Finite Group Databasebeta

← C139×#23878 #48018474

Subgroups — C139×#23878 #48018474

Order 35584.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C139C211yesmaximal, characteristic, complemented
2#3488×C139C211yesmaximal, characteristic, complemented
3C2×#455×C139C211yesmaximal, characteristic, complemented
4C2×#453×C139C211yesmaximal, characteristic, complemented
5#3005×C139C211yesmaximal, characteristic, complemented
6#2431×C139C211yesmaximal, characteristic, complemented
7#2007×C139C211yesmaximal, characteristic, complemented
8#2006×C139C211yesmaximal, characteristic, complemented
9#2004×C139C211yesmaximal, characteristic, complemented
10#2002×C139C211yesmaximal, characteristic, complemented
11#1900×C139C211yesmaximal, characteristic, complemented
12#1883×C139C211yesmaximal, characteristic, complemented
13#1882×C139C211yesmaximal, characteristic, complemented
14#1871×C139C211yesmaximal, characteristic, complemented
15#1789×C139C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×#41×C139C2211yescharacteristic, complemented
19#575×C139—24no—
20#575×C139—24no—
21C2×#137×C139—21no—
22C2×#137×C139C2211yescharacteristic
23C2×#137×C139C2211yescharacteristic, complemented
24C2×#137×C139C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C139—21no—
26C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
29C2×#135×C139—21no—
30C2×#135×C139—21no—
31C22×M16×C139C2211yescharacteristic, complemented
32#550×C139—21no—
33#548×C139—21no—
34#546×C139—21no—
35#546×C139—22no—
36D42×C139—22no—
37D42×C139—21no—
38#537×C139—21no—
39#537×C139C2211yescharacteristic
40#535×C139—21no—
41#535×C139C2211yescharacteristic
42C2×#127×C139C2211yescharacteristic, complemented
43C2×#124×C139C2211yescharacteristic, complemented
44#525×C139—21no—
45#525×C139C2211yescharacteristic
46C2×#121×C139—21no—
47C2×#121×C139C2211yescharacteristic
48#520×C139C2211yescharacteristic
49#455×C139—24no—
50#453×C139—24no—
51#452×C139—21no—
52#452×C139—21no—
53#449×C139—21no—
54#449×C139—21no—
55C2×#104×C139C2211yescharacteristic
56C2×#104×C139C2211yescharacteristic
57C2×#104×C139C2211yescharacteristic, complemented
58C2×#104×C139C2211yescharacteristic, complemented
59C2×#104×C139C2211yescharacteristic, complemented
60C2×#104×C139C2211yescharacteristic, complemented
61#419×C139C2211yescharacteristic, complemented
62#418×C139C2211yescharacteristic, complemented
63C2×#100×C139C2211yescharacteristic, complemented
64C2×#100×C139C2211yescharacteristic, complemented
65#407×C139C2211yescharacteristic, complemented
66#392×C139—22no—
67#391×C139C2211yescharacteristic, complemented
68#390×C139C2211yescharacteristic, complemented
69#386×C139—22no—
70C4×C22⋊C4×C139C2211yescharacteristic, complemented
71#343×C139C2211yescharacteristic, complemented
72#343×C139C2211yescharacteristic, complemented
73#339×C139C2211yescharacteristic, complemented
74#339×C139C2211yescharacteristic, complemented
75H(5,𝔽2)×C139—22no—
76H(5,𝔽2)×C139—22no—
77H(5,𝔽2)×C139—41no—
78H(5,𝔽2)×C139—41no—
