Finite Group Databasebeta

← C139×#24472 #48019068

Subgroups — C139×#24472 #48019068

Order 35584.

1372 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C139C211yesmaximal, characteristic, complemented
2#3068×C139C211yesmaximal, characteristic, complemented
3#3038×C139C211yesmaximal, characteristic, complemented
4#3021×C139C211yesmaximal, characteristic, complemented
5C2×#453×C139C211yesmaximal, characteristic, complemented
6#2901×C139C211yesmaximal, characteristic, complemented
7#2050×C139C211yesmaximal, characteristic, complemented
8#2048×C139C211yesmaximal, characteristic, complemented
9#2008×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1906×C139C211yesmaximal, characteristic, complemented
12#1903×C139C211yesmaximal, characteristic, complemented
13#1903×C139C211yesmaximal, characteristic, complemented
14#1861×C139C211yesmaximal, characteristic, complemented
15#1795×C139C211yesmaximal, characteristic, complemented
16#585×C139C2211yescharacteristic
17C2×H(5,𝔽2)×C139C2211yescharacteristic
18#577×C139—22no—
19#577×C139—22no—
20#576×C139—22no—
21#576×C139—22no—
22#575×C139—22no—
23#575×C139C2211yescharacteristic
24#575×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139—22no—
26C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
31#568×C139C2211yescharacteristic
32#568×C139C2211yescharacteristic, complemented
33#535×C139C2211yescharacteristic, complemented
34C2×#127×C139C2211yescharacteristic, complemented
35C4×#41×C139C2211yescharacteristic, complemented
36#472×C139—22no—
37#471×C139—22no—
38#460×C139—22no—
39#459×C139—22no—
40#454×C139—22no—
41#453×C139—22no—
42#453×C139—22no—
43#453×C139—22no—
44#430×C139C2211yescharacteristic, complemented
45#423×C139C2211yescharacteristic, complemented
46#421×C139—22no—
47#421×C139C2211yescharacteristic
48#421×C139C2211yescharacteristic
49#421×C139C2211yescharacteristic, complemented
50#421×C139C2211yescharacteristic, complemented
51C2×#104×C139—22no—
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic, complemented
54C2×#104×C139C2211yescharacteristic, complemented
55#418×C139C2211yescharacteristic, complemented
56#418×C139C2211yescharacteristic, complemented
57#418×C139C2211yescharacteristic, complemented
58#413×C139C2211yescharacteristic, complemented
59#413×C139C2211yescharacteristic, complemented
60C2×#100×C139C2211yescharacteristic, complemented
61C2×#100×C139C2211yescharacteristic, complemented
62#410×C139C2211yescharacteristic, complemented
63#344×C139C2211yescharacteristic, complemented
64#344×C139C2211yescharacteristic, complemented
65#339×C139C2211yescharacteristic, complemented
66#338×C139C2211yescharacteristic, complemented
672−1+4×C139—21no—
682−1+4×C139—21no—
692−1+4×C139D412yescomplemented
70H(5,𝔽2)×C139—22no—
71H(5,𝔽2)×C139—21no—
72H(5,𝔽2)×C139—22no—
73H(5,𝔽2)×C139—21no—
74H(5,𝔽2)×C139—22no—
75H(5,𝔽2)×C139—41no—
76H(5,𝔽2)×C139—41no—
77H(5,𝔽2)×C139D412yescomplemented
78C2×#41×C139—22no—
79C2×#41×C139—22no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—41no—
83C2×#41×C139C2311yescharacteristic
84C2×#41×C139C2311yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C2×#41×C139C2311yescharacteristic
87C22×D4×C139—21no—
88C22×D4×C139—21no—
