Finite Group Databasebeta

← C139×#25180 #48019776

Subgroups — C139×#25180 #48019776

Order 35584.

1074 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#472×C139C211yesmaximal, characteristic, complemented
2#3041×C139C211yesmaximal, characteristic, complemented
3C2×#453×C139C211yesmaximal, characteristic, complemented
4#3008×C139C211yesmaximal, characteristic, complemented
5#2946×C139C211yesmaximal, characteristic, complemented
6#2897×C139C211yesmaximal, characteristic, complemented
7#2063×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2037×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1978×C139C211yesmaximal, characteristic, complemented
12#1929×C139C211yesmaximal, characteristic, complemented
13#1887×C139C211yesmaximal, characteristic, complemented
14#1883×C139C211yesmaximal, characteristic, complemented
15#1866×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic
21C22×D8×C139C2211yescharacteristic, complemented
22C2×#131×C139C2211yescharacteristic
23#535×C139C2211yescharacteristic
24C2×#127×C139C2211yescharacteristic
25#520×C139C2211yescharacteristic
26#518×C139C2211yescharacteristic, complemented
27#472×C139—24no—
28#463×C139—21no—
29#463×C139—21no—
30#459×C139—21no—
31#459×C139—21no—
32#453×C139—24no—
33#449×C139—21no—
34#449×C139—21no—
35#447×C139—21no—
36#447×C139—21no—
37#442×C139—21no—
38#440×C139—21no—
39C4×SD16×C139—21no—
40C4×D8×C139—21no—
41C2×#108×C139C2211yescharacteristic, complemented
42C2×#108×C139C2211yescharacteristic, complemented
43#428×C139C2211yescharacteristic, complemented
44#424×C139C2211yescharacteristic, complemented
45C2×#104×C139C2211yescharacteristic
46C2×#104×C139C2211yescharacteristic
47#418×C139—21no—
48#418×C139C2211yescharacteristic
49#418×C139C2211yescharacteristic
50#418×C139C2211yescharacteristic, complemented
51#417×C139—21no—
52#417×C139C2211yescharacteristic
53#416×C139—21no—
54#416×C139C2211yescharacteristic
55#416×C139C2211yescharacteristic
56C2×#102×C139—21no—
57C2×#102×C139C2211yescharacteristic
58C2×#102×C139C2211yescharacteristic, complemented
59C2×#100×C139C2211yescharacteristic
60C2×#100×C139C2211yescharacteristic, complemented
61C2×#100×C139C2211yescharacteristic, complemented
62#408×C139C2211yescharacteristic
63#405×C139C2211yescharacteristic, complemented
64#390×C139C2211yescharacteristic, complemented
65#343×C139C2211yescharacteristic, complemented
66#339×C139C2211yescharacteristic, complemented
67#339×C139C2211yescharacteristic, complemented
68#336×C139C2211yescharacteristic, complemented
69H(5,𝔽2)×C139—22no—
70H(5,𝔽2)×C139—22no—
71H(5,𝔽2)×C139—22no—
72H(5,𝔽2)×C139—41no—
73C2×#41×C139—21no—
74C2×#41×C139—21no—
75C2×#41×C139C2311yescharacteristic
76C2×#41×C139C2311yescharacteristic
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—41no—
80C22×D4×C139—41no—
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2311yescharacteristic
84AGL(1,ℤ/8)×C139—22no—
85AGL(1,ℤ/8)×C139—22no—
86AGL(1,ℤ/8)×C139—22no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—41no—
89AGL(1,ℤ/8)×C139D414yescomplemented
90C2×SD16×C139—21no—
91C2×SD16×C139—21no—
92C2×SD16×C139—21no—
93C2×D8×C139—21no—
94C2×D8×C139—21no—
95C2×D8×C139—21no—
96C2×D8×C139—22no—
97C2×D8×C139—22no—
98C2×D8×C139—21no—
99C2×D8×C139—21no—
100C2×D8×C139—21no—
101C2×D8×C139—21no—
102C2×D8×C139—41no—
103C2×D8×C139—41no—
104#131×C139—22no—
105#131×C139—41no—
106C2×M16×C139—21no—
107C2×M16×C139C2311yescharacteristic
108C2×M16×C139C2311yescharacteristic
109C2×M16×C139C2311yescharacteristic
110C2×M16×C139C2311yescharacteristic
111C22×C8×C139—21no—
112C22×C8×C139C2311yescharacteristic
113C22×C8×C139C2311yescharacteristic
114#127×C139—22no—
115#127×C139—21no—
116#127×C139—22no—
117#124×C139—21no—
118#121×C139—21no—
119#121×C139—21no—
120#120×C139—41no—
121C4×Q8×C139—21no—
122C4×D4×C139—21no—