79C2×#41×C139—21no—
80C2×#41×C139—21no—
81C2×#41×C139—21no—
82C2×#41×C139—21no—
83C2×#41×C139—22no—
84C2×#41×C139—22no—
85C2×#41×C139—22no—
86C2×#41×C139—22no—
87C2×#41×C139—21no—
88C2×#41×C139—21no—
89C2×#41×C139—21no—
90C2×#41×C139—21no—
91C2×#41×C139—41no—
92C2×#41×C139—41no—
93C2×#41×C139—41no—
94C2×#41×C139—41no—
95C2×#41×C139D411yescharacteristic, complemented
96C2×#41×C139D411yescharacteristic, complemented
97C2×#41×C139C2311yescharacteristic
98C2×#41×C139C2311yescharacteristic
99C2×#41×C139C2311yescharacteristic
100C22×Q8×C139D411yescharacteristic, complemented
101C22×Q8×C139C2311yescharacteristic
102C22×D4×C139—21no—
103C22×D4×C139—22no—
104C22×D4×C139—22no—
105C22×D4×C139—21no—
106C22×D4×C139—21no—
107C22×D4×C139—21no—
108C22×D4×C139—22no—
109C22×D4×C139D412yes—
110C22×D4×C139D411yescharacteristic, complemented
111C22×D4×C139C2311yescharacteristic
112C22×D4×C139C2311yescharacteristic
113C23×C4×C139—21no—
114C23×C4×C139—21no—
115C23×C4×C139C2311yescharacteristic
116#137×C139—28no—
117#137×C139—22no—
118#137×C139—22no—
119#137×C139—22no—
120#137×C139—22no—
121#137×C139—41no—
122#137×C139D414yescomplemented
123AGL(1,ℤ/8)×C139—28no—
124AGL(1,ℤ/8)×C139—22no—
125AGL(1,ℤ/8)×C139—22no—
126AGL(1,ℤ/8)×C139—22no—
127AGL(1,ℤ/8)×C139—22no—
128AGL(1,ℤ/8)×C139—41no—
129AGL(1,ℤ/8)×C139D414yescomplemented
130#135×C139—28no—
131#135×C139—28no—
132C2×Q16×C139—21no—
133C2×Q16×C139—21no—
134C2×Q16×C139—21no—
135C2×SD16×C139—21no—
136C2×SD16×C139—21no—
137C2×SD16×C139—21no—
138C2×SD16×C139—21no—
139C2×SD16×C139—21no—
140C2×SD16×C139—21no—
141C2×D8×C139—21no—
142C2×D8×C139—21no—
143C2×D8×C139—21no—
144C2×M16×C139—21no—
145C2×M16×C139—22no—
146C2×M16×C139—22no—
147C2×M16×C139C2311yescharacteristic
148C2×M16×C139C2311yescharacteristic
149C2×M16×C139C2311yescharacteristic
150C2×M16×C139C2311yescharacteristic
151C22×C8×C139—21no—
152#127×C139—22no—
153#127×C139—21no—
154#127×C139—22no—
155#127×C139—41no—
156#124×C139—22no—
157#124×C139—21no—
158#124×C139—22no—
159#124×C139—41no—
160#123×C139—22no—
161#123×C139—21no—
162C22⋊Q8×C139—22no—
163C22⋊Q8×C139—21no—
164C22⋊Q8×C139—21no—
165C22⋊Q8×C139D411yescharacteristic, complemented
166C22⋊Q8×C139D411yescharacteristic, complemented
167#121×C139—22no—
168#121×C139—22no—
169#121×C139—22no—
170#121×C139—22no—
171#121×C139—22no—
172#121×C139—21no—
173#121×C139—21no—
174#121×C139—21no—
175#121×C139—21no—
176#121×C139—21no—
177#121×C139—21no—
178#121×C139—22no—
179#121×C139—21no—
180#121×C139—21no—
181#121×C139D411yescharacteristic, complemented
182#121×C139D411yescharacteristic, complemented
183#120×C139—22no—
184#120×C139—22no—
185#120×C139—22no—
186#120×C139—21no—
187#120×C139—22no—
188C4×Q8×C139—21no—
189C4×D4×C139—22no—
190C4×D4×C139—22no—
191C4×D4×C139—21no—
192C4×D4×C139—22no—
193C4×D4×C139—21no—
194C4×D4×C139—21no—
195#117×C139—21no—
196#117×C139C2311yescharacteristic
197C2×C4⋊C4×C139—21no—
198C2×C4⋊C4×C139C2311yescharacteristic
199C2×C22⋊C4×C139—22no—
200C2×C22⋊C4×C139—22no—
201C2×C22⋊C4×C139—21no—
