018C2×C13911yescharacteristic, complemented
407#1978C2×C13911yescharacteristic, complemented
408#1977C2×C13911yescharacteristic, complemented
409#1811C2×C13911yescharacteristic, complemented
410#1785C2×C13911yescharacteristic, complemented
411#1783C2×C13911yescharacteristic, complemented
412C22×#41C22×C13911yescharacteristic
413C23×D4C22×C13911yescharacteristic
414C2×#137C22×C13911yescharacteristic, complemented
415C2×AGL(1,ℤ/8)—24no—
416C2×AGL(1,ℤ/8)—24no—
417C2×AGL(1,ℤ/8)—22no—
418C2×AGL(1,ℤ/8)—22no—
419C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
420C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
421C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
422C22×SD16C22×C13911yescharacteristic
423C22×SD16C22×C13911yescharacteristic
424C22×D8C22×C13911yescharacteristic
425C22×D8C22×C13911yescharacteristic
426C2×#131C22×C13911yescharacteristic, complemented
427C22×M16C22×C13911yescharacteristic
428#525C22×C13911yescharacteristic
429#472—24no—
430#471—24no—
431#452—22no—
432#450—22no—
433#449—22no—
434#447—22no—
435#436—22no—
436#435—22no—
437C2×#108C22×C13911yescharacteristic, complemented
438C2×#108C22×C13911yescharacteristic, complemented
439#424C22×C13911yescharacteristic, complemented
440#419C22×C13911yescharacteristic, complemented
441#418C22×C13911yescharacteristic
442#418C22×C13911yescharacteristic
443#418C22×C13911yescharacteristic, complemented
444C2×#101C22×C13911yescharacteristic, complemented
445C2×#101C22×C13911yescharacteristic, complemented
446C2×#100C22×C13911yescharacteristic
447C2×#100C22×C13911yescharacteristic
448C2×#100C22×C13911yescharacteristic
449C2×#100C22×C13911yescharacteristic
450C2×#100C22×C13911yescharacteristic, complemented
451C2×#100C22×C13911yescharacteristic, complemented
452#408C22×C13911yescharacteristic, complemented
453#407C22×C13911yescharacteristic
454#407C22×C13911yescharacteristic
455#407C22×C13911yescharacteristic
456#405C22×C13911yescharacteristic, complemented
457#341C22×C13911yescharacteristic, complemented
458#341C22×C13911yescharacteristic, complemented
459C25—21no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41C23×C13911yescharacteristic
467C22×Q8C23×C13911yescharacteristic
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C13911yescharacteristic
477C22×D4C23×C13911yescharacteristic
478C22×D4C23×C13911yescharacteristic
479C23×C4—21no—
480C23×C4C23×C13911yescharacteristic
481#137—22no—
482#137—41no—
483AGL(1,ℤ/8)—216no—
484AGL(1,ℤ/8)—216no—
485AGL(1,ℤ/8)—22no—
486AGL(1,ℤ/8)—22no—
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—41no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×Q16—21no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—21no—
498C2×SD16—22no—
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—22no—
502C2×SD16D4×C13914yescomplemented
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—21no—
508C2×D8—22no—
509C2×D8—21no—
510C2×D8—21no—
511C2×D8—22no—
512C2×D8D4×C13914yescomplemented
513#131—22no—
514#131—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—21no—
518C2×M16D4×C13912yes—
519C2×M16D4×C13912yes—
520C2×M16C23×C13911yescharacteristic
521C2×M16C23×C13911yescharacteristic
522C2×M16C23×C13911yescharacteristic
523C2×M16C23×C13911yescharacteristic
524C2×M16C23×C13911yescharacteristic
525C2×M16C23×C13911yescharacteristic
526C22×C8—21no—
527C22×C8C23×C13911yescharacteristic
528C22×C8C23×C13911yescharacteristic
529#123—21no—
530C22⋊Q8D4×C13912yes—
531#121D4×C13912yes—
532#120—21no—
533C4×D4—22no—
534#117C23×C13911yescharacteristic
535#108—22no—
536#108—22no—
537C4⋊C8—22no—
538#103—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#101—22no—
543#101—41no—
544#100—22no—
545#100—22no—
546#100—22no—
547#100—41no—
548#100—41no—
549#100—41no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554#97—21no—
555C4×C8—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—84no—
563C24#41×C13911yescharacteristic
564#41—28no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C13912yes—
578C2×Q8C2×D4×C13911yescharacteristic
579C2×D4—28no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×D4×C13912yes—
607C2×D4C2×D4×C13912yes—
608C2×D4C2×D4×C13912yes—
