Finite Group Databasebeta

← C139×#12753 #48007349

Subgroups — C139×#12753 #48007349

Order 35584.

936 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3532×C139C211yesmaximal, characteristic
2#2127×C139C211yesmaximal, characteristic, complemented
3#2121×C139C211yesmaximal, characteristic, complemented
4C2×AΣL(1,𝔽16)×C139C211yesmaximal, characteristic, complemented
5#1913×C139C211yesmaximal, characteristic, complemented
6#1911×C139C211yesmaximal, characteristic, complemented
7#1889×C139C211yesmaximal, characteristic, complemented
8H(3,𝔽4)×C139C411yescharacteristic, complemented
9#560×C139—21no—
10#560×C139C411yescharacteristic, complemented
11#551×C139—21no—
12#551×C139C411yescharacteristic, complemented
13#546×C139—21no—
14#546×C139—21no—
15#546×C139—21no—
16D42×C139—21no—
17D42×C139C411yescharacteristic, complemented
18#538×C139—21no—
19#538×C139—21no—
20#538×C139—21no—
21#535×C139—21no—
22#535×C139C2211yescharacteristic
23#534×C139—21no—
24#534×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×#120×C139C2211yescharacteristic
27#518×C139C2211yescharacteristic, complemented
28#421×C139—21no—
29C2×#100×C139C2211yescharacteristic, complemented
30C2×#99×C139—21no—
31C2×#99×C139C2211yescharacteristic, complemented
32C2×#99×C139C2211yescharacteristic, complemented
33#379×C139—21no—
34#354×C139—21no—
35#353×C139—21no—
36#352×C139—21no—
37AΣL(1,𝔽16)×C139—21no—
38AΣL(1,𝔽16)×C139—21no—
39AΣL(1,𝔽16)×C139—21no—
40#342×C139—21no—
41#342×C139—21no—
42H(3,ℤ/4)×C139—21no—
43C25×C139D411yescharacteristic
44C2×#41×C139—21no—
45C2×#41×C139D411yescharacteristic
46C22×D4×C139—21no—
47C22×D4×C139—21no—
48C22×D4×C139—21no—
49C22×D4×C139—21no—
50C22×D4×C139—21no—
51C22×D4×C139D411yescharacteristic
52C22×D4×C139C2311yescharacteristic
53C2×M16×C139—21no—
54#127×C139—21no—
55#127×C139C2×C411yescharacteristic
56#127×C139D411yescharacteristic
57#126×C139—21no—
58#126×C139—21no—
59#126×C139—21no—
60#126×C139—21no—
61#124×C139—21no—
62#124×C139—21no—
63#124×C139—21no—
64#124×C139—21no—
65#124×C139—21no—
66#124×C139C2×C411yescharacteristic
67#124×C139D411yescharacteristic
68#123×C139—21no—
69#123×C139—21no—
70#123×C139—21no—
71#123×C139—21no—
72#123×C139—21no—
73#123×C139—21no—
74#123×C139—21no—
75#123×C139—21no—
76#123×C139C2×C411yescharacteristic
77#123×C139D411yescharacteristic
78C22⋊Q8×C139—21no—
79C22⋊Q8×C139—21no—
80C22⋊Q8×C139—21no—
81#121×C139—21no—
82#121×C139—21no—
83#121×C139—21no—
84#121×C139—21no—
85#121×C139—21no—
86#121×C139—21no—
87#121×C139—21no—
88#121×C139—21no—
89#121×C139—21no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—21no—
93#121×C139—21no—
94#121×C139—21no—
95#121×C139—21no—
96#120×C139—21no—
97#120×C139—21no—
98#120×C139—21no—
99#120×C139—21no—
100#120×C139—21no—
101#120×C139—21no—
102#120×C139—21no—
103#120×C139—21no—
104#120×C139—21no—
105#120×C139—21no—
106#120×C139—21no—
107#120×C139—21no—
108#120×C139—21no—
109#120×C139—21no—
110#120×C139C2×C411yescharacteristic
111#120×C139C2×C411yescharacteristic
112#120×C139C2×C411yescharacteristic
113#120×C139D411yescharacteristic
114#120×C139D411yescharacteristic
115#120×C139D411yescharacteristic
116C4×D4×C139—21no—
117C4×D4×C139—21no—
118C4×D4×C139—21no—
119C4×D4×C139—21no—
120C4×D4×C139—21no—
121C4×D4×C139—21no—
122C4×D4×C139—42no—
123#117×C139—21no—
124#117×C139—21no—
125#117×C139D411yescharacteristic
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—42no—
136C2×C22⋊C4×C139D411yescharacteristic
