Finite Group Databasebeta

← C139×#18228 #48012824

Subgroups — C139×#18228 #48012824

Order 35584.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3537×C139C211yesmaximal, characteristic, complemented
2#3006×C139C211yesmaximal, characteristic, complemented
3#3002×C139C211yesmaximal, characteristic, complemented
4#2615×C139C211yesmaximal, characteristic, complemented
5#1606×C139C212yesmaximal, complemented
6#1601×C139C212yesmaximal, complemented
7#1600×C139C212yesmaximal, complemented
8#1595×C139C212yesmaximal, complemented
9#1519×C139C211yesmaximal, characteristic, complemented
10#1513×C139C211yesmaximal, characteristic, complemented
11#1471×C139C211yesmaximal, characteristic, complemented
12C22×#41×C139C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C139—21no—
14C2×#135×C139—21no—
15#560×C139—22no—
16#553×C139—21no—
17#553×C139—21no—
18D42×C139—22no—
19D42×C139—21no—
20D42×C139—21no—
21#540×C139—21no—
22#538×C139—21no—
23#538×C139C2212yes—
24#535×C139—21no—
25#534×C139—21no—
26#534×C139C2212yes—
27#525×C139C2211yescharacteristic
28C2×#121×C139—21no—
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31#452×C139—21no—
32#451×C139C2211yescharacteristic, complemented
33#450×C139C2211yescharacteristic, complemented
34#449×C139—21no—
35#449×C139—22no—
36#448×C139C2211yescharacteristic, complemented
37#448×C139C2212yescomplemented
38#447×C139C2211yescharacteristic, complemented
39#447×C139C2212yescomplemented
40#417×C139—21no—
41#416×C139—21no—
42#407×C139C2211yescharacteristic, complemented
43C2×C22⋊C8×C139C2211yescharacteristic, complemented
44#393×C139C2212yescomplemented
45#392×C139—22no—
46#392×C139C2212yescomplemented
47#380×C139—21no—
48#380×C139C2211yescharacteristic, complemented
49#328×C139C2212yescomplemented
50#327×C139C2212yescomplemented
51#327×C139C2212yescomplemented
52#327×C139C2212yescomplemented
53#323×C139C2212yescomplemented
54#323×C139C2212yescomplemented
55C2×#41×C139—21no—
56C2×#41×C139—21no—
57C2×#41×C139—21no—
58C2×#41×C139—21no—
59C2×#41×C139—44no—
60C2×#41×C139D411yescharacteristic, complemented
61C22×Q8×C139C2311yescharacteristic
62C22×D4×C139—22no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—22no—
68C22×D4×C139D411yescharacteristic
69C22×D4×C139D412yes—
70C22×D4×C139D411yescharacteristic, complemented
71C22×D4×C139C2311yescharacteristic
72C23×C4×C139—21no—
73C23×C4×C139C2311yescharacteristic
74AGL(1,ℤ/8)×C139—44no—
75#135×C139—44no—
76C2×Q16×C139—21no—
77C2×SD16×C139—21no—
78C2×SD16×C139—21no—
79C2×SD16×C139—22no—
80C2×D8×C139—21no—
81C2×D8×C139—22no—
82C2×M16×C139—21no—
83C22×C8×C139—21no—
84#127×C139—22no—
85#127×C139—21no—
86#126×C139—22no—
87#126×C139—22no—
88#125×C139—21no—
89#124×C139—22no—
90#123×C139—22no—
91#123×C139—21no—
92#123×C139—22no—
93#123×C139—22no—
94#123×C139—22no—
95C22⋊Q8×C139D411yescharacteristic, complemented
96C22⋊Q8×C139C2311yescharacteristic
97#121×C139—22no—
98#121×C139—21no—
99#121×C139—21no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139—21no—
105#121×C139—21no—
106#121×C139—21no—
107#121×C139—21no—
108#121×C139—21no—
109#121×C139—21no—
110#121×C139—22no—
111#121×C139—44no—
112#121×C139D412yescomplemented
113#121×C139D411yescharacteristic, complemented
114#121×C139C2312yes—
115#121×C139C2311yescharacteristic
116#120×C139—22no—
117#120×C139—22no—
118#120×C139—22no—
119#120×C139—21no—
120#120×C139—22no—
121#120×C139—22no—
122#120×C139—22no—
123C4×D4×C139—22no—
124C4×D4×C139—21no—
125C4×D4×C139—21no—
126C4×D4×C139—21no—
127C4×D4×C139—21no—
128C4×D4×C139—22no—
129#117×C139—21no—
130#117×C139D411yescharacteristic, complemented
131C2×C4⋊C4×C139—21no—
132C2×C4⋊C4×C139D411yescharacteristic
133C2×C4⋊C4×C139D411yescharacteristic, complemented
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—22no—
136C2×C22⋊C4×C139—21no—
