Finite Group Databasebeta

← C139×#24295 #48018891

Subgroups — C139×#24295 #48018891

Order 35584.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C139C211yesmaximal, characteristic, complemented
2#3067×C139C211yesmaximal, characteristic, complemented
3#3057×C139C211yesmaximal, characteristic, complemented
4#3020×C139C211yesmaximal, characteristic, complemented
5#3019×C139C211yesmaximal, characteristic, complemented
6#2955×C139C211yesmaximal, characteristic, complemented
7#2049×C139C211yesmaximal, characteristic, complemented
8#2048×C139C211yesmaximal, characteristic, complemented
9#2009×C139C211yesmaximal, characteristic, complemented
10#2008×C139C211yesmaximal, characteristic, complemented
11#1977×C139C211yesmaximal, characteristic, complemented
12#1976×C139C211yesmaximal, characteristic, complemented
13#1814×C139C211yesmaximal, characteristic, complemented
14#1796×C139C211yesmaximal, characteristic, complemented
15#1795×C139C211yesmaximal, characteristic, complemented
16C2×2−1+4×C139C2211yescharacteristic
17C2×H(5,𝔽2)×C139C2211yescharacteristic
18#577×C139—22no—
19#577×C139—22no—
20#577×C139—22no—
21#577×C139—22no—
22#575×C139C2211yescharacteristic
23#575×C139C2211yescharacteristic
24#575×C139C2211yescharacteristic, complemented
25C2×#137×C139—21no—
26C2×#137×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139—21no—
28C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
29C2×#135×C139—21no—
30C2×#135×C139C2211yescharacteristic
31C22×SD16×C139—21no—
32C22×SD16×C139C2211yescharacteristic
33C2×#131×C139C2211yescharacteristic
34C2×#131×C139C2211yescharacteristic, complemented
35#536×C139C2211yescharacteristic, complemented
36#535×C139C2211yescharacteristic
37#473×C139—21no—
38#472×C139—21no—
39#471×C139—21no—
40#471×C139—21no—
41#468×C139—22no—
42#465×C139—22no—
43#456×C139—22no—
44#455×C139—22no—
45#454×C139—22no—
46#453×C139—22no—
47#444×C139—22no—
48#443×C139—22no—
49#430×C139C2211yescharacteristic, complemented
50C2×#108×C139C2211yescharacteristic, complemented
51#427×C139C2211yescharacteristic, complemented
52#421×C139C2211yescharacteristic
53#421×C139C2211yescharacteristic
54#421×C139C2211yescharacteristic
55#421×C139C2211yescharacteristic
56#421×C139C2211yescharacteristic, complemented
57#421×C139C2211yescharacteristic, complemented
58#419×C139C2211yescharacteristic, complemented
59#419×C139C2211yescharacteristic, complemented
60#418×C139C2211yescharacteristic
61#418×C139C2211yescharacteristic
62#413×C139C2211yescharacteristic
63#413×C139C2211yescharacteristic, complemented
64C2×#101×C139C2211yescharacteristic, complemented
65C2×#100×C139C2211yescharacteristic
66#410×C139C2211yescharacteristic
67#410×C139C2211yescharacteristic, complemented
68#405×C139C2211yescharacteristic, complemented
69#344×C139C2211yescharacteristic, complemented
70#344×C139C2211yescharacteristic, complemented
712−1+4×C139—22no—
722−1+4×C139—22no—
732−1+4×C139—22no—
742−1+4×C139—41no—
75H(5,𝔽2)×C139—22no—
76H(5,𝔽2)×C139—22no—
77H(5,𝔽2)×C139—22no—
78H(5,𝔽2)×C139—41no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—21no—
83C2×#41×C139—41no—
84C2×#41×C139C2311yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C2×#41×C139C2311yescharacteristic
