Finite Group Databasebeta

← C139×#33553 #48028149

Subgroups — C139×#33553 #48028149

Order 35584.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C139C211yesmaximal, characteristic, complemented
2#3027×C139C211yesmaximal, characteristic, complemented
3#3025×C139C211yesmaximal, characteristic, complemented
4#3021×C139C211yesmaximal, characteristic, complemented
5#2200×C139C214yesmaximal, complemented
6#2196×C139C214yesmaximal, complemented
7#2128×C139C211yesmaximal, characteristic, complemented
8#2122×C139C211yesmaximal, characteristic, complemented
9#2120×C139C211yesmaximal, characteristic, complemented
10#585×C139C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C139—21no—
12#560×C139—21no—
13#560×C139C2212yescomplemented
14#553×C139—21no—
15#553×C139—21no—
16D42×C139—21no—
17D42×C139—21no—
18D42×C139—21no—
19D42×C139C2212yescomplemented
20#540×C139—21no—
21#538×C139—22no—
22#535×C139—21no—
23#535×C139C2211yescharacteristic
24#535×C139C2211yescharacteristic
25#534×C139—22no—
26#525×C139—21no—
27#525×C139C2211yescharacteristic
28C2×#121×C139—21no—
29#458×C139—21no—
30#458×C139C2212yescomplemented
31B(4,𝔽2)×C139—21no—
32B(4,𝔽2)×C139—22no—
33B(4,𝔽2)×C139C2212yescomplemented
34B(4,𝔽2)×C139C2214yescomplemented
35#454×C139—22no—
36#453×C139C2214yescomplemented
37#421×C139—21no—
38#413×C139C2211yescharacteristic, complemented
39#410×C139—21no—
40#410×C139—21no—
41#410×C139C2211yescharacteristic, complemented
42#410×C139C2211yescharacteristic, complemented
43#353×C139C2214yescomplemented
44#352×C139C2212yescomplemented
45AΣL(1,𝔽16)×C139C2212yescomplemented
46AΣL(1,𝔽16)×C139C2214yescomplemented
472−1+4×C139—21no—
482−1+4×C139—41no—
49H(5,𝔽2)×C139—21no—
50H(5,𝔽2)×C139—21no—
51H(5,𝔽2)×C139—41no—
52H(5,𝔽2)×C139C2312yes—
53C2×#41×C139—21no—
54C2×#41×C139—21no—
55C2×#41×C139—21no—
56C2×#41×C139—42no—
57C2×#41×C139C2311yescharacteristic
58C22×D4×C139—21no—
59C22×D4×C139—22no—
60C22×D4×C139—22no—
61C22×D4×C139—22no—
62C22×D4×C139D411yescharacteristic, complemented
63C22×D4×C139D411yescharacteristic, complemented
64C23×C4×C139D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C139—24no—
66AGL(1,ℤ/8)×C139—42no—
67C2×SD16×C139—41no—
68C2×D8×C139—41no—
69C2×M16×C139—21no—
70#127×C139—21no—
71#127×C139—21no—
72#127×C139—41no—
73#127×C139C2312yes—
74#126×C139—22no—
75#126×C139—22no—
76#125×C139—21no—
77#124×C139—21no—
78#124×C139—41no—
79#124×C139D412yescomplemented
80#123×C139—22no—
81#123×C139—22no—
82#123×C139—22no—
83#123×C139—22no—
84#123×C139—22no—
85#123×C139D411yescharacteristic, complemented
86#123×C139C2311yescharacteristic
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—41no—
89#121×C139—22no—
90#121×C139—21no—
91#121×C139—21no—
92#121×C139—22no—
93#121×C139—22no—
94#121×C139—21no—
95#121×C139—22no—
96#121×C139—21no—
97#121×C139—21no—
98#121×C139—22no—
99#121×C139—21no—
100#121×C139—21no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139—42no—
105#121×C139—41no—
106#120×C139—22no—
107#120×C139—22no—
108#120×C139—22no—
109#120×C139—21no—
110#120×C139—21no—
111#120×C139—22no—
112#120×C139—22no—
113#120×C139—24no—
114#120×C139D411yescharacteristic, complemented
115#120×C139D412yescomplemented
116#120×C139C2311yescharacteristic
117#120×C139C2312yes—
118C4×D4×C139—22no—
119C4×D4×C139—21no—
120C4×D4×C139—21no—
121C4×D4×C139—21no—
122C4×D4×C139—21no—
123C4×D4×C139—22no—
124C4×D4×C139—42no—
125#117×C139—21no—
126#117×C139—21no—
127#117×C139D411yescharacteristic, complemented
128#117×C139D411yescharacteristic, complemented
129#117×C139D411yescharacteristic, complemented
130C2×C4⋊C4×C139—21no—
131C2×C22⋊C4×C139—22no—
132#104×C139—24no—
133#101×C139—21no—
