Finite Group Databasebeta

← C139×#18224 #48012820

Subgroups — C139×#18224 #48012820

Order 35584.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C139C211yesmaximal, characteristic, complemented
2#3003×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic, complemented
4#2613×C139C211yesmaximal, characteristic, complemented
5#1600×C139C212yesmaximal, complemented
6#1598×C139C212yesmaximal, complemented
7#1597×C139C212yesmaximal, complemented
8#1595×C139C212yesmaximal, complemented
9#1516×C139C211yesmaximal, characteristic, complemented
10#1510×C139C211yesmaximal, characteristic, complemented
11#1468×C139C211yesmaximal, characteristic, complemented
12C23×D4×C139C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C139—21no—
14C22×D8×C139—21no—
15#562×C139—21no—
16#560×C139—21no—
17#553×C139—21no—
18#551×C139—21no—
19#546×C139—21no—
20#546×C139—21no—
21#546×C139—21no—
22D42×C139—21no—
23#540×C139—21no—
24#539×C139—21no—
25#539×C139C2211yescharacteristic, complemented
26#538×C139—21no—
27#538×C139C2211yescharacteristic, complemented
28#537×C139C2211yescharacteristic, complemented
29#534×C139—21no—
30#534×C139C2211yescharacteristic, complemented
31#525×C139C2211yescharacteristic
32C2×#123×C139C2211yescharacteristic
33C2×#121×C139C2211yescharacteristic
34C2×#120×C139—21no—
35#450×C139—21no—
36#450×C139C2212yescomplemented
37#447×C139—21no—
38#447×C139—21no—
39#447×C139—21no—
40#447×C139C2212yes—
41#447×C139C2212yescomplemented
42#447×C139C2212yescomplemented
43#418×C139—21no—
44C2×#102×C139—21no—
45#407×C139C2211yescharacteristic, complemented
46C2×C22⋊C8×C139C2211yescharacteristic, complemented
47#394×C139—21no—
48#394×C139C2212yescomplemented
49#392×C139—21no—
50#392×C139C2212yescomplemented
51#381×C139C2211yescharacteristic, complemented
52#379×C139—21no—
53#328×C139C2212yescomplemented
54#327×C139C2212yescomplemented
55#327×C139C2212yescomplemented
56#327×C139C2212yescomplemented
57#324×C139C2212yescomplemented
58#323×C139C2212yescomplemented
59C25×C139—21no—
60C2×#41×C139—21no—
61C2×#41×C139D411yescharacteristic, complemented
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—44no—
72C22×D4×C139D411yescharacteristic
73C22×D4×C139D411yescharacteristic, complemented
74C22×D4×C139C2312yes—
75C23×C4×C139C2311yescharacteristic
76AGL(1,ℤ/8)×C139—44no—
77C2×SD16×C139—22no—
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C2×D8×C139—44no—
82C2×M16×C139—21no—
83C22×C8×C139—21no—
84#127×C139—21no—
85#126×C139—21no—
86#126×C139—21no—
87#126×C139—21no—
88#126×C139—21no—
89#125×C139—21no—
90#125×C139—21no—
91#124×C139—21no—
92#124×C139—21no—
93#124×C139—21no—
94#123×C139—21no—
95#123×C139—21no—
96#123×C139—21no—
97#123×C139—21no—
98#123×C139—21no—
99#123×C139—21no—
100#123×C139—21no—
101#123×C139—21no—
102#123×C139—21no—
103#123×C139—21no—
104#123×C139—21no—
105#123×C139—21no—
106#123×C139—21no—
107#123×C139—21no—
108C22⋊Q8×C139—21no—
109C22⋊Q8×C139—21no—
110C22⋊Q8×C139—21no—
111C22⋊Q8×C139—21no—
112C22⋊Q8×C139—21no—
113C22⋊Q8×C139D411yescharacteristic, complemented
114C22⋊Q8×C139C2311yescharacteristic
115#121×C139—21no—
116#121×C139—21no—
117#121×C139—21no—
118#121×C139—21no—
119#121×C139—21no—
120#121×C139—21no—
121#121×C139—21no—
122#121×C139—21no—
123#121×C139—21no—
124#121×C139—21no—
125#121×C139—21no—
126#121×C139—21no—