123C4×D4×C139—21no—
124C4×D4×C139—21no—
125C4×D4×C139—21no—
126C4×D4×C139—21no—
127C4×D4×C139—41no—
128#117×C139—21no—
129#117×C139C2311yescharacteristic
130#117×C139C2311yescharacteristic
131C2×C4⋊C4×C139—21no—
132C2×C4⋊C4×C139C2311yescharacteristic
133C2×C22⋊C4×C139—41no—
134C2×C22⋊C4×C139—41no—
135C2×C42×C139C2311yescharacteristic
136#108×C139—22no—
137#108×C139—41no—
138#107×C139—21no—
139#106×C139—21no—
140C4⋊C8×C139—21no—
141C4⋊C8×C139—21no—
142#104×C139—22no—
143#104×C139—22no—
144#103×C139—21no—
145#103×C139D411yescharacteristic, complemented
146#103×C139D411yescharacteristic, complemented
147#103×C139D411yescharacteristic, complemented
148#103×C139D411yescharacteristic, complemented
149#102×C139—21no—
150#102×C139—21no—
151#102×C139—21no—
152#102×C139—21no—
153#102×C139—21no—
154#102×C139—21no—
155#102×C139—21no—
156#102×C139—21no—
157#102×C139—21no—
158#102×C139—21no—
159#102×C139—21no—
160#102×C139D411yescharacteristic, complemented
161#102×C139D411yescharacteristic, complemented
162#102×C139D411yescharacteristic, complemented
163#102×C139D411yescharacteristic, complemented
164#100×C139—22no—
165#100×C139—22no—
166#100×C139—22no—
167C22⋊C8×C139—21no—
168C22⋊C8×C139—21no—
169#97×C139—21no—
170C4×C8×C139—21no—
171C24×C139—21no—
172C24×C139—21no—
173C24×C139—21no—
174C24×C139—41no—
175#41×C139—21no—
176#41×C139—21no—
177#41×C139—24no—
178#41×C139—21no—
179#41×C139—21no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—42no—
183#41×C139—42no—
184#41×C139—42no—
185#41×C139C2×D412yes—
186#41×C139#4112yes—
187C2×Q8×C139C2×D411yescharacteristic
188C2×Q8×C139C2×D411yescharacteristic
189C2×D4×C139—21no—
190C2×D4×C139—24no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—42no—
209C2×D4×C139—41no—
210C2×D4×C139—41no—
211C2×D4×C139—41no—
212C2×D4×C139—41no—
213C2×D4×C139—42no—
214C2×D4×C139—44no—
215C2×D4×C139—44no—
216C2×D4×C139—42no—
217C2×D4×C139—44no—
218C2×D4×C139—82no—
219C2×D4×C139—82no—
220C2×D4×C139C2×D412yes—
221C2×D4×C139C2×D411yescharacteristic
222C2×D4×C139C2×D411yescharacteristic
223C2×D4×C139#4112yes—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—41no—
229C22×C4×C139—41no—
230C22×C4×C139—41no—
231C22×C4×C139—41no—
232C22×C4×C139C2411yescharacteristic
233SD16×C139—24no—
234SD16×C139—42no—
235SD16×C139—42no—
236D8×C139—24no—
237D8×C139—42no—
238D8×C139—42no—
239D8×C139—42no—
240D8×C139—42no—
241D8×C139—42no—
242D8×C139—42no—
243M16×C139—21no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—42no—
251M16×C139C2×D412yes—
252C2×C8×C139—21no—
253C2×C8×C139—21no—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—42no—
261C2×C8×C139C2×D411yescharacteristic
262C2×C8×C139C2×D411yescharacteristic
263C2×C8×C139C2×D411yescharacteristic
264C2×C8×C139C2×D411yescharacteristic
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—41no—
268C4⋊C4×C139C2×D411yescharacteristic
269C4⋊C4×C139C2×D411yescharacteristic
270C4⋊C4×C139C2×D411yescharacteristic
271C4⋊C4×C139C2×D411yescharacteristic
272C22⋊C4×C139—21no—
273C22⋊C4×C139—21no—
274C22⋊C4×C139—41no—
275C22⋊C4×C139—41no—
276C22⋊C4×C139—41no—
277C22⋊C4×C139—41no—
278C22⋊C4×C139—41no—
279C22⋊C4×C139—82no—
280C42×C139—21no—
281C42×C139—21no—
282C42×C139—21no—
283C42×C139—21no—
284C42×C139—41no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—22no—
288C23×C139—22no—
289C23×C139—44no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—81no—
298C23×C139—81no—
299C23×C139—81no—
300C23×C139—81no—
301C23×C139—81no—
302C23×C139—81no—
303C23×C139—161no—
304C23×C139—161no—
305C23×C139H(5,𝔽2)11yescharacteristic
306Q8×C139—21no—
307Q8×C139—21no—
308Q8×C139—21no—
309Q8×C139#12112yes—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—21no—
314D4×C139—22no—
315D4×C139—22no—
316D4×C139—21no—
317D4×C139—21no—
318D4×C139—22no—
319D4×C139—44no—
320D4×C139—44no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—88no—
