Finite Group Databasebeta

← C139×#24459 #48019055

Subgroups — C139×#24459 #48019055

Order 35584.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C139C211yesmaximal, characteristic
2C2×#471×C139C211yesmaximal, characteristic, complemented
3#3046×C139C211yesmaximal, characteristic, complemented
4C2×#455×C139C211yesmaximal, characteristic, complemented
5#3009×C139C211yesmaximal, characteristic, complemented
6#2897×C139C211yesmaximal, characteristic, complemented
7#2051×C139C211yesmaximal, characteristic, complemented
8#2045×C139C211yesmaximal, characteristic, complemented
9#2012×C139C211yesmaximal, characteristic, complemented
10#2003×C139C211yesmaximal, characteristic, complemented
11#1908×C139C211yesmaximal, characteristic, complemented
12#1883×C139C211yesmaximal, characteristic, complemented
13#1876×C139C211yesmaximal, characteristic, complemented
14#1866×C139C211yesmaximal, characteristic, complemented
15#1792×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C2×H(5,𝔽2)×C139C2211yescharacteristic
18#576×C139—24no—
19#576×C139—24no—
20C2×#137×C139C2211yescharacteristic
21C2×#137×C139C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C139—21no—
23C2×AGL(1,ℤ/8)×C139—21no—
24C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
26C2×#135×C139—21no—
27C2×#135×C139C2211yescharacteristic
28C22×SD16×C139C2211yescharacteristic, complemented
29C22×D8×C139—21no—
30C22×D8×C139C2211yescharacteristic
31C2×#131×C139C2211yescharacteristic
32C2×#131×C139C2211yescharacteristic, complemented
33#536×C139C2211yescharacteristic, complemented
34C2×#124×C139C2211yescharacteristic, complemented
35#520×C139C2211yescharacteristic, complemented
36#471×C139—24no—
37#464×C139—21no—
38#463×C139—21no—
39#462×C139—21no—
40#461×C139—21no—
41#455×C139—24no—
42#452×C139—21no—
43#452×C139—21no—
44#450×C139—21no—
45#450×C139—21no—
46C2×#108×C139C2211yescharacteristic, complemented
47#424×C139C2211yescharacteristic, complemented
48C2×#104×C139C2211yescharacteristic
49C2×#104×C139C2211yescharacteristic, complemented
50C2×#104×C139C2211yescharacteristic, complemented
51#418×C139—21no—
52#418×C139C2211yescharacteristic, complemented
53#418×C139C2211yescharacteristic, complemented
54#417×C139—21no—
55#417×C139C2211yescharacteristic
56#417×C139C2211yescharacteristic, complemented
57#416×C139—21no—
58#416×C139C2211yescharacteristic
59C2×#103×C139C2211yescharacteristic, complemented
60C2×#102×C139—21no—
61C2×#102×C139C2211yescharacteristic, complemented
62C2×#101×C139C2211yescharacteristic, complemented
63C2×#100×C139C2211yescharacteristic, complemented
64C2×#100×C139C2211yescharacteristic, complemented
65#408×C139C2211yescharacteristic, complemented
66#390×C139C2211yescharacteristic, complemented
67#343×C139C2211yescharacteristic, complemented
68#341×C139C2211yescharacteristic, complemented
69#339×C139C2211yescharacteristic, complemented
70#336×C139C2211yescharacteristic, complemented
71H(5,𝔽2)×C139—22no—
72H(5,𝔽2)×C139—22no—
73H(5,𝔽2)×C139—22no—
74H(5,𝔽2)×C139—22no—
75H(5,𝔽2)×C139—22no—
76H(5,𝔽2)×C139—41no—
77H(5,𝔽2)×C139—41no—
78H(5,𝔽2)×C139D414yes—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—21no—
83C2×#41×C139C2311yescharacteristic
84C2×#41×C139C2311yescharacteristic
85C2×#41×C139C2311yescharacteristic
86C22×Q8×C139C2311yescharacteristic
87C22×D4×C139—21no—
88C22×D4×C139—21no—
89C22×D4×C139—21no—
90C22×D4×C139—21no—
91C22×D4×C139—41no—
92C22×D4×C139—41no—
