Finite Group Databasebeta

← C139×#24460 #48019056

Subgroups — C139×#24460 #48019056

Order 35584.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C139C211yesmaximal, characteristic, complemented
2C2×#472×C139C211yesmaximal, characteristic, complemented
3#3045×C139C211yesmaximal, characteristic, complemented
4C2×#454×C139C211yesmaximal, characteristic, complemented
5#3008×C139C211yesmaximal, characteristic, complemented
6#2898×C139C211yesmaximal, characteristic, complemented
7#2052×C139C211yesmaximal, characteristic, complemented
8#2046×C139C211yesmaximal, characteristic, complemented
9#2012×C139C211yesmaximal, characteristic, complemented
10#2004×C139C211yesmaximal, characteristic, complemented
11#1907×C139C211yesmaximal, characteristic, complemented
12#1883×C139C211yesmaximal, characteristic, complemented
13#1876×C139C211yesmaximal, characteristic, complemented
14#1866×C139C211yesmaximal, characteristic, complemented
15#1792×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, complemented
26C2×#135×C139—21no—
27C2×#135×C139C2211yescharacteristic
28C22×SD16×C139—21no—
29C22×SD16×C139C2211yescharacteristic
30C22×D8×C139C2211yescharacteristic
31C2×#131×C139C2211yescharacteristic
32C2×#131×C139C2211yescharacteristic, complemented
33#535×C139C2211yescharacteristic
34C2×#124×C139C2211yescharacteristic, complemented
35#520×C139C2211yescharacteristic, complemented
36#472×C139—24no—
37#464×C139—21no—
38#463×C139—21no—
39#460×C139—21no—
40#459×C139—21no—
41#454×C139—24no—
42#449×C139—21no—
43#449×C139—21no—
44#447×C139—21no—
45#447×C139—21no—
46C2×#108×C139C2211yescharacteristic, complemented
47#424×C139C2211yescharacteristic, complemented
48C2×#104×C139C2211yescharacteristic
49C2×#104×C139C2211yescharacteristic
50C2×#104×C139C2211yescharacteristic, complemented
51#419×C139—21no—
52#419×C139C2211yescharacteristic, complemented
53#418×C139C2211yescharacteristic
54#417×C139—21no—
55#417×C139C2211yescharacteristic
56#417×C139C2211yescharacteristic
57#416×C139—21no—
58#416×C139C2211yescharacteristic
59C2×#103×C139—21no—
60C2×#103×C139C2211yescharacteristic, complemented
61C2×#102×C139C2211yescharacteristic, complemented
62C2×#101×C139C2211yescharacteristic, complemented
63C2×#100×C139C2211yescharacteristic
64C2×#100×C139C2211yescharacteristic, complemented
65#408×C139C2211yescharacteristic
66#390×C139C2211yescharacteristic
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—41no—
742−1+4×C139D414yescomplemented
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
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×C139C2311yescharacteristic
94C22×D4×C139C2311yescharacteristic
95#137×C139—28no—
96#137×C139—22no—
97#137×C139—22no—
98AGL(1,ℤ/8)×C139—28no—
99AGL(1,ℤ/8)×C139—22no—
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)×C139D414yescomplemented
105#135×C139—28no—
106#135×C139—22no—
107#135×C139—22no—
108C2×Q16×C139—21no—
109C2×Q16×C139D411yescharacteristic
110C2×SD16×C139—28no—
111C2×SD16×C139—21no—
112C2×SD16×C139—22no—
113C2×SD16×C139—21no—
114C2×SD16×C139—22no—
115C2×SD16×C139—21no—
116C2×SD16×C139—21no—
117C2×SD16×C139—21no—
118C2×SD16×C139—21no—
119C2×SD16×C139D411yescharacteristic
120C2×SD16×C139D411yescharacteristic
121C2×D8×C139—21no—
122C2×D8×C139—21no—
123C2×D8×C139—21no—
124C2×D8×C139—22no—
125C2×D8×C139—21no—
126C2×D8×C139—21no—
127C2×D8×C139—41no—
128C2×D8×C139D411yescharacteristic
129#131×C139—22no—
130#131×C139—22no—
131#131×C139—22no—
132#131×C139—41no—
133C2×M16×C139—21no—
134C2×M16×C139—21no—
135C2×M16×C139C2311yescharacteristic
136C2×M16×C139C2311yescharacteristic
