Finite Group Databasebeta

← C139×#24464 #48019060

Subgroups — C139×#24464 #48019060

Order 35584.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C139C211yesmaximal, characteristic, complemented
2#3055×C139C211yesmaximal, characteristic, complemented
3C2×#453×C139C211yesmaximal, characteristic, complemented
4#3006×C139C211yesmaximal, characteristic, complemented
5C22×#104×C139C211yesmaximal, characteristic, complemented
6#2856×C139C211yesmaximal, characteristic, complemented
7#2039×C139C211yesmaximal, characteristic, complemented
8#2037×C139C211yesmaximal, characteristic, complemented
9#2006×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1900×C139C211yesmaximal, characteristic, complemented
12#1896×C139C211yesmaximal, characteristic, complemented
13#1883×C139C211yesmaximal, characteristic, complemented
14#1859×C139C211yesmaximal, characteristic, complemented
15#1792×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
21C22×M16×C139C2211yescharacteristic, complemented
22#550×C139—21no—
23#548×C139—21no—
24#546×C139—21no—
25#546×C139—22no—
26D42×C139—22no—
27D42×C139—21no—
28#537×C139—21no—
29#537×C139C2211yescharacteristic
30#535×C139—21no—
31#535×C139C2211yescharacteristic
32C2×#127×C139C2211yescharacteristic, complemented
33#525×C139—21no—
34#525×C139C2211yescharacteristic
35C2×#121×C139—21no—
36C2×#121×C139—22no—
37C2×#121×C139C2211yescharacteristic
38C2×#121×C139C2211yescharacteristic, complemented
39#520×C139C2211yescharacteristic
40C22×C42×C139C2211yescharacteristic, complemented
41#469×C139—21no—
42#468×C139—21no—
43#466×C139—21no—
44#465×C139—21no—
45#453×C139—24no—
46#449×C139—21no—
47#449×C139—21no—
48#448×C139—21no—
49#447×C139—21no—
50#428×C139C2211yescharacteristic, complemented
51C2×#104×C139—24no—
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic
54C2×#104×C139C2211yescharacteristic, complemented
55C2×#104×C139C2211yescharacteristic, complemented
56C2×#104×C139C2211yescharacteristic, complemented
57C2×#104×C139C2211yescharacteristic, complemented
58#418×C139C2211yescharacteristic, complemented
59#417×C139C2211yescharacteristic
60#417×C139C2211yescharacteristic, complemented
61#417×C139C2211yescharacteristic, complemented
62C2×#100×C139C2211yescharacteristic, complemented
63C2×#100×C139C2211yescharacteristic, complemented
64#407×C139C2211yescharacteristic, complemented
65#390×C139—22no—
66#390×C139C2211yescharacteristic, complemented
67#390×C139C2211yescharacteristic, complemented
68#384×C139C2211yescharacteristic, complemented
69#343×C139C2211yescharacteristic, complemented
70#343×C139C2211yescharacteristic, complemented
71#339×C139C2211yescharacteristic, complemented
72#339×C139C2211yescharacteristic, complemented
73H(5,𝔽2)×C139—22no—
74H(5,𝔽2)×C139—22no—
75H(5,𝔽2)×C139—41no—
76H(5,𝔽2)×C139—41no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—22no—
82C2×#41×C139—22no—
83C2×#41×C139—41no—
84C2×#41×C139—41no—
85C2×#41×C139D411yescharacteristic, complemented
86C2×#41×C139D411yescharacteristic, complemented
87C2×#41×C139C2311yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C2×#41×C139C2311yescharacteristic
90C22×Q8×C139D411yescharacteristic, complemented
91C22×D4×C139—21no—
92C22×D4×C139—22no—
93C22×D4×C139—22no—
94C22×D4×C139—21no—
