Finite Group Databasebeta

← C139×#24283 #48018879

Subgroups — C139×#24283 #48018879

Order 35584.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C139C211yesmaximal, characteristic, complemented
2C2×#473×C139C211yesmaximal, characteristic, complemented
3C2×#471×C139C211yesmaximal, characteristic, complemented
4#3005×C139C211yesmaximal, characteristic
5#3004×C139C211yesmaximal, characteristic, complemented
6#2930×C139C211yesmaximal, characteristic, complemented
7#2047×C139C211yesmaximal, characteristic, complemented
8#2046×C139C211yesmaximal, characteristic, complemented
9#2020×C139C211yesmaximal, characteristic, complemented
10#2019×C139C211yesmaximal, characteristic, complemented
11#1979×C139C211yesmaximal, characteristic, complemented
12#1977×C139C211yesmaximal, characteristic, complemented
13#1811×C139C211yesmaximal, characteristic, complemented
14#1785×C139C211yesmaximal, characteristic, complemented
15#1784×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18C2×#137×C139—24no—
19C2×#137×C139—24no—
20C2×#137×C139—22no—
21C2×#137×C139—22no—
22C2×#137×C139C2211yescharacteristic
23C2×#137×C139C2211yescharacteristic
24C2×#137×C139C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
26C22×Q16×C139C2211yescharacteristic
27C22×Q16×C139C2211yescharacteristic
28C22×SD16×C139C2211yescharacteristic
29C22×SD16×C139C2211yescharacteristic
30C2×#131×C139C2211yescharacteristic
31C22×M16×C139C2211yescharacteristic
32#525×C139C2211yescharacteristic
33#473×C139—24no—
34#471×C139—24no—
35#452×C139—22no—
36#451×C139—22no—
37#449×C139—22no—
38#448×C139—22no—
39#436×C139—22no—
40#435×C139—22no—
41C2×#108×C139C2211yescharacteristic
42C2×#108×C139C2211yescharacteristic
43#424×C139C2211yescharacteristic
44#419×C139C2211yescharacteristic
45#419×C139C2211yescharacteristic
46#419×C139C2211yescharacteristic
47#418×C139C2211yescharacteristic
48C2×#101×C139C2211yescharacteristic
49C2×#101×C139C2211yescharacteristic
50C2×#101×C139C2211yescharacteristic
51C2×#101×C139C2211yescharacteristic
52C2×#101×C139C2211yescharacteristic
53C2×#101×C139C2211yescharacteristic
54C2×#100×C139C2211yescharacteristic
55C2×#100×C139C2211yescharacteristic
56#408×C139C2211yescharacteristic
57#407×C139C2211yescharacteristic
58#407×C139C2211yescharacteristic
59#407×C139C2211yescharacteristic
60#405×C139C2211yescharacteristic
61#341×C139C2211yescharacteristic
62#341×C139C2211yescharacteristic
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C2×#41×C139C2311yescharacteristic
70C22×Q8×C139—21no—
71C22×Q8×C139—22no—
72C22×Q8×C139—22no—
73C22×Q8×C139—22no—
74C22×Q8×C139—22no—
75C22×Q8×C139—41no—
76C22×Q8×C139—41no—
77C22×Q8×C139C2311yescharacteristic
78C22×Q8×C139C2311yescharacteristic
79C22×Q8×C139C2311yescharacteristic
80C22×D4×C139—21no—
81C22×D4×C139C2311yescharacteristic
82C23×C4×C139—21no—
83C23×C4×C139—21no—
84C23×C4×C139C2311yescharacteristic
85#137×C139—216no—
86#137×C139—216no—
87#137×C139—22no—
88#137×C139—22no—
89#137×C139—22no—
90#137×C139—41no—
91#137×C139—41no—
92#137×C139—41no—
93AGL(1,ℤ/8)×C139—22no—
94AGL(1,ℤ/8)×C139—41no—
95C2×Q16×C139—22no—