93C22×D4×C139C2311yescharacteristic
94C22×D4×C139C2311yescharacteristic
95#137×C139—22no—
96#137×C139—22no—
97#137×C139—22no—
98#137×C139—22no—
99AGL(1,ℤ/8)×C139—28no—
100AGL(1,ℤ/8)×C139—28no—
101AGL(1,ℤ/8)×C139—22no—
102AGL(1,ℤ/8)×C139—22no—
103AGL(1,ℤ/8)×C139—22no—
104AGL(1,ℤ/8)×C139D414yes—
105#135×C139—28no—
106#135×C139—22no—
107#135×C139—22no—
108C2×Q16×C139—21no—
109C2×Q16×C139—21no—
110C2×Q16×C139D411yescharacteristic
111C2×SD16×C139—21no—
112C2×SD16×C139—21no—
113C2×SD16×C139—21no—
114C2×SD16×C139—21no—
115C2×SD16×C139—22no—
116C2×SD16×C139—21no—
117C2×SD16×C139—21no—
118C2×SD16×C139—41no—
119C2×SD16×C139D411yescharacteristic
120C2×SD16×C139D411yescharacteristic
121C2×D8×C139—28no—
122C2×D8×C139—21no—
123C2×D8×C139—21no—
124C2×D8×C139—22no—
125C2×D8×C139—22no—
126C2×D8×C139—21no—
127C2×D8×C139—21no—
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
143C4⋊Q8×C139—21no—
144#124×C139—22no—
145#124×C139—21no—
146#124×C139—41no—
147#123×C139—41no—
148C22⋊Q8×C139—21no—
149C22⋊Q8×C139—21no—
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×C139D411yescharacteristic
171#103×C139D411yescharacteristic
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×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—
190C24×C139—41no—
191#41×C139—21no—
192#41×C139—21no—
193#41×C139—21no—
194#41×C139—21no—
195#41×C139—24no—
196#41×C139—24no—
197#41×C139—24no—
198#41×C139—21no—
199#41×C139—21no—
200#41×C139—21no—
201#41×C139—21no—
202#41×C139—42no—
203#41×C139—42no—
204#41×C139—42no—
205#41×C139—42no—
206#41×C139—42no—
207#41×C139C2×D412yes—
208#41×C139C2×D412yes—
209#41×C139C2×D412yes—
210#41×C139#4112yes—
211C2×Q8×C139—21no—
212C2×Q8×C139—21no—
213C2×Q8×C139—21no—
214C2×Q8×C139—21no—
215C2×Q8×C139—21no—
216C2×Q8×C139—21no—
217C2×Q8×C139C2×D411yescharacteristic
218C2×Q8×C139C2×D411yescharacteristic
219C2×Q8×C139C2×D411yescharacteristic
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—24no—
223C2×D4×C139—24no—
224C2×D4×C139—24no—
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—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—41no—
240C2×D4×C139—41no—
241C2×D4×C139—41no—
242C2×D4×C139—41no—
243C2×D4×C139—44no—
244C2×D4×C139—42no—
245C2×D4×C139—44no—
246C2×D4×C139—44no—
247C2×D4×C139—44no—
248C2×D4×C139—42no—
249C2×D4×C139C2×D412yes—
250C2×D4×C139C2×D412yes—
251C2×D4×C139C2×D411yescharacteristic
252C2×D4×C139C2×D411yescharacteristic
253C2×D4×C139C2×D411yescharacteristic
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—41no—
261C22×C4×C139—41no—
262C22×C4×C139—41no—
263C22×C4×C139C2411yescharacteristic
264Q16×C139—22no—
265Q16×C139—42no—
266Q16×C139—42no—
267SD16×C139—24no—
268SD16×C139—24no—
269SD16×C139—22no—
270SD16×C139—22no—
271SD16×C139—42no—
272SD16×C139—42no—
273SD16×C139—42no—
274SD16×C139—42no—
275D8×C139—24no—
276D8×C139—24no—
277D8×C139—24no—
278D8×C139—22no—
279D8×C139—24no—
280M16×C139—24no—
281M16×C139—21no—
282M16×C139—21no—
283M16×C139—21no—
284M16×C139—21no—
285M16×C139—21no—
286M16×C139—21no—
287M16×C139—21no—
288M16×C139—42no—
289M16×C139C2×D412yes—
290C2×C8×C139—24no—
291C2×C8×C139—21no—
292C2×C8×C139—21no—
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—42no—
300C2×C8×C139C2×D411yescharacteristic
301C2×C8×C139C2×D411yescharacteristic
302C2×C8×C139C2×D411yescharacteristic
303C2×C8×C139C2×D411yescharacteristic
304C4⋊C4×C139—21no—
305C4⋊C4×C139—21no—
306C4⋊C4×C139—41no—
307C4⋊C4×C139—41no—
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—22no—
