Finite Group Databasebeta

← C139×#25141 #48019737

Subgroups — C139×#25141 #48019737

Order 35584.

1022 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
1C2×#472×C139C211yesmaximal, characteristic, complemented
2#3055×C139C211yesmaximal, characteristic, complemented
3#3005×C139C211yesmaximal, characteristic, complemented
4C2×#449×C139C211yesmaximal, characteristic, complemented
5#2933×C139C211yesmaximal, characteristic, complemented
6C2×#413×C139C211yesmaximal, characteristic, complemented
7#2064×C139C211yesmaximal, characteristic, complemented
8#2051×C139C211yesmaximal, characteristic, complemented
9#2045×C139C211yesmaximal, characteristic, complemented
10#2019×C139C211yesmaximal, characteristic, complemented
11#1977×C139C211yesmaximal, characteristic, complemented
12#1931×C139C211yesmaximal, characteristic, complemented
13#1908×C139C211yesmaximal, characteristic, complemented
14#1900×C139C211yesmaximal, characteristic, complemented
15#1855×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#137×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21C22×D8×C139C2211yescharacteristic
22C2×#131×C139C2211yescharacteristic
23C22×M16×C139C2211yescharacteristic
24C22×M16×C139C2211yescharacteristic
25#525×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27#472×C139—24no—
28#469×C139—21no—
29#468×C139—21no—
30#466×C139—21no—
31#465×C139—21no—
32#452×C139—21no—
33#452×C139—21no—
34#449×C139—21no—
35#449×C139—21no—
36#449×C139—21no—
37#449×C139—21no—
38#449×C139—21no—
39#449×C139—21no—
40#436×C139—21no—
41#435×C139—21no—
42#435×C139—21no—
43C8×D4×C139—21no—
44C2×#108×C139C2211yescharacteristic
45C2×#108×C139C2211yescharacteristic
46#428×C139C2211yescharacteristic
47#424×C139C2211yescharacteristic
48#419×C139C2211yescharacteristic
49#418×C139C2211yescharacteristic
50#418×C139C2211yescharacteristic
51#417×C139C2211yescharacteristic
52C2×#103×C139C2211yescharacteristic
53C2×#102×C139C2211yescharacteristic
54#413×C139—24no—
55C2×#101×C139C2211yescharacteristic
56C2×#101×C139C2211yescharacteristic
57C2×#100×C139C2211yescharacteristic
58C2×#100×C139C2211yescharacteristic
59C2×#100×C139C2211yescharacteristic
60C2×#100×C139C2211yescharacteristic
61#408×C139C2211yescharacteristic
62#407×C139C2211yescharacteristic
63C2×C22⋊C8×C139C2211yescharacteristic
64#405×C139C2211yescharacteristic
65#343×C139C2211yescharacteristic
66#343×C139C2211yescharacteristic
67#341×C139C2211yescharacteristic
68#341×C139C2211yescharacteristic
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—21no—
72C2×#41×C139—21no—
73C2×#41×C139—21no—
74C2×#41×C139—21no—
75C2×#41×C139—41no—
76C2×#41×C139—41no—
77C2×#41×C139C2311yescharacteristic
78C22×Q8×C139C2311yescharacteristic
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139C2311yescharacteristic
85#137×C139—22no—
86#137×C139—41no—
87AGL(1,ℤ/8)×C139—22no—
88AGL(1,ℤ/8)×C139—22no—
89AGL(1,ℤ/8)×C139—41no—
90AGL(1,ℤ/8)×C139—41no—
91C2×Q16×C139—21no—
92C2×SD16×C139—21no—
93C2×SD16×C139—21no—
94C2×SD16×C139—22no—
95C2×SD16×C139—21no—
96C2×SD16×C139—21no—
97C2×SD16×C139—21no—
98C2×SD16×C139—41no—
99C2×D8×C139—21no—
100C2×D8×C139—21no—
101C2×D8×C139—22no—
102C2×D8×C139—21no—
103C2×D8×C139—21no—
104C2×D8×C139—41no—
105#131×C139—22no—
106#131×C139—41no—
107C2×M16×C139—21no—
108C2×M16×C139—21no—
109C2×M16×C139—21no—
110C2×M16×C139—22no—
111C2×M16×C139—22no—
112C2×M16×C139—41no—
113C2×M16×C139—41no—
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C2×M16×C139C2311yescharacteristic
120C22×C8×C139—21no—
121C22×C8×C139—21no—
122C22×C8×C139—21no—
123C22×C8×C139C2311yescharacteristic
124C22×C8×C139C2311yescharacteristic
125#123×C139—21no—
126C22⋊Q8×C139D411yescharacteristic
127C22⋊Q8×C139D411yescharacteristic
128#121×C139—21no—
129#121×C139—21no—
130#121×C139—21no—
131#121×C139—21no—
132#121×C139D411yescharacteristic
133#121×C139D411yescharacteristic
134#120×C139—21no—
135C4×D4×C139—21no—
136C4×D4×C139—21no—
