Finite Group Databasebeta

← C139×#19010 #48013606

Subgroups — C139×#19010 #48013606

Order 35584.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3529×C139C211yesmaximal, characteristic, complemented
2#3219×C139C211yesmaximal, characteristic, complemented
3#3214×C139C211yesmaximal, characteristic, complemented
4#3180×C139C211yesmaximal, characteristic, complemented
5#1664×C139C211yesmaximal, characteristic, complemented
6#1662×C139C211yesmaximal, characteristic, complemented
7#1661×C139C211yesmaximal, characteristic, complemented
8#1659×C139C211yesmaximal, characteristic, complemented
9#1657×C139C211yesmaximal, characteristic, complemented
10#1656×C139C211yesmaximal, characteristic, complemented
11#1656×C139C211yesmaximal, characteristic, complemented
12#1655×C139C211yesmaximal, characteristic, complemented
13#1535×C139C211yesmaximal, characteristic, complemented
14#1532×C139C211yesmaximal, characteristic, complemented
15#1530×C139C211yesmaximal, characteristic, complemented
16#563×C139—21no—
17#563×C139C2211yescharacteristic
18#562×C139—21no—
19#562×C139—21no—
20#562×C139C2211yescharacteristic
21#562×C139C2211yescharacteristic
22H(3,𝔽4)×C139C2211yescharacteristic
23#560×C139—21no—
24#560×C139—21no—
25#560×C139—21no—
26#532×C139—21no—
27#532×C139C2211yescharacteristic
28#532×C139C2211yescharacteristic, complemented
29#529×C139—21no—
30#529×C139—21no—
31#529×C139C2211yescharacteristic
32#529×C139C2211yescharacteristic
33#525×C139—21no—
34#525×C139—21no—
35#525×C139—21no—
36#501×C139C2211yescharacteristic, complemented
37#497×C139C2211yescharacteristic
38#496×C139C2211yescharacteristic
39#496×C139C2211yescharacteristic
40#496×C139C2211yescharacteristic
41#496×C139C2211yescharacteristic, complemented
42#491×C139C2211yescharacteristic, complemented
43#490×C139C2211yescharacteristic, complemented
44#490×C139C2211yescharacteristic, complemented
45#489×C139C2211yescharacteristic
46#489×C139C2211yescharacteristic
47#489×C139C2211yescharacteristic, complemented
48#466×C139—21no—
49#465×C139—21no—
50#464×C139—21no—
51#463×C139—21no—
52#461×C139—21no—
53#459×C139—21no—
54#452×C139—21no—
55#449×C139—21no—
56#449×C139—21no—
57#449×C139—21no—
58#442×C139—21no—
59#440×C139—21no—
60#432×C139C2211yescharacteristic, complemented
61#432×C139C2211yescharacteristic, complemented
62C2×#97×C139C2211yescharacteristic, complemented
63#330×C139C2211yescharacteristic, complemented
64#330×C139C2211yescharacteristic, complemented
65#330×C139C2211yescharacteristic, complemented
66#330×C139C2211yescharacteristic, complemented
67#329×C139C2211yescharacteristic
68#329×C139C2211yescharacteristic
69#329×C139C2211yescharacteristic
70#329×C139C2211yescharacteristic
71#329×C139C2211yescharacteristic
72#329×C139C2211yescharacteristic
73#329×C139C2211yescharacteristic, complemented
74#329×C139C2211yescharacteristic, complemented
75C2×#41×C139—21no—
76C2×#41×C139—21no—
77C2×#41×C139D411yescharacteristic
78C2×#41×C139D411yescharacteristic
79C23×C4×C139—21no—
80C2×Q16×C139—21no—
81C2×SD16×C139—21no—
82C2×SD16×C139—21no—
83C2×SD16×C139—21no—
84C2×SD16×C139—21no—
85C2×SD16×C139—21no—
86C2×D8×C139—21no—
87C2×D8×C139—21no—
88C2×D8×C139—21no—
89C2×D8×C139—21no—
90C22×C8×C139—21no—
91C4⋊Q8×C139—21no—
92C4⋊Q8×C139D411yescharacteristic
93C4⋊Q8×C139C2311yescharacteristic
94#127×C139—21no—
95#127×C139D411yescharacteristic
96#127×C139C2311yescharacteristic
97#126×C139—21no—