89C22×D4×C139—41no—
90C22×D4×C139—41no—
91C22×D4×C139C2311yescharacteristic
92C22×D4×C139C2311yescharacteristic
93#137×C139—24no—
94#137×C139—21no—
95#137×C139—21no—
96#137×C139—21no—
97#137×C139D412yescomplemented
98AGL(1,ℤ/8)×C139—24no—
99AGL(1,ℤ/8)×C139—24no—
100AGL(1,ℤ/8)×C139—24no—
101AGL(1,ℤ/8)×C139—22no—
102AGL(1,ℤ/8)×C139—22no—
103AGL(1,ℤ/8)×C139—21no—
104AGL(1,ℤ/8)×C139—22no—
105AGL(1,ℤ/8)×C139—21no—
106AGL(1,ℤ/8)×C139—21no—
107AGL(1,ℤ/8)×C139—22no—
108AGL(1,ℤ/8)×C139—22no—
109AGL(1,ℤ/8)×C139—22no—
110AGL(1,ℤ/8)×C139—22no—
111AGL(1,ℤ/8)×C139—22no—
112AGL(1,ℤ/8)×C139—22no—
113AGL(1,ℤ/8)×C139—41no—
114AGL(1,ℤ/8)×C139D412yescomplemented
115#135×C139—24no—
116#135×C139—24no—
117#135×C139—22no—
118#135×C139—22no—
119C2×SD16×C139—24no—
120C2×SD16×C139—21no—
121C2×SD16×C139—21no—
122C2×SD16×C139—21no—
123C2×SD16×C139—21no—
124C2×SD16×C139D412yescomplemented
125C2×D8×C139—24no—
126C2×D8×C139—21no—
127C2×D8×C139—21no—
128C2×D8×C139—21no—
129C2×D8×C139—21no—
130C2×D8×C139D412yescomplemented
131#131×C139—22no—
132#131×C139—22no—
133#131×C139—22no—
134#131×C139—41no—
135C2×M16×C139—22no—
136C2×M16×C139—22no—
137C2×M16×C139C2311yescharacteristic
138C2×M16×C139C2311yescharacteristic
139C2×M16×C139C2311yescharacteristic
140C2×M16×C139C2311yescharacteristic
141C2×M16×C139C2311yescharacteristic
142C2×M16×C139C2311yescharacteristic
143#127×C139—21no—
144#127×C139—22no—
145#127×C139—21no—
146#127×C139—21no—
147#124×C139—21no—
148#121×C139—41no—
149#120×C139—41no—
150C4×Q8×C139—21no—
151C4×D4×C139—21no—
152C4×D4×C139—41no—
153#117×C139—21no—
154#117×C139C2311yescharacteristic
155#117×C139C2311yescharacteristic
156C2×C42×C139—21no—
157C2×C42×C139C2311yescharacteristic
158#108×C139—22no—
159C4⋊C8×C139—22no—
160#104×C139—22no—
161#104×C139—22no—
162#104×C139—22no—
163#104×C139—22no—
164#104×C139—21no—
165#104×C139—21no—
166#104×C139—21no—
167#104×C139—21no—
168#104×C139D412yescomplemented
169#104×C139D412yescomplemented
170#102×C139—22no—
171#102×C139—22no—
172#102×C139—41no—
173#101×C139—21no—
174#101×C139—21no—
175#100×C139—21no—
176#100×C139—21no—
177#100×C139—22no—
178#100×C139—22no—
179#99×C139—41no—
180C24×C139—21no—
181C24×C139—21no—
182C24×C139—41no—
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—21no—
186#41×C139—21no—
187#41×C139—24no—
188#41×C139—22no—
189#41×C139—22no—
190#41×C139—22no—
191#41×C139—22no—
192#41×C139—21no—
193#41×C139—21no—
194#41×C139—21no—
195#41×C139—21no—
196#41×C139—21no—
197#41×C139—21no—
198#41×C139—21no—
199#41×C139—21no—
200#41×C139—42no—
201#41×C139—42no—
202#41×C139—42no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—42no—
206#41×C139—41no—
207#41×C139—41no—
208#41×C139—42no—
209#41×C139C2×D412yes—
210#41×C139C2×D412yes—
211#41×C139C2×D412yes—
212#41×C139C2×D412yes—
213C2×Q8×C139—22no—
214C2×Q8×C139—22no—
215C2×Q8×C139—41no—
216C2×Q8×C139C2×D411yescharacteristic
217C2×Q8×C139C2×D411yescharacteristic
218C2×Q8×C139C2×D411yescharacteristic
219C2×Q8×C139#4111yescharacteristic
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—24no—
223C2×D4×C139—22no—
224C2×D4×C139—22no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—21no—
229C2×D4×C139—21no—
230C2×D4×C139—21no—
231C2×D4×C139—21no—