137C2×C22⋊C4×C139—22no—
138C2×C22⋊C4×C139C2312yes—
139#103×C139—21no—
140#103×C139—21no—
141#103×C139—22no—
142#102×C139—21no—
143#102×C139—21no—
144#102×C139—22no—
145C22⋊C8×C139—21no—
146C22⋊C8×C139—21no—
147C22⋊C8×C139C2311yescharacteristic
148C22⋊C8×C139C2311yescharacteristic
149C22⋊C8×C139C2312yes—
150#95×C139—22no—
151#95×C139C2312yes—
152C24×C139—22no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139C2×D412yes—
156C24×C139C2×D411yescharacteristic
157#41×C139—24no—
158#41×C139—24no—
159#41×C139—42no—
160#41×C139—42no—
161#41×C139—42no—
162#41×C139—42no—
163#41×C139—42no—
164#41×C139—42no—
165#41×C139—42no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139—42no—
169C2×Q8×C139C2×D411yescharacteristic
170C2×D4×C139—22no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—22no—
174C2×D4×C139—22no—
175C2×D4×C139—22no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—22no—
179C2×D4×C139—21no—
180C2×D4×C139—22no—
181C2×D4×C139—22no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—41no—
193C2×D4×C139—41no—
194C2×D4×C139—44no—
195C2×D4×C139—82no—
196C2×D4×C139—82no—
197C2×D4×C139—82no—
198C2×D4×C139—82no—
199C2×D4×C139—81no—
200C2×D4×C139—81no—
201C2×D4×C139—82no—
202C2×D4×C139—82no—
203C2×D4×C139—84no—
204C2×D4×C139C2×D411yescharacteristic
205C2×D4×C139C2×D412yes—
206C22×C4×C139—24no—
207C22×C4×C139—21no—
208C22×C4×C139—22no—
209C22×C4×C139—22no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—22no—
213C22×C4×C139—42no—
214C22×C4×C139—42no—
215C22×C4×C139—41no—
216C22×C4×C139—41no—
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2×D412yes—
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2411yescharacteristic
224Q16×C139—42no—
225SD16×C139—42no—
226SD16×C139—42no—
227SD16×C139—44no—
228D8×C139—42no—
229D8×C139—44no—
230M16×C139—42no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—22no—
234C2×C8×C139—42no—
235C4⋊C4×C139—22no—
236C4⋊C4×C139—22no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—42no—
243C4⋊C4×C139C2×D412yes—
244C4⋊C4×C139C2×D411yescharacteristic
245C4⋊C4×C139C2×D411yescharacteristic
246C22⋊C4×C139—22no—
247C22⋊C4×C139—22no—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—22no—
251C22⋊C4×C139—21no—
252C22⋊C4×C139—21no—
253C22⋊C4×C139—21no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—21no—
256C22⋊C4×C139—22no—
257C22⋊C4×C139—22no—
258C22⋊C4×C139—22no—
259C22⋊C4×C139—21no—
260C22⋊C4×C139—44no—
261C22⋊C4×C139—81no—
262C22⋊C4×C139—82no—
263C42×C139—22no—
264C42×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—22no—
268C23×C139—22no—
269C23×C139—22no—
270C23×C139—21no—
271C23×C139—22no—
272C23×C139—22no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—42no—
279C23×C139—42no—
280C23×C139—42no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—81no—
285C23×C139—81no—
286C23×C139—82no—
287C23×C139—82no—
288C23×C139—82no—
289C23×C139#12011yescharacteristic
290C23×C139#12011yescharacteristic
291C23×C139C22×D411yescharacteristic
292Q8×C139—22no—
293Q8×C139—22no—
294Q8×C139—41no—
295Q8×C139—41no—
296Q8×C139—41no—
297D4×C139—22no—
298D4×C139—22no—
299D4×C139—42no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—44no—
304D4×C139—42no—
305D4×C139—44no—
306D4×C139—44no—
307D4×C139—42no—
308D4×C139—41no—
309D4×C139—42no—
310D4×C139—41no—
311D4×C139—42no—
312D4×C139—42no—
313D4×C139—81no—
314D4×C139—82no—
315D4×C139—82no—
316D4×C139—81no—
317D4×C139—82no—
318D4×C139—82no—
319D4×C139—82no—
320D4×C139—82no—
321D4×C139—82no—
322D4×C139—88no—
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
326C2×C4×C139—22no—
327C2×C4×C139—21no—
328C2×C4×C139—22no—
329C2×C4×C139—22no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—44no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—44no—
339C2×C4×C139—42no—
340C2×C4×C139—42no—
341C2×C4×C139—42no—