332D4×C139—161no—
333D4×C139—161no—
334D4×C139#12112yes—
335C2×C4×C139—21no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—44no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—81no—
351C2×C4×C139—161no—
352C2×C4×C139—161no—
353C2×C4×C139—161no—
354C2×C4×C139C22×D411yescharacteristic
355C2×C4×C139C22×D411yescharacteristic
356C2×C4×C139C22×D411yescharacteristic
357C2×C4×C139C2×#4111yescharacteristic
358C2×C4×C139C2×#4111yescharacteristic
359C2×C4×C139H(5,𝔽2)11yescharacteristic
360C8×C139—22no—
361C8×C139—21no—
362C8×C139—21no—
363C8×C139—21no—
364C8×C139—21no—
365C8×C139—41no—
366C8×C139—41no—
367C8×C139—41no—
368C22×C139—21no—
369C22×C139—21no—
370C22×C139—22no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—41no—
374C22×C139—42no—
375C22×C139—42no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—82no—
379C22×C139—82no—
380C22×C139—82no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—161no—
389C22×C139—161no—
390C22×C139—161no—
391C22×C139—164no—
392C22×C139#53811yescharacteristic
393C22×C139D4211yescharacteristic
394C22×C139#54611yescharacteristic
395C4×C139—22no—
396C4×C139—42no—
397C4×C139—41no—
398C4×C139—41no—
399C4×C139—41no—
400C4×C139—41no—
401C4×C139—41no—
402C4×C139—81no—
403C4×C139C2×#12111yescharacteristic
404C4×C139#52511yescharacteristic
405C4×C139D4211yescharacteristic
406C4×C139#54611yescharacteristic
407C2×C139—21no—
408C2×C139—21no—
409C2×C139—42no—
410C2×C139—81no—
411C2×C139—82no—
412C2×C139—82no—
413C2×C139—161no—
414C2×C139#242411yescharacteristic
415C2×C139#328811yescharacteristic
416C2×C139#329211yescharacteristic
417#25180C13911yesmaximal, characteristic, direct product factor, Sylow
418C139#2518011yescharacteristic, direct product factor, Sylow
419C2×#472C2×C13911yescharacteristic, complemented
420#3041C2×C13911yescharacteristic, complemented
421C2×#453C2×C13911yescharacteristic, complemented
422#3008C2×C13911yescharacteristic, complemented
423#2946C2×C13911yescharacteristic, complemented
424#2897C2×C13911yescharacteristic, complemented
425#2063C2×C13911yescharacteristic, complemented
426#2051C2×C13911yescharacteristic, complemented
427#2037C2×C13911yescharacteristic, complemented
428#2011C2×C13911yescharacteristic, complemented
429#1978C2×C13911yescharacteristic, complemented
430#1929C2×C13911yescharacteristic, complemented
431#1887C2×C13911yescharacteristic, complemented
432#1883C2×C13911yescharacteristic, complemented
433#1866C2×C13911yescharacteristic, complemented
434C2×H(5,𝔽2)C22×C13911yescharacteristic
435C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
436C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
437C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
438C22×D8C22×C13911yescharacteristic
439C22×D8C22×C13911yescharacteristic, complemented
440C2×#131C22×C13911yescharacteristic
441#535C22×C13911yescharacteristic
442C2×#127C22×C13911yescharacteristic
443#520C22×C13911yescharacteristic
444#518C22×C13911yescharacteristic, complemented
445#472—24no—
446#463—21no—
447#463—21no—
448#459—21no—
449#459—21no—
450#453—24no—
451#449—21no—
452#449—21no—
453#447—21no—
454#447—21no—
455#442—21no—
456#440—21no—
457C4×SD16—21no—
458C4×D8—21no—
459C2×#108C22×C13911yescharacteristic, complemented
460C2×#108C22×C13911yescharacteristic, complemented
461#428C22×C13911yescharacteristic, complemented
462#424C22×C13911yescharacteristic, complemented
463C2×#104C22×C13911yescharacteristic
464C2×#104C22×C13911yescharacteristic
465#418—21no—
466#418C22×C13911yescharacteristic
467#418C22×C13911yescharacteristic
468#418C22×C13911yescharacteristic, complemented
469#417—21no—
470#417C22×C13911yescharacteristic
471#416—21no—
472#416C22×C13911yescharacteristic
473#416C22×C13911yescharacteristic
474C2×#102—21no—
