Finite Group Databasebeta

← C139×#23412 #48018008

Subgroups — C139×#23412 #48018008

Order 35584.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic, complemented
2C2×#575×C139C211yesmaximal, characteristic, complemented
3#3449×C139C211yesmaximal, characteristic, complemented
4C2×#421×C139C211yesmaximal, characteristic, complemented
5#2896×C139C211yesmaximal, characteristic, complemented
6C2×#410×C139C211yesmaximal, characteristic, complemented
7#2009×C139C214yesmaximal, complemented
8#2008×C139C214yesmaximal, complemented
9C2×#344×C139C211yesmaximal, characteristic, complemented
10C22×#41×C139C2211yescharacteristic
11C22×#41×C139C2211yescharacteristic
12C22×#41×C139C2211yescharacteristic
13#575×C139—22no—
14#575×C139—22no—
15#575×C139—22no—
16#575×C139—22no—
17#575×C139—22no—
18#575×C139—22no—
19#575×C139—22no—
20#575×C139C2214yes—
21C2×#137×C139—21no—
22C2×#137×C139—21no—
23C2×#137×C139—21no—
24C2×#137×C139C2212yescomplemented
25C2×AGL(1,ℤ/8)×C139—21no—
26C2×AGL(1,ℤ/8)×C139—21no—
27C2×AGL(1,ℤ/8)×C139—21no—
28C2×AGL(1,ℤ/8)×C139C2212yescomplemented
29C2×#135×C139—22no—
30C2×#135×C139—22no—
31C22×M16×C139C2211yescharacteristic
32C22×M16×C139C2211yescharacteristic
33#537×C139—22no—
34#536×C139—21no—
35#536×C139C2212yescomplemented
36#535×C139—21no—
37#535×C139C2212yescomplemented
38#534×C139—22no—
39#532×C139—22no—
40#525×C139—22no—
41#525×C139—22no—
42C2×#117×C139C2211yescharacteristic
43C2×#117×C139C2211yescharacteristic
44#421×C139—22no—
45#421×C139C2214yescomplemented
46C2×#104×C139—22no—
47#419×C139C2212yescomplemented
48#418×C139C2212yescomplemented
49#417×C139—22no—
50#416×C139—22no—
51#410×C139—22no—
52#410×C139C2214yescomplemented
53C2×#99×C139—22no—
54#344×C139C2214yescomplemented
55C2×#41×C139—21no—
56C2×#41×C139—21no—
57C2×#41×C139—21no—
58C2×#41×C139—21no—
59C2×#41×C139—21no—
60C2×#41×C139—21no—
61C2×#41×C139—21no—
62C2×#41×C139—21no—
63C2×#41×C139—21no—
64C2×#41×C139—21no—
65C2×#41×C139—21no—
66C2×#41×C139—21no—
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—21no—
74C2×#41×C139—21no—
75C2×#41×C139—21no—
76C2×#41×C139—21no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—21no—
83C2×#41×C139—21no—
84C2×#41×C139—21no—
85C2×#41×C139D412yes—
86C2×#41×C139D412yes—
87C2×#41×C139D412yes—
88C2×#41×C139D412yescomplemented
89C2×#41×C139C2312yes—
90C2×#41×C139C2312yes—
91C22×Q8×C139D411yescharacteristic
92C22×Q8×C139D411yescharacteristic, complemented
93C22×Q8×C139C2311yescharacteristic
94C22×D4×C139—21no—
95C22×D4×C139—21no—
96C22×D4×C139—21no—
97C22×D4×C139D411yescharacteristic
98C22×D4×C139D411yescharacteristic, complemented
99C22×D4×C139C2311yescharacteristic
100C23×C4×C139—21no—
101C23×C4×C139—21no—
102C23×C4×C139—21no—
103C23×C4×C139C2311yescharacteristic
104#137×C139—24no—
105#137×C139—24no—
106#137×C139—24no—
107#137×C139—24no—
108#137×C139—24no—
109#137×C139—24no—
110#137×C139—24no—
111#137×C139—24no—
112AGL(1,ℤ/8)×C139—24no—
113AGL(1,ℤ/8)×C139—24no—
114AGL(1,ℤ/8)×C139—24no—
115AGL(1,ℤ/8)×C139—24no—
116AGL(1,ℤ/8)×C139—24no—
117AGL(1,ℤ/8)×C139—24no—
118AGL(1,ℤ/8)×C139—24no—