342C2×C4×C139—42no—
343C2×C4×C139—42no—
344C2×C4×C139—81no—
345C2×C4×C139—82no—
346C2×C4×C139—82no—
347C2×C4×C139#12011yescharacteristic
348C2×C4×C139#12011yescharacteristic
349C2×C4×C139C22×D411yescharacteristic
350C2×C4×C139C22×D411yescharacteristic
351C8×C139—41no—
352C8×C139—41no—
353C8×C139—42no—
354C22×C139—21no—
355C22×C139—21no—
356C22×C139—21no—
357C22×C139—21no—
358C22×C139—21no—
359C22×C139—21no—
360C22×C139—21no—
361C22×C139—21no—
362C22×C139—42no—
363C22×C139—42no—
364C22×C139—42no—
365C22×C139—42no—
366C22×C139—41no—
367C22×C139—42no—
368C22×C139—42no—
369C22×C139—41no—
370C22×C139—42no—
371C22×C139—41no—
372C22×C139—42no—
373C22×C139—42no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—82no—
377C22×C139—82no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—162no—
383C22×C139—164no—
384C22×C139C2×#12011yescharacteristic
385C22×C139#57611yescharacteristic
386C22×C139#57711yescharacteristic
387C4×C139—21no—
388C4×C139—21no—
389C4×C139—21no—
390C4×C139—42no—
391C4×C139—41no—
392C4×C139—42no—
393C4×C139—41no—
394C4×C139—42no—
395C4×C139—41no—
396C4×C139—82no—
397C4×C139B(4,𝔽2)12yes—
398C2×C139—21no—
399C2×C139—21no—
400C2×C139—41no—
401C2×C139—41no—
402C2×C139—82no—
403C2×C139—82no—
404C2×C139—82no—
405C2×C139—81no—
406C2×C139#301211yescharacteristic
407C2×C139#301911yescharacteristic
408C2×C139C2×B(4,𝔽2)11yescharacteristic
409#18228C13911yesmaximal, characteristic, direct product factor, Sylow
410C139#1822811yescharacteristic, direct product factor, Sylow
411#3537C2×C13911yescharacteristic, complemented
412#3006C2×C13911yescharacteristic, complemented
413#3002C2×C13911yescharacteristic, complemented
414#2615C2×C13911yescharacteristic, complemented
415#1606C2×C13912yescomplemented
416#1601C2×C13912yescomplemented
417#1600C2×C13912yescomplemented
418#1595C2×C13912yescomplemented
419#1519C2×C13911yescharacteristic, complemented
420#1513C2×C13911yescharacteristic, complemented
421#1471C2×C13911yescharacteristic, complemented
422C22×#41C22×C13911yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C13912yes—
434#535—21no—
435#534—21no—
436#534C22×C13912yes—
437#525C22×C13911yescharacteristic
438C2×#121—21no—
439C2×#121C22×C13911yescharacteristic
440C2×#121C22×C13911yescharacteristic
441#452—21no—
442#451C22×C13911yescharacteristic, complemented
443#450C22×C13911yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C13911yescharacteristic, complemented
447#448C22×C13912yescomplemented
448#447C22×C13911yescharacteristic, complemented
449#447C22×C13912yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C13911yescharacteristic, complemented
453C2×C22⋊C8C22×C13911yescharacteristic, complemented
454#393C22×C13912yescomplemented
455#392—22no—
456#392C22×C13912yescomplemented
457#380—21no—
458#380C22×C13911yescharacteristic, complemented
459#328C22×C13912yescomplemented
460#327C22×C13912yescomplemented
461#327C22×C13912yescomplemented
462#327C22×C13912yescomplemented
463#323C22×C13912yescomplemented
464#323C22×C13912yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C13911yescharacteristic, complemented
471C22×Q8C23×C13911yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C13911yescharacteristic
479C22×D4D4×C13912yes—
480C22×D4D4×C13911yescharacteristic, complemented
481C22×D4C23×C13911yescharacteristic
482C23×C4—21no—
483C23×C4C23×C13911yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C13911yescharacteristic, complemented
506C22⋊Q8C23×C13911yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C13912yescomplemented
523#121D4×C13911yescharacteristic, complemented
524#121C23×C13912yes—
525#121C23×C13911yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C13911yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C13911yescharacteristic
