Finite Group Databasebeta

← C139×#24524 #48019120

Subgroups — C139×#24524 #48019120

Order 35584.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C139C211yesmaximal, characteristic, complemented
2C2×#449×C139C211yesmaximal, characteristic
3#2924×C139C211yesmaximal, characteristic, complemented
4#2896×C139C211yesmaximal, characteristic, complemented
5#2064×C139C211yesmaximal, characteristic, complemented
6#2063×C139C211yesmaximal, characteristic, complemented
7#2046×C139C211yesmaximal, characteristic, complemented
8#2045×C139C211yesmaximal, characteristic, complemented
9#1978×C139C211yesmaximal, characteristic, complemented
10#1977×C139C211yesmaximal, characteristic, complemented
11#1931×C139C211yesmaximal, characteristic, complemented
12#1930×C139C211yesmaximal, characteristic, complemented
13#1900×C139C211yesmaximal, characteristic, complemented
14#1855×C139C211yesmaximal, characteristic, complemented
15#1785×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×#117×C139C2211yescharacteristic
22#482×C139—21no—
23#482×C139—21no—
24#481×C139—21no—
25#480×C139—21no—
26#449×C139—21no—
27#449×C139—21no—
28#449×C139—21no—
29#449×C139—21no—
30#433×C139—21no—
31#433×C139—21no—
32#432×C139—21no—
33#431×C139—21no—
34C2×#108×C139C2211yescharacteristic
35C2×#108×C139C2211yescharacteristic
36#428×C139C2211yescharacteristic
37#428×C139C2211yescharacteristic
38#424×C139C2211yescharacteristic
39#424×C139C2211yescharacteristic
40#419×C139C2211yescharacteristic
41#419×C139C2211yescharacteristic
42#418×C139C2211yescharacteristic
43#418×C139C2211yescharacteristic
44#418×C139C2211yescharacteristic
45#418×C139C2211yescharacteristic
46#417×C139—21no—
47#417×C139—21no—
48#416×C139—21no—
49#416×C139—21no—
50C2×#103×C139C2211yescharacteristic
51C2×#102×C139C2211yescharacteristic
52C2×#101×C139C2211yescharacteristic
53C2×#101×C139C2211yescharacteristic
54C2×#100×C139C2211yescharacteristic
55C2×#100×C139C2211yescharacteristic
56C2×#100×C139C2211yescharacteristic
57C2×#100×C139C2211yescharacteristic
58#407×C139C2211yescharacteristic
59#407×C139C2211yescharacteristic
60C2×C22⋊C8×C139C2211yescharacteristic
61#405×C139C2211yescharacteristic
62#405×C139C2211yescharacteristic
63#343×C139C2211yescharacteristic
64#343×C139C2211yescharacteristic
65#341×C139C2211yescharacteristic
66#341×C139C2211yescharacteristic
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C22×Q8×C139C2311yescharacteristic
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139C2311yescharacteristic
79C22×D4×C139C2311yescharacteristic
80C23×C4×C139—21no—
81C23×C4×C139C2311yescharacteristic
82C2×SD16×C139—22no—
83C2×SD16×C139—21no—
84C2×SD16×C139—21no—
85C2×SD16×C139—41no—
86C2×D8×C139—22no—
87C2×D8×C139—21no—
88C2×D8×C139—21no—
89C2×D8×C139—41no—
90C2×M16×C139—21no—
91C2×M16×C139—41no—
92C2×M16×C139—41no—
93C2×M16×C139C2311yescharacteristic
94C2×M16×C139C2311yescharacteristic
95C2×M16×C139C2311yescharacteristic
96C2×M16×C139C2311yescharacteristic
97C2×M16×C139C2311yescharacteristic
98C2×M16×C139C2311yescharacteristic
99C22×C8×C139—21no—
100C22×C8×C139C2311yescharacteristic
101C22×C8×C139C2311yescharacteristic
102#121×C139—21no—
103#121×C139—21no—
104#121×C139—21no—
105#121×C139—21no—
106#117×C139—21no—
107#117×C139—21no—
108#117×C139D411yescharacteristic
109#117×C139D411yescharacteristic
110#117×C139C2311yescharacteristic
111#117×C139C2311yescharacteristic
112C2×C4⋊C4×C139D411yescharacteristic
113C2×C4⋊C4×C139D411yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C42×C139—21no—
118#108×C139—41no—
119#108×C139—41no—
120#107×C139—21no—
121#107×C139—21no—