95C22×D4×C139—21no—
96C22×D4×C139—21no—
97C22×D4×C139—22no—
98C22×D4×C139D412yes—
99C22×D4×C139D411yescharacteristic, complemented
100C22×D4×C139C2311yescharacteristic
101C22×D4×C139C2311yescharacteristic
102C23×C4×C139—21no—
103C23×C4×C139—21no—
104C23×C4×C139C2311yescharacteristic
105AGL(1,ℤ/8)×C139—22no—
106AGL(1,ℤ/8)×C139—22no—
107AGL(1,ℤ/8)×C139—22no—
108AGL(1,ℤ/8)×C139—41no—
109AGL(1,ℤ/8)×C139—41no—
110AGL(1,ℤ/8)×C139—41no—
111C2×SD16×C139—21no—
112C2×SD16×C139—21no—
113C2×SD16×C139—21no—
114C2×D8×C139—21no—
115C2×D8×C139—21no—
116C2×D8×C139—21no—
117C2×M16×C139—21no—
118C2×M16×C139—22no—
119C2×M16×C139—41no—
120C2×M16×C139C2311yescharacteristic
121C2×M16×C139C2311yescharacteristic
122C2×M16×C139C2311yescharacteristic
123C2×M16×C139C2311yescharacteristic
124C22×C8×C139—21no—
125#127×C139—22no—
126#127×C139—21no—
127#127×C139—22no—
128#127×C139—41no—
129#124×C139—22no—
130#124×C139—21no—
131#123×C139—22no—
132#123×C139—21no—
133C22⋊Q8×C139—22no—
134C22⋊Q8×C139—21no—
135C22⋊Q8×C139—21no—
136C22⋊Q8×C139D411yescharacteristic, complemented
137C22⋊Q8×C139D411yescharacteristic, complemented
138#121×C139—22no—
139#121×C139—22no—
140#121×C139—22no—
141#121×C139—22no—
142#121×C139—22no—
143#121×C139—21no—
144#121×C139—21no—
145#121×C139—21no—
146#121×C139—21no—
147#121×C139—21no—
148#121×C139—21no—
149#121×C139—22no—
150#121×C139—21no—
151#121×C139—21no—
152#121×C139—21no—
153#121×C139—21no—
154#121×C139—21no—
155#121×C139—21no—
156#121×C139—48no—
157#121×C139D411yescharacteristic, complemented
158#121×C139D411yescharacteristic, complemented
159#120×C139—22no—
160#120×C139—22no—
161#120×C139—22no—
162#120×C139—21no—
163#120×C139—22no—
164C4×Q8×C139—21no—
165C4×D4×C139—22no—
166C4×D4×C139—22no—
167C4×D4×C139—21no—
168C4×D4×C139—22no—
169C4×D4×C139—21no—
170C4×D4×C139—21no—
171#117×C139—21no—
172#117×C139C2311yescharacteristic
173C2×C4⋊C4×C139—21no—
174C2×C4⋊C4×C139—22no—
175C2×C4⋊C4×C139C2311yescharacteristic
176C2×C4⋊C4×C139C2311yescharacteristic
177C2×C22⋊C4×C139—22no—
178C2×C22⋊C4×C139—22no—
179C2×C22⋊C4×C139—22no—
180C2×C22⋊C4×C139—21no—
181C2×C22⋊C4×C139D412yes—
182C2×C42×C139—22no—
183C2×C42×C139—21no—
184C2×C42×C139—41no—
185C2×C42×C139C2311yescharacteristic
186C2×C42×C139C2311yescharacteristic
187#107×C139—21no—
188#106×C139—21no—
189#104×C139—22no—
190#104×C139—22no—
191#104×C139—22no—
192#104×C139—22no—
193#104×C139—41no—
194#104×C139D414yescomplemented
195#103×C139—21no—
196#103×C139—21no—
197#103×C139—21no—
198#102×C139—21no—
199#102×C139—21no—
200#102×C139—21no—
201#102×C139—21no—
202#102×C139—21no—
203#100×C139—22no—
204#100×C139—41no—
205C22⋊C8×C139—21no—
206C22⋊C8×C139—21no—
207C24×C139—22no—
208C24×C139—21no—
209C24×C139—21no—
210C24×C139C2×D411yescharacteristic
211C24×C139C2×D412yes—
212#41×C139—21no—
213#41×C139—21no—
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—42no—
225#41×C139—42no—
226#41×C139—41no—
227#41×C139—41no—
228#41×C139—42no—
229#41×C139—42no—
230#41×C139—42no—
231#41×C139—42no—
232#41×C139—42no—
233#41×C139—42no—
234#41×C139C2×D412yes—
235#41×C139#4112yes—
236C2×Q8×C139—21no—
237C2×Q8×C139—22no—
238C2×Q8×C139—41no—
239C2×Q8×C139C2×D411yescharacteristic
240C2×Q8×C139C2×D411yescharacteristic
241C2×Q8×C139C2×D411yescharacteristic