137#117×C139C2311yescharacteristic
138C2×C4⋊C4×C139C2311yescharacteristic
139C2×C22⋊C4×C139—21no—
140#108×C139—22no—
141#108×C139—41no—
142#107×C139—21no—
143#106×C139—21no—
144C4⋊C8×C139—21no—
145C4⋊C8×C139—21no—
146#103×C139—21no—
147#103×C139—21no—
148#103×C139—21no—
149#103×C139—21no—
150#103×C139—21no—
151#102×C139—21no—
152#102×C139—21no—
153#102×C139—21no—
154#102×C139—21no—
155#102×C139—21no—
156#102×C139—21no—
157#102×C139—21no—
158#101×C139—22no—
159#101×C139—22no—
160#100×C139—22no—
161#100×C139—22no—
162#100×C139—41no—
163#100×C139D414yescomplemented
164C22⋊C8×C139—21no—
165C22⋊C8×C139—21no—
166C22⋊C8×C139—21no—
167C22⋊C8×C139—21no—
168C22⋊C8×C139D411yescharacteristic
169C22⋊C8×C139D411yescharacteristic
170C22⋊C8×C139D411yescharacteristic
171C22⋊C8×C139D411yescharacteristic
172#97×C139—21no—
173C4×C8×C139—21no—
174C24×C139—21no—
175C24×C139—21no—
176C24×C139#4111yescharacteristic
177#41×C139—21no—
178#41×C139—21no—
179#41×C139—21no—
180#41×C139—21no—
181#41×C139—42no—
182#41×C139—42no—
183#41×C139—42no—
184#41×C139—42no—
185#41×C139—42no—
186#41×C139—42no—
187#41×C139—42no—
188#41×C139—42no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139—21no—
192C2×Q8×C139—21no—
193C2×Q8×C139—21no—
194C2×Q8×C139C2×D411yescharacteristic
195C2×Q8×C139#4112yes—
196C2×D4×C139—24no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—42no—
212C2×D4×C139—41no—
213C2×D4×C139—41no—
214C2×D4×C139—41no—
215C2×D4×C139—41no—
216C2×D4×C139—82no—
217C2×D4×C139C2×D412yes—
218C2×D4×C139C2×D411yescharacteristic
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—24no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—42no—
228C22×C4×C139—41no—
229C22×C4×C139—41no—
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139#4111yescharacteristic
235C22×C4×C139C2411yescharacteristic
236Q16×C139—42no—
237SD16×C139—42no—
238SD16×C139—42no—
239SD16×C139—42no—
240SD16×C139—42no—
241SD16×C139—42no—
242D8×C139—42no—
243D8×C139—42no—
244D8×C139—42no—
245D8×C139—42no—
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—21no—
255M16×C139—21no—
256M16×C139—42no—
257M16×C139—42no—
258M16×C139—42no—
259M16×C139C2×D412yes—
260M16×C139C2×D412yes—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—21no—
271C2×C8×C139—42no—
272C2×C8×C139—42no—
273C2×C8×C139—42no—
274C2×C8×C139C2×D411yescharacteristic
275C2×C8×C139C2×D411yescharacteristic
276C2×C8×C139C2×D411yescharacteristic
277C2×C8×C139C2×D411yescharacteristic
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139C2×D411yescharacteristic
283C4⋊C4×C139C2×D411yescharacteristic
284C22⋊C4×C139—21no—
285C22⋊C4×C139—21no—
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—41no—
290C22⋊C4×C139—41no—
291C42×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—22no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—81no—
304C23×C139—81no—
305C23×C139—81no—
306C23×C139—81no—
307C23×C139#12111yescharacteristic
308C23×C139#12111yescharacteristic
309C23×C139C2×#4111yescharacteristic
310Q8×C139—21no—
311Q8×C139—22no—
312Q8×C139—22no—
313Q8×C139—21no—
314Q8×C139—41no—
315Q8×C139—41no—
316D4×C139—21no—
317D4×C139—22no—
318D4×C139—22no—
319D4×C139—21no—
320D4×C139—42no—
321D4×C139—44no—
322D4×C139—44no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—81no—
332D4×C139—82no—
333D4×C139—82no—
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—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—22no—
348C2×C4×C139—44no—
349C2×C4×C139—44no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—81no—
356C2×C4×C139#12111yescharacteristic
357C2×C4×C139#12111yescharacteristic
358C2×C4×C139C22×D411yescharacteristic
359C2×C4×C139C22×D411yescharacteristic
360C2×C4×C139C22×D411yescharacteristic
361C2×C4×C139C2×#4111yescharacteristic
362C2×C4×C139H(5,𝔽2)11yescharacteristic
363C2×C4×C139H(5,𝔽2)11yescharacteristic
364C8×C139—21no—
365C8×C139—21no—
366C8×C139—22no—
367C8×C139—22no—
368C8×C139—21no—