122#106×C139—21no—
123#106×C139—21no—
124C4⋊C8×C139—21no—
125C4⋊C8×C139—21no—
126C4⋊C8×C139—21no—
127C4⋊C8×C139—21no—
128#103×C139—21no—
129#103×C139—21no—
130#103×C139—21no—
131#103×C139—21no—
132#103×C139—21no—
133#103×C139—21no—
134#102×C139—21no—
135#102×C139—21no—
136#102×C139—21no—
137#102×C139—21no—
138#102×C139—21no—
139#102×C139—21no—
140#102×C139—21no—
141#102×C139—21no—
142#102×C139—21no—
143#102×C139—21no—
144#101×C139—22no—
145#101×C139—41no—
146#100×C139—22no—
147#100×C139—41no—
148#100×C139—41no—
149#100×C139—41no—
150C22⋊C8×C139—21no—
151C22⋊C8×C139—21no—
152C22⋊C8×C139—21no—
153C22⋊C8×C139—21no—
154C22⋊C8×C139D411yescharacteristic
155C22⋊C8×C139D411yescharacteristic
156C22⋊C8×C139D411yescharacteristic
157C22⋊C8×C139D411yescharacteristic
158#97×C139—21no—
159#97×C139—21no—
160C4×C8×C139—21no—
161C4×C8×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139#4111yescharacteristic
165#41×C139—24no—
166#41×C139—24no—
167#41×C139—42no—
168#41×C139—42no—
169#41×C139—42no—
170#41×C139—42no—
171#41×C139—42no—
172#41×C139—42no—
173C2×Q8×C139—21no—
174C2×Q8×C139—21no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139#4112yes—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—21no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—41no—
193C2×D4×C139—41no—
194C2×D4×C139—41no—
195C2×D4×C139—41no—
196C2×D4×C139—82no—
197C2×D4×C139#4112yes—
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—21no—
206C22×C4×C139—42no—
207C22×C4×C139—42no—
208C22×C4×C139—41no—
209C22×C4×C139—41no—
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139#4111yescharacteristic
215C22×C4×C139C2411yescharacteristic
216SD16×C139—42no—
217SD16×C139—42no—
218D8×C139—42no—
219D8×C139—42no—
220M16×C139—21no—
221M16×C139—21no—
222M16×C139—21no—
223M16×C139—21no—
224M16×C139—21no—
225M16×C139—21no—
226M16×C139—21no—
227M16×C139—21no—
228M16×C139—21no—
229M16×C139—21no—
230M16×C139—21no—
231M16×C139—21no—
232M16×C139—42no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—42no—
244C2×C8×C139C2×D411yescharacteristic
245C2×C8×C139C2×D411yescharacteristic
246C2×C8×C139C2×D411yescharacteristic
247C2×C8×C139C2×D411yescharacteristic
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139C2×D411yescharacteristic
253C4⋊C4×C139C2×D411yescharacteristic
254C4⋊C4×C139C2×D411yescharacteristic
255C4⋊C4×C139C2×D411yescharacteristic
256C22⋊C4×C139—21no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—21no—
259C22⋊C4×C139—21no—
260C22⋊C4×C139—41no—
261C22⋊C4×C139—41no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—21no—
265C42×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—22no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—81no—
277C23×C139—81no—
278C23×C139—81no—
279C23×C139—81no—
280C23×C139#12111yescharacteristic
281C23×C139#12111yescharacteristic
282C23×C139C2×#4111yescharacteristic
283Q8×C139—22no—
284Q8×C139—22no—
285Q8×C139—41no—
286Q8×C139—41no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—44no—
290D4×C139—44no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—82no—
298D4×C139—82no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—22no—
314C2×C4×C139—44no—
315C2×C4×C139—44no—
316C2×C4×C139—42no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—81no—
321C2×C4×C139—81no—
322C2×C4×C139#12111yescharacteristic
323C2×C4×C139#12111yescharacteristic
324C2×C4×C139C22×D411yescharacteristic
325C2×C4×C139C22×D411yescharacteristic
326C2×C4×C139C2×#4111yescharacteristic
327C2×C4×C139C2×#4111yescharacteristic
328C2×C4×C139H(5,𝔽2)11yescharacteristic
329C2×C4×C139H(5,𝔽2)11yescharacteristic
330C8×C139—21no—
331C8×C139—21no—