87C2×#41×C139C2311yescharacteristic
88C22×Q8×C139—21no—
89C22×Q8×C139—21no—
90C22×Q8×C139C2311yescharacteristic
91C22×D4×C139—21no—
92C22×D4×C139—21no—
93C22×D4×C139—41no—
94C22×D4×C139C2311yescharacteristic
95#137×C139—24no—
96#137×C139—24no—
97#137×C139—22no—
98#137×C139—21no—
99#137×C139—21no—
100#137×C139—21no—
101#137×C139—21no—
102#137×C139—21no—
103#137×C139—22no—
104#137×C139D412yes—
105AGL(1,ℤ/8)×C139—24no—
106AGL(1,ℤ/8)×C139—24no—
107AGL(1,ℤ/8)×C139—22no—
108AGL(1,ℤ/8)×C139—21no—
109AGL(1,ℤ/8)×C139—21no—
110AGL(1,ℤ/8)×C139—21no—
111AGL(1,ℤ/8)×C139—21no—
112AGL(1,ℤ/8)×C139—21no—
113AGL(1,ℤ/8)×C139—22no—
114AGL(1,ℤ/8)×C139D412yes—
115#135×C139—24no—
116#135×C139—24no—
117#135×C139—22no—
118#135×C139—21no—
119#135×C139—21no—
120#135×C139—21no—
121#135×C139—21no—
122#135×C139—41no—
123#135×C139—41no—
124C2×Q16×C139—21no—
125C2×Q16×C139D411yescharacteristic, complemented
126C2×SD16×C139—24no—
127C2×SD16×C139—24no—
128C2×SD16×C139—21no—
129C2×SD16×C139—21no—
130C2×SD16×C139—21no—
131C2×SD16×C139—21no—
132C2×SD16×C139—21no—
133C2×SD16×C139—21no—
134C2×SD16×C139D412yes—
135C2×SD16×C139D412yes—
136C2×SD16×C139D411yescharacteristic, complemented
137C2×SD16×C139D411yescharacteristic, complemented
138C2×D8×C139—21no—
139C2×D8×C139D411yescharacteristic, complemented
140#131×C139—21no—
141#131×C139—21no—
142#131×C139—21no—
143#131×C139—21no—
144#131×C139—21no—
145#131×C139—21no—
146#131×C139D412yescomplemented
147#131×C139D412yescomplemented
148C2×M16×C139—21no—
149C2×M16×C139—21no—
150C2×M16×C139C2311yescharacteristic
151C2×M16×C139C2311yescharacteristic
152C2×M16×C139C2311yescharacteristic
153C2×M16×C139C2311yescharacteristic
154C2×M16×C139C2311yescharacteristic
155C22×C8×C139—21no—
156C22×C8×C139—21no—
157C22×C8×C139C2311yescharacteristic
158C4⋊Q8×C139—21no—
159#127×C139—21no—
160#124×C139—21no—
161#124×C139—21no—
162#123×C139—41no—
163C22⋊Q8×C139—22no—
164#121×C139—22no—
165#120×C139—41no—
166#117×C139C2311yescharacteristic
167#117×C139C2311yescharacteristic
168#117×C139C2311yescharacteristic
169#108×C139—22no—
170#108×C139—21no—
171#108×C139—21no—
172#107×C139—21no—
173#106×C139—21no—
174#104×C139—22no—
175#104×C139—22no—
176#104×C139—22no—
177#104×C139—22no—
178#104×C139—22no—
179#104×C139—22no—
180#103×C139—22no—
181#103×C139—41no—
182#102×C139—22no—
183#102×C139—41no—
184#101×C139—21no—
185#101×C139—21no—
186#101×C139—22no—
187#100×C139—21no—
188#100×C139—21no—
189#100×C139—22no—
190#99×C139—41no—
191#99×C139—41no—
192#97×C139—21no—
193C4×C8×C139—21no—
194C24×C139—21no—
195C24×C139—41no—
196#41×C139—21no—
197#41×C139—21no—
198#41×C139—24no—
199#41×C139—24no—
200#41×C139—21no—
201#41×C139—21no—
202#41×C139—21no—
203#41×C139—21no—
204#41×C139—21no—
205#41×C139—21no—
206#41×C139—21no—
207#41×C139—21no—
208#41×C139—21no—
209#41×C139—21no—
210#41×C139—21no—
211#41×C139—21no—
212#41×C139—42no—
213#41×C139—44no—
214#41×C139—42no—
215#41×C139—42no—
216#41×C139—42no—
217#41×C139—44no—
218#41×C139—42no—
219#41×C139—42no—
220#41×C139C2×D412yes—
221#41×C139C2×D412yes—
222C2×Q8×C139—21no—
223C2×Q8×C139—24no—
224C2×Q8×C139—21no—
225C2×Q8×C139—21no—
226C2×Q8×C139—21no—
227C2×Q8×C139—21no—
228C2×Q8×C139—41no—
229C2×Q8×C139—42no—
230C2×Q8×C139—42no—