232C2×D4×C139—21no—
233C2×D4×C139—21no—
234C2×D4×C139—21no—
235C2×D4×C139—21no—
236C2×D4×C139—21no—
237C2×D4×C139—21no—
238C2×D4×C139—42no—
239C2×D4×C139—41no—
240C2×D4×C139—41no—
241C2×D4×C139—42no—
242C2×D4×C139—42no—
243C2×D4×C139—42no—
244C2×D4×C139—42no—
245C2×D4×C139—41no—
246C2×D4×C139—44no—
247C2×D4×C139—42no—
248C2×D4×C139—42no—
249C2×D4×C139—44no—
250C2×D4×C139—42no—
251C2×D4×C139—42no—
252C2×D4×C139—84no—
253C2×D4×C139C2×D411yescharacteristic
254C2×D4×C139C2×D411yescharacteristic
255C2×D4×C139C2×D412yes—
256C2×D4×C139C2×D411yescharacteristic
257C2×D4×C139#4111yescharacteristic
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—41no—
264C22×C4×C139—42no—
265C22×C4×C139—41no—
266C22×C4×C139C2411yescharacteristic
267Q16×C139—22no—
268Q16×C139—22no—
269SD16×C139—24no—
270SD16×C139—22no—
271SD16×C139—22no—
272SD16×C139—22no—
273SD16×C139—24no—
274SD16×C139—22no—
275SD16×C139—42no—
276SD16×C139—42no—
277SD16×C139—42no—
278D8×C139—24no—
279D8×C139—22no—
280D8×C139—22no—
281D8×C139—24no—
282D8×C139—42no—
283D8×C139—42no—
284D8×C139—42no—
285M16×C139—24no—
286M16×C139—21no—
287M16×C139—21no—
288M16×C139—21no—
289M16×C139—21no—
290M16×C139—21no—
291M16×C139—21no—
292M16×C139—21no—
293M16×C139—21no—
294M16×C139—21no—
295M16×C139—21no—
296M16×C139—42no—
297M16×C139C2×D412yes—
298M16×C139C2×D412yes—
299C2×C8×C139—24no—
300C2×C8×C139—21no—
301C2×C8×C139—21no—
302C2×C8×C139—21no—
303C2×C8×C139—21no—
304C2×C8×C139—21no—
305C2×C8×C139—42no—
306C2×C8×C139C2×D412yes—
307C4⋊C4×C139—21no—
308C4⋊C4×C139—21no—
309C4⋊C4×C139—41no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—21no—
312C22⋊C4×C139—41no—
313C22⋊C4×C139—42no—
314C42×C139—21no—
315C42×C139—21no—
316C42×C139—21no—
317C42×C139—41no—
318C42×C139C2×D411yescharacteristic
319C42×C139C2×D411yescharacteristic
320C23×C139—21no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—22no—
324C23×C139—21no—
325C23×C139—42no—
326C23×C139—44no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—82no—
333C23×C139—82no—
334C23×C139—162no—
335C23×C139H(5,𝔽2)11yescharacteristic
336Q8×C139—21no—
337Q8×C139—21no—
338Q8×C139—21no—
339Q8×C139—21no—
340Q8×C139—21no—
341Q8×C139—21no—
342Q8×C139—42no—
343Q8×C139#12012yes—
344Q8×C139#12112yes—
345D4×C139—22no—
346D4×C139—22no—
347D4×C139—22no—
348D4×C139—22no—
349D4×C139—21no—
350D4×C139—21no—
351D4×C139—22no—
352D4×C139—21no—
353D4×C139—21no—
354D4×C139—21no—
355D4×C139—21no—
356D4×C139—22no—
357D4×C139—42no—
358D4×C139—42no—
359D4×C139—44no—
360D4×C139—42no—
361D4×C139—44no—
362D4×C139—41no—
363D4×C139—41no—
364D4×C139—41no—
365D4×C139—41no—
366D4×C139—41no—
367D4×C139—41no—
368D4×C139—41no—
369D4×C139—41no—
370D4×C139—41no—
371D4×C139—41no—
372D4×C139—84no—
373D4×C139—84no—
374D4×C139—162no—
375D4×C139#12012yes—
376D4×C139#12112yes—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—22no—
381C2×C4×C139—22no—
382C2×C4×C139—22no—
383C2×C4×C139—22no—
384C2×C4×C139—21no—
385C2×C4×C139—21no—
386C2×C4×C139—21no—
387C2×C4×C139—42no—
388C2×C4×C139—42no—
389C2×C4×C139—42no—
390C2×C4×C139—42no—
391C2×C4×C139—44no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—41no—
396C2×C4×C139—41no—
397C2×C4×C139—41no—
398C2×C4×C139—82no—
