Finite Group Databasebeta

← C139×#18810 #48013406

Subgroups — C139×#18810 #48013406

Order 35584.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3519×C139C211yesmaximal, characteristic, complemented
2#3251×C139C211yesmaximal, characteristic, complemented
3#3207×C139C211yesmaximal, characteristic, complemented
4#3036×C139C211yesmaximal, characteristic, complemented
5#1646×C139C211yesmaximal, characteristic, complemented
6#1643×C139C211yesmaximal, characteristic, complemented
7#1642×C139C211yesmaximal, characteristic, complemented
8#1639×C139C211yesmaximal, characteristic, complemented
9#1624×C139C211yesmaximal, characteristic, complemented
10#1622×C139C211yesmaximal, characteristic, complemented
11#1621×C139C211yesmaximal, characteristic, complemented
12#1619×C139C211yesmaximal, characteristic, complemented
13#1560×C139C211yesmaximal, characteristic, complemented
14#1495×C139C211yesmaximal, characteristic, complemented
15#1486×C139C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C139—21no—
17#555×C139C2211yescharacteristic
18#554×C139C2211yescharacteristic
19#553×C139—21no—
20#553×C139—21no—
21#550×C139C2211yescharacteristic
22#546×C139—22no—
23#546×C139—21no—
24D42×C139—21no—
25D42×C139C2211yescharacteristic
26#540×C139—21no—
27#538×C139—22no—
28#532×C139C2211yescharacteristic
29#532×C139C2211yescharacteristic, complemented
30#529×C139C2211yescharacteristic
31#525×C139—21no—
32C2×#121×C139—21no—
33#518×C139—21no—
34C2×C4×D4×C139C2211yescharacteristic
35#493×C139C2211yescharacteristic, complemented
36#492×C139C2211yescharacteristic, complemented
37#487×C139C2211yescharacteristic, complemented
38#486×C139C2211yescharacteristic, complemented
39#478×C139—21no—
40#475×C139C2211yescharacteristic, complemented
41#474×C139C2211yescharacteristic, complemented
42#469×C139—21no—
43#468×C139—21no—
44#463×C139—22no—
45#463×C139—21no—
46#463×C139—21no—
47#463×C139—21no—
48#461×C139C2211yescharacteristic
49#461×C139C2211yescharacteristic, complemented
50#460×C139C2211yescharacteristic, complemented
51#459×C139C2211yescharacteristic
52#459×C139C2211yescharacteristic, complemented
53#459×C139C2211yescharacteristic, complemented
54#449×C139—22no—
55#431×C139C2211yescharacteristic, complemented
56#423×C139C2211yescharacteristic, complemented
57#423×C139C2211yescharacteristic, complemented
58#417×C139—21no—
59#333×C139C2211yescharacteristic, complemented
60#333×C139C2211yescharacteristic, complemented
61#331×C139C2211yescharacteristic, complemented
62#331×C139C2211yescharacteristic, complemented
63Q8⋊C8×C139C2211yescharacteristic, complemented
64Q8⋊C8×C139C2211yescharacteristic, complemented
65D4⋊C8×C139C2211yescharacteristic
66D4⋊C8×C139C2211yescharacteristic
67D4⋊C8×C139C2211yescharacteristic, complemented
68D4⋊C8×C139C2211yescharacteristic, complemented
69D4⋊C8×C139C2211yescharacteristic, complemented
70D4⋊C8×C139C2211yescharacteristic, complemented
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139D412yes—
74C22×D4×C139—22no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139D411yescharacteristic
78C23×C4×C139—21no—
79AGL(1,ℤ/8)×C139—44no—
80C2×SD16×C139—21no—
81C2×SD16×C139—21no—
82C2×SD16×C139—22no—
83C2×SD16×C139—21no—
84C2×D8×C139—21no—
85C2×D8×C139—21no—
86C2×D8×C139—22no—
87C2×D8×C139—21no—
88C2×M16×C139—21no—
89C2×M16×C139—21no—
90C4⋊Q8×C139C2311yescharacteristic
91C4⋊Q8×C139C2311yescharacteristic
92#127×C139—21no—
93#127×C139C2311yescharacteristic
94#127×C139C2311yescharacteristic
95#126×C139—22no—
96#126×C139—21no—