231C2×Q8×C139—42no—
232C2×Q8×C139C2×D411yescharacteristic
233C2×Q8×C139C2×D411yescharacteristic
234C2×Q8×C139C2×D412yes—
235C2×Q8×C139C2×D411yescharacteristic
236C2×Q8×C139#4111yescharacteristic
237C2×D4×C139—21no—
238C2×D4×C139—24no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—21no—
243C2×D4×C139—21no—
244C2×D4×C139—21no—
245C2×D4×C139—21no—
246C2×D4×C139—21no—
247C2×D4×C139—42no—
248C2×D4×C139—41no—
249C2×D4×C139—41no—
250C2×D4×C139—42no—
251C2×D4×C139—44no—
252C2×D4×C139—44no—
253C2×D4×C139—41no—
254C2×D4×C139—42no—
255C2×D4×C139—42no—
256C2×D4×C139C2×D411yescharacteristic
257C2×D4×C139C2×D411yescharacteristic
258C2×D4×C139C2×D412yes—
259C2×D4×C139C2×D411yescharacteristic
260C2×D4×C139#4111yescharacteristic
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—21no—
265C22×C4×C139—21no—
266C22×C4×C139—41no—
267C22×C4×C139—41no—
268C22×C4×C139—41no—
269C22×C4×C139C2411yescharacteristic
270Q16×C139—24no—
271Q16×C139—22no—
272Q16×C139—21no—
273Q16×C139—21no—
274Q16×C139—41no—
275Q16×C139—41no—
276SD16×C139—24no—
277SD16×C139—24no—
278SD16×C139—22no—
279SD16×C139—22no—
280SD16×C139—22no—
281SD16×C139—22no—
282SD16×C139—21no—
283SD16×C139—21no—
284SD16×C139—22no—
285SD16×C139—22no—
286SD16×C139—21no—
287SD16×C139—21no—
288SD16×C139—41no—
289SD16×C139—41no—
290SD16×C139—41no—
291SD16×C139—41no—
292D8×C139—24no—
293D8×C139—22no—
294D8×C139—21no—
295D8×C139—21no—
296D8×C139—41no—
297D8×C139—41no—
298M16×C139—21no—
299M16×C139—21no—
300M16×C139—22no—
301M16×C139—22no—
302M16×C139—21no—
303M16×C139—21no—
304M16×C139—21no—
305M16×C139—21no—
306M16×C139—21no—
307M16×C139—21no—
308M16×C139—41no—
309M16×C139—41no—
310M16×C139C2×D412yes—
311M16×C139C2×D412yes—
312C2×C8×C139—21no—
313C2×C8×C139—21no—
314C2×C8×C139—22no—
315C2×C8×C139—22no—
316C2×C8×C139—21no—
317C2×C8×C139—21no—
318C2×C8×C139—21no—
319C2×C8×C139—41no—
320C2×C8×C139—41no—
321C2×C8×C139C2×D411yescharacteristic
322C2×C8×C139C2×D411yescharacteristic
323C2×C8×C139C2×D411yescharacteristic
324C2×C8×C139C2×D411yescharacteristic
325C2×C8×C139C2×D411yescharacteristic
326C2×C8×C139C2×D411yescharacteristic
327C4⋊C4×C139—21no—
328C4⋊C4×C139—21no—
329C4⋊C4×C139—21no—
330C4⋊C4×C139—42no—
331C22⋊C4×C139—21no—
332C22⋊C4×C139—21no—
333C22⋊C4×C139—21no—
334C22⋊C4×C139—42no—
335C22⋊C4×C139—42no—
336C42×C139—21no—
337C42×C139—21no—
338C42×C139—21no—
339C23×C139—21no—
340C23×C139—21no—
341C23×C139—22no—
342C23×C139—21no—
343C23×C139—21no—
344C23×C139—44no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—161no—
348C23×C139—162no—
349C23×C139H(5,𝔽2)11yescharacteristic
350Q8×C139—21no—
351Q8×C139—21no—
352Q8×C139—22no—
353Q8×C139—21no—
354Q8×C139—21no—
355Q8×C139—21no—
356Q8×C139—21no—
357Q8×C139—21no—
358Q8×C139—22no—
359Q8×C139—44no—
360Q8×C139—41no—
361Q8×C139—41no—
362Q8×C139#12112yes—
363D4×C139—22no—
364D4×C139—22no—
365D4×C139—21no—
366D4×C139—22no—
367D4×C139—21no—
368D4×C139—21no—
369D4×C139—21no—
370D4×C139—21no—
371D4×C139—21no—
372D4×C139—21no—
373D4×C139—22no—
374D4×C139—44no—
375D4×C139—44no—
376D4×C139—44no—
377D4×C139—41no—
378D4×C139—41no—
379D4×C139—41no—
380D4×C139—41no—
381D4×C139—41no—
382D4×C139—41no—
383D4×C139—41no—
384D4×C139—41no—
385D4×C139—162no—
386D4×C139#12112yes—
387C2×C4×C139—21no—