326C23×C139—44no—
327C23×C139—44no—
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×C139—161no—
339C23×C139—161no—
340C23×C139H(5,𝔽2)11yescharacteristic
341Q8×C139—21no—
342Q8×C139—21no—
343Q8×C139—21no—
344Q8×C139—21no—
345Q8×C139—41no—
346Q8×C139—41no—
347Q8×C139—41no—
348Q8×C139—41no—
349Q8×C139#12012yes—
350Q8×C139#12112yes—
351D4×C139—22no—
352D4×C139—22no—
353D4×C139—22no—
354D4×C139—22no—
355D4×C139—22no—
356D4×C139—22no—
357D4×C139—21no—
358D4×C139—22no—
359D4×C139—21no—
360D4×C139—22no—
361D4×C139—21no—
362D4×C139—21no—
363D4×C139—44no—
364D4×C139—44no—
365D4×C139—44no—
366D4×C139—44no—
367D4×C139—41no—
368D4×C139—41no—
369D4×C139—41no—
370D4×C139—41no—
371D4×C139—41no—
372D4×C139—41no—
373D4×C139#12012yes—
374D4×C139#12112yes—
375C2×C4×C139—21no—
376C2×C4×C139—21no—
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—41no—
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—42no—
422C22×C139—41no—
423C22×C139—41no—
424C22×C139—82no—
425C22×C139—82no—
426C22×C139—81no—
427C22×C139—81no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139—161no—
431C22×C139—161no—
432C22×C139—164no—
433C22×C139—164no—
434C22×C139#53411yescharacteristic
435C22×C139D4211yescharacteristic
436C22×C139#54611yescharacteristic
437C4×C139—22no—
438C4×C139—22no—
439C4×C139—41no—
440C4×C139—41no—
441C4×C139—41no—
442C4×C139—81no—
443C4×C139—81no—
444C4×C139—81no—
445C4×C139C2×#12011yescharacteristic
446C4×C139C2×#12111yescharacteristic
447C4×C139D4211yescharacteristic
448C4×C139#54611yescharacteristic
449C2×C139—21no—
450C2×C139—21no—
451C2×C139—42no—
452C2×C139—42no—
453C2×C139—81no—
454C2×C139—82no—
455C2×C139—82no—
456C2×C139#241011yescharacteristic
457C2×C139#328811yescharacteristic
458C2×C139#329011yescharacteristic
459#24459C13911yesmaximal, characteristic, direct product factor, Sylow
460C139#2445911yescharacteristic, direct product factor, Sylow
461C2×#576C2×C13911yescharacteristic
462C2×#471C2×C13911yescharacteristic, complemented
463#3046C2×C13911yescharacteristic, complemented
464C2×#455C2×C13911yescharacteristic, complemented
465#3009C2×C13911yescharacteristic, complemented
466#2897C2×C13911yescharacteristic, complemented
467#2051C2×C13911yescharacteristic, complemented
468#2045C2×C13911yescharacteristic, complemented
469#2012C2×C13911yescharacteristic, complemented
470#2003C2×C13911yescharacteristic, complemented
471#1908C2×C13911yescharacteristic, complemented
472#1883C2×C13911yescharacteristic, complemented
473#1876C2×C13911yescharacteristic, complemented
474#1866C2×C13911yescharacteristic, complemented
475#1792C2×C13911yescharacteristic, complemented
476C2×H(5,𝔽2)C22×C13911yescharacteristic
477C2×H(5,𝔽2)C22×C13911yescharacteristic
478#576—24no—
479#576—24no—
480C2×#137C22×C13911yescharacteristic
481C2×#137C22×C13911yescharacteristic, complemented
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
485C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
486C2×#135—21no—
487C2×#135C22×C13911yescharacteristic
488C22×SD16C22×C13911yescharacteristic, complemented
489C22×D8—21no—
490C22×D8C22×C13911yescharacteristic
491C2×#131C22×C13911yescharacteristic
492C2×#131C22×C13911yescharacteristic, complemented
493#536C22×C13911yescharacteristic, complemented
494C2×#124C22×C13911yescharacteristic, complemented
495#520C22×C13911yescharacteristic, complemented
496#471—24no—
497#464—21no—
498#463—21no—
499#462—21no—
500#461—21no—