97#125×C139—21no—
98#125×C139D411yescharacteristic
99#124×C139—22no—
100#124×C139—21no—
101#124×C139D411yescharacteristic
102#124×C139D412yes—
103#123×C139—22no—
104#123×C139—22no—
105#123×C139—22no—
106#123×C139—21no—
107C22⋊Q8×C139—21no—
108C22⋊Q8×C139—22no—
109C22⋊Q8×C139D411yescharacteristic
110#121×C139—22no—
111#121×C139—22no—
112#121×C139—22no—
113#121×C139—22no—
114#121×C139—21no—
115#121×C139—22no—
116#121×C139—21no—
117#121×C139—21no—
118#121×C139—21no—
119#121×C139—21no—
120#121×C139—21no—
121#121×C139—21no—
122#121×C139—21no—
123#121×C139—21no—
124#121×C139D411yescharacteristic
125#120×C139—22no—
126#120×C139—22no—
127#120×C139—22no—
128C4×Q8×C139C2311yescharacteristic
129C4×D4×C139—22no—
130C4×D4×C139—22no—
131C4×D4×C139—22no—
132C4×D4×C139—21no—
133C4×D4×C139—21no—
134C4×D4×C139—21no—
135C4×D4×C139—21no—
136C4×D4×C139—21no—
137C4×D4×C139—21no—
138C4×D4×C139—21no—
139C4×D4×C139—21no—
140C4×D4×C139—21no—
141C4×D4×C139D411yescharacteristic
142C4×D4×C139D411yescharacteristic
143C4×D4×C139C2311yescharacteristic
144C4×D4×C139C2311yescharacteristic
145C4×D4×C139C2311yescharacteristic
146#117×C139—21no—
147#117×C139—21no—
148#117×C139—21no—
149C2×C4⋊C4×C139—21no—
150C2×C4⋊C4×C139D411yescharacteristic
151C2×C22⋊C4×C139—22no—
152C2×C22⋊C4×C139—22no—
153C2×C22⋊C4×C139—21no—
154C2×C42×C139C2311yescharacteristic
155#107×C139—21no—
156#106×C139—21no—
157C4⋊C8×C139—21no—
158C4⋊C8×C139—21no—
159C4⋊C8×C139—21no—
160C4⋊C8×C139C2311yescharacteristic
161C4⋊C8×C139C2311yescharacteristic
162C4⋊C8×C139C2311yescharacteristic
163C4⋊C8×C139C2311yescharacteristic
164#103×C139—22no—
165#103×C139—21no—
166#103×C139—21no—
167#103×C139—21no—
168#102×C139—22no—
169#102×C139—21no—
170#102×C139—21no—
171#102×C139—21no—
172#102×C139—21no—
173#102×C139—21no—
174C22⋊C8×C139—21no—
175C4×C8×C139C2311yescharacteristic
176C4×C8×C139C2311yescharacteristic
177C24×C139—22no—
178C24×C139—21no—
179#41×C139—42no—
180#41×C139—42no—
181#41×C139—81no—
182#41×C139—81no—
183#41×C139—82no—
184C2×Q8×C139—21no—
185C2×Q8×C139C2×D411yescharacteristic
186C2×Q8×C139C2×D412yes—
187C2×D4×C139—22no—
188C2×D4×C139—22no—
189C2×D4×C139—22no—
190C2×D4×C139—21no—
191C2×D4×C139—22no—
192C2×D4×C139—22no—
193C2×D4×C139—22no—
194C2×D4×C139—22no—
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—41no—
202C2×D4×C139—42no—
203C2×D4×C139—42no—
204C2×D4×C139—41no—
205C2×D4×C139—81no—
206C2×D4×C139—81no—
207C2×D4×C139—84no—
208C2×D4×C139C2×D411yescharacteristic
209C2×D4×C139C2×D411yescharacteristic
210C2×D4×C139C2×D411yescharacteristic
211C2×D4×C139C2×D412yes—
212C22×C4×C139—22no—
213C22×C4×C139—22no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—22no—
220C22×C4×C139—21no—
221C22×C4×C139—41no—
222C22×C4×C139—81no—
223C22×C4×C139—81no—
224C22×C4×C139C2×D411yescharacteristic
225C22×C4×C139C2×D411yescharacteristic
226C22×C4×C139C2×D411yescharacteristic
227SD16×C139—42no—
228SD16×C139—42no—
229SD16×C139—81no—
230SD16×C139—82no—
231D8×C139—42no—
232D8×C139—42no—
233D8×C139—81no—
234D8×C139—82no—
235M16×C139—42no—
236M16×C139—81no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C4⋊C4×C139—22no—
244C4⋊C4×C139—22no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139C2×D411yescharacteristic
255C4⋊C4×C139C2×D411yescharacteristic
256C4⋊C4×C139C2×D411yescharacteristic
257C4⋊C4×C139C2×D411yescharacteristic
258C22⋊C4×C139—22no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—22no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—21no—
264C22⋊C4×C139—21no—
265C22⋊C4×C139—21no—