242C2×D4×C139—21no—
243C2×D4×C139—22no—
244C2×D4×C139—22no—
245C2×D4×C139—22no—
246C2×D4×C139—22no—
247C2×D4×C139—21no—
248C2×D4×C139—21no—
249C2×D4×C139—21no—
250C2×D4×C139—21no—
251C2×D4×C139—21no—
252C2×D4×C139—22no—
253C2×D4×C139—22no—
254C2×D4×C139—22no—
255C2×D4×C139—21no—
256C2×D4×C139—22no—
257C2×D4×C139—21no—
258C2×D4×C139—21no—
259C2×D4×C139—21no—
260C2×D4×C139—21no—
261C2×D4×C139—21no—
262C2×D4×C139—21no—
263C2×D4×C139—21no—
264C2×D4×C139—21no—
265C2×D4×C139—21no—
266C2×D4×C139—21no—
267C2×D4×C139—21no—
268C2×D4×C139—21no—
269C2×D4×C139—21no—
270C2×D4×C139—41no—
271C2×D4×C139—42no—
272C2×D4×C139—42no—
273C2×D4×C139—44no—
274C2×D4×C139—44no—
275C2×D4×C139—44no—
276C2×D4×C139—42no—
277C2×D4×C139—42no—
278C2×D4×C139—44no—
279C2×D4×C139—44no—
280C2×D4×C139—42no—
281C2×D4×C139—42no—
282C2×D4×C139—44no—
283C2×D4×C139—44no—
284C2×D4×C139—41no—
285C2×D4×C139—41no—
286C2×D4×C139—84no—
287C2×D4×C139C2×D411yescharacteristic
288C2×D4×C139C2×D411yescharacteristic
289C2×D4×C139C2×D411yescharacteristic
290C22×C4×C139—21no—
291C22×C4×C139—21no—
292C22×C4×C139—21no—
293C22×C4×C139—21no—
294C22×C4×C139—21no—
295C22×C4×C139—21no—
296C22×C4×C139—22no—
297C22×C4×C139—24no—
298C22×C4×C139—21no—
299C22×C4×C139—21no—
300C22×C4×C139—22no—
301C22×C4×C139—21no—
302C22×C4×C139—21no—
303C22×C4×C139—21no—
304C22×C4×C139—21no—
305C22×C4×C139—21no—
306C22×C4×C139—42no—
307C22×C4×C139—42no—
308C22×C4×C139—42no—
309C22×C4×C139—42no—
310C22×C4×C139C2×D411yescharacteristic
311C22×C4×C139C2×D411yescharacteristic
312C22×C4×C139C2×D411yescharacteristic
313C22×C4×C139C2×D411yescharacteristic
314C22×C4×C139C2×D411yescharacteristic
315C22×C4×C139C2×D412yes—
316C22×C4×C139C2411yescharacteristic
317SD16×C139—42no—
318SD16×C139—42no—
319SD16×C139—42no—
320D8×C139—42no—
321D8×C139—42no—
322D8×C139—42no—
323M16×C139—21no—
324M16×C139—21no—
325M16×C139—21no—
326M16×C139—21no—
327M16×C139—21no—
328M16×C139—21no—
329M16×C139—21no—
330M16×C139—42no—
331M16×C139C2×D412yescomplemented
332C2×C8×C139—21no—
333C2×C8×C139—21no—
334C2×C8×C139—21no—
335C2×C8×C139—21no—
336C2×C8×C139—42no—
337C4⋊C4×C139—22no—
338C4⋊C4×C139—22no—
339C4⋊C4×C139—21no—
340C4⋊C4×C139—21no—
341C4⋊C4×C139—21no—
342C4⋊C4×C139—21no—
343C4⋊C4×C139—21no—
344C4⋊C4×C139—21no—
345C4⋊C4×C139—44no—
346C4⋊C4×C139C2×D411yescharacteristic
347C4⋊C4×C139C2×D411yescharacteristic
348C22⋊C4×C139—22no—
349C22⋊C4×C139—22no—
350C22⋊C4×C139—22no—
351C22⋊C4×C139—22no—
352C22⋊C4×C139—22no—
353C22⋊C4×C139—21no—
354C22⋊C4×C139—21no—
355C22⋊C4×C139—21no—
356C22⋊C4×C139—21no—
357C22⋊C4×C139—22no—
358C22⋊C4×C139—22no—
359C22⋊C4×C139—21no—
360C22⋊C4×C139—44no—
361C22⋊C4×C139—44no—
362C22⋊C4×C139—41no—
363C22⋊C4×C139—41no—
364C42×C139—22no—
365C42×C139—21no—
366C42×C139—21no—
367C42×C139—21no—
368C42×C139—21no—
369C42×C139—42no—
370C42×C139C2×D412yescomplemented
371C23×C139—21no—
372C23×C139—21no—
373C23×C139—21no—
374C23×C139—22no—
375C23×C139—22no—
376C23×C139—21no—
377C23×C139—21no—
378C23×C139—22no—
379C23×C139—22no—
380C23×C139—41no—
381C23×C139—42no—
382C23×C139—44no—
383C23×C139—42no—
384C23×C139—42no—
385C23×C139—42no—
386C23×C139—42no—
387C23×C139—42no—
388C23×C139—41no—
389C23×C139—41no—
390C23×C139—41no—
391C23×C139—81no—
392C23×C139—82no—
393C23×C139—82no—