96C2×Q16×C139—22no—
97C2×Q16×C139—21no—
98C2×Q16×C139—21no—
99C2×Q16×C139—21no—
100C2×Q16×C139—22no—
101C2×Q16×C139—21no—
102C2×Q16×C139—21no—
103C2×Q16×C139—22no—
104C2×Q16×C139D414yescomplemented
105C2×SD16×C139—22no—
106C2×SD16×C139—22no—
107C2×SD16×C139—21no—
108C2×SD16×C139—21no—
109C2×SD16×C139—21no—
110C2×SD16×C139—21no—
111C2×SD16×C139—22no—
112C2×SD16×C139—21no—
113C2×SD16×C139—21no—
114C2×SD16×C139—22no—
115C2×SD16×C139D414yescomplemented
116C2×D8×C139—21no—
117#131×C139—22no—
118#131×C139—22no—
119C2×M16×C139—22no—
120C2×M16×C139—22no—
121C2×M16×C139—21no—
122C2×M16×C139D412yes—
123C2×M16×C139D412yes—
124C2×M16×C139C2311yescharacteristic
125C2×M16×C139C2311yescharacteristic
126C2×M16×C139C2311yescharacteristic
127C2×M16×C139C2311yescharacteristic
128C2×M16×C139C2311yescharacteristic
129C2×M16×C139C2311yescharacteristic
130C22×C8×C139—21no—
131C22×C8×C139C2311yescharacteristic
132C22×C8×C139C2311yescharacteristic
133#123×C139—21no—
134C22⋊Q8×C139D412yes—
135#121×C139D412yes—
136#120×C139—21no—
137C4×D4×C139—22no—
138#117×C139C2311yescharacteristic
139#108×C139—22no—
140#108×C139—22no—
141C4⋊C8×C139—22no—
142#103×C139—22no—
143#103×C139—22no—
144#103×C139—22no—
145#102×C139—22no—
146#101×C139—22no—
147#101×C139—22no—
148#101×C139—22no—
149#101×C139—41no—
150#101×C139—41no—
151#101×C139—41no—
152#100×C139—22no—
153#100×C139—41no—
154C22⋊C8×C139—22no—
155C22⋊C8×C139—22no—
156C22⋊C8×C139—22no—
157C22⋊C8×C139—22no—
158#97×C139—21no—
159C4×C8×C139—21no—
160C24×C139—21no—
161C24×C139#4111yescharacteristic
162#41×C139—28no—
163#41×C139—21no—
164#41×C139—21no—
165#41×C139—21no—
166#41×C139—21no—
167#41×C139—44no—
168#41×C139—44no—
169#41×C139—44no—
170C2×Q8×C139—21no—
171C2×Q8×C139—21no—
172C2×Q8×C139—21no—
173C2×Q8×C139—28no—
174C2×Q8×C139—21no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—42no—
187C2×Q8×C139—42no—
188C2×Q8×C139—44no—
189C2×Q8×C139—44no—
190C2×Q8×C139—44no—
191C2×Q8×C139—42no—
192C2×Q8×C139C2×D412yes—
193C2×Q8×C139C2×D412yes—
194C2×Q8×C139C2×D412yes—
195C2×Q8×C139C2×D411yescharacteristic
196C2×D4×C139—21no—
197C2×D4×C139—22no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—42no—
204C2×D4×C139—42no—
205C2×D4×C139—42no—
206C2×D4×C139C2×D412yes—
207C2×D4×C139C2×D411yescharacteristic
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—42no—
217C22×C4×C139—42no—
218C22×C4×C139—42no—
219C22×C4×C139—42no—
220C22×C4×C139—42no—
221C22×C4×C139—42no—
222C22×C4×C139C2×D412yes—
223C22×C4×C139C2×D412yes—
224C22×C4×C139#4111yescharacteristic
225C22×C4×C139C2411yescharacteristic
226Q16×C139—28no—
227Q16×C139—24no—
228Q16×C139—24no—
229Q16×C139—42no—
230Q16×C139—42no—
231Q16×C139—42no—
232SD16×C139—28no—
233SD16×C139—24no—
234SD16×C139—24no—
235SD16×C139—42no—
236SD16×C139—42no—
237SD16×C139—42no—
238SD16×C139—42no—
239D8×C139—42no—
240M16×C139—24no—
241M16×C139—24no—
242M16×C139—21no—
243M16×C139—21no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—21no—
254M16×C139—42no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—42no—
264C2×C8×C139C2×D412yes—
265C2×C8×C139C2×D411yescharacteristic