266C22⋊C4×C139—21no—
267C22⋊C4×C139—22no—
268C22⋊C4×C139—21no—
269C22⋊C4×C139—21no—
270C22⋊C4×C139—22no—
271C22⋊C4×C139—21no—
272C22⋊C4×C139—21no—
273C22⋊C4×C139—21no—
274C22⋊C4×C139—41no—
275C22⋊C4×C139—41no—
276C42×C139—22no—
277C42×C139—21no—
278C42×C139C2×D411yescharacteristic
279C42×C139C2×D411yescharacteristic
280C42×C139C2×D411yescharacteristic
281C42×C139C2411yescharacteristic
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—22no—
286C23×C139—42no—
287C23×C139—42no—
288C23×C139—44no—
289C23×C139—41no—
290C23×C139—81no—
291C23×C139—82no—
292C23×C139—82no—
293C23×C139#12011yescharacteristic
294Q8×C139—21no—
295Q8×C139—21no—
296Q8×C139—42no—
297Q8×C139—41no—
298Q8×C139—41no—
299D4×C139—21no—
300D4×C139—21no—
301D4×C139—21no—
302D4×C139—21no—
303D4×C139—21no—
304D4×C139—42no—
305D4×C139—42no—
306D4×C139—42no—
307D4×C139—44no—
308D4×C139—42no—
309D4×C139—44no—
310D4×C139—41no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—82no—
319D4×C139—82no—
320D4×C139—82no—
321D4×C139—82no—
322D4×C139—82no—
323D4×C139AGL(1,ℤ/8)12yes—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—22no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—81no—
343C2×C4×C139—81no—
344C2×C4×C139—82no—
345C2×C4×C139—82no—
346C2×C4×C139—81no—
347C2×C4×C139—82no—
348C2×C4×C139—82no—
349C2×C4×C139#12011yescharacteristic
350C2×C4×C139#12011yescharacteristic
351C2×C4×C139#12011yescharacteristic
352C2×C4×C139C22×D411yescharacteristic
353C2×C4×C139C22×D411yescharacteristic
354C2×C4×C139C22×D411yescharacteristic
355C8×C139—41no—
356C8×C139—41no—
357C8×C139—41no—
358C8×C139—41no—
359C8×C139—41no—
360C8×C139—41no—
361C22×C139—21no—
362C22×C139—22no—
363C22×C139—21no—
364C22×C139—21no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—42no—
370C22×C139—41no—
371C22×C139—42no—
372C22×C139—41no—
373C22×C139—42no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—84no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—164no—
381C22×C139C2×#12011yescharacteristic
382C4×C139—21no—
383C4×C139—21no—
384C4×C139—21no—
385C4×C139—21no—
386C4×C139—41no—
387C4×C139—41no—
388C4×C139—41no—
389C4×C139—41no—
390C4×C139—41no—
391C4×C139—42no—
392C4×C139—81no—
393C4×C139C2×AGL(1,ℤ/8)11yescharacteristic
394C4×C139#57511yescharacteristic
395C4×C139#57611yescharacteristic
396C4×C139#57711yescharacteristic
397C2×C139—41no—
398C2×C139—42no—
399C2×C139—81no—
400C2×C139—82no—
401C2×C139—81no—
402C2×C139—161no—
403C2×C139#300611yescharacteristic
404C2×C139#301211yescharacteristic
405C2×C139#301911yescharacteristic
406#18810C13911yesmaximal, characteristic, direct product factor, Sylow
407C139#1881011yescharacteristic, direct product factor, Sylow
408#3519C2×C13911yescharacteristic, complemented
409#3251C2×C13911yescharacteristic, complemented
410#3207C2×C13911yescharacteristic, complemented
411#3036C2×C13911yescharacteristic, complemented
412#1646C2×C13911yescharacteristic, complemented
413#1643C2×C13911yescharacteristic, complemented
414#1642C2×C13911yescharacteristic, complemented
415#1639C2×C13911yescharacteristic, complemented
416#1624C2×C13911yescharacteristic, complemented
417#1622C2×C13911yescharacteristic, complemented
418#1621C2×C13911yescharacteristic, complemented
419#1619C2×C13911yescharacteristic, complemented
420#1560C2×C13911yescharacteristic, complemented
421#1495C2×C13911yescharacteristic, complemented
422#1486C2×C13911yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424#555C22×C13911yescharacteristic
425#554C22×C13911yescharacteristic
426#553—21no—