399C2×C4×C139C22×D411yescharacteristic
400C2×C4×C139C22×D411yescharacteristic
401C2×C4×C139C22×D411yescharacteristic
402C2×C4×C139C22×D411yescharacteristic
403C2×C4×C139C2×#4111yescharacteristic
404C2×C4×C139H(5,𝔽2)11yescharacteristic
405C8×C139—22no—
406C8×C139—22no—
407C8×C139—22no—
408C8×C139—41no—
409C8×C139—41no—
410C8×C139—41no—
411C22×C139—22no—
412C22×C139—22no—
413C22×C139—41no—
414C22×C139—41no—
415C22×C139—42no—
416C22×C139—41no—
417C22×C139—81no—
418C22×C139—81no—
419C22×C139—82no—
420C22×C139—81no—
421C22×C139—81no—
422C22×C139—82no—
423C22×C139—82no—
424C22×C139—82no—
425C22×C139—81no—
426C22×C139—161no—
427C22×C139—161no—
428C22×C139—162no—
429C22×C139—164no—
430C22×C139#53411yescharacteristic
431C22×C139D4211yescharacteristic
432C22×C139#54611yescharacteristic
433C4×C139—22no—
434C4×C139—22no—
435C4×C139—22no—
436C4×C139—41no—
437C4×C139—41no—
438C4×C139—41no—
439C4×C139—81no—
440C4×C139—81no—
441C4×C139C2×#12011yescharacteristic
442C4×C139C2×#12111yescharacteristic
443C4×C139D4211yescharacteristic
444C4×C139#54611yescharacteristic
445C2×C139—21no—
446C2×C139—21no—
447C2×C139—21no—
448C2×C139—42no—
449C2×C139—42no—
450C2×C139—82no—
451C2×C139—81no—
452C2×C139—81no—
453C2×C139—161no—
454C2×C139#241011yescharacteristic
455#24472C13911yesmaximal, characteristic, direct product factor, Sylow
456C139#2447211yescharacteristic, direct product factor, Sylow
457#3585C2×C13911yescharacteristic, complemented
458#3068C2×C13911yescharacteristic, complemented
459#3038C2×C13911yescharacteristic, complemented
460#3021C2×C13911yescharacteristic, complemented
461C2×#453C2×C13911yescharacteristic, complemented
462#2901C2×C13911yescharacteristic, complemented
463#2050C2×C13911yescharacteristic, complemented
464#2048C2×C13911yescharacteristic, complemented
465#2008C2×C13911yescharacteristic, complemented
466#2002C2×C13911yescharacteristic, complemented
467#1906C2×C13911yescharacteristic, complemented
468#1903C2×C13911yescharacteristic, complemented
469#1903C2×C13911yescharacteristic, complemented
470#1861C2×C13911yescharacteristic, complemented
471#1795C2×C13911yescharacteristic, complemented
472#585C22×C13911yescharacteristic
473C2×H(5,𝔽2)C22×C13911yescharacteristic
474#577—22no—
475#577—22no—
476#576—22no—
477#576—22no—
478#575—22no—
479#575C22×C13911yescharacteristic
480#575C22×C13911yescharacteristic
481C2×AGL(1,ℤ/8)—22no—
482C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
483C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
484C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
485C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
486C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
487#568C22×C13911yescharacteristic
488#568C22×C13911yescharacteristic, complemented
489#535C22×C13911yescharacteristic, complemented
490C2×#127C22×C13911yescharacteristic, complemented
491C4×#41C22×C13911yescharacteristic, complemented
492#472—22no—
493#471—22no—
494#460—22no—
495#459—22no—
496#454—22no—
497#453—22no—
498#453—22no—
499#453—22no—
500#430C22×C13911yescharacteristic, complemented
501#423C22×C13911yescharacteristic, complemented
502#421—22no—
503#421C22×C13911yescharacteristic
504#421C22×C13911yescharacteristic