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic, complemented
477C2×#100C22×C13911yescharacteristic
478C2×#100C22×C13911yescharacteristic, complemented
479C2×#100C22×C13911yescharacteristic, complemented
480#408C22×C13911yescharacteristic
481#405C22×C13911yescharacteristic, complemented
482#390C22×C13911yescharacteristic, complemented
483#343C22×C13911yescharacteristic, complemented
484#339C22×C13911yescharacteristic, complemented
485#339C22×C13911yescharacteristic, complemented
486#336C22×C13911yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C13911yescharacteristic
494C2×#41C23×C13911yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4C23×C13911yescharacteristic
500C22×D4C23×C13911yescharacteristic
501C22×D4C23×C13911yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)D4×C13914yescomplemented
508C2×SD16—21no—
509C2×SD16—21no—
510C2×SD16—21no—
511C2×D8—21no—
512C2×D8—22no—
513C2×D8—21no—
514C2×D8—21no—
515C2×D8—22no—
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8—21no—
520C2×D8—41no—
521C2×D8—41no—
522#131—22no—
523#131—41no—
524C2×M16—21no—
525C2×M16C23×C13911yescharacteristic
526C2×M16C23×C13911yescharacteristic
527C2×M16C23×C13911yescharacteristic
528C2×M16C23×C13911yescharacteristic
529C22×C8—21no—
530C22×C8C23×C13911yescharacteristic
531C22×C8C23×C13911yescharacteristic
532#127—22no—
533#127—21no—
534#127—22no—
535#124—21no—
536#121—21no—
537#121—21no—
538#120—41no—
539C4×Q8—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—41no—
546#117—21no—
547#117C23×C13911yescharacteristic
548#117C23×C13911yescharacteristic
549C2×C4⋊C4—21no—
550C2×C4⋊C4C23×C13911yescharacteristic
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C42C23×C13911yescharacteristic
554#108—22no—
555#108—41no—
556#107—21no—
557#106—21no—
558C4⋊C8—21no—
559C4⋊C8—21no—
560#104—22no—
561#104—22no—
562#103—21no—
563#103D4×C13911yescharacteristic, complemented
564#103D4×C13911yescharacteristic, complemented
565#103D4×C13911yescharacteristic, complemented
566#103D4×C13911yescharacteristic, complemented
567#102—21no—
568#102—21no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102D4×C13911yescharacteristic, complemented
579#102D4×C13911yescharacteristic, complemented
580#102D4×C13911yescharacteristic, complemented
581#102D4×C13911yescharacteristic, complemented
582#100—22no—
583#100—22no—
584#100—22no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587#97—21no—
588C4×C8—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41C2×D4×C13912yes—
604#41#41×C13912yes—
605C2×Q8C2×D4×C13911yescharacteristic
606C2×Q8C2×D4×C13911yescharacteristic
607C2×D4—21no—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—44no—
636C2×D4—82no—
637C2×D4—82no—
638C2×D4C2×D4×C13912yes—
639C2×D4C2×D4×C13911yescharacteristic
640C2×D4C2×D4×C13911yescharacteristic
641C2×D4#41×C13912yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C24×C13911yescharacteristic
651SD16—24no—
652SD16—42no—
653SD16—42no—
654D8—24no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659D8—42no—
660D8—42no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—42no—
669M16C2×D4×C13912yes—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—42no—
679C2×C8C2×D4×C13911yescharacteristic
680C2×C8C2×D4×C13911yescharacteristic
681C2×C8C2×D4×C13911yescharacteristic
682C2×C8C2×D4×C13911yescharacteristic
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C13911yescharacteristic
687C4⋊C4C2×D4×C13911yescharacteristic
688C4⋊C4C2×D4×C13911yescharacteristic
689C4⋊C4C2×D4×C13911yescharacteristic
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—41no—
697C22⋊C4—82no—
698C42—21no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—41no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—44no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—81no—
720C23—81no—
721C23—161no—
722C23—161no—