332C8×C139—21no—
333C8×C139—21no—
334C8×C139—41no—
335C8×C139—41no—
336C8×C139—41no—
337C8×C139—41no—
338C8×C139—41no—
339C8×C139—41no—
340C22×C139—21no—
341C22×C139—21no—
342C22×C139—21no—
343C22×C139—21no—
344C22×C139—21no—
345C22×C139—21no—
346C22×C139—21no—
347C22×C139—21no—
348C22×C139—42no—
349C22×C139—81no—
350C22×C139—81no—
351C22×C139—82no—
352C22×C139—82no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—161no—
359C22×C139—161no—
360C22×C139C2×#12111yescharacteristic
361C22×C139#55111yescharacteristic
362C22×C139#55111yescharacteristic
363C4×C139—21no—
364C4×C139—21no—
365C4×C139—42no—
366C4×C139—41no—
367C4×C139—41no—
368C4×C139—41no—
369C4×C139—41no—
370C4×C139—81no—
371C4×C139#52511yescharacteristic
372C4×C139#53511yescharacteristic
373C4×C139#54611yescharacteristic
374C4×C139#54611yescharacteristic
375C2×C139—21no—
376C2×C139—21no—
377C2×C139—41no—
378C2×C139—41no—
379C2×C139—82no—
380C2×C139—161no—
381C2×C139#241111yescharacteristic
382C2×C139#306711yescharacteristic
383C2×C139#306811yescharacteristic
384#24524C13911yesmaximal, characteristic, direct product factor, Sylow
385C139#2452411yescharacteristic, direct product factor, Sylow
386#3094C2×C13911yescharacteristic, complemented
387C2×#449C2×C13911yescharacteristic
388#2924C2×C13911yescharacteristic, complemented
389#2896C2×C13911yescharacteristic, complemented
390#2064C2×C13911yescharacteristic, complemented
391#2063C2×C13911yescharacteristic, complemented
392#2046C2×C13911yescharacteristic, complemented
393#2045C2×C13911yescharacteristic, complemented
394#1978C2×C13911yescharacteristic, complemented
395#1977C2×C13911yescharacteristic, complemented
396#1931C2×C13911yescharacteristic, complemented
397#1930C2×C13911yescharacteristic, complemented
398#1900C2×C13911yescharacteristic, complemented
399#1855C2×C13911yescharacteristic, complemented
400#1785C2×C13911yescharacteristic, complemented
401C22×#41C22×C13911yescharacteristic
402C22×SD16C22×C13911yescharacteristic
403C22×D8C22×C13911yescharacteristic
404C22×M16C22×C13911yescharacteristic
405C2×#121C22×C13911yescharacteristic
406C2×#117C22×C13911yescharacteristic
407#482—21no—
408#482—21no—
409#481—21no—
410#480—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#449—21no—
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C13911yescharacteristic
420C2×#108C22×C13911yescharacteristic
421#428C22×C13911yescharacteristic
422#428C22×C13911yescharacteristic
423#424C22×C13911yescharacteristic
424#424C22×C13911yescharacteristic
425#419C22×C13911yescharacteristic
426#419C22×C13911yescharacteristic
427#418C22×C13911yescharacteristic
428#418C22×C13911yescharacteristic
429#418C22×C13911yescharacteristic
430#418C22×C13911yescharacteristic
431#417—21no—
432#417—21no—
433#416—21no—
434#416—21no—
435C2×#103C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×#101C22×C13911yescharacteristic
438C2×#101C22×C13911yescharacteristic
439C2×#100C22×C13911yescharacteristic
440C2×#100C22×C13911yescharacteristic
441C2×#100C22×C13911yescharacteristic
442C2×#100C22×C13911yescharacteristic
443#407C22×C13911yescharacteristic
444#407C22×C13911yescharacteristic
445C2×C22⋊C8C22×C13911yescharacteristic
446#405C22×C13911yescharacteristic
447#405C22×C13911yescharacteristic
448#343C22×C13911yescharacteristic
449#343C22×C13911yescharacteristic
450#341C22×C13911yescharacteristic
451#341C22×C13911yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C13911yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C13911yescharacteristic
464C22×D4C23×C13911yescharacteristic
465C23×C4—21no—