505#421C22×C13911yescharacteristic, complemented
506#421C22×C13911yescharacteristic, complemented
507C2×#104—22no—
508C2×#104C22×C13911yescharacteristic
509C2×#104C22×C13911yescharacteristic, complemented
510C2×#104C22×C13911yescharacteristic, complemented
511#418C22×C13911yescharacteristic, complemented
512#418C22×C13911yescharacteristic, complemented
513#418C22×C13911yescharacteristic, complemented
514#413C22×C13911yescharacteristic, complemented
515#413C22×C13911yescharacteristic, complemented
516C2×#100C22×C13911yescharacteristic, complemented
517C2×#100C22×C13911yescharacteristic, complemented
518#410C22×C13911yescharacteristic, complemented
519#344C22×C13911yescharacteristic, complemented
520#344C22×C13911yescharacteristic, complemented
521#339C22×C13911yescharacteristic, complemented
522#338C22×C13911yescharacteristic, complemented
5232−1+4—21no—
5242−1+4—21no—
5252−1+4D4×C13912yescomplemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—21no—
528H(5,𝔽2)—22no—
529H(5,𝔽2)—21no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—41no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)D4×C13912yescomplemented
534C2×#41—22no—
535C2×#41—22no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—41no—
539C2×#41C23×C13911yescharacteristic
540C2×#41C23×C13911yescharacteristic
541C2×#41C23×C13911yescharacteristic
542C2×#41C23×C13911yescharacteristic
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4C23×C13911yescharacteristic
548C22×D4C23×C13911yescharacteristic
549#137—24no—
550#137—21no—
551#137—21no—
552#137—21no—
553#137D4×C13912yescomplemented
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—24no—
556AGL(1,ℤ/8)—24no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—21no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—21no—
562AGL(1,ℤ/8)—21no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—22no—
569AGL(1,ℤ/8)—41no—
570AGL(1,ℤ/8)D4×C13912yescomplemented
571#135—24no—
572#135—24no—
573#135—22no—
574#135—22no—
575C2×SD16—24no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16D4×C13912yescomplemented
581C2×D8—24no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8D4×C13912yescomplemented
587#131—22no—
588#131—22no—
589#131—22no—
590#131—41no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16C23×C13911yescharacteristic
594C2×M16C23×C13911yescharacteristic
595C2×M16C23×C13911yescharacteristic
596C2×M16C23×C13911yescharacteristic
597C2×M16C23×C13911yescharacteristic
598C2×M16C23×C13911yescharacteristic
599#127—22no—
600#127—21no—
601#127—21no—
602#127—21no—
603#124—21no—
604#121—41no—
605#120—41no—
606C4×Q8—21no—
607C4×D4—21no—
608C4×D4—41no—
609#117—21no—
610#117C23×C13911yescharacteristic
611#117C23×C13911yescharacteristic
612C2×C42—21no—
613C2×C42C23×C13911yescharacteristic
614#108—22no—
615C4⋊C8—22no—
616#104—22no—
617#104—22no—
618#104—22no—
619#104—22no—
620#104—21no—
621#104—21no—
622#104—21no—
623#104—21no—
624#104D4×C13912yescomplemented
625#104D4×C13912yescomplemented
626#102—22no—
627#102—22no—
628#102—41no—
629#101—21no—
630#101—21no—
631#100—21no—
632#100—21no—
633#100—22no—
634#100—22no—
635#99—41no—
636C24—21no—
637C24—21no—