388C2×C4×C139—22no—
389C2×C4×C139—22no—
390C2×C4×C139—21no—
391C2×C4×C139—22no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—44no—
395C2×C4×C139—44no—
396C2×C4×C139—44no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139C22×D411yescharacteristic
409C2×C4×C139C22×D411yescharacteristic
410C2×C4×C139C22×D411yescharacteristic
411C2×C4×C139C22×D411yescharacteristic
412C2×C4×C139C2×#4111yescharacteristic
413C2×C4×C139H(5,𝔽2)11yescharacteristic
414C8×C139—22no—
415C8×C139—22no—
416C8×C139—41no—
417C8×C139—41no—
418C8×C139—41no—
419C8×C139#12011yescharacteristic
420C8×C139#12011yescharacteristic
421C8×C139#12011yescharacteristic
422C8×C139#12011yescharacteristic
423C22×C139—22no—
424C22×C139—41no—
425C22×C139—42no—
426C22×C139—42no—
427C22×C139—41no—
428C22×C139—42no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—82no—
432C22×C139—81no—
433C22×C139—81no—
434C22×C139—82no—
435C22×C139—161no—
436C22×C139—164no—
437C22×C139#53511yescharacteristic
438C22×C139D4211yescharacteristic
439C22×C139#54611yescharacteristic
440C4×C139—22no—
441C4×C139—41no—
442C4×C139—42no—
443C4×C139—41no—
444C4×C139—41no—
445C4×C139—81no—
446C4×C139—81no—
447C4×C139—81no—
448C4×C139C2×#12011yescharacteristic
449C4×C139C2×#12111yescharacteristic
450C4×C139D4211yescharacteristic
451C4×C139#54611yescharacteristic
452C2×C139—21no—
453C2×C139—21no—
454C2×C139—21no—
455C2×C139—42no—
456C2×C139—81no—
457C2×C139—81no—
458C2×C139—82no—
459C2×C139—81no—
460C2×C139#240811yescharacteristic
461#24295C13911yesmaximal, characteristic, direct product factor, Sylow
462C139#2429511yescharacteristic, direct product factor, Sylow
463C2×#577C2×C13911yescharacteristic, complemented
464#3067C2×C13911yescharacteristic, complemented
465#3057C2×C13911yescharacteristic, complemented
466#3020C2×C13911yescharacteristic, complemented
467#3019C2×C13911yescharacteristic, complemented
468#2955C2×C13911yescharacteristic, complemented
469#2049C2×C13911yescharacteristic, complemented
470#2048C2×C13911yescharacteristic, complemented
471#2009C2×C13911yescharacteristic, complemented
472#2008C2×C13911yescharacteristic, complemented
473#1977C2×C13911yescharacteristic, complemented
474#1976C2×C13911yescharacteristic, complemented
475#1814C2×C13911yescharacteristic, complemented
476#1796C2×C13911yescharacteristic, complemented
477#1795C2×C13911yescharacteristic, complemented
478C2×2−1+4C22×C13911yescharacteristic
479C2×H(5,𝔽2)C22×C13911yescharacteristic
480#577—22no—
481#577—22no—
482#577—22no—
483#577—22no—
484#575C22×C13911yescharacteristic
485#575C22×C13911yescharacteristic
486#575C22×C13911yescharacteristic, complemented
487C2×#137—21no—
488C2×#137C22×C13911yescharacteristic
489C2×AGL(1,ℤ/8)—21no—
490C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
491C2×#135—21no—
492C2×#135C22×C13911yescharacteristic
493C22×SD16—21no—
494C22×SD16C22×C13911yescharacteristic
495C2×#131C22×C13911yescharacteristic
496C2×#131C22×C13911yescharacteristic, complemented
497#536C22×C13911yescharacteristic, complemented
498#535C22×C13911yescharacteristic
499#473—21no—
500#472—21no—
501#471—21no—
502#471—21no—
503#468—22no—
504#465—22no—
505#456—22no—
506#455—22no—
507#454—22no—
508#453—22no—
509#444—22no—