137C2×C22⋊C4×C139D411yescharacteristic
138#104×C139—42no—
139#100×C139—21no—
140#100×C139—21no—
141#99×C139—21no—
142#99×C139—21no—
143#99×C139—21no—
144#99×C139—21no—
145#99×C139—42no—
146C24×C139—21no—
147C24×C139—21no—
148C24×C139—21no—
149C24×C139—41no—
150C24×C139—41no—
151C24×C139—82no—
152C24×C139C22⋊C411yescharacteristic
153C24×C139C22⋊C411yescharacteristic
154C24×C139C22⋊C411yescharacteristic, complemented
155C24×C139C2×D411yescharacteristic
156C24×C139C2×D411yescharacteristic
157#41×C139—41no—
158#41×C139—41no—
159#41×C139—82no—
160C2×Q8×C139—21no—
161C2×Q8×C139C22⋊C411yescharacteristic, complemented
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—41no—
183C2×D4×C139—41no—
184C2×D4×C139—41no—
185C2×D4×C139—41no—
186C2×D4×C139—82no—
187C2×D4×C139—82no—
188C2×D4×C139—82no—
189C2×D4×C139—82no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139C22⋊C411yescharacteristic, complemented
193C2×D4×C139C22×C411yescharacteristic
194C2×D4×C139C2×D411yescharacteristic
195C2×D4×C139C2×D411yescharacteristic
196C2×D4×C139C2×D411yescharacteristic
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—22no—
206C22×C4×C139—41no—
207C22×C4×C139—41no—
208C22×C4×C139—41no—
209C22×C4×C139C22⋊C411yescharacteristic, complemented
210C22×C4×C139C2×D411yescharacteristic
211M16×C139—41no—
212M16×C139—41no—
213C2×C8×C139—41no—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—41no—
224C22⋊C4×C139—21no—
225C22⋊C4×C139—21no—
226C22⋊C4×C139—21no—
227C22⋊C4×C139—21no—
228C22⋊C4×C139—21no—
229C22⋊C4×C139—21no—
230C22⋊C4×C139—21no—
231C22⋊C4×C139—21no—
232C22⋊C4×C139—21no—
233C22⋊C4×C139—21no—
234C22⋊C4×C139—21no—
235C22⋊C4×C139—21no—
236C22⋊C4×C139—21no—
237C22⋊C4×C139—21no—
238C22⋊C4×C139—21no—
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—21no—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—41no—
251C22⋊C4×C139—41no—
252C22⋊C4×C139—41no—
253C22⋊C4×C139—41no—
254C22⋊C4×C139—41no—
255C22⋊C4×C139—41no—
256C22⋊C4×C139—84no—
257C22⋊C4×C139C22⋊C411yescharacteristic
258C22⋊C4×C139C22⋊C411yescharacteristic
259C22⋊C4×C139C22⋊C411yescharacteristic, complemented
260C22⋊C4×C139C22⋊C411yescharacteristic, complemented
261C42×C139—21no—
262C42×C139—21no—
263C42×C139—22no—
264C42×C139C22⋊C411yescharacteristic, complemented
265C42×C139C22⋊C411yescharacteristic, complemented
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—42no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—42no—
278C23×C139—42no—
279C23×C139—42no—
280C23×C139—41no—
281C23×C139—44no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—81no—
285C23×C139—81no—
286C23×C139—81no—
287C23×C139—81no—
288C23×C139—81no—
289C23×C139—81no—
290C23×C139—81no—
291C23×C139—81no—
292C23×C139—81no—
293C23×C139—82no—
294C23×C139—82no—
295C23×C139—82no—
296C23×C139C2×C22⋊C411yescharacteristic
297C23×C139C2×C22⋊C411yescharacteristic
298C23×C139#12011yescharacteristic
299C23×C139#12011yescharacteristic
300C23×C139#12011yescharacteristic
301Q8×C139—41no—
302Q8×C139—81no—
303D4×C139—41no—
304D4×C139—41no—
305D4×C139—41no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—42no—
309D4×C139—42no—
310D4×C139—42no—
311D4×C139—42no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—81no—
317D4×C139—81no—
318D4×C139—81no—
319D4×C139—81no—
320D4×C139—81no—
321D4×C139—81no—
322D4×C139—81no—
323D4×C139—81no—
324D4×C139—81no—
325D4×C139—81no—
326D4×C139—81no—
327D4×C139—81no—
328D4×C139—81no—