427#553—21no—
428#550C22×C13911yescharacteristic
429#546—22no—
430#546—21no—
431D42—21no—
432D42C22×C13911yescharacteristic
433#540—21no—
434#538—22no—
435#532C22×C13911yescharacteristic
436#532C22×C13911yescharacteristic, complemented
437#529C22×C13911yescharacteristic
438#525—21no—
439C2×#121—21no—
440#518—21no—
441C2×C4×D4C22×C13911yescharacteristic
442#493C22×C13911yescharacteristic, complemented
443#492C22×C13911yescharacteristic, complemented
444#487C22×C13911yescharacteristic, complemented
445#486C22×C13911yescharacteristic, complemented
446#478—21no—
447#475C22×C13911yescharacteristic, complemented
448#474C22×C13911yescharacteristic, complemented
449#469—21no—
450#468—21no—
451#463—22no—
452#463—21no—
453#463—21no—
454#463—21no—
455#461C22×C13911yescharacteristic
456#461C22×C13911yescharacteristic, complemented
457#460C22×C13911yescharacteristic, complemented
458#459C22×C13911yescharacteristic
459#459C22×C13911yescharacteristic, complemented
460#459C22×C13911yescharacteristic, complemented
461#449—22no—
462#431C22×C13911yescharacteristic, complemented
463#423C22×C13911yescharacteristic, complemented
464#423C22×C13911yescharacteristic, complemented
465#417—21no—
466#333C22×C13911yescharacteristic, complemented
467#333C22×C13911yescharacteristic, complemented
468#331C22×C13911yescharacteristic, complemented
469#331C22×C13911yescharacteristic, complemented
470Q8⋊C8C22×C13911yescharacteristic, complemented
471Q8⋊C8C22×C13911yescharacteristic, complemented
472D4⋊C8C22×C13911yescharacteristic
473D4⋊C8C22×C13911yescharacteristic
474D4⋊C8C22×C13911yescharacteristic, complemented
475D4⋊C8C22×C13911yescharacteristic, complemented
476D4⋊C8C22×C13911yescharacteristic, complemented
477D4⋊C8C22×C13911yescharacteristic, complemented
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C13912yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C13911yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C13911yescharacteristic
498C4⋊Q8C23×C13911yescharacteristic
499#127—21no—
500#127C23×C13911yescharacteristic
501#127C23×C13911yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C13911yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C13911yescharacteristic
509#124D4×C13912yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C13911yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C13911yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C13911yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C13911yescharacteristic
549C4×D4D4×C13911yescharacteristic
550C4×D4C23×C13911yescharacteristic
551C4×D4C23×C13911yescharacteristic
552C4×D4C23×C13911yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C13911yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C13911yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C13911yescharacteristic
568C4⋊C8C23×C13911yescharacteristic
569C4⋊C8C23×C13911yescharacteristic
570C4⋊C8C23×C13911yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C13911yescharacteristic
583C4×C8C23×C13911yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C13911yescharacteristic
593C2×Q8C2×D4×C13912yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C13911yescharacteristic
616C2×D4C2×D4×C13911yescharacteristic
617C2×D4C2×D4×C13911yescharacteristic
618C2×D4C2×D4×C13912yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C13911yescharacteristic
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13911yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C13911yescharacteristic
662C4⋊C4C2×D4×C13911yescharacteristic