723C23H(5,𝔽2)×C13911yescharacteristic
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C13912yes—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—21no—
732D4—22no—
733D4—22no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4#121×C13912yes—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—81no—
769C2×C4—161no—
770C2×C4—161no—
771C2×C4—161no—
772C2×C4C22×D4×C13911yescharacteristic
773C2×C4C22×D4×C13911yescharacteristic
774C2×C4C22×D4×C13911yescharacteristic
775C2×C4C2×#41×C13911yescharacteristic
776C2×C4C2×#41×C13911yescharacteristic
777C2×C4H(5,𝔽2)×C13911yescharacteristic
778C8—22no—
779C8—21no—
780C8—21no—
781C8—21no—
782C8—21no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—21no—
787C22—21no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—161no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C13911yescharacteristic
811C22D42×C13911yescharacteristic
812C22#546×C13911yescharacteristic
813C4—22no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—81no—
821C4C2×#121×C13911yescharacteristic
822C4#525×C13911yescharacteristic
823C4D42×C13911yescharacteristic
824C4#546×C13911yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2#2424×C13911yescharacteristic
833C2#3288×C13911yescharacteristic
834C2#3292×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×#472×C139C2semidirect
2. #3041×C139C2semidirect
3. C2×#453×C139C2semidirect
4. #3008×C139C2semidirect
5. #2946×C139C2semidirect
6. #2897×C139C2semidirect
7. #2063×C139C2semidirect
8. #2051×C139C2semidirect
9. #2037×C139C2semidirect
10. #2011×C139C2semidirect
11. #1978×C139C2semidirect
12. #1929×C139C2semidirect
13. #1887×C139C2semidirect
14. #1883×C139C2semidirect
15. #1866×C139C2semidirect
21. C22×D8×C139C22semidirect
26. #518×C139C22semidirect
41. C2×#108×C139C22semidirect
42. C2×#108×C139C22semidirect
43. #428×C139C22semidirect
44. #424×C139C22semidirect
50. #418×C139C22semidirect
58. C2×#102×C139C22semidirect
60. C2×#100×C139C22semidirect
61. C2×#100×C139C22semidirect
63. #405×C139C22semidirect
64. #390×C139C22semidirect
65. #343×C139C22semidirect
66. #339×C139C22semidirect
67. #339×C139C22semidirect
68. #336×C139C22semidirect
89. AGL(1,ℤ/8)×C139D4semidirect
145. #103×C139D4semidirect
146. #103×C139D4semidirect
147. #103×C139D4semidirect
148. #103×C139D4semidirect
160. #102×C139D4semidirect
161. #102×C139D4semidirect
162. #102×C139D4semidirect
163. #102×C139D4semidirect
417. #25180C139direct (N × H)
418. C139#25180direct (N × H)
419. C2×#472C2×C139semidirect
420. #3041C2×C139semidirect
421. C2×#453C2×C139semidirect
422. #3008C2×C139semidirect
423. #2946C2×C139semidirect
424. #2897C2×C139semidirect
425. #2063C2×C139semidirect
426. #2051C2×C139semidirect
427. #2037C2×C139semidirect
428. #2011C2×C139semidirect
429. #1978C2×C139semidirect
430. #1929C2×C139semidirect
431. #1887C2×C139semidirect
432. #1883C2×C139semidirect
433. #1866C2×C139semidirect
439. C22×D8C22×C139semidirect
444. #518C22×C139semidirect
459. C2×#108C22×C139semidirect
460. C2×#108C22×C139semidirect
461. #428C22×C139semidirect
462. #424C22×C139semidirect
468. #418C22×C139semidirect
476. C2×#102C22×C139semidirect
478. C2×#100C22×C139semidirect
479. C2×#100C22×C139semidirect
481. #405C22×C139semidirect
482. #390C22×C139semidirect
483. #343C22×C139semidirect
484. #339C22×C139semidirect
485. #339C22×C139semidirect
486. #336C22×C139semidirect
507. AGL(1,ℤ/8)D4×C139semidirect
563. #103D4×C139semidirect
564. #103D4×C139semidirect
565. #103D4×C139semidirect
566. #103D4×C139semidirect
578. #102D4×C139semidirect
579. #102D4×C139semidirect
580. #102D4×C139semidirect
581. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1392
#3041×C1392
C2×#453×C1392
#3008×C1392
#2946×C1392
#2897×C1392
#2063×C1392
#2051×C1392
#2037×C1392
#2011×C1392
#1978×C1392
#1929×C1392
#1887×C1392
#1883×C1392
#1866×C1392
#25180139