202C2×C22⋊C4×C139—22no—
203C2×C22⋊C4×C139D412yes—
204C2×C42×C139C2311yescharacteristic
205C2×C42×C139C2311yescharacteristic
206#104×C139—22no—
207#104×C139—22no—
208#104×C139—22no—
209#104×C139—22no—
210#104×C139—41no—
211#104×C139—41no—
212#103×C139—21no—
213#103×C139—21no—
214#102×C139—21no—
215#102×C139—21no—
216#100×C139—22no—
217#100×C139—22no—
218C22⋊C8×C139—21no—
219C22⋊C8×C139—21no—
220#95×C139—21no—
221#95×C139—22no—
222C24×C139—22no—
223C24×C139—21no—
224C24×C139—21no—
225C24×C139C2×D412yes—
226C24×C139C2×D411yescharacteristic
227#41×C139—21no—
228#41×C139—21no—
229#41×C139—24no—
230#41×C139—24no—
231#41×C139—22no—
232#41×C139—22no—
233#41×C139—21no—
234#41×C139—21no—
235#41×C139—21no—
236#41×C139—21no—
237#41×C139—21no—
238#41×C139—21no—
239#41×C139—21no—
240#41×C139—21no—
241#41×C139—42no—
242#41×C139—42no—
243#41×C139—41no—
244#41×C139—41no—
245#41×C139—42no—
246#41×C139—42no—
247#41×C139—42no—
248#41×C139—42no—
249#41×C139—42no—
250#41×C139—42no—
251#41×C139—42no—
252#41×C139—42no—
253#41×C139—42no—
254#41×C139—42no—
255#41×C139—42no—
256#41×C139—42no—
257#41×C139C2×D412yes—
258#41×C139C2×D412yes—
259C2×Q8×C139—21no—
260C2×Q8×C139—21no—
261C2×Q8×C139—22no—
262C2×Q8×C139—21no—
263C2×Q8×C139—21no—
264C2×Q8×C139—21no—
265C2×Q8×C139—21no—
266C2×Q8×C139—41no—
267C2×Q8×C139C2×D411yescharacteristic
268C2×Q8×C139C2×D411yescharacteristic
269C2×Q8×C139C2×D411yescharacteristic
270C2×Q8×C139C2×D412yescomplemented
271C2×D4×C139—21no—
272C2×D4×C139—22no—
273C2×D4×C139—22no—
274C2×D4×C139—22no—
275C2×D4×C139—22no—
276C2×D4×C139—21no—
277C2×D4×C139—21no—
278C2×D4×C139—21no—
279C2×D4×C139—21no—
280C2×D4×C139—21no—
281C2×D4×C139—22no—
282C2×D4×C139—22no—
283C2×D4×C139—22no—
284C2×D4×C139—21no—
285C2×D4×C139—22no—
286C2×D4×C139—21no—
287C2×D4×C139—21no—
288C2×D4×C139—21no—
289C2×D4×C139—21no—
290C2×D4×C139—21no—
291C2×D4×C139—21no—
292C2×D4×C139—21no—
293C2×D4×C139—21no—
294C2×D4×C139—21no—
295C2×D4×C139—21no—
296C2×D4×C139—21no—
297C2×D4×C139—21no—
298C2×D4×C139—41no—
299C2×D4×C139—42no—
300C2×D4×C139—42no—
301C2×D4×C139—42no—
302C2×D4×C139—44no—
303C2×D4×C139—42no—
304C2×D4×C139—42no—
305C2×D4×C139—44no—
306C2×D4×C139—44no—
307C2×D4×C139—42no—
308C2×D4×C139—42no—
309C2×D4×C139—41no—
310C2×D4×C139—41no—
311C2×D4×C139—42no—
312C2×D4×C139—44no—
313C2×D4×C139—82no—
314C2×D4×C139—82no—
315C2×D4×C139—84no—
316C2×D4×C139C2×D411yescharacteristic
317C2×D4×C139C2×D411yescharacteristic
318C2×D4×C139C2×D411yescharacteristic
319C2×D4×C139C2×D412yescomplemented
320C22×C4×C139—21no—
321C22×C4×C139—21no—
322C22×C4×C139—21no—
323C22×C4×C139—21no—
324C22×C4×C139—21no—
325C22×C4×C139—22no—
326C22×C4×C139—21no—
327C22×C4×C139—21no—
328C22×C4×C139—21no—
329C22×C4×C139—22no—
330C22×C4×C139—21no—
331C22×C4×C139—21no—
332C22×C4×C139—21no—
333C22×C4×C139—21no—
334C22×C4×C139—21no—
335C22×C4×C139—42no—
336C22×C4×C139—42no—
337C22×C4×C139—42no—
338C22×C4×C139—42no—
339C22×C4×C139—41no—
340C22×C4×C139—41no—
341C22×C4×C139C2×D411yescharacteristic
