Finite Group Databasebeta

← C139×#24457 #48019053

Subgroups — C139×#24457 #48019053

Order 35584.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C139C211yesmaximal, characteristic, complemented
2C2×#471×C139C211yesmaximal, characteristic, complemented
3#3045×C139C211yesmaximal, characteristic, complemented
4C2×#453×C139C211yesmaximal, characteristic, complemented
5#3010×C139C211yesmaximal, characteristic, complemented
6#2897×C139C211yesmaximal, characteristic, complemented
7#2051×C139C211yesmaximal, characteristic, complemented
8#2046×C139C211yesmaximal, characteristic, complemented
9#2014×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1907×C139C211yesmaximal, characteristic, complemented
12#1882×C139C211yesmaximal, characteristic, complemented
13#1876×C139C211yesmaximal, characteristic, complemented
14#1866×C139C211yesmaximal, characteristic, complemented
15#1793×C139C211yesmaximal, characteristic, complemented
16C2×2−1+4×C139C2211yescharacteristic
17C2×H(5,𝔽2)×C139C2211yescharacteristic
18#577×C139—24no—
19#577×C139—24no—
20C2×#137×C139—21no—
21C2×#137×C139C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C139—21no—
23C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
26C2×#135×C139—21no—
27C2×#135×C139C2211yescharacteristic
28C22×SD16×C139—21no—
29C22×SD16×C139C2211yescharacteristic
30C22×SD16×C139C2211yescharacteristic, complemented
31C2×#131×C139C2211yescharacteristic
32C2×#131×C139C2211yescharacteristic
33#535×C139C2211yescharacteristic, complemented
34C2×#127×C139C2211yescharacteristic
35#520×C139C2211yescharacteristic
36#471×C139—24no—
37#464×C139—21no—
38#463×C139—21no—
39#460×C139—21no—
40#459×C139—21no—
41#453×C139—24no—
42#449×C139—21no—
43#449×C139—21no—
44#448×C139—21no—
45#448×C139—21no—
46C2×#108×C139C2211yescharacteristic, complemented
47#424×C139C2211yescharacteristic, complemented
48C2×#104×C139C2211yescharacteristic
49C2×#104×C139C2211yescharacteristic
50C2×#104×C139C2211yescharacteristic, complemented
51#419×C139C2211yescharacteristic, complemented
52#418×C139—21no—
53#418×C139C2211yescharacteristic
54#417×C139—21no—
55#417×C139C2211yescharacteristic
56#417×C139C2211yescharacteristic, complemented
57#416×C139—21no—
58#416×C139C2211yescharacteristic
59C2×#102×C139—21no—
60C2×#102×C139C2211yescharacteristic
61C2×#102×C139C2211yescharacteristic, complemented
62C2×#101×C139C2211yescharacteristic, complemented
63C2×#100×C139C2211yescharacteristic
64C2×#100×C139C2211yescharacteristic, complemented
65#408×C139C2211yescharacteristic, complemented
66#391×C139C2211yescharacteristic, complemented
67#343×C139C2211yescharacteristic, complemented
68#341×C139C2211yescharacteristic, complemented
69#339×C139C2211yescharacteristic, complemented
70#336×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—41no—
78H(5,𝔽2)×C139D414yescomplemented
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
87C22×Q8×C139—21no—
88C22×Q8×C139—21no—
89C22×Q8×C139C2311yescharacteristic
90C22×D4×C139—21no—
91C22×D4×C139—21no—
92C22×D4×C139—41no—
93C22×D4×C139—41no—
94C22×D4×C139C2311yescharacteristic
95C22×D4×C139C2311yescharacteristic
96#137×C139—28no—
97#137×C139—22no—
98#137×C139D414yescomplemented
99AGL(1,ℤ/8)×C139—28no—
100AGL(1,ℤ/8)×C139—22no—
101AGL(1,ℤ/8)×C139—22no—
102AGL(1,ℤ/8)×C139—22no—
103AGL(1,ℤ/8)×C139—22no—
104AGL(1,ℤ/8)×C139—22no—
105AGL(1,ℤ/8)×C139—22no—
106#135×C139—28no—
107#135×C139—22no—
108#135×C139—22no—
109C2×Q16×C139—21no—
110C2×Q16×C139D411yescharacteristic, complemented
111C2×SD16×C139—28no—
112C2×SD16×C139—21no—
113C2×SD16×C139—22no—