119AGL(1,ℤ/8)×C139—24no—
120#135×C139—28no—
121#135×C139—28no—
122#135×C139—28no—
123#135×C139—28no—
124C2×Q16×C139—22no—
125C2×Q16×C139—22no—
126C2×SD16×C139—22no—
127C2×SD16×C139—22no—
128C2×SD16×C139—22no—
129C2×SD16×C139—22no—
130C2×D8×C139—22no—
131C2×D8×C139—22no—
132C2×M16×C139—21no—
133C2×M16×C139—21no—
134C2×M16×C139—21no—
135C2×M16×C139—21no—
136C2×M16×C139—21no—
137C2×M16×C139—21no—
138C2×M16×C139—21no—
139C2×M16×C139D412yescomplemented
140C2×M16×C139D412yescomplemented
141C2×M16×C139D412yescomplemented
142C2×M16×C139C2312yes—
143C2×M16×C139C2312yes—
144C22×C8×C139—21no—
145C22×C8×C139D412yescomplemented
146C4⋊Q8×C139—22no—
147#127×C139—22no—
148#124×C139—22no—
149#124×C139—22no—
150#123×C139—24no—
151#123×C139—24no—
152C22⋊Q8×C139—24no—
153C22⋊Q8×C139—24no—
154#121×C139—24no—
155#121×C139—28no—
156#121×C139—24no—
157#120×C139—24no—
158#120×C139—24no—
159C4×D4×C139—28no—
160#117×C139—21no—
161#117×C139—21no—
162#117×C139—21no—
163#117×C139—21no—
164#117×C139—21no—
165#117×C139D412yes—
166#117×C139C2312yes—
167#117×C139C2312yes—
168C2×C4⋊C4×C139—21no—
169C2×C4⋊C4×C139—21no—
170C2×C22⋊C4×C139—21no—
171C2×C22⋊C4×C139D412yes—
172C2×C42×C139—21no—
173C2×C42×C139—21no—
174#104×C139—28no—
175#103×C139—24no—
176#102×C139—24no—
177#99×C139—28no—
178C24×C139—21no—
179C24×C139—21no—
180C24×C139—21no—
181C24×C139C2×D411yescharacteristic
182#41×C139—22no—
183#41×C139—22no—
184#41×C139—22no—
185#41×C139—22no—
186#41×C139—22no—
187#41×C139—22no—
188#41×C139—22no—
189#41×C139—22no—
190#41×C139—22no—
191#41×C139—22no—
192#41×C139—22no—
193#41×C139—22no—
194#41×C139—22no—
195#41×C139—22no—
196#41×C139—22no—
197#41×C139—22no—
198#41×C139—22no—
199#41×C139—22no—
200#41×C139—22no—
201#41×C139—22no—
202#41×C139—22no—
203#41×C139—22no—
204#41×C139—22no—
205#41×C139—22no—
206#41×C139—41no—
207#41×C139—41no—
208#41×C139—41no—
209#41×C139—41no—
210#41×C139—41no—
211#41×C139—41no—
212#41×C139—41no—
213#41×C139—41no—
214#41×C139—41no—
215#41×C139—41no—
216#41×C139—41no—
217#41×C139—41no—
218#41×C139—41no—
219#41×C139—41no—
220#41×C139—41no—
221#41×C139—41no—
222#41×C139—41no—
223#41×C139—41no—
224#41×C139—41no—
225#41×C139—41no—
226#41×C139—41no—
227#41×C139—41no—
228#41×C139—41no—
229#41×C139—41no—
230C2×Q8×C139—21no—
231C2×Q8×C139—21no—
232C2×Q8×C139—21no—
233C2×Q8×C139—21no—
234C2×Q8×C139—21no—
235C2×Q8×C139—21no—
236C2×Q8×C139—21no—
237C2×Q8×C139—21no—
238C2×Q8×C139—21no—
239C2×Q8×C139—21no—
240C2×Q8×C139—21no—
241C2×Q8×C139—21no—
242C2×Q8×C139—21no—
243C2×Q8×C139—21no—
244C2×Q8×C139—21no—
245C2×Q8×C139C2×D412yes—
246C2×Q8×C139C2×D412yes—
247C2×Q8×C139C2×D412yes—
248C2×D4×C139—22no—
249C2×D4×C139—22no—
250C2×D4×C139—22no—
251C2×D4×C139—22no—
252C2×D4×C139—22no—
253C2×D4×C139—22no—
254C2×D4×C139—28no—
255C2×D4×C139—21no—
256C2×D4×C139—21no—
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—41no—
272C2×D4×C139—41no—
273C2×D4×C139—41no—
274C2×D4×C139—41no—
275C2×D4×C139—41no—
276C2×D4×C139—41no—
277C2×D4×C139—41no—
278C2×D4×C139—41no—
279C2×D4×C139—41no—
280C2×D4×C139—41no—
281C2×D4×C139—41no—