663C4⋊C4C2×D4×C13911yescharacteristic
664C4⋊C4C2×D4×C13911yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C13911yescharacteristic
686C42C2×D4×C13911yescharacteristic
687C42C2×D4×C13911yescharacteristic
688C42C24×C13911yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C13911yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C13912yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C13911yescharacteristic
757C2×C4#120×C13911yescharacteristic
758C2×C4#120×C13911yescharacteristic
759C2×C4C22×D4×C13911yescharacteristic
760C2×C4C22×D4×C13911yescharacteristic
761C2×C4C22×D4×C13911yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C13911yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C13911yescharacteristic
801C4#575×C13911yescharacteristic
802C4#576×C13911yescharacteristic
803C4#577×C13911yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2#3006×C13911yescharacteristic
811C2#3012×C13911yescharacteristic
812C2#3019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC42C24×C139
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3519×C139C2semidirect
2. #3251×C139C2semidirect
3. #3207×C139C2semidirect
4. #3036×C139C2semidirect
5. #1646×C139C2semidirect
6. #1643×C139C2semidirect
7. #1642×C139C2semidirect
8. #1639×C139C2semidirect
9. #1624×C139C2semidirect
10. #1622×C139C2semidirect
11. #1621×C139C2semidirect
12. #1619×C139C2semidirect
13. #1560×C139C2semidirect
14. #1495×C139C2semidirect
15. #1486×C139C2semidirect
29. #532×C139C22semidirect
35. #493×C139C22semidirect
36. #492×C139C22semidirect
37. #487×C139C22semidirect
38. #486×C139C22semidirect
40. #475×C139C22semidirect
41. #474×C139C22semidirect
49. #461×C139C22semidirect
50. #460×C139C22semidirect
52. #459×C139C22semidirect
53. #459×C139C22semidirect
55. #431×C139C22semidirect
56. #423×C139C22semidirect
57. #423×C139C22semidirect
59. #333×C139C22semidirect
60. #333×C139C22semidirect
61. #331×C139C22semidirect
62. #331×C139C22semidirect
63. Q8⋊C8×C139C22semidirect
64. Q8⋊C8×C139C22semidirect
67. D4⋊C8×C139C22semidirect
68. D4⋊C8×C139C22semidirect
69. D4⋊C8×C139C22semidirect
70. D4⋊C8×C139C22semidirect
406. #18810C139direct (N × H)
407. C139#18810direct (N × H)
408. #3519C2×C139semidirect
409. #3251C2×C139semidirect
410. #3207C2×C139semidirect
411. #3036C2×C139semidirect
412. #1646C2×C139semidirect
413. #1643C2×C139semidirect
414. #1642C2×C139semidirect
415. #1639C2×C139semidirect
416. #1624C2×C139semidirect
417. #1622C2×C139semidirect
418. #1621C2×C139semidirect
419. #1619C2×C139semidirect
420. #1560C2×C139semidirect
421. #1495C2×C139semidirect
422. #1486C2×C139semidirect
436. #532C22×C139semidirect
442. #493C22×C139semidirect
443. #492C22×C139semidirect
444. #487C22×C139semidirect
445. #486C22×C139semidirect
447. #475C22×C139semidirect
448. #474C22×C139semidirect
456. #461C22×C139semidirect
457. #460C22×C139semidirect
459. #459C22×C139semidirect
460. #459C22×C139semidirect
462. #431C22×C139semidirect
463. #423C22×C139semidirect
464. #423C22×C139semidirect
466. #333C22×C139semidirect
467. #333C22×C139semidirect
468. #331C22×C139semidirect
469. #331C22×C139semidirect
470. Q8⋊C8C22×C139semidirect
471. Q8⋊C8C22×C139semidirect
474. D4⋊C8C22×C139semidirect
475. D4⋊C8C22×C139semidirect
476. D4⋊C8C22×C139semidirect
477. D4⋊C8C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3519×C1392
#3251×C1392
#3207×C1392
#3036×C1392
#1646×C1392
#1643×C1392
#1642×C1392
#1639×C1392
#1624×C1392
#1622×C1392
#1621×C1392
#1619×C1392
#1560×C1392
#1495×C1392
#1486×C1392
#18810139