501#455—24no—
502#452—21no—
503#452—21no—
504#450—21no—
505#450—21no—
506C2×#108C22×C13911yescharacteristic, complemented
507#424C22×C13911yescharacteristic, complemented
508C2×#104C22×C13911yescharacteristic
509C2×#104C22×C13911yescharacteristic, complemented
510C2×#104C22×C13911yescharacteristic, complemented
511#418—21no—
512#418C22×C13911yescharacteristic, complemented
513#418C22×C13911yescharacteristic, complemented
514#417—21no—
515#417C22×C13911yescharacteristic
516#417C22×C13911yescharacteristic, complemented
517#416—21no—
518#416C22×C13911yescharacteristic
519C2×#103C22×C13911yescharacteristic, complemented
520C2×#102—21no—
521C2×#102C22×C13911yescharacteristic, complemented
522C2×#101C22×C13911yescharacteristic, complemented
523C2×#100C22×C13911yescharacteristic, complemented
524C2×#100C22×C13911yescharacteristic, complemented
525#408C22×C13911yescharacteristic, complemented
526#390C22×C13911yescharacteristic, complemented
527#343C22×C13911yescharacteristic, complemented
528#341C22×C13911yescharacteristic, complemented
529#339C22×C13911yescharacteristic, complemented
530#336C22×C13911yescharacteristic, complemented
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C13914yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C13911yescharacteristic
544C2×#41C23×C13911yescharacteristic
545C2×#41C23×C13911yescharacteristic
546C22×Q8C23×C13911yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C13911yescharacteristic
554C22×D4C23×C13911yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C13914yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C13911yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C13911yescharacteristic
580C2×SD16D4×C13911yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C13911yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C13911yescharacteristic
596C2×M16C23×C13911yescharacteristic
597C2×M16C23×C13911yescharacteristic
598C2×M16C23×C13911yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C13911yescharacteristic
602C22×C8C23×C13911yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C13911yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C13911yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
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
631#103D4×C13911yescharacteristic
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
641#102D4×C13911yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
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—42no—
664#41—42no—
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—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C13911yescharacteristic
678C2×Q8C2×D4×C13911yescharacteristic
679C2×Q8C2×D4×C13911yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
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—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C13912yes—
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×C4C24×C13911yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C13912yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C13911yescharacteristic
761C2×C8C2×D4×C13911yescharacteristic
762C2×C8C2×D4×C13911yescharacteristic
763C2×C8C2×D4×C13911yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C13911yescharacteristic
770C4⋊C4C2×D4×C13911yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C13911yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C13912yes—
810Q8#121×C13912yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C13912yes—