282C2×D4×C139C2×D412yes—
283C2×D4×C139C2×D412yes—
284C2×D4×C139C2×D412yes—
285C22×C4×C139—21no—
286C22×C4×C139—21no—
287C22×C4×C139—21no—
288C22×C4×C139—22no—
289C22×C4×C139—22no—
290C22×C4×C139—22no—
291C22×C4×C139—22no—
292C22×C4×C139—22no—
293C22×C4×C139—22no—
294C22×C4×C139—22no—
295C22×C4×C139—41no—
296C22×C4×C139—41no—
297C22×C4×C139—41no—
298C22×C4×C139—41no—
299C22×C4×C139—41no—
300C22×C4×C139—41no—
301C22×C4×C139—41no—
302C22×C4×C139—41no—
303C22×C4×C139—41no—
304C22×C4×C139—41no—
305C22×C4×C139—41no—
306C22×C4×C139—41no—
307C22×C4×C139—41no—
308C22×C4×C139C2×D411yescharacteristic
309C22×C4×C139C2×D411yescharacteristic
310C22×C4×C139C2×D411yescharacteristic
311C22×C4×C139C2×D411yescharacteristic
312C22×C4×C139C2×D411yescharacteristic
313C22×C4×C139C2×D411yescharacteristic
314C22×C4×C139C2×D411yescharacteristic
315C22×C4×C139C2×D411yescharacteristic
316C22×C4×C139C2×D411yescharacteristic
317C22×C4×C139C2×D411yescharacteristic
318C22×C4×C139C2×D411yescharacteristic
319C22×C4×C139#4111yescharacteristic
320C22×C4×C139#4111yescharacteristic
321C22×C4×C139C2411yescharacteristic
322Q16×C139—28no—
323Q16×C139—28no—
324SD16×C139—28no—
325SD16×C139—28no—
326SD16×C139—28no—
327SD16×C139—28no—
328D8×C139—28no—
329D8×C139—28no—
330M16×C139—22no—
331M16×C139—22no—
332M16×C139—22no—
333M16×C139—22no—
334M16×C139—22no—
335M16×C139—22no—
336M16×C139—22no—
337M16×C139C2×D414yes—
338C2×C8×C139—22no—
339C2×C8×C139—22no—
340C2×C8×C139—22no—
341C2×C8×C139—22no—
342C2×C8×C139—22no—
343C2×C8×C139C2×D414yes—
344C4⋊C4×C139—28no—
345C4⋊C4×C139—22no—
346C4⋊C4×C139—22no—
347C4⋊C4×C139—22no—
348C4⋊C4×C139—41no—
349C22⋊C4×C139—28no—
350C22⋊C4×C139—28no—
351C22⋊C4×C139—22no—
352C22⋊C4×C139—22no—
353C22⋊C4×C139—41no—
354C22⋊C4×C139C2×D414yes—
355C42×C139—22no—
356C42×C139—22no—
357C42×C139—22no—
358C42×C139—41no—
359C23×C139—22no—
360C23×C139—22no—
361C23×C139—22no—
362C23×C139—41no—
363C23×C139—41no—
364C23×C139—41no—
365C23×C139—41no—
366C23×C139—41no—
367C23×C139—41no—
368C23×C139—81no—
369C23×C139—82no—
370C23×C139—82no—
371C23×C139—82no—
372C23×C139#12011yescharacteristic
373C23×C139#12011yescharacteristic
374C23×C139#12111yescharacteristic
375C23×C139#12111yescharacteristic
376C23×C139#12711yescharacteristic
377C23×C139#12711yescharacteristic
378C23×C139C22×D411yescharacteristic
379Q8×C139—22no—
380Q8×C139—22no—
381Q8×C139—22no—
382Q8×C139—22no—
383Q8×C139—22no—
384Q8×C139—22no—
385Q8×C139—41no—
386Q8×C139—41no—
387Q8×C139—41no—
388Q8×C139—41no—
389Q8×C139—41no—
390Q8×C139—41no—
391D4×C139—22no—
392D4×C139—22no—
393D4×C139—22no—
394D4×C139—22no—
395D4×C139—22no—
396D4×C139—22no—
397D4×C139—42no—
398D4×C139—42no—
399D4×C139—42no—
400D4×C139—42no—
401D4×C139—42no—
402D4×C139—42no—
403D4×C139—42no—
404D4×C139—42no—
405D4×C139—42no—
406D4×C139—42no—
407D4×C139—42no—
408D4×C139—42no—
409D4×C139—41no—
410D4×C139—41no—
411D4×C139—41no—
412D4×C139—41no—
413D4×C139—41no—
414D4×C139—41no—
415D4×C139—88no—
416C2×C4×C139—24no—
417C2×C4×C139—22no—
418C2×C4×C139—22no—
419C2×C4×C139—22no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—42no—