342C22×C4×C139C2×D411yescharacteristic
343C22×C4×C139C2×D411yescharacteristic
344C22×C4×C139C2×D411yescharacteristic
345C22×C4×C139C2×D411yescharacteristic
346C22×C4×C139C2×D412yes—
347C22×C4×C139C2411yescharacteristic
348Q16×C139—24no—
349Q16×C139—24no—
350Q16×C139—42no—
351SD16×C139—24no—
352SD16×C139—24no—
353SD16×C139—24no—
354SD16×C139—24no—
355SD16×C139—42no—
356SD16×C139—42no—
357D8×C139—24no—
358D8×C139—24no—
359D8×C139—42no—
360M16×C139—24no—
361M16×C139—21no—
362M16×C139—21no—
363M16×C139—21no—
364M16×C139—21no—
365M16×C139—21no—
366M16×C139—21no—
367M16×C139C2×D412yescomplemented
368M16×C139C2×D412yescomplemented
369C2×C8×C139—24no—
370C2×C8×C139—21no—
371C2×C8×C139—21no—
372C2×C8×C139—21no—
373C2×C8×C139—21no—
374C4⋊C4×C139—22no—
375C4⋊C4×C139—22no—
376C4⋊C4×C139—21no—
377C4⋊C4×C139—21no—
378C4⋊C4×C139—21no—
379C4⋊C4×C139—21no—
380C4⋊C4×C139C2×D411yescharacteristic
381C4⋊C4×C139C2×D411yescharacteristic
382C22⋊C4×C139—22no—
383C22⋊C4×C139—22no—
384C22⋊C4×C139—22no—
385C22⋊C4×C139—22no—
386C22⋊C4×C139—22no—
387C22⋊C4×C139—21no—
388C22⋊C4×C139—21no—
389C22⋊C4×C139—21no—
390C22⋊C4×C139—21no—
391C22⋊C4×C139—22no—
392C22⋊C4×C139—22no—
393C22⋊C4×C139—21no—
394C22⋊C4×C139—44no—
395C22⋊C4×C139—42no—
396C22⋊C4×C139—82no—
397C42×C139—22no—
398C42×C139—21no—
399C42×C139—21no—
400C42×C139—21no—
401C42×C139—21no—
402C42×C139—21no—
403C23×C139—21no—
404C23×C139—21no—
405C23×C139—21no—
406C23×C139—22no—
407C23×C139—21no—
408C23×C139—21no—
409C23×C139—22no—
410C23×C139—22no—
411C23×C139—22no—
412C23×C139—41no—
413C23×C139—41no—
414C23×C139—42no—
415C23×C139—42no—
416C23×C139—42no—
417C23×C139—42no—
418C23×C139—44no—
419C23×C139—42no—
420C23×C139—42no—
421C23×C139—41no—
422C23×C139—41no—
423C23×C139—81no—
424C23×C139—82no—
425C23×C139—82no—
426C23×C139#12011yescharacteristic
427C23×C139#12011yescharacteristic
428C23×C139C22×D411yescharacteristic
429Q8×C139—21no—
430Q8×C139—21no—
431Q8×C139—22no—
432Q8×C139—21no—
433Q8×C139—21no—
434Q8×C139—22no—
435Q8×C139—21no—
436Q8×C139—42no—
437Q8×C139—41no—
438Q8×C139—41no—
439Q8×C139#12012yes—
440D4×C139—22no—
441D4×C139—22no—
442D4×C139—21no—
443D4×C139—22no—
444D4×C139—21no—
445D4×C139—21no—
446D4×C139—21no—
447D4×C139—22no—
448D4×C139—21no—
449D4×C139—42no—
450D4×C139—42no—
451D4×C139—44no—
452D4×C139—42no—
453D4×C139—44no—
454D4×C139—44no—
455D4×C139—42no—
456D4×C139—44no—
457D4×C139—44no—
458D4×C139—41no—
459D4×C139—41no—
460D4×C139—41no—
461D4×C139—41no—
462D4×C139—41no—
463D4×C139—41no—
464D4×C139—41no—
465D4×C139—41no—
466D4×C139—41no—
467D4×C139—41no—
468D4×C139—81no—
469D4×C139—82no—
470D4×C139—82no—
471D4×C139—82no—
472D4×C139—82no—
473D4×C139—88no—
474D4×C139#12012yes—
475C2×C4×C139—21no—
476C2×C4×C139—21no—
477C2×C4×C139—21no—
478C2×C4×C139—21no—
479C2×C4×C139—21no—
480C2×C4×C139—21no—
481C2×C4×C139—21no—
482C2×C4×C139—21no—
483C2×C4×C139—21no—
484C2×C4×C139—21no—
485C2×C4×C139—21no—
486C2×C4×C139—22no—
487C2×C4×C139—22no—
488C2×C4×C139—22no—
489C2×C4×C139—21no—
490C2×C4×C139—22no—