134#100×C139C2312yes—
135#99×C139—21no—
136#99×C139—21no—
137#99×C139—24no—
138#99×C139—22no—
139#99×C139—22no—
140#99×C139C2312yes—
141#99×C139C2312yes—
142C24×C139—22no—
143C24×C139—21no—
144C24×C139C2×D411yescharacteristic
145C24×C139C2×D412yes—
146#41×C139—22no—
147#41×C139—22no—
148#41×C139—41no—
149#41×C139—41no—
150#41×C139—42no—
151#41×C139—41no—
152#41×C139—41no—
153#41×C139—41no—
154#41×C139—41no—
155#41×C139—41no—
156#41×C139—42no—
157#41×C139—42no—
158#41×C139—42no—
159#41×C139—41no—
160#41×C139—41no—
161#41×C139—41no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—42no—
166C2×Q8×C139C2×D411yescharacteristic
167C2×D4×C139—21no—
168C2×D4×C139—22no—
169C2×D4×C139—22no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—22no—
174C2×D4×C139—22no—
175C2×D4×C139—21no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—22no—
179C2×D4×C139—22no—
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—22no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—41no—
187C2×D4×C139—41no—
188C2×D4×C139—41no—
189C2×D4×C139—41no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—41no—
194C2×D4×C139—42no—
195C2×D4×C139—44no—
196C2×D4×C139—81no—
197C2×D4×C139—81no—
198C2×D4×C139—84no—
199C2×D4×C139—84no—
200C2×D4×C139—84no—
201C2×D4×C139C2×D411yescharacteristic
202C2×D4×C139C2×D411yescharacteristic
203C2×D4×C139C2×D412yes—
204C2×D4×C139C2411yescharacteristic
205C22×C4×C139—22no—
206C22×C4×C139—22no—
207C22×C4×C139—22no—
208C22×C4×C139—22no—
209C22×C4×C139—22no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—41no—
213C22×C4×C139—41no—
214C22×C4×C139—41no—
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219SD16×C139—44no—
220D8×C139—44no—
221M16×C139—22no—
222M16×C139—41no—
223C2×C8×C139—41no—
224C4⋊C4×C139—22no—
225C4⋊C4×C139—22no—
226C4⋊C4×C139—22no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—41no—
233C4⋊C4×C139—41no—
234C4⋊C4×C139—42no—
235C22⋊C4×C139—22no—
236C22⋊C4×C139—22no—
237C22⋊C4×C139—22no—
238C22⋊C4×C139—22no—
239C22⋊C4×C139—21no—
240C22⋊C4×C139—21no—
241C22⋊C4×C139—21no—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—22no—
244C22⋊C4×C139—21no—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—21no—
247C22⋊C4×C139—22no—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—44no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139C2×D412yes—
254C22⋊C4×C139C2×D411yescharacteristic
255C22⋊C4×C139C2×D411yescharacteristic
256C42×C139—21no—
257C42×C139—21no—
258C42×C139—41no—
259C42×C139—41no—
260C42×C139C2×D412yes—
261C23×C139—21no—
262C23×C139—22no—
263C23×C139—22no—
264C23×C139—22no—
265C23×C139—22no—
266C23×C139—41no—
267C23×C139—42no—
268C23×C139—41no—
269C23×C139—44no—
270C23×C139—42no—
271C23×C139—81no—
272C23×C139—82no—
273C23×C139—82no—
274C23×C139—82no—
275C23×C139—82no—
276C23×C139#12011yescharacteristic
277C23×C139C22×D411yescharacteristic
278C23×C139C22×D411yescharacteristic
279Q8×C139—22no—
280Q8×C139—41no—
281Q8×C139—41no—
282Q8×C139—41no—
283Q8×C139—41no—
284D4×C139—22no—
285D4×C139—41no—
286D4×C139—41no—
287D4×C139—41no—
288D4×C139—42no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—42no—
292D4×C139—42no—
293D4×C139—42no—
294D4×C139—42no—
295D4×C139—44no—
296D4×C139—44no—
297D4×C139—42no—
298D4×C139—42no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—41no—
304D4×C139—81no—
305D4×C139—82no—
306D4×C139—82no—
307D4×C139—82no—
308D4×C139—82no—
309D4×C139—82no—
310D4×C139—82no—
311D4×C139—82no—
312D4×C139—84no—
313D4×C139—164no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—21no—
320C2×C4×C139—22no—
321C2×C4×C139—22no—
322C2×C4×C139—22no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—22no—
326C2×C4×C139—21no—