427C2×C4×C139—42no—
428C2×C4×C139—42no—
429C2×C4×C139—42no—
430C2×C4×C139—42no—
431C2×C4×C139—42no—
432C2×C4×C139—42no—
433C2×C4×C139—42no—
434C2×C4×C139—42no—
435C2×C4×C139—42no—
436C2×C4×C139—42no—
437C2×C4×C139—42no—
438C2×C4×C139—42no—
439C2×C4×C139—82no—
440C2×C4×C139—82no—
441C2×C4×C139#12011yescharacteristic
442C2×C4×C139#12011yescharacteristic
443C2×C4×C139#12011yescharacteristic
444C2×C4×C139#12011yescharacteristic
445C2×C4×C139#12011yescharacteristic
446C2×C4×C139#12011yescharacteristic
447C2×C4×C139#12011yescharacteristic
448C2×C4×C139#12011yescharacteristic
449C2×C4×C139#12011yescharacteristic
450C2×C4×C139#12011yescharacteristic
451C2×C4×C139#12111yescharacteristic
452C2×C4×C139#12111yescharacteristic
453C2×C4×C139#12111yescharacteristic
454C2×C4×C139#12111yescharacteristic
455C2×C4×C139#12111yescharacteristic
456C2×C4×C139#12111yescharacteristic
457C2×C4×C139#12111yescharacteristic
458C2×C4×C139#12111yescharacteristic
459C2×C4×C139#12111yescharacteristic
460C2×C4×C139#12111yescharacteristic
461C2×C4×C139#12711yescharacteristic
462C2×C4×C139#12711yescharacteristic
463C2×C4×C139C22×D411yescharacteristic
464C2×C4×C139C22×D411yescharacteristic
465C2×C4×C139C22×D411yescharacteristic
466C2×C4×C139C22×D411yescharacteristic
467C2×C4×C139C22×D411yescharacteristic
468C2×C4×C139C2×#4111yescharacteristic
469C8×C139—24no—
470C8×C139—24no—
471C22×C139—41no—
472C22×C139—41no—
473C22×C139—41no—
474C22×C139—41no—
475C22×C139—41no—
476C22×C139—41no—
477C22×C139—41no—
478C22×C139—44no—
479C22×C139—44no—
480C22×C139—42no—
481C22×C139—42no—
482C22×C139—42no—
483C22×C139—82no—
484C22×C139—82no—
485C22×C139—82no—
486C22×C139—82no—
487C22×C139—82no—
488C22×C139—82no—
489C22×C139—82no—
490C22×C139#39211yescharacteristic
491C22×C139#39211yescharacteristic
492C22×C139#39211yescharacteristic
493C22×C139#39211yescharacteristic
494C22×C139C2×#12011yescharacteristic
495C22×C139C2×#12111yescharacteristic
496C22×C139C2×#12711yescharacteristic
497C4×C139—44no—
498C4×C139—42no—
499C4×C139—42no—
500C4×C139—42no—
501C4×C139—82no—
502C4×C139#39211yescharacteristic
503C4×C139#39211yescharacteristic
504C4×C139#39211yescharacteristic
505C4×C139#39211yescharacteristic
506C4×C139C2×#12011yescharacteristic
507C4×C139C2×#12011yescharacteristic
508C4×C139C2×#12111yescharacteristic
509C4×C139C2×#12111yescharacteristic
510C2×C139—21no—
511C2×C139—21no—
512C2×C139—21no—
513C2×C139—21no—
514C2×C139—21no—
515C2×C139—21no—
516C2×C139—21no—
517C2×C139—82no—
518C2×C139—82no—
519C2×C139—82no—
520C2×C139C2×#39211yescharacteristic
521#23412C13911yesmaximal, characteristic, direct product factor, Sylow
522C139#2341211yescharacteristic, direct product factor, Sylow
523C2×#575C2×C13911yescharacteristic, complemented
524C2×#575C2×C13911yescharacteristic, complemented
525#3449C2×C13911yescharacteristic, complemented
526C2×#421C2×C13911yescharacteristic, complemented
527#2896C2×C13911yescharacteristic, complemented
528C2×#410C2×C13911yescharacteristic, complemented
529#2009C2×C13914yescomplemented
530#2008C2×C13914yescomplemented
