Finite Group Databasebeta

← C139×#23894 #48018490

Subgroups — C139×#23894 #48018490

Order 35584.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C139C211yesmaximal, characteristic, complemented
2#3585×C139C211yesmaximal, characteristic, complemented
3#3020×C139C211yesmaximal, characteristic, complemented
4#3019×C139C211yesmaximal, characteristic, complemented
5#3010×C139C211yesmaximal, characteristic, complemented
6#3009×C139C211yesmaximal, characteristic, complemented
7#2019×C139C211yesmaximal, characteristic, complemented
8#2017×C139C211yesmaximal, characteristic, complemented
9#2009×C139C211yesmaximal, characteristic, complemented
10#2008×C139C211yesmaximal, characteristic, complemented
11#1903×C139C211yesmaximal, characteristic, complemented
12#1902×C139C211yesmaximal, characteristic, complemented
13#1881×C139C211yesmaximal, characteristic, complemented
14#1881×C139C211yesmaximal, characteristic, complemented
15#1794×C139C211yesmaximal, characteristic, complemented
16#585×C139C2211yescharacteristic
17C2×2−1+4×C139C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C139C2211yescharacteristic
19#578×C139—22no—
20#578×C139—22no—
21#577×C139—22no—
22#577×C139—22no—
23#577×C139—22no—
24#577×C139—22no—
25#576×C139—22no—
26#576×C139—22no—
27#575×C139—22no—
28#575×C139—22no—
29#575×C139C2211yescharacteristic
30#575×C139C2211yescharacteristic
31#575×C139C2211yescharacteristic
32#575×C139C2211yescharacteristic, complemented
33#575×C139C2211yescharacteristic, complemented
34C2×#137×C139—22no—
35C2×#137×C139C2211yescharacteristic
36C2×#137×C139C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C139—22no—
38C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
40C22×SD16×C139C2211yescharacteristic, complemented
41#568×C139C2211yescharacteristic
42#568×C139C2211yescharacteristic, complemented
43#536×C139C2211yescharacteristic, complemented
44#535×C139C2211yescharacteristic, complemented
45#456×C139—22no—
46#455×C139—22no—
47#454×C139—22no—
48#453×C139—22no—
49#452×C139—22no—
50#450×C139—22no—
51#449×C139—22no—
52#448×C139—22no—
53#421×C139C2211yescharacteristic
54#421×C139C2211yescharacteristic, complemented
55#421×C139C2211yescharacteristic, complemented
56#421×C139C2211yescharacteristic, complemented
57#419×C139C2211yescharacteristic, complemented
58#418×C139C2211yescharacteristic, complemented
59#416×C139C2211yescharacteristic
60#416×C139C2211yescharacteristic, complemented
61C2×#101×C139C2211yescharacteristic, complemented
62C2×#100×C139C2211yescharacteristic, complemented
63#410×C139C2211yescharacteristic, complemented
64#408×C139C2211yescharacteristic, complemented
65#408×C139C2211yescharacteristic, complemented
66#408×C139C2211yescharacteristic, complemented
67#344×C139C2211yescharacteristic, complemented
68#344×C139C2211yescharacteristic, complemented
69#341×C139C2211yescharacteristic, complemented
70#338×C139C2211yescharacteristic, complemented
712−1+4×C139—22no—
722−1+4×C139—21no—
732−1+4×C139—22no—
742−1+4×C139—21no—
752−1+4×C139—22no—
762−1+4×C139—41no—
772−1+4×C139D412yescomplemented
78H(5,𝔽2)×C139—22no—
79H(5,𝔽2)×C139—21no—
80H(5,𝔽2)×C139—22no—
81H(5,𝔽2)×C139—21no—
82H(5,𝔽2)×C139—22no—
83H(5,𝔽2)×C139—41no—
84H(5,𝔽2)×C139—41no—
85H(5,𝔽2)×C139D412yescomplemented
86C2×#41×C139—22no—
87C2×#41×C139—22no—
88C2×#41×C139—21no—
89C2×#41×C139—21no—
90C2×#41×C139—21no—
91C2×#41×C139—21no—
92C2×#41×C139—41no—
93C2×#41×C139—41no—