98#126×C139—21no—
99#126×C139—21no—
100#126×C139—21no—
101#126×C139—21no—
102#126×C139—21no—
103#125×C139—21no—
104#125×C139—21no—
105#125×C139C2311yescharacteristic
106#125×C139C2311yescharacteristic
107#124×C139—21no—
108#124×C139—21no—
109#124×C139—21no—
110#124×C139—21no—
111#124×C139—21no—
112#124×C139C2311yescharacteristic
113#124×C139C2311yescharacteristic
114#124×C139C2311yescharacteristic
115#124×C139C2311yescharacteristic
116#123×C139—21no—
117#123×C139—21no—
118#123×C139—21no—
119#123×C139—21no—
120#123×C139—21no—
121#123×C139—21no—
122#123×C139—21no—
123#123×C139—21no—
124#123×C139—21no—
125#123×C139—21no—
126#123×C139—21no—
127#123×C139—21no—
128C22⋊Q8×C139—21no—
129C22⋊Q8×C139—21no—
130C22⋊Q8×C139—21no—
131C22⋊Q8×C139—21no—
132C22⋊Q8×C139—21no—
133C22⋊Q8×C139—21no—
134C22⋊Q8×C139—21no—
135C22⋊Q8×C139—21no—
136C22⋊Q8×C139D411yescharacteristic
137C22⋊Q8×C139D411yescharacteristic
138#121×C139—21no—
139#121×C139—21no—
140#121×C139—21no—
141#121×C139—21no—
142#121×C139—21no—
143#121×C139—21no—
144#121×C139—21no—
145#121×C139—21no—
146#121×C139—21no—
147#121×C139—21no—
148#121×C139—21no—
149#121×C139—21no—
150#121×C139—21no—
151#121×C139—21no—
152#121×C139—21no—
153#121×C139—21no—
154#121×C139D411yescharacteristic
155#121×C139D411yescharacteristic
156#120×C139—21no—
157#120×C139—21no—
158#120×C139—21no—
159#120×C139—21no—
160#120×C139—21no—
161#120×C139—21no—
162C4×Q8×C139D411yescharacteristic
163C4×Q8×C139D411yescharacteristic
164C4×D4×C139—21no—
165C4×D4×C139—21no—
166C4×D4×C139—21no—
167C4×D4×C139—21no—
168C4×D4×C139—21no—
169C4×D4×C139—21no—
170C4×D4×C139—21no—
171C4×D4×C139—21no—
172C4×D4×C139—21no—
173C4×D4×C139—21no—
174C4×D4×C139D411yescharacteristic
175C4×D4×C139D411yescharacteristic
176#117×C139—21no—
177#117×C139—21no—
178#117×C139—21no—
179C2×C42×C139—21no—
180C2×C42×C139C2311yescharacteristic
181#107×C139—21no—
182#106×C139—21no—
183C4⋊C8×C139—21no—
184C4⋊C8×C139—21no—
185#103×C139—21no—
186#103×C139—21no—
187#103×C139—21no—
188#103×C139—21no—
189#103×C139—21no—
190#102×C139—21no—
191#102×C139—21no—
192#102×C139—21no—
193#102×C139—21no—
194#102×C139—21no—
195#102×C139—21no—
196#102×C139—21no—
197C22⋊C8×C139—21no—
198C22⋊C8×C139—21no—
199#97×C139—21no—
200#97×C139C2311yescharacteristic
201#97×C139C2311yescharacteristic
202#97×C139C2311yescharacteristic
203#97×C139C2311yescharacteristic
204#97×C139C2311yescharacteristic
205#97×C139C2311yescharacteristic
206C24×C139—21no—
207#41×C139—81no—
208#41×C139—81no—
209#41×C139—82no—
210#41×C139—81no—
211#41×C139—81no—
212C2×Q8×C139—21no—
213C2×Q8×C139—21no—
214C2×Q8×C139C2×D411yescharacteristic
215C2×Q8×C139C2×D411yescharacteristic
216C2×Q8×C139C2×D411yescharacteristic
217C2×Q8×C139C2×D411yescharacteristic
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
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—41no—
235C2×D4×C139C2×D411yescharacteristic
236C2×D4×C139C2×D411yescharacteristic
237C2×D4×C139C2×D411yescharacteristic
238C2×D4×C139C2×D411yescharacteristic
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—41no—
249C22×C4×C139—82no—
250C22×C4×C139C2×D411yescharacteristic
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139C2×D411yescharacteristic
253Q16×C139—81no—
254SD16×C139—42no—
255SD16×C139—81no—
256SD16×C139—81no—
257SD16×C139—81no—
258SD16×C139—81no—
259D8×C139—42no—
260D8×C139—81no—
261D8×C139—81no—