531C2×#344C2×C13911yescharacteristic, complemented
532C22×#41C22×C13911yescharacteristic
533C22×#41C22×C13911yescharacteristic
534C22×#41C22×C13911yescharacteristic
535#575—22no—
536#575—22no—
537#575—22no—
538#575—22no—
539#575—22no—
540#575—22no—
541#575—22no—
542#575C22×C13914yes—
543C2×#137—21no—
544C2×#137—21no—
545C2×#137—21no—
546C2×#137C22×C13912yescomplemented
547C2×AGL(1,ℤ/8)—21no—
548C2×AGL(1,ℤ/8)—21no—
549C2×AGL(1,ℤ/8)—21no—
550C2×AGL(1,ℤ/8)C22×C13912yescomplemented
551C2×#135—22no—
552C2×#135—22no—
553C22×M16C22×C13911yescharacteristic
554C22×M16C22×C13911yescharacteristic
555#537—22no—
556#536—21no—
557#536C22×C13912yescomplemented
558#535—21no—
559#535C22×C13912yescomplemented
560#534—22no—
561#532—22no—
562#525—22no—
563#525—22no—
564C2×#117C22×C13911yescharacteristic
565C2×#117C22×C13911yescharacteristic
566#421—22no—
567#421C22×C13914yescomplemented
568C2×#104—22no—
569#419C22×C13912yescomplemented
570#418C22×C13912yescomplemented
571#417—22no—
572#416—22no—
573#410—22no—
574#410C22×C13914yescomplemented
575C2×#99—22no—
576#344C22×C13914yescomplemented
577C2×#41—21no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—21no—
584C2×#41—21no—
585C2×#41—21no—
586C2×#41—21no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41D4×C13912yes—
608C2×#41D4×C13912yes—
609C2×#41D4×C13912yes—
610C2×#41D4×C13912yescomplemented
611C2×#41C23×C13912yes—
612C2×#41C23×C13912yes—
613C22×Q8D4×C13911yescharacteristic
614C22×Q8D4×C13911yescharacteristic, complemented
615C22×Q8C23×C13911yescharacteristic
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C13911yescharacteristic
620C22×D4D4×C13911yescharacteristic, complemented
621C22×D4C23×C13911yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C13911yescharacteristic
626#137—24no—
627#137—24no—
628#137—24no—
629#137—24no—
630#137—24no—
631#137—24no—
632#137—24no—
633#137—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—24no—
638AGL(1,ℤ/8)—24no—
639AGL(1,ℤ/8)—24no—
640AGL(1,ℤ/8)—24no—
641AGL(1,ℤ/8)—24no—
642#135—28no—
643#135—28no—
644#135—28no—
645#135—28no—
646C2×Q16—22no—
647C2×Q16—22no—
648C2×SD16—22no—
649C2×SD16—22no—
650C2×SD16—22no—
651C2×SD16—22no—
652C2×D8—22no—
653C2×D8—22no—
654C2×M16—21no—
655C2×M16—21no—
656C2×M16—21no—
657C2×M16—21no—
658C2×M16—21no—
659C2×M16—21no—
660C2×M16—21no—
661C2×M16D4×C13912yescomplemented
662C2×M16D4×C13912yescomplemented
663C2×M16D4×C13912yescomplemented
664C2×M16C23×C13912yes—
665C2×M16C23×C13912yes—
666C22×C8—21no—
667C22×C8D4×C13912yescomplemented
668C4⋊Q8—22no—
669#127—22no—
670#124—22no—
671#124—22no—
672#123—24no—
673#123—24no—
674C22⋊Q8—24no—
675C22⋊Q8—24no—
676#121—24no—
677#121—28no—
678#121—24no—
679#120—24no—
680#120—24no—
681C4×D4—28no—
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117D4×C13912yes—
688#117C23×C13912yes—
689#117C23×C13912yes—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4D4×C13912yes—
694C2×C42—21no—
695C2×C42—21no—
696#104—28no—
697#103—24no—
698#102—24no—
699#99—28no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24C2×D4×C13911yescharacteristic