638C24—41no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—24no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—21no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—42no—
657#41—42no—
658#41—42no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—41no—
663#41—41no—
664#41—42no—
665#41C2×D4×C13912yes—
666#41C2×D4×C13912yes—
667#41C2×D4×C13912yes—
668#41C2×D4×C13912yes—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×D4×C13911yescharacteristic
673C2×Q8C2×D4×C13911yescharacteristic
674C2×Q8C2×D4×C13911yescharacteristic
675C2×Q8#41×C13911yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—24no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—42no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—44no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—84no—
709C2×D4C2×D4×C13911yescharacteristic
710C2×D4C2×D4×C13911yescharacteristic
711C2×D4C2×D4×C13912yes—
712C2×D4C2×D4×C13911yescharacteristic
713C2×D4#41×C13911yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—41no—
720C22×C4—42no—
721C22×C4—41no—
722C22×C4C24×C13911yescharacteristic
723Q16—22no—
724Q16—22no—
725SD16—24no—
726SD16—22no—
727SD16—22no—
728SD16—22no—
729SD16—24no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734D8—24no—
735D8—22no—
736D8—22no—
737D8—24no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—42no—
753M16C2×D4×C13912yes—
754M16C2×D4×C13912yes—
755C2×C8—24no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—42no—
762C2×C8C2×D4×C13912yes—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—41no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—41no—
769C22⋊C4—42no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—41no—
774C42C2×D4×C13911yescharacteristic
775C42C2×D4×C13911yescharacteristic
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—42no—
782C23—44no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—82no—
789C23—82no—
790C23—162no—
791C23H(5,𝔽2)×C13911yescharacteristic
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—21no—
798Q8—42no—
799Q8#120×C13912yes—
800Q8#121×C13912yes—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—22no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—22no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—42no—
817D4—44no—
818D4—41no—
819D4—41no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—84no—
829D4—84no—
830D4—162no—
831D4#120×C13912yes—
832D4#121×C13912yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—82no—
855C2×C4C22×D4×C13911yescharacteristic
856C2×C4C22×D4×C13911yescharacteristic
857C2×C4C22×D4×C13911yescharacteristic
858C2×C4C22×D4×C13911yescharacteristic
859C2×C4C2×#41×C13911yescharacteristic
860C2×C4H(5,𝔽2)×C13911yescharacteristic
861C8—22no—
862C8—22no—
863C8—22no—
864C8—41no—
865C8—41no—
866C8—41no—
867C22—22no—
868C22—22no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—81no—
882C22—161no—
883C22—161no—
884C22—162no—
885C22—164no—
886C22#534×C13911yescharacteristic
887C22D42×C13911yescharacteristic
888C22#546×C13911yescharacteristic
889C4—22no—
890C4—22no—
891C4—22no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—81no—
896C4—81no—
897C4C2×#120×C13911yescharacteristic
898C4C2×#121×C13911yescharacteristic
899C4D42×C13911yescharacteristic
900C4#546×C13911yescharacteristic