394C23×C139#12011yescharacteristic
395C23×C139#12011yescharacteristic
396C23×C139C22×D411yescharacteristic
397Q8×C139—21no—
398Q8×C139—21no—
399Q8×C139—21no—
400Q8×C139—21no—
401Q8×C139—21no—
402Q8×C139—42no—
403Q8×C139#12112yescomplemented
404D4×C139—22no—
405D4×C139—22no—
406D4×C139—21no—
407D4×C139—21no—
408D4×C139—21no—
409D4×C139—21no—
410D4×C139—21no—
411D4×C139—42no—
412D4×C139—42no—
413D4×C139—44no—
414D4×C139—42no—
415D4×C139—44no—
416D4×C139—41no—
417D4×C139—41no—
418D4×C139—41no—
419D4×C139—41no—
420D4×C139—44no—
421D4×C139—42no—
422D4×C139—41no—
423D4×C139—41no—
424D4×C139—41no—
425D4×C139—41no—
426D4×C139—41no—
427D4×C139—41no—
428D4×C139—41no—
429D4×C139—41no—
430D4×C139—88no—
431D4×C139—81no—
432D4×C139—82no—
433D4×C139—82no—
434D4×C139—82no—
435D4×C139—82no—
436D4×C139—82no—
437D4×C139—82no—
438D4×C139#12112yescomplemented
439C2×C4×C139—22no—
440C2×C4×C139—22no—
441C2×C4×C139—21no—
442C2×C4×C139—22no—
443C2×C4×C139—21no—
444C2×C4×C139—21no—
445C2×C4×C139—21no—
446C2×C4×C139—21no—
447C2×C4×C139—21no—
448C2×C4×C139—21no—
449C2×C4×C139—21no—
450C2×C4×C139—21no—
451C2×C4×C139—22no—
452C2×C4×C139—21no—
453C2×C4×C139—21no—
454C2×C4×C139—22no—
455C2×C4×C139—22no—
456C2×C4×C139—21no—
457C2×C4×C139—22no—
458C2×C4×C139—21no—
459C2×C4×C139—21no—
460C2×C4×C139—21no—
461C2×C4×C139—42no—
462C2×C4×C139—42no—
463C2×C4×C139—42no—
464C2×C4×C139—48no—
465C2×C4×C139—44no—
466C2×C4×C139—41no—
467C2×C4×C139—41no—
468C2×C4×C139—41no—
469C2×C4×C139—41no—
470C2×C4×C139—41no—
471C2×C4×C139—41no—
472C2×C4×C139—42no—
473C2×C4×C139—42no—
474C2×C4×C139—41no—
475C2×C4×C139—82no—
476C2×C4×C139#12011yescharacteristic
477C2×C4×C139#12011yescharacteristic
478C2×C4×C139C22×D411yescharacteristic
479C2×C4×C139C22×D411yescharacteristic
480C2×C4×C139C22×D411yescharacteristic
481C2×C4×C139C2×#4111yescharacteristic
482C2×C4×C139H(5,𝔽2)11yescharacteristic
483C2×C4×C139H(5,𝔽2)11yescharacteristic
484C8×C139—22no—
485C8×C139—41no—
486C8×C139—41no—
487C8×C139—41no—
488C22×C139—21no—
489C22×C139—21no—
490C22×C139—21no—
491C22×C139—21no—
492C22×C139—21no—
493C22×C139—22no—
494C22×C139—21no—
495C22×C139—21no—
496C22×C139—42no—
497C22×C139—42no—
498C22×C139—41no—
499C22×C139—41no—
500C22×C139—41no—
501C22×C139—41no—
502C22×C139—42no—
503C22×C139—42no—
504C22×C139—41no—
505C22×C139—41no—
506C22×C139—41no—
507C22×C139—42no—
508C22×C139—41no—
509C22×C139—84no—
510C22×C139—82no—
511C22×C139—82no—
512C22×C139—82no—
513C22×C139—82no—
514C22×C139—81no—
515C22×C139—81no—
516C22×C139—81no—
517C22×C139—164no—
518C22×C139#45312yescomplemented
519C22×C139C2×#12011yescharacteristic
520C22×C139D4211yescharacteristic
521C22×C139#54611yescharacteristic
522C4×C139—24no—
523C4×C139—21no—
524C4×C139—21no—
525C4×C139—22no—
526C4×C139—42no—
527C4×C139—41no—
528C4×C139—41no—
529C4×C139—42no—
530C4×C139—41no—
531C4×C139—41no—
532C4×C139—81no—
533C4×C139C2×#12111yescharacteristic
534C4×C139#53411yescharacteristic
535C4×C139D4211yescharacteristic
536C4×C139#54611yescharacteristic
537C2×C139—21no—
538C2×C139—21no—
539C2×C139—22no—
540C2×C139—41no—
541C2×C139—42no—
542C2×C139—81no—
543C2×C139—82no—
544C2×C139—81no—
545C2×C139—161no—
546C2×C139#241011yescharacteristic
547C2×C139C2×#45311yescharacteristic
548C2×C139#301811yescharacteristic