114C2×SD16×C139—21no—
115C2×SD16×C139—22no—
116C2×SD16×C139—21no—
117C2×SD16×C139—21no—
118C2×SD16×C139—22no—
119C2×SD16×C139—21no—
120C2×SD16×C139—21no—
121C2×SD16×C139—21no—
122C2×SD16×C139—21no—
123C2×SD16×C139—41no—
124C2×SD16×C139D411yescharacteristic, complemented
125C2×SD16×C139D411yescharacteristic, complemented
126C2×D8×C139—21no—
127C2×D8×C139—21no—
128C2×D8×C139—21no—
129C2×D8×C139D411yescharacteristic, complemented
130#131×C139—22no—
131#131×C139—22no—
132#131×C139—22no—
133#131×C139—41no—
134C2×M16×C139—21no—
135C2×M16×C139—21no—
136C2×M16×C139C2311yescharacteristic
137C2×M16×C139C2311yescharacteristic
138C2×M16×C139C2311yescharacteristic
139C2×M16×C139C2311yescharacteristic
140C22×C8×C139—21no—
141C22×C8×C139—21no—
142C22×C8×C139C2311yescharacteristic
143C22×C8×C139C2311yescharacteristic
144#127×C139—22no—
145#127×C139—21no—
146#127×C139—41no—
147#124×C139—21no—
148#121×C139—21no—
149#121×C139—21no—
150#120×C139—41no—
151C4×Q8×C139—21no—
152C4×D4×C139—21no—
153C4×D4×C139—41no—
154#117×C139—21no—
155#117×C139C2311yescharacteristic
156C2×C4⋊C4×C139—21no—
157C2×C4⋊C4×C139C2311yescharacteristic
158C2×C42×C139C2311yescharacteristic
159#108×C139—22no—
160C4⋊C8×C139—21no—
161C4⋊C8×C139—21no—
162#104×C139—22no—
163#104×C139—22no—
164#104×C139—41no—
165#103×C139—21no—
166#103×C139—21no—
167#103×C139—21no—
168#103×C139—21no—
169#103×C139D411yescharacteristic, complemented
170#103×C139D411yescharacteristic, complemented
171#102×C139—21no—
172#102×C139—21no—
173#102×C139—21no—
174#102×C139—21no—
175#102×C139—21no—
176#102×C139—21no—
177#102×C139—21no—
178#102×C139—21no—
179#102×C139D411yescharacteristic, complemented
180#102×C139D411yescharacteristic, complemented
181#101×C139—22no—
182#100×C139—22no—
183#100×C139—22no—
184C22⋊C8×C139—21no—
185C22⋊C8×C139—21no—
186#95×C139—41no—
187C24×C139—21no—
188C24×C139—21no—
189C24×C139—41no—
190#41×C139—21no—
191#41×C139—21no—
192#41×C139—21no—
193#41×C139—21no—
194#41×C139—24no—
195#41×C139—24no—
196#41×C139—24no—
197#41×C139—21no—
198#41×C139—21no—
199#41×C139—21no—
200#41×C139—21no—
201#41×C139—42no—
202#41×C139—44no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—42no—
206#41×C139—44no—
207#41×C139—42no—
208#41×C139C2×D412yes—
209#41×C139C2×D412yes—
210#41×C139C2×D412yes—
211#41×C139#4112yes—
212C2×Q8×C139—21no—
213C2×Q8×C139—24no—
214C2×Q8×C139—21no—
215C2×Q8×C139—21no—
216C2×Q8×C139—21no—
217C2×Q8×C139—21no—
218C2×Q8×C139—41no—
219C2×Q8×C139—42no—
220C2×Q8×C139—42no—
221C2×Q8×C139—42no—
222C2×Q8×C139C2×D412yes—
223C2×Q8×C139C2×D411yescharacteristic
224C2×Q8×C139C2×D411yescharacteristic
225C2×Q8×C139C2×D411yescharacteristic
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—24no—
229C2×D4×C139—24no—
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—21no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—21no—
242C2×D4×C139—42no—
243C2×D4×C139—42no—
244C2×D4×C139—41no—
245C2×D4×C139—41no—
246C2×D4×C139—41no—
247C2×D4×C139—41no—
248C2×D4×C139—44no—
249C2×D4×C139—44no—
250C2×D4×C139—41no—
251C2×D4×C139—44no—
252C2×D4×C139—82no—
253C2×D4×C139—82no—
254C2×D4×C139C2×D412yes—
255C2×D4×C139C2×D411yescharacteristic
256C2×D4×C139C2×D411yescharacteristic
257C2×D4×C139C2×D411yescharacteristic
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—41no—
265C22×C4×C139—41no—
266C22×C4×C139—41no—
267C22×C4×C139—41no—
268C22×C4×C139C2411yescharacteristic
269Q16×C139—24no—
270Q16×C139—22no—
271SD16×C139—24no—
272SD16×C139—24no—
273SD16×C139—24no—
274SD16×C139—22no—
275SD16×C139—22no—
276SD16×C139—24no—
277SD16×C139—42no—