901C2—21no—
902C2—21no—
903C2—21no—
904C2—42no—
905C2—42no—
906C2—82no—
907C2—81no—
908C2—81no—
909C2—161no—
910C2#2410×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2410
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. #3585×C139C2semidirect
2. #3068×C139C2semidirect
3. #3038×C139C2semidirect
4. #3021×C139C2semidirect
5. C2×#453×C139C2semidirect
6. #2901×C139C2semidirect
7. #2050×C139C2semidirect
8. #2048×C139C2semidirect
9. #2008×C139C2semidirect
10. #2002×C139C2semidirect
11. #1906×C139C2semidirect
12. #1903×C139C2semidirect
13. #1903×C139C2semidirect
14. #1861×C139C2semidirect
15. #1795×C139C2semidirect
29. C2×AGL(1,ℤ/8)×C139C22semidirect
30. C2×AGL(1,ℤ/8)×C139C22semidirect
32. #568×C139C22semidirect
33. #535×C139C22semidirect
34. C2×#127×C139C22semidirect
35. C4×#41×C139C22semidirect
44. #430×C139C22semidirect
45. #423×C139C22semidirect
49. #421×C139C22semidirect
50. #421×C139C22semidirect
53. C2×#104×C139C22semidirect
54. C2×#104×C139C22semidirect
55. #418×C139C22semidirect
56. #418×C139C22semidirect
57. #418×C139C22semidirect
58. #413×C139C22semidirect
59. #413×C139C22semidirect
60. C2×#100×C139C22semidirect
61. C2×#100×C139C22semidirect
62. #410×C139C22semidirect
63. #344×C139C22semidirect
64. #344×C139C22semidirect
65. #339×C139C22semidirect
66. #338×C139C22semidirect
69. 2−1+4×C139D4semidirect
77. H(5,𝔽2)×C139D4semidirect
97. #137×C139D4semidirect
114. AGL(1,ℤ/8)×C139D4semidirect
124. C2×SD16×C139D4semidirect
130. C2×D8×C139D4semidirect
168. #104×C139D4semidirect
169. #104×C139D4semidirect
455. #24472C139direct (N × H)
456. C139#24472direct (N × H)
457. #3585C2×C139semidirect
458. #3068C2×C139semidirect
459. #3038C2×C139semidirect
460. #3021C2×C139semidirect
461. C2×#453C2×C139semidirect
462. #2901C2×C139semidirect
463. #2050C2×C139semidirect
464. #2048C2×C139semidirect
465. #2008C2×C139semidirect
466. #2002C2×C139semidirect
467. #1906C2×C139semidirect
468. #1903C2×C139semidirect
469. #1903C2×C139semidirect
470. #1861C2×C139semidirect
471. #1795C2×C139semidirect
485. C2×AGL(1,ℤ/8)C22×C139semidirect
486. C2×AGL(1,ℤ/8)C22×C139semidirect
488. #568C22×C139semidirect
489. #535C22×C139semidirect
490. C2×#127C22×C139semidirect
491. C4×#41C22×C139semidirect
500. #430C22×C139semidirect
501. #423C22×C139semidirect
505. #421C22×C139semidirect
506. #421C22×C139semidirect
509. C2×#104C22×C139semidirect
510. C2×#104C22×C139semidirect
511. #418C22×C139semidirect
512. #418C22×C139semidirect
513. #418C22×C139semidirect
514. #413C22×C139semidirect
515. #413C22×C139semidirect
516. C2×#100C22×C139semidirect
517. C2×#100C22×C139semidirect
518. #410C22×C139semidirect
519. #344C22×C139semidirect
520. #344C22×C139semidirect
521. #339C22×C139semidirect
522. #338C22×C139semidirect
525. 2−1+4D4×C139semidirect
533. H(5,𝔽2)D4×C139semidirect
553. #137D4×C139semidirect
570. AGL(1,ℤ/8)D4×C139semidirect
580. C2×SD16D4×C139semidirect
586. C2×D8D4×C139semidirect
624. #104D4×C139semidirect
625. #104D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3585×C1392
#3068×C1392
#3038×C1392
#3021×C1392
C2×#453×C1392
#2901×C1392
#2050×C1392
#2048×C1392
#2008×C1392
#2002×C1392
#1906×C1392
#1903×C1392
#1861×C1392
#1795×C1392
#24472139