137C2×M16×C139C2311yescharacteristic
138C2×M16×C139C2311yescharacteristic
139C22×C8×C139—21no—
140C22×C8×C139—21no—
141C22×C8×C139C2311yescharacteristic
142C22×C8×C139C2311yescharacteristic
143#127×C139—21no—
144#124×C139—22no—
145#124×C139—21no—
146#124×C139—41no—
147#121×C139—21no—
148#121×C139—21no—
149#120×C139—41no—
150C4×Q8×C139—21no—
151C4×D4×C139—21no—
152C4×D4×C139—41no—
153#117×C139—21no—
154#117×C139C2311yescharacteristic
155C2×C4⋊C4×C139—21no—
156C2×C4⋊C4×C139C2311yescharacteristic
157C2×C22⋊C4×C139—41no—
158C2×C22⋊C4×C139—41no—
159C2×C42×C139C2311yescharacteristic
160#108×C139—22no—
161C4⋊C8×C139—21no—
162C4⋊C8×C139—21no—
163#104×C139—22no—
164#104×C139—22no—
165#104×C139—41no—
166#103×C139—21no—
167#103×C139—21no—
168#103×C139—21no—
169#103×C139—21no—
170#103×C139—21no—
171#103×C139—21no—
172#103×C139D411yescharacteristic
173#103×C139D411yescharacteristic
174#102×C139—21no—
175#102×C139—21no—
176#102×C139—21no—
177#102×C139—21no—
178#102×C139—21no—
179#102×C139—21no—
180#102×C139D411yescharacteristic
181#102×C139D411yescharacteristic
182#101×C139—22no—
183#100×C139—22no—
184#100×C139—22no—
185C22⋊C8×C139—21no—
186C22⋊C8×C139—21no—
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—44no—
202#41×C139—42no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—44no—
206#41×C139—42no—
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—24no—
215C2×Q8×C139—21no—
216C2×Q8×C139—21no—
217C2×Q8×C139—21no—
218C2×Q8×C139—21no—
219C2×Q8×C139—41no—
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—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—21no—
239C2×D4×C139—21no—
240C2×D4×C139—21no—
241C2×D4×C139—42no—
242C2×D4×C139—41no—
243C2×D4×C139—41no—
244C2×D4×C139—41no—
245C2×D4×C139—41no—
246C2×D4×C139—42no—
247C2×D4×C139—44no—
248C2×D4×C139—44no—
249C2×D4×C139—41no—
250C2×D4×C139—42no—
251C2×D4×C139C2×D412yes—
252C2×D4×C139C2×D411yescharacteristic
253C2×D4×C139C2×D411yescharacteristic
254C2×D4×C139C2×D411yescharacteristic
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—41no—
262C22×C4×C139—41no—
263C22×C4×C139—41no—
264C22×C4×C139—41no—
265C22×C4×C139C2411yescharacteristic
266Q16×C139—24no—
267Q16×C139—22no—
268SD16×C139—24no—
269SD16×C139—24no—
270SD16×C139—24no—
271SD16×C139—22no—
272SD16×C139—24no—
273SD16×C139—22no—
274SD16×C139—42no—
275SD16×C139—42no—
276D8×C139—24no—
277D8×C139—22no—
278D8×C139—42no—
279D8×C139—42no—
280D8×C139—42no—
281D8×C139—42no—
282M16×C139—24no—
283M16×C139—21no—
284M16×C139—21no—
285M16×C139—21no—
286M16×C139—21no—
287M16×C139—21no—
288M16×C139—21no—
289M16×C139—21no—
290M16×C139—42no—
291M16×C139C2×D412yes—
292C2×C8×C139—24no—
293C2×C8×C139—21no—
294C2×C8×C139—21no—
295C2×C8×C139—21no—
296C2×C8×C139—21no—
297C2×C8×C139—21no—
298C2×C8×C139—21no—
299C2×C8×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139—42no—
302C2×C8×C139C2×D411yescharacteristic
303C2×C8×C139C2×D411yescharacteristic
304C2×C8×C139C2×D411yescharacteristic
305C2×C8×C139C2×D411yescharacteristic
306C4⋊C4×C139—21no—
307C4⋊C4×C139—21no—
308C4⋊C4×C139—41no—
309C4⋊C4×C139C2×D411yescharacteristic
310C4⋊C4×C139C2×D411yescharacteristic
311C22⋊C4×C139—21no—
312C22⋊C4×C139—41no—
313C22⋊C4×C139—41no—
314C22⋊C4×C139—41no—
315C22⋊C4×C139—44no—
316C22⋊C4×C139—82no—
317C42×C139—21no—
318C42×C139—21no—
319C42×C139—21no—
320C42×C139—41no—
321C23×C139—21no—
322C23×C139—21no—
323C23×C139—21no—
324C23×C139—22no—
325C23×C139—44no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—81no—
332C23×C139—81no—
333C23×C139—81no—
334C23×C139—81no—
335C23×C139—161no—