327C2×C4×C139—42no—
328C2×C4×C139—42no—
329C2×C4×C139—42no—
330C2×C4×C139—41no—
331C2×C4×C139—42no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—42no—
336C2×C4×C139—42no—
337C2×C4×C139—81no—
338C2×C4×C139—82no—
339C2×C4×C139—82no—
340C2×C4×C139—82no—
341C2×C4×C139#12011yescharacteristic
342C2×C4×C139#12011yescharacteristic
343C2×C4×C139#12011yescharacteristic
344C2×C4×C139C22×D411yescharacteristic
345C8×C139—42no—
346C22×C139—22no—
347C22×C139—21no—
348C22×C139—21no—
349C22×C139—21no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—42no—
355C22×C139—42no—
356C22×C139—42no—
357C22×C139—42no—
358C22×C139—42no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—42no—
362C22×C139—42no—
363C22×C139—81no—
364C22×C139—82no—
365C22×C139—82no—
366C22×C139—84no—
367C22×C139—161no—
368C22×C139—164no—
369C22×C139—162no—
370C22×C139C2×#12011yescharacteristic
371C4×C139—21no—
372C4×C139—21no—
373C4×C139—21no—
374C4×C139—42no—
375C4×C139—41no—
376C4×C139—41no—
377C4×C139—42no—
378C4×C139—42no—
379C4×C139—41no—
380C4×C139—82no—
381C4×C139—82no—
382C4×C139B(4,𝔽2)11yescharacteristic
383C4×C139B(4,𝔽2)11yescharacteristic
384C2×C139—21no—
385C2×C139—41no—
386C2×C139—41no—
387C2×C139—42no—
388C2×C139—41no—
389C2×C139—82no—
390C2×C139—82no—
391C2×C139—82no—
392C2×C139C2×B(4,𝔽2)11yescharacteristic
393#33553C13911yesmaximal, characteristic, direct product factor, Sylow
394C139#3355311yescharacteristic, direct product factor, Sylow
395#3537C2×C13911yescharacteristic, complemented
396#3027C2×C13911yescharacteristic, complemented
397#3025C2×C13911yescharacteristic, complemented
398#3021C2×C13911yescharacteristic, complemented
399#2200C2×C13914yescomplemented
400#2196C2×C13914yescomplemented
401#2128C2×C13911yescharacteristic, complemented
402#2122C2×C13911yescharacteristic, complemented
403#2120C2×C13911yescharacteristic, complemented
404#585C22×C13911yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—21no—
406#560—21no—
407#560C22×C13912yescomplemented
408#553—21no—
409#553—21no—
410D42—21no—
411D42—21no—
412D42—21no—
413D42C22×C13912yescomplemented
414#540—21no—
415#538—22no—
416#535—21no—
417#535C22×C13911yescharacteristic
418#535C22×C13911yescharacteristic
419#534—22no—
420#525—21no—
421#525C22×C13911yescharacteristic
422C2×#121—21no—
423#458—21no—
424#458C22×C13912yescomplemented
425B(4,𝔽2)—21no—
426B(4,𝔽2)—22no—
427B(4,𝔽2)C22×C13912yescomplemented
428B(4,𝔽2)C22×C13914yescomplemented
429#454—22no—
430#453C22×C13914yescomplemented
431#421—21no—
432#413C22×C13911yescharacteristic, complemented
433#410—21no—
434#410—21no—
435#410C22×C13911yescharacteristic, complemented
436#410C22×C13911yescharacteristic, complemented
437#353C22×C13914yescomplemented
438#352C22×C13912yescomplemented
439AΣL(1,𝔽16)C22×C13912yescomplemented
440AΣL(1,𝔽16)C22×C13914yescomplemented
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C13912yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C13911yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C13911yescharacteristic, complemented
457C22×D4D4×C13911yescharacteristic, complemented
458C23×C4D4×C13911yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C13912yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C13912yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C13911yescharacteristic, complemented
480#123C23×C13911yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C13911yescharacteristic, complemented
509#120D4×C13912yescomplemented
510#120C23×C13911yescharacteristic
511#120C23×C13912yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C13911yescharacteristic, complemented
522#117D4×C13911yescharacteristic, complemented