510#443—22no—
511#430C22×C13911yescharacteristic, complemented
512C2×#108C22×C13911yescharacteristic, complemented
513#427C22×C13911yescharacteristic, complemented
514#421C22×C13911yescharacteristic
515#421C22×C13911yescharacteristic
516#421C22×C13911yescharacteristic
517#421C22×C13911yescharacteristic
518#421C22×C13911yescharacteristic, complemented
519#421C22×C13911yescharacteristic, complemented
520#419C22×C13911yescharacteristic, complemented
521#419C22×C13911yescharacteristic, complemented
522#418C22×C13911yescharacteristic
523#418C22×C13911yescharacteristic
524#413C22×C13911yescharacteristic
525#413C22×C13911yescharacteristic, complemented
526C2×#101C22×C13911yescharacteristic, complemented
527C2×#100C22×C13911yescharacteristic
528#410C22×C13911yescharacteristic
529#410C22×C13911yescharacteristic, complemented
530#405C22×C13911yescharacteristic, complemented
531#344C22×C13911yescharacteristic, complemented
532#344C22×C13911yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C13911yescharacteristic
547C2×#41C23×C13911yescharacteristic
548C2×#41C23×C13911yescharacteristic
549C2×#41C23×C13911yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C13911yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C13911yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C13912yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C13912yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C13911yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C13912yes—
597C2×SD16D4×C13912yes—
598C2×SD16D4×C13911yescharacteristic, complemented
599C2×SD16D4×C13911yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C13911yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C13912yescomplemented
609#131D4×C13912yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C13911yescharacteristic
613C2×M16C23×C13911yescharacteristic
614C2×M16C23×C13911yescharacteristic
615C2×M16C23×C13911yescharacteristic
616C2×M16C23×C13911yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C13911yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C13911yescharacteristic
629#117C23×C13911yescharacteristic
630#117C23×C13911yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C13912yes—
683#41C2×D4×C13912yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C13911yescharacteristic
695C2×Q8C2×D4×C13911yescharacteristic
696C2×Q8C2×D4×C13912yes—
697C2×Q8C2×D4×C13911yescharacteristic
698C2×Q8#41×C13911yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C13911yescharacteristic
719C2×D4C2×D4×C13911yescharacteristic
720C2×D4C2×D4×C13912yes—
721C2×D4C2×D4×C13911yescharacteristic
722C2×D4#41×C13911yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C13911yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C13912yes—
773M16C2×D4×C13912yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C13911yescharacteristic
784C2×C8C2×D4×C13911yescharacteristic
785C2×C8C2×D4×C13911yescharacteristic
786C2×C8C2×D4×C13911yescharacteristic
787C2×C8C2×D4×C13911yescharacteristic
788C2×C8C2×D4×C13911yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C13911yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C13912yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C13912yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C13911yescharacteristic