549#24464C13911yesmaximal, characteristic, direct product factor, Sylow
550C139#2446411yescharacteristic, direct product factor, Sylow
551#3488C2×C13911yescharacteristic, complemented
552#3055C2×C13911yescharacteristic, complemented
553C2×#453C2×C13911yescharacteristic, complemented
554#3006C2×C13911yescharacteristic, complemented
555C22×#104C2×C13911yescharacteristic, complemented
556#2856C2×C13911yescharacteristic, complemented
557#2039C2×C13911yescharacteristic, complemented
558#2037C2×C13911yescharacteristic, complemented
559#2006C2×C13911yescharacteristic, complemented
560#2002C2×C13911yescharacteristic, complemented
561#1900C2×C13911yescharacteristic, complemented
562#1896C2×C13911yescharacteristic, complemented
563#1883C2×C13911yescharacteristic, complemented
564#1859C2×C13911yescharacteristic, complemented
565#1792C2×C13911yescharacteristic, complemented
566C2×H(5,𝔽2)C22×C13911yescharacteristic
567C22×#41C22×C13911yescharacteristic
568C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
569C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
570C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
571C22×M16C22×C13911yescharacteristic, complemented
572#550—21no—
573#548—21no—
574#546—21no—
575#546—22no—
576D42—22no—
577D42—21no—
578#537—21no—
579#537C22×C13911yescharacteristic
580#535—21no—
581#535C22×C13911yescharacteristic
582C2×#127C22×C13911yescharacteristic, complemented
583#525—21no—
584#525C22×C13911yescharacteristic
585C2×#121—21no—
586C2×#121—22no—
587C2×#121C22×C13911yescharacteristic
588C2×#121C22×C13911yescharacteristic, complemented
589#520C22×C13911yescharacteristic
590C22×C42C22×C13911yescharacteristic, complemented
591#469—21no—
592#468—21no—
593#466—21no—
594#465—21no—
595#453—24no—
596#449—21no—
597#449—21no—
598#448—21no—
599#447—21no—
600#428C22×C13911yescharacteristic, complemented
601C2×#104—24no—
602C2×#104C22×C13911yescharacteristic
603C2×#104C22×C13911yescharacteristic
604C2×#104C22×C13911yescharacteristic, complemented
605C2×#104C22×C13911yescharacteristic, complemented
606C2×#104C22×C13911yescharacteristic, complemented
607C2×#104C22×C13911yescharacteristic, complemented
608#418C22×C13911yescharacteristic, complemented
609#417C22×C13911yescharacteristic
610#417C22×C13911yescharacteristic, complemented
611#417C22×C13911yescharacteristic, complemented
612C2×#100C22×C13911yescharacteristic, complemented
613C2×#100C22×C13911yescharacteristic, complemented
614#407C22×C13911yescharacteristic, complemented
615#390—22no—
616#390C22×C13911yescharacteristic, complemented
617#390C22×C13911yescharacteristic, complemented
618#384C22×C13911yescharacteristic, complemented
619#343C22×C13911yescharacteristic, complemented
620#343C22×C13911yescharacteristic, complemented
621#339C22×C13911yescharacteristic, complemented
622#339C22×C13911yescharacteristic, complemented
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C13911yescharacteristic, complemented
636C2×#41D4×C13911yescharacteristic, complemented
637C2×#41C23×C13911yescharacteristic
638C2×#41C23×C13911yescharacteristic
639C2×#41C23×C13911yescharacteristic
640C22×Q8D4×C13911yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C13912yes—
649C22×D4D4×C13911yescharacteristic, complemented