329D4×C139—81no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—42no—
341C2×C4×C139—41no—
342C2×C4×C139—42no—
343C2×C4×C139—81no—
344C2×C4×C139—81no—
345C2×C4×C139—81no—
346C2×C4×C139—81no—
347C2×C4×C139—81no—
348C2×C4×C139—81no—
349C2×C4×C139—81no—
350C2×C4×C139—82no—
351C2×C4×C139—81no—
352C2×C4×C139—81no—
353C2×C4×C139—82no—
354C2×C4×C139—161no—
355C2×C4×C139—161no—
356C2×C4×C139C2×C22⋊C411yescharacteristic
357C2×C4×C139#12011yescharacteristic
358C8×C139—81no—
359C22×C139—22no—
360C22×C139—21no—
361C22×C139—21no—
362C22×C139—21no—
363C22×C139—21no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—42no—
370C22×C139—41no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—41no—
377C22×C139—42no—
378C22×C139—41no—
379C22×C139—42no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—82no—
387C22×C139—82no—
388C22×C139—81no—
389C22×C139—84no—
390C22×C139—81no—
391C22×C139—161no—
392C22×C139—162no—
393C22×C139#37911yescharacteristic
394C22×C139B(4,𝔽2)11yescharacteristic
395C22×C139#45811yescharacteristic
396C4×C139—21no—
397C4×C139—21no—
398C4×C139—41no—
399C4×C139—41no—
400C4×C139—41no—
401C4×C139—41no—
402C4×C139—41no—
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—41no—
406C4×C139—82no—
407C4×C139—161no—
408C4×C139—161no—
409C2×C139—21no—
410C2×C139—21no—
411C2×C139—21no—
412C2×C139—41no—
413C2×C139—41no—
414C2×C139—41no—
415C2×C139—42no—
416C2×C139—41no—
417C2×C139—81no—
418C2×C139—81no—
419C2×C139—81no—
420C2×C139#179011yescharacteristic
421#12753C13911yesmaximal, characteristic, direct product factor, Sylow
422C139#1275311yescharacteristic, direct product factor, Sylow
423#3532C2×C13911yescharacteristic
424#2127C2×C13911yescharacteristic, complemented
425#2121C2×C13911yescharacteristic, complemented
426C2×AΣL(1,𝔽16)C2×C13911yescharacteristic, complemented
427#1913C2×C13911yescharacteristic, complemented
428#1911C2×C13911yescharacteristic, complemented
429#1889C2×C13911yescharacteristic, complemented
430H(3,𝔽4)C4×C13911yescharacteristic, complemented
431#560—21no—
432#560C4×C13911yescharacteristic, complemented
433#551—21no—
434#551C4×C13911yescharacteristic, complemented
435#546—21no—
436#546—21no—
437#546—21no—
438D42—21no—
439D42C4×C13911yescharacteristic, complemented
440#538—21no—
441#538—21no—
442#538—21no—
443#535—21no—
444#535C22×C13911yescharacteristic
445#534—21no—
446#534C22×C13911yescharacteristic
447C2×#120—21no—
448C2×#120C22×C13911yescharacteristic
449#518C22×C13911yescharacteristic, complemented
450#421—21no—
451C2×#100C22×C13911yescharacteristic, complemented
452C2×#99—21no—
453C2×#99C22×C13911yescharacteristic, complemented
454C2×#99C22×C13911yescharacteristic, complemented
455#379—21no—
456#354—21no—
457#353—21no—
458#352—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461AΣL(1,𝔽16)—21no—
462#342—21no—
463#342—21no—
464H(3,ℤ/4)—21no—
465C25D4×C13911yescharacteristic
466C2×#41—21no—
467C2×#41D4×C13911yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C13911yescharacteristic
474C22×D4C23×C13911yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C13911yescharacteristic
478#127D4×C13911yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C13911yescharacteristic
489#124D4×C13911yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C13911yescharacteristic
499#123D4×C13911yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C13911yescharacteristic
533#120C2×C4×C13911yescharacteristic
534#120C2×C4×C13911yescharacteristic