543C2×C4⋊C4D4×C13911yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C13912yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C13911yescharacteristic
558C22⋊C8C23×C13911yescharacteristic
559C22⋊C8C23×C13912yes—
560#95—22no—
561#95C23×C13912yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C13912yes—
566C24C2×D4×C13911yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C13911yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C13911yescharacteristic
615C2×D4C2×D4×C13912yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C13911yescharacteristic
628C22×C4C2×D4×C13911yescharacteristic
629C22×C4C2×D4×C13911yescharacteristic
630C22×C4C2×D4×C13912yes—
631C22×C4C2×D4×C13911yescharacteristic
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C24×C13911yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C13912yes—
654C4⋊C4C2×D4×C13911yescharacteristic
655C4⋊C4C2×D4×C13911yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C13911yescharacteristic
700C23#120×C13911yescharacteristic
701C23C22×D4×C13911yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C13911yescharacteristic
758C2×C4#120×C13911yescharacteristic
759C2×C4C22×D4×C13911yescharacteristic
760C2×C4C22×D4×C13911yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C13911yescharacteristic
795C22#576×C13911yescharacteristic
796C22#577×C13911yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C13912yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—81no—
815C2—82no—
816C2#3012×C13911yescharacteristic
817C2#3019×C13911yescharacteristic
818C2C2×B(4,𝔽2)×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3537×C139C2semidirect
2. #3006×C139C2semidirect
3. #3002×C139C2semidirect
4. #2615×C139C2semidirect
5. #1606×C139C2semidirect
6. #1601×C139C2semidirect
7. #1600×C139C2semidirect
8. #1595×C139C2semidirect
9. #1519×C139C2semidirect
10. #1513×C139C2semidirect
11. #1471×C139C2semidirect
12. C22×#41×C139C22semidirect
32. #451×C139C22semidirect
33. #450×C139C22semidirect
36. #448×C139C22semidirect
37. #448×C139C22semidirect
38. #447×C139C22semidirect
39. #447×C139C22semidirect
42. #407×C139C22semidirect
43. C2×C22⋊C8×C139C22semidirect
44. #393×C139C22semidirect
46. #392×C139C22semidirect
48. #380×C139C22semidirect
49. #328×C139C22semidirect
50. #327×C139C22semidirect
51. #327×C139C22semidirect
52. #327×C139C22semidirect
53. #323×C139C22semidirect
54. #323×C139C22semidirect
60. C2×#41×C139D4semidirect
70. C22×D4×C139D4semidirect
95. C22⋊Q8×C139D4semidirect
112. #121×C139D4semidirect
113. #121×C139D4semidirect
130. #117×C139D4semidirect
133. C2×C4⋊C4×C139D4semidirect
409. #18228C139direct (N × H)
410. C139#18228direct (N × H)
411. #3537C2×C139semidirect
412. #3006C2×C139semidirect
413. #3002C2×C139semidirect
414. #2615C2×C139semidirect
415. #1606C2×C139semidirect
416. #1601C2×C139semidirect
417. #1600C2×C139semidirect
418. #1595C2×C139semidirect
419. #1519C2×C139semidirect
420. #1513C2×C139semidirect
421. #1471C2×C139semidirect
422. C22×#41C22×C139semidirect
442. #451C22×C139semidirect
443. #450C22×C139semidirect
446. #448C22×C139semidirect
447. #448C22×C139semidirect
448. #447C22×C139semidirect
449. #447C22×C139semidirect
452. #407C22×C139semidirect
453. C2×C22⋊C8C22×C139semidirect
454. #393C22×C139semidirect
456. #392C22×C139semidirect
458. #380C22×C139semidirect
459. #328C22×C139semidirect
460. #327C22×C139semidirect
461. #327C22×C139semidirect
462. #327C22×C139semidirect
463. #323C22×C139semidirect
464. #323C22×C139semidirect
470. C2×#41D4×C139semidirect
480. C22×D4D4×C139semidirect
505. C22⋊Q8D4×C139semidirect
522. #121D4×C139semidirect
523. #121D4×C139semidirect
540. #117D4×C139semidirect
543. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3537×C1392
#3006×C1392
#3002×C1392
#2615×C1392
#1606×C1392
#1601×C1392
#1600×C1392
#1595×C1392
#1519×C1392
#1513×C1392
#1471×C1392
#18228139