650C22×D4C23×C13911yescharacteristic
651C22×D4C23×C13911yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C13911yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C13911yescharacteristic
671C2×M16C23×C13911yescharacteristic
672C2×M16C23×C13911yescharacteristic
673C2×M16C23×C13911yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C13911yescharacteristic, complemented
687C22⋊Q8D4×C13911yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C13911yescharacteristic, complemented
708#121D4×C13911yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C13911yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C13911yescharacteristic
726C2×C4⋊C4C23×C13911yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C13912yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C13911yescharacteristic
736C2×C42C23×C13911yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C13914yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C13911yescharacteristic
761C24C2×D4×C13912yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C13912yes—
785#41#41×C13912yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C13911yescharacteristic
790C2×Q8C2×D4×C13911yescharacteristic
791C2×Q8C2×D4×C13911yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C13911yescharacteristic
838C2×D4C2×D4×C13911yescharacteristic
839C2×D4C2×D4×C13911yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C13911yescharacteristic
861C22×C4C2×D4×C13911yescharacteristic
862C22×C4C2×D4×C13911yescharacteristic
863C22×C4C2×D4×C13911yescharacteristic
864C22×C4C2×D4×C13911yescharacteristic
865C22×C4C2×D4×C13912yes—
866C22×C4C24×C13911yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C13912yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C13911yescharacteristic
897C4⋊C4C2×D4×C13911yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C13912yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C13911yescharacteristic
945C23#120×C13911yescharacteristic
946C23C22×D4×C13911yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C13912yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—82no—
982D4—81no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C13912yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C13911yescharacteristic
1027C2×C4#120×C13911yescharacteristic
1028C2×C4C22×D4×C13911yescharacteristic
1029C2×C4C22×D4×C13911yescharacteristic
1030C2×C4C22×D4×C13911yescharacteristic
1031C2×C4C2×#41×C13911yescharacteristic
1032C2×C4H(5,𝔽2)×C13911yescharacteristic
1033C2×C4H(5,𝔽2)×C13911yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22#453×C13912yescomplemented
1069C22C2×#120×C13911yescharacteristic
1070C22D42×C13911yescharacteristic
1071C22#546×C13911yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C13911yescharacteristic
1084C4#534×C13911yescharacteristic
1085C4D42×C13911yescharacteristic
1086C4#546×C13911yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2#2410×C13911yescharacteristic
1097C2C2×#453×C13911yescharacteristic
1098C2#3018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
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. #3488×C139C2semidirect
2. #3055×C139C2semidirect
3. C2×#453×C139C2semidirect
4. #3006×C139C2semidirect
5. C22×#104×C139C2semidirect