94C2×#41×C139C2311yescharacteristic
95C2×#41×C139C2311yescharacteristic
96C2×#41×C139C2311yescharacteristic
97C2×#41×C139C2311yescharacteristic
98C2×#41×C139C2311yescharacteristic
99C22×Q8×C139—21no—
100C22×Q8×C139—21no—
101C22×Q8×C139C2311yescharacteristic
102C22×D4×C139—21no—
103C22×D4×C139—21no—
104C22×D4×C139—41no—
105C22×D4×C139C2311yescharacteristic
106#137×C139—24no—
107#137×C139—24no—
108#137×C139—24no—
109#137×C139—24no—
110#137×C139—22no—
111#137×C139—22no—
112#137×C139—21no—
113#137×C139—22no—
114#137×C139—21no—
115#137×C139—21no—
116#137×C139—21no—
117#137×C139—21no—
118#137×C139—21no—
119#137×C139—21no—
120#137×C139—21no—
121#137×C139—22no—
122#137×C139D412yes—
123#137×C139D412yescomplemented
124AGL(1,ℤ/8)×C139—24no—
125AGL(1,ℤ/8)×C139—24no—
126AGL(1,ℤ/8)×C139—24no—
127AGL(1,ℤ/8)×C139—24no—
128AGL(1,ℤ/8)×C139—22no—
129AGL(1,ℤ/8)×C139—22no—
130AGL(1,ℤ/8)×C139—21no—
131AGL(1,ℤ/8)×C139—22no—
132AGL(1,ℤ/8)×C139—21no—
133AGL(1,ℤ/8)×C139—21no—
134AGL(1,ℤ/8)×C139—21no—
135AGL(1,ℤ/8)×C139—21no—
136AGL(1,ℤ/8)×C139—21no—
137AGL(1,ℤ/8)×C139—21no—
138AGL(1,ℤ/8)×C139—21no—
139AGL(1,ℤ/8)×C139—22no—
140AGL(1,ℤ/8)×C139D412yes—
141AGL(1,ℤ/8)×C139D412yescomplemented
142#135×C139—24no—
143#135×C139—24no—
144#135×C139—24no—
145#135×C139—24no—
146#135×C139—22no—
147#135×C139—22no—
148#135×C139—22no—
149#135×C139—22no—
150#135×C139—41no—
151C2×Q16×C139—24no—
152C2×Q16×C139—21no—
153C2×Q16×C139D412yescomplemented
154C2×SD16×C139—24no—
155C2×SD16×C139—24no—
156C2×SD16×C139—21no—
157C2×SD16×C139—21no—
158C2×SD16×C139—22no—
159C2×SD16×C139—22no—
160C2×SD16×C139—41no—
161C2×SD16×C139D412yes—
162C2×SD16×C139D412yescomplemented
163C2×D8×C139—24no—
164C2×D8×C139—21no—
165C2×D8×C139D412yes—
166#131×C139—22no—
167#131×C139—22no—
168#131×C139—22no—
169#131×C139—22no—
170C2×M16×C139—22no—
171C2×M16×C139—22no—
172C2×M16×C139C2311yescharacteristic
173C2×M16×C139C2311yescharacteristic
174C2×M16×C139C2311yescharacteristic
175C2×M16×C139C2311yescharacteristic
176C2×M16×C139C2311yescharacteristic
177C22×C8×C139C2311yescharacteristic
178C4⋊Q8×C139—21no—
179#127×C139—21no—
180#124×C139—21no—
181#124×C139—21no—
182#123×C139—41no—
183C22⋊Q8×C139—22no—
184#121×C139—22no—
185#120×C139—41no—
186#117×C139C2311yescharacteristic
187#117×C139C2311yescharacteristic
188#104×C139—22no—
189#104×C139—22no—
190#104×C139—22no—
191#104×C139—22no—
192#103×C139—21no—
193#103×C139—21no—
194#103×C139—22no—
195#102×C139—21no—
196#102×C139—21no—
197#102×C139—22no—
198#101×C139—22no—
199#100×C139—22no—
200#99×C139—41no—
201C22⋊C8×C139—22no—
202C22⋊C8×C139—22no—
203C22⋊C8×C139—41no—
204C24×C139—21no—
205C24×C139—41no—
206#41×C139—21no—
207#41×C139—21no—
208#41×C139—21no—
209#41×C139—21no—
210#41×C139—24no—
211#41×C139—24no—
212#41×C139—22no—
213#41×C139—22no—
214#41×C139—22no—
215#41×C139—22no—
216#41×C139—21no—
217#41×C139—21no—
218#41×C139—21no—
219#41×C139—21no—
220#41×C139—21no—
221#41×C139—21no—
222#41×C139—21no—
223#41×C139—21no—
224#41×C139—21no—
225#41×C139—21no—
226#41×C139—21no—
227#41×C139—21no—
228#41×C139—42no—
229#41×C139—42no—
230#41×C139—42no—
231#41×C139—42no—
232#41×C139—42no—
233#41×C139—44no—
234#41×C139—42no—
235#41×C139—42no—
236#41×C139—42no—
237#41×C139—41no—
238#41×C139—41no—
239#41×C139—44no—
240#41×C139—42no—
241#41×C139—42no—
242#41×C139C2×D412yes—
243#41×C139C2×D412yes—
244#41×C139C2×D412yes—
245#41×C139C2×D412yes—
246C2×Q8×C139—21no—
247C2×Q8×C139—24no—