609C2×D4C2×D4×C13911yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×D4×C13912yes—
620C22×C4C2×D4×C13912yes—
621C22×C4#41×C13911yescharacteristic
622C22×C4C24×C13911yescharacteristic
623Q16—42no—
624SD16—28no—
625SD16—24no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—28no—
632D8—24no—
633D8—24no—
634D8—42no—
635D8—42no—
636D8—42no—
637M16—24no—
638M16—24no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—42no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8C2×D4×C13912yes—
662C2×C8C2×D4×C13911yescharacteristic
663C2×C8C2×D4×C13911yescharacteristic
664C2×C8C2×D4×C13912yes—
665C2×C8C2×D4×C13912yes—
666C4⋊C4—22no—
667C4⋊C4C2×D4×C13912yes—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C42—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—48no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23#121×C13912yes—
694C23C2×#41×C13911yescharacteristic
695Q8—22no—
696Q8—21no—
697Q8—21no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—21no—
705D4—21no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—48no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4#121×C13912yes—
735C2×C4C22×D4×C13911yescharacteristic
736C2×C4C22×D4×C13911yescharacteristic
737C2×C4C22×D4×C13911yescharacteristic
738C2×C4C22×D4×C13911yescharacteristic
739C2×C4H(5,𝔽2)×C13911yescharacteristic
740C2×C4H(5,𝔽2)×C13911yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8#120×C13912yes—
749C8#120×C13912yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×#121×C13911yescharacteristic
772C22#546×C13911yescharacteristic
773C22#546×C13911yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—41no—
778C4C2×#120×C13911yescharacteristic
779C4#535×C13911yescharacteristic
780C4D42×C13911yescharacteristic
781C4D42×C13911yescharacteristic
782C2—21no—
783C2—21no—
784C2—42no—
785C2—81no—
786C2—82no—
787C2—82no—
788C2—82no—
789C2#2408×C13911yescharacteristic
790C2#3068×C13912yes—
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C139C2semidirect
2. C2×#472×C139C2semidirect
3. C2×#471×C139C2semidirect
4. #3005×C139C2semidirect
5. #3003×C139C2semidirect
6. #2930×C139C2semidirect
7. #2046×C139C2semidirect
8. #2045×C139C2semidirect
9. #2019×C139C2semidirect
10. #2018×C139C2semidirect
11. #1978×C139C2semidirect
12. #1977×C139C2semidirect
13. #1811×C139C2semidirect
14. #1785×C139C2semidirect
15. #1783×C139C2semidirect
18. C2×#137×C139C22semidirect
25. C2×AGL(1,ℤ/8)×C139C22semidirect
30. C2×#131×C139C22semidirect
41. C2×#108×C139C22semidirect
42. C2×#108×C139C22semidirect
43. #424×C139C22semidirect
44. #419×C139C22semidirect
47. #418×C139C22semidirect
48. C2×#101×C139C22semidirect
49. C2×#101×C139C22semidirect
54. C2×#100×C139C22semidirect
55. C2×#100×C139C22semidirect
56. #408×C139C22semidirect
60. #405×C139C22semidirect
61. #341×C139C22semidirect
62. #341×C139C22semidirect
106. C2×SD16×C139D4semidirect
116. C2×D8×C139D4semidirect
395. #24284C139direct (N × H)
396. C139#24284direct (N × H)
397. C22×AGL(1,ℤ/8)C2×C139semidirect
398. C2×#472C2×C139semidirect
399. C2×#471C2×C139semidirect
400. #3005C2×C139semidirect
401. #3003C2×C139semidirect
402. #2930C2×C139semidirect
403. #2046C2×C139semidirect
404. #2045C2×C139semidirect
405. #2019C2×C139semidirect
406. #2018C2×C139semidirect
407. #1978C2×C139semidirect
408. #1977C2×C139semidirect
409. #1811C2×C139semidirect
410. #1785C2×C139semidirect
411. #1783C2×C139semidirect
414. C2×#137C22×C139semidirect
421. C2×AGL(1,ℤ/8)C22×C139semidirect
426. C2×#131C22×C139semidirect
437. C2×#108C22×C139semidirect
438. C2×#108C22×C139semidirect
439. #424C22×C139semidirect
440. #419C22×C139semidirect
443. #418C22×C139semidirect
444. C2×#101C22×C139semidirect
445. C2×#101C22×C139semidirect
450. C2×#100C22×C139semidirect
451. C2×#100C22×C139semidirect
452. #408C22×C139semidirect
456. #405C22×C139semidirect
457. #341C22×C139semidirect
458. #341C22×C139semidirect
502. C2×SD16D4×C139semidirect
512. C2×D8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1392
C2×#472×C1392
C2×#471×C1392
#3005×C1392
#3003×C1392
#2930×C1392
#2046×C1392
#2045×C1392
#2019×C1392
#2018×C1392
#1978×C1392
#1977×C1392
#1811×C1392
#1785×C1392
#1783×C1392
#24284139