262D8×C139—81no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—42no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139—21no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139C2×D411yescharacteristic
289C4⋊C4×C139C2×D411yescharacteristic
290C4⋊C4×C139C2×D411yescharacteristic
291C4⋊C4×C139C2×D411yescharacteristic
292C22⋊C4×C139—21no—
293C22⋊C4×C139—21no—
294C22⋊C4×C139—21no—
295C22⋊C4×C139—21no—
296C22⋊C4×C139—21no—
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—21no—
304C22⋊C4×C139—21no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—21no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—21no—
312C22⋊C4×C139—21no—
313C22⋊C4×C139—21no—
314C22⋊C4×C139—21no—
315C22⋊C4×C139—21no—
316C22⋊C4×C139—41no—
317C22⋊C4×C139—41no—
318C42×C139—21no—
319C42×C139—21no—
320C42×C139—21no—
321C42×C139—21no—
322C42×C139C2×D411yescharacteristic
323C42×C139C2×D411yescharacteristic
324C42×C139C2×D411yescharacteristic
325C42×C139C2411yescharacteristic
326C23×C139—21no—
327C23×C139—21no—
328C23×C139—21no—
329C23×C139—21no—
330C23×C139—41no—
331C23×C139—81no—
332C23×C139—81no—
333C23×C139—81no—
334C23×C139#12011yescharacteristic
335Q8×C139—41no—
336Q8×C139—41no—
337Q8×C139—41no—
338Q8×C139—41no—
339Q8×C139—41no—
340Q8×C139—41no—
341Q8×C139—81no—
342D4×C139—41no—
343D4×C139—41no—
344D4×C139—41no—
345D4×C139—41no—
346D4×C139—41no—
347D4×C139—41no—
348D4×C139—41no—
349D4×C139—41no—
350D4×C139—41no—
351D4×C139—41no—
352D4×C139—81no—
353D4×C139—81no—
354D4×C139—81no—
355D4×C139—81no—
356D4×C139—81no—
357D4×C139—81no—
358D4×C139—81no—
359D4×C139—81no—
360D4×C139—81no—
361D4×C139—81no—
362D4×C139—81no—
363D4×C139—81no—
364D4×C139—81no—
365D4×C139—82no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—21no—
369C2×C4×C139—21no—
370C2×C4×C139—21no—
371C2×C4×C139—21no—
372C2×C4×C139—21no—
373C2×C4×C139—21no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—42no—
378C2×C4×C139—42no—
379C2×C4×C139—42no—
380C2×C4×C139—42no—
381C2×C4×C139—41no—
382C2×C4×C139—82no—
383C2×C4×C139—81no—
384C2×C4×C139—81no—
385C2×C4×C139—81no—
386C2×C4×C139—81no—
387C2×C4×C139—81no—
388C2×C4×C139#12011yescharacteristic
389C2×C4×C139#12011yescharacteristic
390C2×C4×C139#12011yescharacteristic
391C2×C4×C139C22×D411yescharacteristic
392C2×C4×C139C22×D411yescharacteristic
393C2×C4×C139C22×D411yescharacteristic
394C8×C139—22no—
395C8×C139—41no—
396C8×C139—41no—
397C8×C139—41no—
398C8×C139—41no—
399C8×C139—41no—
400C22×C139—21no—
401C22×C139—21no—
402C22×C139—21no—
403C22×C139—41no—
404C22×C139—41no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—41no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—41no—
414C22×C139—41no—
415C22×C139—84no—
416C22×C139—81no—
417C22×C139—81no—
418C22×C139—81no—
419C22×C139C2×#12011yescharacteristic
420C4×C139—21no—
421C4×C139—21no—
422C4×C139—21no—
423C4×C139—21no—
424C4×C139—21no—
425C4×C139—21no—
426C4×C139—41no—
427C4×C139—41no—
428C4×C139—41no—
429C4×C139—41no—
430C4×C139—41no—
431C4×C139—41no—
432C4×C139—41no—
433C4×C139—41no—
434C4×C139—81no—
435C2×C139—41no—
436C2×C139—81no—
437C2×C139—81no—
438C2×C139—81no—
439C2×C139—81no—
440C2×C139—161no—
441C2×C139#301811yescharacteristic
442C2×C139#301911yescharacteristic
443C2×C139#302111yescharacteristic
444#19010C13911yesmaximal, characteristic, direct product factor, Sylow
445C139#1901011yescharacteristic, direct product factor, Sylow
446#3529C2×C13911yescharacteristic, complemented