491C2×C4×C139—21no—
492C2×C4×C139—21no—
493C2×C4×C139—21no—
494C2×C4×C139—22no—
495C2×C4×C139—42no—
496C2×C4×C139—42no—
497C2×C4×C139—42no—
498C2×C4×C139—44no—
499C2×C4×C139—44no—
500C2×C4×C139—44no—
501C2×C4×C139—41no—
502C2×C4×C139—41no—
503C2×C4×C139—41no—
504C2×C4×C139—41no—
505C2×C4×C139—41no—
506C2×C4×C139—41no—
507C2×C4×C139—41no—
508C2×C4×C139—41no—
509C2×C4×C139—42no—
510C2×C4×C139—41no—
511C2×C4×C139—41no—
512C2×C4×C139—41no—
513C2×C4×C139—82no—
514C2×C4×C139#12011yescharacteristic
515C2×C4×C139#12011yescharacteristic
516C2×C4×C139C22×D411yescharacteristic
517C2×C4×C139C22×D411yescharacteristic
518C2×C4×C139C22×D411yescharacteristic
519C2×C4×C139C22×D411yescharacteristic
520C2×C4×C139H(5,𝔽2)11yescharacteristic
521C2×C4×C139H(5,𝔽2)11yescharacteristic
522C8×C139—22no—
523C8×C139—22no—
524C8×C139—41no—
525C8×C139—41no—
526C22×C139—21no—
527C22×C139—21no—
528C22×C139—21no—
529C22×C139—21no—
530C22×C139—22no—
531C22×C139—21no—
532C22×C139—21no—
533C22×C139—21no—
534C22×C139—21no—
535C22×C139—44no—
536C22×C139—41no—
537C22×C139—41no—
538C22×C139—41no—
539C22×C139—42no—
540C22×C139—41no—
541C22×C139—42no—
542C22×C139—41no—
543C22×C139—42no—
544C22×C139—41no—
545C22×C139—42no—
546C22×C139—41no—
547C22×C139—41no—
548C22×C139—81no—
549C22×C139—81no—
550C22×C139—82no—
551C22×C139—82no—
552C22×C139—82no—
553C22×C139—84no—
554C22×C139—81no—
555C22×C139—81no—
556C22×C139—164no—
557C22×C139C2×#12011yescharacteristic
558C22×C139D4211yescharacteristic
559C22×C139D4211yescharacteristic
560C4×C139—21no—
561C4×C139—21no—
562C4×C139—22no—
563C4×C139—42no—
564C4×C139—41no—
565C4×C139—41no—
566C4×C139—42no—
567C4×C139—41no—
568C4×C139—42no—
569C4×C139—41no—
570C4×C139—81no—
571C4×C139C2×#12011yescharacteristic
572C4×C139#53411yescharacteristic
573C4×C139D4211yescharacteristic
574C4×C139D4211yescharacteristic
575C2×C139—21no—
576C2×C139—21no—
577C2×C139—41no—
578C2×C139—41no—
579C2×C139—42no—
580C2×C139—82no—
581C2×C139—81no—
582C2×C139—82no—
583C2×C139—81no—
584C2×C139#240311yescharacteristic
585C2×C139#301811yescharacteristic
586C2×C139#301911yescharacteristic
587#23878C13911yesmaximal, characteristic, direct product factor, Sylow
588C139#2387811yescharacteristic, direct product factor, Sylow
589C2×#575C2×C13911yescharacteristic, complemented
590#3488C2×C13911yescharacteristic, complemented
591C2×#455C2×C13911yescharacteristic, complemented
592C2×#453C2×C13911yescharacteristic, complemented
593#3005C2×C13911yescharacteristic, complemented
594#2431C2×C13911yescharacteristic, complemented
595#2007C2×C13911yescharacteristic, complemented
596#2006C2×C13911yescharacteristic, complemented
597#2004C2×C13911yescharacteristic, complemented
598#2002C2×C13911yescharacteristic, complemented
599#1900C2×C13911yescharacteristic, complemented
600#1883C2×C13911yescharacteristic, complemented
601#1882C2×C13911yescharacteristic, complemented
602#1871C2×C13911yescharacteristic, complemented
603#1789C2×C13911yescharacteristic, complemented