266C2×C8×C139C2×D411yescharacteristic
267C2×C8×C139C2×D412yes—
268C2×C8×C139C2×D412yes—
269C4⋊C4×C139—22no—
270C4⋊C4×C139C2×D412yes—
271C22⋊C4×C139—22no—
272C22⋊C4×C139—21no—
273C22⋊C4×C139—22no—
274C42×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—22no—
279C23×C139—42no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—82no—
283C23×C139#12112yes—
284C23×C139C2×#4111yescharacteristic
285Q8×C139—22no—
286Q8×C139—22no—
287Q8×C139—22no—
288Q8×C139—21no—
289Q8×C139—22no—
290Q8×C139—22no—
291Q8×C139—22no—
292Q8×C139—21no—
293Q8×C139—48no—
294Q8×C139—41no—
295Q8×C139—41no—
296Q8×C139—41no—
297Q8×C139—41no—
298Q8×C139—41no—
299Q8×C139—41no—
300D4×C139—22no—
301D4×C139—21no—
302D4×C139—22no—
303D4×C139—21no—
304D4×C139—48no—
305D4×C139—41no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—41no—
309D4×C139—82no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—22no—
313C2×C4×C139—22no—
314C2×C4×C139—22no—
315C2×C4×C139—22no—
316C2×C4×C139—22no—
317C2×C4×C139—21no—
318C2×C4×C139—22no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—48no—
322C2×C4×C139—48no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139#12112yes—
332C2×C4×C139C22×D411yescharacteristic
333C2×C4×C139C22×D411yescharacteristic
334C2×C4×C139C22×D411yescharacteristic
335C2×C4×C139C22×D411yescharacteristic
336C2×C4×C139H(5,𝔽2)11yescharacteristic
337C2×C4×C139H(5,𝔽2)11yescharacteristic
338C8×C139—22no—
339C8×C139—41no—
340C8×C139—41no—
341C8×C139—41no—
342C8×C139—41no—
343C8×C139—41no—
344C8×C139—41no—
345C8×C139#12012yes—
346C8×C139#12012yes—
347C22×C139—22no—
348C22×C139—22no—
349C22×C139—22no—
350C22×C139—22no—
351C22×C139—42no—
352C22×C139—42no—
353C22×C139—42no—
354C22×C139—41no—
355C22×C139—42no—
356C22×C139—82no—
357C22×C139—82no—
358C22×C139—82no—
359C22×C139C2×#12111yescharacteristic
360C22×C139#54611yescharacteristic
361C22×C139#54611yescharacteristic
362C4×C139—22no—
363C4×C139—42no—
364C4×C139—42no—
365C4×C139—42no—
366C4×C139—41no—
367C4×C139—42no—
368C4×C139C2×#12011yescharacteristic
369C4×C139#53511yescharacteristic
370C4×C139D4211yescharacteristic
371C4×C139D4211yescharacteristic
372C2×C139—21no—
373C2×C139—21no—
374C2×C139—42no—
375C2×C139—81no—
376C2×C139—82no—
377C2×C139#240811yescharacteristic
378C2×C139#306912yes—
379#24283C13911yesmaximal, characteristic, direct product factor, Sylow
380C139#2428311yescharacteristic, direct product factor, Sylow
381C22×#137C2×C13911yescharacteristic, complemented
382C2×#473C2×C13911yescharacteristic, complemented
383C2×#471C2×C13911yescharacteristic, complemented
384#3005C2×C13911yescharacteristic
385#3004C2×C13911yescharacteristic, complemented
386#2930C2×C13911yescharacteristic, complemented
387#2047C2×C13911yescharacteristic, complemented
388#2046C2×C13911yescharacteristic, complemented
389#2020C2×C13911yescharacteristic, complemented
390#2019C2×C13911yescharacteristic, complemented
391#1979C2×C13911yescharacteristic, complemented
392#1977C2×C13911yescharacteristic, complemented
393#1811C2×C13911yescharacteristic, complemented
394#1785C2×C13911yescharacteristic, complemented
395#1784C2×C13911yescharacteristic, complemented