447#3219C2×C13911yescharacteristic, complemented
448#3214C2×C13911yescharacteristic, complemented
449#3180C2×C13911yescharacteristic, complemented
450#1664C2×C13911yescharacteristic, complemented
451#1662C2×C13911yescharacteristic, complemented
452#1661C2×C13911yescharacteristic, complemented
453#1659C2×C13911yescharacteristic, complemented
454#1657C2×C13911yescharacteristic, complemented
455#1656C2×C13911yescharacteristic, complemented
456#1656C2×C13911yescharacteristic, complemented
457#1655C2×C13911yescharacteristic, complemented
458#1535C2×C13911yescharacteristic, complemented
459#1532C2×C13911yescharacteristic, complemented
460#1530C2×C13911yescharacteristic, complemented
461#563—21no—
462#563C22×C13911yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C13911yescharacteristic
466#562C22×C13911yescharacteristic
467H(3,𝔽4)C22×C13911yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C13911yescharacteristic
473#532C22×C13911yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C13911yescharacteristic
477#529C22×C13911yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C13911yescharacteristic, complemented
482#497C22×C13911yescharacteristic
483#496C22×C13911yescharacteristic
484#496C22×C13911yescharacteristic
485#496C22×C13911yescharacteristic
486#496C22×C13911yescharacteristic, complemented
487#491C22×C13911yescharacteristic, complemented
488#490C22×C13911yescharacteristic, complemented
489#490C22×C13911yescharacteristic, complemented
490#489C22×C13911yescharacteristic
491#489C22×C13911yescharacteristic
492#489C22×C13911yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C13911yescharacteristic, complemented
506#432C22×C13911yescharacteristic, complemented
507C2×#97C22×C13911yescharacteristic, complemented
508#330C22×C13911yescharacteristic, complemented
509#330C22×C13911yescharacteristic, complemented
510#330C22×C13911yescharacteristic, complemented
511#330C22×C13911yescharacteristic, complemented
512#329C22×C13911yescharacteristic
513#329C22×C13911yescharacteristic
514#329C22×C13911yescharacteristic
515#329C22×C13911yescharacteristic
516#329C22×C13911yescharacteristic
517#329C22×C13911yescharacteristic
518#329C22×C13911yescharacteristic, complemented
519#329C22×C13911yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C13911yescharacteristic
523C2×#41D4×C13911yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C13911yescharacteristic
538C4⋊Q8C23×C13911yescharacteristic
539#127—21no—
540#127D4×C13911yescharacteristic
541#127C23×C13911yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C13911yescharacteristic
551#125C23×C13911yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C13911yescharacteristic
558#124C23×C13911yescharacteristic
559#124C23×C13911yescharacteristic
560#124C23×C13911yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C13911yescharacteristic
582C22⋊Q8D4×C13911yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C13911yescharacteristic
600#121D4×C13911yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C13911yescharacteristic
608C4×Q8D4×C13911yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C13911yescharacteristic
620C4×D4D4×C13911yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C13911yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C13911yescharacteristic
646#97C23×C13911yescharacteristic
647#97C23×C13911yescharacteristic
648#97C23×C13911yescharacteristic
649#97C23×C13911yescharacteristic