604C2×H(5,𝔽2)C22×C13911yescharacteristic
605C22×#41C22×C13911yescharacteristic
606C22×#41C22×C13911yescharacteristic, complemented
607#575—24no—
608#575—24no—
609C2×#137—21no—
610C2×#137C22×C13911yescharacteristic
611C2×#137C22×C13911yescharacteristic, complemented
612C2×#137C22×C13911yescharacteristic, complemented
613C2×AGL(1,ℤ/8)—21no—
614C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
615C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
616C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
617C2×#135—21no—
618C2×#135—21no—
619C22×M16C22×C13911yescharacteristic, complemented
620#550—21no—
621#548—21no—
622#546—21no—
623#546—22no—
624D42—22no—
625D42—21no—
626#537—21no—
627#537C22×C13911yescharacteristic
628#535—21no—
629#535C22×C13911yescharacteristic
630C2×#127C22×C13911yescharacteristic, complemented
631C2×#124C22×C13911yescharacteristic, complemented
632#525—21no—
633#525C22×C13911yescharacteristic
634C2×#121—21no—
635C2×#121C22×C13911yescharacteristic
636#520C22×C13911yescharacteristic
637#455—24no—
638#453—24no—
639#452—21no—
640#452—21no—
641#449—21no—
642#449—21no—
643C2×#104C22×C13911yescharacteristic
644C2×#104C22×C13911yescharacteristic
645C2×#104C22×C13911yescharacteristic, complemented
646C2×#104C22×C13911yescharacteristic, complemented
647C2×#104C22×C13911yescharacteristic, complemented
648C2×#104C22×C13911yescharacteristic, complemented
649#419C22×C13911yescharacteristic, complemented
650#418C22×C13911yescharacteristic, complemented
651C2×#100C22×C13911yescharacteristic, complemented
652C2×#100C22×C13911yescharacteristic, complemented
653#407C22×C13911yescharacteristic, complemented
654#392—22no—
655#391C22×C13911yescharacteristic, complemented
656#390C22×C13911yescharacteristic, complemented
657#386—22no—
658C4×C22⋊C4C22×C13911yescharacteristic, complemented
659#343C22×C13911yescharacteristic, complemented
660#343C22×C13911yescharacteristic, complemented
661#339C22×C13911yescharacteristic, complemented
662#339C22×C13911yescharacteristic, complemented
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C13911yescharacteristic, complemented
684C2×#41D4×C13911yescharacteristic, complemented
685C2×#41C23×C13911yescharacteristic
686C2×#41C23×C13911yescharacteristic
687C2×#41C23×C13911yescharacteristic
688C22×Q8D4×C13911yescharacteristic, complemented
689C22×Q8C23×C13911yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C13912yes—
698C22×D4D4×C13911yescharacteristic, complemented
699C22×D4C23×C13911yescharacteristic
700C22×D4C23×C13911yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C13911yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C13914yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C13914yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C13911yescharacteristic
736C2×M16C23×C13911yescharacteristic
737C2×M16C23×C13911yescharacteristic
738C2×M16C23×C13911yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C13911yescharacteristic, complemented