466C23×C4C23×C13911yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C13911yescharacteristic
479C2×M16C23×C13911yescharacteristic
480C2×M16C23×C13911yescharacteristic
481C2×M16C23×C13911yescharacteristic
482C2×M16C23×C13911yescharacteristic
483C2×M16C23×C13911yescharacteristic
484C22×C8—21no—
485C22×C8C23×C13911yescharacteristic
486C22×C8C23×C13911yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C13911yescharacteristic
494#117D4×C13911yescharacteristic
495#117C23×C13911yescharacteristic
496#117C23×C13911yescharacteristic
497C2×C4⋊C4D4×C13911yescharacteristic
498C2×C4⋊C4D4×C13911yescharacteristic
499C2×C4⋊C4C23×C13911yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C13911yescharacteristic
540C22⋊C8D4×C13911yescharacteristic
541C22⋊C8D4×C13911yescharacteristic
542C22⋊C8D4×C13911yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C13911yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C13912yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C13912yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4C2×D4×C13911yescharacteristic
597C22×C4C2×D4×C13911yescharacteristic
598C22×C4C2×D4×C13911yescharacteristic
599C22×C4#41×C13911yescharacteristic
600C22×C4C24×C13911yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C13911yescharacteristic
630C2×C8C2×D4×C13911yescharacteristic
631C2×C8C2×D4×C13911yescharacteristic
632C2×C8C2×D4×C13911yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C13911yescharacteristic
638C4⋊C4C2×D4×C13911yescharacteristic
639C4⋊C4C2×D4×C13911yescharacteristic
640C4⋊C4C2×D4×C13911yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C13911yescharacteristic
666C23#121×C13911yescharacteristic
667C23C2×#41×C13911yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C13911yescharacteristic
708C2×C4#121×C13911yescharacteristic
709C2×C4C22×D4×C13911yescharacteristic
710C2×C4C22×D4×C13911yescharacteristic
711C2×C4C2×#41×C13911yescharacteristic
712C2×C4C2×#41×C13911yescharacteristic
713C2×C4H(5,𝔽2)×C13911yescharacteristic
714C2×C4H(5,𝔽2)×C13911yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C13911yescharacteristic
746C22#551×C13911yescharacteristic
747C22#551×C13911yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—81no—
756C4#525×C13911yescharacteristic
757C4#535×C13911yescharacteristic
758C4#546×C13911yescharacteristic
759C4#546×C13911yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2#2411×C13911yescharacteristic
767C2#3067×C13911yescharacteristic
768C2#3068×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#449×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. #3094×C139C2semidirect
3. #2924×C139C2semidirect
4. #2896×C139C2semidirect
5. #2064×C139C2semidirect
6. #2063×C139C2semidirect
7. #2046×C139C2semidirect
8. #2045×C139C2semidirect
9. #1978×C139C2semidirect
10. #1977×C139C2semidirect
11. #1931×C139C2semidirect
12. #1930×C139C2semidirect
13. #1900×C139C2semidirect
14. #1855×C139C2semidirect
15. #1785×C139C2semidirect
384. #24524C139direct (N × H)
385. C139#24524direct (N × H)
386. #3094C2×C139semidirect
388. #2924C2×C139semidirect
389. #2896C2×C139semidirect
390. #2064C2×C139semidirect
391. #2063C2×C139semidirect
392. #2046C2×C139semidirect
393. #2045C2×C139semidirect
394. #1978C2×C139semidirect
395. #1977C2×C139semidirect
396. #1931C2×C139semidirect
397. #1930C2×C139semidirect
398. #1900C2×C139semidirect
399. #1855C2×C139semidirect
400. #1785C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3094×C1392
C2×#449×C1392
#2924×C1392
#2896×C1392
#2064×C1392
#2063×C1392
#2046×C1392
#2045×C1392
#1978×C1392
#1977×C1392
#1931×C1392
#1930×C1392
#1900×C1392
#1855×C1392
#1785×C1392
#24524139