871C2×C4C22×D4×C13911yescharacteristic
872C2×C4C22×D4×C13911yescharacteristic
873C2×C4C22×D4×C13911yescharacteristic
874C2×C4C2×#41×C13911yescharacteristic
875C2×C4H(5,𝔽2)×C13911yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C13911yescharacteristic
882C8#120×C13911yescharacteristic
883C8#120×C13911yescharacteristic
884C8#120×C13911yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22#535×C13911yescharacteristic
900C22D42×C13911yescharacteristic
901C22#546×C13911yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C13911yescharacteristic
911C4C2×#121×C13911yescharacteristic
912C4D42×C13911yescharacteristic
913C4#546×C13911yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2#2408×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2408
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. C2×#577×C139C2semidirect
2. #3067×C139C2semidirect
3. #3057×C139C2semidirect
4. #3020×C139C2semidirect
5. #3019×C139C2semidirect
6. #2955×C139C2semidirect
7. #2049×C139C2semidirect
8. #2048×C139C2semidirect
9. #2009×C139C2semidirect
10. #2008×C139C2semidirect
11. #1977×C139C2semidirect
12. #1976×C139C2semidirect
13. #1814×C139C2semidirect
14. #1796×C139C2semidirect
15. #1795×C139C2semidirect
24. #575×C139C22semidirect
34. C2×#131×C139C22semidirect
35. #536×C139C22semidirect
49. #430×C139C22semidirect
50. C2×#108×C139C22semidirect
51. #427×C139C22semidirect
56. #421×C139C22semidirect
57. #421×C139C22semidirect
58. #419×C139C22semidirect
59. #419×C139C22semidirect
63. #413×C139C22semidirect
64. C2×#101×C139C22semidirect
67. #410×C139C22semidirect
68. #405×C139C22semidirect
69. #344×C139C22semidirect
70. #344×C139C22semidirect
125. C2×Q16×C139D4semidirect
136. C2×SD16×C139D4semidirect
137. C2×SD16×C139D4semidirect
139. C2×D8×C139D4semidirect
146. #131×C139D4semidirect
147. #131×C139D4semidirect
461. #24295C139direct (N × H)
462. C139#24295direct (N × H)
463. C2×#577C2×C139semidirect
464. #3067C2×C139semidirect
465. #3057C2×C139semidirect
466. #3020C2×C139semidirect
467. #3019C2×C139semidirect
468. #2955C2×C139semidirect
469. #2049C2×C139semidirect
470. #2048C2×C139semidirect
471. #2009C2×C139semidirect
472. #2008C2×C139semidirect
473. #1977C2×C139semidirect
474. #1976C2×C139semidirect
475. #1814C2×C139semidirect
476. #1796C2×C139semidirect
477. #1795C2×C139semidirect
486. #575C22×C139semidirect
496. C2×#131C22×C139semidirect
497. #536C22×C139semidirect
511. #430C22×C139semidirect
512. C2×#108C22×C139semidirect
513. #427C22×C139semidirect
518. #421C22×C139semidirect
519. #421C22×C139semidirect
520. #419C22×C139semidirect
521. #419C22×C139semidirect
525. #413C22×C139semidirect
526. C2×#101C22×C139semidirect
529. #410C22×C139semidirect
530. #405C22×C139semidirect
531. #344C22×C139semidirect
532. #344C22×C139semidirect
587. C2×Q16D4×C139semidirect
598. C2×SD16D4×C139semidirect
599. C2×SD16D4×C139semidirect
601. C2×D8D4×C139semidirect
608. #131D4×C139semidirect
609. #131D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1392
#3067×C1392
#3057×C1392
#3020×C1392
#3019×C1392
#2955×C1392
#2049×C1392
#2048×C1392
#2009×C1392
#2008×C1392
#1977×C1392
#1976×C1392
#1814×C1392
#1796×C1392
#1795×C1392
#24295139