336C23×C139—161no—
337C23×C139H(5,𝔽2)11yescharacteristic
338Q8×C139—21no—
339Q8×C139—21no—
340Q8×C139—22no—
341Q8×C139—21no—
342Q8×C139—22no—
343Q8×C139—21no—
344Q8×C139—44no—
345Q8×C139—41no—
346Q8×C139—41no—
347Q8×C139#12012yes—
348Q8×C139#12112yes—
349D4×C139—22no—
350D4×C139—22no—
351D4×C139—22no—
352D4×C139—22no—
353D4×C139—22no—
354D4×C139—21no—
355D4×C139—21no—
356D4×C139—22no—
357D4×C139—21no—
358D4×C139—21no—
359D4×C139—44no—
360D4×C139—44no—
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—161no—
371D4×C139—161no—
372D4×C139#12012yes—
373D4×C139#12112yes—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—22no—
377C2×C4×C139—22no—
378C2×C4×C139—22no—
379C2×C4×C139—22no—
380C2×C4×C139—22no—
381C2×C4×C139—21no—
382C2×C4×C139—21no—
383C2×C4×C139—21no—
384C2×C4×C139—44no—
385C2×C4×C139—44no—
386C2×C4×C139—44no—
387C2×C4×C139—41no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—81no—
396C2×C4×C139—161no—
397C2×C4×C139C22×D411yescharacteristic
398C2×C4×C139C22×D411yescharacteristic
399C2×C4×C139C22×D411yescharacteristic
400C2×C4×C139C22×D411yescharacteristic
401C2×C4×C139C2×#4111yescharacteristic
402C2×C4×C139H(5,𝔽2)11yescharacteristic
403C8×C139—21no—
404C8×C139—22no—
405C8×C139—21no—
406C8×C139—21no—
407C8×C139—21no—
408C8×C139—41no—
409C8×C139—41no—
410C8×C139—41no—
411C22×C139—21no—
412C22×C139—21no—
413C22×C139—22no—
414C22×C139—22no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—41no—
418C22×C139—41no—
419C22×C139—41no—
420C22×C139—42no—
421C22×C139—41no—
422C22×C139—41no—
423C22×C139—82no—
424C22×C139—82no—
425C22×C139—81no—
426C22×C139—81no—
427C22×C139—81no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139—161no—
431C22×C139—161no—
432C22×C139—164no—
433C22×C139#53411yescharacteristic
434C22×C139D4211yescharacteristic
435C22×C139#54611yescharacteristic
436C4×C139—22no—
437C4×C139—22no—
438C4×C139—41no—
439C4×C139—42no—
440C4×C139—41no—
441C4×C139—41no—
442C4×C139—81no—
443C4×C139—81no—
444C4×C139C2×#12011yescharacteristic
445C4×C139C2×#12111yescharacteristic
446C4×C139D4211yescharacteristic
447C4×C139#54611yescharacteristic
448C2×C139—21no—
449C2×C139—21no—
450C2×C139—42no—
451C2×C139—42no—
452C2×C139—81no—
453C2×C139—82no—
454C2×C139—161no—
455C2×C139#241011yescharacteristic
456C2×C139#328811yescharacteristic
457C2×C139#329011yescharacteristic
458#24460C13911yesmaximal, characteristic, direct product factor, Sylow
459C139#2446011yescharacteristic, direct product factor, Sylow
460C2×#577C2×C13911yescharacteristic, complemented
461C2×#472C2×C13911yescharacteristic, complemented
462#3045C2×C13911yescharacteristic, complemented
463C2×#454C2×C13911yescharacteristic, complemented
464#3008C2×C13911yescharacteristic, complemented
465#2898C2×C13911yescharacteristic, complemented
466#2052C2×C13911yescharacteristic, complemented
467#2046C2×C13911yescharacteristic, complemented
468#2012C2×C13911yescharacteristic, complemented
469#2004C2×C13911yescharacteristic, complemented
470#1907C2×C13911yescharacteristic, complemented
471#1883C2×C13911yescharacteristic, complemented
472#1876C2×C13911yescharacteristic, complemented
473#1866C2×C13911yescharacteristic, complemented
474#1792C2×C13911yescharacteristic, complemented
475C2×2−1+4C22×C13911yescharacteristic
476C2×H(5,𝔽2)C22×C13911yescharacteristic
477#577—24no—
478#577—24no—
479C2×#137—21no—
480C2×#137C22×C13911yescharacteristic
481C2×AGL(1,ℤ/8)—21no—
482C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
483C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
484C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