535#120D4×C13911yescharacteristic
536#120D4×C13911yescharacteristic
537#120D4×C13911yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C13911yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C13911yescharacteristic
559C2×C22⋊C4D4×C13911yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C13911yescharacteristic
575C24C22⋊C4×C13911yescharacteristic
576C24C22⋊C4×C13911yescharacteristic, complemented
577C24C2×D4×C13911yescharacteristic
578C24C2×D4×C13911yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C13911yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C13911yescharacteristic, complemented
615C2×D4C22×C4×C13911yescharacteristic
616C2×D4C2×D4×C13911yescharacteristic
617C2×D4C2×D4×C13911yescharacteristic
618C2×D4C2×D4×C13911yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C13911yescharacteristic, complemented
632C22×C4C2×D4×C13911yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C13911yescharacteristic
680C22⋊C4C22⋊C4×C13911yescharacteristic
681C22⋊C4C22⋊C4×C13911yescharacteristic, complemented
682C22⋊C4C22⋊C4×C13911yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C13911yescharacteristic, complemented
687C42C22⋊C4×C13911yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C13911yescharacteristic
719C23C2×C22⋊C4×C13911yescharacteristic
720C23#120×C13911yescharacteristic
721C23#120×C13911yescharacteristic
722C23#120×C13911yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C13911yescharacteristic
779C2×C4#120×C13911yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22#379×C13911yescharacteristic
816C22B(4,𝔽2)×C13911yescharacteristic
817C22#458×C13911yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2#1790×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1790
commutatorC2×D4C22×C4×C139
Frattini, cosocleC22×D4C23×C139
prime radical#3532×C139C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C23×C139 ◁ C22×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2127×C139C2semidirect
3. #2121×C139C2semidirect
4. C2×AΣL(1,𝔽16)×C139C2semidirect
5. #1913×C139C2semidirect
6. #1911×C139C2semidirect
7. #1889×C139C2semidirect
8. H(3,𝔽4)×C139C4semidirect
10. #560×C139C4semidirect
12. #551×C139C4semidirect
17. D42×C139C4semidirect
27. #518×C139C22semidirect
29. C2×#100×C139C22semidirect
31. C2×#99×C139C22semidirect
32. C2×#99×C139C22semidirect
154. C24×C139C22⋊C4semidirect
161. C2×Q8×C139C22⋊C4semidirect
192. C2×D4×C139C22⋊C4semidirect
209. C22×C4×C139C22⋊C4semidirect
259. C22⋊C4×C139C22⋊C4semidirect
260. C22⋊C4×C139C22⋊C4semidirect
264. C42×C139C22⋊C4semidirect
265. C42×C139C22⋊C4semidirect
421. #12753C139direct (N × H)
422. C139#12753direct (N × H)
424. #2127C2×C139semidirect
425. #2121C2×C139semidirect
426. C2×AΣL(1,𝔽16)C2×C139semidirect
427. #1913C2×C139semidirect
428. #1911C2×C139semidirect
429. #1889C2×C139semidirect
430. H(3,𝔽4)C4×C139semidirect
432. #560C4×C139semidirect
434. #551C4×C139semidirect
439. D42C4×C139semidirect
449. #518C22×C139semidirect
451. C2×#100C22×C139semidirect
453. C2×#99C22×C139semidirect
454. C2×#99C22×C139semidirect
576. C24C22⋊C4×C139semidirect
583. C2×Q8C22⋊C4×C139semidirect
614. C2×D4C22⋊C4×C139semidirect
631. C22×C4C22⋊C4×C139semidirect
681. C22⋊C4C22⋊C4×C139semidirect
682. C22⋊C4C22⋊C4×C139semidirect
686. C42C22⋊C4×C139semidirect
687. C42C22⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3532×C1392
#2127×C1392
#2121×C1392
C2×AΣL(1,𝔽16)×C1392
#1913×C1392
#1911×C1392
#1889×C1392
#12753139