248C2×Q8×C139—22no—
249C2×Q8×C139—22no—
250C2×Q8×C139—21no—
251C2×Q8×C139—21no—
252C2×Q8×C139—21no—
253C2×Q8×C139—21no—
254C2×Q8×C139—41no—
255C2×Q8×C139—42no—
256C2×Q8×C139—42no—
257C2×Q8×C139—41no—
258C2×Q8×C139—42no—
259C2×Q8×C139C2×D412yes—
260C2×Q8×C139C2×D411yescharacteristic
261C2×Q8×C139C2×D411yescharacteristic
262C2×Q8×C139C2×D411yescharacteristic
263C2×Q8×C139C2×D411yescharacteristic
264C2×Q8×C139C2×D411yescharacteristic
265C2×D4×C139—21no—
266C2×D4×C139—21no—
267C2×D4×C139—24no—
268C2×D4×C139—22no—
269C2×D4×C139—22no—
270C2×D4×C139—21no—
271C2×D4×C139—21no—
272C2×D4×C139—21no—
273C2×D4×C139—21no—
274C2×D4×C139—21no—
275C2×D4×C139—21no—
276C2×D4×C139—21no—
277C2×D4×C139—21no—
278C2×D4×C139—42no—
279C2×D4×C139—41no—
280C2×D4×C139—41no—
281C2×D4×C139—42no—
282C2×D4×C139—42no—
283C2×D4×C139—41no—
284C2×D4×C139—44no—
285C2×D4×C139—42no—
286C2×D4×C139—42no—
287C2×D4×C139—44no—
288C2×D4×C139—41no—
289C2×D4×C139—42no—
290C2×D4×C139—42no—
291C2×D4×C139C2×D412yes—
292C2×D4×C139C2×D411yescharacteristic
293C2×D4×C139C2×D411yescharacteristic
294C2×D4×C139C2×D411yescharacteristic
295C2×D4×C139C2×D411yescharacteristic
296C2×D4×C139C2×D411yescharacteristic
297C22×C4×C139—21no—
298C22×C4×C139—21no—
299C22×C4×C139—21no—
300C22×C4×C139—21no—
301C22×C4×C139—21no—
302C22×C4×C139—21no—
303C22×C4×C139—41no—
304C22×C4×C139—42no—
305C22×C4×C139—41no—
306C22×C4×C139—41no—
307C22×C4×C139C2411yescharacteristic
308Q16×C139—24no—
309Q16×C139—22no—
310Q16×C139—22no—
311Q16×C139—22no—
312Q16×C139—24no—
313Q16×C139—22no—
314Q16×C139—41no—
315SD16×C139—24no—
316SD16×C139—22no—
317SD16×C139—24no—
318SD16×C139—22no—
319SD16×C139—22no—
320SD16×C139—22no—
321SD16×C139—22no—
322SD16×C139—24no—
323SD16×C139—22no—
324SD16×C139—22no—
325SD16×C139—24no—
326SD16×C139—22no—
327SD16×C139—44no—
328SD16×C139—41no—
329SD16×C139—41no—
330D8×C139—24no—
331D8×C139—22no—
332D8×C139—22no—
333D8×C139—22no—
334D8×C139—24no—
335D8×C139—22no—
336D8×C139—41no—
337M16×C139—24no—
338M16×C139—24no—
339M16×C139—21no—
340M16×C139—21no—
341M16×C139—21no—
342M16×C139—21no—
343M16×C139—21no—
344M16×C139—21no—
345M16×C139—21no—
346M16×C139—21no—
347M16×C139C2×D412yes—
348M16×C139C2×D412yes—
349C2×C8×C139—24no—
350C2×C8×C139—24no—
351C2×C8×C139—21no—
352C2×C8×C139—21no—
353C2×C8×C139—21no—
354C2×C8×C139—21no—
355C2×C8×C139—21no—
356C2×C8×C139—21no—
357C2×C8×C139C2×D412yes—
358C2×C8×C139C2×D412yes—
359C4⋊C4×C139—21no—
360C4⋊C4×C139—21no—
361C4⋊C4×C139—42no—
362C22⋊C4×C139—21no—
363C22⋊C4×C139—21no—
364C22⋊C4×C139—42no—
365C22⋊C4×C139—42no—
366C42×C139—21no—
367C42×C139—21no—
368C23×C139—21no—
369C23×C139—21no—
370C23×C139—21no—
371C23×C139—21no—
372C23×C139—21no—
373C23×C139—22no—
374C23×C139—42no—
375C23×C139—44no—
376C23×C139—41no—
377C23×C139—41no—
378C23×C139—161no—
379C23×C139—162no—
380C23×C139H(5,𝔽2)11yescharacteristic
381Q8×C139—21no—
382Q8×C139—21no—
383Q8×C139—21no—
384Q8×C139—21no—
385Q8×C139—22no—
386Q8×C139—21no—
387Q8×C139—21no—
388Q8×C139—22no—
389Q8×C139—21no—
390Q8×C139—21no—
391Q8×C139—42no—
392Q8×C139—44no—
393Q8×C139—41no—
394Q8×C139—41no—
395Q8×C139#12012yes—
396Q8×C139#12012yes—
397D4×C139—22no—
398D4×C139—22no—
399D4×C139—22no—
400D4×C139—22no—
401D4×C139—21no—
402D4×C139—21no—
403D4×C139—22no—
404D4×C139—21no—
405D4×C139—21no—
406D4×C139—21no—
407D4×C139—21no—
408D4×C139—21no—
409D4×C139—21no—
410D4×C139—22no—
411D4×C139—42no—
412D4×C139—42no—
413D4×C139—44no—