523#117D4×C13911yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C13912yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C13912yes—
535#99C23×C13912yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C13911yescharacteristic
539C24C2×D4×C13912yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C13911yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C13911yescharacteristic
596C2×D4C2×D4×C13911yescharacteristic
597C2×D4C2×D4×C13912yes—
598C2×D4C24×C13911yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C13911yescharacteristic
610C22×C4C2×D4×C13911yescharacteristic
611C22×C4C2×D4×C13911yescharacteristic
612C22×C4C2×D4×C13911yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C13912yes—
648C22⋊C4C2×D4×C13911yescharacteristic
649C22⋊C4C2×D4×C13911yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C13912yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C13911yescharacteristic
671C23C22×D4×C13911yescharacteristic
672C23C22×D4×C13911yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C13911yescharacteristic
736C2×C4#120×C13911yescharacteristic
737C2×C4#120×C13911yescharacteristic
738C2×C4C22×D4×C13911yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C13911yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4B(4,𝔽2)×C13911yescharacteristic
777C4B(4,𝔽2)×C13911yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×B(4,𝔽2)×C13911yescharacteristic
subgroupG/H
center, socleC2×C139C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C139
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C2×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3537×C139C2semidirect
2. #3027×C139C2semidirect
3. #3025×C139C2semidirect
4. #3021×C139C2semidirect
5. #2200×C139C2semidirect
6. #2196×C139C2semidirect
7. #2128×C139C2semidirect
8. #2122×C139C2semidirect
9. #2120×C139C2semidirect
10. #585×C139C22semidirect
13. #560×C139C22semidirect
19. D42×C139C22semidirect
30. #458×C139C22semidirect
33. B(4,𝔽2)×C139C22semidirect
34. B(4,𝔽2)×C139C22semidirect
36. #453×C139C22semidirect
38. #413×C139C22semidirect
41. #410×C139C22semidirect
42. #410×C139C22semidirect
43. #353×C139C22semidirect
44. #352×C139C22semidirect
45. AΣL(1,𝔽16)×C139C22semidirect
46. AΣL(1,𝔽16)×C139C22semidirect
62. C22×D4×C139D4semidirect
63. C22×D4×C139D4semidirect
64. C23×C4×C139D4semidirect
79. #124×C139D4semidirect
85. #123×C139D4semidirect
114. #120×C139D4semidirect
115. #120×C139D4semidirect
127. #117×C139D4semidirect
128. #117×C139D4semidirect
129. #117×C139D4semidirect
393. #33553C139direct (N × H)
394. C139#33553direct (N × H)
395. #3537C2×C139semidirect
396. #3027C2×C139semidirect
397. #3025C2×C139semidirect
398. #3021C2×C139semidirect
399. #2200C2×C139semidirect
400. #2196C2×C139semidirect
401. #2128C2×C139semidirect
402. #2122C2×C139semidirect
403. #2120C2×C139semidirect
404. #585C22×C139semidirect
407. #560C22×C139semidirect
413. D42C22×C139semidirect
424. #458C22×C139semidirect
427. B(4,𝔽2)C22×C139semidirect
428. B(4,𝔽2)C22×C139semidirect
430. #453C22×C139semidirect
432. #413C22×C139semidirect
435. #410C22×C139semidirect
436. #410C22×C139semidirect
437. #353C22×C139semidirect
438. #352C22×C139semidirect
439. AΣL(1,𝔽16)C22×C139semidirect
440. AΣL(1,𝔽16)C22×C139semidirect
456. C22×D4D4×C139semidirect
457. C22×D4D4×C139semidirect
458. C23×C4D4×C139semidirect
473. #124D4×C139semidirect
479. #123D4×C139semidirect
508. #120D4×C139semidirect
509. #120D4×C139semidirect
521. #117D4×C139semidirect
522. #117D4×C139semidirect
523. #117D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3537×C1392
#3027×C1392
#3025×C1392
#3021×C1392
#2200×C1392
#2196×C1392
#2128×C1392
#2122×C1392
#2120×C1392
#33553139