485C2×#135—21no—
486C2×#135C22×C13911yescharacteristic
487C22×SD16—21no—
488C22×SD16C22×C13911yescharacteristic
489C22×D8C22×C13911yescharacteristic
490C2×#131C22×C13911yescharacteristic
491C2×#131C22×C13911yescharacteristic, complemented
492#535C22×C13911yescharacteristic
493C2×#124C22×C13911yescharacteristic, complemented
494#520C22×C13911yescharacteristic, complemented
495#472—24no—
496#464—21no—
497#463—21no—
498#460—21no—
499#459—21no—
500#454—24no—
501#449—21no—
502#449—21no—
503#447—21no—
504#447—21no—
505C2×#108C22×C13911yescharacteristic, complemented
506#424C22×C13911yescharacteristic, complemented
507C2×#104C22×C13911yescharacteristic
508C2×#104C22×C13911yescharacteristic
509C2×#104C22×C13911yescharacteristic, complemented
510#419—21no—
511#419C22×C13911yescharacteristic, complemented
512#418C22×C13911yescharacteristic
513#417—21no—
514#417C22×C13911yescharacteristic
515#417C22×C13911yescharacteristic
516#416—21no—
517#416C22×C13911yescharacteristic
518C2×#103—21no—
519C2×#103C22×C13911yescharacteristic, complemented
520C2×#102C22×C13911yescharacteristic, complemented
521C2×#101C22×C13911yescharacteristic, complemented
522C2×#100C22×C13911yescharacteristic
523C2×#100C22×C13911yescharacteristic, complemented
524#408C22×C13911yescharacteristic
525#390C22×C13911yescharacteristic
526#343C22×C13911yescharacteristic, complemented
527#341C22×C13911yescharacteristic, complemented
528#339C22×C13911yescharacteristic, complemented
529#336C22×C13911yescharacteristic, complemented
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C13914yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C13911yescharacteristic
544C2×#41C23×C13911yescharacteristic
545C2×#41C23×C13911yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C13911yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C13911yescharacteristic
553C22×D4C23×C13911yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C13914yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C13911yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C13911yescharacteristic
579C2×SD16D4×C13911yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C13911yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C13911yescharacteristic
595C2×M16C23×C13911yescharacteristic
596C2×M16C23×C13911yescharacteristic
597C2×M16C23×C13911yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C13911yescharacteristic
601C22×C8C23×C13911yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C13911yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C13911yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C13911yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C13911yescharacteristic
632#103D4×C13911yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C13911yescharacteristic
640#102D4×C13911yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C13912yes—
668#41C2×D4×C13912yes—
669#41C2×D4×C13912yes—
670#41#41×C13912yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C13912yes—
682C2×Q8C2×D4×C13911yescharacteristic
683C2×Q8C2×D4×C13911yescharacteristic
684C2×Q8C2×D4×C13911yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
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—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C13912yes—
711C2×D4C2×D4×C13911yescharacteristic
712C2×D4C2×D4×C13911yescharacteristic
713C2×D4C2×D4×C13911yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C13911yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C13912yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C13911yescharacteristic