278SD16×C139—42no—
279SD16×C139—42no—
280SD16×C139—42no—
281D8×C139—24no—
282D8×C139—22no—
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—42no—
294M16×C139C2×D412yes—
295C2×C8×C139—24no—
296C2×C8×C139—21no—
297C2×C8×C139—21no—
298C2×C8×C139—21no—
299C2×C8×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139—21no—
302C2×C8×C139—21no—
303C2×C8×C139—21no—
304C2×C8×C139—42no—
305C2×C8×C139C2×D411yescharacteristic
306C2×C8×C139C2×D411yescharacteristic
307C2×C8×C139C2×D411yescharacteristic
308C2×C8×C139C2×D411yescharacteristic
309C4⋊C4×C139—21no—
310C4⋊C4×C139—21no—
311C4⋊C4×C139—41no—
312C4⋊C4×C139C2×D411yescharacteristic
313C4⋊C4×C139C2×D411yescharacteristic
314C22⋊C4×C139—21no—
315C22⋊C4×C139—41no—
316C22⋊C4×C139—41no—
317C22⋊C4×C139—41no—
318C42×C139—21no—
319C42×C139—21no—
320C42×C139—21no—
321C42×C139—41no—
322C23×C139—21no—
323C23×C139—21no—
324C23×C139—21no—
325C23×C139—22no—
326C23×C139—44no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—81no—
333C23×C139—81no—
334C23×C139—81no—
335C23×C139—81no—
336C23×C139—161no—
337C23×C139—161no—
338C23×C139H(5,𝔽2)11yescharacteristic
339Q8×C139—21no—
340Q8×C139—21no—
341Q8×C139—22no—
342Q8×C139—21no—
343Q8×C139—22no—
344Q8×C139—21no—
345Q8×C139—44no—
346Q8×C139—41no—
347Q8×C139—41no—
348Q8×C139#12012yes—
349Q8×C139#12112yes—
350D4×C139—22no—
351D4×C139—22no—
352D4×C139—22no—
353D4×C139—22no—
354D4×C139—21no—
355D4×C139—22no—
356D4×C139—22no—
357D4×C139—21no—
358D4×C139—21no—
359D4×C139—21no—
360D4×C139—44no—
361D4×C139—44no—
362D4×C139—44no—
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—88no—
372D4×C139—161no—
373D4×C139—161no—
374D4×C139#12012yes—
375D4×C139#12112yes—
376C2×C4×C139—21no—
377C2×C4×C139—21no—
378C2×C4×C139—22no—
379C2×C4×C139—22no—
380C2×C4×C139—22no—
381C2×C4×C139—22no—
382C2×C4×C139—22no—
383C2×C4×C139—21no—
384C2×C4×C139—21no—
385C2×C4×C139—21no—
386C2×C4×C139—22no—
387C2×C4×C139—44no—
388C2×C4×C139—44no—
389C2×C4×C139—41no—
390C2×C4×C139—44no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—41no—
396C2×C4×C139—41no—
397C2×C4×C139—81no—
398C2×C4×C139—161no—
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—21no—
406C8×C139—22no—
407C8×C139—21no—
408C8×C139—21no—
409C8×C139—21no—
410C8×C139—41no—
411C8×C139—41no—
412C8×C139—41no—
413C22×C139—21no—
414C22×C139—21no—
415C22×C139—22no—
416C22×C139—22no—
417C22×C139—41no—
418C22×C139—41no—
419C22×C139—41no—
420C22×C139—41no—
421C22×C139—41no—
422C22×C139—42no—
423C22×C139—41no—
424C22×C139—41no—
425C22×C139—82no—
426C22×C139—82no—
427C22×C139—81no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139—81no—
431C22×C139—81no—
432C22×C139—161no—
433C22×C139—161no—
434C22×C139—164no—
435C22×C139#53411yescharacteristic
436C22×C139D4211yescharacteristic
437C22×C139#54611yescharacteristic
438C4×C139—22no—
439C4×C139—22no—
440C4×C139—42no—
441C4×C139—41no—
442C4×C139—42no—
443C4×C139—41no—
444C4×C139—41no—
445C4×C139—81no—
446C4×C139C2×#12011yescharacteristic
447C4×C139C2×#12111yescharacteristic
448C4×C139D4211yescharacteristic
449C4×C139#54611yescharacteristic
450C2×C139—21no—
451C2×C139—21no—
452C2×C139—42no—
453C2×C139—42no—
454C2×C139—81no—
455C2×C139—82no—
456C2×C139—161no—
457C2×C139#241011yescharacteristic
458C2×C139#328811yescharacteristic
459C2×C139#329111yescharacteristic
460#24457C13911yesmaximal, characteristic, direct product factor, Sylow
461C139#2445711yescharacteristic, direct product factor, Sylow
462C2×#577C2×C13911yescharacteristic, complemented
463C2×#471C2×C13911yescharacteristic, complemented
464#3045C2×C13911yescharacteristic, complemented