6. #2856×C139C2semidirect
7. #2039×C139C2semidirect
8. #2037×C139C2semidirect
9. #2006×C139C2semidirect
10. #2002×C139C2semidirect
11. #1900×C139C2semidirect
12. #1896×C139C2semidirect
13. #1883×C139C2semidirect
14. #1859×C139C2semidirect
15. #1792×C139C2semidirect
19. C2×AGL(1,ℤ/8)×C139C22semidirect
20. C2×AGL(1,ℤ/8)×C139C22semidirect
21. C22×M16×C139C22semidirect
32. C2×#127×C139C22semidirect
38. C2×#121×C139C22semidirect
40. C22×C42×C139C22semidirect
50. #428×C139C22semidirect
54. C2×#104×C139C22semidirect
55. C2×#104×C139C22semidirect
56. C2×#104×C139C22semidirect
57. C2×#104×C139C22semidirect
58. #418×C139C22semidirect
60. #417×C139C22semidirect
61. #417×C139C22semidirect
62. C2×#100×C139C22semidirect
63. C2×#100×C139C22semidirect
64. #407×C139C22semidirect
66. #390×C139C22semidirect
67. #390×C139C22semidirect
68. #384×C139C22semidirect
69. #343×C139C22semidirect
70. #343×C139C22semidirect
71. #339×C139C22semidirect
72. #339×C139C22semidirect
85. C2×#41×C139D4semidirect
86. C2×#41×C139D4semidirect
90. C22×Q8×C139D4semidirect
99. C22×D4×C139D4semidirect
136. C22⋊Q8×C139D4semidirect
137. C22⋊Q8×C139D4semidirect
157. #121×C139D4semidirect
158. #121×C139D4semidirect
194. #104×C139D4semidirect
331. M16×C139C2×D4semidirect
370. C42×C139C2×D4semidirect
403. Q8×C139#121semidirect
438. D4×C139#121semidirect
518. C22×C139#453semidirect
549. #24464C139direct (N × H)
550. C139#24464direct (N × H)
551. #3488C2×C139semidirect
552. #3055C2×C139semidirect
553. C2×#453C2×C139semidirect
554. #3006C2×C139semidirect
555. C22×#104C2×C139semidirect
556. #2856C2×C139semidirect
557. #2039C2×C139semidirect
558. #2037C2×C139semidirect
559. #2006C2×C139semidirect
560. #2002C2×C139semidirect
561. #1900C2×C139semidirect
562. #1896C2×C139semidirect
563. #1883C2×C139semidirect
564. #1859C2×C139semidirect
565. #1792C2×C139semidirect
569. C2×AGL(1,ℤ/8)C22×C139semidirect
570. C2×AGL(1,ℤ/8)C22×C139semidirect
571. C22×M16C22×C139semidirect
582. C2×#127C22×C139semidirect
588. C2×#121C22×C139semidirect
590. C22×C42C22×C139semidirect
600. #428C22×C139semidirect
604. C2×#104C22×C139semidirect
605. C2×#104C22×C139semidirect
606. C2×#104C22×C139semidirect
607. C2×#104C22×C139semidirect
608. #418C22×C139semidirect
610. #417C22×C139semidirect
611. #417C22×C139semidirect
612. C2×#100C22×C139semidirect
613. C2×#100C22×C139semidirect
614. #407C22×C139semidirect
616. #390C22×C139semidirect
617. #390C22×C139semidirect
618. #384C22×C139semidirect
619. #343C22×C139semidirect
620. #343C22×C139semidirect
621. #339C22×C139semidirect
622. #339C22×C139semidirect
635. C2×#41D4×C139semidirect
636. C2×#41D4×C139semidirect
640. C22×Q8D4×C139semidirect
649. C22×D4D4×C139semidirect
686. C22⋊Q8D4×C139semidirect
687. C22⋊Q8D4×C139semidirect
707. #121D4×C139semidirect
708. #121D4×C139semidirect
744. #104D4×C139semidirect
881. M16C2×D4×C139semidirect
920. C42C2×D4×C139semidirect
953. Q8#121×C139semidirect
988. D4#121×C139semidirect
1068. C22#453×C139semidirect

Maximal subgroups

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

subgroupindex
#3488×C1392
#3055×C1392
C2×#453×C1392
#3006×C1392
C22×#104×C1392
#2856×C1392
#2039×C1392
#2037×C1392
#2006×C1392
#2002×C1392
#1900×C1392
#1896×C1392
#1883×C1392
#1859×C1392
#1792×C1392
#24464139