650#97C23×C13911yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C13911yescharacteristic
660C2×Q8C2×D4×C13911yescharacteristic
661C2×Q8C2×D4×C13911yescharacteristic
662C2×Q8C2×D4×C13911yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C13911yescharacteristic
681C2×D4C2×D4×C13911yescharacteristic
682C2×D4C2×D4×C13911yescharacteristic
683C2×D4C2×D4×C13911yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C13911yescharacteristic
696C22×C4C2×D4×C13911yescharacteristic
697C22×C4C2×D4×C13911yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C13911yescharacteristic
734C4⋊C4C2×D4×C13911yescharacteristic
735C4⋊C4C2×D4×C13911yescharacteristic
736C4⋊C4C2×D4×C13911yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C13911yescharacteristic
768C42C2×D4×C13911yescharacteristic
769C42C2×D4×C13911yescharacteristic
770C42C24×C13911yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C13911yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C13911yescharacteristic
834C2×C4#120×C13911yescharacteristic
835C2×C4#120×C13911yescharacteristic
836C2×C4C22×D4×C13911yescharacteristic
837C2×C4C22×D4×C13911yescharacteristic
838C2×C4C22×D4×C13911yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C13911yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2#3018×C13911yescharacteristic
887C2#3019×C13911yescharacteristic
888C2#3021×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. #3529×C139C2semidirect
2. #3219×C139C2semidirect
3. #3214×C139C2semidirect
4. #3180×C139C2semidirect
5. #1664×C139C2semidirect
6. #1662×C139C2semidirect
7. #1661×C139C2semidirect
8. #1659×C139C2semidirect
9. #1657×C139C2semidirect
10. #1656×C139C2semidirect
11. #1656×C139C2semidirect
12. #1655×C139C2semidirect
13. #1535×C139C2semidirect
14. #1532×C139C2semidirect
15. #1530×C139C2semidirect
28. #532×C139C22semidirect
36. #501×C139C22semidirect
41. #496×C139C22semidirect
42. #491×C139C22semidirect
43. #490×C139C22semidirect
44. #490×C139C22semidirect
47. #489×C139C22semidirect
60. #432×C139C22semidirect
61. #432×C139C22semidirect
62. C2×#97×C139C22semidirect
63. #330×C139C22semidirect
64. #330×C139C22semidirect
65. #330×C139C22semidirect
66. #330×C139C22semidirect
73. #329×C139C22semidirect
74. #329×C139C22semidirect
444. #19010C139direct (N × H)
445. C139#19010direct (N × H)
446. #3529C2×C139semidirect
447. #3219C2×C139semidirect
448. #3214C2×C139semidirect
449. #3180C2×C139semidirect
450. #1664C2×C139semidirect
451. #1662C2×C139semidirect
452. #1661C2×C139semidirect
453. #1659C2×C139semidirect
454. #1657C2×C139semidirect
455. #1656C2×C139semidirect
456. #1656C2×C139semidirect
457. #1655C2×C139semidirect
458. #1535C2×C139semidirect
459. #1532C2×C139semidirect
460. #1530C2×C139semidirect
473. #532C22×C139semidirect
481. #501C22×C139semidirect
486. #496C22×C139semidirect
487. #491C22×C139semidirect
488. #490C22×C139semidirect
489. #490C22×C139semidirect
492. #489C22×C139semidirect
505. #432C22×C139semidirect
506. #432C22×C139semidirect
507. C2×#97C22×C139semidirect
508. #330C22×C139semidirect
509. #330C22×C139semidirect
510. #330C22×C139semidirect
511. #330C22×C139semidirect
518. #329C22×C139semidirect
519. #329C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3529×C1392
#3219×C1392
#3214×C1392
#3180×C1392
#1664×C1392
#1662×C1392
#1661×C1392
#1659×C1392
#1657×C1392
#1656×C1392
#1655×C1392
#1535×C1392
#1532×C1392
#1530×C1392
#19010139