396C22×#41C22×C13911yescharacteristic
397C23×Q8C22×C13911yescharacteristic
398C2×#137—24no—
399C2×#137—24no—
400C2×#137—22no—
401C2×#137—22no—
402C2×#137C22×C13911yescharacteristic
403C2×#137C22×C13911yescharacteristic
404C2×#137C22×C13911yescharacteristic
405C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
406C22×Q16C22×C13911yescharacteristic
407C22×Q16C22×C13911yescharacteristic
408C22×SD16C22×C13911yescharacteristic
409C22×SD16C22×C13911yescharacteristic
410C2×#131C22×C13911yescharacteristic
411C22×M16C22×C13911yescharacteristic
412#525C22×C13911yescharacteristic
413#473—24no—
414#471—24no—
415#452—22no—
416#451—22no—
417#449—22no—
418#448—22no—
419#436—22no—
420#435—22no—
421C2×#108C22×C13911yescharacteristic
422C2×#108C22×C13911yescharacteristic
423#424C22×C13911yescharacteristic
424#419C22×C13911yescharacteristic
425#419C22×C13911yescharacteristic
426#419C22×C13911yescharacteristic
427#418C22×C13911yescharacteristic
428C2×#101C22×C13911yescharacteristic
429C2×#101C22×C13911yescharacteristic
430C2×#101C22×C13911yescharacteristic
431C2×#101C22×C13911yescharacteristic
432C2×#101C22×C13911yescharacteristic
433C2×#101C22×C13911yescharacteristic
434C2×#100C22×C13911yescharacteristic
435C2×#100C22×C13911yescharacteristic
436#408C22×C13911yescharacteristic
437#407C22×C13911yescharacteristic
438#407C22×C13911yescharacteristic
439#407C22×C13911yescharacteristic
440#405C22×C13911yescharacteristic
441#341C22×C13911yescharacteristic
442#341C22×C13911yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41C23×C13911yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C13911yescharacteristic
458C22×Q8C23×C13911yescharacteristic
459C22×Q8C23×C13911yescharacteristic
460C22×D4—21no—
461C22×D4C23×C13911yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C13911yescharacteristic
465#137—216no—
466#137—216no—
467#137—22no—
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—41no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—22no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16D4×C13914yescomplemented
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16D4×C13914yescomplemented
496C2×D8—21no—
497#131—22no—
498#131—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—21no—
502C2×M16D4×C13912yes—
503C2×M16D4×C13912yes—
504C2×M16C23×C13911yescharacteristic
505C2×M16C23×C13911yescharacteristic
506C2×M16C23×C13911yescharacteristic
507C2×M16C23×C13911yescharacteristic
508C2×M16C23×C13911yescharacteristic
509C2×M16C23×C13911yescharacteristic
510C22×C8—21no—
511C22×C8C23×C13911yescharacteristic
512C22×C8C23×C13911yescharacteristic
513#123—21no—
514C22⋊Q8D4×C13912yes—
515#121D4×C13912yes—
516#120—21no—
517C4×D4—22no—
518#117C23×C13911yescharacteristic
519#108—22no—
520#108—22no—
521C4⋊C8—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#101—22no—
527#101—22no—
528#101—22no—
529#101—41no—
530#101—41no—
531#101—41no—
532#100—22no—
533#100—41no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538#97—21no—
539C4×C8—21no—
540C24—21no—
541C24#41×C13911yescharacteristic