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—22no—
717#41—22no—
718#41—22no—
719#41—22no—
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740#41—41no—
741#41—41no—
742#41—41no—
743#41—41no—
744#41—41no—
745#41—41no—
746#41—41no—
747#41—41no—
748#41—41no—
749#41—41no—
750#41—41no—
751#41—41no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8C2×D4×C13912yes—
768C2×Q8C2×D4×C13912yes—
769C2×Q8C2×D4×C13912yes—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—28no—
777C2×D4—21no—
778C2×D4—21no—
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—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—41no—
793C2×D4—41no—
794C2×D4—41no—
795C2×D4—41no—
796C2×D4—41no—
797C2×D4—41no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C2×D4C2×D4×C13912yes—
805C2×D4C2×D4×C13912yes—
806C2×D4C2×D4×C13912yes—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4C2×D4×C13911yescharacteristic
831C22×C4C2×D4×C13911yescharacteristic
832C22×C4C2×D4×C13911yescharacteristic
833C22×C4C2×D4×C13911yescharacteristic
834C22×C4C2×D4×C13911yescharacteristic
835C22×C4C2×D4×C13911yescharacteristic
836C22×C4C2×D4×C13911yescharacteristic
837C22×C4C2×D4×C13911yescharacteristic
838C22×C4C2×D4×C13911yescharacteristic
839C22×C4C2×D4×C13911yescharacteristic
840C22×C4C2×D4×C13911yescharacteristic
841C22×C4#41×C13911yescharacteristic
842C22×C4#41×C13911yescharacteristic
843C22×C4C24×C13911yescharacteristic
844Q16—28no—
845Q16—28no—
846SD16—28no—
847SD16—28no—
848SD16—28no—
849SD16—28no—
850D8—28no—
851D8—28no—
852M16—22no—
853M16—22no—
854M16—22no—
855M16—22no—
856M16—22no—
857M16—22no—
858M16—22no—
859M16C2×D4×C13914yes—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—22no—
865C2×C8C2×D4×C13914yes—
866C4⋊C4—28no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—41no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—41no—
876C22⋊C4C2×D4×C13914yes—
877C42—22no—
878C42—22no—
879C42—22no—
880C42—41no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—81no—
891C23—82no—
892C23—82no—
893C23—82no—
894C23#120×C13911yescharacteristic
895C23#120×C13911yescharacteristic
896C23#121×C13911yescharacteristic
897C23#121×C13911yescharacteristic
898C23#127×C13911yescharacteristic
899C23#127×C13911yescharacteristic
900C23C22×D4×C13911yescharacteristic
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—22no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912Q8—41no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—22no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—88no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4#120×C13911yescharacteristic
964C2×C4#120×C13911yescharacteristic
965C2×C4#120×C13911yescharacteristic
966C2×C4#120×C13911yescharacteristic
967C2×C4#120×C13911yescharacteristic
968C2×C4#120×C13911yescharacteristic
969C2×C4#120×C13911yescharacteristic
970C2×C4#120×C13911yescharacteristic
971C2×C4#120×C13911yescharacteristic
972C2×C4#120×C13911yescharacteristic
973C2×C4#121×C13911yescharacteristic
974C2×C4#121×C13911yescharacteristic
975C2×C4#121×C13911yescharacteristic