754C22⋊Q8D4×C13911yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C13911yescharacteristic, complemented
770#121D4×C13911yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C13911yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C13911yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C13912yes—
792C2×C42C23×C13911yescharacteristic
793C2×C42C23×C13911yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C13912yes—
814C24C2×D4×C13911yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C13912yes—
846#41C2×D4×C13912yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C13911yescharacteristic
856C2×Q8C2×D4×C13911yescharacteristic
857C2×Q8C2×D4×C13911yescharacteristic
858C2×Q8C2×D4×C13912yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C13911yescharacteristic
905C2×D4C2×D4×C13911yescharacteristic
906C2×D4C2×D4×C13911yescharacteristic
907C2×D4C2×D4×C13912yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C13911yescharacteristic
930C22×C4C2×D4×C13911yescharacteristic
931C22×C4C2×D4×C13911yescharacteristic
932C22×C4C2×D4×C13911yescharacteristic
933C22×C4C2×D4×C13911yescharacteristic
934C22×C4C2×D4×C13912yes—
935C22×C4C24×C13911yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C13912yescomplemented
956M16C2×D4×C13912yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C13911yescharacteristic
969C4⋊C4C2×D4×C13911yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C13911yescharacteristic
1015C23#120×C13911yescharacteristic
1016C23C22×D4×C13911yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C13912yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C13912yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C13911yescharacteristic
1103C2×C4#120×C13911yescharacteristic
1104C2×C4C22×D4×C13911yescharacteristic
1105C2×C4C22×D4×C13911yescharacteristic
1106C2×C4C22×D4×C13911yescharacteristic
1107C2×C4C22×D4×C13911yescharacteristic
1108C2×C4H(5,𝔽2)×C13911yescharacteristic
1109C2×C4H(5,𝔽2)×C13911yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—22no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—42no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C13911yescharacteristic
1146C22D42×C13911yescharacteristic
1147C22D42×C13911yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—41no—
1154C4—42no—
1155C4—41no—
1156C4—42no—
1157C4—41no—
1158C4—81no—
1159C4C2×#120×C13911yescharacteristic
1160C4#534×C13911yescharacteristic
1161C4D42×C13911yescharacteristic
1162C4D42×C13911yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2#2403×C13911yescharacteristic
1173C2#3018×C13911yescharacteristic
1174C2#3019×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C139C2semidirect
2. #3488×C139C2semidirect
3. C2×#455×C139C2semidirect
4. C2×#453×C139C2semidirect
5. #3005×C139C2semidirect
6. #2431×C139C2semidirect
7. #2007×C139C2semidirect
8. #2006×C139C2semidirect
9. #2004×C139C2semidirect
10. #2002×C139C2semidirect
11. #1900×C139C2semidirect
12. #1883×C139C2semidirect
13. #1882×C139C2semidirect
14. #1871×C139C2semidirect