127#121×C139—21no—
128#121×C139—21no—
129#121×C139—21no—
130#121×C139D411yescharacteristic, complemented
131#121×C139D411yescharacteristic, complemented
132#121×C139D411yescharacteristic, complemented
133#121×C139C2311yescharacteristic
134#121×C139C2311yescharacteristic
135#121×C139C2311yescharacteristic
136#120×C139—21no—
137#120×C139—21no—
138#120×C139—21no—
139#120×C139—21no—
140#120×C139—21no—
141#120×C139—21no—
142#120×C139—21no—
143#120×C139—21no—
144#120×C139—44no—
145C4×D4×C139—21no—
146C4×D4×C139—21no—
147C4×D4×C139—21no—
148C4×D4×C139—21no—
149C4×D4×C139—21no—
150C4×D4×C139—21no—
151C4×D4×C139—21no—
152C4×D4×C139—21no—
153#117×C139—21no—
154#117×C139D411yescharacteristic, complemented
155C2×C4⋊C4×C139D411yescharacteristic
156C2×C4⋊C4×C139D411yescharacteristic, complemented
157C2×C4⋊C4×C139C2311yescharacteristic
158C2×C22⋊C4×C139—21no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—21no—
161C2×C22⋊C4×C139—21no—
162C2×C22⋊C4×C139—22no—
163C2×C22⋊C4×C139—22no—
164C2×C22⋊C4×C139—22no—
165C2×C22⋊C4×C139D411yescharacteristic
166C2×C22⋊C4×C139D411yescharacteristic
167C2×C22⋊C4×C139C2311yescharacteristic
168#102×C139—22no—
169#102×C139—22no—
170#102×C139—22no—
171#102×C139—22no—
172C22⋊C8×C139—21no—
173C22⋊C8×C139—21no—
174C22⋊C8×C139C2312yes—
175C22⋊C8×C139C2312yes—
176#95×C139—21no—
177#95×C139C2312yes—
178C24×C139—24no—
179C24×C139—21no—
180C24×C139—22no—
181C24×C139—21no—
182C24×C139—42no—
183C24×C139—41no—
184C24×C139—41no—
185C24×C139—82no—
186C24×C139—82no—
187C24×C139C2×D411yescharacteristic
188C24×C139C2×D411yescharacteristic
189#41×C139—42no—
190#41×C139—82no—
191C2×Q8×C139—21no—
192C2×Q8×C139C2×D411yescharacteristic
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—21no—
196C2×D4×C139—21no—
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—21no—
212C2×D4×C139—22no—
213C2×D4×C139—22no—
214C2×D4×C139—42no—
215C2×D4×C139—42no—
216C2×D4×C139—42no—
217C2×D4×C139—44no—
218C2×D4×C139—44no—
219C2×D4×C139—44no—
220C2×D4×C139—44no—
221C2×D4×C139—42no—
222C2×D4×C139—44no—
223C2×D4×C139—41no—
224C2×D4×C139—41no—
225C2×D4×C139—82no—
226C2×D4×C139—82no—
227C2×D4×C139—82no—
228C2×D4×C139—82no—
229C2×D4×C139—82no—
230C2×D4×C139C2×D411yescharacteristic
231C2×D4×C139C2×D411yescharacteristic
232C2×D4×C139C2×D411yescharacteristic
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—22no—
241C22×C4×C139—42no—
242C22×C4×C139C2×D411yescharacteristic
243C22×C4×C139C2×D411yescharacteristic
244C22×C4×C139C2×D411yescharacteristic
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D411yescharacteristic
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2411yescharacteristic
251SD16×C139—44no—
252D8×C139—44no—
253D8×C139—44no—
254D8×C139—44no—
255M16×C139—42no—
256C2×C8×C139—22no—
257C2×C8×C139—22no—
258C2×C8×C139—42no—
259C4⋊C4×C139—21no—
260C4⋊C4×C139—21no—
261C4⋊C4×C139—21no—
262C4⋊C4×C139—21no—
263C4⋊C4×C139—21no—
264C4⋊C4×C139—21no—
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139C2×D411yescharacteristic
273C4⋊C4×C139C2×D411yescharacteristic
274C4⋊C4×C139C2×D411yescharacteristic
275C4⋊C4×C139C2×D411yescharacteristic
276C22⋊C4×C139—21no—
277C22⋊C4×C139—21no—
278C22⋊C4×C139—21no—
279C22⋊C4×C139—21no—
280C22⋊C4×C139—21no—
281C22⋊C4×C139—21no—
282C22⋊C4×C139—21no—
283C22⋊C4×C139—21no—
284C22⋊C4×C139—21no—
285C22⋊C4×C139—21no—