834D4#121×C13912yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
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—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C13911yescharacteristic
858C2×C4C22×D4×C13911yescharacteristic
859C2×C4C22×D4×C13911yescharacteristic
860C2×C4C22×D4×C13911yescharacteristic
861C2×C4C2×#41×C13911yescharacteristic
862C2×C4H(5,𝔽2)×C13911yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22#534×C13911yescharacteristic
895C22D42×C13911yescharacteristic
896C22#546×C13911yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C13911yescharacteristic
906C4C2×#121×C13911yescharacteristic
907C4D42×C13911yescharacteristic
908C4#546×C13911yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2#2410×C13911yescharacteristic
917C2#3288×C13911yescharacteristic
918C2#3290×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#576×C139C2
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
2. C2×#471×C139C2semidirect
3. #3046×C139C2semidirect
4. C2×#455×C139C2semidirect
5. #3009×C139C2semidirect
6. #2897×C139C2semidirect
7. #2051×C139C2semidirect
8. #2045×C139C2semidirect
9. #2012×C139C2semidirect
10. #2003×C139C2semidirect
11. #1908×C139C2semidirect
12. #1883×C139C2semidirect
13. #1876×C139C2semidirect
14. #1866×C139C2semidirect
15. #1792×C139C2semidirect
21. C2×#137×C139C22semidirect
28. C22×SD16×C139C22semidirect
32. C2×#131×C139C22semidirect
33. #536×C139C22semidirect
34. C2×#124×C139C22semidirect
35. #520×C139C22semidirect
46. C2×#108×C139C22semidirect
47. #424×C139C22semidirect
49. C2×#104×C139C22semidirect
50. C2×#104×C139C22semidirect
52. #418×C139C22semidirect
53. #418×C139C22semidirect
56. #417×C139C22semidirect
59. C2×#103×C139C22semidirect
61. C2×#102×C139C22semidirect
62. C2×#101×C139C22semidirect
63. C2×#100×C139C22semidirect
64. C2×#100×C139C22semidirect
65. #408×C139C22semidirect
66. #390×C139C22semidirect
67. #343×C139C22semidirect
68. #341×C139C22semidirect
69. #339×C139C22semidirect
70. #336×C139C22semidirect
459. #24459C139direct (N × H)
460. C139#24459direct (N × H)
462. C2×#471C2×C139semidirect
463. #3046C2×C139semidirect
464. C2×#455C2×C139semidirect
465. #3009C2×C139semidirect
466. #2897C2×C139semidirect
467. #2051C2×C139semidirect
468. #2045C2×C139semidirect
469. #2012C2×C139semidirect
470. #2003C2×C139semidirect
471. #1908C2×C139semidirect
472. #1883C2×C139semidirect
473. #1876C2×C139semidirect
474. #1866C2×C139semidirect
475. #1792C2×C139semidirect
481. C2×#137C22×C139semidirect
488. C22×SD16C22×C139semidirect
492. C2×#131C22×C139semidirect
493. #536C22×C139semidirect
494. C2×#124C22×C139semidirect
495. #520C22×C139semidirect
506. C2×#108C22×C139semidirect
507. #424C22×C139semidirect
509. C2×#104C22×C139semidirect
510. C2×#104C22×C139semidirect
512. #418C22×C139semidirect
513. #418C22×C139semidirect
516. #417C22×C139semidirect
519. C2×#103C22×C139semidirect
521. C2×#102C22×C139semidirect
522. C2×#101C22×C139semidirect
523. C2×#100C22×C139semidirect
524. C2×#100C22×C139semidirect
525. #408C22×C139semidirect
526. #390C22×C139semidirect
527. #343C22×C139semidirect
528. #341C22×C139semidirect
529. #339C22×C139semidirect
530. #336C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1392
C2×#471×C1392
#3046×C1392
C2×#455×C1392
#3009×C1392
#2897×C1392
#2051×C1392
#2045×C1392
#2012×C1392
#2003×C1392
#1908×C1392
#1883×C1392
#1876×C1392
#1866×C1392
#1792×C1392
#24459139