15. #1789×C139C2semidirect
18. C22×#41×C139C22semidirect
23. C2×#137×C139C22semidirect
24. C2×#137×C139C22semidirect
27. C2×AGL(1,ℤ/8)×C139C22semidirect
28. C2×AGL(1,ℤ/8)×C139C22semidirect
31. C22×M16×C139C22semidirect
42. C2×#127×C139C22semidirect
43. C2×#124×C139C22semidirect
57. C2×#104×C139C22semidirect
58. C2×#104×C139C22semidirect
59. C2×#104×C139C22semidirect
60. C2×#104×C139C22semidirect
61. #419×C139C22semidirect
62. #418×C139C22semidirect
63. C2×#100×C139C22semidirect
64. C2×#100×C139C22semidirect
65. #407×C139C22semidirect
67. #391×C139C22semidirect
68. #390×C139C22semidirect
70. C4×C22⋊C4×C139C22semidirect
71. #343×C139C22semidirect
72. #343×C139C22semidirect
73. #339×C139C22semidirect
74. #339×C139C22semidirect
95. C2×#41×C139D4semidirect
96. C2×#41×C139D4semidirect
100. C22×Q8×C139D4semidirect
110. C22×D4×C139D4semidirect
122. #137×C139D4semidirect
129. AGL(1,ℤ/8)×C139D4semidirect
165. C22⋊Q8×C139D4semidirect
166. C22⋊Q8×C139D4semidirect
181. #121×C139D4semidirect
182. #121×C139D4semidirect
270. C2×Q8×C139C2×D4semidirect
319. C2×D4×C139C2×D4semidirect
367. M16×C139C2×D4semidirect
368. M16×C139C2×D4semidirect
587. #23878C139direct (N × H)
588. C139#23878direct (N × H)
589. C2×#575C2×C139semidirect
590. #3488C2×C139semidirect
591. C2×#455C2×C139semidirect
592. C2×#453C2×C139semidirect
593. #3005C2×C139semidirect
594. #2431C2×C139semidirect
595. #2007C2×C139semidirect
596. #2006C2×C139semidirect
597. #2004C2×C139semidirect
598. #2002C2×C139semidirect
599. #1900C2×C139semidirect
600. #1883C2×C139semidirect
601. #1882C2×C139semidirect
602. #1871C2×C139semidirect
603. #1789C2×C139semidirect
606. C22×#41C22×C139semidirect
611. C2×#137C22×C139semidirect
612. C2×#137C22×C139semidirect
615. C2×AGL(1,ℤ/8)C22×C139semidirect
616. C2×AGL(1,ℤ/8)C22×C139semidirect
619. C22×M16C22×C139semidirect
630. C2×#127C22×C139semidirect
631. C2×#124C22×C139semidirect
645. C2×#104C22×C139semidirect
646. C2×#104C22×C139semidirect
647. C2×#104C22×C139semidirect
648. C2×#104C22×C139semidirect
649. #419C22×C139semidirect
650. #418C22×C139semidirect
651. C2×#100C22×C139semidirect
652. C2×#100C22×C139semidirect
653. #407C22×C139semidirect
655. #391C22×C139semidirect
656. #390C22×C139semidirect
658. C4×C22⋊C4C22×C139semidirect
659. #343C22×C139semidirect
660. #343C22×C139semidirect
661. #339C22×C139semidirect
662. #339C22×C139semidirect
683. C2×#41D4×C139semidirect
684. C2×#41D4×C139semidirect
688. C22×Q8D4×C139semidirect
698. C22×D4D4×C139semidirect
710. #137D4×C139semidirect
717. AGL(1,ℤ/8)D4×C139semidirect
753. C22⋊Q8D4×C139semidirect
754. C22⋊Q8D4×C139semidirect
769. #121D4×C139semidirect
770. #121D4×C139semidirect
858. C2×Q8C2×D4×C139semidirect
907. C2×D4C2×D4×C139semidirect
955. M16C2×D4×C139semidirect
956. M16C2×D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1392
#3488×C1392
C2×#455×C1392
C2×#453×C1392
#3005×C1392
#2431×C1392
#2007×C1392
#2006×C1392
#2004×C1392
#2002×C1392
#1900×C1392
#1883×C1392
#1882×C1392
#1871×C1392
#1789×C1392
#23878139