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—21no—
292C22⋊C4×C139—21no—
293C22⋊C4×C139—21no—
294C22⋊C4×C139—21no—
295C22⋊C4×C139—21no—
296C22⋊C4×C139—21no—
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—44no—
302C22⋊C4×C139—42no—
303C22⋊C4×C139—82no—
304C22⋊C4×C139—82no—
305C42×C139—21no—
306C42×C139—21no—
307C42×C139—21no—
308C23×C139—22no—
309C23×C139—22no—
310C23×C139—24no—
311C23×C139—21no—
312C23×C139—21no—
313C23×C139—21no—
314C23×C139—21no—
315C23×C139—22no—
316C23×C139—41no—
317C23×C139—42no—
318C23×C139—42no—
319C23×C139—44no—
320C23×C139—42no—
321C23×C139—41no—
322C23×C139—41no—
323C23×C139—42no—
324C23×C139—42no—
325C23×C139—42no—
326C23×C139—44no—
327C23×C139—42no—
328C23×C139—81no—
329C23×C139—81no—
330C23×C139—82no—
331C23×C139—82no—
332C23×C139—82no—
333C23×C139—82no—
334C23×C139—88no—
335C23×C139—81no—
336C23×C139—81no—
337C23×C139—81no—
338C23×C139—88no—
339C23×C139#12011yescharacteristic
340C23×C139#12011yescharacteristic
341C23×C139C22×D411yescharacteristic
342Q8×C139—41no—
343Q8×C139—81no—
344D4×C139—24no—
345D4×C139—24no—
346D4×C139—41no—
347D4×C139—41no—
348D4×C139—41no—
349D4×C139—42no—
350D4×C139—42no—
351D4×C139—44no—
352D4×C139—44no—
353D4×C139—42no—
354D4×C139—42no—
355D4×C139—42no—
356D4×C139—42no—
357D4×C139—42no—
358D4×C139—81no—
359D4×C139—81no—
360D4×C139—81no—
361D4×C139—81no—
362D4×C139—81no—
363D4×C139—81no—
364D4×C139—81no—
365D4×C139—81no—
366D4×C139—81no—
367D4×C139—81no—
368D4×C139—81no—
369D4×C139—81no—
370D4×C139—88no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—21no—
374C2×C4×C139—21no—
375C2×C4×C139—21no—
376C2×C4×C139—21no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—21no—
381C2×C4×C139—22no—
382C2×C4×C139—41no—
383C2×C4×C139—41no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139—42no—
389C2×C4×C139—42no—
390C2×C4×C139—42no—
391C2×C4×C139—81no—
392C2×C4×C139—81no—
393C2×C4×C139—81no—
394C2×C4×C139—81no—
395C2×C4×C139—81no—
396C2×C4×C139—81no—
397C2×C4×C139—81no—
398C2×C4×C139#12011yescharacteristic
399C2×C4×C139#12011yescharacteristic
400C2×C4×C139C22×D411yescharacteristic
401C2×C4×C139C22×D411yescharacteristic
402C8×C139—42no—
403C8×C139—42no—
404C22×C139—21no—
405C22×C139—21no—
406C22×C139—21no—
407C22×C139—21no—
408C22×C139—21no—
409C22×C139—21no—
410C22×C139—21no—
411C22×C139—44no—
412C22×C139—44no—
413C22×C139—44no—
414C22×C139—41no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—41no—
418C22×C139—41no—
419C22×C139—41no—
420C22×C139—41no—
421C22×C139—41no—
422C22×C139—41no—
423C22×C139—41no—
424C22×C139—44no—
425C22×C139—41no—
426C22×C139—41no—
427C22×C139—82no—
428C22×C139—82no—
429C22×C139—82no—
430C22×C139—88no—
431C22×C139—88no—
432C22×C139—82no—
433C22×C139—82no—
434C22×C139—162no—
435C22×C139—162no—
436C22×C139B(4,𝔽2)12yes—
437C22×C139C2×#12011yescharacteristic
438C22×C139#57612yes—
439C4×C139—21no—
440C4×C139—21no—
441C4×C139—21no—
442C4×C139—21no—
443C4×C139—41no—
444C4×C139—41no—
445C4×C139—41no—
446C4×C139—41no—
447C4×C139—41no—
448C4×C139—41no—
449C4×C139—41no—
450C4×C139—41no—
451C4×C139—82no—
452C2×C139—22no—
453C2×C139—22no—
454C2×C139—41no—
455C2×C139—84no—
456C2×C139—81no—
457C2×C139—81no—
458C2×C139—81no—
459C2×C139—81no—
460C2×C139#300811yescharacteristic
461C2×C139#302111yescharacteristic
462C2×C139C2×B(4,𝔽2)11yescharacteristic