762C2×C8C2×D4×C13911yescharacteristic
763C2×C8C2×D4×C13911yescharacteristic
764C2×C8C2×D4×C13911yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C13911yescharacteristic
769C4⋊C4C2×D4×C13911yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C13911yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—22no—
800Q8—21no—
801Q8—22no—
802Q8—21no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C13912yes—
807Q8#121×C13912yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—21no—
814D4—21no—
815D4—22no—
816D4—21no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C13912yes—
832D4#121×C13912yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C13911yescharacteristic
857C2×C4C22×D4×C13911yescharacteristic
858C2×C4C22×D4×C13911yescharacteristic
859C2×C4C22×D4×C13911yescharacteristic
860C2×C4C2×#41×C13911yescharacteristic
861C2×C4H(5,𝔽2)×C13911yescharacteristic
862C8—21no—
863C8—22no—
864C8—21no—
865C8—21no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22#534×C13911yescharacteristic
893C22D42×C13911yescharacteristic
894C22#546×C13911yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4C2×#120×C13911yescharacteristic
904C4C2×#121×C13911yescharacteristic
905C4D42×C13911yescharacteristic
906C4#546×C13911yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2#2410×C13911yescharacteristic
915C2#3288×C13911yescharacteristic
916C2#3290×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×#472×C139C2semidirect
3. #3045×C139C2semidirect
4. C2×#454×C139C2semidirect
5. #3008×C139C2semidirect
6. #2898×C139C2semidirect
7. #2052×C139C2semidirect
8. #2046×C139C2semidirect
9. #2012×C139C2semidirect
10. #2004×C139C2semidirect
11. #1907×C139C2semidirect
12. #1883×C139C2semidirect
13. #1876×C139C2semidirect
14. #1866×C139C2semidirect
15. #1792×C139C2semidirect
25. C2×AGL(1,ℤ/8)×C139C22semidirect
32. C2×#131×C139C22semidirect
34. C2×#124×C139C22semidirect
35. #520×C139C22semidirect
46. C2×#108×C139C22semidirect
47. #424×C139C22semidirect
50. C2×#104×C139C22semidirect
52. #419×C139C22semidirect
60. C2×#103×C139C22semidirect
61. C2×#102×C139C22semidirect
62. C2×#101×C139C22semidirect
64. C2×#100×C139C22semidirect
67. #343×C139C22semidirect
68. #341×C139C22semidirect
69. #339×C139C22semidirect
70. #336×C139C22semidirect
74. 2−1+4×C139D4semidirect
104. AGL(1,ℤ/8)×C139D4semidirect
458. #24460C139direct (N × H)
459. C139#24460direct (N × H)
460. C2×#577C2×C139semidirect
461. C2×#472C2×C139semidirect
462. #3045C2×C139semidirect
463. C2×#454C2×C139semidirect
464. #3008C2×C139semidirect
465. #2898C2×C139semidirect
466. #2052C2×C139semidirect
467. #2046C2×C139semidirect
468. #2012C2×C139semidirect
469. #2004C2×C139semidirect
470. #1907C2×C139semidirect
471. #1883C2×C139semidirect
472. #1876C2×C139semidirect
473. #1866C2×C139semidirect
474. #1792C2×C139semidirect
484. C2×AGL(1,ℤ/8)C22×C139semidirect
491. C2×#131C22×C139semidirect
493. C2×#124C22×C139semidirect
494. #520C22×C139semidirect
505. C2×#108C22×C139semidirect
506. #424C22×C139semidirect
509. C2×#104C22×C139semidirect
511. #419C22×C139semidirect
519. C2×#103C22×C139semidirect
520. C2×#102C22×C139semidirect
521. C2×#101C22×C139semidirect
523. C2×#100C22×C139semidirect
526. #343C22×C139semidirect
527. #341C22×C139semidirect
528. #339C22×C139semidirect
529. #336C22×C139semidirect
533. 2−1+4D4×C139semidirect
563. AGL(1,ℤ/8)D4×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×#472×C1392
#3045×C1392
C2×#454×C1392
#3008×C1392
#2898×C1392
#2052×C1392
#2046×C1392
#2012×C1392
#2004×C1392
#1907×C1392
#1883×C1392
#1876×C1392
#1866×C1392
#1792×C1392
#24460139