414D4×C139—42no—
415D4×C139—44no—
416D4×C139—44no—
417D4×C139—41no—
418D4×C139—41no—
419D4×C139—41no—
420D4×C139—41no—
421D4×C139—41no—
422D4×C139—41no—
423D4×C139—41no—
424D4×C139—41no—
425D4×C139—162no—
426D4×C139#12012yes—
427D4×C139#12012yes—
428C2×C4×C139—21no—
429C2×C4×C139—21no—
430C2×C4×C139—22no—
431C2×C4×C139—22no—
432C2×C4×C139—22no—
433C2×C4×C139—22no—
434C2×C4×C139—21no—
435C2×C4×C139—21no—
436C2×C4×C139—22no—
437C2×C4×C139—21no—
438C2×C4×C139—42no—
439C2×C4×C139—42no—
440C2×C4×C139—42no—
441C2×C4×C139—44no—
442C2×C4×C139—44no—
443C2×C4×C139—44no—
444C2×C4×C139—41no—
445C2×C4×C139—41no—
446C2×C4×C139—41no—
447C2×C4×C139—41no—
448C2×C4×C139—41no—
449C2×C4×C139—41no—
450C2×C4×C139—41no—
451C2×C4×C139—41no—
452C2×C4×C139—41no—
453C2×C4×C139—41no—
454C2×C4×C139C22×D411yescharacteristic
455C2×C4×C139C22×D411yescharacteristic
456C2×C4×C139C22×D411yescharacteristic
457C2×C4×C139C22×D411yescharacteristic
458C2×C4×C139C22×D411yescharacteristic
459C2×C4×C139H(5,𝔽2)11yescharacteristic
460C8×C139—22no—
461C8×C139—22no—
462C8×C139—22no—
463C8×C139—22no—
464C8×C139—41no—
465C8×C139—41no—
466C22×C139—22no—
467C22×C139—22no—
468C22×C139—41no—
469C22×C139—42no—
470C22×C139—42no—
471C22×C139—41no—
472C22×C139—41no—
473C22×C139—41no—
474C22×C139—42no—
475C22×C139—81no—
476C22×C139—81no—
477C22×C139—82no—
478C22×C139—81no—
479C22×C139—82no—
480C22×C139—161no—
481C22×C139—162no—
482C22×C139—164no—
483C22×C139#53411yescharacteristic
484C22×C139D4211yescharacteristic
485C22×C139D4211yescharacteristic
486C4×C139—22no—
487C4×C139—22no—
488C4×C139—41no—
489C4×C139—41no—
490C4×C139—41no—
491C4×C139—42no—
492C4×C139—81no—
493C4×C139—81no—
494C4×C139C2×#12011yescharacteristic
495C4×C139C2×#12011yescharacteristic
496C4×C139D4211yescharacteristic
497C4×C139D4211yescharacteristic
498C2×C139—21no—
499C2×C139—21no—
500C2×C139—21no—
501C2×C139—42no—
502C2×C139—42no—
503C2×C139—81no—
504C2×C139—81no—
505C2×C139—82no—
506C2×C139—81no—
507C2×C139#240311yescharacteristic
508#23894C13911yesmaximal, characteristic, direct product factor, Sylow
509C139#2389411yescharacteristic, direct product factor, Sylow
510#3586C2×C13911yescharacteristic, complemented
511#3585C2×C13911yescharacteristic, complemented
512#3020C2×C13911yescharacteristic, complemented
513#3019C2×C13911yescharacteristic, complemented
514#3010C2×C13911yescharacteristic, complemented
515#3009C2×C13911yescharacteristic, complemented
516#2019C2×C13911yescharacteristic, complemented
517#2017C2×C13911yescharacteristic, complemented
518#2009C2×C13911yescharacteristic, complemented
519#2008C2×C13911yescharacteristic, complemented
520#1903C2×C13911yescharacteristic, complemented
521#1902C2×C13911yescharacteristic, complemented
522#1881C2×C13911yescharacteristic, complemented
523#1881C2×C13911yescharacteristic, complemented
524#1794C2×C13911yescharacteristic, complemented
525#585C22×C13911yescharacteristic
526C2×2−1+4C22×C13911yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C13911yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C13911yescharacteristic
539#575C22×C13911yescharacteristic
540#575C22×C13911yescharacteristic
541#575C22×C13911yescharacteristic, complemented
542#575C22×C13911yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C13911yescharacteristic
545C2×#137C22×C13911yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
548C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