463#18224C13911yesmaximal, characteristic, direct product factor, Sylow
464C139#1822411yescharacteristic, direct product factor, Sylow
465#3534C2×C13911yescharacteristic, complemented
466#3003C2×C13911yescharacteristic, complemented
467C2×#447C2×C13911yescharacteristic, complemented
468#2613C2×C13911yescharacteristic, complemented
469#1600C2×C13912yescomplemented
470#1598C2×C13912yescomplemented
471#1597C2×C13912yescomplemented
472#1595C2×C13912yescomplemented
473#1516C2×C13911yescharacteristic, complemented
474#1510C2×C13911yescharacteristic, complemented
475#1468C2×C13911yescharacteristic, complemented
476C23×D4C22×C13911yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C13911yescharacteristic, complemented
490#538—21no—
491#538C22×C13911yescharacteristic, complemented
492#537C22×C13911yescharacteristic, complemented
493#534—21no—
494#534C22×C13911yescharacteristic, complemented
495#525C22×C13911yescharacteristic
496C2×#123C22×C13911yescharacteristic
497C2×#121C22×C13911yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C13912yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C13912yes—
505#447C22×C13912yescomplemented
506#447C22×C13912yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C13911yescharacteristic, complemented
510C2×C22⋊C8C22×C13911yescharacteristic, complemented
511#394—21no—
512#394C22×C13912yescomplemented
513#392—21no—
514#392C22×C13912yescomplemented
515#381C22×C13911yescharacteristic, complemented
516#379—21no—
517#328C22×C13912yescomplemented
518#327C22×C13912yescomplemented
519#327C22×C13912yescomplemented
520#327C22×C13912yescomplemented
521#324C22×C13912yescomplemented
522#323C22×C13912yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C13911yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C13911yescharacteristic
537C22×D4D4×C13911yescharacteristic, complemented
538C22×D4C23×C13912yes—
539C23×C4C23×C13911yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C13911yescharacteristic, complemented
578C22⋊Q8C23×C13911yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C13911yescharacteristic, complemented
595#121D4×C13911yescharacteristic, complemented
596#121D4×C13911yescharacteristic, complemented
597#121C23×C13911yescharacteristic
598#121C23×C13911yescharacteristic
599#121C23×C13911yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C13911yescharacteristic, complemented
619C2×C4⋊C4D4×C13911yescharacteristic
620C2×C4⋊C4D4×C13911yescharacteristic, complemented
621C2×C4⋊C4C23×C13911yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C13911yescharacteristic
630C2×C22⋊C4D4×C13911yescharacteristic
631C2×C22⋊C4C23×C13911yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C13912yes—
639C22⋊C8C23×C13912yes—
640#95—21no—
641#95C23×C13912yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C13911yescharacteristic
652C24C2×D4×C13911yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C13911yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C13911yescharacteristic
695C2×D4C2×D4×C13911yescharacteristic
696C2×D4C2×D4×C13911yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C13911yescharacteristic
707C22×C4C2×D4×C13911yescharacteristic
708C22×C4C2×D4×C13911yescharacteristic
709C22×C4C2×D4×C13911yescharacteristic
710C22×C4C2×D4×C13911yescharacteristic
711C22×C4C2×D4×C13911yescharacteristic