465C2×#453C2×C13911yescharacteristic, complemented
466#3010C2×C13911yescharacteristic, complemented
467#2897C2×C13911yescharacteristic, complemented
468#2051C2×C13911yescharacteristic, complemented
469#2046C2×C13911yescharacteristic, complemented
470#2014C2×C13911yescharacteristic, complemented
471#2002C2×C13911yescharacteristic, complemented
472#1907C2×C13911yescharacteristic, complemented
473#1882C2×C13911yescharacteristic, complemented
474#1876C2×C13911yescharacteristic, complemented
475#1866C2×C13911yescharacteristic, complemented
476#1793C2×C13911yescharacteristic, complemented
477C2×2−1+4C22×C13911yescharacteristic
478C2×H(5,𝔽2)C22×C13911yescharacteristic
479#577—24no—
480#577—24no—
481C2×#137—21no—
482C2×#137C22×C13911yescharacteristic
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
485C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
486C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
487C2×#135—21no—
488C2×#135C22×C13911yescharacteristic
489C22×SD16—21no—
490C22×SD16C22×C13911yescharacteristic
491C22×SD16C22×C13911yescharacteristic, complemented
492C2×#131C22×C13911yescharacteristic
493C2×#131C22×C13911yescharacteristic
494#535C22×C13911yescharacteristic, complemented
495C2×#127C22×C13911yescharacteristic
496#520C22×C13911yescharacteristic
497#471—24no—
498#464—21no—
499#463—21no—
500#460—21no—
501#459—21no—
502#453—24no—
503#449—21no—
504#449—21no—
505#448—21no—
506#448—21no—
507C2×#108C22×C13911yescharacteristic, complemented
508#424C22×C13911yescharacteristic, complemented
509C2×#104C22×C13911yescharacteristic
510C2×#104C22×C13911yescharacteristic
511C2×#104C22×C13911yescharacteristic, complemented
512#419C22×C13911yescharacteristic, complemented
513#418—21no—
514#418C22×C13911yescharacteristic
515#417—21no—
516#417C22×C13911yescharacteristic
517#417C22×C13911yescharacteristic, complemented
518#416—21no—
519#416C22×C13911yescharacteristic
520C2×#102—21no—
521C2×#102C22×C13911yescharacteristic
522C2×#102C22×C13911yescharacteristic, complemented
523C2×#101C22×C13911yescharacteristic, complemented
524C2×#100C22×C13911yescharacteristic
525C2×#100C22×C13911yescharacteristic, complemented
526#408C22×C13911yescharacteristic, complemented
527#391C22×C13911yescharacteristic, complemented
528#343C22×C13911yescharacteristic, complemented
529#341C22×C13911yescharacteristic, complemented
530#339C22×C13911yescharacteristic, complemented
531#336C22×C13911yescharacteristic, complemented
5322−1+4—22no—
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—41no—
539H(5,𝔽2)D4×C13914yescomplemented
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—41no—
545C2×#41C23×C13911yescharacteristic
546C2×#41C23×C13911yescharacteristic
547C2×#41C23×C13911yescharacteristic
548C22×Q8—21no—
549C22×Q8—21no—
550C22×Q8C23×C13911yescharacteristic
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4—41no—
555C22×D4C23×C13911yescharacteristic
556C22×D4C23×C13911yescharacteristic
557#137—28no—
558#137—22no—
559#137D4×C13914yescomplemented
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567#135—28no—
568#135—22no—
569#135—22no—
570C2×Q16—21no—
571C2×Q16D4×C13911yescharacteristic, complemented
572C2×SD16—28no—
573C2×SD16—21no—
574C2×SD16—22no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×SD16—21no—
581C2×SD16—21no—
582C2×SD16—21no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C13911yescharacteristic, complemented
586C2×SD16D4×C13911yescharacteristic, complemented
587C2×D8—21no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8D4×C13911yescharacteristic, complemented