542#41—28no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C13912yes—
573C2×Q8C2×D4×C13912yes—
574C2×Q8C2×D4×C13912yes—
575C2×Q8C2×D4×C13911yescharacteristic
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×D4×C13912yes—
587C2×D4C2×D4×C13911yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C13912yes—
603C22×C4C2×D4×C13912yes—
604C22×C4#41×C13911yescharacteristic
605C22×C4C24×C13911yescharacteristic
606Q16—28no—
607Q16—24no—
608Q16—24no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612SD16—28no—
613SD16—24no—
614SD16—24no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619D8—42no—
620M16—24no—
621M16—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C2×C8C2×D4×C13912yes—
645C2×C8C2×D4×C13911yescharacteristic
646C2×C8C2×D4×C13911yescharacteristic
647C2×C8C2×D4×C13912yes—
648C2×C8C2×D4×C13912yes—
649C4⋊C4—22no—
650C4⋊C4C2×D4×C13912yes—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C42—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23#121×C13912yes—
664C23C2×#41×C13911yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#121×C13912yes—
712C2×C4C22×D4×C13911yescharacteristic
713C2×C4C22×D4×C13911yescharacteristic
714C2×C4C22×D4×C13911yescharacteristic
715C2×C4C22×D4×C13911yescharacteristic
716C2×C4H(5,𝔽2)×C13911yescharacteristic
717C2×C4H(5,𝔽2)×C13911yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8#120×C13912yes—
726C8#120×C13912yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×#121×C13911yescharacteristic
740C22#546×C13911yescharacteristic
741C22#546×C13911yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—41no—
748C4C2×#120×C13911yescharacteristic
749C4#535×C13911yescharacteristic
750C4D42×C13911yescharacteristic
751C4D42×C13911yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2#2408×C13911yescharacteristic
758C2#3069×C13912yes—
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#3005×C139C2
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. C22×#137×C139C2semidirect
2. C2×#473×C139C2semidirect
3. C2×#471×C139C2semidirect
5. #3004×C139C2semidirect
6. #2930×C139C2semidirect
7. #2047×C139C2semidirect
8. #2046×C139C2semidirect
9. #2020×C139C2semidirect
10. #2019×C139C2semidirect
11. #1979×C139C2semidirect
12. #1977×C139C2semidirect
13. #1811×C139C2semidirect
14. #1785×C139C2semidirect
15. #1784×C139C2semidirect
104. C2×Q16×C139D4semidirect
115. C2×SD16×C139D4semidirect
379. #24283C139direct (N × H)
380. C139#24283direct (N × H)
381. C22×#137C2×C139semidirect
382. C2×#473C2×C139semidirect
383. C2×#471C2×C139semidirect
385. #3004C2×C139semidirect
386. #2930C2×C139semidirect
387. #2047C2×C139semidirect
388. #2046C2×C139semidirect
389. #2020C2×C139semidirect
390. #2019C2×C139semidirect
391. #1979C2×C139semidirect
392. #1977C2×C139semidirect
393. #1811C2×C139semidirect
394. #1785C2×C139semidirect
395. #1784C2×C139semidirect
484. C2×Q16D4×C139semidirect
495. C2×SD16D4×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1392
C2×#473×C1392
C2×#471×C1392
#3005×C1392
#3004×C1392
#2930×C1392
#2047×C1392
#2046×C1392
#2020×C1392
#2019×C1392
#1979×C1392
#1977×C1392
#1811×C1392
#1785×C1392
#1784×C1392
#24283139