712C22×C4C2×D4×C13911yescharacteristic
713C22×C4C2×D4×C13911yescharacteristic
714C22×C4C24×C13911yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C13911yescharacteristic
737C4⋊C4C2×D4×C13911yescharacteristic
738C4⋊C4C2×D4×C13911yescharacteristic
739C4⋊C4C2×D4×C13911yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C13911yescharacteristic
804C23#120×C13911yescharacteristic
805C23C22×D4×C13911yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C13911yescharacteristic
863C2×C4#120×C13911yescharacteristic
864C2×C4C22×D4×C13911yescharacteristic
865C2×C4C22×D4×C13911yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—44no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C13912yes—
901C22C2×#120×C13911yescharacteristic
902C22#576×C13912yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2#3008×C13911yescharacteristic
925C2#3021×C13911yescharacteristic
926C2C2×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. #3534×C139C2semidirect
2. #3003×C139C2semidirect
3. C2×#447×C139C2semidirect
4. #2613×C139C2semidirect
5. #1600×C139C2semidirect
6. #1598×C139C2semidirect
7. #1597×C139C2semidirect
8. #1595×C139C2semidirect
9. #1516×C139C2semidirect
10. #1510×C139C2semidirect
11. #1468×C139C2semidirect
12. C23×D4×C139C22semidirect
25. #539×C139C22semidirect
27. #538×C139C22semidirect
28. #537×C139C22semidirect
30. #534×C139C22semidirect
36. #450×C139C22semidirect
41. #447×C139C22semidirect
42. #447×C139C22semidirect
45. #407×C139C22semidirect
46. C2×C22⋊C8×C139C22semidirect
48. #394×C139C22semidirect
50. #392×C139C22semidirect
51. #381×C139C22semidirect
53. #328×C139C22semidirect
54. #327×C139C22semidirect
55. #327×C139C22semidirect
56. #327×C139C22semidirect
57. #324×C139C22semidirect
58. #323×C139C22semidirect
61. C2×#41×C139D4semidirect
73. C22×D4×C139D4semidirect
113. C22⋊Q8×C139D4semidirect
130. #121×C139D4semidirect
131. #121×C139D4semidirect
132. #121×C139D4semidirect
154. #117×C139D4semidirect
156. C2×C4⋊C4×C139D4semidirect
463. #18224C139direct (N × H)
464. C139#18224direct (N × H)
465. #3534C2×C139semidirect
466. #3003C2×C139semidirect
467. C2×#447C2×C139semidirect
468. #2613C2×C139semidirect
469. #1600C2×C139semidirect
470. #1598C2×C139semidirect
471. #1597C2×C139semidirect
472. #1595C2×C139semidirect
473. #1516C2×C139semidirect
474. #1510C2×C139semidirect
475. #1468C2×C139semidirect
476. C23×D4C22×C139semidirect
489. #539C22×C139semidirect
491. #538C22×C139semidirect
492. #537C22×C139semidirect
494. #534C22×C139semidirect
500. #450C22×C139semidirect
505. #447C22×C139semidirect
506. #447C22×C139semidirect
509. #407C22×C139semidirect
510. C2×C22⋊C8C22×C139semidirect
512. #394C22×C139semidirect
514. #392C22×C139semidirect
515. #381C22×C139semidirect
517. #328C22×C139semidirect
518. #327C22×C139semidirect
519. #327C22×C139semidirect
520. #327C22×C139semidirect
521. #324C22×C139semidirect
522. #323C22×C139semidirect
525. C2×#41D4×C139semidirect
537. C22×D4D4×C139semidirect
577. C22⋊Q8D4×C139semidirect
594. #121D4×C139semidirect
595. #121D4×C139semidirect
596. #121D4×C139semidirect
618. #117D4×C139semidirect
620. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3534×C1392
#3003×C1392
C2×#447×C1392
#2613×C1392
#1600×C1392
#1598×C1392
#1597×C1392
#1595×C1392
#1516×C1392
#1510×C1392
#1468×C1392
#18224139