976C2×C4#121×C13911yescharacteristic
977C2×C4#121×C13911yescharacteristic
978C2×C4#121×C13911yescharacteristic
979C2×C4#121×C13911yescharacteristic
980C2×C4#121×C13911yescharacteristic
981C2×C4#121×C13911yescharacteristic
982C2×C4#121×C13911yescharacteristic
983C2×C4#127×C13911yescharacteristic
984C2×C4#127×C13911yescharacteristic
985C2×C4C22×D4×C13911yescharacteristic
986C2×C4C22×D4×C13911yescharacteristic
987C2×C4C22×D4×C13911yescharacteristic
988C2×C4C22×D4×C13911yescharacteristic
989C2×C4C22×D4×C13911yescharacteristic
990C2×C4C2×#41×C13911yescharacteristic
991C8—24no—
992C8—24no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22#392×C13911yescharacteristic
1013C22#392×C13911yescharacteristic
1014C22#392×C13911yescharacteristic
1015C22#392×C13911yescharacteristic
1016C22C2×#120×C13911yescharacteristic
1017C22C2×#121×C13911yescharacteristic
1018C22C2×#127×C13911yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4#392×C13911yescharacteristic
1025C4#392×C13911yescharacteristic
1026C4#392×C13911yescharacteristic
1027C4#392×C13911yescharacteristic
1028C4C2×#120×C13911yescharacteristic
1029C4C2×#120×C13911yescharacteristic
1030C4C2×#121×C13911yescharacteristic
1031C4C2×#121×C13911yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×#392×C13911yescharacteristic
subgroupG/H
centerC4×C139#392
commutator, Frattini, cosocleC22×C4C24×C139
socleC2×C139C2×#392
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C139C2semidirect
2. C2×#575×C139C2semidirect
3. #3449×C139C2semidirect
4. C2×#421×C139C2semidirect
5. #2896×C139C2semidirect
6. C2×#410×C139C2semidirect
7. #2009×C139C2semidirect
8. #2008×C139C2semidirect
9. C2×#344×C139C2semidirect
24. C2×#137×C139C22semidirect
28. C2×AGL(1,ℤ/8)×C139C22semidirect
35. #536×C139C22semidirect
37. #535×C139C22semidirect
45. #421×C139C22semidirect
47. #419×C139C22semidirect
48. #418×C139C22semidirect
52. #410×C139C22semidirect
54. #344×C139C22semidirect
88. C2×#41×C139D4semidirect
92. C22×Q8×C139D4semidirect
98. C22×D4×C139D4semidirect
139. C2×M16×C139D4semidirect
140. C2×M16×C139D4semidirect
141. C2×M16×C139D4semidirect
145. C22×C8×C139D4semidirect
521. #23412C139direct (N × H)
522. C139#23412direct (N × H)
523. C2×#575C2×C139semidirect
524. C2×#575C2×C139semidirect
525. #3449C2×C139semidirect
526. C2×#421C2×C139semidirect
527. #2896C2×C139semidirect
528. C2×#410C2×C139semidirect
529. #2009C2×C139semidirect
530. #2008C2×C139semidirect
531. C2×#344C2×C139semidirect
546. C2×#137C22×C139semidirect
550. C2×AGL(1,ℤ/8)C22×C139semidirect
557. #536C22×C139semidirect
559. #535C22×C139semidirect
567. #421C22×C139semidirect
569. #419C22×C139semidirect
570. #418C22×C139semidirect
574. #410C22×C139semidirect
576. #344C22×C139semidirect
610. C2×#41D4×C139semidirect
614. C22×Q8D4×C139semidirect
620. C22×D4D4×C139semidirect
661. C2×M16D4×C139semidirect
662. C2×M16D4×C139semidirect
663. C2×M16D4×C139semidirect
667. C22×C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1392
#3449×C1392
C2×#421×C1392
#2896×C1392
C2×#410×C1392
#2009×C1392
#2008×C1392
C2×#344×C1392
#23412139