369C8×C139—21no—
370C8×C139—41no—
371C8×C139—41no—
372C8×C139—41no—
373C8×C139—41no—
374C22×C139—21no—
375C22×C139—21no—
376C22×C139—21no—
377C22×C139—21no—
378C22×C139—21no—
379C22×C139—21no—
380C22×C139—21no—
381C22×C139—21no—
382C22×C139—42no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—82no—
389C22×C139—82no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—161no—
396C22×C139—161no—
397C22×C139C2×#12111yescharacteristic
398C22×C139#52511yescharacteristic
399C22×C139#53811yescharacteristic
400C4×C139—21no—
401C4×C139—21no—
402C4×C139—42no—
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—41no—
406C4×C139—81no—
407C4×C139D4211yescharacteristic
408C4×C139D4211yescharacteristic
409C4×C139#54611yescharacteristic
410C4×C139#54611yescharacteristic
411C2×C139—21no—
412C2×C139—21no—
413C2×C139—41no—
414C2×C139—41no—
415C2×C139—81no—
416C2×C139—82no—
417C2×C139—161no—
418C2×C139#242411yescharacteristic
419C2×C139#306711yescharacteristic
420C2×C139#306811yescharacteristic
421#25141C13911yesmaximal, characteristic, direct product factor, Sylow
422C139#2514111yescharacteristic, direct product factor, Sylow
423C2×#472C2×C13911yescharacteristic, complemented
424#3055C2×C13911yescharacteristic, complemented
425#3005C2×C13911yescharacteristic, complemented
426C2×#449C2×C13911yescharacteristic, complemented
427#2933C2×C13911yescharacteristic, complemented
428C2×#413C2×C13911yescharacteristic, complemented
429#2064C2×C13911yescharacteristic, complemented
430#2051C2×C13911yescharacteristic, complemented
431#2045C2×C13911yescharacteristic, complemented
432#2019C2×C13911yescharacteristic, complemented
433#1977C2×C13911yescharacteristic, complemented
434#1931C2×C13911yescharacteristic, complemented
435#1908C2×C13911yescharacteristic, complemented
436#1900C2×C13911yescharacteristic, complemented
437#1855C2×C13911yescharacteristic, complemented
438C22×#41C22×C13911yescharacteristic
439C2×#137C22×C13911yescharacteristic
440C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
441C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
442C22×SD16C22×C13911yescharacteristic
443C22×D8C22×C13911yescharacteristic
444C2×#131C22×C13911yescharacteristic
445C22×M16C22×C13911yescharacteristic
446C22×M16C22×C13911yescharacteristic
447#525C22×C13911yescharacteristic
448C2×#121C22×C13911yescharacteristic
449#472—24no—
450#469—21no—
451#468—21no—
452#466—21no—
453#465—21no—
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#449—21no—
462#436—21no—
463#435—21no—
464#435—21no—
465C8×D4—21no—
466C2×#108C22×C13911yescharacteristic
467C2×#108C22×C13911yescharacteristic
468#428C22×C13911yescharacteristic
469#424C22×C13911yescharacteristic
470#419C22×C13911yescharacteristic
471#418C22×C13911yescharacteristic
472#418C22×C13911yescharacteristic
473#417C22×C13911yescharacteristic
474C2×#103C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476#413—24no—
477C2×#101C22×C13911yescharacteristic
478C2×#101C22×C13911yescharacteristic
479C2×#100C22×C13911yescharacteristic
480C2×#100C22×C13911yescharacteristic
481C2×#100C22×C13911yescharacteristic
482C2×#100C22×C13911yescharacteristic
483#408C22×C13911yescharacteristic
484#407C22×C13911yescharacteristic
485C2×C22⋊C8C22×C13911yescharacteristic
486#405C22×C13911yescharacteristic
487#343C22×C13911yescharacteristic
488#343C22×C13911yescharacteristic
489#341C22×C13911yescharacteristic
490#341C22×C13911yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C13911yescharacteristic
500C22×Q8C23×C13911yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C13911yescharacteristic
504C22×D4C23×C13911yescharacteristic
505C23×C4—21no—
506C23×C4C23×C13911yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×SD16—22no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—22no—
522C2×D8—21no—
523C2×D8—21no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C13911yescharacteristic
537C2×M16C23×C13911yescharacteristic