549C22×SD16C22×C13911yescharacteristic, complemented
550#568C22×C13911yescharacteristic
551#568C22×C13911yescharacteristic, complemented
552#536C22×C13911yescharacteristic, complemented
553#535C22×C13911yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C13911yescharacteristic
563#421C22×C13911yescharacteristic, complemented
564#421C22×C13911yescharacteristic, complemented
565#421C22×C13911yescharacteristic, complemented
566#419C22×C13911yescharacteristic, complemented
567#418C22×C13911yescharacteristic, complemented
568#416C22×C13911yescharacteristic
569#416C22×C13911yescharacteristic, complemented
570C2×#101C22×C13911yescharacteristic, complemented
571C2×#100C22×C13911yescharacteristic, complemented
572#410C22×C13911yescharacteristic, complemented
573#408C22×C13911yescharacteristic, complemented
574#408C22×C13911yescharacteristic, complemented
575#408C22×C13911yescharacteristic, complemented
576#344C22×C13911yescharacteristic, complemented
577#344C22×C13911yescharacteristic, complemented
578#341C22×C13911yescharacteristic, complemented
579#338C22×C13911yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C13912yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C13912yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C13911yescharacteristic
604C2×#41C23×C13911yescharacteristic
605C2×#41C23×C13911yescharacteristic
606C2×#41C23×C13911yescharacteristic
607C2×#41C23×C13911yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C13911yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C13911yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C13912yes—
632#137D4×C13912yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C13912yes—
650AGL(1,ℤ/8)D4×C13912yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C13912yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C13912yes—
671C2×SD16D4×C13912yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C13912yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C13911yescharacteristic
682C2×M16C23×C13911yescharacteristic
683C2×M16C23×C13911yescharacteristic
684C2×M16C23×C13911yescharacteristic
685C2×M16C23×C13911yescharacteristic
686C22×C8C23×C13911yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C13911yescharacteristic
696#117C23×C13911yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C13912yes—
752#41C2×D4×C13912yes—
753#41C2×D4×C13912yes—
754#41C2×D4×C13912yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C13912yes—
769C2×Q8C2×D4×C13911yescharacteristic
770C2×Q8C2×D4×C13911yescharacteristic
771C2×Q8C2×D4×C13911yescharacteristic
772C2×Q8C2×D4×C13911yescharacteristic
773C2×Q8C2×D4×C13911yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C13912yes—
801C2×D4C2×D4×C13911yescharacteristic
802C2×D4C2×D4×C13911yescharacteristic
803C2×D4C2×D4×C13911yescharacteristic
804C2×D4C2×D4×C13911yescharacteristic
805C2×D4C2×D4×C13911yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C13911yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C13912yes—
857M16C2×D4×C13912yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C13912yes—
867C2×C8C2×D4×C13912yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C13911yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C13912yes—
905Q8#120×C13912yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C13912yes—
936D4#120×C13912yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C13911yescharacteristic
964C2×C4C22×D4×C13911yescharacteristic