591#131—22no—
592#131—22no—
593#131—22no—
594#131—41no—
595C2×M16—21no—
596C2×M16—21no—
597C2×M16C23×C13911yescharacteristic
598C2×M16C23×C13911yescharacteristic
599C2×M16C23×C13911yescharacteristic
600C2×M16C23×C13911yescharacteristic
601C22×C8—21no—
602C22×C8—21no—
603C22×C8C23×C13911yescharacteristic
604C22×C8C23×C13911yescharacteristic
605#127—22no—
606#127—21no—
607#127—41no—
608#124—21no—
609#121—21no—
610#121—21no—
611#120—41no—
612C4×Q8—21no—
613C4×D4—21no—
614C4×D4—41no—
615#117—21no—
616#117C23×C13911yescharacteristic
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C13911yescharacteristic
619C2×C42C23×C13911yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C13911yescharacteristic, complemented
631#103D4×C13911yescharacteristic, complemented
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C13911yescharacteristic, complemented
641#102D4×C13911yescharacteristic, complemented
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647#95—41no—
648C24—21no—
649C24—21no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—44no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41—44no—
668#41—42no—
669#41C2×D4×C13912yes—
670#41C2×D4×C13912yes—
671#41C2×D4×C13912yes—
672#41#41×C13912yes—
673C2×Q8—21no—
674C2×Q8—24no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—41no—
680C2×Q8—42no—
681C2×Q8—42no—
682C2×Q8—42no—
683C2×Q8C2×D4×C13912yes—
684C2×Q8C2×D4×C13911yescharacteristic
685C2×Q8C2×D4×C13911yescharacteristic
686C2×Q8C2×D4×C13911yescharacteristic
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—24no—
690C2×D4—24no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—41no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—41no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—41no—
712C2×D4—44no—
713C2×D4—82no—
714C2×D4—82no—
715C2×D4C2×D4×C13912yes—
716C2×D4C2×D4×C13911yescharacteristic
717C2×D4C2×D4×C13911yescharacteristic
718C2×D4C2×D4×C13911yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—41no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—41no—
729C22×C4C24×C13911yescharacteristic
730Q16—24no—
731Q16—22no—
732SD16—24no—
733SD16—24no—
734SD16—24no—
735SD16—22no—
736SD16—22no—
737SD16—24no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741SD16—42no—
742D8—24no—
743D8—22no—
744D8—42no—
745D8—42no—
746M16—24no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16—21no—
754M16—42no—
755M16C2×D4×C13912yes—
756C2×C8—24no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—42no—
766C2×C8C2×D4×C13911yescharacteristic
767C2×C8C2×D4×C13911yescharacteristic
768C2×C8C2×D4×C13911yescharacteristic
769C2×C8C2×D4×C13911yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—41no—
773C4⋊C4C2×D4×C13911yescharacteristic
774C4⋊C4C2×D4×C13911yescharacteristic
775C22⋊C4—21no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—41no—
779C42—21no—
780C42—21no—
781C42—21no—
782C42—41no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—81no—
797C23—161no—
798C23—161no—
799C23H(5,𝔽2)×C13911yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—22no—
803Q8—21no—
804Q8—22no—
805Q8—21no—
806Q8—44no—
807Q8—41no—
808Q8—41no—
809Q8#120×C13912yes—
810Q8#121×C13912yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—22no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—88no—
833D4—161no—
834D4—161no—
835D4#120×C13912yes—
836D4#121×C13912yes—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—81no—
859C2×C4—161no—
860C2×C4C22×D4×C13911yescharacteristic
861C2×C4C22×D4×C13911yescharacteristic