538C2×M16C23×C13911yescharacteristic
539C2×M16C23×C13911yescharacteristic
540C2×M16C23×C13911yescharacteristic
541C2×M16C23×C13911yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C13911yescharacteristic
546C22×C8C23×C13911yescharacteristic
547#123—21no—
548C22⋊Q8D4×C13911yescharacteristic
549C22⋊Q8D4×C13911yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C13911yescharacteristic
555#121D4×C13911yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C13911yescharacteristic
560C2×C4⋊C4C23×C13911yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101—22no—
582#100—22no—
583#100—22no—
584#100—41no—
585#100D4×C13914yescomplemented
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C13911yescharacteristic
591C22⋊C8D4×C13911yescharacteristic
592C22⋊C8D4×C13911yescharacteristic
593C22⋊C8D4×C13911yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C13911yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C13911yescharacteristic
617C2×Q8#41×C13912yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C13912yes—
640C2×D4C2×D4×C13911yescharacteristic
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4C2×D4×C13911yescharacteristic
654C22×C4C2×D4×C13911yescharacteristic
655C22×C4C2×D4×C13911yescharacteristic
656C22×C4#41×C13911yescharacteristic
657C22×C4C24×C13911yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C13912yes—
682M16C2×D4×C13912yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C13911yescharacteristic
697C2×C8C2×D4×C13911yescharacteristic
698C2×C8C2×D4×C13911yescharacteristic
699C2×C8C2×D4×C13911yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C13911yescharacteristic
705C4⋊C4C2×D4×C13911yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C13911yescharacteristic
730C23#121×C13911yescharacteristic
731C23C2×#41×C13911yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—22no—
741D4—21no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C13911yescharacteristic
779C2×C4#121×C13911yescharacteristic
780C2×C4C22×D4×C13911yescharacteristic
781C2×C4C22×D4×C13911yescharacteristic
782C2×C4C22×D4×C13911yescharacteristic
783C2×C4C2×#41×C13911yescharacteristic
784C2×C4H(5,𝔽2)×C13911yescharacteristic
785C2×C4H(5,𝔽2)×C13911yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C13911yescharacteristic
820C22#525×C13911yescharacteristic
821C22#538×C13911yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C13911yescharacteristic
830C4D42×C13911yescharacteristic
831C4#546×C13911yescharacteristic
832C4#546×C13911yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2#2424×C13911yescharacteristic
841C2#3067×C13911yescharacteristic
842C2#3068×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
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×#472×C139C2semidirect
2. #3055×C139C2semidirect
3. #3005×C139C2semidirect
4. C2×#449×C139C2semidirect
5. #2933×C139C2semidirect
6. C2×#413×C139C2semidirect
7. #2064×C139C2semidirect
8. #2051×C139C2semidirect
9. #2045×C139C2semidirect
10. #2019×C139C2semidirect
11. #1977×C139C2semidirect
12. #1931×C139C2semidirect
13. #1908×C139C2semidirect
14. #1900×C139C2semidirect
15. #1855×C139C2semidirect
163. #100×C139D4semidirect
421. #25141C139direct (N × H)
422. C139#25141direct (N × H)
423. C2×#472C2×C139semidirect
424. #3055C2×C139semidirect
425. #3005C2×C139semidirect
426. C2×#449C2×C139semidirect
427. #2933C2×C139semidirect
428. C2×#413C2×C139semidirect
429. #2064C2×C139semidirect
430. #2051C2×C139semidirect
431. #2045C2×C139semidirect
432. #2019C2×C139semidirect
433. #1977C2×C139semidirect
434. #1931C2×C139semidirect
435. #1908C2×C139semidirect
436. #1900C2×C139semidirect
437. #1855C2×C139semidirect
585. #100D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#472×C1392
#3055×C1392
#3005×C1392
C2×#449×C1392
#2933×C1392
C2×#413×C1392
#2064×C1392
#2051×C1392
#2045×C1392
#2019×C1392
#1977×C1392
#1931×C1392
#1908×C1392
#1900×C1392
#1855×C1392
#25141139