965C2×C4C22×D4×C13911yescharacteristic
966C2×C4C22×D4×C13911yescharacteristic
967C2×C4C22×D4×C13911yescharacteristic
968C2×C4H(5,𝔽2)×C13911yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C13911yescharacteristic
993C22D42×C13911yescharacteristic
994C22D42×C13911yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C13911yescharacteristic
1004C4C2×#120×C13911yescharacteristic
1005C4D42×C13911yescharacteristic
1006C4D42×C13911yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2#2403×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2403
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. #3585×C139C2semidirect
3. #3020×C139C2semidirect
4. #3019×C139C2semidirect
5. #3010×C139C2semidirect
6. #3009×C139C2semidirect
7. #2019×C139C2semidirect
8. #2017×C139C2semidirect
9. #2009×C139C2semidirect
10. #2008×C139C2semidirect
11. #1903×C139C2semidirect
12. #1902×C139C2semidirect
13. #1881×C139C2semidirect
14. #1881×C139C2semidirect
15. #1794×C139C2semidirect
17. C2×2−1+4×C139C22semidirect
32. #575×C139C22semidirect
33. #575×C139C22semidirect
36. C2×#137×C139C22semidirect
40. C22×SD16×C139C22semidirect
42. #568×C139C22semidirect
43. #536×C139C22semidirect
44. #535×C139C22semidirect
54. #421×C139C22semidirect
55. #421×C139C22semidirect
56. #421×C139C22semidirect
57. #419×C139C22semidirect
58. #418×C139C22semidirect
60. #416×C139C22semidirect
61. C2×#101×C139C22semidirect
62. C2×#100×C139C22semidirect
63. #410×C139C22semidirect
64. #408×C139C22semidirect
65. #408×C139C22semidirect
66. #408×C139C22semidirect
67. #344×C139C22semidirect
68. #344×C139C22semidirect
69. #341×C139C22semidirect
70. #338×C139C22semidirect
77. 2−1+4×C139D4semidirect
85. H(5,𝔽2)×C139D4semidirect
123. #137×C139D4semidirect
141. AGL(1,ℤ/8)×C139D4semidirect
153. C2×Q16×C139D4semidirect
162. C2×SD16×C139D4semidirect
508. #23894C139direct (N × H)
509. C139#23894direct (N × H)
510. #3586C2×C139semidirect
511. #3585C2×C139semidirect
512. #3020C2×C139semidirect
513. #3019C2×C139semidirect
514. #3010C2×C139semidirect
515. #3009C2×C139semidirect
516. #2019C2×C139semidirect
517. #2017C2×C139semidirect
518. #2009C2×C139semidirect
519. #2008C2×C139semidirect
520. #1903C2×C139semidirect
521. #1902C2×C139semidirect
522. #1881C2×C139semidirect
523. #1881C2×C139semidirect
524. #1794C2×C139semidirect
526. C2×2−1+4C22×C139semidirect
541. #575C22×C139semidirect
542. #575C22×C139semidirect
545. C2×#137C22×C139semidirect
549. C22×SD16C22×C139semidirect
551. #568C22×C139semidirect
552. #536C22×C139semidirect
553. #535C22×C139semidirect
563. #421C22×C139semidirect
564. #421C22×C139semidirect
565. #421C22×C139semidirect
566. #419C22×C139semidirect
567. #418C22×C139semidirect
569. #416C22×C139semidirect
570. C2×#101C22×C139semidirect
571. C2×#100C22×C139semidirect
572. #410C22×C139semidirect
573. #408C22×C139semidirect
574. #408C22×C139semidirect
575. #408C22×C139semidirect
576. #344C22×C139semidirect
577. #344C22×C139semidirect
578. #341C22×C139semidirect
579. #338C22×C139semidirect
586. 2−1+4D4×C139semidirect
594. H(5,𝔽2)D4×C139semidirect
632. #137D4×C139semidirect
650. AGL(1,ℤ/8)D4×C139semidirect
662. C2×Q16D4×C139semidirect
671. C2×SD16D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3586×C1392
#3585×C1392
#3020×C1392
#3019×C1392
#3010×C1392
#3009×C1392
#2019×C1392
#2017×C1392
#2009×C1392
#2008×C1392
#1903×C1392
#1902×C1392
#1881×C1392
#1794×C1392
#23894139