862C2×C4C22×D4×C13911yescharacteristic
863C2×C4C22×D4×C13911yescharacteristic
864C2×C4C2×#41×C13911yescharacteristic
865C2×C4H(5,𝔽2)×C13911yescharacteristic
866C8—21no—
867C8—22no—
868C8—21no—
869C8—21no—
870C8—21no—
871C8—41no—
872C8—41no—
873C8—41no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—82no—
887C22—82no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—161no—
894C22—161no—
895C22—164no—
896C22#534×C13911yescharacteristic
897C22D42×C13911yescharacteristic
898C22#546×C13911yescharacteristic
899C4—22no—
900C4—22no—
901C4—42no—
902C4—41no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—81no—
907C4C2×#120×C13911yescharacteristic
908C4C2×#121×C13911yescharacteristic
909C4D42×C13911yescharacteristic
910C4#546×C13911yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2—42no—
915C2—81no—
916C2—82no—
917C2—161no—
918C2#2410×C13911yescharacteristic
919C2#3288×C13911yescharacteristic
920C2#3291×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C139C2semidirect
2. C2×#471×C139C2semidirect
3. #3045×C139C2semidirect
4. C2×#453×C139C2semidirect
5. #3010×C139C2semidirect
6. #2897×C139C2semidirect
7. #2051×C139C2semidirect
8. #2046×C139C2semidirect
9. #2014×C139C2semidirect
10. #2002×C139C2semidirect
11. #1907×C139C2semidirect
12. #1882×C139C2semidirect
13. #1876×C139C2semidirect
14. #1866×C139C2semidirect
15. #1793×C139C2semidirect
30. C22×SD16×C139C22semidirect
33. #535×C139C22semidirect
46. C2×#108×C139C22semidirect
47. #424×C139C22semidirect
50. C2×#104×C139C22semidirect
51. #419×C139C22semidirect
56. #417×C139C22semidirect
61. C2×#102×C139C22semidirect
62. C2×#101×C139C22semidirect
64. C2×#100×C139C22semidirect
65. #408×C139C22semidirect
66. #391×C139C22semidirect
67. #343×C139C22semidirect
68. #341×C139C22semidirect
69. #339×C139C22semidirect
70. #336×C139C22semidirect
78. H(5,𝔽2)×C139D4semidirect
98. #137×C139D4semidirect
110. C2×Q16×C139D4semidirect
124. C2×SD16×C139D4semidirect
125. C2×SD16×C139D4semidirect
129. C2×D8×C139D4semidirect
169. #103×C139D4semidirect
170. #103×C139D4semidirect
179. #102×C139D4semidirect
180. #102×C139D4semidirect
460. #24457C139direct (N × H)
461. C139#24457direct (N × H)
462. C2×#577C2×C139semidirect
463. C2×#471C2×C139semidirect
464. #3045C2×C139semidirect
465. C2×#453C2×C139semidirect
466. #3010C2×C139semidirect
467. #2897C2×C139semidirect
468. #2051C2×C139semidirect
469. #2046C2×C139semidirect
470. #2014C2×C139semidirect
471. #2002C2×C139semidirect
472. #1907C2×C139semidirect
473. #1882C2×C139semidirect
474. #1876C2×C139semidirect
475. #1866C2×C139semidirect
476. #1793C2×C139semidirect
491. C22×SD16C22×C139semidirect
494. #535C22×C139semidirect
507. C2×#108C22×C139semidirect
508. #424C22×C139semidirect
511. C2×#104C22×C139semidirect
512. #419C22×C139semidirect
517. #417C22×C139semidirect
522. C2×#102C22×C139semidirect
523. C2×#101C22×C139semidirect
525. C2×#100C22×C139semidirect
526. #408C22×C139semidirect
527. #391C22×C139semidirect
528. #343C22×C139semidirect
529. #341C22×C139semidirect
530. #339C22×C139semidirect
531. #336C22×C139semidirect
539. H(5,𝔽2)D4×C139semidirect
559. #137D4×C139semidirect
571. C2×Q16D4×C139semidirect
585. C2×SD16D4×C139semidirect
586. C2×SD16D4×C139semidirect
590. C2×D8D4×C139semidirect
630. #103D4×C139semidirect
631. #103D4×C139semidirect
640. #102D4×C139semidirect
641. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1392
C2×#471×C1392
#3045×C1392
C2×#453×C1392
#3010×C1392
#2897×C1392
#2051×C1392
#2046×C1392
#2014×C1392
#2002×C1392
#1907×C1392
#1882×C1392
#1876×C1392
#1866×C1392
#1793×C1392
#24457139